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Q:
How to explain slick.js / slick-theme.css strange dot style loading issue?
In my testing of slick.js front-end slider plugin, I found in Chrome browser, sometimes the navigation dot in class ".slick-dots li button:before"
suddenly changed
from
content: '•';
to
content: '•';
by itself.
However, I wanted the dots
to display
as
instead of
It's wierd when i use incognito to refresh page, it turns back to normal again, but if it already became image 2 via unknown trigger, you are just not able to refresh these dots back to normal in any none-incognito mode;
so what could be the cause of the issue and how to avoid it?
A:
It's probably caused by your code editor. Make sure u saving file in UTF-8 encoding.
|
using System.Linq;
using NUnit.Framework;
using Rubberduck.CodeAnalysis.Inspections;
using Rubberduck.CodeAnalysis.Inspections.Concrete;
using Rubberduck.Parsing.VBA;
using Rubberduck.VBEditor.SafeComWrappers;
namespace RubberduckTests.Inspections
{
[TestFixture]
public class UseOfBangNotationInspectionTests : InspectionTestsBase
{
[Test]
[Category("Inspections")]
public void DictionaryAccessExpression_OneResult()
{
var class1Code = @"
Public Function Foo(bar As String) As Class2
Attribute Foo.VB_UserMemId = 0
End Function
";
var class2Code = @"
Public Function Baz(bar As String) As Class2
Attribute Baz.VB_UserMemId = 0
End Function
";
var moduleCode = @"
Private Function Foo() As Class2
Dim cls As New Class1
Set Foo = cls!newClassObject
End Function
";
var inspectionResults = InspectionResultsForModules(
("Class1", class1Code, ComponentType.ClassModule),
("Class2", class2Code, ComponentType.ClassModule),
("Module1", moduleCode, ComponentType.StandardModule));
Assert.AreEqual(1, inspectionResults.Count());
}
[Test]
[Category("Inspections")]
public void WithDictionaryAccessExpression_OneResult()
{
var class1Code = @"
Public Function Foo(bar As String) As Class2
Attribute Foo.VB_UserMemId = 0
End Function
";
var class2Code = @"
Public Function Baz(bar As String) As Class2
Attribute Baz.VB_UserMemId = 0
End Function
";
var moduleCode = @"
Private Function Foo() As Class2
With New Class1
Set Foo = !newClassObject
End With
End Function
";
var inspectionResults = InspectionResultsForModules(
("Class1", class1Code, ComponentType.ClassModule),
("Class2", class2Code, ComponentType.ClassModule),
("Module1", moduleCode, ComponentType.StandardModule));
Assert.AreEqual(1, inspectionResults.Count());
}
[Test]
[Category("Inspections")]
public void ChainedDictionaryAccessExpression_OneResultEach()
{
var class1Code = @"
Public Function Foo(bar As String) As Class2
Attribute Foo.VB_UserMemId = 0
End Function
";
var class2Code = @"
Public Function Baz(bar As String) As Class2
Attribute Baz.VB_UserMemId = 0
End Function
";
var moduleCode = @"
Private Function Foo() As Class2
Dim cls As New Class1
Set Foo = cls!newClassObject!whatever
End Function
";
var inspectionResults = InspectionResultsForModules(
("Class1", class1Code, ComponentType.ClassModule),
("Class2", class2Code, ComponentType.ClassModule),
("Module1", moduleCode, ComponentType.StandardModule));
}
[Test]
[Category("Inspections")]
public void IndexedDefaultMemberAccessExpression_NoResult()
{
var class1Code = @"
Public Function Foo(bar As String) As Class2
Attribute Foo.VB_UserMemId = 0
End Function
";
var class2Code = @"
Public Function Baz(bar As String) As Class2
Attribute Baz.VB_UserMemId = 0
End Function
";
var moduleCode = @"
Private Function Foo() As Class2
Dim cls As New Class1
Set Foo = cls(""newClassObject"")
End Function
";
var inspectionResults = InspectionResultsForModules(
("Class1", class1Code, ComponentType.ClassModule),
("Class2", class2Code, ComponentType.ClassModule),
("Module1", moduleCode, ComponentType.StandardModule));
Assert.AreEqual(0, inspectionResults.Count());
}
[Test]
[Category("Inspections")]
public void ExplicitCall_NoResult()
{
var class1Code = @"
Public Function Foo(bar As String) As Class2
Attribute Foo.VB_UserMemId = 0
End Function
";
var class2Code = @"
Public Function Baz(bar As String) As Class2
Attribute Baz.VB_UserMemId = 0
End Function
";
var moduleCode = @"
Private Function Foo() As Class2
Dim cls As New Class1
Set Foo = cls.Foo(""newClassObject"")
End Function
";
var inspectionResults = InspectionResultsForModules(
("Class1", class1Code, ComponentType.ClassModule),
("Class2", class2Code, ComponentType.ClassModule),
("Module1", moduleCode, ComponentType.StandardModule));
Assert.AreEqual(0, inspectionResults.Count());
}
[Test]
[Category("Inspections")]
//Covered by UseOfUnboundBangInspection.
public void UnboundDictionaryAccessExpression_NoResult()
{
var class1Code = @"
Public Function Foo(bar As String) As Class2
Attribute Foo.VB_UserMemId = 0
Set Foo = New Class2
End Function
";
var class2Code = @"
Public Function Baz(bar As String) As Class2
Attribute Baz.VB_UserMemId = 0
Set Baz = New Class2
End Function
";
var moduleCode = @"
Private Function Foo() As Class2
Dim cls As Object
Set Foo = cls!newClassObject
End Function
";
var inspectionResults = InspectionResultsForModules(
("Class1", class1Code, ComponentType.ClassModule),
("Class2", class2Code, ComponentType.ClassModule),
("Module1", moduleCode, ComponentType.StandardModule));
Assert.AreEqual(0, inspectionResults.Count());
}
[Test]
[Category("Inspections")]
public void DictionaryAccessOnDefaultMemberArrayAccess_OneResult()
{
var class1Code = @"
Public Function Foo() As Class2()
Attribute Foo.VB_UserMemId = 0
End Function
";
var class2Code = @"
Public Function Baz(bar As String) As Class2
Attribute Baz.VB_UserMemId = 0
End Function
";
var moduleCode = @"
Private Function Foo() As Class2
Dim cls As New Class1
Set Foo = cls(0)!newClassObject
End Function
";
var inspectionResults = InspectionResultsForModules(
("Class1", class1Code, ComponentType.ClassModule),
("Class2", class2Code, ComponentType.ClassModule),
("Module1", moduleCode, ComponentType.StandardModule));
Assert.AreEqual(1, inspectionResults.Count());
}
[Test]
[Category("Inspections")]
//Covered by UseOfRecursiveBangInspection.
public void RecursiveDictionaryAccessOnDefaultMemberArrayAccess_NoResult()
{
var class1Code = @"
Public Function Foo() As Class3()
Attribute Foo.VB_UserMemId = 0
End Function
";
var class2Code = @"
Public Function Baz(bar As String) As Class2
Attribute Baz.VB_UserMemId = 0
End Function
";
var class3Code = @"
Public Function Baz() As Class2
Attribute Baz.VB_UserMemId = 0
End Function
";
var moduleCode = @"
Private Function Foo() As Class2
Dim cls As New Class1
Set Foo = cls(0)!newClassObject
End Function
";
var inspectionResults = InspectionResultsForModules(
("Class1", class1Code, ComponentType.ClassModule),
("Class2", class2Code, ComponentType.ClassModule),
("Class3", class3Code, ComponentType.ClassModule),
("Module1", moduleCode, ComponentType.StandardModule));
Assert.AreEqual(0, inspectionResults.Count());
}
[Test]
[Category("Inspections")]
//Covered by UseOfUnboundBangInspection.
public void RecursiveUnboundDictionaryAccessExpression_NoResult()
{
var class1Code = @"
Public Function Foo() As Object
Attribute Foo.VB_UserMemId = 0
End Function
";
var class2Code = @"
Public Function Baz(bar As String) As Class2
Attribute Baz.VB_UserMemId = 0
End Function
";
var moduleCode = @"
Private Function Foo() As Class2
Dim cls As New Class1
Set Foo = cls!newClassObject
End Function
";
var inspectionResults = InspectionResultsForModules(
("Class1", class1Code, ComponentType.ClassModule),
("Class2", class2Code, ComponentType.ClassModule),
("Module1", moduleCode, ComponentType.StandardModule));
Assert.AreEqual(0, inspectionResults.Count());
}
protected override IInspection InspectionUnderTest(RubberduckParserState state)
{
return new UseOfBangNotationInspection(state);
}
}
} |
For many of us with a lil boot, junk, onion, ba-dunk-a-donk it is increasingly difficult to find jeans. If you have the classic curvy shape which resembles the Baby Got Back song then TOOMBAS are the jeans for you. The creator and CEO of the company happens to be a friend but that is not the reason I am promoting her product. She has put in countless hours of meticulously measuring and has developed a TOOMBAS sizing chart meant to help aid in choosing the correct jeans for your figure. So for my regular readers Phelps excluded (unless there is something you are not sharing ;-)) you should give these jeans a try.
The No-Gap jeans are the BEST! If there is one thing I hate the most about jeans are finding a pair that actually fit great everywhere except when it comes time to sit down. I don’t particularly like having all my goodies displayed. The No-Gap jeans are exactly that No-gap you can wear a belt as an accessory instead of a necessity. The jeans are designed with patterns and washes that you can find in any department store. The dark blue denim are instant favorites, because they are made with just the right amount of stretch. I am so very proud of her for stepping out and deciding to follow her dream. If you have difficulty or are inclined to spend an entire day in search of the perfect jeans then give Toombas a try.
Welcome to Glued Ideas Subtle For Blogger
Thank you for taking the time to visit my blog! Take a second to peak around and check out some of my previous posts. Of course, I would love to find out what you think as well, so make sure to comment. See you around! |
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Russia
India Unleashed: Russia
The Russian M&A market is recovering. According to Mergermarket, the aggregate deal value of Russian M&A equaled USD35 billion in 2016: there were 172 deals and the average deal size was USD203.5 million. The largest M&A deals involving foreign investors were: |
Into its 4th Season now, Dinosaur Train was co-produced by Sparky Animation (Singapore) and Jim Henson Company (USA). The first episode premiered on PBS in September 2009. Since then, this series has scored the highest viewership in PBS Kids’ entire history and was also named “Top Kids’ Show” by Hollywood’s renowned, People Magazine. The series was subsequently nominated for multiple Emmy Awards under the category of “Outstanding Children’s Animated Program”.
The story is set in a whimsical but realistic prehistoric world of jungles, swamps, active volcanoes, and oceans teeming with fauna. A shiny steam engine, the Dinosaur Train, runs through these lands and is used by all species of dinosaurs. Circling the globe, crossing oceans and inland seas, it time-travels the Mesozoic Era, the “Age of Dinosaurs”, by using magical Time Tunnels to visit the Triassic, Jurassic, and Cretaceous periods.
In season four, we’ll go for a deeper exploration of Biodiversity. We’ll show how in the Mesozoic Era, just like in our modern Era, each creature has an important place in the ecosystem, from tiny bugs in the ground to the largest predators at the top of the food chain. And when one species disappears, for whatever reason, Mother Nature adapts and readjusts, keeping the delicate balance in the diverse ecosystem. |
Disclosure Policy
August 18, 2011
Excerpt: County Line by Bill Cameron
No One Home
By Bill Cameron,
Author of County Line
To
my credit, the first thing I don't do is go stand in the street outside
her bedroom window, iPod in my pocket and portable speakers raised
above my head. Not that she has a bedroom window -- nothing so prosaic
for Ruby Jane Whittaker. The point is I show uncharacteristic restraint
and so -- lucky me -- miss out on the chance to watch a man die.
I've
been away a month. Ruby Jane called it a retreat, a chance to get my
head screwed on at last after a long winter brooding and recovering from
a bloody confrontation which left three dead and me with a near-fatal
gunshot wound. She's the one who found The Last Homely House, an
out-of-the-way bed-and-breakfast at the coast esteemed for a
breathtaking ocean view and the curative powers of its hot springs. When
I asked if she'd chosen the spot because it sat in a cellular dead zone
in a dale on a precipitous headland, she laughed and told me I'd have
to hike into town if I wanted to call her. Doctor's orders were for lots
of walking, but despite repeated marches down the mountain, I managed
to reach her only a couple of times during my sojourn, the last a couple
of weeks earlier. She hasn't picked up since.
Too long for me,
maybe not long enough for Ruby Jane. She dropped me off, and had planned
to pick me up again. But as radio silence lengthened, I arranged for an
overpriced rental car instead.
I dial her cell before getting on
the highway. She doesn't pick up. During the drive to Portland --
ninety-three-point-nine miles according to Google Maps -- I keep my hand
on my phone as though I can pull a signal from the air through the
power of touch. By the time I'm negotiating the vehicular chop on Route
26 through Hillsboro and Beaverton, I've succumbed to the urge to redial
at least twice as often as I've resisted. Doesn't matter anyway. Every
attempt goes straight to voicemail.
Self-delusion was easier in the days before Caller ID and 24-hour digital accessibility.
I
pull up in front of Uncommon Cup at Twelfth and Ash shortly before
seven. Her apartment is a few blocks away, but I'm more likely to find
her at one of her shops. Through the window I can see a guy mopping.
He's mid-twenties, with dark flyaway hair and a five-day beard. As I
watch, he spins and kicks one leg to the side. Fred Astaire with a mop
handle. I don't recognize him -- no surprise. Ruby Jane employs a couple
dozen people now. A lone customer sits at a table next to the window, a
fellow thick with layers. Thermal shirt under flannel under a
half-zipped hoodie under a denim jacket. He holds a ceramic cup under
his nose. There's no sign of Ruby Jane.
As I get out of the car,
the guy in all the layers looks up, then checks his watch. He unwinds
from his chair and is coming out as I reach the door. Tall and lean,
baby-faced, with blue eyes peeking out from inside his hood. "Quitting
time, man."
"I won't be settling in."
He slides past me
out the door. Inside, I breathe warm air laced with the scents of coffee
and bleach. The space is cast in dark wood, and sandblasted brick with
mix-n-match tables and chairs from a half-dozen different diners. Barbra
Streisand caterwauls from hidden speakers. The guy with the mop pauses
mid-pirouette when he sees me.
"Sorry, man. We're closed."
"I'm looking for Ruby Jane."
He props himself up on the upright mop handle. His eyes gaze two different directions, neither at me. "Who?"
"Ruby Jane Whittaker? The owner?"
He
sniffs. "Oh. Sure, Whittaker. I didn't make the connection." He looks
around the shop as if he expects to catch her hiding under a table.
"She's not here."
"So I see. Is she at one of the other shops?"
"How would I even know that, man?"
I don't like his tone, or maybe I don't like feeling so out of touch. "Who's the manager today?"
He turns his back. "Marcy's the only manager I know."
"Do you know where she is?"
"She took off at five. Something about seeing a band."
I take a breath and finger my cell phone. Ruby Jane's newest location, I haven't been to this shop more than a couple of times.
"Pal?" I look up. "I've got to finish up here, man."
Streisand
gives way to Sinatra and I wonder what possessed this jackhole to tune
in the Starbucks channel on the satellite radio. "Do you have Marcy's
number?"
"Her phone number?"
"No, her social security number."
"I don't know you. I don't think she'd appreciate me giving out her number to a stranger."
"I'm Skin Kadash."
"Am I supposed to know who that is?"
My
cheek twitches. "Who I am is a guy who has enough sway with the woman
who signs your checks that you don't want to keep fucking with me." My
fingertips run across a patch of red skin on my throat the color and
texture of raw hamburger.
His eyes come into sudden alignment and he ducks his head. "It's just, well, I'm new here and I don't know you."
Now
I'm the jackhole. I lower my chin and turn my hands over, conciliatory.
"How about you call Marcy? Tell her Skin needs to talk to her. I'll be
quick."
He considers that for a moment, eyes fixed on my hands.
"Okay. Hang on a second." He props the mop handle against a table and
goes back behind the counter. I wonder if I can convince him to sell me a
bagel, closing time or not. I haven't eaten since morning. He checks a
notebook from under the counter, dials a number.
I take a moment to respond. "Cell service was spotty where I was staying."
"She must not have been able to get through."
She could have left a voicemail, if nothing else. "You've no idea what's going on?"
"She said there was nothing to worry about, if that's what you're thinking."
"What do you think?"
"This
is RJ we're talking about. I'm sure she's fine." I can almost hear her
shrug through the phone. "Listen, I'm supposed to meet some people, but
tell you what. I'll be working at Hollywood tomorrow. Why don't you come
by? We'll catch up."
"Okay. Thanks, Marcy."
"Good to have you back, Skin."
Then she's gone. Alvin takes the phone, places it back on the charger behind the counter. "Find out what you need?"
"Uh,
yeah." Ruby Jane, gone and out of touch, without explanation. Doesn't
make sense. In all the time I've known her, she's taken only one
vacation -- a trip to Victoria with her one-time beau Peter and me. She
fretted about the shop the whole time we were gone.
"You need anything else, man? Call you a cab maybe?"
Alvin's
color is coming back, his expression growing impatient. I don't know if
he senses my dismay or has recovered from the sight of my neck, but
sudden heat rises in my chest. "Marcy told me to tell you to crack the
register and sell me a bagel."
His lips form a line and a crease appears between his eyebrows. "Yeah. Sure. Fine."
"Sesame seed, with cream cheese. Toasted."
But when I reach for my wallet, my pocket is empty. Back straight, Alvin slices the bagel and drops it in the toaster.
"Hang
on a second, I need my wallet." As I head for my car, I think about the
guy in layers who brushed past me as I came in. I look up and down
Twelfth. There's no sign of him. My wallet is in the gutter beside the
rental car.
Alvin thinks for a moment, glances at my neck as he wraps the bagel. "I hope he left you your debit card."
The above is an excerpt from the book County Line by
Bill Cameron. The above excerpt is a digitally scanned reproduction of
text from print. Although this excerpt has been proofread, occasional
errors may appear due to the scanning process. Please refer to the
finished book for accuracy.
Bill Cameron, is the author of dark, Portland-based mysteries featuring Skin Kadash: Lost Dog, Chasing Smoke, Day One, and County Line. His stories have appeared in Killer Year, Portland Noir, West Coast Crime Wave, and the 2010 ITW anthology First Thrills.
His books have been finalists for multiple awards, including three
times for the Spotted Owl Award for Best Northwest Mystery. Cameron
lives in Portland, Oregon, where he is at work on his next novel. |
The effect of lipofuscin on cellular function.
The neurons of the supraoptic nucleus of male C57BL/Icrfat mice at 6 or 28 months of age were examined from normally hydrated, osmotically loaded and osmotically loaded-rehydrated animals. Using quantitative morphological techniques, a reduction in the concentration of lipofuscin in the neurons was observed in osmotically loaded mice at both ages, and these levels were restored to control values during rehydration. In addition, there was a significant difference in the pattern of response of lipofuscin levels between the two age groups during the experiment. The concentration of hormone containing neurosecretory granules in the neurons of the supraoptic nucleus did not differ significantly between the two age groups during the experiment. However, the surface area of rough endoplasmic reticulum per unit volume of the supraoptic nucleus cell did differ significantly between the two age groups over the course of the experiment. It is concluded that increasing concentrations of lipofuscin do not affect the ability of the cell to control the concentration of neurosecretory granules or rough endoplasmic reticulum. The simplistic view that lipofuscin accumulates with age to the detriment of cell function must be revised. |
Julia Skupchenko
Julia is a subject matter expert on the Oil & Gas Industry in Russia, with a focus on the Russian North. Her experience is in Risks Analysis and Stakeholder Management. She has applied these skills to world class assets and opportunities within the upstream industry, working for Shell. She has a masters degree in International Relations, as well as a bachelors degree in Arctic Studies through a pan-university program delivered in the north of Sweden, Norway, and Canada. With her expertise on the Russian Arctic, she was made an International Research Associate of the Canadian Polar Commission. Former Shell International employee. |
Q:
Chrome for android lags down after many setInterval
I was trying this demo for one of my application but one of a touch screen TV is using android tablet 6.0.1 and it really lags after multiple clicks. Im suspecting due to the setinterval script there.
https://codepen.io/ShawnCG/pen/ZYVada
Here is the main javascript from that demo.
var d = document, $d = $(d),
w = window, $w = $(w),
wWidth = $w.width(), wHeight = $w.height(),
credit = $('.credit > a'),
particles = $('.particles'),
particleCount = 0,
sizes = [
15, 20, 25, 35, 45
],
colors = [
'#f44336', '#e91e63', '#9c27b0', '#673ab7', '#3f51b5',
'#2196f3', '#03a9f4', '#00bcd4', '#009688', '#4CAF50',
'#8BC34A', '#CDDC39', '#FFEB3B', '#FFC107', '#FF9800',
'#FF5722', '#795548', '#9E9E9E', '#607D8B', '#777777'
],
mouseX = $w.width() / 2, mouseY = $w.height() / 2;
function updateParticleCount () {
$('.particle-count > .number').text(particleCount);
};
$w
.on( 'resize' , function () {
wWidth = $w.width();
wHeight = $w.height();
});
$d
.on( 'mousemove touchmove' , function ( event ) {
event.preventDefault();
event.stopPropagation();
mouseX = event.clientX;
mouseY = event.clientY;
if( !!event.originalEvent.touches ) {
mouseX = event.originalEvent.touches[0].clientX;
mouseY = event.originalEvent.touches[0].clientY;
}
})
.on( 'mousedown touchstart' , function( event ) {
if( event.target === credit.get(0) ){
return;
}
mouseX = event.clientX;
mouseY = event.clientY;
if( !!event.originalEvent.touches ) {
mouseX = event.originalEvent.touches[0].clientX;
mouseY = event.originalEvent.touches[0].clientY;
}
var timer = setInterval(function () {
$d
.one('mouseup mouseleave touchend touchcancel touchleave', function () {
clearInterval( timer );
})
createParticle( event );
}, 1000 / 60)
});
function createParticle ( event ) {
var particle = $('<div class="particle"/>'),
size = sizes[Math.floor(Math.random() * sizes.length)],
color = colors[Math.floor(Math.random() * colors.length)],
negative = size/2,
speedHorz = Math.random() * 10,
speedUp = Math.random() * 25,
spinVal = 360 * Math.random(),
spinSpeed = ((36 * Math.random())) * (Math.random() <=.5 ? -1 : 1),
otime,
time = otime = (1 + (.5 * Math.random())) * 1000,
top = (mouseY - negative),
left = (mouseX - negative),
direction = Math.random() <=.5 ? -1 : 1 ,
life = 10;
particle
.css({
height: size + 'px',
width: size + 'px',
top: top + 'px',
left: left + 'px',
background: color,
transform: 'rotate(' + spinVal + 'deg)',
webkitTransform: 'rotate(' + spinVal + 'deg)'
})
.appendTo( particles );
particleCount++;
updateParticleCount();
var particleTimer = setInterval(function () {
time = time - life;
left = left - (speedHorz * direction);
top = top - speedUp;
speedUp = Math.min(size, speedUp - 1);
spinVal = spinVal + spinSpeed;
particle
.css({
height: size + 'px',
width: size + 'px',
top: top + 'px',
left: left + 'px',
opacity: ((time / otime)/2) + .25,
transform: 'rotate(' + spinVal + 'deg)',
webkitTransform: 'rotate(' + spinVal + 'deg)'
});
if( time <= 0 || left <= -size || left >= wWidth + size || top >= wHeight + size ) {
particle.remove();
particleCount--;
updateParticleCount();
clearInterval(particleTimer);
}
}, 1000 / 60);
}
I have changed the jquery to gsap for the same animation. So instead of $(element).css(), im using Tweenlite.set()
Is there a way hardware speed up the browser for this sort of animation?
Any help would be appreciated.
A:
The biggest performance hit is because you're using DOM elements. If you were to use <canvas> for your particles instead, it would perform much better (you could get hundreds or thousands of particles without much of a performance risk if you wanted to).
However, you can make this DOM animation much more performant than it is currently. The biggest thing to change is to use transforms instead of top and left. In GSAP you can do that by affecting the x and y properties. You should also use transform's scale instead of affecting width/height. In GSAP you should also set the rotation instead of the actual transform itself (it generates the property transform for you). I also recommend using GSAP's .set() method instead of jQuery's .css(). For even more performance, use GSAP's .quickSetter() method.
Using GSAP's .delayedCall instead of setInterval will also be more reliable. Even better, use gsap.ticker() and call all of the update functions from within that!
Altogether you get this demo.
Other optimizations could be done, such as reusing the same particles and not creating/destroying the old ones, but the performance is about at its cap in terms of DOM animation. Like I said at the beginning, this sort of thing is perfect for <canvas>.
|
(Photo by JIM WATSON/AFP via Getty Images)
(CNSNews.com) - Sen. Elizabeth Warren said Wednesday thath she considers abortion to be a human right and that if abortion was made illegal, “rich women will still get abortions.”
During the MSNBC-Washington Post Democratic presidential debate, MSNBC’s Rachel Maddow asked Warren, “Just this weekend, Louisiana re-elected a Democratic governor, John Bel Edwards. He has signed one of the country's toughest laws restricting abortion. Is there room in the democratic party for someone like him? Someone who can win in a deep red state but who does not support abortion rights?”
“I believe that abortion rights are human rights. I believe that they are also economic rights, and protecting the right of a woman to be able to make decisions about her own body is fundamentally what we do and what we stand for as a Democratic Party,” Warren said.
“Understand this. When someone makes abortion illegal in America, rich women will still get abortions. It's just going to fall hard on poor women. It's going to fall hard on girls, women who don't even know that they're pregnant, because they have been molested by an uncle. I want to be an America where everybody has a chance, and I know it can be a hard decision for people,” she said.
“But here's the thing. When it comes down to that decision, a woman should be able to call on her mother. She should be able to call on her partner. She should be able to call on her priest or her rabbi, but the one entity that should not be in the middle of that decision is the government,” Warren added.
“Senator Warren, I'm going to push you on this a little bit for a specific answer to the question. Governor John Bel Edwards in Louisiana is an anti-abortion governor who has signed abortion restrictions in Louisiana. Is there room for him in the Democratic Party with those politics?” Maddow asked.
“I have made clear what I think the Democratic Party stands for. I'm not here to try to drive anyone out of this party. I'm not here to try to build fences, but I am here to say this is what I will fight for as president of the United States. The women of America can count on that,” Warren said.
|
I've seen the vast majority of his NHL games, and a few of his AHL games, and he's shown serious tunnel vision in most of them. Of course you can find a few good passes, all NHLers make good passes, but compared to other NHLers Frattin is really not a playmaker. That's not to say that he can't improve in this regard, but watch him play and it's clear that he looks very strongly for his shot, and often fails to recognize when his team mates are in good positions. If Frattin had great vision he'd be a good 1st line player, because everything else about his game is great (good skater, excellent shot, strong, solid puck handler, solid 2-way plat), it's his weak vision that makes him more of a "3rd liner with 2nd line upside." I like Frattin, he's a good player, but when he gets the puck his mentality is very similar to someone like Jason Blake.
Just so we're on the same page, when I talk about playmaking/passing, I'm not talking about the ability to hit a target with a pass, all NHLers can do that. I'm talking about his playmaking ability, vision, whatever you want to call it. The ability to consistently recognize when your team mates are in good positions, and to get the puck to them, or to even draw defenders and/or wait out the opposition specifically to put your team mates in good positions. Frattin is legitimately fairly bad at this compared to other NHLers. He can definitely score goals, but he does not use his team mates well.
Again, I do like Frattin as a player, but to say that he's an average playmaker (i.e. better than roughly 50% of all NHLers) is IMO way off.
+1, guy has all the physical attributes to be and incredible player but doesnt have the head to be a complete or star player, a mentally disabled (in terms of hockey sense) Ovechkin if you will. |
The Minnesota Vikings' offensive coordinator last season and a former head coach of the Cleveland Browns, Shurmur took the Giants' job on Jan. 22 and has not announced his staff. Yet, there's one assistant on the list -- Townsend, who has spent the past two seasons as the defensive-backs coach for the Tennessee Titans.
Tennessee coach Mike Mularkey was fired after the Titans lost in the second round of the AFC playoffs to the New England Patriots. He's been replaced by former Houston Texans defensive coordinator Mike Vrabel, who built a new staff for the Titans with Kerry Coombs as the secondary coach.
Townsend was a four-year starter at cornerback at Alabama from 1994 through 1997 before going to the Pittsburgh Steelers in the fourth round of the 1998 NFL Draft. Townsend spent 12 seasons with the Steelers before finishing his NFL career with the Indianapolis Colts in 2010.
Townsend played in two Super Bowls with the Steelers. He was in the starting lineup for Pittsburgh's 21-10 victory over the Seattle Seahawks on Feb. 5, 2006, and he also played in a 27-23 victory over the Arizona Cardinals on Feb. 1, 2009. Townsend is one of the six former Alabama players who have been on two Super Bowl winners. The others are Dont'a Hightower, Larry Roberts, Jeff Rutledge, Bart Starr and Steve Wright.
FOR MORE OF AL.COM'S COMPREHENSIVE COVERAGE OF THE NFL, GO TO OUR NFL PAGE
Another former Alabama standout who was a teammate of Townsend's and also played in the NFL found a spot on an NFL coaching staff this week. The Browns announced on Wednesday that Sam Shade had been added as the assistant special-teams coach.
This will be Shade's first NFL coaching position. He coached cornerbacks at Georgia State last season after spending seven years on the staff at Samford.
Shade was a 1,000-yard rusher and an All-Southern selection at defensive back as a senior at Wenonah High School in 1990. He was the strong safety on Alabama's national-championship team in 1992 and a team captain for the Crimson Tide in 1994.
Selected by the Cincinnati Bengals in the fourth round of the 1995 NFL Draft, Shade spent eight seasons in the NFL -- four with the Bengals and four with the Washington Redskins.
Shade will work with another former Alabama player, Amos Jones, who is Cleveland's special-teams coordinator. Freddie Kitchens, a former teammate of Shade's at Alabama, is the Browns' associate head coach and running-backs coach. |
Q:
Is a dashed parametric circle possible?
I'm using parametric circles like
fx(u,v)=r*cos(v)
fy(u,v)=r*sin(v)
fz(u,v)=0
and I want some of them to be dashed. Is that somhow possible
A:
To plot a dashed curve you need a terminal compatible with dashes. The shape of the curve is irrelevant here. The usual terminal, wxt, can be used with the dashed option:
set term wxt dashed
set parametric
set size ratio -1
r = 1.
plot r*cos(t),r*sin(t) lt 2 lc 1
|
Apple Inc.’s largest iPhone assembler, Foxconn Technology Group, is considering producing the devices in India, people familiar with the matter said, a move that could reduce Apple’s dependence on China for manufacturing and potentially for sales.
Executives at Foxconn, a contract manufacturer that assembles a large portion of the world’s iPhones in China, are studying whether to include an India project in budget plans, one of the people said. Senior executives, possibly including Chairman Terry Gou, plan to visit India after next month’s Lunar New Year to discuss plans, the people familiar said.
Foxconn’s look at India comes as sustained friction between Washington and Beijing over trade and technology is pushing many companies to consider diversifying their supply chains away from China, a global center of assembly for smartphones, computers and other electronics.
Apple currently manufactures most of its iPhones in China through Foxconn, a Taiwan-based company formally known as Hon Hai Precision Industry Co., as well as via other contract manufacturers. That business model, along with a sizable reliance on sales in China, has made Apple vulnerable to rising U.S.-China tensions over trade and geopolitical rivalry.
Foxconn said in a statement it doesn’t comment on current or potential customers or any of their products. An Apple spokesman in India declined to comment. |
One of the most dramatic aspects of virology is the emergence of new virus diseases, which often receives widespread attention from the scientific community and the lay public. Considering that the discipline of animal virology was established over 100 years ago, it may seem surprising that new virus diseases are still being discovered. How this happens is the subject of this chapter.
1. How Do New Viral Diseases Emerge? {#s0010}
====================================
There are many recent books and reviews (see [Further Reading](#fread0010){ref-type="sec"}) that list the plethora of determinants that can lead to the emergence of infectious diseases ([Table 1](#t0010){ref-type="table"} ). In this chapter, we concentrate on those determinants that relate to viral pathogenesis and deal only briefly with the many societal and environmental factors that can be instrumental in disease emergence.Table 1Some of the Factors that Lead to Emergence or Reemergence of Viral DiseasesFactors Leading to EmergenceDeterminantEconomic and social developmentPopulation growth, density, distributionEnvironmental changes such as deforestation, dam building, global warmingIncreased global travelIncreased international commerceAgribusiness, food processing, distributionPovertyInadequate public health systemsOpen defecationLack of safe waterSocietal breakdownCivil chaosWarHuman factorsSexual activitySubstance abuseBiological factorsNatural mutationAntimicrobial resistanceImmunosuppression
1.1. Discovery of the Etiology of an Existing Disease {#s0015}
-----------------------------------------------------
In some instances, the "emergence" of a viral disease represents the first identification of the cause of a well-recognized disease. An example is La Crosse virus, a mosquito-transmitted bunyavirus that was first isolated from a fatal case of encephalitis in 1964. The isolation of the causal agent and the development of serological tests made it possible to distinguish La Crosse encephalitis from the rubric of "arbovirus encephalitis, etiology unknown." Since that time, about 100 cases have been reported annually, without any significant increase since the 1970s. It appears that the emergence of this "new" disease reflected only the newfound ability to identify this etiologic entity, rather than any true change in its occurrence.
Hantavirus pulmonary syndrome is another example of the "emergence" of an existing but previously unrecognized disease. In 1993, in the four corners area of the southwestern United States, there occurred a small outbreak of cases of acute pulmonary illness with a high mortality. Epidemiologic and laboratory investigation rapidly identified the causal agent, a previously unknown hantavirus, now named Sin Nombre virus (SNV). SNV is an indigenous virus of deer mice (*Peromyscus maniculatus*) that are persistently infected and excrete the virus. Apparently deer mice produce virus-infected excreta and, when they infest human dwellings, aerosolized fomites can result in occasional human infections. The 1993 outbreak is thought to reflect a transient rise in deer mouse populations associated with an unusual crop of pine nuts, a major food source for these rodents. The recognition of SNV soon led to the discovery of other heretofore unrecognized hantaviruses in North, Central and South America, many of which also cause serious human disease.
1.2. Increase in Disease Caused by an Existing Virus {#s0020}
----------------------------------------------------
On occasion, a virus that is already widespread in a population can emerge as a cause of epidemic or endemic disease, due to an increase in the ratio of cases to infections. Such an increase can be caused by either an increase in host susceptibility or enhancement of the virulence of the virus. Although counterintuitive, there are some dramatic instances of such phenomena.
**Increase in host susceptibility.** Poliomyelitis first appeared as a cause of summer outbreaks of acute infantile paralysis in Sweden and the United States late in the nineteenth century ([Figure 1](#f0010){ref-type="fig"} ). Isolated cases of infantile paralysis had been recorded in prior centuries, and an Eygptian tomb painting indicates that poliomyelitis probably occurred in early recorded history. Why then did poliomyelitis emerge abruptly as an epidemic disease? When personal hygiene and public health were primitive, poliovirus circulated as a readily transmitted enterovirus, and most infants were infected while they still carried maternal antibodies (up to 9--12 months of age). Under these circumstances, the virus produced immunizing infections of the enteric tract, but passively acquired circulating antibodies prevented invasion of the spinal cord. With the improvement of personal hygiene in the late-nineteenth century, infections were delayed until 1--3 years of age, after the waning of maternal antibodies. Infections now occurred in susceptible children, resulting in outbreaks of infantile paralysis. This reconstruction is supported by seroepidemiological studies conducted in North Africa in the 1950s, when epidemic poliomyelitis first emerged in this region.Figure 1The appearance of epidemic poliomyelitis in the United States, 1885--1916. The graph is based on reported cases (mainly paralytic) during an era when reporting was estimated at about 50%.Data from Lavinder CH, Freeman SW, Frost WH. Epidemiologic studies of poliomyelitis in New York City and the northeastern United States during the year 1916. Washington: United States Public Health Service (1918).
**Increase in viral virulence.** Viruses may undergo sudden increases in virulence resulting in emergence of dramatic outbreaks. An outbreak of lethal avian influenza in Pennsylvania in 1983 is one documented example. In eastern Pennsylvania, avian influenza appeared in chicken farms early in 1983, but the virus was relatively innocuous and most infections were mild. However, in the fall of that year a fatal influenza pandemic spread rapidly through the same farms. When viruses from the spring and fall were compared, it appeared that both isolates had almost identical genomes. The fall virus had acquired a single point mutation in the viral hemagglutinin that facilitated the cleavage of the hemagglutinin. The virus could now replicate outside the respiratory tract, markedly increasing its virulence (discussed in Chapter 7, Patterns of infection). This point mutation led to the emergence of an overwhelming epizootic, which was only controlled by a widespread slaughter program involving millions of birds. Similar outbreaks of avian influenza have occurred subsequently in other countries.
1.3. Accumulation of Susceptible Hosts and Viral Reemergence {#s0025}
------------------------------------------------------------
A virus that is endemic in a population may "fade out" and disappear, because the number of susceptibles has fallen below the critical level required for perpetuation in that population. If the population is somewhat isolated, the virus may remain absent for many years. During this interval, there will be an accumulation of birth cohorts of children who are susceptible. If the virus is then reintroduced, it can "reemerge" as an acute outbreak. In the years 1900--1950, Iceland had a population of about 200,000, which was too small to maintain measles virus, and measles periodically disappeared. When travelers to Iceland reintroduced the virus, measles reemerged in epidemic proportions.
1.4. Virus New to a Specific Population {#s0030}
---------------------------------------
On occasion, a virus can enter and spread in a region where it had never previously circulated, leading to the emergence of a disease new to that locale. A dramatic example is afforded by the emergence of West Nile virus (WNV) in the United States, beginning in 1999 ([Figure 2](#f0015){ref-type="fig"} ). WNV, like most arboviruses, is usually confined to a finite geographic area, based on the range of its vertebrate reservoir hosts and permissive vectors. In an unusual event, WNV was imported into New York City, probably by the introduction of infected vector mosquitoes that were inadvertent passengers on a flight from the Middle East, where the virus is enzootic. This hypothesis was supported by the finding that the genomic sequence of the New York isolates was closely related to the sequence of contemporary isolates from Israel. Some American mosquito species were competent vectors for WNV, and certain avian species such as American crows were highly susceptible. As a result, West Nile encephalitis emerged as a significant disease new to the United States. Over a period of several years WNV spread across the continent, finally reaching the west coast and many areas in Latin America.Figure 2The emergence of West Nile virus in the United States, 1999--2005. West Nile virus neuroinvasive disease incidence reported to CDC ArboNET, by state, United States, 1999, 2001, 2002, and 2005.Accessed via <http://www.cdc.gov/westnile/statsMaps/finalMapsData/index.html>, December 20, 2014.
Chikungunya virus (CHIKV), another mosquito-borne arbovirus, has been endemic for many years in regions of Africa and Asia where it periodically caused outbreaks of a febrile illness associated with severe arthritis and arthralgia. In 2005--2006, CHIKV caused a large epidemic on the island of Reunion in the Indian Ocean, apparently associated with a mutation that allowed the virus to be more efficiently transmitted by vector mosquitoes. Chikungunya subsequently spread to India and elsewhere in Asia, followed by the Americas. As of November 2014, transmission of CHIKV had been documented in 40 countries or territories in the Caribbean, Central, South and North America, resulting in nearly one million suspected cases each year. It appears that CHIKV may become established in the New World, where virtually the entire human population currently lacks immunity.
2. Zoonotic Infections as a Source of Emerging Viral Diseases {#s0035}
=============================================================
Zoonotic infections of animals that can be transmitted to humans are a major cause of emerging virus diseases of humans. These viruses are transmitted by direct contact, by virus-laden droplets or aerosols, or by insect vectors. All zoonotic viruses have one or more animal reservoir hosts, which play an important role in the epidemiological dynamics of human infections. Although many zoonotic viruses can be transmitted to humans on occasion, their relative ability to spread from human to human determines whether or not they emerge as significant new virus diseases of mankind ([Table 2](#t0015){ref-type="table"} ).Table 2Zoonotic Virus Infections of Humans and the Extent of Their Human-to-Human TransmissionExtent of Human-to-Human SpreadVirusMaintenance Cycle in NatureNot contagious from human-to-human (humans are dead-end hosts; representative examples); the most frequent patternWest Nile (flavivirus)Mosquitoes, birdsYellow fever (flavivirus)Mosquitoes, primatesLa Crosse encephalitis (bunyavirus)Mosquitoes, wild rodentsRabies (rhabdovirus)Raccoons, skunks, bats, dogsLimited (\<10) human-to-human transmissions; an uncommon patternCrimean Congo hemorrhagic fever (bunyavirus)\
1--3 serial infectionsTicks, agricultural and wild animalsLassa, Machupo, Junin (arenavirus)\
1--8 serial infectionsRodentsMonkeypox (poxvirus)\
\<6 serial infectionsRodentsEbola, Marburg (filovirus)\
1--4 serial infections[∗](#tbl2fn1){ref-type="table-fn"}Bats?MERS (coronavirus)Bats? camels?Nipah (paramyxovirus)Bats, pigsUnlimited human-to-human transmission (a new human virus); a rare patternHIV (lentivirus)Monkeys, apesSARS (coronavirus)Bats, other animals?Influenza (type A influenza virus)Wild birds, domestic poultry, domestic pigsEbola, Marburg (filovirus)\
\>10 serial infectionsBats?[^1]
2.1. Dead-end Hosts {#s0040}
-------------------
Most zoonotic viruses that are transmitted to humans cannot be spread directly from person to person, so humans are considered to be "dead-end hosts." One familiar example is rabies, which is enzootic in several animal hosts, such as dogs, skunks, foxes, raccoons, and bats. Humans are infected by bite of a rabid animal or by aerosol exposure (in caves with roosting bats). Several zoonotic arenaviruses, such as Lassa, Machupo (Bolivian hemorrhagic fever), and Junin (Argentine hemorrhagic fever) viruses, are likely transmitted from the reservoir host (wild rodents) by inhalation of contaminated aerosols.
There are more than 500 viruses---belonging to several virus families---that are also classified as arboviruses (arthropod-borne viruses), based on a vertebrate--arthropod maintenance cycle in nature. Arboviruses replicate in both the vertebrate host and the arthropod vector (mosquitoes, ticks, sandflies, and others), and transmission occurs when the vector takes a blood meal. Typically, arboviruses have only a few vertebrate hosts and are transmitted by a narrow range of arthropods. Humans are not the reservoir vertebrate hosts of most arboviruses, but can be infected by many of these viruses, if they happen to be bitten by an infected vector. In most instances, arbovirus-infected humans are dead-end hosts for several reasons. Many arthropod vectors competent to transmit a zoonotic arbovirus prefer nonhuman hosts as a blood source, reducing the likelihood of transmission from human to vector. Also, infected humans are usually not sufficiently permissive to experience a high titer viremia, so they cannot serve as effective links in the transmission cycle. There are only a few exceptions: in urban settings, dengue, urban yellow fever, Oropouche, and Chikungunya viruses can be maintained by an arthropod vector--human cycle.
2.2. Limited Spread among Humans {#s0045}
--------------------------------
As [Table 2](#t0015){ref-type="table"} shows, a few zoonotic viruses can be transmitted directly from human to human, at least for a few passages, and can emerge as the cause of outbreaks involving a few to several hundred cases. Since many viruses in this group cause a high mortality in humans, even a small outbreak constitutes a public health emergency. These viruses belong to many different virus families, and there is no obvious biological clue why they should be able to spread from human to human, in contrast to other closely related viruses. Typically, infections are mainly limited to caregivers or family members who have intimate contact with patients, often in a hospital setting. However, transmission is marginal, so that most outbreaks end after fewer than 5--10 serial transmissions, either spontaneously or due to infection-control practices.
2.3. Crossing the Species Barrier {#s0050}
---------------------------------
In the history of modern virology (the last 50 years) there are very few documented instances where zoonotic viruses have established themselves in the human population and emerged as new viral diseases of mankind ([Table 2](#t0015){ref-type="table"}). Most viruses have evolved to optimize their ability to be perpetuated within one or a few host species, and this creates what is sometimes called the "species barrier." In most instances, a virus must undergo some adaptive mutations to become established in a new species.
**SARS coronavirus.** In November, 2002, an outbreak of severe acute respiratory disease (SARS) began in Guangdong Province, in southeast China near the Hong Kong border. In retrospect, the first cases were concentrated in food handlers, who then spread the virus to the general population in that region. Although not recognized immediately as a new disease, the outbreak continued to spread both locally and in other parts of China. In February, 2003, a physician who had been treating likely SARS patients, traveled to Hong Kong, where he transmitted SARS to a large number of contacts in a hotel. These persons, in turn, spread the infection to Singapore, Taiwan, Vietnam, and Canada, initiating a global pandemic that eventually involved almost 30 countries. From patient samples, several research groups isolated a novel coronavirus, which has been named the SARS coronavirus (SARS CoV). Clearly, this virus is new to the human population, and there is circumstantial evidence that it was contracted from exotic food animals that are raised for sale in restaurants in Guangdong Province. Recent studies suggest that horseshoe bats (genus *Rhinolophus*) may be the reservoir hosts and palm civets, consumed as food in China, may be the intermediary hosts for SARS CoV.
SARS CoV went through a large number of human passages (perhaps 25) before being contained by primary control measures, such as respiratory precautions, isolation, and quarantine. The virus has been eliminated from the human population, but the 2003 outbreak showed that it could be maintained by human-to-human transmission. From that perspective, it is potentially capable of becoming an indigenous virus of humans. Since many coronaviruses infect the respiratory system and are transmitted by the respiratory route, the SARS virus did not have to undergo any change in its pathogenesis. However, the virus did have to replicate efficiently in cells of the human respiratory tract and it is unknown whether this required some adaptive mutations from the virus that is enzootic in its reservoir hosts.
**Middle Eastern respiratory syndrome.** MERS is an acute respiratory disease of humans that was first recognized in 2012, when a novel coronavirus (MERS-CoV) was isolated from two fatal human cases in Saudi Arabia and Qatar. Since that time, more than 1400 clinical cases of MERS have been recognized, the great majority in Saudi Arabia but also in most of the other countries in the Arabian Peninsula and beyond ([Figure 3](#f0020){ref-type="fig"} ). Hospitalized cases of MERS are characterized by an acute respiratory disease syndrome (ARDS) with a fatality rate over 25%. However, evolving evidence suggests that there may be many additional human infections with little or no associated illness.Figure 3Distribution of reported cases of MERS, December, 2014.Redrawn from Enserik, M. Mission to MERS. Science 2014, 346: 1218--1220.
What is the origin of this new disease? Based on fragmentary data now available, it appears that MERS-CoV is likely to be an enzootic virus of one or more species of bats. Camels are probably an intermediary host, and humans in close contact with camels can acquire infection. Also, MERS-CoV can spread from human to human, particularly to caretakers or others in close contact with acutely ill patients. However, there are many unknowns in this speculative reconstruction: How do camels become infected? Are camels the main source of human infections? What has caused this disease to emerge in 2012, or had it preexisted but was just recognized at that time? Is this an evolving outbreak, and if so, what is driving it?
Several relevant facts have been ascertained from basic studies. MERS-CoV replicates well in cell cultures obtained from many species, including bats and humans. The pantropic nature of this virus is explained in part by its cellular receptor, dipeptidyl peptidase 4 (DPPT4), a widely distributed cell surface molecule. This would facilitate the transmission of this zoonotic infection from bats to camels to humans. Of interest, MERS-CoV infects type II alveolar pneumocytes while SARS CoV uses a different cell receptor (angiotensin-converting enzyme 2, ACE2) and infects type I alveolar pneumocytes. However, both viruses appear to cause a similar ARDS.
**Type A influenza virus.** Genetic evidence strongly implicates avian and porcine type A influenza viruses as the source of some past pandemics of human influenza. It appears that new epidemic strains are often derived as reassortants between the hemagglutinin (and the neuraminidase in some cases) of avian influenza viruses with other genes of existing human influenza viruses. The new surface proteins provide a novel antigenic signature to which many humans are immunologically naïve. The human influenza virus genes contribute to the ability of the reassortant virus to replicate efficiently in human cells. It is thought that reassortment may take place in pigs that are dually infected with avian and human viruses.
Currently, there is concern that a new pandemic strain of Type A influenza could emerge as a derivative of highly virulent avian H5N1 or H7N9 influenza viruses now causing epidemics in domestic chickens in southeast Asia. There have been several hundred documented human infections with each of these avian viruses in recent years---mainly among poultry workers---with significant mortality. However, few if any of these infections have spread from human to human, perhaps because the infecting avian virus has not undergone reassortment with a human influenza virus. A critical determinant is that avian influenza viruses preferentially attach to α2-3 sialic acid receptors while human viruses attach to α2-6 sialic acid receptors.
The 1918 pandemic of influenza is presumed to be an example of a zoonotic influenza virus that crossed the species barrier and became established in humans where it caused an excess mortality estimated at 20--40 million persons. Recent viral molecular archaeology has recovered the sequences of the 1918 H1N1 influenza virus from the tissues of patients who died during the epidemic. All of the genes of the reconstructed virus are avian in origin, but it is unknown whether the virus underwent mutations that enhanced its ability to be transmitted within the human population. The reconstructed hemagglutinin of the 1918 virus has been inserted into recombinant influenza viruses, and---in mice---markedly increases the virulence of primary human isolates of influenza virus ([Table 3](#t0020){ref-type="table"} ), but the full virulence phenotype appears to require many of the avian influenza genes. Several physiological factors play a role in disease enhancement, including increased replication in pulmonary tissues and an enhanced ability to stimulate macrophages to secrete pro-inflammatory cytokines which, in turn, cause severe pneumonitis.Table 3Genetic Determinants of the Virulence of the 1918 Type A Influenza Virus (Spanish Strain) Based on Intranasal Infection of Mice with Reassortant Viruses. The M88 Isolate is a Human Type A Influenza Virus Which is Relatively Avirulent in Mice, Typical of Human Isolates. The Hemagglutinin (H) of the 1918 "Spanish" Virus Confers Virulence Upon the M88 Isolate and the Neuraminidase (N) Does Not Appear to Enhance the Effect of the Hemagglutinin. MLD 50: Mouse 50% Lethal Dose Determined by Intranasal Infection with Serial Virus DilutionsVirus StrainOrigin of Viral GenesLog 10 MLD 50Log 10 Virus Titer in Lung (Day 3 after Infection)HNOthersM88M88M88M88\>6.22.9M88/H^sp^Sp (1918)M88M884.45.1M88/H^sp^/N^sp^Sp (1918)Sp (1918)M885.24.7[^2]
**Human immunodeficiency virus.** HIV has emerged as the greatest pandemic in the recent history of medical science. Modern methods have made it possible to reconstruct its history in great detail (see Chapter 9, HIV/AIDS). A provisional reconstruction of the sequence of events is summarized in [Figure 4](#f0025){ref-type="fig"} . The emergence of HIV may be divided into two phases: What was the zoonotic source of HIV and when did it cross into humans? And when did HIV spread from the first human cases to become a global plague?Figure 4Speculative reconstruction of events following the transmission of SIVcpz to humans.This reconstruction is based on data in Sharp and Hahn (2011), Pepin (2011).
There have been several transmissions of simian immunodeficiency virus (SIV) to humans (Sharp and Hahn, 2011), and this account will focus on HIV-1 which appears to have been transmitted to humans in at least four separate instances, identified by individual HIV-1 lineages called groups (M, N, O, P). Of these, the most important was the M group of HIV-1, which has been responsible for the vast majority of human infections. Furthermore, HIV-1 is most closely related to SIVcpz, the SIV strain infecting two subpopulations of chimpanzees. Different segments of the SIVcpz genome, in turn, are closely related to genome segments of two SIVs of African monkeys, red-capped monkeys and *Cercopithecus* monkeys. It is hypothesized that chimpanzees, which regularly kill and eat monkeys, were infected during consumption of their prey; and that a recombination event produced SIVcpz, which was derived from parts of the genomes of the two acquired monkey viruses. It is speculated that a further transmission from chimpanzees may have occurred during the butchering of nonhuman primates, which occurs in rural Africa ([Figure 5](#f0030){ref-type="fig"} ).Figure 5Bushmeat is part of the diet in rural Africa.Photograph courtesy of Billy Karesh (2015).
Amazingly, genomic similarities tentatively map the substrain of SIVcpz that is the ancestor of the M group of HIV-1, to chimpanzees in the southeastern corner of Cameroon, a small country in West Africa. Using a sequence analysis to compare diversity within current isolates, the common parent of the M group can be reconstructed. A molecular clock, derived from dated isolates, indicates that this virus was transmitted to humans during the period 1910--1930.
The period from 1930 to 1980 is a mystery (Pepin, 2011), but there are fragmentary data suggesting that the virus persisted as a rare and unrecognized infection in residents of jungle villages in West Africa during this time. It has also been proposed that the reuse of unsterilized needles---a frequent practice during the period of colonial rule---could have inadvertently helped to spread the virus. Starting about 1980, the virus began to spread more rapidly. It appears that accelerated spread began in the region centered on Kinshasa (previously Leopoldville) in the Democratic Republic of the Congo (previously the Belgian Congo, then Zaire) and Brazzaville, just across the Congo River in Congo. Transmission was exacerbated by the chaos in postcolonial Zaire.
During the period 1985--2004, HIV infection spread widely in Africa as shown in [Figure 6](#f0035){ref-type="fig"} . In the countries worst affected, the prevalence of infection among adults aged 15--49 years reached levels higher than 30%. The rapid spread was driven by many factors among which were: (1) a high frequency of concurrent sexual contacts in some segments of the population and the hidden nature of sexual networks; (2) the long asymptomatic incubation period during which infected individuals able to transmit the virus were sexually active; (3) the spread along commercial routes of travel within Africa; (4) the failure of health systems to publicize the risks and the underutilization of condoms and other measures to reduce transmission; and (5) the slow introduction of antiviral treatment after it became available in the northern countries about 1996.Figure 6The spread of HIV in Africa, showing the prevalence of HIV in the adult population, 1988--2003. The map ends in 2003, but the prevalence has remained very similar during the period 2004--2015. (After UNAIDS 2004 report on global AIDS epidemic.)
Concomitantly with the spread of HIV in Africa, the M group of HIV-1 evolved into nine different subtypes (A--D, F--H, J, K), based on sequence diversity. During the spread within Africa, there were population bottlenecks that resulted in the predominance of different M group subtypes in different regions. Subtype C is most frequent in southern Africa, and subtypes A and D are most frequent in eastern Africa. During the 1980s, HIV also spread globally, although prevalence rates did not reach the levels seen in some African countries. Subtype B is dominant in the western hemisphere and Europe, while subtype C is most frequent in India and some other Asian countries. This implies that each of these regional epidemics was initiated by a small number of founder strains of HIV-1, improbable though that may seem.
Thirty years after its appearance as a global disease, almost 40 million persons have died, and there are more than 30 million people living with HIV/AIDS. Although the global incidence of HIV has fallen slightly since 2010, there are still more than two million new infections each year (2014).
**Ebola hemorrhagic fever.** The Ebola pandemic of 2014--15 is the most recent emerging virus disease that has riveted the attention of the world. Where did it come from? Why did it cause a pandemic? Why did the international health community fail to control it? Where will it end? These questions are discussed below.
Ebola is a filovirus indigenous to Africa that is maintained in one or more reservoir species of wild animals, among which bats are a likely host. The transmission cycle is not well documented but it is thought that humans get infected, either by direct contact with bats, or while slaughtering infected wild animals who may act as intermediate hosts. Human-to-human spread can then occur.
The pathogenesis of Ebola virus infection may be briefly summarized. Presumably Ebola enters the human host via the mucous membranes or cuts in the skin. The virus infects mononuclear cells including macrophages and dendritic cells and traffics to lymph nodes, whence it spreads to target organs including the liver, spleen, and adrenal glands. It causes a high titer viremia and a dysregulation of the innate immune system. Clinically, Ebola patients undergo severe vomiting and diarrhea with massive fluid losses and become very dehydrated, with a mortality that varies from 25% to 75%. In fatal cases, the infection of the liver leads to disseminated intravascular coagulopathy, a shock syndrome, and multiorgan failure, although the sequential details are not well understood. Infection is transmitted between humans by contact with bodily fluids of patients, but not by aerosols. Therefore, the virus is spread most frequently to caregivers or others who are in intimate contact with patients and their fomites. Rituals associated with funerals and burial practices often serve to transmit the virus.
Ebola virus was first isolated in 1976 in an outbreak near the Ebola River in the Democratic Republic of the Congo (then called Zaire) and almost concurrently in a second outbreak in southern Sudan. Viruses recovered from these two outbreaks were subsequently shown to be different and are now known as Ebola-Zaire and Ebola-Sudan. Since that time there have been more than 25 individual outbreaks of Ebola disease, mainly in central Africa. Past outbreaks have been controlled by use of protective garments by caregivers and quarantine of infected or potentially infected contacts. These controlled outbreaks have been limited to no more than ∼5 serial human-to-human transmissions, and mainly ranged from about 25 to 300 cases.
In December, 2013, an Ebola-Zaire outbreak began in Guinea, West Africa. It appears that the initial case was in an infant who may have been infected by contact with bats. The outbreak then spread to two contiguous countries, Liberia and Sierra Leone. By the fall, 2014, the epidemic had become a catastrophe, and was raging out of control in several parts of these three countries. Although the data are incomplete, it is estimated that there have been at least 20,000 cases (with at least 50% mortality) through February, 2015 ([Figure 7](#f0040){ref-type="fig"} ). The infection has spread to Nigeria, Senegal, Mali, the United States, and a few European countries, but these invasions have so far been controlled, with limited secondary cases. A global effort to control this pandemic was initiated, with participation from Doctors without Borders, the Red Cross, other nongovernment organizations, the World Health Organization, and the U.S. Centers for Disease Control and Prevention. As of March, 2015, it appeared that the epidemic was coming under control. Aggressive border screening, both on exit from the affected countries and on arrival at destinations, has limited spread by air travelers, but the porous land borders remain areas of concern.Figure 7The journalistic face of the 2013--2015 Ebola epidemic.Photograph courtesy of Tom Ksiazek, 2014.
From an epidemiological viewpoint, why did this outbreak of Ebola explode into a massive pandemic, in contrast to the many prior outbreaks that were limited to no more than a few hundred cases at most? The outbreak began in Guinea and was mainly confined to that country for about 6 months before it spread to neighboring Liberia and Sierra Leone ([Figure 8](#f0045){ref-type="fig"} ). During this first 6 months, incidence in Guinea varied from a few to about 50 cases a week, and cases were concentrated in rural areas. From a public health viewpoint, this represented a missed opportunity to contain the outbreak. Contributing to this omission were a combination of factors: a weak health system fragmented by social disruption, a failure of local health authorities to recognize or respond to the outbreak, the failure of international health organizations such as WHO to take aggressive action, and local societal norms that brought family and friends into close contact with Ebola victims, during their illness and at their funerals (Washington Post, October 5, 2014; Cohen, 2014). Once Ebola infections spread from rural villages to urban centers, the outbreak exploded.Figure 8Ebola pandemic, by country, through April, 2015. After WHO: Ebola situation report, 29 April, 2015.
Beginning in the fall of 2014, it was recognized that the pandemic was a global threat. In response, a number of countries and international organizations provided resources to Africa, including building facilities, sending equipment, and recruiting personnel to work in the pandemic areas. A major effort was made to get the local population to temporarily change some of their normal social responses to illness and death, to reduce the spread within the population. Combined with the efforts of the affected countries, these initiatives started to take hold about January, 2015. However, as of March, 2015, the epidemic was not yet terminated. In retrospect, the international community has acknowledged that it lacks a contingency plan to respond to global outbreaks wherever they may occur. Futhermore, because Ebola was a "neglected" disease, the tools to combat it had not been developed. The Ebola pandemic has spurred crash programs to develop a rapid diagnostic test, drugs and antibodies for treatment, and a vaccine for prevention (Product, 2015; Mire et al., 2015).
**Canine parvovirus.** CPV is another example of a disease that emerged due to the appearance of a virus new to its host species. In the late 1970s, a highly lethal pandemic disease appeared in the dog populations of the world. The etiologic agent was a parvovirus previously unknown in canines. The sequence of CPV is almost identical to that of feline panleukopenia virus (FPV), an established parvovirus of cats, which causes acutely fatal disease in kittens. CPV has a few point mutations that distinguish it from FPV, and these mutations permit CPV to bind to and infect canine cells, a property not possessed by FPV. It is presumed that these mutations permitted the emergence of a new virus disease of dogs.
2.4. The Species Barrier and Host Defenses {#s0055}
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Many mammalian viruses have evolved with their hosts so that different members of a virus family are associated with each host species. Furthermore, under natural circumstances, each member of the virus family usually "respects" the species barrier and does not cross into other species, although it spreads readily between individual animals within its host species. Diverse mechanisms contribute to the species barrier, including host defenses and viral genes. For a zoonotic virus to establish itself in humans or another new species, it is probable that mutations are needed for full adaptation. This requirement is likely part of the explanation for the rarity of such events.
One of the best-studied examples is the transmission of SIVcpz, a virus of chimpanzees, to HIV, a human virus. Several recent studies have shown that APOBEC3 and tetherin are two very important gate keepers for transmission of lentiviruses between different primate species (reviewed in Sharp and Hahn, 2011). APOBEC3 proteins represent a powerful first line of defense, believed to be responsible for preventing the transmission of SIVs from monkeys to chimpanzees and from monkeys to humans (Etienne et al., 2013). However, APOBEC3 proteins can be counteracted by the HIV/SIV viral infectivity factor (Vif), albeit generally in a species-specific fashion. Thus, mutations in Vif were required for monkey SIVs to be able to infect chimpanzees and then humans (Letko et al., 2013). Tetherin is a second line of defense, and only HIVs that have evolved an effective tetherin antagonism have spread widely in humans (Kluge et al., 2014). Different lentiviruses use different viral proteins to antagonize tetherin: HIV-1 group M uses the viral protein U (Vpu); HIV-2 group A uses the envelope glycoprotein (Env), and HIV-1 group O uses the negative regulatory factor (Nef). In contrast, HIV-1 groups N and P, whose spread in the human population has remained very limited, are unable to counteract tetherin efficiently.
Turning to another virus, recent studies using a mouse-adapted strain of Ebola virus to infect a panel of inbred mice provided by the Collaborative Cross (see Chapter 10, Animal models) found striking variation in the response to Ebola virus infection, from complete resistance to severe hemorrhagic fever with 100% mortality. This underlines the role of host genetic background as a determinant of susceptibility. Consistent with this are comments of clinicians that there are unpredictable differences in the outcome of individual Ebola cases. These studies suggest a dynamic relationship between host and pathogen that may determine when a virus can cross the species barrier and create a new virus disease of humankind.
3. Why Viral Diseases Are Emerging at an Increasing Frequency {#s0060}
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Although difficult to document in a rigorous manner, it does appear that new virus diseases of humans (and perhaps of other species) are emerging at an increased tempo. There are a number of reasons for this trend ([Table 1](#t0010){ref-type="table"}).
3.1. Human Ecology {#s0065}
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The human population is growing inexorably, and is becoming urbanized even faster. As a result, there are an increasing number of large-crowded cities, which provide an optimal setting for the rapid spread of any newly emergent infectious agent.
In the nineteenth century, it was noteworthy that someone could circumnavigate the globe in 80 days, but now it can be done in less than 80 h. However, the incubation period of viral infections (several days to several months) has stayed constant. Someone can be infected in one location and---within a single incubation period---arrive at any other site on earth. This enhances the opportunity for a new human virus to spread as a global infection before it has even been recognized, markedly increasing the opportunity for the emergence of a new disease. The same dynamics also apply to viral diseases of animals and plants, which has important economic and social consequences for humankind. The SARS pandemic of 2002--2003, described above, is an example of how rapidly and widely a new virus disease can emerge and spread globally. In this instance, it is extraordinary that the disease was brought under control---and eradicated from the human population---by the simple methods of isolation, quarantine, and respiratory precautions. Although conceptually simple, a heroic effort was required for success. Another example is the 2009 emergence of a novel H1N1 strain of influenza A virus that spread rapidly around the world before a vaccine could be produced.
Remote areas of the world are now being colonized at a high frequency, driven by population pressures and economic motives, such as the reclamation of land for agriculture or other uses, and the harvest of valuable trees and exotic animals. The construction of new dams, roads, and other alterations of the natural environment create new ecological niches. It is possible that this is the origin of urban yellow fever. Yellow fever virus is an arbovirus maintained in a monkey--mosquito cycle in the jungles of South America and Africa. Humans who entered jungle areas became infected. When they returned to villages or urban centers, an urban cycle was initiated, where *Aedes aegypti* mosquitoes---that are well adapted to the urban environment and preferentially feed on humans---maintained the virus.
In the last 25 years, agriculture has undergone a dramatic evolution with the development of "agribusiness." Food and food animals are now raised on an unprecedented scale and under very artificial conditions, where the proximity of many members of a single plant or animal species permits an infection to spread like wildfire. Furthermore, increasing numbers of plants, animals, and food products are rapidly transported over large distances; we enjoy fresh fruits and vegetables at any time, regardless of the season. International shipment of plants and animals can import viruses into new settings where they may lead to the emergence of unforeseen diseases. One example is the 2003 outbreak of monkeypox that caused about 80 human cases in the United States. This was traced to the importation from Africa of Gambian giant rats as exotic pets; several rodent species in west Africa appear to be reservoir hosts of this poxvirus. Monkeypox spread from these animals to pet prairie dogs and from prairie dogs to their owners. Because monkeypox causes infections in humans that resemble mild cases of smallpox, this outbreak was a major cause of public health concern.
3.2. Deliberate Introduction of a Virus New to a Specific Population {#s0070}
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On occasion, a virus has been deliberately introduced into a susceptible population where it caused the emergence of a disease epidemic. For sport, rabbits were imported from Europe into Australia in the mid-nineteenth century. Because of the absence of any natural predator the rabbits multiplied to biblical numbers, and threatened natural grasslands and agricultural crops over extensive areas of southern Australia. To control this problem, myxomatosis virus was deliberately introduced in 1950 (Fenner, 1983). This poxvirus is transmitted mechanically by the bite of insects and is indigenous to wild rabbits in South America, in which it causes nonlethal skin tumors. However, myxomatosis virus causes an acutely lethal infection in European rabbits, and its introduction in Australia resulted in a pandemic in the rabbit population.
Following the introduction of myxomatosis virus in 1950, co-evolution of both virus and host were observed. The introduced strain was highly virulent and caused epizootics with very high mortality. However, with the passage of time field isolates exhibited reduced virulence, and there was a selection for rabbits that were genetically somewhat resistant to the virus. Strains of moderate virulence probably became dominant because strains of lowest virulence were less transmissible and strains of maximum virulence killed rabbits very quickly.
Concern has also been raised about disease emergence due to the deliberate introduction of viruses into either human or animal populations, as acts of bioterrorism.
3.3. Xenotransplantation {#s0075}
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Because of the shortage of human organs for transplantation recipients, there is considerable research on the use of other species---particularly pigs---as organ donors. This has raised the question whether known or unknown latent or persistent viruses in donor organs might be transmitted to transplant recipients. Since transplant recipients are immunosuppressed to reduce graft rejection, they could be particularly susceptible to infection with viruses from the donor species. In the worst scenario, this could enable a foreign virus to cross the species barrier and become established as a new human virus that might spread from the graft recipient to other persons.
4.. How Are Emergent Viruses Identified? {#s0080}
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The impetus to identify a new pathogenic virus usually arises under one of two circumstances. First, a disease outbreak that cannot be attributed to a known pathogen may set off a race to identify a potentially new infectious agent. Identification of the causal agent will aid in the control of the disease and in prevention or preparedness for potential future epidemics. SARS coronavirus, West Nile virus, and Sin Nombre Virus are examples of emergent viruses that were identified in the wake of outbreaks, using both classical and modern methods. Alternatively, an important new virus may be discovered as a serendipitous by-product of research directed to a different goal, as was the case with hepatitis B virus (HBV). In this instance, a search for alloantigens uncovered a new serum protein that turned out to be the surface antigen (HBsAg) of HBV, leading to the discovery of the virus.
When a disease outbreak cannot be attributed to a known pathogen, and where classical virus isolation, propagation, and identification fail, molecular virology is required. Hepatitis C virus (HCV), Sin Nombre and other hantaviruses, certain rotaviruses, and Kaposi's sarcoma herpesvirus (HHV8), are examples of emergent viruses that were first discovered as a result of molecular technologies. Below, we briefly describe some methods of viral detection and identification. More detailed information and technical specifics can be found in several current texts.
4.1. Classic Methods of Virus Discovery {#s0085}
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The first question that confronts the investigator faced with a disease of unknown etiology is whether or not it has an infectious etiology? Evidence that suggests an infectious etiology is an acute onset and short duration, clinical similarity to known infectious diseases, a grouping of similar illnesses in time and place, and a history of transmission between individuals presenting with the same clinical picture. For chronic illnesses, the infectious etiology may be much less apparent and a subject for debate.
Faced with a disease that appears to be infectious, the next question is whether it is caused by a virus. A classical example that predates modern virology is the etiology of yellow fever. In a set of experiments that would now be prohibited as unethical, the Yellow Fever Commission, working with the US soldiers and other volunteers in Cuba in 1900, found that the blood of a patient with acute disease could transmit the infection to another person by intravenous injection. Furthermore, it was shown that the infectious agent could pass through a bacteria-retaining filter and therefore could be considered a "filterable virus."
**Virus isolation in cell culture and animals.** The first step in identification of a putative virus is to establish a system in which the agent can be propagated. Before the days of cell culture, experimental animals were used for this purpose. Many viruses could be isolated by intracerebral injection of suckling mice, and some viruses that did not infect mice could be transmitted to other experimental animals. Human polioviruses---because of their cellular receptor requirements---were restricted to old world monkeys and great apes; the virus was first isolated in 1908 by intracerebral injection of monkeys and was maintained by monkey-to-monkey passage until 1949 when it was shown to replicate in primary cultures of human fibroblasts.
The modern era of virology (beginning about 1950) can be dated to the introduction of cultured cells as the standard method for the isolation, propagation, and quantification of viruses. There are now a vast range of cell culture lines that can be used for the isolation of viruses, and currently this is the first recourse in attempting to isolate a suspected novel virus. Some viruses will replicate in a wide variety of cells but others are more fastidious and it can be hard to predict which cells will support their replication.
It is also important to recognize that some viruses will replicate in cell culture without exhibiting a cytopathic effect. An important example is the identification of simian virus 40 (SV40). Poliovirus was usually grown in primary cell cultures obtained from the kidneys of rhesus monkeys, but SV40 had escaped detection because it replicated without causing a cytopathic effect. When poliovirus harvests were tested in similar cultures prepared from African green monkeys, a cytopathic effect (vacuolation) was observed, leading to the discovery of SV40 virus in 1960. Because inactivated poliovirus vaccine produced from 1955 to 1960 had been prepared from virus grown in rhesus monkey cultures, many lots were contaminated with this previously unknown virus, which inadvertently had been administered to humans. Since that time, viral stocks and cell cultures have been screened to exclude SV40 and other potential virus contaminants.
A number of methods are available to detect a noncytopathic virus that is growing in cell culture. These include visualization of the virus by electron microscopy, detection of viral antigens by immunological methods such as immunofluorescence or immunocytochemistry, the agglutination of erythrocytes of various animal species by virus bound on the cell surface (hemagglutination), the production of interferon or viral interference, and the detection of viral nucleic acids.
**Detection of nonreplicating viruses.** During the period from 1950 to 1980, there was a concerted effort to identify the causes of acute infections of infants and children. In seeking the etiology of diarrheal diseases of infants, it was hypothesized that---in addition to bacteria, which accounted for less than half of the cases---one or more viruses might be responsible for some cases of infantile diarrhea. Numerous unsuccessful attempts were made to grow viruses from stools of patients with acute diarrhea. It was conjectured that it might be possible to visualize a putative fastidious virus by electron microscopy of concentrated fecal specimens. When patients' convalescent serum was added to filtered and concentrated stool specimens, aggregates of 70 nm virions were observed in stools from some infants with acute gastroenteritis. The ability of convalescent but not acute illness serum to mediate virion aggregation provided a temporal association of the immune response with an acute diarrheal illness. Within 5 years, rotavirus was recognized as the most common cause of diarrhea in infants and young children worldwide, accounting for approximately one-third of cases of severe diarrhea requiring hospitalization.
Once an emergent virus has been identified, it is necessary to classify it, in order to determine whether it is a known virus, a new member of a recognized virus group, or represents a novel virus taxon. This information provides clues relevant to diagnosis, prognosis, therapy, and prevention.
In 1967, an outbreak of acute hemorrhagic fever occurred in laboratory workers in Marburg, Germany, who were harvesting kidneys from African green monkeys (*Chlorocebus aethiops*, formerly *Cercopithecus aethiops*). In addition, the disease spread to hospital contacts of the index cases, with a total of over 30 cases and 25% mortality. Clinical and epidemiological observations immediately suggested a transmissible agent, but attempts to culture bacteria were unsuccessful. However, the agent was readily passed to guinea pigs which died with an acute illness that resembled hemorrhagic fever. After considerable effort, the agent was adapted to tissue culture and shown to be an RNA virus. When concentrated tissue culture harvests were examined by electron microscopy, it was immediately recognized that this agent differed from known families of RNA viruses, since the virions consisted of very long cylindrical filaments about 70 nm in diameter. This was the discovery of Marburg virus, the first recognized member of the filoviruses, which now include Marburg and Ebola viruses.
4.2. The Henle--Koch Postulates {#s0090}
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Isolation of a virus from patients suffering from an emergent disease provides an association, but not proof of a causal relationship. Formal demonstration that an isolated virus is the causal agent involves several criteria formulated over the past 100 years. These are often called the Henle--Koch postulates, after two nineteenth-century scientists who first attempted to enunciate the rules of evidence. [Sidebar 1](#b0010){ref-type="boxed-text"} summarizes these postulates, which have been modernized in view of current knowledge and experimental methods.Sidebar 1The Henle--Koch postulates (requirements to identify the causal agent of a specific disease)The Henle--Koch postulates were formulated in 1840 by Henle, revised by Koch in 1890, and have undergone periodic updates to incorporate technical advances and the identification of fastidious agents with insidious disease pathogenesis.Many of the following criteria should be met to establish a causal relationship between an infectious agent and a disease syndrome.1.The putative causal agent should be isolated from patients with the disease; or the genome or other evidence of the causal agent should be found in patients' tissues or excreta; and less frequently from appropriate comparison subjects. Temporally, the disease should follow exposure to the putative agent; if incubation periods can be documented they may exhibit a log-normal distribution.2.If an immune response to the putative agent can be measured, this response should correlate in time with the occurrence of the disease. Subjects with evidence of immunity may be less susceptible than naïve individuals.3.Experimental reproduction of the disease should occur in higher incidence in animals or humans appropriately exposed to the putative cause than in those not so exposed. Alternatively, a similar infectious agent may cause an analogous disease in experimental animals.4.Elimination or modification of the putative cause should decrease the incidence of the disease. If immunization or therapy is available, they should decrease or eliminate the disease.5.The data should fit an internally consistent pattern that supports a causal association.
The classic version of the Henle--Koch postulates required that the causal agent be grown in culture. However, as discussed below, a number of viruses that cannot be grown in culture have been convincingly associated with a specific disease. Usually, this requires that many of the following criteria can be met: (1) Viral sequences can be found in the diseased tissue in many patients, and are absent in appropriate control subjects; (2) Comparison of acute and convalescent sera document induction of an immune response specific for the putative causal virus; (3) The disease occurs in persons who lack a preexisting immune response to the putative virus, but not in those who are immune; (4) The implicated virus or a homologous virus causes a similar disease in experimental animals; and (5) Epidemiological patterns of disease and infection are consistent with a causal relationship.
4.3. Methods for Detection of Viruses that Are Difficult to Grow in Cell Culture {#s0095}
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Some very important human diseases---such as hepatitis B and hepatitis C---are caused by viruses that cannot readily be grown in cell culture. Experiences with these viruses have given credibility to the view that an infectious etiology can be inferred by clinical and epidemiological observations in the absence of a method for growing the causal agent. Also, they have stimulated researchers to devise novel techniques that bypass the requirement for replication in cell culture. Furthermore, the application of molecular biology, beginning about 1970, has led to an array of new methods---such as the polymerase chain reaction (PCR), deep sequencing, and genomic databases---that can be applied to the search for unknown viruses. Several case histories illustrate the inferences that lead to the hypothesis of a viral etiology, the strategy used to identify the putative causal agent, and the methods exploited by ingenious and tenacious researchers.
**Sin Nombre virus.** Hantavirus pulmonary syndrome was described above, as an example of an emerging virus disease. The disease was first reported in mid-May, 1993, and tissues and blood samples from these cases were tested extensively, but no virus was initially isolated in cell culture. However, when sera from recovered cases were tested, they were found to cross-react with a battery of antigens from known hantaviruses, providing the first lead (in June, 1993). DNA primers were then designed, based on conserved hantavirus sequences, and these were used in a PCR applied to DNA transcribed from RNA isolated from tissues of fatal cases. Sequence of the resulting amplicon suggested that it was a fragment of a putative new hantavirus (July, 1993), yielding a presumptive identification of the emerging virus within 2 months after the report of the outbreak. An intense effort by three research teams led to the successful isolation of several strains of SNV by November, 1993. SNV is a fastidious virus that replicates in Vero E6 cells but not in many other cell lines.
**Kaposi's sarcoma herpesvirus (HHV8).** KS was described over 100 years ago as a relatively uncommon sarcoma of the skin in older men in eastern Europe and the Mediterranean region. In the 1980s, KS emerged at much higher frequency, as one of the diseases associated with AIDS. Furthermore, KS exhibited an enigmatic epidemiological pattern, since its incidence in gay men was more than 10-fold greater than in other AIDS patients, such as injecting drug users and blood recipients. These observations led to the hypothesis that KS was caused by a previously undetected infectious agent that was more prevalent among gay men than among other HIV risk groups. However, researchers were unable to isolate a virus from KS tissues.
Searching for footprints of such a putative agent, Chang and colleagues used the method of representational difference analysis to identify DNA sequences specific for KS tumor tissue. Several DNA fragments were identified, and found to be homologous with sequences in known human and primate herpesviruses. In turn, these sequences were used to design primers to obtain the complete genome of a previously undescribed herpesvirus, since named HHV8, human herpesvirus 8. To this date, HHV8 defies cultivation in tissue culture.
4.4. Computer Modeling of Emerging Infections {#s0100}
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Is computer modeling a useful adjunct to the analysis or control of emerging viral diseases? The 2014--15 Ebola pandemic in West Africa offers an interesting case study. As the epidemic unfolded, several groups attempted to project how it would evolve (Meltzer et al., 2014; Butler, 2014). These projections had very wide confidence limits, and several of them had upper limits in the range of 100,000 or more cases. What the modelers could not foretell was that the infection did not spread across sub-Saharan Africa, and that several introductions (into countries such as Nigeria and Mali) were controlled by case isolation, contact tracing, and quarantine. However, modeling did contribute useful insights. Dobson (2014) suggested that rapid quarantine (within 5--7 days) of contacts of Ebola patients could be critical in epidemic control.
5. Reprise {#s0105}
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One of the most exciting current issues in virology is the emergence of new viral diseases of humans, animals, and plants. Even though the era of modern virology has been well established for more than 65 years, virus diseases continue to appear or reemerge. The Ebola pandemic of 2014--15 highlights the associated dangers and obstacles to control.
There are several explanations for emergence: (1) discovery of the cause of a recognized disease; (2) increase in disease due to changes in host susceptibility or in virus virulence; (3) reintroduction of a virus that has disappeared from a specific population; (4) crossing the barrier into a new species previously uninfected. Many zoonotic viruses that are maintained in a nonhuman species can infect humans, but most cause dead-end infections that are not transmitted between humans. A few zoonotic viruses can be transmitted between humans but most fade out after a few person-to-person transmissions. Rarely, as in the case of HIV, SARS coronavirus, and Ebola filovirus, a zoonotic virus becomes established in humans, causing a disease that is truly new to the human species.
There are many reasons for the apparent increase in the frequency of emergence of new virus diseases, most of which can be traced to human intervention in global ecosystems. Emergent viruses are identified using both classical methods of virology and newer genome-based technologies. Once a candidate virus has been identified, a causal relationship to a disease requires several lines of evidence that have been encoded in the Henle--Koch postulates, guidelines that are periodically updated as the science of virology evolves. Identifying, analyzing, and controlling emerging viruses involve many aspects of virological science. Virus--host interactions play a key role, to explain persistence in zoonotic reservoirs, transmission across the species barrier, and establishment in human hosts. Thus, the issues discussed in many other chapters contribute to our understanding of emerging viral diseases.
[^1]: Ebola in West Africa involved unlimited human-to-human transmission for over one year (see following).
[^2]: After Kobasa D, Takada A, Shinya K, et al. Enhanced Virulence of Influenza a Viruses with the Haemagglutinin of the 1918 Pandemic Virus. *Nature*, 2004, 431: 703--707, with Permission
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---
author:
- Igor Kriz
title: Perturbative deformations of conformal field theories revisited
---
Introduction
============
Recently, there has been renewed interest in the mathematics of the moduli space of conformal field theories, in particular in connection with speculations about elliptic cohomology. The purpose of this paper is to investigate this space by perturbative methods from first principles and from a purely “worldsheet” point of view. It is conjectured that at least at generic points, the moduli space of CFT’s is a manifold, and in fact, its tangent space consists of marginal fields, i.e. primary fields of weight $(1,1)$ of the conformal field theory (that is in the bosonic case, in the supersymmetric case there are modifications which we will discuss later). This then means that there should exist an exponential map from the tangent space at a point to the moduli space, i.e. it should be possible to construct a continuous $1$-parameter set of conformal field theories by “turning on” a given marginal field.
There is a more or less canonical mathematical procedure for applying a “$Pexp$” type construction to the field which has been turned on, and obtaining a perturbative expansion in the deformation parameter. This process, however, returns certain cohomological obstructions, similar to Gerstenhaber’s obstructions to the existence of deformations of associative algebras [@gerst]. Physically, these obstructions can be interpreted as changes of dimension of the deforming field, and can occur, in principle, at any order of the perturbative path. The primary obstruction is well known, and was used e.g. by Ginsparg in his work on $c=1$ conformal field theories [@ginsparg]. The obstruction also occured in earlier work, see [@kad; @kadb; @kadw; @wilson; @wilson1; @wilson2; @wegner], from the point of view of continuous lines in the space of critical models. In the models considered, notably the Baxter model [@bax], the Ashkin-Teller model [@ashten] and the Gaussian model [@kohmoto], vanishing of the primary obstruction did correspond to a continuous line of deformations, and it was therefore believed that the primary obstruction tells the whole story. (A similar story also occurs in the case of deformations of boundary sectors, see [@konref1; @konref2; @konref3; @konref4; @konref5; @konref6; @konref7; @kondo].)
In a certain sense, the main point of the present paper is analyzing, or giving examples of, the role of the hihger obstructions. We shall see that these obstructions can be non-zero in cases where the deformation is believed to exist, most notably in the case of deforming the Gepner model of the Fermat quintic along a cc field, cf. [@ag; @ns; @fried; @vw; @w1; @w2; @w3; @39a; @39b; @39c]. Some discussion of marginality of primary field in $N=2$-supersymmetric theories to higher order exists in the literature. Notably, Dixon, [@dixon] verified the vanishing for any $N=(2,2)$-theory, and any linear combination of cc,ac,ca and ac field, of an amplitude integral which physically expresses the change of central charge (a similar calculation is also given in Distler-Greene [@distler]). Earlier work of Zamolodchikov [@za; @zb] showed that the renormalization $\beta$-function vanishes for theories where $c$ does not change during the renormalization process. However, we find that the calculation [@dixon] does not guarantee that the primary field would remain marginal along the perturbative deformation path, due to subtleties involving singularities of the integral. The obstruction we discuss in this paper is an amplitude integral which physically expresses directly the change of dimension of the deforming field, and it turns out this may not vanish. We will return to this discussion in Section \[sexp\] below.
This puzzle of having obstructions where none should appear will not be fully explained in this paper, although a likely interpretation of the result will be discussed. Very likely, our effect does not impact the general question of the existence of the non-linear $\sigma$-model, which is widely believed to exist (e.g. [@ag; @ns; @fried; @vw; @w1; @w2; @w3; @39a; @39b; @39c]), but simply concerns questions of its perturbative construction. One caveat is that the case we investigate here is still not truly physical, since we specialize to the case of $cc$ fields, which are not real. The actual physical deformations of CFT’s should occur along real fields, e.g. a combination of a cc field and its complex-conjugate $aa$ field (we give a discussion of this in case of the free field theory at the end of Section \[sfree\]). The case of the corresponding real field in the Gepner model is much more difficult to analyze, in particular it requires regularization of the deforming parameter, and is not discussed here. Nevertheless, it is still surprising that an obstruction occurs for a single $cc$ field; for example, this does not happen in the case of the (compactified or uncompactified) free field theory.
Since an $n$’th order obstruction indeed means that the marginal field gets deformed into a field of non-zero weight, which changes to the order of the $n$’th power of the deformation parameter, usually [@ginsparg; @kad; @kadb; @kadw; @wilson; @wilson1; @wilson2; @wegner], when obstructions occur, one therefore concludes that the CFT does not possess continuous deformations in the given direction. Other interpretations are possible. One thing to observe is that our conclusion is only valid for [*purely perturbative*]{} theories where we assume that all fields have power series expansion in the deformation parameters with coefficients which are fields in the original theory. This is not the only possible scenario. Therefore, as remarked above, our results merely indicate that in the case when our algebraic obstruction is non-zero, non-perturbative corrections must be made to the theory to maintain the presence of marginal fields along the deformation path.
In fact, evidence in favor of this interpretation exists in the form of the analysis of Nemeschansky and Sen [@ns; @gvz] of higher order corrections to the $\beta$-function of the non-linear $\sigma$-model. Grisaru, Van de Ven and Zanon [@gvz] found that the four-loop contribution to the $\beta$-function of the non-linear $\sigma$ model for Calabi-Yau manifolds is non-zero, and [@ns] found a recipe how to cancel this singularity by deforming the manifold to metric which is non-Ricci flat at higher orders of the deformation parameter. The expansion [@af] used in this analysis is around the $0$ curvature tensor, but assuming for the moment that a similar phenomenon occurs if we expanded around the Fermat quintic vacuum, then there are no fields present in the Gepner model which would correspond perturbatively to these higher order corrections in the direction of non-Ricci flat metric: bosonically, such fields would have to have critical conformal dimension classically, since the $\sigma$-model Lagrangian is classically conformally invariant for non-Ricci flat target Kähler manifolds. However, quantum mechanically, there is a one-loop correction proportional to the Ricci tensor, thus indicating that fields expressing such perturbative deformations would have to be of generalized weight (cf. [@zhang; @zhang1; @huang; @huang1]). Fields of generalized weight, however, are not present in the Gepner model, which is a rational CFT, and more generally are excluded by unitarity (see discussions in Remarks after Theorems \[t1\], \[t2\] in Section \[sexp\] below). Thus, although this argument is not completely mathematical, renormalization analysis seems to confirm our finding that deformations of the Fermat quintic model must in general be non-perturbative. It is also noteworthy that the $\beta$-function is known to vanish to all orders for $K3$-surfaces because of $N=(4,4)$ supersymmetry. Accordingly, we also find that the phenomenon we see for the Fermat quintic is not present in the case of the Fermat quartic (see Section \[sk3\] below). It is also worth noting that other non-perturbative phenomena such as instanton corrections also arise when passing from $K3$-surfaces to Calabi-Yau $3$-folds ([@39a; @39b; @39c]). Finally, one must also remark that the proof of [@ns] of the $\beta$-function cancellation is not mathematically complete because of convergence questions, and thus one still cannot exclude even the scenario that not all non-linear $\sigma$ models would exist as exact CFT’s, thus creating some type of “string landscape” picture also in this context (cf. [@dt]).
In this paper, we shall be mostly interested in the strictly perturbative picture. The main point of this paper is an analysis of the algebraic obstructions in certain canonical cases. We discuss two main kinds of examples, namely the free field theory (both bosonic and $N=1$-supersymmetric), and the Gepner models of the Fermat quintic and quartic, which are exactly solvable $N=2$-supersymmetric conformal field theories conjectured to be the non-linear $\sigma$-models of the Fermat quintic Calabi-Yau $3$-fold and the Fermat quartic $K3$-surface. In the case of the free field theory, what happens is essentially that all non-trivial gravitational deformations of the free field theory are algebraically obstructed. In the case of a free theory compactified on a torus, the only gravitational deformations which are algebraically unobstructed come from linear change of metric on the torus. (We will focus on gravitational deformations; there are other examples, for example the sine-Gordon interaction [@sineg; @cgep], which are not discussed in detail here.)
The Gepner case deserves special attention. From the moduli space of Calabi-Yau $3$-folds, there is supposed to be a $\sigma$-model map into the moduli space of CFT’s. In fact, when we have an exactly solvable Calabi-Yau $\sigma$-model, one gets operators in CFT corresponding to the cohomology groups $H^{11}$ and $H^{21}$, which measure deformations of complex structure and Kähler metric, respectively, and these in turn give rise to [*infinitesimal*]{} deformations. Now the Fermat quintic [$$\label{eintro+}x^5+y^5+z^5+t^5+u^5=0$$]{} in $\C P^4$ has a model conjectured by Gepner [@gepner; @gepner1] which is embedded in the tensor product of $5$ copies of the $N=2$-supersymmetric minimal model of central charge $9/5$. The weight $(1/2,1/2)$ $cc$ and $ac$ fields correspond to the $100$ infinitesimal deformation of complex structure and $1$ infinitesimal deformation of Kähler metric of the quintic [(\[eintro+\])]{}. Despite the numerical matches in dimension, however, it is not quite correct to say that the gravitational deformations, corresponding to the moduli space of Calabi-Yau manifolds, occurs by turning on $cc$ and $ac$ fields. This is because, to preserve unitarity, a physical deformation can only occur when we turn on a real field, and the fields in question are not real. In fact, the complex conjugate of a $cc$ field is an $aa$ field, and the complex conjugate of an $ac$ field is a $ca$ field. The complex conjugate must be added to get a real field, and a physical deformation (we discuss this calculationally in the case of the free field theory in Section \[sfree\]).
In this paper, we do not discuss deformations of the Gepner model by turning on real fields. As shown in the case of the free field theory in Section \[sfree\], such deformations require for example regularization of the deformation parameter, and are much more difficult to calculate. Because of this, we work with only with the case of one $cc$ and one $ac$ field. We will show that at least one $cc$ deformation, whose real version corresponds to the quintics [$$\label{eintro++}x^5+y^5+z^5+t^5+u^5+\lambda x^3y^2=0$$]{} for small (but not infinitesimal) $\lambda$ is algebraically obstructed. (One suspects that similar algebraic obstructions also occur for other fields, but the computation is too difficult at the moment; for the $cc$ field corresponding to $xyztu$, there is some evidence suggesting that the deformation may exponentiate.)
It is an interesting question if non-linear $\sigma$-models of Calabi-Yau $3$-folds must also contain non-perturbative terms. If so, likely, this phenomenon is generic, which could be a reason why mathematicians so far discovered so few of these conformal field theories, despite ample physical evidence of their existence [@ag; @ns; @fried; @vw; @w1; @w2; @w3].
Originally prompted by a question of Igor Frenkel, we also consider the case of the Fermat quartic $K3$ surface $$x^4+y^4+z^4+t^4=0$$ in $\C P^3$. This is done in Section \[sk3\]. It is interesting that the problems of the Fermat quintic do not arise in this case, and all the infinitesimally critical fields exponentiate in the purely perturbative sense. This dovetails with the result of Alvarez-Gaume and Ginsparg [@agg] that the $\beta$-function vanishes to all orders for critical perturbative models with $N=(4,4)$ supersymmetry, and hence from the renormalization point of view, the non-linear $\sigma$ model is conformal for the Ricci flat metric on $K3$-surfaces. There are also certain differences between the ways mathematical considerations of moduli space and mirror symmetry vary in the $K3$ and Calabi-Yau $3$-fold cases, which could be related to the behavior of the non-perturbative effects. This will be discussed in Section \[scd\].
To relate more precisely in what setup these results occur, we need to describe what kind of deformations we are considering. It is well known that one can obtain infinitesimal deformations from primary fields. In the bosonic case, the weight of these fields must be $(1,1)$, in the $N=1$-supersymmetric case in the NS-NS sector the critical weight is $(1/2,1/2)$ and in the $N=2$-supersymmetric case the infinitesimal deformations we consider are along so called ac or cc fields of weight $(1/2,1/2)$. For more specific discussion, see section \[sinf\] below. There may exist infinitesimal deformations which are not related to primary fields (see the remarks at the end of Section \[sexp\]). However, they are excluded under a certain continuity assumption which we also state in section \[sinf\].
Therefore, the approach we follow is exponentiating infinitesimal deformations along primary fields of appropriate weights. In the “algebraic” approach, we assume that both the primary field and amplitudes can be updated at all points of the deformation parameter. Additionally, we assume one can obtain a perturbative power series expansion in the deformation parameter, and we do not allow counterterms of generalized weight or non-perturbative corrections. We describe a cohomological obstruction theory similar to Gerstenhaber’s theory [@gerst] for associative algebras, which in principle controls the coefficients at individual powers of the deformation parameter. Obstructions can be written down explicitly under certain conditions. This is done in section \[sexp\]. The primary obstruction in fact is the one which occurs for the deformations of the free field theory at gravitational fields of non-zero momentum (“gravitational waves”). In the case of the Gepner model of the Fermat quintic, the primary obstruction vanishes but in the case [(\[eintro++\])]{}, one can show there is an algebraic obstruction of order $5$ (i.e given by a $7$ point function in the Gepner model).
It should be pointed out that even in the “algebraic” case, there are substantial complications we must deal with. The moduli space of CFT’s is not yet well defined. There are different definitions of conformal field theory, for example the Segal approach [@scft; @hk; @hkd] is quite substantially different from the vertex operator approach (see [@huang] and references therein). Since these definitions are not known to be equivalent, and their realizations are supposed to be points of the moduli space, the space itself therefore cannot be defined until a particular definition is selected. Next, it remains to be specified what structure there should be on the moduli space. Presumably, there should at least be a topology, so than we need to ask what is a nearby conformal field theory. That, too, has not been answered.
These foundational questions are enormously difficult, mostly from the philosophical point of view: it is very easy to define ad hoc notions which immediately turn out insufficiently general to be desirable. Because of that, we only make minimal definitions needed to examine the existing paradigm in the context outlined. Let us, then, confine ourselves to observing that even in the perturbative case, the situation is not purely algebraic, and rather involves infinite sums which need to be discussed in terms of analysis. For example, the obstructions may in fact be undefined, because they may involve infinite sums which do not converge. Such phenomenon must be treated carefully, since it doesn’t mean automatically that perturbative exponentiation fails. In fact, because the deformed primary fields are only determined up to a scalar factor, there is a possibility of regularization along the deformation parameter. We briefly discuss this theoretically in section \[sexp\], and then give an example in the case of the free field theory in section \[sfree\].
We also briefly discuss sufficient conditions for exponentiation. The main method we use is the case when Theorem \[l1\] gives a truly local formula for the infinitesimal amplitude changes, which could be interpreted as an “infinitesimal isomorphism” in a special case. We then give in section \[sexp\] conditions under which such infinitesimal isomorphisms can be exponentiated. This includes the case of a coset theory, which doesn’t require regularization, and a more general case when regularization may occur.
In the final sections \[s1\], \[sexam\], namely the case of the Gepner model, the main problem is finding a setup for the vertex operators which would be explicit enough to allow evaluating the obstructions in question; the positive result is obtained using a generalisation of the coset construction. The formulas required are obtained from the Coulomb gas approach (=Feigin-Fuchs realization), which is taken from [@gh].
The present paper is organized as follows: In section \[sinf\], we give the general setup in which we work, show under which condition we can restrict ourselves to deformations along a primary field, and derive the formula for infinitesimally deformed amplitudes, given in Theorem \[l1\]. In section \[sexp\], we discuss exponentiation theoretically, in terms of obstruction theory, explicit formulas for the primary and higher obstructions, and regularization. We also discuss supersymmetry, and in the end show a mechanism by which non-perturbative deformations may still be possible when algebraic obstructions occur. In section \[sfree\], we give the example of the free field theories, the trivial deformations which come from $0$ momentum gravitational deforming fields, and the primary obstruction to deforming along primary fields of nonzero momentum. In section \[s1\], we will discuss the Gepner model of the Fermat quintic, and in section \[sexam\], we will discuss examples of non-zero algebraic obstructions to perturbative deformations in this case, as well as speculations about unobstructed deformations. In Section \[sk3\], we will discuss the (unobstructed) deformations for the Fermat quartic $K3$ surface, and in Section \[scd\], we attempt to summarize and discuss our possible conclusions.
[**Acknowledgements:**]{} The author thanks D.Burns, I.Dolgachev, I.Frenkel, Doron Gepner, Y.Z.Huang, I.Melnikov, K.Wendland and E.Witten for explanations and discussions. Special thanks to H.Xing, who contributed many useful ideas to this project before changing his field of interest.
Infinitesimal deformations of conformal field theories {#sinf}
======================================================
In a bosonic (=non-supersymmetric) CFT $\mathcal{H}$, if we have a primary field $u$ of weight $(1,1)$, then, as observed in [@scft], we can make an infinitesimal deformation of $\mathcal{H}$ as follows: For a worldsheet $\Sigma$ with vacuum $U_{\Sigma}$ (the worldsheet vacuum is the same thing as the “spacetime”, or string, amplitude), the infinitesimal deformation of the vacuum is [$$\label{einf1}V_{\Sigma}=\int_{x\in\Sigma} U_{\Sigma^{x}_{u}}.$$]{} Here $U_{\Sigma^{x}_{u}}$ is obtained by choosing a holomorphic embedding $f:D\r\Sigma$, $f(0)=x$, where $D$ is the standard disk. Let $\Sigma^{\prime}$ be the worldsheet obtained by cutting $f(D)$ out of $\Sigma$, and let $U_{\Sigma^{x}_{u}}$ be obtained by gluing the vacuum $U_{\Sigma^{\prime}}$ with the field $u$ inserted at $f(\partial D)$. The element $U_{\Sigma^{x}_{u}}$ is proportional to $||f^{\prime}(0)||^2$, since $u$ is $(1,1)$-primary, so it transforms the same way as a measure and we can define the integral [(\[einf1\])]{} without coupling with a measure. The integral [(\[einf1\])]{} is an infinitesimal deformation of the original CFT structure in the sense that $$U_{\Sigma}+V_{\Sigma}\epsilon$$ satisfies CFT gluing identities in the ring $\C[\epsilon]/\epsilon^2$.
The main topic of this paper is studying (in this and analogous supersymmetric cases) the question as to when the infinitesimal deformation [(\[einf1\])]{} can be exponentiated at least to perturbative level, i.e. when there exist for each $n\in\mathbb{N}$ elements $$u^0,...,u^{n-1}\in\mh, \; u^0=u$$ and for every worldsheet $\Sigma$ $$U^{0}_{\Sigma},...,U^{n}_{\Sigma}\in\bigotimes \mh^*\otimes \mh$$ such that [$$\label{einf2}U_{\Sigma}(m)={\begin{array}{c}
{\scriptstyle m}\\
\sum\\
{\scriptstyle i=0}\end{array}} U^{i}_{\Sigma}\epsilon^i,
U^{0}_{\Sigma}=U_{\Sigma}$$]{} satisfy gluing axioms in $\C[\epsilon]/\epsilon^{m+1}$, $0\leq m\leq n$, [$$\label{einf3}u(m)={\begin{array}{c}
{\scriptstyle m}\\
\sum\\
{\scriptstyle i=0}\end{array}}u^i\epsilon^i$$]{} is primary of weight $(1,1)$ with respect to [(\[einf2\])]{}, $0<m\leq n$, and [$$\label{einf4}
\frac{dU_{\Sigma}(m)}{d\epsilon}=\int_{x\in\Sigma}U_{\Sigma^{x}_{u(m-1)}}(m-1)$$]{} in the same sense as in [(\[einf1\])]{}.
We should remark that a priori, it is not known that all deformations of CFT come from primary fields: One could, in principle, simply ask for the existence of vacua [(\[einf2\])]{} such that [(\[einf2\])]{} satisfy gluing axioms over $\C[\epsilon]/\epsilon^{m+1}$. As remarked in [@scft], it is not known whether all perturbative deformations of CFT’s are obtained from primary fields $u$ as describe above. However, one can indeed prove that the primary fields $u$ exist given suitable [*continuity assumptions*]{}. Suppose the vacua $U_{\Sigma}(m)$ exist for $0\leq m\leq n$. We notice that the integral on the right hand side of [(\[einf4\])]{} is, by definition, the limit of integrals over regions $R$ which are proper subsets of $\Sigma$ such that the measure of $\Sigma-R$ goes to $0$ (fix an analytic metric on $\Sigma$ compatible with the complex structure). Let, thus, $\Sigma_{D_1,...,D_k}$ be a worldsheet obtained from $\Sigma$ by cutting out disjoint holomorphically embedded copies $D_1,...,D_k$ of the unit disk $D$. Then we calculate $$\begin{array}{l}
\frac{dU_{\Sigma}(m)}{d\epsilon}=\int_{x\in\Sigma}U_{\Sigma^{x}_{u(m-1)}}(m-1)\\
={\begin{array}{c}
{\scriptstyle }\\
\lim\\
{\scriptstyle \mu(\Sigma_{D_1,...,D_k})\r0}\end{array}}U_{\Sigma_{D_1,...,D_k}}(m-1)
\int_{x\in \bigcup D_i} U_{(\bigcup D_i)_{u(m-1)}^{x}}(m-1)\\
={\begin{array}{c}
{\scriptstyle }\\
\lim\\
{\scriptstyle \mu(\Sigma_{D_1,...,D_k})\r0}\end{array}}{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle i}\end{array}}U_{\Sigma_{D_i}}(m-1)
\int_{x\in D_i} U_{(D_i)_{u(m-1)}^{x}}(m-1)\\
={\begin{array}{c}
{\scriptstyle }\\
\lim\\
{\scriptstyle \mu(\Sigma_{D_1,...,D_k})\r0}\end{array}}{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle i}\end{array}}U_{\Sigma_{D_i}}(m-1)
\frac{
dU_{D_i}(m)}{d\epsilon}
\end{array}$$ assuming [(\[einf4\])]{} for $\Sigma=D$, so the assumption we need is [$$\label{einf5}\frac{dU_{\Sigma}}{d\epsilon}={\begin{array}{c}
{\scriptstyle }\\
\lim\\
{\scriptstyle \mu(
\Sigma_{D_1,...,D_k})\r0}\end{array}} {\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle i}\end{array}}U_{\Sigma_{D_i}}(m)\circ \frac{
dU_{D_i}(m)}{d\epsilon}.$$]{} The composition notation on the right hand side means gluing. Granted [(\[einf5\])]{}, we can recover $\frac{d U_{\Sigma}(m)}{d\epsilon}$ from $\frac{d U_{D}(m)}{d\epsilon}$ for the unit disk $D$. Now in the case of the unit disk, we get a candidate for $u(m-1)$ in the following way:
Assume that $\mh$ is topologically spanned by subspaces $\mh_{(m_1,m_2)}$ of $\epsilon$-weight $(m_1,m_2)$ where $m_1,m_2\geq 0$, $\mh_{(0,0)}=\langle U_D\rangle$. Then $U_{D}(m)$ is invariant under rigid notation, so [$$\label{einf6}U_{D}(m)\in{\begin{array}{c}
{\scriptstyle }\\
\hat{\bigotimes}\\
{\scriptstyle k\geq 0}\end{array}}
\mh_{(k,k)}[\epsilon]/\epsilon^{m+1}.$$]{} We see that if $A_q$ is the standard annulus with boundary components $S^1$, $qS^1$ with standard parametrizations, then [$$\label{einf7}u(m-1)={\begin{array}{c}
{\scriptstyle }\\
\lim\\
{\scriptstyle q\r 0}\end{array}}\frac{1}{||q||^2}U_{A_q}
\frac{dU_{D}(m)}{d\epsilon}$$]{} exists and is equal to the weight $(1,1)$ summand of [(\[einf6\])]{}. In fact, by [(\[einf5\])]{} and the definition of integral, we already see that [(\[einf4\])]{} holds. We don’t know however yet that $u(m-1)$ is primary. To see that, however, we note that for any annulus $A=D-D^{\prime}$ where $f:D\r D^{\prime}$ is a holomorphic embedding with derivative $r$, [(\[einf5\])]{} also implies (for the same reason - the exhaustion principle) that [(\[einf4\])]{} is valid with $u(m-1)$ replaced by [$$\label{einf*}\frac{U_{A}u(m-1)}{||r||^2}.$$]{} Since this is true for any $\Sigma$, in particular where $\Sigma$ is any disk, the integrands must be equal, so [(\[einf\*\])]{} and $u(m-1)$ have the same vertex operators, so at least in the absence of null elements, [$$\label{einf8}\frac{U_{A}u(m-1)}{||r||^2}=u(m-1)$$]{} which means that $u(m-1)$ is primary.
We shall see however that there are problems with this formulation even in the simplest possible case: Consider the free (bosonic) CFT of dimension $1$, and the primary field $x_{-1}\tilde{x}_{-1}$. (We disregard here the issue that $\mh$ itself lacks a satisfactory Hilbert space structure, see [@hkd], we could eliminate this problem by compactifying the theory on a torus or by considering the state spaces of given momentum.) Let us calculate [$$\label{einf9}\begin{array}{l}U_{D}^{1}=
\int_D \exp(zL_{-1})\exp(\overline{z}\tilde{L}_{-1})x_{-1}\tilde{x}_{-1}
\\
=\frac{1}{2}{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle k\geq 1}\end{array}}\frac{x_{-k}\tilde{x}_{-k}}{k}.
\end{array}$$]{} We see that the element [(\[einf9\])]{} is not an element of $\mh$, since its norm is ${\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle k\geq 1}\end{array}}1=\infty$. The explanation is that the $2$-point function changes during the deformation, and so therefore does the inner product. Hence, if we Hilbert-complete, the Hilbert space will change as well.
For various reasons however we find this type of direct approach difficult here. For one thing, we wish to consider theories which really do not have Hilbert axiomatizations in the proper sense, including Minkowski signature theories, where the Hilbert approach is impossible for physical reasons. Therefore, we prefer a “vertex operator algebra” approach where we discard the Hilbert completion and restrict ourselves to examining tree level amplitudes. One such axiomatization of such theories was given in [@huang] under the term “full field algebra”. In the present paper, however, we prefer to work from scratch, listing the properties we will use explicitly, and referring to our objects as conformal field theories in the vertex operator formulation.
We will then consider untopologized vector spaces [$$\label{einf10}V=\bigoplus V_{(w_L,w_R)}.$$]{} Here $(w_L,w_R)$ are weights (we refer to $w_L$ resp. $w_R$ as the left resp. right component of the weight), so we assume $w_L-w_R\in \Z$ and usually [$$\label{einf10a}w_L,w_R\geq 0,$$]{} [$$\label{einf11}V_{(0,0)}=\langle U_D\rangle.$$]{} The “no ghost” assumptions [(\[einf10a\])]{}, [(\[einf11\])]{} will sometimes be dropped. If there is a Hilbert space $\mh$, then $V$ is interpreted as the “subspace of states of finite weights”. We assume that for $u\in V_{w_L,w_R}$, we have vertex operators of the form [$$\label{einf12}Y(u,z,\overline{z})=
{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle (v_L,v_R)}\end{array}}u_{-v_L-w_L,-v_R-w_R}z^{v_L}\overline{z}^{v_R}.$$]{} Here $u_{a,b}$ are operators which raise the left (resp. right) component of weight by $a$ (resp. $b$). We additionally assume $v_L-v_R\in\Z$ and that for a given $w$, the weights of operators which act on $w$ are discrete. Even more strongly, we assume that [$$\label{einf13}Y(u,z,\overline{z})={\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle i}\end{array}}Y_i(u,z)\tilde{Y}_i(u,\overline{z})$$]{} where [$$\label{einf13a}\begin{array}{l}Y_i(u,z)=\sum u_{i;-v_L-w_L}z^{v_L},\\
\tilde{Y}_i(u,\overline{z})=\sum \tilde{u}_{i;-v_R-w_R}\overline{z}^{v_R}
\end{array}$$]{} where all the operators $Y_i(u,z)$ commute with all $\tilde{Y}_j(v,\overline{z})$. The main axiom [(\[einf12\])]{} must satisfy is “commutativity” and “associativity” analogous to the case of vertex operator algebras, i.e. there must exist for fields $u,v,w\in V$ and $w^{\prime}\in V^\vee$ of finite weight, a “$4$-point function” [$$\label{einfz}w^{\prime}Z(u,v,z,\overline{z},t,\overline{t})w$$]{} which is real-analytic and unbranched outside the loci of $z=0$, $t=0$ and $z=t$, and whose expansion in $t$ first and $z$ second (resp. $z$ first and $t$ second, resp. $z-t$ first and $t$ second) is $$w^{\prime}
Y(u,z,\overline{z})Y(v,t,\overline{t})w,$$ $$w^{\prime}Y(v,t,\overline{t})Y(u,z,\overline{z})w,$$ $$w^{\prime}Y(Y(u,z-t,\overline{z-t})v,t,\overline{t})w,$$ respectively. Here, for example, by an expansion in $t$ first and $z$ second we mean a series in the variable $z$ whose coefficients are series in the variable $t$, and the other cases are analogous.
We also assume that Virasoro algebras $\langle L_n\rangle$, $\langle \tilde{L}_n
\rangle$ with equal central charges $c_L=c_R$ act and that [$$\label{einf14}
\begin{array}{l}
Y(L_{-1}u,z,\overline{z})=\frac{\partial}{\partial z} Y(u,z,\overline{z}),\\
Y(\tilde{L}_{-1}u,z,\overline{z})=\frac{\partial}{\partial \overline{z}}
Y(u,z,\overline{z})
\end{array}$$]{} and [$$\label{einf15}
\text{$V_{w_L,w_R}$ is the weight $(w_L,w_R)$ subspace of $(L_0,\tilde{L}_0)$.}$$]{}
[**Remark:**]{} Even the axioms outlined here are meant for theories which are initial points of the proposed perturbative deformations, they are two restrictive for the theories obtained as a result of the deformations themselves. To capture those deformations, it is best to revert to Segal’s approach, restricting attention to genus $0$ worldsheets with a unique outbound boundary component (tree level amplitudes). Operators will then be expanded both in the weight grading and in the perturbative parameter (i.e. the coefficient at each power of the deformation parameter will be an element of the product-completed state space of the original theory). To avoid discussion of topology, we simply require that perturbative coefficients of all compositions of such operators converge in the product topology with respect to the weight grading, and the analytic topology in each graded summand.
In this section, we discuss infinitesimal perturbations, i.e. the deformed theory is defined over $\C[\epsilon]/(\epsilon^2)$ where $\epsilon$ is the deformation parameter. One case where such infinitesimal deformations can be described explicitly is the following
\[l1\] Consider fields $u,v,w\in V$ where $u$ is primary of weight $(1,1)$. Next, assume that $$Z(u,v,z,\overline{z},t,\overline{t})={\begin{array}{c}
{\scriptstyle }\\
\bigoplus\\
{\scriptstyle \alpha,\beta}\end{array}}
Z_{\alpha,\beta}(u,v,z,\overline{z},t,\overline{t})$$ where $$Z_{\alpha,\beta}(u,v,z,\overline{z},t,\overline{t})=
{\begin{array}{c}
{\scriptstyle }\\
\bigoplus\\
{\scriptstyle i}\end{array}}Z_{\alpha,\beta,i}(u,v,z,t)\tilde{Z}_{\alpha,\beta,i}
(u,v,\overline{z},\overline{t})$$ and for $w^{\prime}\in W^{\vee}$ of finite weight, $w^{\prime}Z_{\alpha,\beta,i}(u,v,z,t)(z-t)^{\alpha}z^{\beta}$
(resp. $w^{\prime}\tilde{Z}_{\alpha,\beta,i}
(u,v,\overline{z},\overline{t})\overline{z-t}^{\alpha}\overline{z}^{\beta}$) is a meromorphic (resp. antimeromorphic) function of $z$ on $\C P^{1}$, with poles (if any) only at $0,t,\infty$. Now write [$$\label{einfl*}Y_{u,\alpha,\beta}(v,t,\overline{t})=
(i/2)\int_{\Sigma}Z_{\alpha,\beta}(u,v,z,\overline{z},t,\overline{t})dzd\overline{z},$$]{} so $$Y_u(v,t,\overline{t})=Y(v,t,\overline{t}) +\epsilon {\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle \alpha,\beta}\end{array}}
Y_{u,\alpha,\beta}(v,t,\overline{t})$$ is the infinitesimally deformed vertex operator where $\Sigma$ is the degenerate worldsheet with unit disks cut out around $0,t,\infty$. Assume now further that we can expand [$$\label{einfl1}Z_{\alpha,\beta,i}(u,v,z,t)=Y_{\alpha,\beta,i}(v,t)Y_{\alpha,\beta,i}(u,z)
\;
\text{when $z$ is near $0$},$$]{} [$$\label{einfl2}Z_{\alpha,\beta,i}(u,v,z,t)=Y^{\prime}_{\alpha,\beta,i}(u,z)Y_{
\alpha,\beta,i}(v,t)
\;
\text{when $z$ is near $\infty$},$$]{} [$$\label{einfl3}Z_{\alpha,\beta,i}(u,v,z,t)=Y_{\alpha,\beta,i}
(Y^{\prime\prime}_{\alpha,\beta,i}(u,z-t))v,
t)\;
\text{when $z$ is near $t$}.$$]{} Write $$Y_{\alpha,\beta,i}(u,z)=\sum u_{\alpha,\beta,i,-n-\beta}z^{n+\beta-1},$$ $$Y_{\alpha,\beta,i}^{\prime}(u,z)=\sum u_{\alpha,\beta,i,-n-\alpha-\beta}^{\prime}
z^{n+\alpha+\beta-1},$$ $$Y_{\alpha,\beta,i}^{\prime\prime}(u,z)=\sum u_{\alpha,\beta,i,n-\alpha}^{\prime
\prime}z^{n+\alpha-1},$$ (Analogously with the $\tilde{}$’s.) Assume now [$$\label{ell*}u_{\alpha,\beta,i,0}w=0,\; u_{\alpha,\beta,i,0}^{\prime\prime}v=0,\;
u_{\alpha,\beta,i,0}^{\prime}Y_{\alpha,\beta,i}(v,t)w=0$$]{} and analogously for the $\tilde{}$’s (note that these conditions are only nontrivial when $\beta=0$, resp. $\alpha=0$, resp. $\alpha=-\beta$). Denote now by $\omega_{\alpha,\beta,i,0}$, $\omega_{\alpha,\beta,i,\infty}$, $\omega_{\alpha,\beta,i,t}$ the indefinite integrals of [(\[einfl1\])]{}, [(\[einfl2\])]{}, [(\[einfl3\])]{} in the variable $z$, obtained using the formula $$\int z^kdz=\frac{z^{k+1}}{k+1}\; k\neq -1$$ (thus fixing the integration constant), and analogously with the $\tilde{}$’s. Let then [$$\label{einfl4}
\begin{array}{l}
C_{\alpha,\beta,i}=\omega_{\alpha,\beta,i,\infty}-\omega_{\alpha,\beta,i,t},\\
D_{\alpha,\beta,i}=\omega_{\alpha,\beta,i,\infty}-\omega_{\alpha,\beta,i,0},\\
\tilde{C}_{\alpha,\beta,i}=\tilde{\omega}_{\alpha,\beta,i,\infty}-\tilde{\omega}_{
\alpha,\beta,i,t},\\
\tilde{D}_{\alpha,\beta,i}=\tilde{\omega}_{\alpha,\beta,i,\infty}-\tilde{\omega}_{
\alpha,\beta,i,0}
\end{array}$$]{} (see the comment in the proof on branching). Let $$\phi_{\alpha,\beta,i}=
\pi {\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle n}\end{array}}\frac{u_{\alpha,\beta,i,-n}\tilde{u}_{\alpha,
\beta,i,-n}}{n}$$ where $$Y_{\alpha,\beta,i}(u,z)=\sum u_{\alpha,\beta,i,-n}z^{n-1}$$ and similarly for the $\tilde{}$’s, the ${}^{\prime}$’s and the ${}^{\prime\prime}$’s. (The definition makes sense when applied to fields on which the term with denominator $0$ vanishes.) Then [$$\label{einfl5}{
\begin{array}{l}\protect
Y_{\alpha,\beta,u}(v,t,\overline{t})w={\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle i}\end{array}}
\phi_{\alpha,\beta,i}^{\prime} Y(v,t,\overline{t})w \\
\protect
-Y(\phi_{\alpha,\beta,i}^{\prime\prime}v,t,\overline{t})w
-Y(v,t,\overline{t})\phi_{\alpha,\beta,i}w+\\
\protect
C_{\alpha,\beta,i}\tilde{C}_{\alpha,\beta,i}
(-1+e^{-2\pi i\alpha})+D_{\alpha,\beta,i}\tilde{D}_{\alpha,\beta,i}(1-e^{2\pi i
\beta}).
\end{array}
}$$]{} Additionally, when $\alpha=0$, then $D_{\alpha,\beta,i}=\tilde{D}_{\alpha,\beta,i}=0$, and when $\beta=0$ then $C_{\alpha,\beta,i}=\tilde{C}_{\alpha,\beta,i}=0,$ and [$$\label{einfl6}\protect
Y_{\alpha,\beta,u}(v,t,\overline{t})w=
{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle i}\end{array}}\phi_{\alpha,\beta,i}^{\prime} Y(v,t,\overline{t})w
-Y(\phi_{\alpha,\beta,i}^{\prime\prime}v,t,\overline{t})w-Y(v,t,\overline{t})\phi_{\alpha,\beta,i}w.$$]{} The equation [(\[einfl6\])]{} is also valid when $\alpha=-\beta$.
[**Remark 1:**]{} Note that technically, the integral [(\[einfl\*\])]{} is not defined on the nondegenerate worldsheet described. This can be treated in the standard way, namely by considering an actual worldsheet $\Sigma^{\prime}$ obtained by gluing on standard annuli on the boundary components. It is easily checked that if we denote by $A^{u}_{q}$ the infinitesimal deformation of $A_q$ by $u$, then $$A_{q}^{u}(w)=\phi A_q(w)- A_q(\phi w).$$ Therefore, the Theorem can be stated equivalently for the worldsheet $\Sigma^{\prime}$. The only change needs to be made in formula [(\[einfl5\])]{}, where $\phi^{\prime\prime}$ needs to be multiplied by $s^{-2n}$ and $\phi$ needs to be multiplied by $r^{-2n}$ where $r$ and $s$ are radii of the corresponding boundary components. Because however this is equivalent, we can pretend to work on the degenerate worldsheet $\Sigma$ directly, in particular avoiding inconvenient scaling factors in the statement.
[**Remark 2:**]{} The validity of this Theorem is rather restricted by its assumptions. Most significantly, its assumption states that the chiral $4$ point function can be rendered meromorphic in one of the variables by multiplying by a factor of the form $z^{\alpha}(z-t)^{\beta}$. This is essentially equivalent to the fusion rules being “abelian”, i.e. $1$-dimensional for each pair of labels, and each pair of labels has exactly one product. As we will see (and as is well known), the $N=2$ minimal model is an example of a “non-abelian” theory.
Even for an abelian theory, the theorem only calculates the deformation in the “$0$ charge sector” because of the assumption [(\[ell\*\])]{}. Because of this, even for a free field theory, we will need to discuss an extension of the argument. Since in that case, however, stating precise assumptions is even more complicated, we prefer to treat the special case only, and to postpone the discussion to Section \[sfree\] below.
Let us work on the scaled real worldsheet $\Sigma^{\prime}$. Let $$\eta_{\alpha,\beta,i}=Z_{\alpha, \beta,i}(u,v,z,t)dz,$$ $$\tilde{\eta}_{\alpha,\beta,i}=\tilde{Z}_{\alpha,
\beta,i}(u,v,\overline{z},\overline{t})d\overline{z}.$$ Denote by $\partial_0$, $\partial_{\infty}$, $\partial_t$ the boundary components of $\Sigma^{\prime}$ near $0$, $\infty$, $t$. Then the form $\omega_{\alpha,\beta,i,\infty}\tilde{\eta}_{\alpha,\beta,i}$ is unbranched on a domain obtained by making a cut $c$ connecting $\partial_0$ and $\partial_t$. We have [$$\label{einfl7}\oint_{\partial_t}\omega_{\alpha,\beta,i,t}\tilde{\eta}=-
Y(\phi_{\alpha,\beta,i} v,t,\overline{t})$$]{} [$$\label{einfl8}\oint_{\partial_0}\omega_{\alpha,\beta,i,0}\tilde{\eta}=-
Y(\phi_{\alpha,\beta,i} v,t,\overline{t})\phi_{\alpha,\beta,i}.$$]{} But we want to integrate $\omega_{\alpha,\beta,i}\tilde{\eta}_{\alpha,\beta,i}$ over th boundary $\partial K$: [$$\label{einfl9}\begin{array}{c}
\oint_{\partial K}\omega_{\alpha,\beta,i}\tilde{\eta}_{\alpha,\beta,i}=\\
\oint_{\partial_t}\omega_{\alpha,\beta,i}\tilde{\eta}_{\alpha,\beta,i}+
\oint_{\partial_0}\omega_{\alpha,\beta,i}\tilde{\eta}_{\alpha,\beta,i}+
\oint_{\partial_\infty}\omega_{\alpha,\beta,i}\tilde{\eta}_{\alpha,\beta,i}\\
+\int_{c^+}\omega_{\alpha,\beta,i}\tilde{\eta}_{\alpha,\beta,i}+
\int_{c^-}\omega_{\alpha,\beta,i}\tilde{\eta}_{\alpha,\beta,i}
\end{array}$$]{} where $c^+$, $c^-$ are the two parts of $\partial K$ along the cut $c$, oriented from $\partial_t$ to $\partial_0$ and back respectively. Before going further, let us look at two points $x^+\in c^+$, $x^-\in c^-$ which project to the same point on $c$. We have $$\begin{array}{l}
C(e^{-2\pi i\alpha}-1)\tilde{\eta}(x^-)=\\
C\tilde{\eta}(x^+)-C\tilde{\eta}(x^-)=(\omega_t+C)\tilde{\eta}(x^+)-
(\omega_t+C)\tilde{\eta}(x^-)=\\
\omega_{\infty}\tilde{\eta}(x^+)-\omega_{\infty}\tilde{\eta}(x^-)=(\omega_0+D)
\tilde{\eta}(x^+)-(\omega_o+D)\tilde(x^{-})=\\
D\tilde{\eta}(x^+)-D\tilde{\eta}(x^{-})=D(e^{2\pi i\beta}-1)\tilde{\eta}(x^-)
\end{array}$$ (the subscripts $\alpha,\beta,i$ were omitted throughout to simplify the notation). This implies the relation [$$\label{einfl10}C_{\alpha,\beta,i}(e^{-2\pi i\alpha}-1)=D_{\alpha,\beta,i}(
e^{2\pi i \beta}-1).$$]{} [**Comment:**]{} This is valid when the constants $C_{\alpha,\beta,i}$, $D_{\alpha,\beta,i}$ are both taken at the point $x^-$; note that since the chiral forms are branched, we would have to adjust the statement if we measured the constants elsewhere. This however will not be of much interest to us as in the present paper we are most interested in the case when the constants vanish.
In any case, note that [(\[einfl10\])]{} implies $C_{\alpha,\beta,i}=0$ when $\beta=0\mod\Z$ and $\alpha\neq 0\mod\Z$, and $D_{\alpha,\beta,i}=0$ when $\alpha=0
\mod\Z$ and $\beta\neq 0\mod\Z$. There is an anlogous relation to [(\[einfl10\])]{} between $\tilde{C}_{\alpha,\beta,i}$, $\tilde{D}_{\alpha,\beta,i}$. Note that when $\alpha=0=\beta$, all the forms in sight are unbranched, and [(\[einfl6\])]{} follows directly. To treat the case $\alpha=-\beta$, proceed analogously, but replacing $\omega_{\alpha,\beta,i,\infty}$ by $\omega_{\alpha,\beta,i,0}$ or $\omega_{\alpha,\beta,i,t}$. Thus, we have finished proving [(\[einfl6\])]{} under its hypotheses.
Returning to the general case, let us study the right hand side of [(\[einfl9\])]{}. Subtracting the first two terms from [(\[einfl7\])]{}, [(\[einfl8\])]{}, we get [$$\label{einfl11}\oint_{\partial_t}C_{\alpha,\beta,i}\tilde{\eta}_{\alpha,
\beta,i}, \;
\oint_{\partial_0}D_{\alpha,\beta,i}\tilde{\eta}_{\alpha,
\beta,i},$$]{} respectively. On the other hand, the sum of the last two terms, looking at points $x^+,x^-$ for each $x\in c$, can be rewritten as [$$\label{einfl12}\int_{c^+} C_{\alpha,\beta,i}(-e^{-2\pi i\alpha}+1)
\tilde{\eta}_{\alpha,\beta,i}=\int_{c^-}D_{\alpha,\beta,i}(-e^{2\pi i \beta}+1)
\tilde{\eta}_{\alpha,\beta,i}.$$]{} Now recall [(\[einfl4\])]{}. Choosing $\tilde{\omega}_{\alpha,\beta,i,\infty}$ as the primitive function of $\tilde{\eta}_{\alpha,\beta,i}$, we see that for the end point $x$ of $c^-$, [$$\label{einfl13}\begin{array}{l}
\tilde{\omega}_{\alpha,\beta,i,\infty}(x^+)-\tilde{\omega}_{\alpha,\beta,i,\infty}(x^-)
=\\
\tilde{\omega}_{\alpha,\beta,i,t}(x^+)-\tilde{\omega}_{\alpha,\beta,i,t}(x^-)=\\
(e^{-2\pi i\alpha}-1)\tilde{\omega}_{\alpha,\beta,i,t}(x^{-})=\\
(e^{-2\pi i\alpha}-1)\tilde{\omega}_{\alpha,\beta,i,\infty}(x^-)+
(e^{-2\pi i\alpha}-1)\tilde{C}_{\alpha,\beta,i}.
\end{array}$$]{} Similarly, for the beginning point $y$ of $c^-$, [$$\label{einfl14}\begin{array}{l}
-\tilde{\omega}_{\alpha,\beta,i,\infty}(y^+)+\tilde{\omega}_{\alpha,\beta,i,\infty}(y^-)
=\\
-\tilde{\omega}_{\alpha,\beta,i,0}(y^+)+\tilde{\omega}_{\alpha,\beta,i,0}(y^-)=\\
-(e^{2\pi i\beta}-1)\tilde{\omega}_{\alpha,\beta,i,0}(y^{-})=\\
-(e^{2\pi i\beta}-1)\tilde{\omega}_{\alpha,\beta,i,\infty}(y^-)-
(e^{2\pi i\beta}-1)\tilde{D}_{\alpha,\beta,i}.
\end{array}$$]{} Then [(\[einfl13\])]{}, [(\[einfl14\])]{} multiplied by $C_{\alpha,\beta,i}$ are the integrals [(\[einfl11\])]{}, while the integral [(\[einfl12\])]{} is [$$\label{einfl15}-D_{\alpha,\beta,i}(1-e^{2\pi i\beta})\tilde{\omega}_{\alpha,
\beta,i,0}(y^-)+C_{\alpha,\beta,i}(1-e^{-2\pi i\alpha})\tilde{\omega}_{
\alpha,\beta,i,0}(x^-).$$]{} Adding this, we get $$C_{\alpha,\beta,i}\tilde{C}_{\alpha,\beta,i}
(-1+e^{-2\pi i\alpha})+D_{\alpha,\beta,i}\tilde{D}_{\alpha,\beta,i}(1-e^{2\pi i
\beta}),$$ as claimed.
Exponentiation of infinitesimal deformations {#sexp}
============================================
Let us now look at primary weight $(1,1)$ fields $u$. We would like to investigate whether the infinitesimal deformation of vertex operators (more precisely worldsheet vacua or string amplitudes) along $u$ indeed continues to a finite deformation, or at least to perturbative level, as discussed in the previous section. Looking again at the equation [(\[einf4\])]{}, we see that we have in principle a series of obstructions similar to those of Gerstenhaber [@gerst], namely if we denote by [$$\label{eexp1}L_n(m)={\begin{array}{c}
{\scriptstyle m}\\
\sum\\
{\scriptstyle i=0}\end{array}}L_{n}^{i}\epsilon^{i},\;
L_{n}^{0}=L_n$$]{} a deformation of the operator $L_n$ in $Hom(V,V)[\epsilon]/\epsilon^m$, we must have [$$\label{eexp2}L_n(m)u(m)=0\in V[\epsilon]/\epsilon^{m+1} \;\text{for $n>0$}$$]{} [$$\label{eexp3}L_0(m)u(m)=u(m)\in V[\epsilon]/\epsilon^{m+1}.$$]{} This can be rewritten as [$$\label{eexp4}\begin{array}{l}
L_n u^m=-{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle i\geq 1}\end{array}}L_{n}^{i}u^{m-i}\\
(L_0-1)u^{m}=-{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle i\geq 1}\end{array}}L_{0}^{i}u^{m-i}.
\end{array}$$]{} (Analogously for the $\tilde{}$’s. In the following, we will work on the obstruction for the chiral part, the antichiral part is analogous.) At first, these equations seem very overdetermined. Similarly as in the case of Gerstenhaber’s obstruction theory, however, of course the obstructions are of cohomological nature. If we denote by $\mathcal{A}$ the Lie algebra $\langle L_0-1,L_1,L_2,...\rangle$, then the system [$$\label{eexp5}\begin{array}{l}
L_n(m)u(m-1)\\
(L_0(m)-1)u(m-1)
\end{array}$$]{} is divisible by $\epsilon^m$ in $V[\epsilon]/\epsilon^{m+1}$, and is obviously a coboundary, hence a cocycle with respect to $\langle L_0(m)-1,L_1(m),...\rangle$. Hence, dividing by $\epsilon^m$, we get a $1$-cocycle of $\mathcal{A}$. Solving [(\[eexp4\])]{} means expressing this $\mathcal{A}$-cocycle as a coboundary.
In the absence of ghosts (=elements of negative weights), there is another simplification we may take advantage of. Suppose we have a $1$-cocycle $c=( x_0,x_1,...)$ of $\mathcal{A}$. (In our applications, we will be interested in the case when the $x_{i}$’s are given by [(\[eexp4\])]{}.) Then we have the equations $$L^{\prime}_{k}x_j-L^{\prime}_{j}x_k=(k-j)x_{j+k},$$ where $L^{\prime}_{k}=L_k$ for $k>0$, $L^{\prime}_{0}=L_0-1$. In particular, $$L^{\prime}_{k}x_0-L^{\prime}_{0}x_k=kx_k,$$ or [$$\label{eexp6}L_kx_0=(L_0+k-1)x_k\;\text{for $k>0$}.$$]{} In the absence of ghosts, [(\[eexp6\])]{} means that for $k\geq 1$, $x_k$ is determined by $x_0$ with the exception of the weight $0$ summand $(x_1)_0$ of $x_1$. Additionally, if we denote the weight $k$ summand of $y$ in general by $y_k$, then [$$\label{eexp6a}c=dy$$]{} means [$$\label{eexp7}(x_0)_k=(k-1)y,$$]{} [$$\label{eexp8}(x_0)_1=0.$$]{} The rest of the equation [(\[eexp6a\])]{} then follows from [(\[eexp6\])]{}, with the exception of the weight $0$ summand of $x_1$. We must, then, have [$$\label{eexp9}(x_1)_0\in Im L_1.$$]{} Conditions [(\[eexp8\])]{}, [(\[eexp9\])]{}, for $$x_k=-{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle i\geq 1}\end{array}}L_{k}^{i}u^{m-i},$$ are the conditions for solving [(\[eexp4\])]{}, i.e. the actual obstruction.
For $m=1$, we get what we call the primary obstruction. We have $$L_{k}^{1}=\tilde{L}_{-k}^{1}={\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle m,i}\end{array}} u_{i,m+k}\tilde{u}_{i,m},$$ so [(\[eexp8\])]{} becomes [$$\label{eexp10}{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle i}\end{array}}u_{i,0}\tilde{u}_{i,0}u=0.$$]{} The condition [(\[eexp9\])]{} becomes [$$\label{eexp11}{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle i}\end{array}}u_{i,1}\tilde{u}_{i,0}u\in Im L_1,
\;{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle i}\end{array}}u_{i,0}\tilde{u}_{i,1}u\in Im \tilde{L}_1.$$]{}
This investigation is also interesting in the supersymmetric context. In the case of $N=1$ worldsheet supersymmetry, we have additional operators $G^{i}_{r}$, and in the $N=2$ SUSY case, we have operators $G^{+i}_{r}$, $G^{-i}_{r}$, $J^{i}_{n}$ (cf. [@greene; @Nconf]), defined as the $\epsilon^i$-coefficient of the deformation of $G_r$, resp. $G^{+}_{r}$, $G^{-}_{r}$, $J_{n}$ analogously to equation [(\[eexp1\])]{}.
In the $N=1$-supersymmetric case, the critical deforming fields have weight $(1/2,1/2)$ (as do $a$- and $c$-fields in the $N=2$ case), so in both cases the first equation [(\[eexp1\])]{} remains the same as in the $N=0$ case, the second becomes [$$\label{ecor39a}(L_0-1/2)u^m=-{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle i\geq 1}\end{array}}L_{0}^{i}u^{m-i}.$$]{} Additionally, for $N=1$, we get [$$\label{ecor39b}G_r u^m=-{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle i\geq 1}\end{array}}G^{i}_{r}u^{m-i},\; r\geq 1/2$$]{} (similarly when $\tilde{\;}$’s are present).
In the $N=1$-supersymmetric case, we therefore deal with the Lie algebra $\mathcal{A}$, which is the free $\C$-vector space on $L_n$, $G_r$, $n\geq 0$, $r\geq 1/2$. For a cocycle which has value $x_k$ on $L_k$ and $z_r$ on $G_r$, the equation [(\[eexp6\])]{} becomes [$$\label{ecor41a}L_k x_0=(L_0+k-1/2)x_k\;\text{for $k>0$},$$]{} so in the absence of ghosts, $x_k$ is always determined by $x_0$. If [$$\label{ecor42a}
\text{the $1$-cocycle $(x_k,z_r)$ is the coboundary of $y$}$$]{} we additionally get $$(x_0)_k=(k-1/2)y,$$ so $$(x_0)_{1/2}=0.$$ On the other hand, on the $z$’s, we get [$$\label{ecorA1}G_r x_0=(L_0+r-1/2)z_r,\; r\geq 1/2,$$]{} so we see that in the absence of ghosts, all $z_r$’s are determined, with the exception of $$(z_{1/2})_0.$$ Therefore our obstruction is [$$\label{ecorA2}(z_0)_{1/2}=0,\;(z_{1/2})_0\in Im(G_{1/2}).$$]{} For the primary obstruction, we have [$$\label{ecorA3}L^{1}_{k}=\tilde{L}^{1}_{-k}=
{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle m}\end{array}}(G_{-1/2}\tilde{G}_{-1/2}u)_{m+k,m}),$$]{} [$$\label{ecorA4}
\begin{array}{l}G^{1}_{r}=2{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle m}\end{array}}(\tilde{G}_{-1/2}u)_{m+r,m},\\
\tilde{G}^{1}_{r}=2{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle m}\end{array}}(G_{-1/2}u)_{m,m+r},
\end{array}$$]{} so the obstruction becomes [$$\label{ecorA5}\begin{array}{l}
{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle m}\end{array}}(G_{-1/2}\tilde{G}_{-1/2}u)_{m,m}=0,\\
{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle m}\end{array}}(\tilde{G}_{-1/2}u)_{m+1/2,m}\in Im(G_{1/2}),\\
{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle m}\end{array}}(G_{-1/2}u)_{m,m+1/2}\in Im(\tilde{G}_{1/2}).
\end{array}$$]{} In the case of $N=2$ supersymmetry, there is an additional complication, namely chirality. This means that in addition to the conditions [$$\label{ecorB1}\begin{array}{l}
(L_0-1/2)u=0,\\
L_n G^{\pm}_{r}u=J_{n-1}=0 \;\text{for}\; n\geq 1, r\geq 1/2,
\end{array}$$]{} we require that $u$ be chiral primary, which means [$$\label{ecorB2}G^{+}_{-1/2}u=0.$$]{} (There is also the possibility of antichiral primary, which has [$$\label{ecorB2'}G^{-}_{-1/2}u=0$$]{} instead, and similarly at the $\tilde{\;}$’s.) Let us now write down the obstruction equations for the chiral primary case. We get the first equation [(\[eexp4\])]{}, [(\[ecor39a\])]{}, and an analogue of [(\[ecor39b\])]{} with $G^{i}_{r}$ replaced by $G^{+i}_{r}$ and $G^{-i}_{r}$. Additionally, we have the equation $$G^{+}_{-1/2}u^m=-{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle i\geq 1}\end{array}}G^{i}_{-1/2}u^{m-i}$$ and analogously for the $\tilde{\;}$’s.
In this situation, we consider the super-Lie algebra $\mathcal{A}_2$ which is the free $\C$-vector space on $L_n$, $J_n$, $n\geq 0$, $G^{-}_{r}$, $r\geq 1/2$ and $G^{+}_{s}$, $s\geq -1/2$. One easily verifies that this is a super-Lie algebra on which the central extension vanishes canonically ([@greene], Section 3.1). Looking at a $1$-cocycle whose value is $x_k$,$z^{\pm}_{r}$, $t_k$ on $L_k$, $G^{\pm}_{r}$, $J_k$ respectively, we get the equation [(\[ecor41a\])]{}, and additionally [$$\label{ecorB3}G^{\pm}_{r}x_0=(L_0+r-1/2)z^{\pm}_{r},
\;\text{$r\geq 1/2$ for $-$, $r\geq -1/2$ for $+$}$$]{} and [$$\label{ecorB4}J_n x_0=(n-1/2)t_n,\; n\geq 0.$$]{} We see that the cocycle is determined by $x_0$, with the exception of $(z_{1/2}^{\pm})_0$, $(z_{-1/2}^{+})_1$. Therefore, we get the condition [$$\label{ecorB5}
\begin{array}{l}
(x_0)_{1/2}=0\\
(z^{\pm}_{1/2})_0\in Im(G^{\pm}_{1/2})\\
(z^{+}_{-1/2})_1=G^{+}_{-1/2}u\;\text{where $G^{+}_{1/2}u=0$}
\end{array}$$]{} and similarly for the $\tilde{\;}$’s.
In the case of deformation along a $cc$ field $u$, we have [$$\label{ecorB6}
L^{1}_{k}=\tilde{L}^{1}_{-k}=
{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle m}\end{array}} (G^{-}_{-1/2}\tilde{G}^{-}_{-1/2}u)_{m+k,m},$$]{} [$$\label{ecorB7}\begin{array}{l}
G^{+,1}_{r}={\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle m}\end{array}}2(\tilde{G}^{-}_{-1/2}u)_{m+r+1/2,m}\\
\tilde{G}^{+,1}_{r}={\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle m}\end{array}}2(G^{-}_{-1/2}u)_{m,m+r+1/2}\\
G^{-,1}_{r}=\tilde{G}^{-,1}_{r}=0\\
J^{1}_{n}=0=\tilde{J}^{1}_{n},
\end{array}$$]{} so the obstructions are, in a sense, analogous to [(\[ecorA5\])]{} with $G_r$ replaced by $G^{-}_{r}$.
[**Remark:**]{} The relevant computation in verifying that [(\[ecorB6\])]{}, [(\[ecorB7\])]{} (and the analogous cases before) form a cocycle uses formulas of the following type ([@zhu]): [$$\label{ecorC1}Res_{z}(a(z)v(w)z^n)-Res_{z}(v(w)a(z)z^n)=
Res_{z-w}((a(z-w)v)(w)z^n).$$]{} For example, when $v$ is primary of weight $1$, $a=L_{-2}$, the right hand side of [(\[ecorC1\])]{} is $$\begin{array}{l}
Res_{z-w}(L_0v(z-w)^{-2}n(z-w)w^{n-1}+L_{-1}v(z-w)^{-1}w^n)\\
=nv(w)w^{n-1}+L_{-1}v(w)w^n\\
=\sum nv_k w^{n-k-2}+\sum (-k-1)v_k w^{n-k-2}\\
=\sum (n-k)v_n w^{n-k-2}.
\end{array}$$ The left hand side is $\sum [L_{n-1},v_{k-n+1}]w^{n-k-2}$, so we get $$[L_{n-1}, v_{k-n+1}]=(n-k-1)v_k,$$ as needed.
Other required identities follow in a similar way. Let us verify one interesting case when $a=G^{-1}_{-3/2}$, $u$ chiral primary. Then the right hand side of [(\[ecorC1\])]{} is $$Res_{z-w}(G^{-}_{-1/2}v(w)(z-w)^{-1}w^n)=(G^{-}_{-1/2}v)(w)=
\sum (G^{-}_{-1/2}v)w^{-n-1}.$$ This implies [$$\label{ek3q*}[G^{-}_{r},u_s]=(G^{-}_{-1/2}u)_{r+s},$$]{} as needed.
We have now analyzed the primary obstructions for exponentiation of infinitesimal CFT deformations. However, in order for a perturbative exponentiation to exist, there are also higher obstructions which must vanish. The basic principle for obtaining these obstructions was formulated above. However, in pratice, it may often happen that those obstructions will not converge. This may happen for two different basic reasons. One possibility is that the deformation of the deforming field itself does not converge. This is essentially a violation of perturbativity, but may in some cases be resolved by regularizing the CFT anomaly along the deformation parameter. We will discuss this at the end of this section, and will give an example in Section \[sfree\] below.
Even if all goes well with the parameter, however, there may be another problem, namely the expressions for $L^{i}_{n}$ etc. may not converge due to the fact that our deformation formulas concern vacua of actual worldsheets, while $L^{i}_{n}$ etc. correspond to degenerate worldsheets. Similarly, vertex operators may not converge in the deformed theories. We will show here how to deal with this problem.
The main strategy is to rephrase the conditions from the above part of this section in terms of “finite annuli”. We start with the $N=0$ (non-supersymmetric) case. Similarly as in [(\[eexp1\])]{}, we can expand [$$\label{ecorf1}U_{A_r}(m)={\begin{array}{c}
{\scriptstyle m}\\
\sum\\
{\scriptstyle h=0}\end{array}}U_{A_{r}}^{h}\epsilon^h.$$]{} In the non-supersymmetric case, the basic fact we have is the following:
\[t1\] Assuming $u^k$ (considered as fields in the original undeformed CFT) have weight $>(1,1)$ for $k<h$, $r\in (0,1)$ we have [$$\label{ecorft1}\begin{array}{l}
U^{h}_{A_r}=\\
{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle m_k}\end{array}}{\begin{array}{c}
{\scriptstyle 1}\\
\int\\
{\scriptstyle s_h=r}\end{array}}s_{h}^{2m_h-1}{\begin{array}{c}
{\scriptstyle s_h}\\
\int\\
{\scriptstyle s_{h-1}=r}\end{array}}
s_{h-1}^{2m_{h-1}-1}...\\
{\begin{array}{c}
{\scriptstyle s_2}\\
\int\\
{\scriptstyle s_{1}=r}\end{array}}
s_{1}^{2m_{1}-1}u_{m_h,m_h}....u_{m_1,m_1}ds_1...ds_h U_{A_r}.
\end{array}$$]{} [$$\label{ecorft2}u^h={\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle m_k}\end{array}}
\frac{1}{2^h(m_h+...+m_1)(m_{h-1}+...+m_1)...m_1}u_{m_h,m_h}...u_{m_1,m_1}u.$$]{} In particular, the obstruction is the vanishing of the sum (with the term $m_h+...m_1$ omitted from the denominator) of the terms in [(\[ecorft2\])]{} with $m_h+...m_1=0$.
The identity [(\[ecorft1\])]{} is essentially by definition. The key point is that in the higher deformed vacua, there are terms in the integrand obtained by inserting $u_k$, $k>1$ to boundaries of disjoint disks $D_i$ cut out of $A_r$. Then there are corrective terms to be integrated on the worldsheets obtained by cutting out those disks. But the point is that under our weight assumption, all the disks $D_i$ can be shrunk to a single point, at which point the term disappears, and we are left with integrals of several copies of $u$ inserted at different points. If we are using vertex operators to express the integral, the operators must additionally be applied in time order (i.e. fields at points of lower modulus are inserted first). There is an $h!$ permutation factor which cancels with the Taylor denominator. This gives [(\[ecorft1\])]{}.
Now [(\[ecorft2\])]{} is proved by induction. For $h=1$, the calculation is done above. Assuming the induction hypothesis, the term of the integral where the $k-1$ innermost integrals have the upper bound and the $k$’th innermost integral has the lower bound is equal to $$U^{h-k}_{A_r}u^k,\; h>k\geq 1.$$ The summand which has all upper bounds except in the last integral is equal to [$$\label{enpert+}\frac{1-r^{2(m_1+...+m_h)}}{2^h
(m_h+...+m_1)(m_{h-1}+...+m_1)...m_1}u_{m_h,m_h}...u_{m_1,m_1}ur^2,$$]{} which is supposed to be equal to $$-U_{A_r}u^h +r^2u^h.$$ This gives the desired solution.
[**Remark:**]{} The formula [(\[enpert+\])]{} of course does not apply to the case $m_1+...+m_h=0$. In that case, the correct formula is [$$\label{enpert++}\frac{-\ln(r)}{
(m_{h-1}+...+m_1)...m_1}u_{m_h,m_h}...u_{m_1,m_1}ur^2.$$]{} So the question becomes whether there could exist a field $u^h$ such that $U_{A_r}u^h-r^2 u^h$ is equal to the quantity [(\[enpert++\])]{}. One sees immediately that such field does not exist in the product-completed space of the original theory. What this approach does not settle however is whether it may be possible to add such non-perturbative fields to the theory and preserve CFT axioms, which could facilitate existence of deformations in some generalized sense, despite the algebraic obstruction. It would have to be, however, a field of generalized weight in the sense of [@zhang; @zhang1; @huang; @huang1].
In effect, written in infinitesimal terms, the relation [(\[enpert++\])]{} becomes $$L_0u^h-u^h=-\frac{1}{(m_{h-1}+...+m_1)...m_1u}_{m_h,m_h}...u_{m_1,m_1}u.$$ The right hand side $w$ is a field of holomorphic weight $1$, so we see that we have a matrix relation $$L_0\left(\begin{array}{l}u^h\\u\end{array}
\right)=\left(\begin{array}{rr}1 &w\\0&1\end{array}
\right)\left(\begin{array}{l}u^h\\u\end{array}
\right)$$ This is an example of what one means by a field of generalized weight. One should note, however, that fields of generalized weight are excluded in unitary conformal field theories. By Wick rotation, the unitary axiom of a conformal field theory becomes the axiom of reflection positivity [@scft]: the operator $U_\Sigma$ associated with a worldsheet $\Sigma$ is defined up to a $1$-dimensional complex line $L_\Sigma$ (which is often more strongly assumed to have a positive real structure). If we denote by $\overline{\Sigma}$ the complex-conjugate worldsheet (note that this reverses orientation of boundary components), then reflection positivity requires that we have an isomorphism $L_{\overline{Sigma}}\cong L_{\Sigma}^{*}
$ (the dual line), and using this isomorphism, an identification $U_{\overline{\Sigma}}=
U_{\Sigma}^{*}$ (here the asterisk denotes the adjoint operator). Specializing to annuli $A_r$, $||r||\leq 1$, we see that the annulus for $r$ real is self-conjugate, so the corresponding operators are self-adjoint, and hence diagonalizable. On the other hand, for $||r||=1$, we obtain unitary operators, and unitary representations of $S^1$ on Hilbert space split into eigenspaces of integral weights. The central extension given by $L$ is then trivial and hence the operators corresponding to all $A_r$ commute, and hence are simultaneously diagonalizable, thus excluding the possibility of generalized weight.
The possibility, of course, remains that the correlation function of the deformed theory can be modified by a non-perturbative correction. Let us note that if left uncorrected, the term [(\[enpert++\])]{} can be interpreted infinitesimally as [$$\label{eiint1}L_0u(\epsilon)-u(\epsilon)= C\epsilon^m v\mod
\epsilon^{m+1},$$]{} where $v$ is another field of weight $1$. Note that in case that $u=v$, [(\[eiint1\])]{} can be interpreted as saying that $u$ changes weight at order $m$ of the perturbation parameter. In the general case, we obtain a matrix involving all the (holomorphic) weight $1$ fields in the unperturbed theory. Excluding fields of generalized weight in the unperturbed theory (which would translate to fields of generalized weight in the perturbed theory), the matrix must have other eigenvalues than $1$, thus showing that some critical fields will change weight.
In the $N=1$-supersymmetric case, an analogous statement holds, except the assumption is that the weight of $u^k$ is greater than $(1/2,1/2)$ for $k<h$, and the integral [(\[ecorft1\])]{} must be replaced by [$$\label{ecorft1a}\begin{array}{l}
U^{h}_{A_r}=\\
{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle m_k}\end{array}}{\begin{array}{c}
{\scriptstyle 1}\\
\int\\
{\scriptstyle s_h=r}\end{array}}s_{h}^{m_h-1}{\begin{array}{c}
{\scriptstyle s_h}\\
\int\\
{\scriptstyle s_{h-1}=r}\end{array}}
s_{h-1}^{m_{h-1}-1}...\\
{\begin{array}{c}
{\scriptstyle s_2}\\
\int\\
{\scriptstyle s_{1}=r}\end{array}}
s_{1}^{m_{1}-1}(G_{-1/2}\tilde{G}_{-1/2}u)_{m_h,m_h}...
(G_{-1/2}\tilde{G}_{-1/2}u)_{m_1,m_1}
ds_1...ds_h U_{A_r},
\end{array}$$]{} and accordingly [$$\label{ecorft2a}
\begin{array}{l}
u^h={\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle m_k}\end{array}}
\frac{1}{2^h(m_h+...+m_1)(m_{h-1}+...+m_1)...m_1}
\\(G_{-1/2}\tilde{G}_{-1/2}u)_{m_h,m_h}
...(G_{-1/2}\tilde{G}_{-1/2}u)_{m_1,m_1}u,
\end{array}$$]{} so the obstruction again states that the term with $m_h+...+m_1=0$ must vanish. In the $N=2$ case, when $u$ is a $cc$ field, we simply replace $G$ by $G^-$ in [(\[ecorft1a\])]{}, [(\[ecorft2a\])]{}.
But in the supersymmetric case, to preserve supersymmetry along the deformation, we must also investigate the “finite" analogs of the obstructions associated with $G_{1/2}$ in the $N=1$ case, and $G^{\pm}_{1/2}$, $G^{+}_{-1/2}$ in the $N=2$ $c$ case (and similarly for the $a$ case, and the $\tilde{\;}$’s). In fact, to tell the whole story, we should seriously investigate integration of the deforming fields over super-Riemann surfaces (=super-worldsheets). This can be done; one approach is to treat the case of the superdisk first, using Stokes theorem twice with the differentials $\partial$, $\overline{\partial}$ replaced by $D$, $\overline{D}$ respectively in the $N=1$ case (and the same at one chirality for the $N=2$ case). A general super-Riemann surface is then partitioned into superdisks.
For the purpose of obstruction theory, the following special case is sufficient. We treat the $N=2$ case, since it is of main interest for us. Let us consider the case of $cc$ fields (the other cases are analogous). First we note (see [(\[ecorB7\])]{}) that $G^-$ is unaffected by deformation via a $cc$ field, so the obstructions derived from $G^{-}_{-1/2}$ and $G^{-}_{1/2}$ are trivial (and similarly at the $\tilde{\;}$’s).
To understand the obstruction associated with $G^{+}_{1/2}$, we will study “finite" (as opposed to infinitesimal) annuli obtained by exponentiating $G^{+}_{1/2}$. Now the element $G^{+}_{1/2}$ is odd. Thinking of the super-semigroup of superannuli as a supermanifold, then it makes no sense to speak of “odd points" of the supermanifold. It makes sense, however, to speak of a family of edd elements parametrized by an odd parameter $s$: this is simply the same thing as a map from the $(0|1)$-dimensional superaffine line into the supermanifold. In this sense, we can speak of the “finite" odd annulus [$$\label{eodd1}\exp(s G^{+}_{1/2}).$$]{} Now we wish to study the deformations of teh operator associated with [(\[eodd1\])]{} along a $cc$ field $u$ as a perturbative expansion in $\epsilon$.
Thinking of $G^{+}_{1/2}$ as an $N=2$-supervector field, we have [$$\label{eodd2}G^{+}_{1/2}=(z+\theta^+\theta^-)\frac{\partial}{\partial\theta^+}-
z\theta^{-}\frac{\partial}{\partial z}.$$]{} We see that [(\[eodd2\])]{} deforms infinitesimally only the variables $\theta^+$ and $z$, not $\theta^-$. Thus, more specifically, [(\[eodd1\])]{} results in the transformation [$$\label{eodd3}
\begin{array}{l}
z\mapsto \exp(s\theta^-)z\\
\theta^-\mapsto\theta^-.
\end{array}$$]{} This gives rise to the formula, valid when $u^k$ have weight $>(1/2,1/2)$ for $1\leq k<h$, [$$\label{eodd4}
\begin{array}{l}
U^{h}_{\exp(sG^{+}_{1/2})}=\\
{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle m_k}\end{array}}{\begin{array}{c}
{\scriptstyle 1}\\
\int\\
{\scriptstyle t_h=\exp(s\theta^-)}\end{array}}t_{h}^{m_h-1}
{\begin{array}{c}
{\scriptstyle t_h}\\
\int\\
{\scriptstyle t_{h-1}=\exp(s\theta^-)}\end{array}}
t_{h-1}^{m_{h-1}-1}...\\
{\begin{array}{c}
{\scriptstyle t_2}\\
\int\\
{\scriptstyle t_{1}=\exp(s\theta^-)}\end{array}}
s_{1}^{m_{1}-1}v_{m_h,m_h}....v_{m_1,m_1}dt_1...dt_h U_{\exp(s G^{+}_{1/2})},
\end{array}$$]{} where $v_{m_k,m_k}$ is equal to [$$\label{eoddD1}(\tilde{G}^{-}_{-1/2}u)_{m_{k+1/2},m_k}$$]{} in summands of [(\[eodd4\])]{} where the factor resulting from integrating the $t_k$ variable has a $\theta^-$ factor, and [$$\label{eoddD2}(G^{-}_{-1/2}\tilde{G}^{-}_{-1/2}u)_{m_k,m_k}$$]{} in other summands. (We see that each summand can be considered as a product of factors resulting from integrating the individual variables $t_k$; in at most one factor, [(\[eoddD1\])]{} can occur, otherwise the product vanishes.)
Realizing that $exp(ms\theta^-)=1+ms\theta^-$, this gives that the obstruction (under the weight assumption for $u^k$) is that the summand for $m_1+...+m_h=0$ (with the denominator $m_1+...+m_h$ omitted) in the following expression vanish: [$$\label{eodd*}
\begin{array}{l}
{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle m_k}\end{array}}{\begin{array}{c}
{\scriptstyle h}\\
\sum\\
{\scriptstyle k=1}\end{array}}\frac{1}{m_1+...+m_h}...
\frac{1}{m_1}\\
(G^{-}_{-1/2}\tilde{G}^{-}_{-1/2}u)_{m_h,m_h}...
m_k
(\tilde{G}^{-}_{-1/2}u)_{m_{k+1/2},m_k}...
(G^{-}_{-1/2}\tilde{G}^{-}_{-1/2}u)_{m_1,m_1}u.
\end{array}$$]{}
To investigate the higher obstructions further, we need the language of correlation functions. Specifically, the CFT’s whose deformations we will consider are “RCFT’s". The simplest way of building an RCFT is from “chiral sectors" $\mathcal{H}_{\lambda}$ where $\lambda$ runs through a set of labels, by the recipe $$\mathcal{H}={\begin{array}{c}
{\scriptstyle }\\
\bigoplus\\
{\scriptstyle \lambda}\end{array}}\mh_{\lambda}\otimes\mh_{\lambda^*}$$ where $\lambda^*$ denotes the contragredient label (cf. [@kondo]). (In the case of the Gepner model, we will need a slightly more general scenario, but our methods still apply to that case analogously.) Further, we will have a symmetric bilinear form $$B:\mh_{\lambda}\otimes \mh_{\lambda^*}\r \C$$ with respect to which the adjoint to $Y(v,z)$ is $$(-z^{-2})^n Y(e^{zL_1}v,1/z)$$ where $v$ is of weight $n$. There is also a real structure $$\mh_{\lambda}\cong\overline{\mh}_{\lambda^*},$$ thus specifying a real structure on $\mh$, $\overline{u\otimes v}=\overline{u}
\otimes \overline{v}$, and inner product $$\langle u_1\otimes v_1,u_2\otimes v_2\rangle=B(u_1,\overline{u_2})B(v_1,
\overline{v_2}).$$ We also have an inner product $$\mh_{\lambda}\otimes_{\R} \mh_{\lambda^*}\r \C$$ given by $$\langle u,v\rangle=B(u,\overline{v}).$$ Then we have the $\P^1$-chiral correlation function [$$\label{ecorel1}\langle u(z_{\infty})^*|v_m(z_m)v_{m-1}(z_{m-1})...v_1(z_1)v_0(z_0)
\rangle$$]{} which can be defined by taking the vacuum operator associated with the degenerate worldsheet $\Sigma$ obtained by “cutting out” unit disks with centers $z_0,...,z_m$ from the unit disk with center $z_\infty$, applying this operator to $v_0\otimes...\otimes v_m$, and taking inner product with $u$. Thus, the correlation function [(\[ecorel1\])]{} is in fact the same thing as applying the field on either side of [(\[ecorel1\])]{} to the identity, and taking the inner product.
This object [(\[ecorel1\])]{} is however not simply a function of $z_0,..., z_\infty$. Instead, there is a finite-dimensional vector space $M_\Sigma$ depending holomorphically on $\Sigma$ (called the modular functor) such that [(\[ecorel1\])]{} is a linear function $$M_{\Sigma}\r \C.$$ However, now one assumes that $M$ is a “unitary modular functor" in the sense of Segal [@scft]. This means that $M_\Sigma$ has the structure of a positive-definite inner product space for not just the $\Sigma$ as above, but an arbitrary worldsheet. The inner product is not valued in $\C$, but in $$||det(\Sigma)||^{2c}$$ where $c$ is the central charge. Since the determinant of $\Sigma$ as above is the same as $det(\P^1)$ (hence in particular constant), we can make the inner product $\C$-valued in our case.
If the deforming field is of the form [$$\label{euotimes}u\otimes\tilde{u},$$]{} the “higher $L_0$ obstruction" (under the weight assumptions given above) can be further written as [$$\label{ecorel+}\begin{array}{l}
{\begin{array}{c}
{\scriptstyle }\\
\int\\
{\scriptstyle 0\leq ||z_1||\leq||z_m||\leq 1}\end{array}}
\langle v(0)^*|u(z_m)...u(z_1)u(0)\rangle\\
\langle \tilde{v}^*|\tilde{u}(\overline{z_m})..\tilde{u}(\overline{z_1})\tilde{u}(0)\rangle
dz_1 d\overline{z}_1....dz_md\overline{z}_m\\
\text{for $w(v)\leq 1$}
\end{array}$$]{} ($w$ is weight) in the $N=0$ case and [$$\label{ecorel++}\begin{array}{l}
{\begin{array}{c}
{\scriptstyle }\\
\int\\
{\scriptstyle 0\leq ||z_1||\leq||z_m||\leq 1}\end{array}}
\langle v(0)^*|(G^{-}_{-1/2}u)(z_m)...(G^{-}_{-1/2}u)(z_1)u(0)\rangle\\
\langle \tilde{v}^*|(\tilde{G}^{-}_{-1/2}\tilde{u})(\overline{z_m})...
(\tilde{G}^{-}_{-1/2}\tilde{u})(\overline{z_1})\tilde{u}(0)\rangle
dz_1 d\overline{z}_1....dz_md\overline{z}_m\\
\text{for $w(v)\leq 1/2$}
\end{array}$$]{} in the $N=2$ $cc$ case. The $G^{+}_{1/2}$-obstruction in the $N=2$ case can be written as [$$\label{ecorel+++}\begin{array}{l}
{\begin{array}{c}
{\scriptstyle }\\
\int\\
{\scriptstyle 0\leq ||z_1||\leq||z_m||\leq 1}\end{array}}
{\begin{array}{c}
{\scriptstyle m}\\
\sum\\
{\scriptstyle k=1}\end{array}}
\langle v(0)^*|(G^{-}_{-1/2}u)(z_m)...u(z_k)...(G^{-}_{-1/2}u)(z_1)u(0)\rangle\\
\langle \tilde{v}^*|(\tilde{G}^{-}_{-1/2}\tilde{u})(\overline{z_m})...
(\tilde{G}^{-}_{-1/2}\tilde{u})(\overline{z_1})\tilde{u}(0)\rangle\\
dz_1 d\overline{z}_1....dz_md\overline{z}_m\;\text{for $w(v)\leq 0$,
$w(\tilde{v})\leq 1/2$}
\end{array}$$]{} and similarly for the $\tilde{\;}$. We see that these obstructions vanish when we have [$$\label{ecoreli}\langle v(z_\infty)^*|u(z_m)....u(z_0)\rangle=0,\;
\text{for $w(v)\leq 1$}$$]{} in the $N=0$ case (and similarly for the $\tilde{\;}$’s), and [$$\label{ecorelii}\langle v(z_\infty)^*|G^{-}_{-1/2}u(z_m)....G^{-}_{-1/2}u(z_1)
u(z_0)\rangle=0,\;
\text{for $w(v)\leq 1/2$,}$$]{} and similarly for the $\tilde{\:}$’s. Observe further that when $$\tilde{u}=\overline{u},$$ the condition for the $\tilde{\:}$’s is equivalent to the condition for $u$, and further [(\[ecoreli\])]{}, [(\[ecorelii\])]{} are also necessary in this case, as in [(\[ecorel+\])]{}, [(\[ecorel++\])]{} we may also choose $\tilde{v}=\overline{v}$, which makes the integrand non-negative (and only $0$ if it is $0$ at each chirality). In the $N=2$ case, it turns the condition [(\[ecorelii\])]{} simplifies further:
\[t2\] Let $u$ be a chiral primary field of weight $1/2$. Then the necessary and sufficient condition [(\[ecorelii\])]{} for existence of perturbative CFT deformations along the field $u\otimes \overline{u}$ is equivalent to the same vanishing condition applied to only chiral primary fields $v$ of weight $1/2$.
In order for the fields [(\[ecorelii\])]{} to correlate, they would have to have the same $J$-charge $Q_J$. We have $$Q_J u=1,\; Q_J (G^{-}_{-1/2}u)=0.$$ As $Q_J$ of the right hand side of [(\[ecorelii\])]{} is $1$. Thus, for the function [(\[ecorelii\])]{} to be possibly non-zero, we must have [$$\label{ecorelti}Q_J v=1.$$]{} But then we have $$w(v)\geq \frac{1}{2}Q_J v=\frac{1}{2}$$ with equality arising if and only if [$$\label{ecoreltii}\text{$v$ is chiral primary of weight $1/2$.}$$]{}
[**Remark 1:**]{} We see therefore that in the $N=2$ SUSY case, there is in fact no need to assume that the weight of $U^k$ is $>(1/2,1/2)$ for $k<h$. If the obstruction vanishes for $k<h$, then we have [$$\label{epert1}u^k=\frac{1}{k!}{\begin{array}{c}
{\scriptstyle }\\
\int\\
{\scriptstyle D}\end{array}}
(G^{-}_{-1/2}\tilde{G}^{-}_{-1/2}u)(z_k)...
(G^{-}_{-1/2}\tilde{G}^{-}_{-1/2}u)(z_1)udz_1...dz_kd\overline{z}_1...
d\overline{z}_k$$]{} where the integrand is understood as a $(k+1)$-point function (and not its power series expansion in any particular range), over the unit disk.
Additionally, for any worldsheet $\Sigma$, [$$\label{epert2}U^{h}_{\Sigma}=\frac{1}{h!}{\begin{array}{c}
{\scriptstyle }\\
\int\\
{\scriptstyle \Sigma}\end{array}}
(G^{-}_{-1/2}\tilde{G}^{-}_{-1/2}u)(z_h)...
(G^{-}_{-1/2}\tilde{G}^{-}_{-1/2}u)(z_1)dz_1...dz_hd\overline{z}_1...
d\overline{z}_h$$]{} (it is to be understood that in both [(\[epert1\])]{}, [(\[epert2\])]{}, the fields are inserted into holomorphic images of disks where the origin maps to the point of insertion with derivative of modulus 1 with respect to the measure of integration).
When the obstruction occurs at step $k$, the integral [(\[epert1\])]{} has a divergence of logarithmic type. In the $N=0$ case, there is a third possibility, namely that the obstruction vanishes, but the field $u_h$ in Theorem \[t1\] has summands of weight $<(1,1)$ ($<(1/2,1/2)$ for $N=1$). In this case, the integral [(\[epert1\])]{} will have a divergence of power type, and the intgral of terms of weight $<(1,1)$ (resp. $<(1/2,1/2)$) has to be taken in range from $\infty$ to $1$ rather than from $0$ to $1$ to get a convergent integral. The formula [(\[epert2\])]{} is not correct in that case.
[**Remark 2:**]{} In [@dixon], a different correlation function is considered as an measure of marginality of $u$ to higher perturbative order. The situation there is actually more general, allowing combinations of both chiral and antichiral primaries. In the present setting of chiral primaries only, the correlation function considered in [@dixon] amounts to [$$\label{edixon}\langle 1|(G^{-}_{-1/2}u)(z_n)...(G^{-}_{-1/2}u)(z_1)\rangle.$$]{} It is easy to see using the standard contour deformation argument to show that [(\[edixon\])]{} indeed vanishes, which is also observed in [@distler]. In [@dixon], this type of vanishing is taken as evidence that the $N=2$ CFT deformations exist. It appears, however, that even though the vanishing of [(\[edixon\])]{} follows from the vanishing of [(\[ecorelii\])]{}, the opposite implication does not hold. (In fact, we will see examples in Section \[sexam\] below.) The explanation seems to be that [@dixon] writes down an integral expressing the change of central charge when deforming by a combination of cc fields and ac fields, and proves its vanishing. While this is correct formally, we see from Remark 1 above that in fact a singularity can occur in the integral when our obstruction is non-zero: the integral can marginally diverge for $k$ points while it is convergent for $<k$ points.
It would be nice if the obstruction theory a la Gerstenhaber we described here settled in general the question of deformations of conformal field theory, at least in the vertex operator formulation. It is, however, not that simple. The trouble is that we are not in a purely algebraic situation. Rather, compositions of operators which are infinite series may not converge, and even if they do, the convergence cannot be understood in the sense of being eventually constant, but in the sense of analysis, i.e. convergence of sequences of real numbers.
Specifically, in our situation, there is the possibility of divergence of the terms on the right hand side of [(\[eexp4\])]{}. Above we dealt with one problem, that in general, we do not expect infinitesimal deformations to converge on the degenerate worldsheets of vertex operators, so we may have to replace [(\[eexp4\])]{} by equations involving finite annuli instead. However, that is not the only problem. We may encounter [*regularization along the flow parameter*]{}. This stems from the fact that the equations [(\[eexp2\])]{}, [(\[eexp3\])]{} only determine $u(\epsilon)$ up to scalar multiple, where the scalar may be of the form [$$\label{eexp20}1+{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle i\geq 1}\end{array}}K_i\epsilon^i=f(\epsilon).$$]{} But the point is (as we shall see in an example in the next section) that we may only be able to get a well defined value of [$$\label{eexp21}f^{-1}(\epsilon)u(\epsilon)=v(\epsilon)$$]{} when the constants $K_i$ are infinite. The obstruction then is [$$\label{eexp22}\begin{array}{l}
L_n(m)f(m)v(m)=0\in V[\epsilon]/\epsilon^{m+1}\;\text{for $n>0$}\\
(1-L_0(m))f(m)v(m)=0\in V[\epsilon]/\epsilon^{m+1}.
\end{array}$$]{} At first, it may seem that it is difficult to make this rigorous mathematically with the infinite constants present. However, we may use the followng trick. Suppose we want to solve [$$\label{eexp23}\begin{array}{c}
c_1a_{11}+...+c_n a_{1n}=b_1\\
...\\
c_1a_{m1}+...+c_n a_{mn}=b_n
\end{array}$$]{} in a, say, finite-dimensional vector space $V$. Then we make rewrite [(\[eexp23\])]{} as [$$\label{eexp24}(b_1,...,b_n)=0\in({\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle m}\end{array}} V)/
\langle(a_{11},...,a_{m1}),...,(a_{1n},...,a_{mn})\rangle.$$]{} This of course doesn’t give anything new in the algebraic situation, i.e when the $a_{ij}$’s are simply elements of the vector space $V$. When, however the vectors $$(a_{11},...,a_{m1}),...,(a_{1n},...,a_{mn})$$ are (possibly divergent) infinite sums $$(a_{1j},...,a_{mj})={\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle k}\end{array}}(a_{1jk},...,a_{mjk}),$$ then the right hand side of [(\[eexp24\])]{} can be interpreted as $$({\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle m}\end{array}}V)/
\langle(a_{11k},...,a_{m1k}),...,(a_{1nk},...,a_{mnk})\rangle.$$ In that sense, [(\[eexp24\])]{} always makes sense, while [(\[eexp23\])]{} may not when interpreted directly. We interpret [(\[eexp22\])]{} in this way.
Let us now turn to the question of sufficient conditions for exponentiation of infinitesimal deformations. Suppose there exists a subspace $W\subset V$ closed under vertex operators which contains $u$ and such that for all elements $v\in W$, we have that $${\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle i}\end{array}}Y_i(u,z)\tilde{Y}_i(u,\overline{z})v$$ involve only $z^n\overline{z}^m$ with $m,n\in\Z$, $m,n\neq -1$. Then, by Theorem \[l1\], $$1-\phi\epsilon:W\r\hat{W}[\epsilon]/\epsilon^2$$ is an infinitesimal isomorphism between $W$ and the infinitesimally $u$-deformed $W$. It follows, in the non-regularized case, that then [$$\label{eexp25}\exp(-\phi\epsilon) u$$]{} is a globally deformed primary field of weight $(1,1)$, and [$$\label{eexp26}\exp(-\phi\epsilon):W
\r \hat{W}[[\epsilon]]$$]{} is an isomorphism between $W$ and the exponentiated deformation of $W$. However, since we now know the primary fields along the deformation, vacua can be recovered from the equation [(\[einf4\])]{} of the last section.
Such nonregularized exponentiation occurs in the case of the [*coset construction*]{}. Setting $$W=\langle v|\parbox{2.5in}{$Y_i(u,z)\tilde{Y}_i(u,\overline{z})v$
involve only $z^n\overline{z}^m$ with $m,n\geq 0$, $m,n\in\Z$}\rangle.$$ Then $W$ is called the coset of $V$ by $u$. Then $W$ is closed under vertex operators, and if $u\in W$, the formulas [(\[eexp25\])]{}, [(\[eexp26\])]{} apply without regularization.
The case with regularization occurs when there exists some constant $$K(\epsilon)=1+{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle n\geq 1}\end{array}}K_n\epsilon^n$$ where $K_n$ are possibly constants such that [$$\label{eexp27}K(\epsilon)\exp(-\phi\epsilon)u$$]{} is finite in the sense described above (see [(\[eexp24\])]{}). We will see an example of this in the next section.
All these constructions are easily adapted to supersymmetry. The formulas [(\[eexp25\])]{}, [(\[eexp26\])]{} hold without change, but the deformation is with respect to $G_{-1/2}\tilde{G}_{-1/2}u$ resp. $G_{-1/2}^{-}\tilde{G}_{-1/2}^{-}u$, $G_{-1/2}^{+}\tilde{G}_{-1/2}^{-}u$ depending on the situation applicable.
The deformations of free field theories {#sfree}
=======================================
As our first application, let us consider the $1$-dimensional bosonic free field conformal field theory, where the deformation field is [$$\label{efree1}u=x_{-1}\tilde{x}_{-1}.$$]{} In this case, the infinitesimal isomorphism of Theorem \[l1\] satisfies [$$\label{efree2} \phi=\pi{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle n\in\Z}\end{array}}\frac{x_{-n}\tilde{x}_{-n}}{n}$$]{} and the sufficient condition of exponentiability from the last section is met when we take $W$ the subspace consisting of states of momentum $0$. Then $W$ is closed under vertex operators, $u\in W$ and the $n=0$ term of [(\[efree2\])]{} drops out in this case. However, this is an example where regularization is needed. It can be realized as follows: Write $$\phi={\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle n>0}\end{array}}\phi_n$$ where $$\phi_n=\pi(\frac{x_{-n}\tilde{x}_{-n}}{n}-\frac{x_{n}\tilde{x}_{n}}{n}).$$ We have [$$\label{efree3}\exp\phi={\begin{array}{c}
{\scriptstyle }\\
\prod\\
{\scriptstyle n>0}\end{array}}\exp\phi_n.$$]{} To calculate $\exp\phi_n$ explicitly, we observe that $$[\frac{x_{-n}\tilde{x}_{-n}}{n},\frac{x_{n}\tilde{x}_{n}}{n}]=
-\frac{x_{-n}x_{n}}{n}-\frac{\tilde{x}_{-n}\tilde{x}_{n}}{n}-1,$$ and setting [$$\label{efree4}\begin{array}{l}
e=\frac{x_{-n}\tilde{x}_{-n}}{n},\\
f=\frac{x_{n}\tilde{x}_{n}}{n},\\
h=-\frac{x_{-n}x_{n}}{n}-\frac{\tilde{x}_{-n}\tilde{x}_{n}}{n}-1,
\end{array}$$]{} we obtain the $sl_2$ Lie algebra [$$\label{efree5}\begin{array}{l}
[e,f]=h,\\
{}[e,h]=2e,\\
{}[f,h]=-2f.
\end{array}$$]{} Note that conventions regarding the normalization of $e,f,h$ vary, but the relations [(\[efree5\])]{} are satisfied for example for [$$\label{efree6}e=\left(\begin{array}{rr}0&1\\0&0\end{array}\right),\;
f=\left(\begin{array}{rr}0&0\\-1&0\end{array}\right),\;
h=\left(\begin{array}{rr}-1&0\\0&1\end{array}\right).$$]{} In $SL_2$, we compute [$$\label{efree7}\begin{array}{l}
\exp\pi\epsilon(-f+e)=\exp\pi\epsilon
\left(\begin{array}{rr}0&1\\1&0\end{array}\right)\\
=\left(\begin{array}{rr}\cosh\pi\epsilon&\sinh\pi\epsilon
\\ \sinh\pi\epsilon&\cosh\pi\epsilon\end{array}\right)\\
\left(\begin{array}{cc}1&\tanh\pi\epsilon\\0&1\end{array}\right)
\left(\begin{array}{cc}\frac{1}{\cosh\pi\epsilon}&0\\0&\cosh\pi\epsilon
\end{array}\right)
\left(\begin{array}{cc}1&0\\\tanh\pi\epsilon&1\end{array}\right).
\end{array}$$]{} In the translation [(\[efree4\])]{}, this is [$$\label{efree8}
\exp(\tanh(\pi\epsilon)\frac{x_{-n}\tilde{x}_{-n}}{n})
\exp((-\ln\cosh\pi\epsilon)(
\frac{x_{-n}x_{n}}{n}+\frac{\tilde{x}_{-n}\tilde{x}_{n}}{n}+1))
\exp(-\tanh(\pi\epsilon)\frac{x_{n}\tilde{x}_{n}}{n}).$$]{} To exponentiate the middle term, we claim [$$\label{efree9}\exp(\frac{x_{-n}x_{n}}{n}z)=
:\exp\frac{x_{-n}x_{n}}{n}(e^z-1)):$$]{} To prove [(\[efree9\])]{}, differentiate both sides by $z$. On the left hand side, we get $$\frac{x_{-n}x_{n}}{n}\exp(\frac{x_{-n}x_{n}}{n}z).$$ Thus, if the derivative by $z$ of the right hand side $y$ of [(\[efree9\])]{} is [$$\label{efree10}\frac{x_{-n}x_{n}}{n}:\exp(\frac{x_{-n}x_{n}}{n}(e^z-1)):,$$]{} then we have the differential equation $y^{\prime}=\frac{x_{-n}x_{n}}{n}y,$ which proves [(\[efree9\])]{} (looking also at the initial condition at $z=0$).
Now we can calculate [(\[efree10\])]{} by moving the $x_n$ occuring before the normal order symbol to the right. If we do this simply by changing [(\[efree10\])]{} to normal order, we get [$$\label{efree11}:\frac{x_{-n}x_{n}}{n}\exp(\frac{x_{-n}x_{n}}{n}(e^z-1)):,$$]{} but if we want equality with [(\[efree10\])]{}, we must add the terms coming from the commutator relations $[x_{n},x_{-n}]=n$, which gives the additional term [$$\label{efree12}(e^z-1)
:\frac{x_{-n}x_{n}}{n}\exp(\frac{x_{-n}x_{n}}{n}(e^z-1)):.$$]{} Adding together [(\[efree11\])]{} and [(\[efree12\])]{} gives [$$\label{efree13}e^z
:\frac{x_{-n}x_{n}}{n}\exp(\frac{x_{-n}x_{n}}{n}(e^z-1)):,$$]{} which is the derivative by $z$ of the right hand side of [(\[efree9\])]{}, as claimed.
Using [(\[efree9\])]{}, [(\[efree8\])]{} becomes [$$\label{efree14}\begin{array}{l}
\Phi_n=\frac{1}{\cosh\pi\epsilon}\exp(\tanh(\pi\epsilon)
\frac{x_{-n}\tilde{x}_{-n}}{n})\\
:\exp((\frac{1}{\cosh\pi\epsilon}-1)(
\frac{x_{-n}x_{n}}{n}+\frac{\tilde{x}_{-n}\tilde{x}_{n}}{n}+1)):
\exp(-\tanh(\pi\epsilon)\frac{x_{n}\tilde{x}_{n}}{n})
\end{array}$$]{} which is in normal order. Let us write [$$\label{eiii*}\Phi_n=\frac{1}{\cosh\pi\epsilon}\Phi^{\prime}_{n}.$$]{} Then the product $$\Phi^{\prime}={\begin{array}{c}
{\scriptstyle }\\
\prod\\
{\scriptstyle n\geq1}\end{array}}\Phi^{\prime}_{n}$$ is in normal order, and is the regularized isomorphism from the exponentiated $\epsilon$-deformation $W_{\epsilon}$ of the conformal field theory in vertex operator formulation on to the original $W$. The inverse, which goes from $W$ to $W_{\epsilon}$, is best calculated by regularizing the exponential of $-\phi$. We get $$\begin{array}{l}
\exp\pi\epsilon(f-e)=\exp\pi\epsilon
\left(\begin{array}{rr}0&-1\\-1&0\end{array}\right)\\
=\left(\begin{array}{rr}\cosh\pi\epsilon&-\sinh\pi\epsilon
\\ -\sinh\pi\epsilon&\cosh\pi\epsilon\end{array}\right)\\
\left(\begin{array}{cc}1&-\tanh\pi\epsilon\\0&1\end{array}\right)
\left(\begin{array}{cc}\frac{1}{\cosh\pi\epsilon}&0\\0&\cosh\pi\epsilon
\end{array}\right)
\left(\begin{array}{cc}1&0\\-\tanh\pi\epsilon&1\end{array}\right)=\\
\frac{1}{\cosh\pi\epsilon}\exp(-\tanh(\pi\epsilon)
\frac{x_{-n}\tilde{x}_{-n}}{n})\\
:\exp((\frac{1}{\cosh\pi\epsilon}-1)(
\frac{x_{-n}x_{n}}{n}+\frac{\tilde{x}_{-n}\tilde{x}_{n}}{n}+1)):
\exp(\tanh(\pi\epsilon)\frac{x_{n}\tilde{x}_{n}}{n}).
\end{array}$$ So expressing this as [$$\label{eiii**}\Psi_n=\frac{1}{\cosh\pi\epsilon}\Psi^{\prime}_{n},$$]{} the product $$\Psi^{\prime}={\begin{array}{c}
{\scriptstyle }\\
\prod\\
{\scriptstyle n\geq 1}\end{array}}\Psi^{\prime}_{n}$$ is the regularized iso from $W$ to $W_{\epsilon}$.
Even though $\Psi^{\prime}$ and $\Phi^{\prime}$ are only elements of $\hat{W}$, the element $u(\epsilon)=\Psi^{\prime}u$ is the regularized chiral primary field in $W_{\epsilon}$, and can be used in a regularized version of the equation [(\[einf4\])]{} to calculate the vacua on $V_{\epsilon}$, which will converge on non-degenerate Segal worldsheets.
In this approach, however, the resulting CFT structure on $V_{\epsilon}$ remains opaque, while as it turns out, in the present case it can be identified by another method.
In fact, to answer the question, we must treat precisely the case missing in Theorem \[l1\], namely when the weight $0$ part of the vertex operator of the deforming field, which in this case is determined by the momentum, doesn’t vanish. The answer is actually known in string theory to correspond to constant deformation of the metric on spacetime, which ends up isomorphic to the original free field theory. From the point of view of string theory, what we shall give is a “purely worldsheet argument” establishing this fact.
Let us look first at the infinitesimal deformation of the operator $Y(v,t,\overline{t})$ for some field $v\in V$ which is an eigenstate of momentum. We have three forms which coincide where defined: [$$\label{efree15}Y(x_{-1}\tilde{x}_{1},z,\overline{z})Y(v,t,\overline{t})dz
d\overline{z}$$]{} [$$\label{efree16}Y(v,t,\overline{t})Y(x_{-1}\tilde{x}_{-1},z,\overline{z})dz
\overline{z}$$]{} [$$\label{efree17}Y(Y(x_{-1}\tilde{x}_{-1},z-t,\overline{z-t})v,t,\overline{t})
dzd\overline{z}.$$]{} By chiral splitting, if we assume $v$ is a monomial in the modes, we can denote [(\[efree15\])]{}, [(\[efree16\])]{}, [(\[efree17\])]{} by $\eta\tilde{\eta}$ (without forming a sum of terms). Again, integrating [(\[efree15\])]{}-[(\[efree17\])]{} term by term $dz$, we get forms $\omega_\infty$, $\omega_0$, $\omega_t$, respectively. Here we set $$\int\frac{1}{z}dz=\ln z.$$ Again, these are branched forms. Selecting points $p_0,p_\infty,p_t$ on the corresponding boundary components, we can, say, make cuts $c_{0,t}$ and $c_{0,\infty}$ connecting the points $p_0,p_t$ and $p_0,p_\infty$. Cutting the worldsheet in this way, we obtain well defined branches $\omega_\infty$, $\omega_0$, $\omega_t$. To complicate things further, we have constant discrepancies [$$\label{efree18}\begin{array}{l}
C_{0t}=\omega_0-\omega_t\\
C_{0\infty}=\omega_0-\omega_\infty.
\end{array}$$]{} These can be calculated for example by comparing with the $4$ point function [$$\label{efree19}Y_+(x_{-1},z)Y(v,t)+Y(v,t)Y_-(x_{-1},z) +Y(Y_-(x_{-1},z-t)v,t)$$]{} where $Y_-(v,z)$ denotes the sum of the terms in $Y(v,z)$ involving negative powers of $z$, and $Y_+(v,z)$ is the sum of the other terms. Another way to approach this is as follows: one notices that [$$\label{efree20}\int Y(x_{-1},z)dz=\partial_{\epsilon}Y(1_{\epsilon},z)S_{-\epsilon}
|_{\epsilon=0}$$]{} where $S_{m}$ denotes the operator which adds $m$ to momentum. It follows that [$$\label{efree21}\begin{array}{l}
C_{0t}=\partial_{\epsilon}(Z(x_{-1},v,z,t)S_{-\epsilon}-
Z(x_{-1},S_{\epsilon}v,z,t))|_{\epsilon=0}\\
C_{0\infty}=\partial_{\epsilon}(Z(x_{-1},v,z,t)S_{-\epsilon}-
S_{\epsilon}Z(x_{-1},v,z,t))|_{\epsilon=0}.
\end{array}$$]{} Now the deformation is obtained by integrating the forms [$$\label{efree22}\omega_0\tilde{\eta}$$]{} [$$\label{efree23}(\omega_t+C_{0t})\tilde{\eta}$$]{} [$$\label{efree24}(\omega_\infty +C_{0\infty})\tilde{\eta}$$]{} on the boundary components around $0$, $t$ and $\infty$, and along both sides of the cuts $c_{0t}$, $c_{0,\infty}$. To get the integrals of the terms in [(\[efree22\])]{}-[(\[efree24\])]{} which do not involve the discrepancy constants, we need to integrate [$$\label{efree25}({\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle n\neq 0}\end{array}}\frac{x_{-n}}{n}z^n+
x_0\ln z)({\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle m}\end{array}}x_{-m}\overline{z}^{m-1}).$$]{} To do this, observe that (pretending we work on the degenerate worldsheet, and hence omitting scaling factors, taking curved integrals over $||z||=1$), [$$\label{efree26}\oint\frac{\ln z}{\overline{z}}d\overline{z}=
-\oint\frac{-\ln\overline{z}}{\overline{z}}d\overline{z}=
-2\pi i\ln\overline{z}-\frac{1}{2}(2\pi i)^2$$]{} [$$\label{efree27}\oint\ln z\cdot \overline{z}^{m-1}d\overline{z}=
-2\pi i \frac{1}{m}\overline{z}^{m}.$$]{} Integrating [(\[efree25\])]{}, we obtain terms [$$\label{efree28}-2\pi ix_0({\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle m\neq 0}\end{array}}\tilde{x}_{-m}\frac{\overline{z}^m}{m}
+\tilde{x}_0\ln\overline{z})$$]{} which will cancel with the integral along the cuts (to calculate the integral over the cuts, pair points on both sides of the cut which project to the same point in the original worldsheet), and “local” terms [$$\label{efree29}\frac{2\pi i}{2}{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle n\neq 0}\end{array}}
\frac{x_{-n}\tilde{x}_{-n}}{n}-\frac{1}{2}(2\pi i)^2 x_0\tilde{x}_0.$$]{} The discrepancies play no role on the cuts (as the forms $C_{0t}\tilde{\eta}$, $C_{0,\infty}\tilde{\eta}$ are unbranched), but using the formula [(\[efree21\])]{}, we can compensate for the discrepancies to linear order in $\epsilon$ by applying on each boundary component [$$\label{efree30}S_{-2\pi i\epsilon\tilde{x}_{0}}.$$]{} In [(\[efree28\])]{}, however, when integrating $\tilde{\eta}$, we obtain also discrepancy terms conjugate to [(\[efree30\])]{}, so the correct expression is [$$\label{efree31}S_{-2\pi i\epsilon\tilde{x}_{0}}\tilde{S}_{-2\pi i\epsilon x_{0}}.$$]{} The term [(\[efree31\])]{} is also “local” on the boundary components, so the sum of [(\[efree29\])]{} and [(\[efree31\])]{} is the formula for the infinitesimal iso between the free CFT and the infinitesimally deformed theory. To exponentiate, suppose now we are working in a $D$-dimensional free CFT, and the deformation field is [$$\label{efree32}Mx_{-1}\tilde{x}_{-1}.$$]{} Then the formula for the exponentiated isomorphism multiplies left momentum by [$$\label{efree33}\exp\epsilon M$$]{} and right momentum by [$$\label{efree34}\exp\epsilon M^T.$$]{} But of course, in the free theory, the left momentum must equal to the right momentum, so this formula works only when $M$ is a symmetric matrix. Thus, to cover the general case, we must discuss the case when $M$ is antisymmetric. In this case, it may seem that we obtain indeed a different CFT which is defined in the same way as the free CFT with the exception that the left momentum $m_L$ and right momentum $m_R$ are related by the formula $$m_L=Am_R$$ for some fixed orthogonal matrix $A$. As it turns out, however, this theory is still isomorphic to the free CFT. The isomorphism replaces the left moving oscillators $x_{i,-n}$ by their transform via the matrix $A$ (which acts on this Heisenberg representation by transport of structure).
Next, let us discuss the case of deforming gravitaitonal field of non-zero momentum, i.e. when [$$\label{efree36}u=Mx_{-1}\tilde{x}_{-1}1_{\lambda}$$]{} with $\lambda\neq 0$. Of course, in order for [(\[efree36\])]{} to be of weight $(1,1)$, we must have [$$\label{efree37}||\lambda||=0.$$]{} Clearly, then, the metric cannot be Euclidean, hence there will be ghosts and a part of our theory doesn’t apply. Note that in order for [(\[efree36\])]{} to be primary, we also must have [$$\label{efree40a}M={\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle i}\end{array}}\mu_i\otimes\tilde{\mu}_i$$]{} where [$$\label{efree40}\langle\mu_i,\lambda\rangle=\langle\tilde{\mu}_{i},\lambda\rangle
=0.$$]{} Despite the indefinite signature, we still have the primary obstruction, which is [$$\label{efree38}coeff_{z^{-1}\tilde{z}^{-1}}:{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle m,n}\end{array}}Mx_{-m}\tilde{x}_{-n}
z^{m-1}\overline{z}^{n-1}\exp\lambda({\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle k\neq 0}\end{array}}
(\frac{x_{-k}}{k}z^{k}+\frac{\tilde{x}_{-k}}{k}\overline{z}^{k})):Mx_{-1}
\tilde{x}_{-1}1_{\lambda}$$]{} (we omit the $z^{\langle\lambda,x_0\rangle}$ term, since the power is $0$ by [(\[efree37\])]{}). In the notation [(\[efree40a\])]{}, this is $$\begin{array}{l}
{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle i,j}\end{array}}(\mu_ix_0-\mu_ix_0\lambda x_{-1}\lambda x_1+
\mu_i x_{-1}\lambda x_{1}+\lambda x_{-1}\mu_i x_{1})\otimes\\
(\tilde{\mu}_j\tilde{x}_0-\tilde{\mu}_j\tilde{x}_0\lambda \tilde{x}_{-1}\lambda
\tilde{x}_1+
\tilde{\mu}_j \tilde{x}_{-1}\lambda \tilde{x}_{1}+\lambda
\tilde{x}_{-1}\tilde{\mu}_j \tilde{x}_{1})Mx_{-1}
\tilde{x}_{-1}1_{\lambda}
\end{array}$$ which in the presence of [(\[efree40\])]{} reduces to the condition [$$\label{efree41}||M||^2\lambda\otimes\lambda x_{-1}\tilde{x}_{-1}=0$$]{} This is false unless [$$\label{efreen}||M||^2=0$$]{} which means that [(\[efree36\])]{} is a null state, along which the deformation is not interesting in the sense of string theory. More generally, the distributional form of [(\[efree41\])]{} is [$$\label{efree42}\int_{||\lambda||^2=0}\lambda\otimes\lambda||M(\lambda)||^2=0.$$]{} If we set $$f(\lambda)=\delta_{||\lambda||^2=0}||M(\lambda)||^2$$ then the Fourier transform of $f$ will be a function $g$ satisfying $$\sum\pm\frac{\partial^2g}{\partial\lambda^{2}_{i}}=0$$ where the sings correspond to the metric, which we assume is diagonal with entries $\pm 1$. The Fourier transform of the condition [(\[efree42\])]{} is then [$$\label{efree43}\frac{\partial^2}{\partial\lambda_i\partial\lambda_j}g=0.$$]{} Assuming a decay condition under which the Fourier transform makes sense, [(\[efree43\])]{} implies $g=0$, hence [(\[efreen\])]{}, so in this case also the obstruction is nonzero unless [(\[efree36\])]{} is a null state.
In this discussion, we restricted our attention to deforming fields of gravitational origin. It is important to note that other choices are possible. As a very basic example, let us look at the $1$-dimensional Euclidean model. Then there is a possibility of critical fields of the form [$$\label{ecomm+}a 1_{\sqrt{2}}+ b1_{-\sqrt{2}}.$$]{} This includes the sine-Gordon interaction [@sineg] when $a=b$. (We see hyperbolic rather than trigonometric functions because we are working in Euclidean spacetime rather than in the time coordinate, which is the case usually discussed.) The primary obstruction in this case states that the weight $(0,0)$ descendant of [(\[ecomm+\])]{} applied to [(\[ecomm+\])]{} is $0$. Since the descendant is $$(4ab)x_{-1},$$ we obtain the condition $a=0$ or $b=0$. It is interesting to note that in the case of the compactification on a circle, these cases where investigated very successfully by Ginsparg [@ginsparg], who used the obstruction to competely characterize the component of the moduli space of $c=1$ CFT’s originating from the free Euclidean compactified free theory. The result is that only free theories compactify at different radii, and their $\Z/2$-orbifolds occur.
There are many other possible choices of non-gravitational deformation fields, one for each field in the physical spectrum of the theory. We do not discuss these cases in the present paper.
Let us now look at the $N=1$-supersymmetric free field theory. In this case, as pointed out above, in the NS-NS sector, critical gravitational fields for deformations have weight $(1/2,1/2)$. We could also consider the NS-R and R-R sectors, where the critical weights are $(1/2,0)$ and $(0,0)$, respectively. These deforming fields parametrize soul directions in the space of infinitesimal deformations. The soul parameters $\theta$, $\tilde{\theta}$ have weights $(1/2,0)$, $(0,1/2)$, which explains the difference of critical weights in these sectors.
Let us, however, focus on the body of the space of gravitational deformations, i.e. the NS-NS sector. Let us first look at the weight $(1/2,1/2)$ primary field [$$\label{efree46}M\psi_{-1/2}\tilde{\psi}_{-1/2}.$$]{} The point is that the infinitesimal deformation is obtained by integrating the insertion operators of $$G_{-1/2}\tilde{G}_{-1/2}M\psi_{-1/2}\tilde{\psi}_{-1/2}=
Mx_{-1}\tilde{x}_{-1}.$$ Therefore, [(\[efree46\])]{} behaves exactly the same was as deformation along the field [(\[efree32\])]{} in the bosonic case. Again, if $M$ is a symmetric matrix, exponentiating the deformation leads to a theory isomorphic via scaling the momenta, while if $M$ is antisymmetric, the isomorphism involves transforming the left moving modes by the orthogonal matrix $\exp(M)$.
In the case of momentum $\lambda\neq 0$, we again have indefinite signature, and the field [$$\label{efree48}u=M\psi_{-1/2}\tilde{\psi}_{-1/2}1_{\lambda}.$$]{} Once again, for [(\[efree48\])]{} to be primary, we must have [(\[efree40a\])]{}, [(\[efree40\])]{}. Moreover, again the actual infinitesimal deformation is got by applying the insertion operators of $G_{-1/2}\tilde{G}_{-1/2}u$, so the treatment is exactly the same as deformation along the field [(\[efree36\])]{} in the bosonic case. Again, we discover that under a suitable decay condition, the obstruction is always nonzero for gravitational deformations of non-zero momentum with suitable decay conditions.
It is worth noting that in both the bosonic and supersymmetric cases, one can apply the same analysis to free field theories compactified on a torus. In this case, however, scaling momenta changes the geometry of the torus, so using deformation fields of $0$ momentum, we find exponential deformations which change (constantly) the metric on the torus. This seems to confirm, in the restricted sense investigated here, a conjecture stated in [@scft].
[**Remark:**]{} Since one can consider Calabi-Yau manifolds which are tori, one sees that there should also exist an $N=2$-supersymmetric version of the free field theory compactified on a torus. (It is in fact not difficult to construct such model directly, it is a standard construction.) Now since we are in the Calabi-Yau case, marginal $cc$ fields should correspond to deformations of complex structure, and marginal $ac$ fields should correspond to deformations of Kähler metric in this case.
But on the other hand, we already identified gravitational fields which should be the sources of such deformations. Additionally, deformations in those direction require regularization of the deformation parameter, and hence cannot satisfy the conclusion of Theorem \[t2\].
This is explained by observing that we must be careful with reality. The gravitational fields we considered are in fact real, but neither chiral nor antichiral primary in either the left or the right moving sector. By contrast, chiral primary fields ( or antiprimary) fields are not real. This is due to the fact that $G^{+}_{-3/2}$ and $G^{-}_{-3/2}$ are not real in the $N=2$ superconformal algebra, but are in fact complex conjugate to each other. Therefore, to get to the real gravitational fields, we must take real parts, or in other words linear combinations of chiral and antichiral primaries, resulting in the need for regularization.
It is in fact a fun exercise to calculate explicitly how our higher $N=2$ obstruction theory operates in this case. Let us consider the $N=2$-supersymmetric free field theory, since the compactification behaves analogously. The minimum number of dimensions for $N=2$ supersymmetry is $2$. Let us denote the bosonic fields by $x,y$ and their fermionic superpartners by $\xi,\psi$. Then the $0$-momentum summand of the state space (NS sector) is (a Hilbert completion of) $$Sym(x_n,y_n|n<0)\otimes \Lambda(\xi_r,\psi_r|
r<0,r\in\Z+\frac{1}{2}).$$ The “body” parts of the bosonic and fermionic vertex operators are given by the usual formulas $$\begin{array}{ll}
Y(x_{-1},z)=\sum x_{-n}z^{n-1}, &
Y(y_{-1},z)=\sum y_{-n}z^{n-1}\\
Y(\xi_{-1/2},z)=\sum \xi_{-s}z^{n-s-1/2}&
Y(\psi_{-1/2},z)=\sum \psi_{-s}z^{n-s-1/2},
\end{array}$$ $$\begin{array}{l}
[\xi_r,\xi_{-r}]= [\psi_r,\psi_{-r}]=1\\{}
[x_n,x_{-n}]= [y_n,y_{-n}]=n.
\end{array}$$ We have, say, $$\begin{array}{l}
G^{1}_{-3/2}=\xi_{-1/2}x_{-1}+\psi_{-1/2}y_{-1}\\
G^{2}_{-3/2}=\xi_{-1/2}y_{1}-\psi_{-1/2}x_{-1}.
\end{array}$$ As usual, $$G^{\pm}_{-3/2}=\frac{1}{\sqrt{2}}(G^{1}_{-3/2}\pm i G^{2}_{-3/2}).$$ With these conventions, we have a critical chiral primary [$$\label{efun0}u=\xi_{-1/2}-i\psi_{-1/2}$$]{} (and its complex conjugate critical antichiral primary). We then see that for a non-ero coefficient $C$, [$$\label{efun1}CG^{-}_{-1/2}u=x_{-1}-iy_{-1}.$$]{} We now notice that formulas analogous to [(\[efree4\])]{} etc. apply to [(\[efun1\])]{}, but the $-1$ summans of $h$ will appear with opposite signs for the real and imaginary summands, so it will cancel out, so the regularization [(\[eiii\*\])]{}, [(\[eiii\*\*\])]{} are not needed, as expected.
Next, let us study the formula [(\[ecorft2a\])]{}. The key observation here is that we have the combinatorial identity [$$\label{efun2}\frac{1}{n_1...n_k}=
{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle \sigma}\end{array}}\frac{1}{(n_{\sigma(1)}+...n_{\sigma(k)})
(n_{\sigma(1)}+...n_{\sigma(k-1)})...n_{\sigma(1)}}$$]{} where the sum on the right is over all permutations on the set $\{1,...,k\}$. Now in the present case, we have the infinitesimal iso on the $0$-momentum part, up to non-zero coefficient, [$$\label{efun3}\phi=
\sum \frac{(x_n-iy_n)(\tilde{x}_{n}+i\tilde{y}_{n})}{n}$$]{} and in the absence of regularization, the expansion of the exponentiated isomorphism on the $0$-momentum parts is simply $$\exp(\phi\epsilon).$$ (The $+$ sign in the $\tilde{\:}$’s is caused by the fact that we are in the complex conjugate Hilbert space.) Applying this to [(\[efun0\])]{}, we see that we have formulas analogous to [(\[efree8\])]{}-[(\[efree14\])]{}, and applying the exponentiated iso to [(\[efun0\])]{}, all the terms in normal order involving $x_{>0}$, $y_{>0}$ will vanish, so we end up with $${\begin{array}{c}
{\scriptstyle }\\
\prod\\
{\scriptstyle n<0}\end{array}}\exp(D\frac{(x_n-iy_n)(\tilde{x}_n+i\tilde{y}_n)}{
n})u$$ for some non-zero coefficient $D$. Applying [(\[efun2\])]{}, we get [(\[ecorft2a\])]{}.
Finally, the obstruction in chiral form $$\langle u^{*}(0),(G^{-}_{-1/2}u)(z_k),...,(G^{-}_{-1/2}u)(z_1),u(0)
\rangle$$ must vanish identically. To see this, we simply observe [(\[efun0\])]{}, [(\[efun1\])]{} that in the present case, $u$ is in the coset model with respect to $G^{-}_{-1/2}u$ (see the discussion below formula [(\[eg66\])]{} below). Thus, in the $N=2$-free field theory, the obstruction theory works as expected, and in the case discussed, the obstructions vanish. It is worth noting that in $2n$-dimensional $N=2$-free field theory, we thus have an $n^2$-dimensional space of $cc+aa$ real fields, and an $n^2$-dimensional space of real $ca+ac$ fields, and although regularization occurs, there is no obstruction to exponentiating the deformation by turning on any linear combination of those fields. For a free $N=2$-theory compactified on an $n$-dimensional abelian variety, this precisely recovers the deformations in the corresponding component of the moduli space of Calabi-Yau varieties.
However, other deformations exist. For an interesting calculation of deformations of the $N=2$-free field theory in “sine-Gordon” directions, see [@cgep].
The Gepner model of the Fermat quintic {#s1}
======================================
The finite weight states of one chirality (say, left moving) of the Gepner model of the Fermat quintic are embedded in the $5$-fold tensor product of the $N=2$-supersymmetric minimal model of central charge $9/5$ [@gepner; @gepner1; @gp]. More precisely, the Gepner model is an orbifold construction. This construction has two versions. In [@gepner; @gepner1; @gp], one is interested in actual string theories, so the $5$-fold tensor product of central charge $9$ of $N=2$ minimal models is tensored with a free supersymmetric CFT on $4$ Minkowski coordinates. This is then viewed in lightcone gauge, so in effect, one tensors with a $2$-dimensional supersymmetric Euclidean free CFT, resulting in $N=2$-supersymmetric CFT of central charge $12$. Finally, one performs an orbifolding/GSO projection to give a candidate for a theory for which both modularity and spacetime SUSY can be verified.
It is also possible to create an orbifold theory of central charge $9$ which is the candidate of the non-linear $\sigma$-model itself, without the spacetime coordinates. (The spacetime coordinates can be added to this construction and usual GSO projection performed if one is interested in the corresponding string theory.)
The essence of this construction not involving the spacetime coordinates is formula (2.10) of [@gvw]. In the case of the level $3$ $N=2$-minimal model, the orbifold construction is with respect to the $\Z/5$-action diagonal which acts on the eigenstates of $J_0$-eigenvalue (=“$U(1)$-charge”) $j/5 $ by $e^{2\pi ij/5}$. As we shall review, the NS part of the level $3$ $N=2$ minimal model has two sectors of $U(1)$-charge $j/5$, which we will for the moment ad hoc denote $H_{j/5}$ and $H^{\prime}_{j/5}$ for $j\in \Z/5\Z$. In the FF realization (see below), these sectors correspond to $\ell=0$, $\ell=1$, respectively. Then the NS-NS sector of the $5$-fold tensor product of minimal model has the form [$$\label{egepp1}
{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle (i_k)}\end{array}} {\begin{array}{c}
{\scriptstyle 5}\\
\hat{\bigotimes}\\
{\scriptstyle k=1}\end{array}}
(H_{i_k/5}\hat{\otimes} H^{*}_{i_k/5}\oplus H^{\prime}_{i_k/5}\hat{\otimes}
H^{\prime*}_{i_k/5}).$$]{} The corresponding sector the orbifold construction (formula (2.10) of [@gvw]) of the orbifold construction has the form [$$\label{egepp2}
{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle (i_k):\sum i_k\in 5\Z}\end{array}} {\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle j\in \Z/5\Z}\end{array}}
{\begin{array}{c}
{\scriptstyle 5}\\
\hat{\bigotimes}\\
{\scriptstyle k=1}\end{array}}
(H_{i_k/5}\hat{\otimes} H^*_{(j+i_k)/5}\oplus H^{\prime}_{i_k/5}\hat{\otimes}
H^{\prime*}_{(j+i_k)/5}).$$]{} Mathematically speaking, this orbifold can be constructed by noting that, ignoring for the moment supersymmetry, the $N=2$-minimal model is a tensor product of the parafermion theory of the same level and a lattice theory (see [@greene] and also below). The orbifold construction does not affect the parafermionic factor, and on the lattice coordinate, which in this case does not possess a non-zero $\Z/2$-valued form, and hence physically models a free theory compactified on a torus, the orbifold simply means replacing the torus by its factor by the free action of the diagonal $\Z/5$ translation group, which is represented by another lattice theory. On this construction, $N=2$ supersymmetry is then easily restored using the same formulas as in [(\[egepp1\])]{}, since the $U(1)$-charge of the $G$’s is integral.
The calculations in this and the next Section proceed entirely in the orbifold [(\[egepp2\])]{}, and hence can be derived from the structure of the level $3$ $N=2$-minimal model. It should be pointed out that a mathematical approach to the fusion rules of the $N=2$ minimal models was given in [@huang1]. We shall use the Coulomb gas realization of the $N=2$-minimal model, cf. [@gh], [@mus]. Let us restrict attention to the NS sector. Then, essentially, the left moving sector of the minimal model is a subquotient of the lattice theory where the lattice is $3$-dimensional, and spanned by $$(\frac{3}{\sqrt{15}},0,0),(\frac{1}{\sqrt{15}},
\frac{i}{2}\sqrt{\frac{2}{5}},\frac{i}{2}\sqrt{\frac{2}{3}}),
(\frac{2}{\sqrt{15}},0,i\sqrt{\frac{2}{3}}).$$ We will adopt the convention that we shall abbreviate $$(k,\ell,m)_{MM}=(k,\ell,m)$$ for the lattice label $$(\frac{k}{\sqrt{15}},\frac{\ell i}{2}\sqrt{\frac{2}{5}},\frac{mi}{2}
\sqrt{\frac{2}{3}}).$$ We shall also write $$(\ell,m)_{MM} =(m,\ell,m)_{MM}.$$ Call the oscillator corresponding to the $j$’th coordinate $x_{j,m}$, $j=0,1,2$. Then the conformal vector is [$$\label{eg7}\frac{1}{2}x_{0,-1}^{2}-\frac{1}{2}x_{1,-1}^{2}
+\frac{i}{2}\sqrt{\frac{2}{5}}x_{1,-2}+\frac{1}{2}x_{2,-1}^{2}.$$]{} The superconformal algebra is generated by [$$\label{eg8}{
\begin{array}{l}
G^{+}_{-3/2}=i\sqrt{\frac{1}{2}}(x_{2,-1}-\sqrt{\frac{5}{3}}x_{1,-1})
1_{(\frac{5}{\sqrt{15}},0,i\sqrt{\frac{2}{3}})}\\
G^{-}_{-3/2}=-i\sqrt{\frac{1}{2}}(x_{2,-1}+\sqrt{\frac{5}{3}}x_{1,-1})
1_{(-\frac{5}{\sqrt{15}},0,-i\sqrt{\frac{2}{3}})}.
\end{array}
}$$]{} For future reference, we will sometimes use the notation $$(a,b,c)x_{n}=ax_{0,n} +bx_{1,n}+cx_{2,n}$$ and also sometimes abbreviate $$(b,c)x_{n}=(0,b,c)x_{n}.$$ The module labels are realized by labels [$$\label{eg9}(\ell,m)=1_{(\frac{m}{\sqrt{15}},-\frac{i\ell}{2}\sqrt{
\frac{2}{3}},\frac{im}{2}\sqrt{\frac{2}{3}})},$$]{} [$$\label{eg9a}0\leq\ell\leq 3,\; m=-\ell,-\ell+2,...,\ell-2,\ell.$$]{} It is obvious that to stay within the range [(\[eg9a\])]{}, we must understand the fusion rules and how they are applied. The basic principle is that labels are indentified as follows: No identifications are imposed on the $0$’th lattice coordinate. This means that upon any identification, the $0$’th coordinate must be the same for the labels identified. Therefore, the identification is governed by the $1$st and $2$nd coordinates, which give the Coulomb gas (=Feigin-Fuchs) realization of the corresponding parafermionic theory (the “$3$ state Potts model”). The key point here are the parafermionic currents [$$\label{eg10}{
\begin{array}{l}
\psi_{1,-2/3}=i\sqrt{\frac{1}{2}}(x_{2,-1}-x_{1,-1}\sqrt{\frac{5}{3}})
1_{(0,i\sqrt{\frac{2}{3}})_{PF}}\\
\psi_{1,-2/3}^{+}=-i\sqrt{\frac{1}{2}}(x_{2,-1}+x_{1,-1}\sqrt{\frac{5}{3}})
1_{(0,-i\sqrt{\frac{2}{3}})_{PF}}
\end{array}
}$$]{} (the $0$’the coordinate is omitted). Clearly, the parafermionic currents act on the labels by [$$\label{11}{
\begin{array}{l}
\psi_{1,-2/3}:(\ell,m)_{PF}\mapsto (\ell,m+2)_{PF}\\
\psi_{1,-2/3}^{+}:(\ell,m)_{PF}\mapsto (\ell,m-2)_{PF}.
\end{array}
}$$]{} The lattice labels $(\ell,m)_{PF}$ allowed are those which have non-negative weight. This condition coincides with [(\[eg9a\])]{}. Now we impose the identification for parafermionic labels: $$(\ell,m)_{PF}=(3-\ell,m-3)_{PF}.$$ This implies [$$\label{eg12}{
\begin{array}{l}
(1,-1)_{PF}\sim(2,2)_{PF}\\
(1,1)_{PF}\sim (2,-2)_{PF}\\
(0,0)_{PF}\sim (3,-3)_{PF}\sim (3,3)_{PF}.
\end{array}
}$$]{} Now in the Gepner model corresponding to the quintic, the $(cc)$-fields allowed are [$$\label{eg15}((3,2,0,0,0)_{L},(3,2,0,0,0)_R),$$]{} [$$\label{eg16}((3,1,1,0,0)_{L},(3,1,1,0,0)_R),$$]{} [$$\label{eg17}((2,2,1,0,0)_{L},(2,2,1,0,0)_R),$$]{} [$$\label{eg18}((2,1,1,1,0)_{L},(2,1,1,1,0)_R),$$]{} [$$\label{eg19}((1,1,1,1,1)_{L},(1,1,1,1,1)_R),$$]{} and the $(ac)$-field allowed is [$$\label{eg20}((-1,-1,-1,-1,-1)_{L},(1,1,1,1,1)_R).$$]{} Here we wrote $\ell$ for $1_{(\ell,\ell)_{MM}}$, $(\ell=0,...,3)$, which is a chiral primary in the $N=2$ minimal model of weight $\ell/10$, and $-\ell$ for $1_{(\ell,-\ell)_{MM}}$, which is antichiral primary of weight $\ell/10$. The tuple notation in [(\[eg15\])]{}-[(\[eg20\])]{} really means tensor product. We omit permutations of the fields [(\[eg15\])]{}-[(\[eg18\])]{}, so counting all permutations, there are $101$ fields [(\[eg15\])]{}-[(\[eg19\])]{}.
We will need an understanding of the fusion rules in the level $3$ Potts model and $N=2$-supersymmetric minimal model of central charge $9/5$. In the level $3$ Potts model, we have $6$ labels [$$\label{eF1}(0,0)_{PF},\; (3,1)_{PF},\; (3,-1)_{PF},$$]{} [$$\label{eF2}(1,1)_{PF},\; (1,-1)_{PF},\; (2,0)_{PF}.$$]{} This can be described as follows: the labels [(\[eF1\])]{} have the same fusion rules as the lattice $L=\langle i\sqrt{6}\rangle\subset \C$, i.e. [$$\label{eF3}L^{\prime}/L$$]{} where $L^{\prime}$ is the dual lattice (into which $L$ is embedded using the standard quadratic form on $\C$). This dual lattice is $\langle \frac{i}{2}\sqrt{\frac{2}{3}}\rangle$, and the fusion rule is “abelian”, which means that the product of labels has only one possible label as outcome, and is described by the product in $L^\prime/L$. The label $\pm \frac{i}{2}\sqrt{\frac{2}{3}}$ corresponds to $(0,\pm2)_{PF}\sim (3,\mp1)_{PF}$.
Next, the product of $(2,0)_{PF}$ with $(3,\mp 1)_{PF}$ has only one possible outcome, $(2,\pm 2)_{PF}=(1,\mp 1)_{PF}$. The product of $(2,0)_{PF}$ with itself has two possible outcomes, $(2,0)_{PF}$ and $(0,0)_{PF}$. All other products are determined by commutativity, associativity and unitality of fusion rules.
The result can be summarized as follows: We call [(\[eF1\])]{} level $0,3$ labels and [(\[eF2\])]{} level $1,2$ labels. Every level $1,2$ label has a corresponding label of level $0,3$. The correspondence is [$$\label{eF4}
\begin{array}{lll}
(0,0)_{PF}&\leftrightarrow&(2,0)_{PF}\\
(3,1)_{PF}&\leftrightarrow&(1,1)_{PF}\\
(3,-1)_{PF}&\leftrightarrow&(1,-1)_{PF}.
\end{array}$$]{} As described above, the fusion rules on level $0,3$ are determined by the lattice theory of $L$. Additionally, multiplication preserves the correspondence [(\[eF4\])]{}, while the level of the product is restricted only by requiring that any level added to level $0,3$ is the original level.
To put it in another way still, the Verlinde algebra is [$$\label{eF5}\Z[\zeta]/(\zeta^3-1)\otimes \Z[\epsilon]/(\epsilon^2-
\epsilon-1)$$]{} where $\zeta=(3,1)_{PF}$ and $\epsilon=(2,0)_{PF}$.
In the $N=2$ supersymmetric minimal model (MM) case, we allow labels [$$\label{eF*}(3k+m,\ell,m)_{MM}$$]{} where $(\ell,m)$ is a PF label, $k\in \Z$. Two labels [(\[eF\*\])]{} are identified subject to identifications of PF labels, and also [$$\label{eF6}(j,\ell,m)_{MM}\sim (j+15,\ell,m)_{MM},$$]{} and, as a result of SUSY, [$$\label{eF7}(j,\ell,m)_{MM}\sim (j-5,\ell,m-2)_{MM}.$$]{} (By $\sim$ we mean that the labels (i.e. VA modules) are identified, but we do not imply that the states involved actually coincide; in the case [(\[eF7\])]{}, they have different weights.) Recalling again that we abbreviate $(m,\ell,m)_{MM}$ as $(\ell,m)_{MM}$, we get the following labels for the $c=9/5$ $N=2$ SUSY MM: [$$\label{eF8}\begin{array}{lll}
(0,0)_{MM}&\leftrightarrow&(2,0)_{MM}\\
(3,3)_{MM}&\leftrightarrow&(2,-2)_{MM}\\
(3,1)_{MM}&\leftrightarrow&(1,1)_{MM}\\
(3,-1)_{MM}&\leftrightarrow&(1,-1)_{MM}\\
(3,-3)_{MM}&\leftrightarrow&(2,2)_{MM}.
\end{array}$$]{} Again, the left column [(\[eF8\])]{} represents $0,3$ level labels, the right column represents level $1,2$ labels. The left column labels multiply as the labels of the lattice super-CFT corresponding to the lattice $\Lambda$ in $\C\oplus\C$ spanned by [$$\label{eF9}(\sqrt{15},0),\; (\frac{5}{\sqrt{15}},i\sqrt{\frac{2}{3}})$$]{} (recall that a super-CFT can be assigned to a lattice with integral quadratic form; the quadratic form on $\C\oplus\C$ is the standard one, the complexification of the Euclidean inner product). The dual lattice of [(\[eF9\])]{} is spanned by [$$\label{eF10}(\frac{3}{\sqrt{15}},0),\; (\frac{5}{\sqrt{15}},i\sqrt{\frac{2}{3}}),$$]{} which correspond to the labels $(3,0,0)_{MM}$, $(5,3,-1)_{MM}$, respectively. We see that [$$\label{eF11}\Lambda^{\prime}/\Lambda\cong \Z/5.$$]{} In [(\[eF8\])]{}, the rows (counted from top to bottom as $0,...,4$) match the corresponding residue class [(\[eF11\])]{}. The fusion rules for $(2,0)_{MM}$, $(0,0)_{MM}$ are the same as in the PF case. Hence, again, multiplication of labels preserves the rows [(\[eF8\])]{}, and the Verlinde algebra is isomorphic to [$$\label{eF12}\Z[\eta]/(\eta^5-1)\otimes \Z[\epsilon]/(\epsilon^2-
\epsilon-1)$$]{} where $\eta$ is $(3,3)_{MM}$.
[**Remark:**]{} As remarked in Section \[sexp\], the positive definiteness of the modular functor, which is crucial for our theory to work, is a requirement for a physical CFT. It is interesting to note, however, that if we do not include this requirement, other possible choices of real structure are possible on the modular functor: The Verlinde algebra of a lattice modular functor with another modular functor $M$ with two labels $1$ and $\epsilon$, and Verlinde algebras [(\[eF5\])]{}, [(\[eF12\])]{} are tensor products of lattice Verlinde algebras and the algebra $$\Z[\epsilon]/(\epsilon^2-\epsilon-1).$$ The real structure of this last modular functor can be changed by multiplying by $-1$ the complex conjugation in $M_\Sigma$ for a worldsheet $\Sigma$ precisely when $\Sigma$ has an odd number of boundary components labelled on level $1$, $2$. The resulting modular functor of this operation is not positive-definite.
Let us now discuss the question of vertex operators in the PF realization of the minimal model. Clearly, since the $0$’th coordinate acts as a lattice coordinate and is not involved in renaming, it suffices the question for the parafermions. Now in the Feigin-Fuchs realization of the level $3$ PF model, any state can be written as [$$\label{eFst}u 1_{\lambda}$$]{} where $\lambda$ is one of the labels [(\[eg9a\])]{} and $u$ is a state of the Heisenberg representation of the Heisenberg algebra generated by $x_{i,m}$, $i=1,2$, $m\neq 0$. The situation is however further complicated by the fact that not all Heisenberg states $u$ are allowed for a given label $\lambda$. We shall call the states which are in the image of the embedding admissible. For example, since the $\lambda=0$ part of the PF model is isomorphic to the coset model $SU(2)/S^1$ of the same level, states [$$\label{eFst1}(a,b)x_{-1}(0,0)_{PF}$$]{} are not admissible for $(a,b)\neq (0,0)$. One can show that admissible states are exactly those which are generated from the ground states [(\[eg9a\])]{} by vertex operators and PF currents. Because not all states are admissible, however, there are also states whose vertex operators are $0$ on admissible states. Let us call them null states. For example, since [(\[eFst1\])]{} is not admissible, it follows that [$$\label{eFst2}(a,b)x_{-1}(3,3)_{PF},$$]{} which is easily seen to be admissible for any choice of $(a,b)$, is null.
Determining explicitly which states are admissible and which are null is extremely tricky (cf. [@gh]). Fortunately, we don’t need to address the question for our purposes. This is because we will only deal with states which are explicitly generated by the primary fields, and hence automatically admissible; because of this, we can ignore null states, which do not affect correlation functions of admissible states.
On the other hand, we do need an explicit formula for vertex operators. One method for obtaining vertex operators is as follows. We may rename fields using the identifications [(\[eg12\])]{} and also PF currents: a PF current applied to a renamed field must be equal to the same current applied to the original field. Note that this way we may get Heisenberg states above labels which fail to satisfy [(\[eg9a\])]{}. Such states are also admissible, even though the corresponding “ground states” (which have the same name as the label) are not. Now if we have two admissible states $$u_i 1_{(\ell_i, m_i)},\; i=1,2$$ where $0\leq \ell_i\leq 3$ and $\ell_1+\ell_2\leq 3$, then the lattice vertex operator [$$\label{eFst10}(u_1 1_{(\ell_1,m_1)})(z)u_21_{(\ell_2,m_2)}$$]{} always satisfies our fusion rules, and (up to scalar multiple constant on each module) is a correct vertex operator of the PF theory. This is easily seen simply by the fact that [(\[eFst10\])]{} intertwines correctly with module vertex operators (which are also lattice operators).
While in our examples, it will suffice to always consider operators obtained in the form [(\[eFst10\])]{}, it is important to realize that they do not describe the PF vertex operators completely. The problem is that when we want to iterate vertex operators, we would have to keep renaming states. But when two ground states $1_{\lambda}$, $1_{\mu}$ are identified via the formula [(\[eg12\])]{}, it does not follow that we would have [$$\label{eFst+}u 1_{\lambda} =u 1_{\mu}$$]{} for every Heisenberg state $u$. On the contrary, we saw for example that [(\[eFst1\])]{} is inadmissible, while [(\[eFst2\])]{} is null. One also notes that one has for example the identification [$$\label{eFst+1}\lambda x_{-1}1_{\lambda}=L_{-1}1_{\lambda}=
L_{-1}1_{\mu} = \mu x_{-1}1_{\mu},$$]{} which is not of the form [(\[eFst+\])]{}.
Because of this, to describe completely the full force of the PF theory, one needs another device for obtaining vertex operators (although we will not need this in the present paper). Briefly, it is shown in [@gh] that up to scalar multiple, any vertex operator $$u(z)v=Y(u,z)(v)$$ where $u,v$ are admissible states can be written as [$$\label{eFst++}\oint...\oint (a_k x_{-1}1_{(0,-2)})(t_k)...(a_1 x_{-1}1_{(0,-2)}(t_1)
u(z)v dt_1...dt_k$$]{} where the operators in the argument [(\[eFst++\])]{} are lattice vertex operators and the number $k$ is selected to conform with the given fusion rule. While it is easy to show that operators of the form [(\[eFst++\])]{} are correct vertex operators on admissible states (again up to scalar multiple constant on each irreducible module), as the “screening operators” $$ax_{-1}1_{(0,-2)}$$ commute with PF currents, selecting the bounds of integration (“contours”) is much more tricky. Despite the notation, it is not correct to imagine these as integrals over closed curves, at least not in general. One approach which works is to bring the argument of [(\[eFst++\])]{} to normal order, which expands it as an infinite sum of terms of the form [$$\label{eFst+++}\prod (t_i-t_j)^{\alpha_{ij}}t_k^{\beta_k}$$]{} (where we put $t_0=z$) with coefficients which are lattice vertex operators. Then to integrate [(\[eFst+++\])]{}, for $\alpha_{ij},\beta_k>0$, we may simply integrate $t_i$ from $0$ to $t_{i-1}$, and define the integral by analytic continuation in the variables $\alpha_{ij}$, $\beta_k$ otherwise.
The functions obtained in this way are generalized hypergeometric functions, and fail for example the assumptions of Theorem \[l1\] (see Remark 2 after the Theorem). The explanation is in the fact that, as we already saw, the fusion rules are not “abelian” in this case.
The Gepner model: the obstruction {#sexam}
=================================
We will now show that for the Gepner model of the Fermat quintic, the function [(\[ecorelii\])]{} may not vanish for the deforming field [(\[eg15\])]{}. This means, not all perturbative deformations corresponding to marginal fields exist in this case. We emphasize that our result applies to deformations of the CFT itself (of central charge $9$). A different approach is possible by embedding the model to string theory, and investigating the deformations in that setting (cf. [@dkl]). Our results do not automatically apply to deformations in that setting.
We will consider $$v=u=(3,3,3)\otimes (2,2,2).$$ (In the remaining three coordinates, we will always put the vacuum, so we will omit them from our notation.) First note that by Theorem [(\[t2\])]{}, this is actually the only relevant case [(\[ecorelii\])]{}, since the only other chiral primary field of weight $1/2$ with only two non-vacuum coordinates is $(2,2,2)\otimes (3,3,3)$, which cannot correlate with the right hand side of [(\[ecorelii\])]{}, whose first coordinate is on level $0,3$. In any case, we will show therefore that the Gepner model has an obstruction against continuous perturbative deformation along the field [(\[eg15\])]{} in the moduli space of exact conformal field theories.
Now the chiral correlation function [(\[ecorelii\])]{} is a complicated multivalued function because of the integrals [(\[eFst+++\])]{}, which are generalized hypergeometric functions. As remarked above, the modular functor has a canonical flat connection on the space of degenerate worldsheets whose boundary components are shifts of the unit circle with the identity parametrization. The flat connection comes from the fact that these degenerate worldsheets are related to each other by applying $\exp (zL_{-1})$ to their boundary components. This is why we can speak of analytic continuation of a branch of the correlation function corresponding to a particular fusion rule. It can further be shown (although we do not need to use that result here) that the continuations of the correlation function corresponding to any one particular fusion rules generate the whole correlation function (i.e. the whole modular functor is generated by any one non-zero section).
Let us now investigate which number $m$ we need in [(\[ecorelii\])]{}. In our case, we have [$$\label{eexam+}G_{-1/2}^{-}(u)=G_{-1/2}^{-}(3,3,3)\otimes (2,2,2)-
(3,3,3)\otimes G^{-}_{-1/2}(2,2,2).$$]{} (The sign will be justified later; it is not needed at this point.) The first summand [(\[eexam+\])]{} has $x_{0,0}$-charge $(-2/\sqrt{15},2/\sqrt{15})$, the second has $x_{0,0}$-charge $(3/\sqrt{15},-3/\sqrt{15})$. Thus, the charges can add up to $0$ only if $m$ is a multiple of $5$. The smallest possible obstruction is therefore for $m=5$, in which case [(\[ecorelii\])]{} is a $7$ point function. Let us focus on this case. This function however is too big to calculate completely. Because of this, we use the following trick.
First, it is equivalent to consider the question of vanishing of the function [$$\label{eexam1}\langle 1|(G^{-1}_{-1/2}u)(z_5)...(G^{-1}_{-1/2}u)(z_1)
u(z_0)\overline{u}(t)\rangle.$$]{} Now by the OPE, it is possible to transform any correlation function of the form [$$\label{eexam2}\langle...|...v(z)w(t)...\rangle$$]{} to the correlation function [$$\label{eexam3}\langle...|...(v_nw)(t)...\rangle$$]{} (all other entries are the same). More precisely, [(\[eexam2\])]{} is expanded, in a certain range and choice of branch, into a series in $z-t$ with coefficients [(\[eexam3\])]{} for values of $n$ belonging to a coset $\Q/\Z$. By the above argument, therefore, the function [(\[eexam2\])]{} vanishes if and only if the function [(\[eexam3\])]{} vanishes for all possible choices of $n$ associated with one fixed choice of fusion rule.
In the case of [(\[eexam1\])]{}, we shall divide the fields on the right hand side into two sets $G_x$, $G_y$ containing two copies of $G^{-}_{-1/2}$ each, and a set $G_z$ containing the remaining three fields $u, \overline{u}$ and $G^{-}_{-1/2}$. Each set $G_x$, $G_y$, $G_z$ will be reduced to a single field using the transition from [(\[eexam2\])]{} to [(\[eexam3\])]{} (twice in the case of $G_z$). To simplify notation (eliminating the subscripts), we will denote the fields resulting from $G_x$, $G_y$, $G_z$ by $a(x)$, $b(y)$, $c(z)$, respectively. Thus, $x,y,z$ are appropriate choices among the variables $z_i,t$, depending how the transition from [(\[eexam2\])]{} to [(\[eexam3\])]{} is applied.
This reduces the correlation function [(\[eexam1\])]{} to [$$\label{eexam4}\langle 1| a(x) b(y) c(z)\rangle.$$]{} Most crucially, however, we make the following simplification: We shall choose the fusion rules in such a way that the fields $a,b,c$ are level $0,3$ in the Feigin-Fuchs realization, and at most one of the charges will be $3$ (in each coordinate). Then, [(\[eexam4\])]{} is just a lattice correlation function, for the computation of which we have an algorithm.
To make the calculation correctly, we must keep careful track of signs. When taking a tensor product of super-CFT’s, one must add appropriate signs analogous to the Koszul-Milnor signs in algebraic topology. Now a modular functor of a super-CFT decomposes into an even part and an odd part. Additionally, more than one choice of this decomposition may be possible for the same theory, depending on which bottom states of irreducible modules are chosen as even or odd. The sign of a fusion rule is then determined by whether composition along the pair of pants with given labels preserves parity of states or not. Mathematically, this phenomenon was noticed by Deligne in the case of the determinant line (cf. [@spin]). (Deligne also noticed that in some cases no consistent choice of signs is possible and a more refined formalism is needed; a single fermion of central charge $1/2$ is an example; this is also discussed in [@spin]. However, this will not be needed here.)
In the case of the $N=2$-minimal model, there is a choice of parities of ground states of irreducible modules which make the whole modular functor (all the fusion rules) even: simply choose the parity of $(k,\ell,m)$ to be $k\mod 2$. We easily see that this is compatible with supersymmetry.
Now in this case of completely even modular functor, the signs simplify, and we put [$$\label{eexam4a}Y(u\otimes v,z)(r\otimes s)=
(-1)^{\pi(u)\pi(v)}Y(u,z)r\otimes Y(v,z)s$$]{} (where $\pi(u)$ means the parity of $u$). Regarding supersymmetry (if present), an element $H$ of the superconformal algebra also acts on a tensor product by [$$\label{eexam5}H(u\otimes v)= Hu\otimes v +(-1)^{\pi(H)\pi(u)}u\otimes Hv,$$]{} in particular [$$\label{eexam6}G^{-}_{-1/2}(u\otimes v)=
(G^{-}_{-1/2}u)\otimes v +(-1)^{\pi(u)}u\otimes (G^{-}_{-1/2}v).$$]{} We see that because of [(\[eexam6\])]{}, the fields $a,b,c$ may have the form of sum of several terms.
[**Example 1:**]{} Recall that the inner product (more precisely symmetric bilinear form) of labels considered as lattice points is [$$\label{eexam7}\langle(r_1,s_1,t_1),(r_2,s_2,t_2)\rangle=
\frac{r_1 r_2}{15}+\frac{s_1 s_2}{10}-\frac{t_1 t_2}{6}.$$]{} Recall also (from the definition of energy-momentum tensor) that weight of the label ground states is calculated by [$$\label{eexam8}w(r,s,t)_{MM}=\frac{r^2}{30}+w(s,t)_{PF}
=\frac{r^2}{30}+\frac{s(s+2)}{20}-\frac{t^2}{12}.$$]{} Now we have [$$\label{eexam10}u=(3,3,3)\otimes (2,2,2)=(3,0,0)\otimes (2,1,-1).$$]{} We begin by choosing the field $c$. Compose first $u$ and [$$\label{eexam11}\overline{u}=(-3,3,-3)\otimes (-2,2,-2)=(-3,0,0)\otimes (-2,1,1).$$]{} We choose the non-zero $u_n \overline{u}$ of the bottom weight for the fusion rule which adds the lattice charges on the right hand side of [(\[eexam10\])]{}, [(\[eexam11\])]{}. The result is [$$\label{eexam12}u_{-1/10}\overline{u}=(0,0,0)\otimes (0,2,0).$$]{} Next, apply $G^{-}_{-1/2}u$ to [(\[eexam12\])]{}. Again, we will choose the bottom descendant. Now $G^{-}_{-1/2}u$ has two summands, [$$\label{eexam13}(-2,3,1)\otimes (2,1,-1)$$]{} and [$$\label{eexam14}(3,0,0)\otimes (0,5,3)x_{-1}(-3,1,3)$$]{} (the term [(\[eexam14\])]{} involves renaming to stay withing no-ghost PF labels after composition). Applying [(\[eexam13\])]{} to [(\[eexam12\])]{} gives bottom descendant [$$\label{eexam15}(-2,3,1)\otimes (2,3,-1)\;\text{of weight $8/5$},$$]{} applying [(\[eexam14\])]{} to [(\[eexam12\])]{} gives bottom descendant [$$\label{eexam16}(3,0,0)\otimes (-3,0,0)\;\text{of weight $3/5$}.$$]{} Since [(\[eexam16\])]{} has lower weight than [(\[eexam15\])]{}, [(\[eexam15\])]{} may be ignored, and we can choose [$$\label{eexam17}c=(3,0,0)\otimes (-3,0,0).$$]{} Now again, using the formula [(\[eexam6\])]{}, we see that in the sets of fields $G_x$, $G_y$ we need one summand [(\[eexam14\])]{} and three summands [(\[eexam13\])]{} to get to $x_{00}$-charge $0$. Thus, one of the groups $G_x$, $G_y$ will contain two summands of [(\[eexam13\])]{} and the other will contain one. We employ the following convention: [$$\label{eexam18}\parbox{3.5in}{We choose $G_y$ to contain
two summands {(\ref{eexam13})} and $G_x$ to contain
one summand {(\ref{eexam13})} and one summand {(\ref{eexam14})}.}$$]{} This leads to the following: [$$\label{eexam18a}\parbox{3.5in}{We must choose the fields $a$
and $b$ of the same weights and symmetrize the resulting
correlation function with respect to $x$ and $y$.}$$]{} We will choose $b$ first. Again, we will choose the bottom weight (nonzero) descendant of [(\[eexam13\])]{} applied to itself renamed as [$$\label{eexam19}(0,5,-3)x_{-1}(-2,0,-2)\otimes (2,2,2),$$]{} which is [$$\label{eexam20}(-4,3,-1)\otimes (4,3,1).$$]{} We rename to level $0$, which gives [$$\label{eexam21}\begin{array}{l}
b=(0,5,3)x_{-1}(-4,0,2)\otimes (0,5,-3)x_{-1}(4,0,-2),\\
w(b)=12/5.
\end{array}$$]{} Then $a$ must have weight $12/5$ to satisfy [(\[eexam18a\])]{}. When calculating $a$, however, there is an additional subtlety. This time, we have actually take into account two summands, from applying [(\[eexam13\])]{} to [(\[eexam14\])]{} and vice versa, i.e. [(\[eexam14\])]{} to [(\[eexam13\])]{}. In both cases, we must rename to get the desired fusion rule. To this end, we may replace [(\[eexam14\])]{} by [$$\label{eexam22}(3,0,0)\otimes (-3,2,0).$$]{} However, when applying [(\[eexam13\])]{} and [(\[eexam22\])]{} to each other in opposite order, the renamings then do not correspond, resulting in the possibility of wrong coefficient/sign (since renaming are correct only up to constants which we haven’t calculated). To reconcile this, we must use exactly the same renamings step by step, related only by applying PF currents. To this end, we may compare the renaming of applying [$$\label{eexam23}(0,5,-3)x_{-1}(-2,0,-2)\otimes (2,2,2)$$]{} to [$$\label{eexam24}(3,0,0)\otimes \frac{1}{2}(0,5,-3)x_{-1}(-3,1,-3)$$]{} (the $\frac{1}{2}$ comes from the PF current $(5,-3)x_{-1}(0,-2)$ which takes $(2,2)$ to $2(2,0)$) and [$$\label{eexam25}(3,0,0)\otimes (-3,2,0)$$]{} to [$$\label{eexam26}(0,5,-3)x_{-1}(-2,0,-2)\otimes (2,1,-1).$$]{} We see that the bottom descendant of applying [(\[eexam23\])]{} to [(\[eexam24\])]{} is [$$\label{eexam27}(0,5,-3)x_{-1}(1,0,-2)\otimes(-1)(-1,3,-1)$$]{} while the bottom descendant of applying [(\[eexam25\])]{} to [(\[eexam26\])]{} is [$$\label{eexam28}(0,5,-3)x_{-1}(1,0,-2)\otimes(-1,3,-1).$$]{} The expression [(\[eexam27\])]{} is the negative of [(\[eexam28\])]{}. On the other hand, we see that the bottom descendants of applying [(\[eexam13\])]{} to [(\[eexam22\])]{} and vice versa are the same. This means that we are allowed to use the names [(\[eexam13\])]{} and [(\[eexam22\])]{} to each other in either order, but we must take the results with opposite signs.
Now [(\[eexam28\])]{} has weight $7/5$, so to get weight $12/5$, we must take the descendant of applying [(\[eexam13\])]{} to [(\[eexam22\])]{} and vice versa which is of weight $1$ higher than the bottom. This gives $$\begin{array}{l}
((-2,3,1)-(3,0,0))x_{-1}(1,3,1)\otimes (-1,3,-1)+\\
(1,3,1)\otimes ((2,1,-1)-(-3,2,0))x_{-1}(-1,3,-1),
\end{array}$$ which is [$$\label{eexam29}
a=(-5,3,1)x_{-1}(1,3,1)\otimes (-1,3,-1)+(1,3,1)\otimes (5,-1,-1)x_{-1}(-1,3,-1).$$]{} Now the correlation function of $a(x)$, $b(y)$, $c(z)$ given in [(\[eexam29\])]{}, [(\[eexam21\])]{}, [(\[eexam17\])]{} is an ordinary lattice correlation function. The algorithm for calculating the lattice correlation function of fields $u_i(x_i)$ which are of the form $$1_{\lambda_i}(x_i)$$ or $$\mu_i x_{-1} 1_{\lambda_i}(x_i)$$ with the label $$1_{\sum \lambda_i}$$ is as follows: The correlation function is a multiple of $${\begin{array}{c}
{\scriptstyle }\\
\prod\\
{\scriptstyle i<j}\end{array}}(x_i-x_j)^{\langle \lambda_i,\lambda_j\rangle}$$ by a certain factor, which is a sum over all the ways we may “absorb" any $\mu_i x_{-1}$ factors. Each such factor may either be absorbed by another $\mu_j x_{-1}$, which results in a factor [$$\label{eexam30}\langle\mu_i,\mu_j\rangle (x_i-x_j)^{-2},\; i\neq j$$]{} or by another lattice label $1_{\lambda_j}$, which results in a factor [$$\label{eexam31}\langle\mu_i,\lambda_j\rangle (x_i-x_j)^{-1},\; i\neq j.$$]{} Each $\mu_i x_{-1}$ must be absorbed exactly once (and the mechanism [(\[eexam30\])]{} is considered as absorbing both $\mu_i$ and $\mu_j$), but one lattice label $1_{\lambda_j}$ may absorb several different $\mu_i x_{-1}$’s via [(\[eexam31\])]{}.
Evaluating the correlation function of $a(x)$, $b(y)$, $c(z)$ with the vacuum using this algorithm, we get $$\frac{2(y-z)}{(x-z)(x-y)^3}.$$ Symmetrizing with respect to $x,y$, we get $$\frac{2(x-2z+y)}{(y-z)(x-z)(x-y)^2},$$ (our total correlation function factor), which is non-zero.
In more detail, we can calculate separately the contributions to the correlation function of the two summands [(\[eexam29\])]{}. For the first summand, the factor before the $\otimes$ sign contributes [$$\label{eexami1}-\frac{1}{(x-z)(y-x)},$$]{} the factor after the $\otimes$ sign contributes [$$\label{eexami2}\frac{1}{y-x}.$$]{} Multiplying [(\[eexami1\])]{} and [(\[eexami2\])]{}, we get $$-\frac{1}{(x-z)(x-y)^2},$$ and symmetrizing with respect to $x$ and $y$, [$$\label{eexami3}-\frac{x-2z+y}{(x-z)(x-y)^2(y-z)},$$]{} which is the total contribution of the first summand [(\[eexam29\])]{}.
For the second summand [(\[eexam29\])]{}, the factor after $\otimes$ contributes [$$\label{eexami4}-\frac{2}{(x-y)^2}-\frac{1}{(x-z)(y-x)},$$]{} and the factor before the $\otimes$ sign contributes [$$\label{eexami5}\frac{1}{y-x}.$$]{} Multiplying, we get $$\frac{x-2z+y}{(x-z)(x-y)^3}.$$ After symmetrizing with respect to $x,y$, we get also [(\[eexami3\])]{}, so both summands of [(\[eexam29\])]{} contribute equally to the correlation function.
[**Example 2:**]{} In this example, we keep the same $a(x)$ and $b(y)$ as in the previous example, but change $c(z)$. To select $c(z)$, this time we start with $G^{-}_{-1/2}u$ represented as [$$\label{eexam32}(3,0,0)\otimes (0,5,-3)x_{-1}(-3,1-3)
+C(-2,3,1)\otimes (2,1,-1)$$]{} ($C$ is a non-zero normalization constant which we do not need to evaluate explicitly), which we apply to $\overline{u}$ represented as [$$\label{eexam33}(-3,0,0)\otimes (-2,1,1).$$]{} From the two summands [(\[eexam32\])]{}, we get bottom descendants [$$\label{eexam34}(0,0,0)\otimes (-5,2,-2)\;\text{of weight $9/10$}$$]{} and [$$\label{eexam35}(-5,3,1)\otimes (0,2,0)\;\text{of weight $19/10$}.$$]{} Therefore, we may ignore [(\[eexam35\])]{} and select [(\[eexam34\])]{} only. Now applying [(\[eexam34\])]{} to $u$ written as [$$\label{eexam36}(3,0,0)\otimes (2,1,-1),$$]{} we select a descendant of weight $1$ above the label $$(3,0,0)\otimes (-3,3,-3).$$ Recalling from the conjugate of [(\[eFst2\])]{} that weight $1$ states above the label $(3,-3)_{PF}=(0,0)_{PF}$ must vanish, we get [$$\label{eexam37}c=(3,0,0)\otimes (1,0,0)x_{-1}(-3,0,0)$$]{} (up to a non-zero multiplicative constant). This gives the correlation function [$$\label{eexam38}\frac{(x-2z+y)^2}{5(y-z)^2(x-z)^2(x-y)^2}.$$]{} Let us write again in more detail the contributions of the two summands [(\[eexam29\])]{}. For the first summand, the contribution of the factor before $\otimes$ is again [(\[eexami1\])]{} (hasn’t changed), and the contribution of the factor after $\otimes$ is [$$\label{eexamj1}\frac{-y-3z+4x}{15(y-z)(x-z)(x-y)}.$$]{} Multiplying, we get $$\frac{-y-3z+4x}{15(y-z)^2(x-z)^2(x-y)},$$ and symmetrizing with respect to $x$, $y$, [$$\label{eexamj2}-\frac{y^2+6yz-6z^2-8xy+6zx+x^2}{15(y-z)^2(x-z)^2(x-y)^2}.$$]{} This is the total contribution of the first summand [(\[eexam29\])]{}.
For the second summand [(\[eexam29\])]{}, the coordinate before $\otimes$ contributes again [(\[eexami5\])]{}, and the coordinate after $\otimes$ contributes [$$\label{eexamj3}\frac{2(-yx-3yz-3xz+3z^2+2x^2+2y^2)}{
15(y-z)(x-z)^2(x-y)^2}.$$]{} Multiplying, we get $$-\frac{-yx-3yz-3xz+3z^2+2x^2+2y^2}{15(y-z)(x-z)^2(x-y)^3}.$$ Symmetrizing with respect to $x,y$, we get [$$\label{eexamj4}\frac{2(-yx-3yz-3xz+3z^2+2x^2+2y^2)}{15(y-z)^2(x-z)^2(x-y)^2}$$]{} which is the total contribution of the second summand [(\[eexam29\])]{}. Adding the contributions [(\[eexamj2\])]{} and [(\[eexamj4\])]{} (which are not equal in this case) gives [(\[eexam38\])]{}.
The remainder of this Section is dedicated to comments on possible perturbative deformations along the fields $(1^5,1^5)$, $(-1^5,1^5)$ (the exponent here denotes repetition of the field in a tensor product, and $1$ again stands for $(1,1,1)_{MM}$, etc.). We will present some evidence (although not proof) that the obstruction might vanish in this case. The results we do obtain will prove useful in the next Section. Such conjecture would have a geometric interpretation. In Gepner’s conjectured interpretation of the model we are investigating as the $\sigma$-model of the Fermat quintic, the field [(\[eg20\])]{} corresponds to the dilaton. It seems reasonable to conjecture that the dilaton deformation should exist, since the theory should not choose a particular global size of the quintic. Similarly, the field [(\[eg19\])]{} can be explained as the dilaton on the mirror manifold of the quintic, which should correspond to deformations of complex structure of the form [$$\label{eg65}x^5+y^5+z^5+t^5+u^5+\lambda xyztu=0.$$]{} Therefore, our analysis predicts that the (body of) the moduli space of $N=2$-supersymmetric CFT’s containing the Gepner model is $2$-dimensional, and contains $\sigma$-models of the quintics [(\[eg65\])]{}, where the metric is any multiple of the metric for which the $\sigma$-model exists (which is unique up to a scalar multiple).
To discuss possible deformations along the fields $(1^5,1^5)$, $(-1^5,1^5)$, let us first review a simpler case, namely the coset construction: In a VOA $V$, we set, for $u\in V$ homogeneous, [$$\label{eg66}\begin{array}{l}
Y(u,z)={\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle n\in\Z}\end{array}}u_{-n+w(u)}z^n,\\
Y_{-}(u,z)={\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle n<0}\end{array}}u_{-n+w(u)}z^n,\\
Y_{+}(u,z)=Y(u,z)-Y_{-}(u,z).
\end{array}$$]{} The coset model of $u$ is [$$\label{eg67}\begin{array}{l}V_{u}=\\
\langle v\in V|Y_{-}(u,z)v=0\;
\text{and $Y_{+}(u,z)$ involves only integral powers of $z$}
\rangle.
\end{array}$$]{} Then $V_u$ is a sub-VOA of $V$. To see this, recall that [$$\label{eg68}
Y(u,z)Y(v,t)w=\\
Y_{+}(u,z)Y_{-}(v,t)w+Y_{+}(v,t)Y_{-}(u,z)w+Y(Y_{-}(u,z-t)v)w.$$]{} When $v,w\in V_u$, the last two terms of the right hand side of [(\[eg68\])]{} vanish, which proves that $$Y(v,t)w\in V_u[[t]][t^{-1}].$$ Now in the case of $N=2$-super-VOA’s, let us stick to the NS sector. Then [(\[eg66\])]{} still correctly describes the “body” of a vertex operator. The complete vertex operator takes the form [$$\label{eg69}\begin{array}{l}
Y(u,z,\theta^+,\theta^-)=\\
{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle n\in\Z}\end{array}}
u_{-n+w(u)}z^n+u_{-n-1/2+w(u)}^{+}z^n\theta^+
+u_{-n-1/2+w(u)}^{-}z^n\theta^-
+u_{-n-1+w(u)}^{\pm}z^n\theta^+\theta^-.
\end{array}$$]{} We still define $Y_{-}(u,z,\theta^+,\theta^-)$ to be the sum of terms involving $n<0$, and $Y_+(u,z,\theta^+,\theta^-)$ the sum of the remaining terms. The compatibility relations for an $N=2$-super-VOA are [$$\label{eg70}\begin{array}{l}
D^+Y(u,z,\theta^+,\theta^-)=Y(G^{+}_{-1/2}u,z,\theta^+,\theta^-)\\
D^-Y(u,z,\theta^+,\theta^-)=Y(G^{-}_{-1/2}u,z,\theta^+,\theta^-)
\end{array}$$]{} where [$$\label{eg71}D^+=\frac{\partial}{\partial\theta^+}+\theta^+\frac{\partial}{
\partial z},\;\;
D^-=\frac{\partial}{\partial\theta^-}+\theta^-\frac{\partial}{
\partial z}.$$]{} Now using [(\[eg68\])]{} again, for $u\in V$ homogeneous, we will have a sub-$N=2$-VOA $V_u$ defined by [(\[eg67\])]{}, which is further endowed with the operators $G^{-}_{-1/2}$, $G^{+}_{-1/2}$.
In the case of lack of locality, only a weaker conclusion holds. Assume first we have “abelian” fusion rules in the same sense as in Remark 2 after Theorem \[l1\].
\[l2\] Suppose we have fields $u_i, i=0,...,n$ such that for $i>j$, [$$\label{ecos1}Y(u_i,z)u_j={\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle n\geq 0}\end{array}}(u_i)_{-n-\alpha_{ij}-w(u_i)}
z^{n+\alpha_{ij}}$$]{} with $0\leq \alpha_{ij}<1$. Consider further points $z_0=0$, $z_1,...,z_n$. Then [$$\label{ecos2}{\begin{array}{c}
{\scriptstyle }\\
\prod\\
{\scriptstyle n\geq i>j\geq 0}\end{array}}
(z_i-z_j)^{-\alpha_{ij}}Y(u_n,z_n)...Y(u_z,z_1)u_0$$]{} where each $(z_i-z_j)^{-\alpha_{ij}}$ are expanded in $z_j$ is a power series whose coefficients involve nonnegative integral powers of $z_0,...,z_n$ only.
Induction on $n$. Assuming the statement is true for $n-1$, note that by assumption, [(\[ecos2\])]{}, when coupled to $w^{\prime}\in V^{\vee}$ of finite weight, is a meromorphic function in $z_n$ with possible singularities at $z_0=0,z_1,...,z_n-1$. Thus, [(\[ecos2\])]{} can be expanded at its singularities, and is equal to [$$\label{ecos3}
\begin{array}{l}
{\begin{array}{c}
{\scriptstyle }\\
\prod\\
{\scriptstyle n-1\geq i>j\geq 0}\end{array}}(z_i-z_j)^{-\alpha_{ij}}\cdot\\
( (z_{n}^{-\alpha_{n0}}expand_{z_n}{\begin{array}{c}
{\scriptstyle }\\
\prod\\
{\scriptstyle j\neq 0}\end{array}}(z_n-z_j)^{-\alpha_{nj}}
Y(u_{n-1},z_{n-1})...Y(u_1,z_1)Y(u_n,z_n)u_0)_{z_{n}^{<0}}\\
+({\begin{array}{c}
{\scriptstyle n-1}\\
\sum\\
{\scriptstyle i=1}\end{array}}(z_n-z_i)^{-\alpha_{ni}}
expand_{(z_n-z_i)}({\begin{array}{c}
{\scriptstyle }\\
\prod\\
{\scriptstyle n-1\geq j\neq i}\end{array}}(z_n-z_j)^{-\alpha_{nj}})\cdot\\
Y(u_{n-1},z_{n-1})...Y(u_{i+1},z_{i+1})Y(Y(u_n,z_n-z_i)u_i,z_i)\cdot\\
Y(u_{i-1},z_{i-1})...Y(u_1,z_1)u_0)_{(z_n-z_i)^{<0}}\\
+(z_{n}^{-\alpha_{n0}-...-\alpha_{n,n-1}}expand_{1/z_n}{\begin{array}{c}
{\scriptstyle n-1}\\
\prod\\
{\scriptstyle j=1}\end{array}}
(1-\frac{z_j}{z_n})^{-\alpha_{nj}}\cdot\\
Y(u_n,z_n)Y(u_{n-1},z_{n-1})...Y(u_1,z_1)u_0)_{z_{n}^{\geq 0}}).
\end{array}$$]{} In [(\[ecos3\])]{}, $expand_{?}(?)$ means that the argument is expanded in the variable given as the subscript. The symbol $(?)_{?^{<0}}$ (resp. $(?)_{?^{\geq 0}}$) means that we take only terms in the argument, (which is a power series in the subscript), which involve negative (resp. non-negative) powers of the subscript.
In any case, by the assumption of the Lemma, all summands [(\[ecos3\])]{} vanish with the exception of the last, which is the induction step.
In the case of non-abelian fusion rules, an analogous result unfortunately fails. Assume for simplicity that [$$\label{efff+}\parbox{3.5in}{$u_0=...=u_n$ holds in {(\ref{ecos3})}
with $0\leq \alpha_{ij}^{F}<1$ true for any fusion rule $F$.}$$]{} We would like to conclude that the correlation function [$$\label{e10l1}\langle v, u(z_n)...u(z_1)u\rangle$$]{} involves only non-negative powes of $z_i$ when expanded in $z_1,...,z_n$ (in this order). Unfortunately, this is not necessarily the case. Note that we know that [(\[e10l1\])]{} converges to $0$ when two of the argument $z_i$ approach while the others remain separate. However, this does not imply that the function [(\[e10l1\])]{} converges to $0$ when three or more of the arguments approach simultaneously.
To give an example, let us consider the solution of the Fuchsian differential equation of $\P^1-\{0,t,\infty\}$ [$$\label{efff*}y^\prime=(\frac{A}{x}+\frac{B}{z-t})y$$]{} for square matrices $A,B$ (with $t\neq 0$ constant). Since the solution $y$ has bounded singularities, multiplying $y$ by $z^m(z-t)^n$ for large enough integers $m$, $n$ makes the resulting function $Y$ converge to $0$ when $z$ approaches $0$ or $t$. If, however, the expansion of $Y$ at $\infty$ involved only non-negative powers of $z$, it would have only finitely many terms, and hence abelian monodromy. It is well known, however, that this is not necessarily the case. In fact, any irreducible monodromy occurs for a solution of the equation [(\[efff\*\])]{} for suitable matrices $A$, $B$ (cf. [@anbo]).
Therefore, the following result may be used as evidence, but not proof, of the exponentiability of deformations along $(1^5, 1^5)$ and $(1^5,-1^5)$.
\[l20\] The assumption [(\[efff+\])]{} is satisfied for the field $$u=G^{-}_{-1/2}((1,1,1),...,(1,1,1))$$ in the $5$-fold tensor product of the $N=2$ minimal model of central charge $9/5$.
Before proving this, let us state the following consequence:
Indeed, assuming Lemma \[l20\] and setting $w=((1,1,1),...,(1,1,1))$, the obstruction is [$$\label{e10t2}\langle w^{\prime}| (G^{-}_{-1/2})w(z_n)...
(G^{-}_{-1/2}w)(z_1)w\rangle.$$]{} (The antichiral primary case is analogous.) But using the fact that $$G^{-}_{-1/2}((G^{-}_{-1/2})w(z_n)...
(G^{-}_{-1/2}w)(z_1)w)=(G^{-}_{-1/2})w(z_n)...
(G^{-}_{-1/2}w)(z_1)G^{-}_{-1/2}w$$ along with injectivity of $G^{-}_{-1/2}$ on chiral primaries of weight $1/2$, we see that the non-vanishing of [(\[e10t2\])]{} implies the non-vanishing of [(\[e10l1\])]{} with $u=G^{-}_{-1/2}w$ for some $v$ of weight $1$, which would contradict Lemma [(\[l20\])]{}.
[**Proof of Lemma \[l20\]:**]{} We have [$$\label{e20l3a}G^{-}_{-1/2}(1,1,1)=(-4,1,-1).$$]{} We have in our lattice [$$\label{e20l3}\begin{array}{l}
(1,1,1)\cdot(1,1,1)=1/15+1/10-1/6=0,\\
(-4,1,-1)\cdot(-4,1,-1)=16/15+1/10-1/6=1,\\
(1,1,1)\cdot (-4,1,-1)=-4/15+1/10+1/6=0,
\end{array}$$]{} so we see that with the fusion rules which stays on levels $1,2$, the vertex operators $u(z)u$ have only non-singular terms.
However, this is not sufficient to verify [(\[efff+\])]{}. In effect, when we use the fusion rule which goes to levels $0,3$, $$(1,1,1)(z)(-4,1,-1)$$ and $$(-4,1,-1)(z)(1,1,1)$$ will have most singular term $z^{-2/5}$, so when we write again $1$ instead of $(1,1,1)$ and $G$ instead of $G^{-}_{-1/2}(1,1,1)$, with the least favorable choice of fusion rules, it seems $u(z)u$ can have singular term $z^{-4/5}$, coming from the expressions [$$\label{e20l4}(G1111)(z)(1G111)$$]{} and [$$\label{e20l5}(1G111)(z)(G1111)$$]{} (and expression obtained by permuting coordinates). Note that with other combinations of fusion rules, various other singular terms can arise with $z^{>-4/5}$.
Now the point is, however, that we will show that with any choice of fusion rule, the most singular terms of [(\[e20l4\])]{} and [(\[e20l5\])]{} come with opposite signs and hence cancel out. Since the $z$ exponents of other terms are higher by an integer, this is all we need.
Recalling the Koszul-Milnor sign rules for the minimal model, recall that $1$ is odd and $G$ is even, so [$$\label{e20l6}(G\otimes 1)(z)(1\otimes G)=-G(z)1\otimes 1(z)G,$$]{} [$$\label{e20l7}(1\otimes G)(z)(G\otimes 1)=1(z)G\otimes G(z)1.$$]{} We have $$1(z)G=(1,1,1)(z)(-4,2,2)=M(-3,0,0)z^{-2/5}+\text{HOT},$$ $$G(Z)1=(-4,2,2)(z)(1,1,1)=N(-3,0,0)z^{-2/5}+\text{HOT},$$ with some non-zero coefficients $M,N$, so the bottom descendants of [(\[e20l6\])]{} and [(\[e20l7\])]{} are $$-MN(-3,0,0)\otimes(-3,0,0)$$ resp. $$MN(-3,0,0)\otimes(-3,0,0),$$ so they cancel out, as required.
The case of the Fermat quartic $K3$-surface {#sk3}
===========================================
The Gepner model of the $K3$ Fermat quartic is an orbifold analogous to [(\[egepp2\])]{} with $5$ replaced by $4$ of the $4$-fold tensor product of the level $2$ $N=2$-minimal model, although one must be careful about certain subtlteties arising from the fact that the level is even. The model has central charge $6$. The level $2$ PF model is the $1$-dimensional fermion (of central charge $1/2$), viewed as a bosonic CFT. As such, that model has $3$ labels, the NS label with integral weights (denote by $NS$), the NS label with weights $\Z+\frac{1}{2}$ (denote by $NS^{\prime}$), and the R label (denote by $R$). The fusion rules are given by the fact that $NS$ is the unit label, [$$\label{ek31}\begin{array}{l}NS^{\prime}*NS^{\prime}=NS,\\
NS^{\prime} *R=R,\\
R*R=NS +NS^{\prime}.
\end{array}$$]{} We shall again find it useful to use the free field realization of the $N=2$ minimal model, which we used in the last two sections. In the present case, the theory is a subquotient of a lattice theory spanned by $$(\frac{1}{\sqrt{2}},0,0),\; (\frac{1}{\sqrt{8}},\frac{i}{\sqrt{8}},
\frac{i}{2}),\;(\frac{1}{\sqrt{2}},0,i).$$ Analogously as before, we write $(k,\ell,m)$ for $$(\frac{k}{\sqrt{8}},\frac{\ell i}{\sqrt{8}},\frac{mi}{2}).$$ The conformal vector is $$\frac{1}{2}x_{0,-1}^{2}-\frac{1}{2}x_{1,-1}^{2}+\frac{i}{2\sqrt{2}}
x_{1,-2}+\frac{1}{2}x_{2,-1}^{2}.$$ The superconformal vectors are $$G_{-3/2}^{-}=(0,4,2)x_{-1}(4,0,2),$$ $$G_{-3/2}^{+}=(0,4,-2)x_{-1}(-4,0,-2).$$ The fermionic labels will again be denoted by omitting the first coordinate: $(\ell,m)_F$. The fermionic identifications are: [$$\label{ek3+}\begin{array}{l}(2,2)_F\sim (2,-2)_F \sim (0,0)_F\\
(1,1)_F\sim (1,-1)_F.
\end{array}$$]{} A priori the lattice $\langle\sqrt{8}\rangle$ has $8$ labels $\frac{k}{\sqrt{8}}$, $0\leq k\leq 7$, but the $G^-$ definition together with [(\[ek3+\])]{} forces the MM identification of labels $$(1,1,1)\sim (-3,1,-1)\sim (-3,1,1).$$ The labels of the level $2$ MM are therefore $$\begin{array}{l}
(2k,0,0),\;0\leq k\leq 3,\\
(2k+1,1,1),\; 0\leq k\leq 1.
\end{array}$$ The fusion rules are $$\begin{array}{l}
(k,0,0)*(\ell,0,0)=(k+\ell,0,0),\\
(k,0,0)*(\ell,1,1)=(k+\ell,1,1),\\
(k,1,1)*(\ell,1,1)=(k+\ell,0,0)+(k+\ell+4,0,0),
\end{array}$$ so the Verlinde algebra is simply $$\Z[a,b]/(a^4=1,\;b^2=a+a^3,\;a^2b=b)$$ where $a=(2,0,0)$, $b=(1,1,1)$.
One subtlety of the even level MM in comparison with odd level concerns signs. Since the $k$-coordinates of $G^-$ and $G^+$ are even, we can no longer use the $k$-coordinate of an element as an indication of parity ($u$ and $G^{\pm}u$ cannot have the same parity). Because of this, we must introduce odd fusion rules. There are various ways of doing this. For example, let the bottom states of $(2k,0,0)$, $(1,1,1)$ and $(-1,1,1)$ be even. Then the fusion rules on level $\ell=0$ are even, as are the fusion rules combining levels $0$ and $1$. The fusion rules $$(1,1,1)*(1,1,1)\mapsto (2,0,0), \; (1,1,1)*(-1,1,1)\mapsto (2,0,0)$$ are even, the remaining fusion rules (adding $4$ to the $k$-coordinate on the right hand side) are odd.
Now the $c$ fields of the MM are $$(0,0,0),\; (1,1,1), \; (2,2,2)$$ and the $a$ fields are $$(0,0,0), \; (-1,1,-1), \; (-2,2,-2).$$ If we denote by $H_{1,2k+1}$ the state space of label $(2k+1,1,1)$, $0\leq k\leq 1$, and by $H_{0,2k}$ the state space of label $(2k,0,0)$, $0\leq k \leq 3$, them the state space of the $4$-fold tensor product of the level $2$ minimal model is [$$\label{ek3p1}{\begin{array}{c}
{\scriptstyle 3}\\
\hat{\bigotimes}\\
{\scriptstyle i=0}\end{array}}(({\begin{array}{c}
{\scriptstyle 3}\\
\bigoplus\\
{\scriptstyle k_i=0}\end{array}}
H_{0,2k_i}\hat{\otimes}H_{0,2k_i}^{*})\oplus
({\begin{array}{c}
{\scriptstyle 1}\\
\bigoplus\\
{\scriptstyle k_i=0}\end{array}}
H_{1,2k_i+1}\hat{\otimes}H_{1,2k_i+1}^{*})).$$]{} The Gepner model is an orbifold with respect to the $\Z/4$-group which acts by $i^\ell$ on products in [(\[ek3p1\])]{} where the sum of the subscripts $2k_i$ or $2k_i+1$ is congruent to $\ell$ modulo $4$. Therefore, the state space of the Gepner model is the sum over $\beta\in\Z/4$ and $\alpha_i\in\Z/4$, $${\begin{array}{c}
{\scriptstyle 3}\\
\sum\\
{\scriptstyle i=0}\end{array}}\alpha_i=0\in\Z/4,$$ of [$$\label{ek3p2}{\begin{array}{c}
{\scriptstyle 3}\\
\hat{\bigotimes}\\
{\scriptstyle i=0}\end{array}}(({\begin{array}{c}
{\scriptstyle }\\
\bigoplus\\
{\scriptstyle 2k_i\equiv \alpha_i\mod
4}\end{array}}
H_{0,2k_i}\hat{\otimes}H_{0,2k_i+2\beta}^{*})\oplus
({\begin{array}{c}
{\scriptstyle }\\
\bigoplus\\
{\scriptstyle 2k_i+1\equiv\alpha_i}\end{array}}
H_{1,2k_i+1}\hat{\otimes}H_{1,2k_i+1+2\beta}^{*})).$$]{} It is important to note that each summand [(\[ek3p2\])]{} in which all the factors have the “odd” subscripts $1,2k_i+1$ occurs twice in the orbifold state space.
If we write again $\ell$ for $(\ell,\ell,\ell)$ and $-\ell$ for $(-\ell,\ell,-\ell)$, then the critical $cc$ fields are chirally symmetric permutations of [$$\label{ek3p3}\begin{array}{l}
(2,2,0,0),\;(2,2,0,0)\\
(2,1,1,0),\;(2,1,1,0)\\
(1,1,1,1),\;(1,1,1,1).
\end{array}$$]{} Note that applying all the possible permutations to the fields [(\[ek3p3\])]{}, we obtain only $19$ fields, while there should be $20$, which is the rank of $H^{11}(X)$ for a $K3$-surface $X$. However, this is where the preceeding comment comes to play: the last field [(\[ek3p3\])]{} corresponds to a term [(\[ek3p2\])]{} where all the factors have odd subscripts, and hence there are two copies of that summand in the model, so the last field [(\[ek3p3\])]{} occurs “twice”.
By the fact that the Fermat quartic Gepner model has $N=(4,4)$ worldsheet supersymmetry (se e.g. [@am; @nw] and references therein), the spectral flow guarantees that the number of critical $ac$ fields is the same as the number of critical $cc$ fields. Concretely, the critical $ac$ fields are the permutations of [$$\label{ek3p4}\begin{array}{l}
(0,0,-2,-2),\;(2,2,0,0)\\
(0,-1,-1,-2),\;(2,1,1,0)\\
(-1,-1,-1,-1),\;(1,1,1,1).
\end{array}$$]{} As above, the last field [(\[ek3p4\])]{} occurs in $2$ copies, thus the rank of the space of critical $ac$ fields is also $20$.
We wish to investigate whether infinitesimal deformations along the fields [(\[ek3p3\])]{}, [(\[ek3p4\])]{} exponentiate perturbatively. To this end, let us first see when the “coset-type scenario” occurs. This is sufficient to prove convergence in the present case. This is due to the fact that in the present theory, there is an even number of fermions, in which case it is well known by the boson-fermion correspondence that the correlation functions follow abelian fusion rules, and therefore Lemma \[l2\] applies. To prove that the coset scenario occurs, let us look at the chiral $c$ fields $$u=(2,2,0,0), \;(2,1,1,0), \; (1,1,1,1)$$ and study the singularities of [$$\label{ek3q2a}G^{-}_{-1/2}(z)(G^{-}_{-1/2}u).$$]{} By Lemma \[l2\], if [(\[ek3q2a\])]{} are non-singular, the obstructions vanish. The inner product is $$\begin{array}{l}
\langle(k,\ell,m),(k^{\prime},\ell^{\prime},m^{\prime})\rangle
=\frac{kk^{\prime}}{8}+\frac{\ell\ell^{\prime}}{8}-\frac{mm^{\prime}}{4},
\\
w(k,\ell,m)=\frac{k^2}{16}+\frac{\ell(\ell+2)}{16}-\frac{m^2}{8}.
\end{array}$$ Next, $(2,2,2)=(2,0,0)$, $$G^{-}_{-1/2}(2,0,0)=(0,4,-2)x_{-1}(-2,0,-2),$$ $$G^{-}_{-1/2}(1,1,1)=(-3,1,-1).$$ if we again replace, to simplify notation, the symbol $G^{-}_{-1/2}$ by $G$, then we have [$$\label{ek3q3}\parbox{3.5in}{The most singular $z$-power of $2(z)2$
is $\frac{2\cdot 2}{8}=\frac{1}{2}$,}$$]{} [$$\label{ek3q4}\parbox{3.5in}{The most singular $z$-power of $G2(z)2$
is $\frac{-2\cdot 2}{8}=-\frac{1}{2}$.}$$]{} For $G2(z)G2$, rename the rightmost $G2$ as $(-2,2,0)$. We get [$$\label{ek3q5}\parbox{3.5in}{The most singular $z$-power of $G2(z)G2$
is $-1+\frac{(-2)\cdot (-2)}{8}=-\frac{1}{2}$,}$$]{} [$$\label{ek3q6}\parbox{3.5in}{The most singular $z$-power of $1(z)1$
is $0$ for the even fusion rule and $1/2$ for the odd fusion rule,}$$]{} [$$\label{ek3q7}\parbox{3.5in}{The most singular $z$-power of $G1(z)1$
is $\frac{-3}{8}+\frac{1}{8}+\frac{1}{4}=0$ for the even fusion rule,
and $-1/2$ for the odd fusion rule,}$$]{} [$$\label{ek3q8}\parbox{3.5in}{The most singular $z$-power of $G1(z)G1$
is $\frac{9}{8}+\frac{1}{8}-\frac{1}{4}=1$
for the even fusion rule and $3/2$ for the odd fusion rule.}$$]{} One therefore sees that for the field $u=(1,1,1,1)$, [(\[ek3q2a\])]{} is non-singular: In the case of the least favorable (odd) fusion rules, the most singular term appears to be $-1$, coming from [$$\label{ek3qa}(G1,1,1,1)\otimes(1,G1,1,1).$$]{} However, this term cancels with [$$\label{ek3qb}(1,G1,1,1)\otimes(G1,1,1,1).$$]{} To see this, note that the last two coordinates do not enter the picture. We have an odd (resp. even) pair of pants $P_-$ resp. $P_+$ in the MM with input $1,1$. They add up to a pair of pants in MM$\otimes$MM. On [(\[ek3qa\])]{}, we have pairs of pants $P_i\in\{P_-,P_+\}$, [$$\label{ek3qc}\begin{array}{l}
P(G1\otimes1)\otimes(1\otimes G1)=\\
(P_1\otimes P_2)(G1\otimes1)\otimes(1\otimes G1)=\\
sP_1(G1\otimes 1)\otimes P_2(1\otimes G1)
\end{array}$$]{} where $s$ is the sign of permuting $P_2$ past $G1\otimes 1$. Here we use the fact that $1$ is even. On the other hand, [$$\label{ek3qd}\begin{array}{l}
P(1\otimes G1)\otimes(G1\otimes 1)=\\
(P_1\otimes P_2)(1\otimes G1)\otimes(G1\otimes 1)=\\
-sP_1(1\otimes G1)\otimes P_2(G1\otimes 1)
\end{array}$$]{} (as $G1$ is odd, so there is a $-$ by permuting it with itself). From [(\[ek3q\*\])]{}, the lowest term of $P_i(1\otimes G1)$ and $P_i(G1\otimes 1)$ have opposite signs, so [(\[ek3qc\])]{} and [(\[ek3qd\])]{} cancel out.
The situation is simpler for $u=(2,2,0,0)$, in which case all the fusion rules are even, and the most singular term of $$(G2\otimes 2)(z)(2\otimes G2)$$ appears to have most singular term $z^{-1}$. However, again note that $2$ is even and $G2$ is odd, so [$$\label{ek3q30}(G2\otimes s)(z)(2\otimes G2)=G2(z)2\otimes 2(z)G2,$$]{} while [$$\label{ek3q40}(2\otimes G2)(z)(G2\otimes 2)=-2(z)G(z)\otimes
G2(z)2.$$]{} Renaming $G2$ as $(-2,2,0)$, the bottom descendant of both $G2(z)2$ and $2(z)G2$ is $(0,2,0)$ with some coefficient, so [(\[ek3q30\])]{} and [(\[ek3q40\])]{} cancel out. Thus, the deformations along the first and last fields of [(\[ek3p3\])]{} and [(\[ek3p4\])]{} exponentiate.
The field $u=(2,1,1,0)$ is difficult to analyse, since in this case, [(\[ek3q2a\])]{} has singular channels and the coset-type scenario does not occur. We do not know how to calculate the obstruction directly in this case. It is however possible to present an indirect argument why these deformations exist.
In one precise formulation, the boson-fermion correspondence asserts that a tensor product of two copies of the $1$-dimensional chiral fermion theory considered bosonically (= the level $2$ parafermion) is an orbifold of the lattice theory $\langle 2\rangle$, by the $\Z/2$-group whose generator acts on the lattice by sign.
This has an $N=2$-supersymmetric version. We tensor with two copies of the lattice theory associated with $\langle\sqrt{8}\rangle$, picking out the sector [$$\label{e21101}(\frac{m}{\sqrt{8}},\frac{n}{\sqrt{8}},\frac{p}{4})\;
\text{where $m\equiv n\equiv p \mod 2$.}$$]{} The fermionic currents of the individual coordinates are [$$\label{e21102}\psi_{-1/2,1}=(1)+(-1),\; \psi_{-1/2,2}=i((1)-(-1)),$$]{} so the SUSY generators are [$$\label{e21103}G^{\pm}_{-3/2,1}=(\pm\frac{4}{\sqrt{8}},0)\otimes((1)+(-1)),
\; G^{\pm}_{-3/2,2}=(0,\pm\frac{4}{\sqrt{8}})\otimes i((1)+(-1)),$$]{} $$G=G_{\cdot 1}+G_{\cdot 2}.$$ The $\Z/2$ group acts trivially on the new lattice coordinate.
A note is due on the signs: To each state, we can assign a pair of parities, which will correspond to the parities of the $2$ coordinates in the orbifold. This then also determines the sign of fusion rules.
Now consider our field as a tensor product of $(2,0)$ and $(1,1)$, each in a tensor product of two copies of the minimal models. Considering each of these factors as orbifold of the $N=2$-supersymmetric lattice theory, let us lift to the lattice theory: [$$\label{e21104}(2,0)\mapsto (\frac{2}{\sqrt{8}},0)\otimes (0),$$]{} [$$\label{e21105}(1,1)\mapsto (\frac{1}{\sqrt{8}},\frac{1}{\sqrt{8}})
\otimes ((1/2)+(-1/2)).$$]{} Then the fields [(\[e21104\])]{}, [(\[e21105\])]{} are $\Z/2$-invariant. In the case of [(\[e21104\])]{}, we can proceed in the lift instead of the orbifold, because the fusion rules in the orbifold are abelian anyway. In the case of [(\[e21105\])]{}, the choice amounts to choosing a particular fusion rule. But now the point is that [$$\label{e21106}G^{-}_{-1/2}(2,0)\mapsto (-\frac{2}{\sqrt{8}},0)
\otimes((1)+(-1)),$$]{} [$$\label{e21107}G^{-}_{-1/2}(1,1)\mapsto (-\frac{3}{\sqrt{8}},\frac{1}{\sqrt{8}})
\otimes((1/2)+(-1/2)),$$]{} [$$\label{e21108}G^{-}_{-1/2}(1,2)\mapsto (\frac{1}{\sqrt{8}},-\frac{3}{\sqrt{8}})
\otimes((1/2)+(-1/2)).$$]{} Thus, the left of $G^{-}_{-1/2}u$ is a sum of lattice labels!
Now the critical summands of the operator [$$\label{e21109}G^{-}_{-1/2}(u)(z_k)...G^{-}_{-1/2}(u)(z_1)(u)(0)$$]{} have $k=4m$, and we have $2m$ summands [(\[e21106\])]{}, and $m$ summands [(\[e21107\])]{}, [(\[e21108\])]{}, respectively. All $$\left(\begin{array}{c}4m\\2m,m,m
\end{array}
\right)$$ possibilities occur. It is the bottom (=label) term which we must compute in order to evaluate our obstruction. But by our sign discussion, when we swap a [(\[e21107\])]{} term with a [(\[e21108\])]{} term, the label summands cancel out. Now adding all such possible $$\left(\begin{array}{c}4m\\2m,m-1,m-1,2
\end{array}
\right)$$ pairs, all critical summands of [(\[e21109\])]{} will occur with equal coefficients by symmetry, and hence also the bottom coefficient of [(\[e21102\])]{} is $0$, thus showing the vanishing of our obstruction for this field lift to the lattice theory.
Since the field [(\[e21105\])]{} is invariant under the $\Z/2$-orbifolding (and although [(\[e21104\])]{} isn’t, the same conclusion holds when replacing it with its orbifold image), the entire perturbative deformation can also be orbifolded, yielding the desired deformation.
We thus conclude that for the Gepner model of the $K3$ Fermat quartic, all the critical fields exponentiate to perturbative deformations.
Conclusions and discussion {#scd}
==========================
In this paper, we have investigated perturbative deformations of CFT’s by turning on a marginal $cc$ field, by the method of recursively updating the field along the deformation path. A certain algebraic obstruction arises. We work out some examples, including free field theories, and some $N=(2,2)$ supersymmetric Gepner models. In the $N=(2,2)$ case, in the case of a single $cc$ field, the obstruction we find can be made very explicit, and perhaps surprisingly, does not automatically vanish. By explicit computation, we found that the obstruction does not vanish for a particular critical $cc$ field in the Gepner model of the Fermat quintic $3$-fold (we saw some indication, although not proof, that it may vanish for the field corresponding to adding the symmetric term $xyztu$ to the superpotential, and for the unique critical $ac$ field). By comparison, the obstruction vanishes for the critical $cc$ fields and $ac$ fields Gepner model of the Fermat quartic $K3$-surface. Our calculations are not completely physical in the sense that $cc$ fields are not real: real fields are obtained by adding in each case the complex-conjugate $aa$ field, in which case the calculation is more complicated and is not done here.
Assuming (as seems likely) that the real field case exhibits similar behaviour as we found, why are the $K3$ and $3$-fold cases different, and what does the obstruction in the $3$-fold case indicate? In the $K3$-case, our perturbative analysis conforms with the Aspinwall-Morrison [@am] of the big moduli space of $K3$’s, and corresponding $(2,2)$- (in fact, $(4,4)$-) CFT’s, and also with the findings of Nahm and Wendland [@nw; @wend].
In the $3$-fold case, however, the straightforward perturbative construction of the deformed non-linear $\sigma$-model fails. This corresponds to the discussion of Nemeschansky-Sen [@ns] of the renormalization of the non-linear $\sigma$-model. They expand around the $0$ curvature tensor, but it seems natural to assume that similar phenomena would occur if we could expand around the Fermat quintic vacuum. Then [@ns] find that non-Ricci flat deformations must be added to the Lagrangian at higher orders of the deformation parameter in order to cancel the $\beta$ function. Therefore, if we want to do this perturbatively, fields must be present in the original (unperturbed) model which would correspond to non-Ricci flat deformation. No such fields are present in the Gepner model. (Even if we do not a priori assume that the marginal fields of the Gepner model correspond to Ricci flat deformations, we see that [*different*]{} fields are needed at higher order of the perturbation parameter, so there are not enough fields in the model.) More generally, ignoring for the moment the worldsheet SUSY, the bosonic superpartners are fields which are of weight $1$ classically (as the classical non-linear $\sigma$-model Lagrangian is conformally invariant even in the non-Ricci flat case). A $1$-loop correction arises in the quantum picture [@af], indicating that the corresponding deformation fields must be of generalized weight (cf. [@zhang; @zhang1; @huang; @huang1]). However, such fields are excluded in unitary CFT’s, which is the reason why these deformations must be non-perturbative. One does not see this phenomenon on the level of the corresponding topological models, since these are invariant under varying the metric within the same cohomological class, and hence do not see the correction term [@topsym]. Also, it is worth noting that in the $K3$-case, the $\beta$ function vanishes directly for the Ricci-flat metric by the $N=(4,4)$ supersymmetry ([@agg]), and hence the correction terms of [@ns] are not needed. Accordingly, we have found that the corresponding perturbative deformations exist.
From the point of view of mirror symmetry, mirror-symmetric families of hypersurfaces in toric varieties were proposed by Batyrev [@bat]. In the case of the Fermat quintic, the exact mirror is a singular orbifold and the non-linear $\sigma$-model deformations corresponding to the Batyrev dual family exist perturbatively by our analysis. To obtain mirror candidates for the additional deformations, one uses crepant resolutions of the mirror orbifold (see [@reid] for a survey). In the $K3$-case, this approach seems validated by the fact that the mirror orbifolds can indeed be viewed as a limit of non-singular $K3$-surfaces [@and]. In the $3$-fold case, however, this is not so clear. The moduli spaces of Calabi-Yau $3$-folds are not locally symmetric spaces. The crepant resolution is not unique even in the more restrictive category of algebraic varieties; different resolutions are merely related by flops. It is therefore not clear what the exact mirrors are of those deformations of the Fermat quntic where the deformation does not naturally occur in the Batyrev family, and resolution of singularities is needed. In other words, the McKay correspondence sees only “topological” invariants, and not the finer geometrical information present in the whole non-linear $\sigma$ model.
In [@ruan], Fan, Jarvis and Ruan constructed exactly mathematically the $A$-models corresponding to Landau-Ginzburg orbifolds via Gromov-Witten theory applied to the Witten equation. Using mirror symmetry conjectures, this may be used to construct mathematically candidates of topological gravity-coupled $A$-models as well as $B$-models of Calabi-Yau varieties. Gromov-Witten theory, however, is a rich source of examples where such gravity-coupled topological models exist, while a full conformally invariant $(2,2)$-$\sigma$-model does not. For example, Gromov-Witten theory can produce highly non-trivial topological models for $0$-dimensional orbifolds (cf. [@okpa; @pdjo]).
Why does our analysis not contradict the calculation of Dixon [@dixon] that the central charge does not change for deformation of any $N=2$ CFT along any linear combination of $ac$ and $cc$ fields? Zamolodchikov [@za; @zb] defined an invariant $c$ which is a non-decreasing function in a renormalization group flow in a $2$-dimensional QFT, and is equal to the central charge in a conformal field theory. It may therefore appear that by [@dixon], all infinitesimal deformations along critical $ac$ and $cc$ fields in an $N=2$-CFT exponentiate. However, we saw that when our obstruction occurs, additional counterterms corresponding to those of Nemeschansky-Sen are needed. This corresponds to non-perturbative corrections of the correlation function needed to fix $c$, and the functions [@dixon] cannot be used directly in our case.
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S. Kachru, E. Witten: Computing The Complete Massless Spectrum of a Landau-Ginzburg Orbifold, [*Nucl. Phys. B*]{} 407 (1993) 637-666
L.P.Kadanoff: Multicritical behavior of the Kosterlitz-Thouless Critical point, [*Ann. Phys.*]{} 120 (1979) 39-71
L.P.Kadanoff, A.C.Brown: Correlation functions on the critical lines of the Baxter and Ashten-Teller models, [*Ann. Phys.*]{} 121 (1979) 318-342
L.P.Kadanoff, F.J.Wegner: Some critical properties of the eight-vertex model, [*Phys. Review D*]{} 4 (1971) 3989-3993
M.Kohmoto and L.P.Kadanoff: Lower bound RSRG approximation for a large system, [*J.Phys. A*]{} 13 (1980) 3339-3343
I.Kriz: Some notes on the $N$-superconformal algebra, http://www.math.lsa.umich.edu/ĩkriz
I.Kriz: On spin and modularity in conformal field theory, [*Ann. Sci. ENS*]{} 36 (2003) 57-112
J.Maldacena, G.Moore, N.Seiberg: $D$-brane instantons and $K$-theory charges, [*JHEP*]{} 111 (2004), 62
G. Moore: K-theory from a physical perspective, [*Topology, geometry and quantum field theory*]{}, London Math. Soc. Lecture Ser. 308, 194-234
G. Mussardo, G. Sotkov, M. Stanishkov: $N=2$ superconformal minimal models, [*International Journal of Modern Physics*]{} A, vol.4, No.5 (1989) 1135-1206
W.Nahm, K.Wendland: A hiker’s guide to $K3$, [*Comm. Math. Phys.*]{} 216 (2001) 85-103
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|
Q:
extract only rows of a certain year, and count the most seen values
I have a thousand of rows, in an excel sheet, which have dates where a patient got infected by a virus, and when she was healed. I also have in a third column, the virus id, which is like a foreign key, and points to another excel sheet, where the name of the virus is stored, along with the virusID. The date format looks like:
column A: patient infected date
2002-01-22 13:25:41
column B: patient healed date
2002-01-24 10:35:21
What i try to do, is have the say 100 most usually seen viruses, that had infected and were healed in the same year, along their titles. (so infection and heal year, must be both say 2002)
something like (order by the number of occurrences, for year 2002):
virus1 | name of virus1 | number of occurrences
virus2 | name of virus2 | number of occurrences
which excel formula should i use? or if someone could point me to an openrefine solution, even better. Have tried INDEX, MATCH, with no luck.
A:
I usually solve these kinds of problems in steps. First, make sure column A and column B are recognized as dates in Excel. Columns C is your virus ID. I'd make column D a year infected column with the formula =YEAR(A2) copied down to the rest of the column's cells. Column E should be Year Healed with =YEAR(B2) copied down to the rest of the column's cells. Column F would indicate whether the years match using =IF(E2=D2,1,0).
Finally, the meat of the work is done with the countifs function. Column G should have cells with the formula =COUNTIFS(C$2:C$541,C2,F$2:F$541,1). In my test example, I only had data through row 541. You'll have however many rows you have. Replace 541 with your last row number. To get the virus name, you'll use the virus ID to match the sheet with the virus ID and the virus name with something like this formula: =LOOKUP(C2,Viruses!A$2:A$4,Viruses!B$2:B$4) this assumes column A is the virus ID and column B is the virus name and they both have a one line header. In my sample, I only had 3 viruses.
Once you have these columns, sort by the count column (largest to smallest), then eliminate duplicates via Data, remove duplicates. Uncheck all the columns except the virus count columns and you should have what you need. If you need only data from a particular year, filter by one of the year columns before removing duplicates.
|
Geez, thatís insane! This isnít for a small player. If that many scouts are there itís for a big name player. I hate to say it but you gotta think it involves turris. Lot of those teams have been searching for a C. Some of those teams are looking for D. Two things weíve got to possibly trade.
Flo The Action
tim1_2 wrote:A billion scouts watching the Sens game last night...we'll be moving a d-man soon, and I assume it'll be Wideman.
Ya think? Why on earth for? Heís not gonna get us much. Nothing we really need. We might as well keep him as depth for the season. Iím all for trading him if itís in a package for a top 6 winger but if itís for a fourth rounder Iíll pass. As injuries happen weíll be happy to have 9dmen that can play.
Iíd say if thereís that much interest itís either for a package deal or for a guy like Ceci. |
Niklas Jahn
Niklas Jahn (born 19 January 2001) is a German footballer who plays as a forward for Carl Zeiss Jena.
Career
Jahn made his professional debut for Carl Zeiss Jena in the 3. Liga on 22 July 2019, coming on as a substitute in the 86th minute for Marian Sarr in the 1–2 home loss against FC Ingolstadt.
References
External links
Profile at DFB.de
Profile at kicker.de
Category:2001 births
Category:Living people
Category:German footballers
Category:Association football forwards
Category:FC Carl Zeiss Jena players
Category:3. Liga players |
Reviews for Graphic Print Fresco Water Bottle - 29oz
Average Rating : 1.00 out of 5
Bottle
I tried this out looking for a tougher Nalgene replacement for climbing and mountaineering. The plastic collar on the lid came off one bottle rendering it useless, and the taste is not as good as other metal bottles. In my mind bad tasting water is not only unpleasant, but may be a sign of something you'd rather not drink in the water (paranoia - likely). The lack of durability and improved taste eliminate the two main reasons to go with a metal bottle. I'd recommend a Kleen Kanteen or Sigg. I prefer the KK for it's wider mouth, but Sigg bottles tend to be more durable, both bottle and lid. |
DEVPATH=/dev/input/by-path/platform-gpio-keys-event
KEY=135
POLARITY=1
TARGET=id-button-pressed.service
EXTRA_ARGS=--continue
|
Reaginic antibody in cattle hypersensitised by foot-and-mouth disease vaccine.
The passive cutaneous anaphylaxis test (PCAT) in calves and goats was used to demonstrate reaginic antibody in the sera of cattle which had shown anaphylaxis following injection with foot-and-mouth disease vaccine. A period of two or three days between the intracutaneous injection of test sera and the intracutaneous or intravenous challenge with components of vaccine was found to be satisfactory. Positive reactions were obtained in calves for up to 49 days but many goats failed to react after eight days. The PCAT had a high degree of reproducibility within any one test animal, but a marked variation was found between individual test animals. |
From a recent Vancouver Sun Article
“The involvement of box stores in the garden business has definitely grown over the years. It has been both a good and a bad thing,” he says. “It is tough to do an exact price comparison as size and quality do play a role. But generally, garden centres offer a more diverse range of plant material and we find customers want expert advice on how to care for the plants they are buying.”
Vander Zalm says what bothers him most about box stores is that they often sell plants that aren’t suitable for gardens in our climate zone.
“I once saw a very large $300 fan palm being sold for outdoors. Unfortunately, it was the kind that is not hardy here. Only the windmill palm (Trachycarpus fortunei) is hardy enough to survive outdoors from one year to another.
“I warned the customer who was unaware and was grateful for the advice. It may have been an oversight on the store’s part, but I think all traditional garden centres do pay attention to this kind of detail because we want customers to go away and have success and come back again.”
Sometimes the way plants are dug in the fields and repotted also make a big difference to the way they will ultimately perform in the garden, says Vander Zalm.
“Most garden centres, for instance, won’t buy hedging cedars that have been machine-dug in rows,” he says. “A machine will run down a row of cedars and lop roots off wherever. We prefer to see cedars hand-dug. This is definitely a more costly way of doing it, but we end up avoiding the potential of cutting off important large roots to the detriment of the plant.”
At the end of the day, box stores are doing a good job at getting more people interested in gardening, he says.
“Box stores and garden centres are different animals. Both will succeed. Many people will shop based on price alone, whereas others will shop for quality, a bigger selection and expert advice.”
Not long ago, there was really only one place to buy plants for your garden – the local garden centre. Today, a lot has changed. Garden centres in Metro Vancouver are being challenged on numerous fronts, especially by stores, such as Home Depot, Canadian Tire, Rona and Costco, but also by supermarkets, like Superstore and Save-On-Foods, and pretty much every corner grocery store, all of whom want a share of the gardening pie.
On July 20th, 2018 at noon Mayor Greg Moore officially opened the Shaughnessy Pop-Up Park. There was live music by Sister Says, artists painting...
PoCo Today is Port Coquitlam's community blog. Local people, businesses and organizations share their news, events, opinions, pictures, announcements, art, stories or anything that PoCo needs to know. Register and contribute to making Port Coquitlam the most informed and connected community in Canada! |
Sessions’ Fmr Counsel: Racism Allegations ‘False’ and ‘Discredited’
As soon as reports started buzzing that President-elect Donald Trump was considering Alabama Senator Jeff Sessions as his potential Attorney General, the media and internet lit up with concerns that the next head of the U.S. Justice Department would be a racist. The worries all stemmed from one particular report, that during confirmation hearings when Sessions was up for a federal judgeship in 1986, a federal prosecutor made harsh allegations against him that cost Seesions the position.
On Monday, William Smith, Sessions’ former counsel, went on ‘Fox & Friends’ to dispute the allegations against the Alabama Senator. “The people who are making the allegations don’t know Jeff Sessions,” Smith said, saying that the person who first made the accusation had been “discredited over time.” It’s not clear what he was referring too. However, Figures, the former U.S. Department of Justice assistant attorney who was instrumental in blockingSessions was reportedly indicted on bribery charges several years after his testimony. Smith, who Sessions hired to be the first black chief counsel on the Senate Judiciary Committee, described the current negative buzz as “false rumors.”
In addition to casting doubt on the known accusations against Sessions, Smith noted that since 1986, there have not been any similar allegations about him. Not only that, but Sessions successfully fought for the death penalty against a KKK leader, and helped desegregate schools in Alabama. “He’s just an outstanding guy,” Smith said. |
//
// Generated by class-dump 3.5 (64 bit) (Debug version compiled Jun 6 2019 20:12:56).
//
// class-dump is Copyright (C) 1997-1998, 2000-2001, 2004-2015 by Steve Nygard.
//
#import <IDEKit/IDEViewController.h>
#import <IDEKit/DVTOutlineViewDelegate-Protocol.h>
#import <IDEKit/IDEScopeableView-Protocol.h>
#import <IDEKit/NSMenuDelegate-Protocol.h>
#import <IDEKit/NSOutlineViewDataSource-Protocol.h>
@class DVTBorderedView, DVTNotificationToken, DVTObservingToken, DVTOutlineView, DVTScopeBarView, DVTScrollView, DVTSearchField, IDEVariableViewRootNode, IDEVariablesViewQuickLookPopover, IDEVariablesViewStateManager, NSArray, NSButton, NSMapTable, NSPopUpButton, NSPopover, NSProgressIndicator, NSString, NSTableColumn, NSTextField, NSView;
@protocol IDEVariablesViewContentProvider;
@interface IDEVariablesView : IDEViewController <NSOutlineViewDataSource, NSMenuDelegate, DVTOutlineViewDelegate, IDEScopeableView>
{
IDEVariableViewRootNode *_root;
NSMapTable *_variableNodesToObservationTokens;
double _timeLodingIndicatorWasShown;
NSPopover *_currentPopover;
IDEVariablesViewQuickLookPopover *_quickLookPopover;
long long _lastRowQuickLookWasShownFor;
unsigned long long _lastEdgeQuickLookWasShownOn;
NSView *_buttonSeparator;
NSButton *_quickLookButton;
DVTObservingToken *_showsSummaryObservationToken;
DVTObservingToken *_showsTypeObservationToken;
DVTObservingToken *_viewModeObservationToken;
DVTNotificationToken *_outlineViewHiddenObservationToken;
DVTObservingToken *_loadingNewVariablesInBackgroundObservationToken;
DVTObservingToken *_recordedStackFrameSelectedObservationToken;
DVTNotificationToken *_outlineViewSelectionObserver;
BOOL _viewWasInstalled;
BOOL _restoringExpandedState;
NSArray *_statusCellsCache;
NSArray *_statusCellCategoriesCache;
int _formatterSizeStyle;
BOOL _scopeBarVisible;
BOOL _showsType;
BOOL _showsRawValues;
DVTScopeBarView *_scopeBarView;
id <IDEVariablesViewContentProvider> _contentProvider;
IDEVariablesViewStateManager *_stateManager;
long long _selectedScopeTag;
DVTOutlineView *_outlineView;
unsigned long long _textAlignment;
NSView *_topContentContainerView;
DVTBorderedView *_containerView;
DVTScrollView *_scrollView;
DVTBorderedView *_unavailableForRecordedFrameView;
NSTextField *_unavailableForRecordedFrameText;
DVTSearchField *_filterField;
NSPopUpButton *_scopePopUp;
NSProgressIndicator *_loadingIndicator;
NSTableColumn *_compoundColumn;
NSTableColumn *_rawValueColumn;
}
+ (long long)version;
+ (void)configureStateSavingObjectPersistenceByName:(id)arg1;
+ (BOOL)automaticallyNotifiesObserversOfSelectedScopeTag;
+ (void)initialize;
@property __weak NSTableColumn *rawValueColumn; // @synthesize rawValueColumn=_rawValueColumn;
@property __weak NSTableColumn *compoundColumn; // @synthesize compoundColumn=_compoundColumn;
@property __weak NSProgressIndicator *loadingIndicator; // @synthesize loadingIndicator=_loadingIndicator;
@property __weak NSPopUpButton *scopePopUp; // @synthesize scopePopUp=_scopePopUp;
@property __weak DVTSearchField *filterField; // @synthesize filterField=_filterField;
@property __weak NSTextField *unavailableForRecordedFrameText; // @synthesize unavailableForRecordedFrameText=_unavailableForRecordedFrameText;
@property __weak DVTBorderedView *unavailableForRecordedFrameView; // @synthesize unavailableForRecordedFrameView=_unavailableForRecordedFrameView;
@property __weak DVTScrollView *scrollView; // @synthesize scrollView=_scrollView;
@property __weak DVTBorderedView *containerView; // @synthesize containerView=_containerView;
@property __weak NSView *topContentContainerView; // @synthesize topContentContainerView=_topContentContainerView;
@property unsigned long long textAlignment; // @synthesize textAlignment=_textAlignment;
@property BOOL showsRawValues; // @synthesize showsRawValues=_showsRawValues;
@property BOOL showsType; // @synthesize showsType=_showsType;
@property(nonatomic) BOOL scopeBarVisible; // @synthesize scopeBarVisible=_scopeBarVisible;
@property(retain) DVTOutlineView *outlineView; // @synthesize outlineView=_outlineView;
@property(nonatomic) long long selectedScopeTag; // @synthesize selectedScopeTag=_selectedScopeTag;
@property(retain) IDEVariablesViewStateManager *stateManager; // @synthesize stateManager=_stateManager;
@property(retain, nonatomic) id <IDEVariablesViewContentProvider> contentProvider; // @synthesize contentProvider=_contentProvider;
@property(retain) DVTScopeBarView *scopeBarView; // @synthesize scopeBarView=_scopeBarView;
- (void).cxx_destruct;
- (void)commitStateToDictionary:(id)arg1;
- (void)revertStateWithDictionary:(id)arg1;
- (void)outlineViewSelectionDidChange:(id)arg1;
- (BOOL)_wasStatusCellItemClickedAtCurrentPoint;
- (BOOL)selectionShouldChangeInOutlineView:(id)arg1;
- (BOOL)outlineView:(id)arg1 shouldTrackCell:(id)arg2 forTableColumn:(id)arg3 item:(id)arg4;
- (void)outlineViewItemDidCollapse:(id)arg1;
- (void)outlineViewItemDidExpand:(id)arg1;
- (BOOL)_shouldExpandItemAsResultOfOptionClick:(id)arg1;
- (BOOL)outlineView:(id)arg1 shouldExpandItem:(id)arg2;
- (BOOL)outlineView:(id)arg1 doCommandBySelector:(SEL)arg2;
- (void)_resetRawValuesColumnWidth;
- (void)_setRawValueColumnWidth:(double)arg1;
- (void)_updateRawValueColumnWidthIfNecessary:(double)arg1;
- (void)outlineView:(id)arg1 willDisplayCell:(id)arg2 forTableColumn:(id)arg3 item:(id)arg4;
- (BOOL)outlineView:(id)arg1 shouldMouseHoverForTableColumn:(id)arg2 row:(long long)arg3;
- (id)outlineView:(id)arg1 dataCellForTableColumn:(id)arg2 item:(id)arg3;
- (void)outlineView:(id)arg1 sortDescriptorsDidChange:(id)arg2;
- (BOOL)outlineView:(id)arg1 writeItems:(id)arg2 toPasteboard:(id)arg3;
- (void)outlineView:(id)arg1 setObjectValue:(id)arg2 forTableColumn:(id)arg3 byItem:(id)arg4;
- (BOOL)outlineView:(id)arg1 shouldEditTableColumn:(id)arg2 item:(id)arg3;
- (id)outlineView:(id)arg1 objectValueForTableColumn:(id)arg2 byItem:(id)arg3;
- (long long)outlineView:(id)arg1 numberOfChildrenOfItem:(id)arg2;
- (BOOL)outlineView:(id)arg1 isItemExpandable:(id)arg2;
- (id)outlineView:(id)arg1 child:(long long)arg2 ofItem:(id)arg3;
- (id)_predicateForMatchString:(id)arg1;
- (void)sortDescending:(id)arg1;
- (void)sortAscending:(id)arg1;
- (void)sortByName:(id)arg1;
- (void)sortByNaturalOrder:(id)arg1;
- (void)toggleShowsRawValues:(id)arg1;
- (void)toggleShowsTypes:(id)arg1;
- (void)filterChanged:(id)arg1;
- (void)copy:(id)arg1;
- (BOOL)validateUserInterfaceItem:(id)arg1;
- (id)_quickLookIconForNode:(id)arg1;
- (void)showQuickLookForRow:(long long)arg1 preferredEdge:(unsigned long long)arg2;
- (void)toggleQuickLookForRow:(long long)arg1 preferredEdge:(unsigned long long)arg2;
- (void)_toggleQuickLookForFirstSelectedRow;
- (void)keyDown:(id)arg1;
- (void)_recursivleyReflectNodeExpansionStateInOutlineView:(id)arg1;
- (void)_recursivelyReflectNodeExpansionStateInOutlineViewStartingAtRoot;
- (void)_ensureExpandedChildrenAreLoadedThenReflectExpansionStateInOutlineView;
- (void)_addSortMenuToMenu:(id)arg1;
- (void)_addToggleShowRawValueMenuItemToMenu:(id)arg1;
- (void)_addToggleShowTypesMenuItemToMenu:(id)arg1;
- (void)_contextualMenuNeedsUpdate:(id)arg1;
- (void)menuNeedsUpdate:(id)arg1;
- (void)addScopeChoice:(id)arg1 tag:(long long)arg2;
- (void)hideCurrentPopoverUsingAnimation;
- (void)hideCurrentPopoverImmediately;
- (void)showPopover:(id)arg1 forRow:(long long)arg2 preferredEdge:(unsigned long long)arg3;
- (void)showPopover:(id)arg1 forRow:(long long)arg2;
- (void)removeChildNodeFromRoot:(id)arg1;
- (void)addChildNodeToRoot:(id)arg1;
- (void)_cancelAndClearAllVariableNodeTokens;
- (void)installNewRootFromChildrenOnceExpandedChildrenAreLoaded:(id)arg1;
- (void)_handleDoubleClick:(id)arg1;
- (void)_updateGutterAndScopeFrames;
- (void)_updateScopePopUpTitle;
@property(readonly) NSString *filterString;
- (BOOL)delegateFirstResponder;
- (void)_reloadNode:(id)arg1 reloadChildren:(BOOL)arg2;
- (void)_handleVariableNode:(id)arg1 change:(id)arg2;
- (void)_notifyOutlineViewOfOldChildren:(id)arg1 replacedWithNewChildren:(id)arg2 forNode:(id)arg3;
- (void)_handleVariableNodesFormattedChildrenChanged:(id)arg1 change:(id)arg2;
- (void)_observeModelObject:(id)arg1;
- (void)_hideLoadingIndicatorIfNecessary;
- (void)_showLoadingIndicatorIfNecessary;
- (void)_handleRecordedStackFrameSelectedChanged;
- (void)_handleLoadingNewVariablesInBackgroundChanged;
- (void)_updateRawValuesColumnVisibility;
- (void)_cancelAndNilOutAllObservationTokens;
- (void)primitiveInvalidate;
- (void)viewWillUninstall;
- (void)viewDidInstall;
- (id)_createQuickLookButton;
- (void)loadView;
- (void)_variablesViewCommonInit;
- (void)awakeFromNib;
- (id)init;
// Remaining properties
@property(readonly, copy) NSString *debugDescription;
@property(readonly, copy) NSString *description;
@property(readonly) unsigned long long hash;
@property(readonly) Class superclass;
@end
|
Q:
How do I get just the accelerometer X, Y, Z values without having an updating value in android?
Hi I have a class that basically gathers GPS data (Longitude, Lattitude, and Bearing), Time (in H, M, and S), and accelerometer data (X,Y,Z) all on button click. So far I have gotten the GPS stuff to work (except Bearing for some reason only shows 0?? Do I need to set some special permissions for this??) and the time to show at the instant the Button is clicked, but the accelerometer X,Y,and Z are constantly changing because they are tied with a listener. Is there a method like getX(), getY(), or getZ() that will give me just one X,Y,Z reading on button click without it changing everytime. Here is my code so far:
package com.example.servicetest3;
import java.util.Calendar;
import android.hardware.Sensor;
import android.hardware.SensorEvent;
import android.hardware.SensorEventListener;
import android.hardware.SensorManager;
import android.location.Location;
import android.location.LocationListener;
import android.location.LocationManager;
import android.os.Bundle;
import android.app.Activity;
import android.content.Context;
import android.view.View;
import android.view.View.OnClickListener;
import android.widget.Button;
import android.widget.TextView;
import android.widget.Toast;
public class MainActivity extends Activity implements SensorEventListener {
private static final long MINIMUM_DISTANCE_CHANGE_FOR_UPDATES = 0; // in Meters
private static final long MINIMUM_TIME_BETWEEN_UPDATES = 1000; // in Milliseconds
protected LocationManager locationManager;
protected Button retrieveLocationButton;
protected TextView displayView;
//accelerometer vars
Sensor accelerometer;
SensorManager sm;
TextView acceleration;
TextView time;
@Override
public void onCreate(Bundle savedInstanceState) {
super.onCreate(savedInstanceState);
setContentView(R.layout.activity_main);
retrieveLocationButton = (Button) findViewById(R.id.retrieve_location_button);
displayView = (TextView) findViewById(R.id.displayView);
locationManager = (LocationManager) getSystemService(Context.LOCATION_SERVICE);
locationManager.requestLocationUpdates(
LocationManager.GPS_PROVIDER,
MINIMUM_TIME_BETWEEN_UPDATES,
MINIMUM_DISTANCE_CHANGE_FOR_UPDATES,
new MyLocationListener()
);
//time
time = (TextView) findViewById(R.id.time);
//set up Accelerometer service and its corresponding textViews
acceleration = (TextView) findViewById(R.id.acceleration);
sm = (SensorManager) getSystemService(SENSOR_SERVICE);
accelerometer = sm.getDefaultSensor(Sensor.TYPE_ACCELEROMETER);
sm.registerListener(this, accelerometer, SensorManager.SENSOR_DELAY_NORMAL);
retrieveLocationButton.setOnClickListener(new OnClickListener() {
@Override
public void onClick(View v) {
showCurrentLocation();
int hour = Calendar.getInstance().get(Calendar.HOUR);
int minute = Calendar.getInstance().get(Calendar.MINUTE);
int second = Calendar.getInstance().get(Calendar.SECOND);
time.setText(Integer.toString(hour) + " | " + Integer.toString(minute) + " | " + Integer.toString(second));
}
});
}
protected void showCurrentLocation() {
Location location = locationManager.getLastKnownLocation(LocationManager.GPS_PROVIDER);
if (location != null) {
String message = String.format(
"Current Location \n Longitude: %1$s \n Latitude: %2$s \n Bearing: %3$s",
location.getLongitude(), location.getLatitude(), location.getBearing()
);
displayView.setText(message);
//Toast.makeText(MainActivity.this, message, Toast.LENGTH_LONG).show();
}
}
private class MyLocationListener implements LocationListener {
public void onLocationChanged(Location location) {
String message = String.format(
"New Location \n Longitude: %1$s \n Latitude: %2$s \n Bearing: %3$s",
location.getLongitude(), location.getLatitude(), location.getBearing()
);
//Toast.makeText(MainActivity.this, message, Toast.LENGTH_LONG).show();
}
public void onStatusChanged(String s, int i, Bundle b) {
Toast.makeText(MainActivity.this, "Provider status changed",
Toast.LENGTH_LONG).show();
}
public void onProviderDisabled(String s) {
Toast.makeText(MainActivity.this,
"Provider disabled by the user. GPS turned off",
Toast.LENGTH_LONG).show();
}
public void onProviderEnabled(String s) {
Toast.makeText(MainActivity.this,
"Provider enabled by the user. GPS turned on",
Toast.LENGTH_LONG).show();
}
}
//accelerometer
public void onSensorChanged(SensorEvent event) {
acceleration.setText("X: " + event.values[0] +
"\nY: " + event.values[1] +
"\nZ: " + event.values[2]);
}
@Override
public void onAccuracyChanged(Sensor sensor, int accuracy) {
// TODO Auto-generated method stub
}
}
Please help ASAP!!! Thanks!
A:
Just unregister the listener in onSensorChanged() after you get your values.
public void onSensorChanged(SensorEvent event) {
acceleration.setText("X: " + event.values[0] +
"\nY: " + event.values[1] +
"\nZ: " + event.values[2]);
sm.unregisterListener(this);
}
|
Q:
Stop Oracle sql query execution automatically using profile limits
I want to limit Oracle user by executing query more then 15 second, for this I've created new profile with this script bellow and assign it to user.
CREATE PROFILE jibo_test_profile LIMIT
SESSIONS_PER_USER UNLIMITED
CPU_PER_SESSION UNLIMITED
CPU_PER_CALL 1500
CONNECT_TIME 45
LOGICAL_READS_PER_SESSION DEFAULT
LOGICAL_READS_PER_CALL 1000
PRIVATE_SGA 15K
COMPOSITE_LIMIT 5000000;
then I tried to execute simple select query (select * from something) which works more then 15 second, but it does not stops when query execution time reaches 15 second ( even 5 minute :) ),
then i tried to assign "CPU_PER_SESSION" 1500, but without any change.
Do you have any ideas why this limits does not works for me?
A:
The reason of problem was, that resource limit was set on "false", so profile limits were not working for user.
To use profile limits, RESOURCE_LIMIT should be set on "true"
ALTER SYSTEM SET RESOURCE_LIMIT = true;
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|
Tagged The Christians
The Christians’s premise has interesting potential; a pastor preaches a controversial sermon to his congregation and must face the landslide of consequences that follow.
What begins as a slightly disjointed ... |
Q:
is there other faster way of doing this
below code does the following: it takes a range, then finds distinct values in a range,
and stores them in a d_distinct array, also for every distinct value it creates the distinct color, then using the Excel.FormatCondition it colors the range... (my current range is A1:HM232)
for (int t = 0; t < d_distinct.Length; t++ )
{
Excel.FormatCondition cond =
(Excel.FormatCondition)range.FormatConditions.Add(
Excel.XlFormatConditionType.xlCellValue,
Excel.XlFormatConditionOperator.xlEqual,
"="+d_distinct[t],
mis, mis, mis, mis, mis);
cond.Interior.PatternColorIndex =
Excel.Constants.xlAutomatic;
cond.Interior.TintAndShade = 0;
cond.Interior.Color = ColorTranslator.ToWin32(c[t]);
cond.StopIfTrue = false;
}
But this works too slow... user will have to sit and wait for about a minute... I did this with this way since, otherwise if I do it with one line of code simply doing this (which colors amazingly fast)
range.FormatConditions.AddColorScale(3);
I will not be able to request the color of the cell... (i can have more than ten distinct values in a range)
can you help me to make my first way work faster? thanks in advance!
A:
Try turning off screen updating while the code is running and turn it back on afterwards. In VBA, that would be:
Application.ScreenUpdating = False
// do stuff
Application.ScreenUpdating = True
As you are not using VBA, try http://msdn.microsoft.com/en-us/library/microsoft.office.interop.excel._application.screenupdating(office.11).aspx for guidance
|
1. Field of Invention.
This invention relates to anchors, and in particular, to those anchors provided with pivotally mounted flukes and with a release mechanism to facilitate its unmooring.
2. Description of the Prior Art.
An anchor moors a vessel to the sea bed, generally by a combination of its own weight and by hooking itself into the bottom. See The Illustrated Science and Invention Encyclopedia, H. S. Stuttman Co., Inc., Publishers, N.Y., Vol. 1, page 110. An ideal anchor is designed so that a near horizontal pull causes it to dig itself in firmly, but an upward pull dislodges it easily. It is attached to the vessel by a cable--this is a heavy chain on large ships. Anchors in use today provide a more or less firm mooring but require winching in the cable and running the vessel over the anchor's position for its unmooring. When the cable is more or less vertical the anchor should dislodge. However, it does not always dislodge easily. Sometimes, an underwater utility cable or mangrove root gets caught between the flukes and pulling the anchor out is just an exercise in futility. One of the most popular anchors, the Danforth anchor, is particularly susceptible to this problem. |
from the third-rate-punk-band,-huh? dept
We've written a couple times about the absolutely ridiculous lawsuit that publishing giant Reed Elsevier filed against the punk band The Vandals. At issue was the fact that, years ago, the band put out an album, in which its logo was designed to parody the logo of Daily Variety, the Hollywood trade rag published by Reed Elsevier.
Way back when the album was first coming out, Variety had sent a cease and desist letter, and rather than fighting it (with a very strong fair use/parody claim) The Vandals caved and agreed not to use the image. However, the image can still be found online -- but not on sites controlled by the band. So Reed Elsevier and Variety are suing the band for somehow not magically stopping these other sites from using the image.
I had thought that once the ridiculousness of this became public, Reed Elsevier would quickly back down, but instead it dug in. Even more ridiculous is that it sued in Delaware, knowing that this would make life more difficult for the band, which is based in LA. Making things even more interesting is that the band's bassist, Joe Escalante, is also a former entertainment industry lawyer, though not a litigator. But, not one to back down from a fight, he decided to represent the band, went about learning the basics of litigation, and even got himself admitted to practice in Delaware.
Escalante emailed us to let us know that all of this has paid off so far, as the band has won the first round of the legal fight, and got the suit tossed out in Delaware and sent to California where it should have been filed in the first place. The short and sweet court order makes it clear that the judge finds it distasteful that Reed appears to have purposely filed the lawsuit across the country from the band to make life difficult for the band. You can see the full order below, but the key point is in the footnote, where the court notes that it certainly could have jurisdiction on the case, but given the circumstances, it feels that it is not appropriate, clearly suggesting that it recognizes the use of the court in Delaware was mainly to inconvenience the band:
The court recognizes that it could, if it were so inclined, choose to exercise jurisdiction over this matter and permit this case to proceed here in Delaware, given that a settlement agreement between the parties contains a clause that names Delaware as the forum for litigating disputes arising from the agreement. That settlement does not bind this court, however, and given the facts and circumstances surrounding this case, the court has decided in its discretion to decline to exercise jurisdiction. First, all relevant conduct and activities appear to have taken place in California, where the defendants reside and operate. Similarly, it appears that the Central District of California would be a far more convenient forum for trial, since the court's reading of the complaint and other documents in the record is that the vast majority of documents and witnesses pertaining to this case are in California. Furthermore, the consent judgment that underlies the plaintiffs' complaint was entered by the United States District Court for the Central District of California, and states that that court retains jurisdiction for the purposes of enforcing the consent judgment and related permanent injunction. It would be far better for that court to determine whether the conduct in question falls within the scope of the consent judgment and permanent injunction. Finally, given the defendants' apparently limited financial resources and the significant costs associated with litigating in Delaware, the court finds that the defendants would be unfairly prejudiced if they were forced to litigate in this district.
In response to this ruling the band has been mocking Variety and its lawyers relentlessly. The link above goes to a pretty incendiary blog post which, frankly, might also open the band up to defamation charges, but that would really only be digging Reed Elsevier deeper into a truly pointless legal battle. Separately, the band has used our favorite movie creation tool, Xtranormal to create this rather hilarious (and probably NSFW) video of a "fictitious meeting" between Variety's outside lawyer on this case and Variety's editor. It made me laugh: |
Quizzing the PM over Kent lorry park
I questioned the Prime Minister over the delivery of a lorry park in Kent and preparations for a "no deal" Brexit. I asked Theresa May how preparations for leaving the European Union without a deal were being "stepped up".
I want these plans to include a lorry park on the roads to the Channel Ports. This was promised two years ago but has not yet been delivered by the Department for Transport.
The Prime Minister told me the new Brexit Secretary Dominic Raab would be in charge of stepping up "no deal" preparations. She added: "Can I say to my honourable friend, I know from previous discussions the concern that he has about the potential lorry park in Kent in relation to the Port of Dover. He champions the rights of his constituents and the needs of his constituents very eloquently in this House."
My question followed the Prime Minister's statement in the House of Commons on the Government's plans for leaving the European Union. |
USDA Already Waffling on New Animal Disaster-Plan Rule
It has been nearly eight years since Hurricane Katrina ravaged the Gulf Coast, forever changing the way America responds to natural disasters. The human and animal suffering wrought by Katrina and Superstorm Sandy should remain fresh in our minds as we enter another hurricane season, and preparedness should top the agendas of animal caretakers and policy makers.
That’s why yesterday we were shocked to learn that the U.S. Department of Agriculture (USDA) may be reconsidering the disaster plan rule requiring all facilities licensed under the federal Animal Welfare Act—this includes breeders, zoos, research facilities, dealers, and other exhibitors and intermediate handlers—to prepare emergency plans for protecting and caring for animals during disasters. Asking those who use animals commercially to demonstrate a level of readiness to protect animals in their custody is fair and reasonable. We are dismayed by the possibility that the USDA would waver on a rule that could save lives at such a small cost.
For the ASPCA responders who experienced Katrina, Sandy, and countless other disaster deployments firsthand, the horrors of these events have not faded from memory: dogs chained in yards and left to drown; cats starving to death in homes after evacuations dragged on and on; animals covered in oil and toxic sludge; dogs stranded on rooftops; animals wandering the streets malnourished, dehydrated, and frightened, many never to be reunited with their owners.
The more that pet owners and animal facilities prepare for emergencies, the better responders can focus their relief efforts when disaster strikes. We hope that ultimately the USDA will remember the heartbreaks of Katrina, Sandy, Joplin, and countless other disasters and renew its resolve to protect imperiled animals under its jurisdiction.
Comments
Humans > Pets/Animals
Glad the USDA allows lost pets to placed in care of breeders, zoos and RESEARCH FACILITIES for them to be experimented on. Heheheheh. Failed experiments are disposed of immediately.
Let me make this clear: The government has yet to prove its case against Chow, power door locks and keyless entry.Front disc and rear drum brakes are standard.and higher ed. KALW’s Holly Kernan spoke with UC’s student liaison to the Regents, There was one demonstration where almost 100 calls went unanswered because the cops were tied up downtown. and the murder last Thursday sort of underscored that. red room in the back is the place to perch yourself and watch the night's characters go by. m. that we would have an independent review. at the demonstrations," a documentary that explores the relationship between two Oregon mushroom hunters. |
Use of a variable-stiffness colonoscope decreases the dose of patient-controlled sedation during colonoscopy: a randomized comparison of 3 colonoscopes.
The variable-stiffness colonoscope incorporates different degrees of stiffness of the insertion tube, which can be adjusted during the examination. Whether its use can lead to reduced procedure-related pain and sedative use is unknown. Our purpose was to compare the use of 3 types of colonoscope with different shaft stiffnesses in relation to procedure-related pain and sedative consumption. Prospective randomized trial. Endoscopy unit of a university-affiliated hospital. Consecutive patients undergoing ambulatory colonoscopy. Random assignment was made of patients into 3 groups to receive colonoscopic examinations by one of the 3 types of colonoscope: conventional standard adult size, 1.3-m; 1.6-m; and the new variable-stiffness adult size, full-length (1.6-m) colonoscope. A mixture of propofol and afentanil, delivered by a patient-controlled syringe pump, was used for sedation in all groups. Outcome measures included dose of patient-controlled sedation consumed, pain score, cecal intubation rate, cecal intubation time, requirement of abdominal pressure and change of patients' positions during colonoscopy, and endoscopists and patients' satisfaction scores according to a visual analog scale. A total of 335 patients were randomized. Patients in group 3 used significantly less propofol (in milligrams per kilograms, mean [SD]) compared with the other 2 groups (group 1: 1.00 [0.75], group 2: 0.93 [0.62], and group 3: 0.75 [0.65]; P = .02; 1-way analysis of variance). The mean (SD) pain score was also lower in group 3. The endoscopists were not blinded. The use of the new variable-stiffness adult-size colonoscope significantly reduced procedure-related pain and doses of sedative medications during colonoscopy. |
545 F.2d 1296
Gulledgev.Toland***
No. 76-1775
United States Court of Appeals, Fifth Circuit
1/5/77
1
N.D.Ala.
AFFIRMED
*
Summary Calendar case; Rule 18, 5 Cir.; see Isbell Enterprises, Inc. v. Citizens Casualty Co. of New York et al., 5 Cir., 1970, 431 F.2d 409
**
Local Rule 21 case; see NLRB v. Amalgamated Clothing Workers of America, 5 Cir., 1970, 430 F.2d 966
|
Q:
Spawning Multiple of the same sprite
I am currently working on a game called Table Wars, a turn based strategy game for two players. Progress has been going smoothly, until I ran into a problem with spawning units.
The program won't spawn multiple of the same unit, or respawn new ones after the old ones die.
Here is some information that may help:
Each class is stored in a variable: (redI = Red_Infantry())
All functions are stored in the main loop.
The sprite classes have hard-coded X and Y values, used when spawning units and moving units.
What should I do?
As requested, here is the class for the Red Infantry:
class Red_Infantry(pygame.sprite.Sprite):
def __init__(self):
pygame.sprite.Sprite.__init__(self)
self.image, self.rect = load_image('Soldier_red.png', -1)
self.selected = 0
self.area = screen.get_rect()
self.rect.topleft = (100, 300)
self.health = 100 #Soldiers are have mediocre toughness.
self.attack_damage = 25
self.range_maximum = 20 #in pixels, this is melee range
self.range_minimum = 0
self.update()
def update(self):
if self.health <= 0:
self.kill()
and the code to spawn this unit:
if spawned_units < 3 and PHASE == 1 and TURN == 'Red':
if REDGOLD < 10:
print "Out of money! Moving to Phase 2!"
PHASE = 2
spawned_units = 0
elif event.type == KEYDOWN and event.key == K_1:
if REDGOLD >= 10 and REDCOMMAND >= 5:
Sprites.append(redI)
REDGOLD -= 10
REDCOMMAND -= 5
spawned_units = spawned_units + 1
else:
print "Not enough gold!"
This is similar style with all units. It performs correctly the first time, but not in the second, third, and so on, meaning I can only have one Soldier. Also, when that soldier dies via self.kill, it won't come back if I try to spawn it.
A:
The part of the spawn procedure you posted doesn't create any new instances. Unless redI is declared as a new Red_Infantry somewhere else, you need to modify the code to create a new instance of Red_Infantry every time you want to spawn a soldier.
sprites.append(Red_Infantry())
To update the sprites:
for sprite in sprites:
sprite.update()
Put movement and other state changes in the update method. This is what pygame expects, but you can use a different style if you want. The main point is you must have multiple instances of Red_Infantry in order to see multiple sprites.
You could also use pygame's Group class instead of a simple list to hold the sprites.
Here's a full example that uses Group instead of list. In the example, an Enemy is spawned each time a key is pressed. Each Enemy prints its unique ID to stdout.
import sys
import random
import pygame
from pygame.locals import *
def main():
pygame.init()
screen = pygame.display.set_mode((480, 320))
enemies = pygame.sprite.Group()
while True:
for event in pygame.event.get():
if event.type == KEYDOWN:
enemies.add(Enemy(screen))
elif event.type == QUIT:
sys.exit()
enemies.update()
screen.fill(pygame.Color("black"))
enemies.draw(screen)
pygame.display.update()
class Enemy(pygame.sprite.Sprite):
def __init__(self, screen):
pygame.sprite.Sprite.__init__(self)
print "created a new sprite:", id(self)
self.image = pygame.image.load("sprite.png")
self.rect = self.image.get_rect()
self.rect.move_ip(random.randint(0, screen.get_width()),
random.randint(0, screen.get_height()))
def update(self):
self.rect.move_ip(random.randint(-3, 3), 0)
if __name__ == "__main__":
main()
|
Q:
Download Zoom Recordings to Local Machine and use Resumable Upload Method to upload the video to Google Drive
I have built a function in Python3 that will retrieve the data from a Google Spreadsheet. The data will contain the Recording's Download_URL and other information.
The function will download the Recording and store it in the local machine. Once the video is saved, the function will upload it to Google Drive using the Resumable Upload method.
Even though the response from the Resumable Upload method is 200 and it also gives me the Id of the file, I can't seem to find the file anywhere in my Google Drive. Below is my code.
import os
import requests
import json
import gspread
from oauth2client.service_account import ServiceAccountCredentials
DOWNLOAD_DIRECTORY = 'Parent_Folder'
def upload_recording(file_location,file_name):
filesize = os.path.getsize(file_location)
# Retrieve session for resumable upload.
headers = {"Authorization": "Bearer " + access_token, "Content-Type": "application/json"}
params = {
"name": file_name,
"mimeType": "video/mp4"
}
r = requests.post(
"https://www.googleapis.com/upload/drive/v3/files?uploadType=resumable",
headers=headers,
data=json.dumps(params)
)
print(r)
location = r.headers['Location']
# Upload the file.
headers = {"Content-Range": "bytes 0-" + str(filesize - 1) + "/" + str(filesize)}
r = requests.put(
location,
headers=headers,
data=open(file_location, 'rb')
)
print(r.text)
return True
def download_recording(download_url, foldername, filename):
upload_success = False
dl_dir = os.sep.join([DOWNLOAD_DIRECTORY, foldername])
full_filename = os.sep.join([dl_dir, filename])
os.makedirs(dl_dir, exist_ok=True)
response = requests.get(download_url, stream=True)
try:
with open(full_filename, 'wb') as fd:
for chunk in response.iter_content(chunk_size=512 * 1024):
fd.write(chunk)
upload_success = upload_recording(full_filename,filename)
return upload_success
except Exception as e:
# if there was some exception, print the error and return False
print(e)
return upload_success
def main():
scope = ["https://spreadsheets.google.com/feeds", "https://www.googleapis.com/auth/spreadsheets",
"https://www.googleapis.com/auth/drive.file", "https://www.googleapis.com/auth/drive"]
creds = ServiceAccountCredentials.from_json_keyfile_name('creds.json', scope)
client = gspread.authorize(creds)
sheet = client.open("Zoom Recordings Data").sheet1
data = sheet.get_all_records()
# Get the Recordings information that are needed to download
for index in range(len(sheet.col_values(9))+1 ,len(data)+2):
success = False
getRow = sheet.row_values(index)
session_name = getRow[0]
topic = getRow[1]
topic = topic.replace('/', '')
topic = topic.replace(':', '')
account_name = getRow[2]
start_date = getRow[3]
file_size = getRow[4]
file_type = getRow[5]
url_token = getRow[6] + '?access_token=' + getRow[7]
file_name = start_date + ' - ' + topic + '.' + file_type.lower()
file_destination = session_name + '/' + account_name + '/' + topic
success |= download_recording(url_token, file_destination, file_name)
# Update status on Google Sheet
if success:
cell = 'I' + str(index)
sheet.update_acell(cell,'success')
if __name__ == "__main__":
credentials = ServiceAccountCredentials.from_json_keyfile_name(
'creds.json',
scopes='https://www.googleapis.com/auth/drive'
)
delegated_credentials = credentials.create_delegated('Service_Account_client_email')
access_token = delegated_credentials.get_access_token().access_token
main()
I'm still trying to figure out how to upload the video to the folder that it needs to be. I'm very new to Python and the Drive API. I would very appreciate if you can give me some suggestions.
A:
How about this answer?
Issue and solution:
Even though the response from the Resumable Upload method is 200 and it also gives me the Id of the file, I can't seem to find the file anywhere in my Google Drive. Below is my code.
I think that your script is correct for the resumable upload. From your above situation and from your script, I understood that your script worked, and the file has been able to be uploaded to Google Drive with the resumable upload.
And, when I saw your issue of I can't seem to find the file anywhere in my Google Drive and your script, I noticed that you are uploading the file using the access token retrieved by the service account. In this case, the uploaded file is put to the Drive of the service account. Your Google Drive is different from the Drive of the service account. By this, you cannot see the uploaded file using the browser. In this case, I would like to propose the following 2 methods.
Pattern 1:
The owner of the uploaded file is the service account. In this pattern, share the uploaded file with your Google account. The function upload_recording is modified as follows. And please set your email address of Google account to emailAddress.
Modified script:
def upload_recording(file_location, file_name):
filesize = os.path.getsize(file_location)
# Retrieve session for resumable upload.
headers1 = {"Authorization": "Bearer " + access_token, "Content-Type": "application/json"} # Modified
params = {
"name": file_name,
"mimeType": "video/mp4"
}
r = requests.post(
"https://www.googleapis.com/upload/drive/v3/files?uploadType=resumable",
headers=headers1, # Modified
data=json.dumps(params)
)
print(r)
location = r.headers['Location']
# Upload the file.
headers2 = {"Content-Range": "bytes 0-" + str(filesize - 1) + "/" + str(filesize)} # Modified
r = requests.put(
location,
headers=headers2, # Modified
data=open(file_location, 'rb')
)
# I added below script.
fileId = r.json()['id']
permissions = {
"role": "writer",
"type": "user",
"emailAddress": "###" # <--- Please set your email address of your Google account.
}
r2 = requests.post(
"https://www.googleapis.com/drive/v3/files/" + fileId + "/permissions",
headers=headers1,
data=json.dumps(permissions)
)
print(r2.text)
return True
When you run above modified script, you can see the uploaded file at "Shared with me" of your Google Drive.
Pattern 2:
In this pattern, the file is uploaded to the shared folder using the resumable upload with the service account. So at first, please prepare a folder in your Google Drive and share the folder with the email of the service account.
Modified script:
Please modify the function upload_recording as follows. And please set the folder ID you shared with the service account.
From:
params = {
"name": file_name,
"mimeType": "video/mp4"
}
To:
params = {
"name": file_name,
"mimeType": "video/mp4",
"parents": ["###"] # <--- Please set the folder ID you shared with the service account.
}
When you run above modified script, you can see the uploaded file at the shared folder of your Google Drive.
Note:
In this case, the owner is the service account. Of course, the owner can be also changed.
Reference:
Permissions: create
|
Lionel Messi and Argentina trolled by Brazilians amid disastrous World Cup qualification run
The rivalry between Argentina and Brazil is a fierce one. So when one of the illustrious nations are struggling to make the World Cup, the other jumps all over it.
It all began after Argentine publication Diario Ole went with a frank assessment of: “We’re f*****”, on Twitter after their goalless draw with Peru on Thursday.
That result leaves them in sixth place in the qualification standings, looking in from the outside as they risk not even grabbing the playoff spot and missing out on the World Cup in Russia next summer.
Only the top four in South American qualifying are guaranteed a spot in the World Cup, while fifth will result in a two-leg playoff with New Zealand.
With one game left, they must now win their qualifier against Ecuador on Wednesday to be in with a chance of qualifying, or one of the world’s biggest stars in Messi and his teammates will be absent from the showpiece event next year.
Brazil meanwhile have strolled to qualification, topping the table with a comfortable gap between them and the chasing pack, and Brazilians are certainly enjoying the moment and rubbing it in for their rivals… |
Next-gen balls.
Hustle Kings developer VooFoo Studios and indie publisher Ripstone have announced Pure Pool for PlayStation 4.
The PlayStation Network game launches in 2014.
Pure Pool is the second of VooFoo's Pure titles to launch on PSN. Pure Chess launched on Sony's digital platform in May 2012. Ripstone chief Phil Gaskell said it was working with VooFoo to "build a strong family of Pure games, and there's more to come".
He added: "What's important though is the expectation gamers will have, titles like Pure Chess and Hustle Kings are visually stunning and we're aiming to help VooFoo deliver a world class game in Pure Pool that I hope will go beyond those expectations and really blow people's minds." |
Jorge Segurado
Jorge Segurado (born 13 November 1960) is an Argentine rower. He competed in the men's coxed four event at the 1976 Summer Olympics.
References
Category:1960 births
Category:Living people
Category:Argentine male rowers
Category:Olympic rowers of Argentina
Category:Rowers at the 1976 Summer Olympics
Category:Place of birth missing (living people) |
Introduction
============
The magic word 'complexity' has been buzzing around in science, policy and society for quite some time now (for recent examples \[[@B1],[@B2]\]). There seems to be a common feel for a 'new way' of doing things, for overcoming the limits of tradition. The 'new way' though is conceived radically differently by two important schools of complexity thinking. Whereas the Santa Fé school \[[@B3],[@B4]\] merely believes that new scientific strategies in the face of complexity in the end will bring us closer to the modern aim of ever more perfect knowledge and control, the critical complexity school \[[@B5]-[@B7]\] points out that limits of knowledge are inherent to complexity, necessitating reduction and critical reflection on the normative basis for any simplification. The intense debates about complexity seem to be mainly located in the salons and saloons of scientific and social debate, focussing not so much on 'how to actually do it' and with little reflection on practical experiences. We will focus on the art of complexity and apply this to one of the most challenging and complex fields of today: the relationship between environment and health. Grand old men in the field of environment and health, Philippe Grandjean \[[@B8],[@B9]\], David Briggs \[[@B10]\] and David Gee \[[@B11]\], critically reflect on the limits of current environment and health science when judged from a problem solving perspective and warn us of the lack of relevance of current scientific practice with respect to complex reality. From the combined perspective of critical complexity thinking and environment and health practise we want to contribute to the development of alternative routines that may help overcome the limitations of traditional environment and health science. We will especially draw attention to the practical complexities involved, confronting us not only with fundamental questions, but also with fundamental challenges.
Review
======
Critical complexity
-------------------
### Complexity
Most environment and health experts will probably agree that the field of environment and health is a characteristic example of complexity: the interaction of all relevant elements, both pollutants and health parameters as well as a wide range of intervening variables such as lifestyle and genetic factors create a very complex interplay that is hardly possible to conceive in all its complexity, let alone fully measure, describe and comprehend. The study of cocktail effects of different chemical agents in interaction with each other and human health is a good example of the natural scientific complexity of environment and health issues. It is recognized to be of the utmost importance for a more realistic view of the field for some time \[[@B12]\], but cocktail effects only seem to be receiving considerable scientific and policy attention in recent years \[[@B13]\]. Moreover it is recognized more and more that the social complexity of environment and health should also be taken into account if we want to create problem solving horizons: social dynamics, both in science, politics and society as a whole, form an integral part of environment and health issues. The growing awareness in the field of climate change that social scientific expertise is essential in order to better deal with the challenges posed on our society by climate change \[[@B14],[@B15]\] is exemplary in this respect. For a more extensive account on natural scientific and social scientific complexity with respect to environment and health see e.g. Keune et al. \[[@B16]\]. We will now focus on critical complexity.
### Critical complexity
The study of cocktail effects is a good example of a different view on complexity in that environment and health issues are no longer reduced to studying single pollutants and their individual potential health effects. Recent insights show that cocktails of pollutants create dynamics surpassing the level of effect of single pollutants and may result in stronger combined health effects than would be expected when simply adding the single pollutants' effects \[[@B13]\]. This means that current mainstream environment and health knowledge does not suffice as a basis for evidence based policy making. We can no longer conclude that safety is assured when individual levels of pollutants are below specific individual thresholds that are believed to be safe. Nevertheless, even though strategies taking into account a bigger and more complex picture of reality by being less reductionist are new in their focus and method, they may remain traditional in their promise of perfect and undisputable knowledge, and may remain traditional in their scientific analysis. The study of cocktail effects may be an example of this. A critical view on complexity challenges our potential knowledge of complex phenomena, stating that because of the intrinsic properties of complexity we are condemned to limited knowledge of complexity. We will not present a complete overview of properties of complexity \[[@B5],[@B17]\] here, we will only refer to some properties so as to illustrate some of the problems of dealing with complexity. One important property of complexity is emergence \[[@B17]\]: the presence of a great number of (often simple) system components that interact in a manner that cannot be explained by the characteristics of the individual components. Another important feature of complexity is non-linearity \[[@B17]\]: due to partly non-linear input - output functions, complex systems will show unpredictable behaviour. Furthermore, complexity is to be characterized by temporality \[[@B18]\]: complex systems echo their history, their memory of the past in the present and future, be it in a selective and non-linear manner. Finally we mention the problematic issue of reduction \[[@B17]\]: any knowledge we have about a complex system is a reduction of its complexity.
We have to realize that the challenge of gaining knowledge about complexity will be as important as the challenge to act based on limited knowledge. Both challenges are interrelated. Cilliers \[[@B17]\]: "*More than one description of a complex system is possible. Different descriptions will decompose the system in different ways. Different descriptions may also have different degrees of complexity."* At the very heart of a critical complexity perspective lie fundamental questions about the nature and status of meaningful knowledge, for which no unambiguous criteria exist (ibid.). The interpretative nature of knowledge is closely related to normative choices, ethical issues, and political issues. Cilliers \[[@B17]\] pleads for a modest attitude towards complexity and knowledge about complexity: "*knowledge is provisional. We cannot make purely objective and final claims about our complex world. We have to make choices and thus we cannot escape the normative or ethical domain*." Philippe Grandjean \[[@B8]\] seems to agree: *"Risk assessment can never become completely objective"*. He is especially critical on environmental health-science from a problem solving perspective: due to complexities traditional science will not be fit to tackle environmental health-problems. *"Risk assessment must become less reductionist and less focused on obtaining complete information on all aspects of individual hazards. Statistical acceptance of the null hypothesis should never be interpreted as proof of safety.* (*...*) *Given that decisions will involve stakeholders*, *risk perception should receive increased attention as a crucial aspect that is not dependent on a formalized scheme of evaluation"*\[[@B8]\]. According to Grandjean, standard scientific approaches do not fully fit issues, in focus and method (too much focus on simplified models and effects of single hazards one by one) or in interpretation (too strict analytical standards). Grandjean stresses the need for a different scientific approach and application in policy practice of a precautionary principle. David Briggs \[[@B10]\] pleads for more integrated methods of assessment. Key challenges do not only relate to the content of analysis, environment and health-problems, but also to the involvement of relevant actor perspectives. With regard to complexity, Briggs (like Grandjean) criticizes traditional forms of assessment, and proposes to focus on a real world perspective in which the issue of problem framing becomes of main importance. The involvement of relevant actors according to Briggs need not be limited to scientists alone: the involvement of stakeholders is also important, at an early stage. According to Briggs, despite numerous pleas for and ambitious ideals with respect to environment and health, the application of integrated approaches in research practice is still in its infancy.
We may conclude here that traditional environment and health science is too self-confident with respect to potential scientific insight in environment and health problems. Environment and health complexity condemns us to limited and ambiguous knowledge. A more modest attitude would be more realistic from that point of view. From a problem solving perspective more boldness is required. Waiting for Godot (perfect undisputed knowledge) will not help us with respect to the challenges posed to society by environment and health problems. Instead of mainly focussing on what we don't know yet we should focus more on what we already do know in order to facilitate more pragmatic problem solving interpretations of environment and health complexity. The traditional focus on strict statistical analysis of the tiny fragments of reality that we are able to measure is challenged by ethical concern from a societal problem solving perspective and demands critical qualitative reflection on the ambitions and responsibilities of environment and health science. A sense of urgency is legitimate: the paralysis by traditional analysis should be overcome. Simultaneously this sense of urgency should not withhold us from investing in the problem solving quality of our endeavour; quality takes time, fastness from a quality perspective often leads us to standstill \[[@B18]\].
### Open choices, enabling limitations
Making choices is essential from a critical complexity perspective in two important respects. One is that we can never have perfect knowledge about complex issues: we choose our picture of reality but have to realize that each picture has limitations. This picture can have many forms, e.g. problem framing, a model, a research ambition, a policy action or public debate. Second, we cannot objectify which picture of complex reality is best or better than other pictures, thus knowledge will not be unambiguous. Does this mean that we should *not* reduce complexity in order to deal with it realistically and that we have to accept that in principal all knowledge is of equal significance? The answer to both questions is no. According to Cilliers \[[@B17]\]: *"Limited' knowledge is not equivalent to 'any' knowledge. If this were so*, *any modest claim*, *i.e. any claim with some provisionality or qualification attached to it*, *would be relativistic.* (*...*) *Modest claims are not relativistic and*, *therefore*, *weak. They become an invitation to continue the process of generating understanding."* And: *"This does not imply that we can know nothing about complex systems*, *or that the knowledge claims we make about them have to be vague*, *insipid or weak. We can make strong claims*, *but since these claims are limited*, *we have to be modest about them."* In the process of knowledge generation we constantly have to make interpretive choices: *"Knowledge is interpreted data. This leads us to the next big question: what is involved in interpretation*, *and who* (*or what*) *can do it?"*\[[@B19]\].
By choosing our picture or reality, we draw boundaries. We draw ontological boundaries that frame the picture of complex reality: knowledge boundaries. And we draw epistemological boundaries with respect to the generation of knowledge on complexity: disciplinary and transdiciplinary boundaries. Moreover do we 'perform' ethics in our boundary work: we choose what we consider to be relevant, important, just, better, best. Ontologically the boundaries can be bold or modest, flexible or inflexible. Epistemologically the boundaries can be closed and inward looking or open and an invitation to dialogue with others and other forms of knowledge. Boundaries create a difference as they distinguish the inside of the picture of complex reality from the outside and distinguish one picture of complex reality from another picture. A picture of the health effects of one pollutant is different to a picture of the health effects of another pollutant, and is different to a picture of the health effects of a cocktail of pollutants. A natural scientific picture of environment and health will focus on other aspects than a social scientific picture, even when looking at the same environment and health issue. In fact scientists with similar disciplinary background will also potentially create completely different pictures of similar environment and health issues. A scientific picture will probably focus on other characteristics of complexity than a picture of policy makers or stakeholders. This does not necessarily mean that some pictures are better than others, nor does it necessarily mean that we should fuse all pictures into one super picture of complex reality. Different pictures may complement and may enrich each other, but may also criticize and compete with each other. The way we choose to deal with difference is of the utmost importance in the case of complexity \[[@B20]\]. We can consider openness to other, different pictures of complexity and other perspectives on complexity important as a test of one's own picture: is our picture of complex reality robust when we compare it to other pictures, can we learn from other pictures and do we pass the test of being criticized by others about the robustness of our picture?
Theoretically this might imply that the more different viewpoints we take on board and the more critical mass we organize to test our endeavour, the more robust our end product, be it knowledge, be it (e.g. policy) action, will be. This would indeed connect well to the ideal of integrated assessment proposed to us by Briggs \[[@B10]\] and the involvement of stakeholders proposed both by Briggs and Grandjean \[[@B8]\]. In fact we may broaden the basis of support for this openness with reference to other approaches in the familiar fields of risk governance and environmental science and policymaking that promote an 'open arms approach', such as the analytical-deliberative approach \[[@B21]\] and the extended peer review approach \[[@B22]\]. Cilliers \[[@B5]\] proposes this theoretical ideal of openness to and respect for differences as an ethics of complexity. Cilliers \[[@B23]\] nuances the ideal by pointing at the notion of power: *"The argument from complexity claims that a single story*, *or in the words of Lyotard*, *a 'coherent meta-narrative' cannot describe any social system fully...The reason why a certain description is acceptable has to do less with rationality and more with power. We do not have to look hard to find examples of master-narratives which oppressed the 'other' in the system*, *whether they be of a different race*, *religion*, *gender or sexual orientation."* Kunneman \[[@B7]\]: "(*...*) *difficulties become visible when we pose the question why we should prefer his ethics of differences above - for example - an ethics of care*, *or the discourse ethics propagated by Jurgen Habermas* (*...*) *or for that matter*, *the aggressively 'masculine' ethics connected with the Hip-Hop scene*, *or the 'tribal' ethics practiced with great brutality and with great economic success by Italian Mafia-families?*" We therefore do not want to proclaim a critical complexity perspective (whatever it would mean in practice) as just because of the intrinsic qualities of complexity, but merely propose it as a worthwhile companion when we picture complex reality. We propose to take the openness to and respect for differences as an ambition that is worthwhile testing, but consider it not to be immune to one of the most important ingredients of critical complexity: critical reflection. An intriguing example of the need for reflection on openness is the growing influence of industry experts in important policy advisory expert panels over the last decades \[[@B24]-[@B26]\], of which the International Agency for Research on Cancer (IARC) is an important environment and health example. The IARC is part of the World Health Organisation and its mission is to coordinate and conduct research on the causes of human cancer, the mechanisms of carcinogenesis, and to develop scientific strategies for cancer control. Huff \[[@B24]\], a former Chief of the Unit responsible for the IARC Monographs, wrote about the unprecedented and growing industry influence on the Monographs. In the case of chemical exposures, this resulted in a lower risk evaluation for chemicals. And this leads us to the conclusion that openness is an ethical issue in itself.
The critical view on complexity is very important in better understanding and discussing the challenges posed by complexity. The critique unmasks weak spots in our understanding of and dealing with complexity. Moreover current critical complexity thinking may inspire to create alternatives routines of understanding of and dealing with complexity. We have to open up and narrow down simultaneously: we have to be more realistic in our reduction; we have to outsmart our limitations. Not by more of the same, but by differentiation. We should not though remain too much on an ideal theoretical level: we need to take into account practicalities, we have to be pragmatic. We have to find a clever balance between respect of complex reality and practical attainability: we have to be both informative and performative. As none of these aspects, choices and strategies can be objectified because of limited knowledge and ambiguity, we cannot refrain from ethics, otherwise we will be either lost in blindness or limitlessness and in fact get nowhere. We have to make conscious choices by asking ourselves what is important, what is relevant, what is the meaning of what we do.
Critical complexification
-------------------------
*Critical complexification* means opening up boundaries that limit our view on complexity, connecting relevant contexts that will enrich our view and will enrich relevant contexts. Simultaneously, *critical complexification* has to set its own boundaries; otherwise nothing will happen, except staring at outer space forever with the friends we gather. Such boundaries will be different in character though than turning ones back to others, to whom and what are excluded. The boundaries are always open for critique, for discussion, for reflexion. *Critical complexification* also means challenge: we challenge complex reality, we challenge ourselves, we challenge others. We also challenge 'our' or 'their' current practice of dealing with complexity. We challenge the actors, we challenge the contexts of those actors, we challenge their knowledge, we challenge their practice. Challenge means critique in a constructive manner. It not only means to ask fundamental and radical questions about what others do and know and by what motives, it also means to invite, cooperate, enable, enrich in order to better deal with complexity. And last but not least, through *critical complexification* we face the challenges practice will have in store for us.
We will use the term *critical complexification* to describe the process of critically dealing with complexity in practice. *Complexification* draws our attention to our selection of relevant of elements of complexity that we want to take on board when picturing complexity in order to do justice both to complex reality and to the ambition(s) we choose with respect to dealing with complex reality. The term *complexification* was used before by other authors in a more or less similar fashion \[[@B27],[@B28]\]. Next to this we mean it also to be a word of action, drawing attention to the practical aspects of the art of complexity: how do we *complexify*? *Critical* draws our attention to critical reflection on our ambitions and actions and to challenging the quality of our activities and outputs. On the one hand this draws our attention to the need to reflect on our choices from an ethical perspective: what is the justification for our ambitions and our actions? On the other hand this draws our attention to the issue of critical mass: what is the basis for challenging the quality of our ambitions and actions, or in other words, which assessment criteria are relevant and who should be involved in the assessment?
In discussing practical elements of *critical complexification* we will refer to two practical contexts in which difference (and diversity) was considered relevant to dealing with the complexity of environment and health and was approached differently than in mainstream environment and health science and policy making. We invite those readers who want to learn more, to read the references, and only introduce the cases very briefly.
### Case analytical deliberative approach (AD)
Instigated by policy representatives together with medical and environmental scientific experts and policymakers, in Flanders (Belgium) an *action-plan* was developed for setting policy priorities with regard to human bio-monitoring results: from research results to policy action \[[@B29]\]. The *action-plan* was inspired by the analytical deliberative approach \[[@B21]\], an approach that combines scientific complexity and social complexity by linking expert debate with social debate. In the practice of the *action-plan* it concerned close interdisciplinary cooperation: the general approach had to be negotiated between totally different disciplinary backgrounds and natural and social scientific data were combined. It also concerned close cooperation with policy representatives: the research had to be policy relevant, which puts totally different demands on research than just scientific ones. Furthermore, both experts and stakeholders were involved. The basic problem that needed to be solved was choosing between policy options that are rather different in nature, e.g. policy on asthma incidence and policy on pollution from pesticides. The choice is based on different assessment criteria: seriousness of health risks, policy aspects and social aspects. The procedure was organised as follows: first desk research provides the different options with background information concerning the different assessment criteria. The environmental and health information relevant to assess the health risk is being gathered by natural scientists. The social scientists are responsible for policy-related and social aspects. Second, the desk research information is assessed in an expert consultation. Experts with regard to environment and health assess the health risk criterion, policy experts the policy aspects as do social experts the social aspects. These assessments result in both *quantitative information* (priority rankings of options on different criteria) and *qualitative information* (arguments, difference of opinion, uncertainties). The outcomes of the expert consultation are processed in a multi-criteria analysis \[[@B30],[@B31]\] as well as in an account of (other) qualifications. Third the results of both desk research and expert consultation are discussed by a stakeholder jury that gives advice on the basis of all information: different from experts a societal view deals with the political question of deciding what's important considering all aspects. Finally the procedure is aimed at a well informed and substantiated decision-making by the policymakers. In the following we will call this the AD-case.
### Case expert elicitation (EE)
The EU HENVINET project had the ambition to synthesize scientific information available on a number of topics of high relevance to policy makers in environment and health \[[@B32]\]: brominated flame retardants, phthalates, the impacts of climate change on asthma and other respiratory disorders, the influence of environment health stressors on cancer induction, the pesticide CPF and nano particles. At first it was the ambition to focus mainly on the state of the art scientific knowledge, with a special interest in gaps of knowledge. By means of expert elicitation the gaps of knowledge were highlighted by using confidence levels for assessment of current scientific knowledge. During the work in progress a complementary focus developed through interdisciplinary reflections. By extending the horizon of the endeavour from only science to the problem solving policy perspective, the ambition was complemented by interpreting the synthesized available knowledge from a policy perspective, addressing the question which kind of policy action experts consider to be justifiable based on the identified state of scientific knowledge. As such the expert elicitation approach became helpful in overcoming the policy action impasse caused by the mere scientific knowledge oriented strategy for dealing with limited knowledge on complex issues. It did so by constructively discussing the weight of existing knowledge for potential policy action, thus stressing more the societal importance of the issues under study and considering to take action, rather than merely betting on the scientific quest for ever more knowledge. Both parts of the expert elicitation, the assessment of state of the art scientific knowledge by means of confidence levels and the problem solving interpretation by means of a qualitative questionnaire and a workshop discussion, were quite challenging for all experts involved, as it did not relate easily to mainstream environment and health scientific practice. In the following we will call this the EE-case.
Practice
--------
### Embrace and structure
Important choices that have to be made when dealing with complexity concern relevant elements of complexity to take on board: which actors and factors are considered relevant? Who and what do we embrace and who are we? Part of the answer is in complex reality: reality poses specific challenges. Part of the answer is in our ambition with respect to reality: what do we hope to achieve? Creating knowledge as such is another challenge than creating policy relevant knowledge and is another ambition than developing problem solving actions. Focussing on individual pollutants poses another challenge than focussing on cocktails. And part of the answer is in the discussion amongst those who are in the driving seat: the cocktail of actors involved will create specific dynamics affecting the process. In the AD-case the team consisted of natural and social scientists and policy representatives. Amongst the actors consulted in the process were other natural and social scientists and policy representatives, and policy experts and stakeholders. Next to environment and health factors, policy and social factors were also taken into account. The ambition of the transdisciplinary team in the AD-case thus was clearly one of open arms, embracing a broad diversity of actors and factors. Moreover the ambition stretched the horizon of scientific research to concrete policy action plans. In the EE-case the ambition of the interdisciplinary team seemed largely limited to science: scientific experts assessing state of the art scientific insights. Nevertheless, initially the knowledge produced in the process was intended to be used in a policy context, rather than in a research context. The horizon in this case thus was also broadened from science to policy. Moreover difference of opinion amongst experts was considered potentially valuable information for policy makers, thus opening the visor to diversity of viewpoints.
Embracing relevant actors and factors cannot do without a procedural and structural way of working: structuring interaction and content and as such complexity. Without structure one runs the risk of endless research and discussion. In the AD-case a practice cycle was developed in which the process was streamlined from organisation of the procedure to the final choice of policy priorities: which actors were supposed to play which role, in which phase and based on which factors. Moreover as an analytical red thread a multi criteria analysis was used by which the diversity of (to a large extent incommensurable) information and opinions could be both embraced and structured so as to fit next steps in the process. In the EE-case the use of confidence levels by means of an online questionnaire initially formed the structuring backbone of the approach.
### Historical identities and the art of negotiation
An openness to and respect for differences and diversity by embracing critical mass in the process of *critical complexification* has to take into account that actors involved have different identities. Identity is to a large extent determined by the social context, be it professional, be it private. In both the AD-case and the EE-case the professional background played important roles. As Ulanowicz \[[@B33]\] points out that systems differ according to their history, so do professional contexts differ in professional tradition. Obvious examples are differences between quantitative and qualitative scientific approaches, between a focus on knowledge and a focus on action, between natural sciences and social sciences, between science and policy. The teams cooperating in both cases had to undertake a lot of negotiation during the process, the importance of which is often underestimated both in terms of impact on the process and its output, but also in practical complexity. The richness of dialogue can be very beneficial to a broader and more integrated view on complexity, but it is not always easy. The mindsets of actors from specific contexts remain largely influenced by and focussed on their home-base contexts, and only to a lesser extent to the new joint context. This is beneficial from the point of view of specific expertise, and this is needed. But it can become problematic in the perception of other expert contexts: one is full of one's own expertise and related complexity, and has only limited sight of the complexity of other expertise, and in fact often underestimates this. This to a large extent cannot be avoided, as experts are often overloaded with complexity from their own context and are constantly attracted by context specific interests, rewards, challenges. This also means that the openness towards other forms of expertise is limited, as they only have limited attention for it and only limited interest. The transferability of expertise from one context to the other is possible of course, but will be more difficult once experts' contexts differ more. This poses the question whether we should invest in transfer of context specific expert knowledge to other expert contexts, or that we should focus on cooperation in well balanced inter- and transdisciplinary teams. From the experience of the social scientific contribution in both cases it can be concluded that teamwork currently is absolutely necessary. Even after years of intense cooperation, natural scientific colleagues often still do not have clear sight of the complexity social science deals with. This would make a plea for constant and direct involvement of social scientists and in fact to the notion of the old saying: 'Let the cobbler stick to his last'. This also holds true for transdisciplinary cooperation between scientists and policy makers.
In the EE-case there was intense debate on whether the 'I don't know option' should be included in the questionnaire for the experts that were to be consulted on their confidence in the state of the art of science. Opponents mainly worried about low response rates and thus mainly took a quantitative perspective on this: the 'I don't know option' would provide the consulted scientists an easy way out of difficult questions, thus lowering the response rate for specific questions. Proponents stated the 'I don't know option' to be important from a qualitative perspective: it would allow analysts to know better if they measured knowledgeable answers or forced and perhaps partly unknowledgeable answers. The proponents considered environment and health issues too complex to expect all scientists to know enough about all relevant aspects in the causal chain from exposure to health effect that was to be addressed. In the end it was decided not to take up the 'I don't know option', thus the 'quantitative camp' won. Afterwards though, some scientists that were consulted in the expert elicitation said they sometimes felt rather uncomfortable due to absence of this option. This example shows how different scientific backgrounds may have completely different perceptions of research quality. When cooperating, they do not always find it easy to reach consensus, and in fact, in this case, it was impossible: both options excluded each other.
### Ambition dynamics
In the AD-case elements of *critical complexification* were introduced by the social scientists: introducing other relevant actors/factors and critical reflection from a problem solving perspective. These aspects were relatively easily agreed upon by the natural scientists and policy makers. Trying to bring ambitions into practice however creates new dynamics that may cause a boomerang effect. Once the application in practice creates pressure on their work (e.g. time pressure, pressure on their role as experts, practical pressure by complicating their own or the joint effort) the enthusiasm of natural scientists and policy makers often was overshadowed by concern for practical and analytical constraints. The ambitions thus are not necessarily stable: developments were never linear or predictable or in one direction and ambitions may always be disputed. The dynamics of ambitions in practice may also take another turn though in that new developments in practice may stimulate ambitions that support a *critical complexification*. In the EE-case initially it was the ambition to encompass all aspects from pollution to health impact, including societal impact. In practice nevertheless the societal aspects hardly got any attention. At a later stage due to interdisciplinary reflections on this gap, some of these aspects were touched upon by integrating a problem solving perspective. Ambitions as such also can have a stimulating impact on a *critical complexification* of practice and thus are strategic in this respect.
### Complexifiers: Trojan horses and other strategies
An essential element of the *critical complexification* of practice was a strategic way of working. An important strategic move in the first stages of the AD-case (the conceptual design phase) that proved to be of decisive importance was an active listening approach: the use of an internal reflective questionnaire. At first the practical relevance of *critical complexification* as such proved difficult to agree upon by the colleagues from natural science and policymaking. However, when elements of *critical complexification* were presented by means of open questions in an in-group questionnaire (who are relevant actors and factors?), based on the group results these elements gained support. In fact, it led to a breakthrough in the conceptual development process and formed the basis for the practice cycle in which questions of openness to relevant actors and factors were pragmatically dealt with. As such the internal reflective questionnaire can be seen as a *complexifier*: an element that will have a catalyst effect on the process of *critical complexification*.
In the EE-case the problem solving turn from mainly focussing on overcoming gaps in science to overcoming gaps between science and policymaking was triggered by using references to ambitions as *complexifiers*. The social scientist involved in the project while trying to introduce a *critical complexification* perspective, realized it was not easy to convince the principal coordinator of the EE-case. The potential benefits of *critical complexification* were countered by pointing out practical complexities that would put further pressure on what in itself was already quite a challenging pioneering endeavour, let alone put pressure on the loyalty to the expert elicitation project of the natural scientists in the team. The social scientist used reference to ambitions that were part of the initial project aims, be it mainly dormant, and ambitions from the professional background of the principal coordinator of the project as *complexifiers*. He pointed out the initial ambition of policy relevance of the project as an argument for integrating a problem solving perspective. Also he referred to two grand old men in the field of environment and health for whom he knew the coordinator had high respect, and who promote a problem solving turn in the field of environment and health \[[@B8],[@B9],[@B11]\]. Being part of the project one of them in fact had criticized the absence of a clear problem solving perspective in the early phases of the project. The fact that idealistic ambitions are often not easily applied in practice thus does not withhold them from being used as *complexifiers*: from a dormant or Ten Commandments' status to becoming seeds of practical change and inspiration. Apart from being an example of how ambitions can be *complexifiers*, the EE-case example also exemplifies how an outsider perspective can function as *complexifier*: the social scientist joined the project at a later stage, thus as a newcomer could reflect on the work in progress from some distance. Another example of the strategic impact of outsider perspectives is the use of external (outside of the team) feedback on the process. In the AD-case all external actors contributing to the project were asked for their feedback on the project. The vast majority evaluate openness to outsider perspectives and diversity of actors to be worthwhile. This is of course a bonus for those organizing such processes and for the end-user of the outcomes (e.g. policymakers). Simultaneously this can be perceived both as a stimulus and a pressure for prolonging such openness.
Experience from the AD-case shows that negative connotations may also be the result of strategic behaviour, resulting in what we in retrospect may characterize as a *Trojan horse strategy*. By joining conceptual discussions on policy interpretation of scientific research outcomes and reflecting on the ambitions of both natural scientists and policy representatives step by step from an active listening approach the role of the social scientist evolved to one of more central importance. The characterization 'Trojan horse' is mirrored in the expression of one of the senior natural scientists involved, saying she (on the level of ambition) approved of the social scientific contribution (which is in the AD-case in fact one of *critical complexification*, and as such is a *complexifier*), but she sometimes felt like an object of some social scientific experiment. Colleagues with natural scientific background sometimes react as if they feel lured into unexpected complexity, unknown to their expertise, difficult to handle and sometimes confrontational, and they either question its usefulness or appear to be unable to articulate the benefits themselves. This is also reflected in the often heard concern of the natural scientists and their counterparts in policy making that the *complexifying* approach is relevant and interesting but should not stand in the way of the research or policy agenda and should not complicate the already complicated research and policy endeavour. In the section on quality (see below) we will return to this issue. First we focus on methodological aspects of *critical complexification*.
### Method: path finding
According to Morin \[[@B6]\]*'the method emerges from the research'*. Here the word method is used in its original meaning as path, indicating that only in travelling the right method appears. This connects well to learning by doing and negotiation, as well as with the diversity of relevant elements of complexity taken into account in *critical complexification*. This does not mean that practice is sacred and methodologies and reflections from methodological expert debate are only of secondary importance. It means that they complement each other so as to serve the ambitions chosen for the endeavour and the challenges posed by practice along the way. The nature of complexity moreover challenges what we might call textbook approaches of strict and unambiguous application of methods, almost as if they should be applied regardless of complexities, of that which cannot be captured, controlled or foreseen completely. With respect to method and complexity the distinguished methodological thinker Patton \[[@B34]\] refers to the following metaphor used by Gleick \[[@B35]\] to explain the very nature of inquiry into chaos: *"It's like walking through a maze whose walls rearrange themselves with every step you take"*.
In the *critical complexification* of practice, dealing with unforeseen complexities and imperfections poses important challenges. Flexibility is essential: the need for context specific manoeuvre also from a methodological point of view. In fact, to a large extent methodological developments are part of the process and contradict the usefulness of a Bible belt approach of strict application of rigour. Moreover flexibility shows in a pluralist approach of using a diversity of methodological concepts whenever considered appropriate: e.g. a diversity of participatory approaches (e.g. the analytical deliberative approach, extended peer review, expert elicitation and participatory evaluation) and analytical approaches (e.g. multi-criteria analysis and qualitative analysis). The concepts of mixed methods and triangulation provide a conceptual basis for this eclectic praxis. Compared to single approach designs, mixed methods research is better equipped for complexity and provides opportunities for presenting a wider range of divergent views \[[@B36]\]. Quantitative methods provide relatively standardized, efficient, amenable information, which can be easily summarized and analyzed. Qualitative methods add contextual and cultural dimensions, which deepen the study by providing more natural information. Combining these two can thus be considered a 'third approach' \[[@B37]\]. Triangulation has been broadly defined by Denzin \[[@B38]\] as *'the combination of methodologies in the study of the same phenomenon'*, incorporating both quantitative and qualitative approaches. The concept of triangulation is helpful not so much as to increase the validity of our findings in a conventional, positivistic sense, but rather as a strategy that allows new and deeper dimensions to emerge. One might get a fuller picture, but not a more 'objective' one \[[@B39]\]. Triangulation facilitates more in-depth-understanding in that it can capture a more complete, holistic, and contextual interpretation of the complex relation between environment and health within the complex social context of disciplines and stakeholders.
In the AD-case the practice cycle developed for the procedure of policy interpretation of research results is an example of this eclectic praxis within the general framework of an analytical deliberative approach: it combines several methodological elements within one process, in which both quantitative and qualitative data and assessment play a role, both expert elicitation and stakeholder consultation, and in which a diversity of relevant actors and factors is combined with multi-criteria and qualitative analysis. The EE-case also exemplifies the use of a diversity of methods: a mainly quantitative questionnaire with confidence levels on state of the art science, a mainly qualitative questionnaire with respect to the weight of knowledge for policy action and an expert workshop based on the outcomes of both questionnaires.
### Quality: challenges and balances
Dealing with complex issues per definition bears the burden of imperfection. Whatever comforting concepts may promise, real life complexity will take its messy toll once travelling from conceptual ambition to real life practice. Practice is messy and stubborn and the scientific method incapable of total control. Moreover conflicting scientific standards and traditions may pose insurmountable ambiguities. A challenging issue in this respect is quality: how can we assess the quality of important but imperfect information. How can we assess the quality of a process of *critical complexification*? How can we balance ambition, importance, practicalities and imperfection? With respect to evaluation of analytical deliberative (or likewise) participatory processes objectifying quality criteria is considered to be very difficult. Renn and Schweizer \[[@B40]\] point out that the diversity of concepts and background philosophies is one of the reasons for this. Rowe et al. \[[@B41]\] conclude that the complexity of participatory processes makes it difficult to identify clear benchmarks for evaluation. Rauschmayer et al. \[[@B42]\] stress the fact that such processes involve a diversity of actors, and as such a diversity of preferences, also from the point of view of process evaluation. This may lead to the fact that process outcomes are valued differently from different actor perspectives. They propose the use of participatory evaluation.
Processes of *critical complexification* have similar characteristics regarding quality assessment. Practical complexity illustrates how *critical complexification* cannot be judged unambiguously: the fact that practice of *critical complexification* is difficult can be seen positively as a necessary and bold challenge and negatively as an insurmountable obstacle or even a threat. On the one hand the ambition of *critical complexification* may be severely challenged by those who are taken by surprise by the (sometimes drastic and often underestimated) practical consequences for their own work and expert status. On the other hand, a positive effect of taking complexity on board is that this will enhance the realistic character and better facilitate a problem solving perspective. Moreover it may be the only way to deal with complexity, implying that dealing with complexity and respecting complexity per definition will be practically complex, leaving no other alternative than leave it untouched. In fact, in the AD-case several participants in the process as well as some international experts reviewing the project, stated that it will lead to a more efficient translation of scientific knowledge in policy actions, thus can be seen as an investment in quality that will potentially have positive returns. As one of the policy representatives in the AD-case pointed out when reflecting on the rather complicated procedure being proposed in the beginning: "*It looks rather complex to me*, *but I cannot think of any alternative in order to better deal with the challenge* (HK: translating environment and health science into policy action) *ahead of us*".
Conclusions
===========
We proposed the concept of *critical complexification* as a companion of alternative boldness: embracing complexity in a realistic and problem solving manner. Simultaneously we have to be pragmatic: we have to have the courage to make choices, thateven though imperfect, will open windows of opportunity of dealing with complexity in respect of both complexity and diversity of viewpoints on complexity. We cannot present a recipe for *critical complexification* or define it like a definition of the speed of light, of a 'how to boil an egg'. Neither can we present an easy approach. Perhaps we best take *'Zen and the Art of Motorcycle Maintenance: An Inquiry into Values'*\[[@B43]\] as a source of inspiration for a combination of traditional and critical complexity science, and at minimum perceive is as an invitation for necessary dialogue and cooperation. Critical reflection on current environment and health science and policy is needed anyhow. Imagine a doctor (environment and health expert) and a patient (polluted society): should the doctor reside to individual ever more specialized diagnosis even though the patient shows serious health complications?
List of abbreviations used
==========================
AD case: analytical deliberative approach case; EE case: expert elicitation case; HENVINET: Health and ENVIronment NETwork; IARC: International Agency for Research on Cancer
Competing interests
===================
The author declares that he has no competing interests.
Acknowledgements
================
The work has been funded by the EU FP6 coordination action HENVINET, contract no 037019. Thanks to Margaret Saunders (University Hospitals Bristol NHS Foundation Trust, United Kingdom) for editing the English.
I sincerely thank Harry Kunneman (University for Humanistics, Utrecht) for his inspiring and stimulating support for writing this paper. I also sincerely thank Adri Smaling (University for Humanistics) and Lou Keune (University of Tilburg) for their critical constructive feedback along the way. Furthermore I thank my colleagues of the EU FP6 HENVINET project and the Flemish Centre of expertise for Environment and Health for their cooperation in the case studies to which the paper refers. I want to also thank the reviewers, Janna Koppe (em. Prof. of Neonatology University of Amsterdam), Paul Cilliers (University of Stellenbosch) and Peter van den Hazel (Hulpverlening Gelderland Midden Public Health Services, Arnhem), for their insightful comments. Finally I want to explicitly thank Harry Kunneman and Paul Cilliers for the inspiration of their thinking and work, and for the opportunity of discussing with them at the Critical complexity Conference in Utrecht in May 2010.
This article has been published as part of *Environmental Health* Volume 11 Supplement 1, 2012: Approaching complexities in health and environment. The full contents of the supplement are available online at <http://www.ehjournal.net/supplements/11/S1>.
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Serum albumin concentration in dialysis patients: why does it remain resistant to therapy?
Serum albumin, transferrin, and prealbumin levels decrease as glomerular filtration rate (GFR) declines, even prior to the start of dialysis. The levels of these serum proteins are also associated with creatinine levels and lean body mass. Lean body mass also decreases with advancing renal failure. While all of these measures are regarded as reflections of nutritional status, each are strongly associated with any of several indicators of inflammation: positive acute-phase proteins or the cytokines that regulate their synthesis rate, in both longitudinal and cross-sectional studies. Inflammation in turn is associated with comorbid conditions, cardiovascular disease, chronic infections, age, and vascular access type. Additionally, dialysis patients are subjected to oxidative stress and exposure of blood to foreign antigens in the dialysis process that also potentially contribute to inflammation. In otherwise healthy individuals reduced protein and calorie intake does not cause hypoalbuminemia since albumin fractional catabolic rate (FCR) and resting energy expenditure (REE) normally decrease in response. The simultaneous occurrence of decreased protein intake and inflammation prevent these homeostatic compensations to reduced nitrogen and energy intake from occurring, resulting in decreasing albumin, transferrin, and prealbumin levels and loss of muscle mass. Nutritional intake may also be challenged as a result of renal failure associated with anorexia, gastroparesis, and socioeconomic factors, which may all cause nutritional intake to be sufficiently marginal so that the combined effects of inflammation and decrease protein intake are expressed as decreased visceral and somatic protein stores. |
[Treatment of drug resistant destructive pulmonary tuberculosis: gemifloxacin and other fluoroquinolones clinical efficiency and tolerance at the end of initial phase of treatment].
Gemifloxacin efficiency and tolerance in comparison to the ofloxacin, levofloxacin and gatifloxacin during the intensive phase of the antituberculosis therapy for drug resistant cases was evaluated. 156 drug resistant TB patients were examined in the open, prospective, randomized research, being divided into 2 groups with similar drug resistance profile. The 1st group received gemifloxacin, the 2nd--other fluoroquinolones. Gemifloxacin efficiency in the treatment regimen for the drug resistant TB patients did not differ from the efficiency of the use of other fluoroquinolones of the 4th generation and was significantly higher in comparison to ofloxacin. At the same time the identical level of side effects was registered in the course of treatment with mentioned drugs. Gemifloxacin is effective and safe at treatment of tuberculosis in comparison to other fluoroquinolones that allows considering it as the drug of choice among fluoroquinolones for treatment of drug resistant TB, including multidrug-resistant TB. |
Various attempts have been set forth to seal lead wires or pins extending from a coil that is encapsulated within an overmolded plastic material. In some of these attempts, a cavity is formed within the overmolded material and the lead wires or pins from the coil extends into the cavity and a rubber grommet is disposed within the cavity. The lead wires extend through holes within the grommet and are sealed by a compressive force exerted on the outer circumference of the grommet. Many times, in these attempts, it is difficult to mold the plastic material around the leads extending therethrough. Many other arrangements are known for connecting leads to coils having overmolded material disposed around the coil. In these other arrangements, the leads that extend from the coil through the overmolded material may not be totally sealed from the outside atmosphere when being subjected to varying temperature. It is well known that when a coil is produced small voids are present after the winding is placed on the bobbin and the overmolded material is injected around the coil. During an increase in temperature, the pressure of the air within these voids expands thus producing an increase in pressure therein which, if not properly sealed, escapes around the leads that passes through the overmolded material. Likewise, as the temperature decreases, a pressure less than atmospheric is created within the voids. Consequently, if the leads are not properly sealed, air is drawn into the voids from the outside atmosphere. If the coil is being used in an environment containing contaminants, the contaminants are drawn into the voids and cause premature failure of the coil. Therefore, it is desirable to provide a positive seal around the leads so that contaminants cannot be drawn into the coil or sealed cavity. Likewise, it is desirable to provide such a seal arrangement to seal around other types of leads to protect sensitive components disposed in an otherwise sealed cavity from outside contaminants.
The present invention is directed to overcoming one or more of the problems as set forth above. |
Automated camera enforcement for alternate side and similar regulations, based on cameras on the front of plows and sweepers, is the best idea I’ve heard for a long time.
In fairness to the media as to all those stories about parking, if you absolutely must have a car in NYC or happen to have one because you once felt you needed it, parking IS an obsession. If you are a fortunate person, it is one of the worst things in your life.
It was great being able to just leave the thing there a few weeks while I got around by bike. And knowing the number of spaces is down because of snow piles, I rushed home yesterday to make sure I could get a legal space (got one a few blocks away).
http://secondavenuesagas.com Benjamin Kabak
The alternate side parking coverage from New York’s media is laughably idiotic.
J
If the Daily News is claiming victory, than we can put the issue to rest simply by adding back a few parking spaces. That is fine by me.
A 20-mph speed limit is a simple low-cost design change highly effective improving quality-of-life and most importantly, safety, to rapidly reduce the extreme dangers that automobiles present on public streets and the resultant monopolies; clearing the way for much more practical mobility solutions.
Marco
So, this seems like as good of a place as anywhere to post this, but I wanted to thank the pair of cyclists who stopped at the red on Sunday at 91st and Riverside. I don’t know if they read this blog, but the matter-of-factly respectful cyclist->pedestrian behavior that they exhibited changes *everything*.
http://www.livablestreets.com/people/Eric Eric McClure
Daily News: “Markowitz initially denied that Scissura had represented him – then claimed, when presented with contradicting documents, that the law applies only to lawyers working for the city as attorneys, not as chiefs of staffs.” |
Keith Packard wrote:> The Intel Open Source Technology Center graphics team is pleased to announce> the immediate availability of free software drivers for the Intel® 965> Express Chipset family graphics controller. These drivers include support> for 2D and 3D graphics features for the newest generation Intel graphics> architecture. The project Web site is http://IntelLinuxGraphics.org.
Very cool, and I definitely applaud Intel for supporting open source here. A couple questions...
* is the 3D stuff available from git somewhere? The download filename includes "-git-", but the checkout instructions reference cvs.
* is anyone working on a more dynamic GLSL compilation system? i.e. a "JIT", in compiler technology terms. |
22.10.11
Gestalt Programme Launching Event
by Ishrat HyattInternational The News, October 22, 2011, City News, p. 19
ISLAMABAD. The Ambassador of Switzerland and Mrs Regula Bubb hosted a function to mark the opening lecture of the Gestalt Educational Programme, which is being supported by the embassies of Switzerland and Germany.
The series of fifteen educational lectures, training sessions and workshops by Argentinean artist, Mariano Akerman architect and historian, Summa cum Laude, has been conceived especially for Pakistani audiences. Focusing on the Swiss-German contribution in the fields of theory and design, it aims at sharing experience and reconsidering the interplay between tradition and modernisation, over 2,500 students have been invited to participate from educational institutions around Islamabad and Rawalpindi.
Ambassadors Bubb and Koch, with the lecturer
After invitees representing the arts had arrived and were seated, the host welcomed them and said he and his wife were delighted to host the event which would showcase the artistic achievements of the great artists from his country as well as neighbouring Germany. He thanked the ambassador of Germany, Dr Michael Koch, for his help and collaboration and said it was so readily forthcoming that he was tempted to ask for it more often. With a few words about the Gestalt programme, he thanked the speaker for his contribution and asked him to take the floor.
Lectures by Mariano Akerman are never boring and you can listen to him for more than the usual length of time even though the subject may not be your cup of tea. His talks combine facts and figures with touches of humour and just a little spice in the form of taking a dig at people and places—in the nicest manner—thrown in for good measure, much to the delight of the audience. The students who attend his series in connection with the Gestalt programme will enjoy his style, probably compare it with that of others and generally come away with a greater understanding of the subject under discussion since he encourages his listeners' participation.
Mariano began by saying he had been in Pakistan for five years because he had a passion for art and because he has been inspired by the interest Pakistanis display in his artistic activities. "When people in Argentina ask when I am coming home, I reply home is here," he said. "Because I feel at home among my friends."
Mariano Akerman: Bridging Cultures
With a slide show to emphasise the points he made, Mariano began by speaking of European art of the 20th century, in particular the period of the Weimar Republic from 1918-1933; its ups and downs especially the economic downside between 1921-23 and the golden years from 1924-29 when there was a switch towards change of accepted norms and practises. It was interesting to hear and see the comparisons he made and how he explained what modern art was all about [...].
In a statement, Mariano says that the Gestalt theory and Bauhaus design are two of the important themes to be explored in this cycle of fifteen lectures, training sessions and workshops. Figure and ground, chance and intention, form and function, the rational and the irrational, repression and expression are discussed [in the Program], which reconsiders the modern idea of form and function integrated in a single, effective whole.
Yet, significantly, close observation may reveal that modernity is not only based on functionality and common sense, as it may present surprises too. Besides, is ornament a crime? Tradition has often associated it with identity. Can abstraction and mass-produced fabrications provide it? And what is the common raison d'être supporting the work of German-Swiss creators so diverse as Walter Gropius, Arp, Alberto Giacometti, Le Corbusier, Meret Oppenheim, Mies van der Rohe, Johannes Itten, Paul Klee, and Max Ernst?
A possible answer is that it was precisely around the 1920s that such inventive creators provided us with the best of Modern Art. Following their example and being characterised by its experimental nature and full-of-prizes collage contest, The Gestalt Programme aims to open a window towards the achievements of geographically and historically distant cultures, stimulating local productivity and inventiveness, without rejecting ancestral traditions.
28 comments:
Nicolas Plattner
said...
The Gestalt series of lectures by Mariano Akerman is an opportunity to bring a most significant European movement closer to the Pakistani audience. Indeed, experimentation and new objectivity are concepts which have shape European modern cultural identity. As always, Mariano Akerman's formidable knowledge of the art and his exceptional ability to captivate a wide audience will be beneficial for students and teachers alike, bringing the Gestalt closer to their own reality. The message conveyed by Klee, Le Corbusier, Arp, and other prominent artists and architects who have animated the Gestalt and Bauhaus is very much actual in today’s world. —Nicolas Plattner, The Swiss Embassy, Islamabad
Dear Mariano, I don't feel that the Gestalt Program is about "distant" cultures since you bring a sense of how some things keep going on ahead, despite and because of the darkest and worst of times, together with a sense of your own mission here—of promoting what is useful and good with reassurances about the capacity and predominance of the human holistic mind, to fill in the missing contextual gaps and links and look to the overall meaningfulness of the larger picture. During the launching lecture of the Gestalt Program people felt you made history come alive for them and made it feel relevant with your exposition on the life of the two schools, Gestalt and Bauhaus, their personnel, ideology and implementations that impacted not only Europe but the world. And they loved your "style" of delivery and the images you put together, they listened, they looked and were held by it all. And found it well, considered and amusingly presented by you, and interesting, stimulating and thought provoking for them, I'm sure. Well done!
I think it was probably the best lecture I have heard and see you do. You were right on form; able to blend your knowledge of the subject with great visual presentation, humour to those of us who perhaps didn't know anything about Gestalt.Your ability to combine, connect, integrate and transfer knowledge to the audience goes way beyond what many professors could do.
Dear Mariano, thank you. I agree the evening was a great success, primarily thanks to your competent, well structured presentation. The holistic approach and the humorous elements contributed to a fascinating learning experience. With kind regards and my best wishes for the series.Christoph Bubb Ambassador Embassy of Switzerland, Islamabad
Dear Mariano. I want to thank you for the wonderful lecture you gave last Thursday. You were brilliant and it is amazing how many things you know. Thank you for sharing this with us: I enjoyed it so much. I would like to participate in more of you lectures.I am sure you'll have a huge success. Good luck! Kind regards, Liuba
Your lectures have made me to come to the conclusion that Gestalt really works in every field. Especially the Form and Function topic has real implications in our lives. Moreover, your lectures really urge one's mind to negotiate and discover something abstract from one's inner self. Thanks for all the new seeds you have cultivated in our minds. I am sure one day their fruit will enlighten the whole world with a name: Mariano Akerman.
Media
documenta
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Sunday, May 30, 2010
As a rule of thumb, movies based on video games are poor in quality, as are video games based on movies. The movie, Prince of Persia: The Sands of Time, may actually be the best movie based on a video game ever made, though we will certainly understand if fans of the Resident Evil franchise wish to file an objection. But 'best' does not always equate to 'good', not that either is necessary for a movie to be enjoyable. Prince of Persia is, at the very least, one of the best video game movies out there, and is certainly enjoyable.
It's still not all that good.
But this is far from enlightening. What's most intriguing about this film is that, in approaching good, we have finally determined to our satisfaction why it is so difficult for movies derived from video games to cross that threshold. We have heard it said, from time to time, that video game plots lack the substance or the complexity to be developed into good movies. Yet the game this was based on has a far more developed plot than, say, the Pirates of the Caribbean ride that gave birth to that franchise. And those movies - especially the original - are far better than this.
The difference between them is that the filmmakers who crafted Curse of the Black Pearl sat down and answered a single question: "What do you mean by 'based on'?"
It is the question all adaptations must confront, and it is likewise the question that tripped up Prince of Persia. Is this adapted from the game or merely inspired by?
The video game actually has a surprisingly thoughtful story. It's not really a complex story, but it's thoughtful nonetheless. While the game also deserves praise for its design and action sequences, the plot is what ties it together.
However, that plot is ultimately limited to three characters: the prince, the princess, and the vizier. While such reductionist stories may function well in game environments, it's difficult to craft an entertaining film from such a skeletal structure.
So, when transitioning from game to movie, they abandoned the story entirely, opting instead to base their film on imagery and sequences from the game. And this is where the film floundered. While the sets and fights were certainly amusing, there was a sense in which the movie felt shackled to its source. If you've played the game, than you've seen these environments. You've explored them, in fact, in more depth than the movie has time to. You've used the Dagger of Time and have mastered it. Watching its application in the movie is somewhat akin to seeing a child pick up the controller without learning the controls first.
Meanwhile, the back story has been entirely changed to better appeal to a wider audience. The original portrayed the prince as spoiled from birth: the events of the game teach him the meaning of consequences and the significance of responsibility. Rather than deal with such complexity, the filmmakers have re-imagined him as a street thief who was adopted by a wise and benevolent king. The arc we're left with is of a man who begins the movie as a brave and noble warrior and ends as a warrior who's learned to trust his already brave and noble heart.
In some ways, this is as much an adaptation of Disney's Aladdin as it is Sands of Time. Ultimately, though, a live-action Aladdin starring Jake Gyllenhaal and Alfred Molina as the genie would probably have been a better film.
In addition, the princess from the game had more depth than appeared here. It didn't help that her animosity towards the prince seemed misplaced here, as Gyllenhaal was, as previously mentioned, brave and noble from the start, and was clearly as much a victim of circumstance as she was. As a result, her continued attempts to ditch or, on one occasion, murder him, come of as foolish, petty, and anti-productive, hardly an appropriate portrayal for the sole female character with a name.
In attempting to skirt the line between allowing themselves the freedom of being inspired by the source material and trying to faithfully adapt the game environments and ideas, the movie leaves fans of the game stranded between what we've already seen and what we miss. There's not enough new to intrigue us and too little of what we loved about the game for us to fully enjoy as an adaptation.
Compare this with Pirates of the Caribbean, which playfully tipped its hat to its inspiration then moved on to a new story, new settings, and new characters.
This isn't to say there's nothing to enjoy. Ironically, we actually did enjoy this film, thanks to the solid acting, amazing sets, and exciting action. We enjoyed it throughout, but, aside from the first big battle and the flashback to the young Dastan, we never loved what we were seeing.
Perhaps, if it should manage a sequel, Prince of Persia will be able to find its own footing. Certainly the elements are in place: Jake Gyllenhaal is a fantastic choice for the role. Now that its dues to the game have been paid, we'd love to see an original swashbuckling adventure story in this world.
Such prospects seem unlikely, however, as the theater we went to was mostly empty. There's little indication this will make enough to warrant another picture.
This movie clearly wants to be Pirates of the Caribbean, so it seems only appropriate to grade on that curve. If Curse of the Black Pearl is a five star film, than Sands of Time is good for two and a half.
Ironically, if you've never played the game this is based on, you're likely to enjoy the setting and fights more than we did. This isn't bad for an adventure movie - it manages to retain a quick pace and light tone throughout. But, frankly, with movies like Iron Man 2 in abundance, we have higher expectations.
Thursday, May 20, 2010
Every year The Middle Room attempts to look towards tomorrow, to predict, with what we hope is near-perfect accuracy, the quality of films yet to come. And, with few exceptions, we typically embarrass ourselves.
Last time, we considered the opening films of summer, but now we must gaze further into the haze of the future and June.
Half of July will be thrown in for good measure.
The A-Team (June 11)
Estimated Tomatometer: 40%
The quality of this film will likely be directly proportionate to the number of times they play the original theme song during the course of the movie. The trailer offers an uneven impression: we're thrilled to see this level of absurdity, but not impressed with some of the CG effects, particularly connected to the falling tank. Even so, this movie has certainly caught our interest.
The Karate Kid (June 11)
Estimated Tomatometer: 55%
While we don't have plans to see this, the fact that two remakes from the eighties are opening the same weekend is worth noting. We don't have anything against the trailer to this movie, actually. A remake of the Karate Kid certainly seems unnecessary, but it certainly appears to have been made in the spirit of the original, even if the martial art in question has changed.
Jonah Hex (June 25)
Estimated Tomatometer: 45%
Divided into its components - into the cellular units the film is constructed of - it is difficult to explain why we are not more excited about this movie. However, the previews offer us little hope that Jonah Hex will deliver an experience equal to its source material. The cause for this discrepancy is fairly straightforward: the filmmakers seem to have approached the character and concept as being comical, when there are few characters who should be treated as seriously as Jonah Hex.
That said, the most venomous insult thrown at Jonah Hex appears to be that it may be no better than Wild Wild West, and despite its many flaws, we kind of enjoyed that film. Regardless of our impression, we doubt critics will be forgiving.
Toy Story 3 (June 25)
Estimated Tomatometer: 99.8%
Neither installment from the Toy Story franchise rates highly on our list of favorites from Pixar. That said, the films are still produced by a company whose worst films exceed the best produced by their rivals (yes, even Cars). On top of that, Toy Story 2 was an improvement on the first. These characters are beloved by the filmmakers, and there is every indication that the third may improve on its predecessors.
While we often disagree with critics on many issues, we generally find ourselves in agreement when it comes to Pixar. Our estimate may be slightly optimistic, but we doubt we'll be off by more than a percentage point or two.
Twilight Saga: Eclipse (June 30)
Estimated Tomatometer: 25%
Before we go on, allow us to assure our readers that we will not see Eclipse. Even if it were to garner critical approval and strong word of mouth recommendations, we are less than eager to sit in a theater surrounded by that many teenagers.
That said, this is movie about vampires and werewolves (or at least things resembling vampires and werewolves), and and as such is, technically, a film related to geek interests. For this reason, we include it on our list, despite the fact the trailer managed to lower the bar on vampire/werewolf fighting with what may be the dullest looking battle sequence imaginable.
Van Helsing seems better all the time....
The Last Airbender (July 2)
Estimated Tomatometer: 50%
It is no coincidence that our estimate falls in the dead center of the scale: the simple fact is, we do not know what to make of this film.
Our thoughts on M. Night Shyamalan are in the public record. While we'd like to believe he's capable of once again crafting a worthwhile production, it's been a long time since such faith was rewarded.
However, the trailers have some promise. Certainly, it's easy to be underwhelmed by some casting choices, but the effects and stylistic choices cannot help but inspire some optimism. And yet, we recall being intrigued by the trailer for The Village.
Our estimate is a shot in the dark; an admission of uncertainty which guarantees we won't miss our mark by more than 50%. We expect our decision to see this will be determined more by word of mouth than by reviews, but we will pay attention.
Predators (July 7)
Estimated Tomatometer: 88%
Are we being optimistic? Perhaps. There is, generally speaking, a law of diminishing returns for the quality of sequels to R-rated movie franchises. But every indication we've seen tells us this will be an exception. More than that, we have a feeling, an instinctual sensation in our gut, that this will bury the Alien Vs. Predator films and surpass at least Predator 2 (a solid picture) in quality.
Time will tell.
Despicable Me (July 9)
Estimated Tomatometer: 45%
With all due respect to the honorable Steve Carell, the trailers for this have been passable at best. While we haven't seen anything offensively bad in connection to this, nothing has struck us as unusually good, either.
If our estimate proves low by forty points or more, we may see this. Barring that, we've little interest in another CG movie without the talent of Pixar behind it.
When next we gather to discuss this subject, we shall leave no reel unturned. Yes, the third installment shall be the last, and our gaze shall be cast all the way to the end of summer.
Friday, May 14, 2010
Many claims have been made about Ridley Scott's Robin Hood. While some are accurate, as many or more are misleading in nature and can lead to confusion about the nature of the film. In the interest of the public well being, we in The Middle Room have decided to dedicate some of our review to rooting out such misconceptions and setting them right.
This is, in essence, the educational portion of our review, and we will be quite upset if we don't begin receiving some form of federal funding as a result.
It has been said that, in this movie, Ridley Scott is attempting to relaunch Robin Hood in the same vein that Batman Begins or Casino Royale relaunched Batman and Bond. While there's a kernel of truth to this claim, it fails to fully convey the experience of the film. The movie may have been shot as if it were a dark and gritty picture, but the writing - and, in many cases, the acting - are another animal entirely.
Imagine, if you will, that the script to the Adam West Batman movie had been picked up by Christopher Nolan, then filmed in the style of The Dark Knight. Christian Bale is still Batman, and he reads every bat-line in the same raspy voice he's known for. The lines about bat-shark repellent and not being able to get rid of a bomb are still there, but they're spoken without humor. Also, the role of the Riddler is played by Frank Gorshin.
Switch the Bale to Crow, Gotham to Nottingham, and Riddler to King John, and you've pretty much described this movie in a nutshell. The only exception is the plot: the story in the Adam West Batman movie made more sense. Far more sense, in fact. More on this in a moment.
It has also been said that this was intended as a more historically accurate version of Robin Hood. This is blatantly false on more counts than we can easily count. There may be accurate props, the costumes may be somewhat more believable, and the setting may be more truthful, but overall this no more historically believable than Robin Hood: Prince of Thieves. Or, for that matter, Men in Tights.
If we're mistaken, than our high school world history teachers have some explaining to do.
This is, frankly, not a good movie. That said, it's not an altogether unenjoyable movie, provided you are willing to dispense with notions like continuity and logic. Characters have a tendency of instantly traveling great distances between scenes. The plot folds over on itself; there is little causal connection between one event and the next, nor is there much in the way of consequences. Meanwhile, characters will occasionally know things in one scene they did not the moment before with no explanation.
This is a movie permeated by images and ideas that feel eerily familiar. Moments echo from other movies you've seen. Sure, there's the obvious tipping of the hat to other Robin Hood films and the expected borrowing from Lord of the Rings and Braveheart, but then Darth Maul shows up and betrays England. And let's not forget the tribe of Lost Boys living in Sherwood. Or the scene from Saving Private Ryan. And none of this comes close to the bizarre echo of Queen Elizabeth: The Golden Age that occurs in the final battle sequence.
Also, we finally learn where the Joker got his scars.
It's easy to have fun watching this, though much of that fun comes at the movie's expense. It's entertaining, for example, to see Alan Doyle from Great Big Sea playing Allan A'Dayle, but he's still singing modern interpretations of folk music. And Oliver Isaac's Prince John is more or less identical to that of the talking lion in Disney's interpretation. Seriously. Watch the first minute or two of this.... then watch this. IT'S THE SAME SCENE.
Our reaction upon walking out of the theater was to ask, "What the hell was that?" We've yet to work out an answer. Was this supposed to be campy? If so, then why film it like it's a historic epic? It's almost as if Ridley Scott either couldn't decide or didn't care what he was making. Is this an update of the Robin Hood of the 1930's? If so, why tell a prequel?
Fortunately, for all its faults, there was plenty of beautiful imagery and solid action to keep us diverted. On the Chronicles of Riddick scale, we'll award this two and a half stars out of five. This was amusing, but, as a ridiculous, medieval prequel adventure with the pretense of serious realism, it falls short of Underworld: Rise of the Lycans. Still, if you enjoy sword fights and the English countryside - as we do - it may be worth a viewing.
Even so, it's hard to endorse this when you could just go see Iron Man 2 again.
Saturday, May 8, 2010
The response from critics towards Iron Man 2 has proven less enthusiastic than we predicted. Fortunately, this discrepancy reveals far more about the critics than the movie itself. A quick glance at Rotten Tomatoes, where Iron Man 2 has earned a respectable, albeit underrated, 74%, offers some context for those who did not enjoy the movie. The primary complaint seems to revolve around plot, which many critics - including several who enjoyed the film overall - maintained was light.
It may surprise you to hear that we agree with this assessment. Where we disagree is in whether this is actually a flaw.
Iron Man 2 is not, strictly speaking, much of a movie in its own right. It doesn't portray the epic struggle between a hero and his nemesis. Sure, there's a supervillain, but he's little more than a minor inconvenience. Tony Stark has always been his own worst enemy, and the movie allows him to serve as both protagonist and adversary.
The events portrayed feel less like a plot than a series of disconnected incidents. The film doesn't even focus its point of view on Stark, but rather widens to explore those around him.
In essence, they've made a film about the Marvel Universe's relationship with Tony Stark. We've heard Iron Man 2 described as a bridge to future Marvel films, and again, there's some truth to this. Only the term carries associations with duller stories, and we find it hard to imagine seeing this as anything less than fascinating.
No, "bridge" is not the word we use. To us, Iron Man 2 felt like a feature length trailer for what's coming. Rather than trying to tell a single story, the filmmakers used Iron Man 2 as an opportunity to explore their universe, pulling in more and more characters and artifacts from their source material. They've offered a vignette of sequences and character arcs exploring the rich universe these films portray.
In comic terms, they've given us the issues between major story lines, the books offering context and development. From a production standpoint, nothing occurs in Iron Man 2 that couldn't have been skipped: they could simply have made the movie after this one and made veiled references to technological improvements, character growth, and relationships, and we'd have taken it at face value. That would have been the easy solution.
But they've done something less expected and more courageous. They've devoted a film to the depth of the Marvel Universe. And they certainly retained everything that made the first movie successful: Tony Stark's eccentric personality, the sense of adventurous fun, the comedy, and the awesome action scenes.
The issue is that movie reviewers are trying to compare Iron Man 2 with Superman 2. But this isn't the issue where Zod conquers Earth: instead, it's akin to stories about Clark trying to balance his job and friendships while dealing with threats from Toyman and Metallo. Iron Man introduced the shared Marvel Universe to theatrical audiences. Its sequel allows that Universe to take a starring role. Meanwhile, Robert Downey Jr. deserves an Oscar for his supporting role.
When we reviewed the first movie, we held it against the best modern superhero movies. Against the same competition, we give Iron Man 2 the same grade: 4 stars out of five. This is a worthy successor in this series, and, more importantly, a fantastic harbinger of what's coming.
Sunday, May 2, 2010
No day in the Geekorian calendar is as holy as the first Saturday in May. It is known by many names: Geek Christmas, Geek Independence Day, and, of course, colloquially as Free Comic Book Day. It is a day when anyone of any age can walk into nearly any comic book store in the country and receive one or more free comic books.
To the cynic, Free Comic Book Day is about nothing more than this: to them, it is a day about comics. But this is a flawed description. Certainly, comic books represent an important aspect to the traditional celebration of Free Comic Book Day, but there is certainly more to the day than mere comic books.
Indeed, we in The Middle Room maintain that were The Leader to steal every issue set to be delivered, Free Comic Book Day would come all the same. "How?" you may ask. Because there is a spirit to the day which cannot be stolen or dismissed.
It is the spirit of Getting. Yes, when you strip away the mass-produced covers and the dozens upon dozens of pages of ads, you find this kernel at the core of every book. If you look behind the grin of every young child clutching their first free bag of comics, you can see that glint in their eye: this didn't cost them a penny.
The store owners, priestly stewards of the holiday, perceive Free Comic Book Day at a different level: those books cost them money. But still, the spirit endures, because they are getting new customers. As are the publishers, who sell the comics at a loss in the hopes of getting new readers who will come back to hand over real money next time for the follow up issue chronicling the coming War of the Supermen.
In some ways, we consider Free Comic Book Day the most quintessentially American of all holidays. Sure, Christmas and Valentines Day have been blatantly distorted into a crass exploitation of commercialism, but the effects of these last for only a single day. Those behind Free Comic Book Day hope to manipulate readers - particularly new readers, children - for an entire year.
Or, if you're like us and are willing to stop by a few stores in New York City, you could well find yourself with a year's worth of free reading material free of charge. In one day, two agents sent from The Middle Room were able to procure 80 comics (39 unique books, 41 duplicates; one of which was signed by Jim Shooter and Dennis Calero), two buttons, one poster, and a War Machine Heroclix figure which will look great beside the Iron Man Heroclix figure we got a few years back.
So, in conclusion, we say to all of you in The Middle Room and beyond, happy Free Comic Book Day, and may Thor bless America. |
[Description of the stability of granules using nongrowth-related parameters].
Qualitative rather than quantitative method was available in the study of aerobic granular sludge. This work therefore investigated two systems, one was the conventional heterotrophic system without anaerobic mix period, the other was the phosphorous removal system with anaerobic period, and it was found that the latter was more stable from the point view of diameter, density and morphology. It was further found that the stability of granule was associated with the metabolic characteristics, i. e., the slow growth system showed more stability may be due to higher fraction of maintenance metabolic energy. In order to evidence that, different size of granule in the slow growth system was obtained for the metabolic character analysis. It was found that the maintenance coefficient m and the ratio of maintenance COD consumption ratio S(min)/COD(influent) was well correlated with the stability of granules. Consequently, it was proposed that these two parameters could be used for the quantitative description of the stability of granules. This study established a new method for the quantitative description of the stability of aerobic granules from the metabolic perspective, which improved the conventional qualitative methods in terms of morphology, diameter and density of granules. |
Q:
Google Drive REST API Documentation working directory
I'm following this instructions of QuickStart Google Drive REST API in PHP but in the part where say "working directory" I need to move the quickstart.php and client_secret.json but I don't know where is the working directory.
I'm using Windows Server 2012 R2 with Apache and PHP 5.6 and only I need to put these files in that working directory, not working in htdocs in Apache folder.
A:
Working directory can be any web accessible directory in htdocs folder, for example my_google_disk. But don't forget to restrict access to the client_secret.json file. You can do it in 3 ways:
1) The most simple will be to save client_secret.json contents in PHP string variable inside your script, for example:
$clientSecretData = '{...}' // client_secret.json data here
Then you just need to decode the contents of the variable to get JSON string as array as follows:
$clientSecretData = json_decode($clientSecretData, true);
2) You can save it in any web accessible directory (htdocs/my_google_disk, for example), but then you need to create .htaccess file in that directory and save there special directives for access control:
<Files "client_secret.json">
Order Allow,Deny
Deny from all
</Files>
After that, try to access this file by URL http://example.com/my_google_disk/client_secret.json (example.com = your domain name) and you'll see a 404 Forbidden error.
You'll be able to get data from that file in htdocs/my_google_disk/quickstart.php as follows:
$clientSecretData = file_get_contents('client_secret.json');
3) Save it inside directory, that is located a level higher than the htdocs directory, for example, C:\apache\private_files. private_files here must be not accessible by URL. Set this directory to include path in your script. Then you'll be able to get data from that file in your script from htdocs/my_google_disk directory as follows:
$clientSecretData = file_get_contents('../../private_files/client_secret.json');
|
Background
==========
Thrombocytopenia is a common treatment-related Grade 3/4 adverse event (AE) and dose-limiting toxicity for various chemotherapy regimens \[[@B1]-[@B4]\]. Doxorubicin and ifosfamide, alone and in combination (AI), are active in the treatment of soft tissue sarcomas (STS), with demonstrated positive response rates and improvements in overall survival; however, both agents have been associated with Grade 3/4 thrombocytopenia that is cumulative with successive chemotherapy cycles \[[@B5]-[@B10]\].
Chemotherapy-induced thrombocytopenia (CIT) may lead to dose reductions or dose delays, resulting in less than optimal disease control. In severe cases, CIT may result in hemorrhage and a need for platelet transfusions, which have cost and safety limitations \[[@B6],[@B8],[@B9],[@B11]\]. Although interleukin-11 (IL-11), a hematopoietic growth factor with thrombopoietic activity, is approved for the treatment of CIT in the US, it is not approved in the EU, it has modest efficacy, and it produces substantial adverse effects that limit its use \[[@B12]-[@B14]\].
Eltrombopag, an oral, nonpeptide, thrombopoietin receptor agonist, increases platelet counts in adult patients with chronic immune thrombocytopenia (ITP) \[[@B15]-[@B19]\] and chronic liver disease due to hepatitis C virus infection \[[@B20],[@B21]\].
A Phase II, multicenter, placebo-controlled study tested 3 different doses of eltrombopag vs placebo in patients with solid tumors receiving carboplatin and paclitaxel chemotherapy. The study demonstrated that eltrombopag administration for 10 days post-chemotherapy administration on Day 1 resulted in increased platelet counts starting at Day 8 compared to placebo, with peak platelet counts reached between Day 18 and Day 22 \[[@B22]\]. The study did not meet its primary endpoint of reducing the platelet count change from Day 1 of Cycle 2 to the platelet nadir of Cycle 2, compared to placebo \[[@B22]\].
Thrombocytopenia remains an important clinical problem in the treatment of cancer. As such, this study explored the safety and tolerability of eltrombopag administered according to 2 dosing schedules in patients with advanced STS treated with the AI chemotherapy regimen.
Methods
=======
Study design
------------
The primary objective of this Phase I study was to determine the safety and tolerability of eltrombopag in patients with locally advanced or metastatic STS receiving combination chemotherapy with AI. Secondary objectives were to determine the optimal biological dose (OBD), pharmacokinetics (PK), and pharmacodynamics (PD) of eltrombopag in these patients; and to evaluate the impact of eltrombopag on the PK of doxorubicin and doxorubicinol in this treatment setting.
The study protocol, any amendments, informed consent, and other information that required pre-approval were reviewed and approved by the sites where patients were recruited into the study: Western Institutional Review Board, Olympia, WA, USA; Institutional Review Board. Pennsylvania Hospital, Philadelphia, PA, USA; and the University of Texas, M. D. Anderson Cancer Center, Surveillance Committee FWA-363, Houston, TX, USA. This study was conducted in accordance with the International Conference on Harmonisation's Guidelines for Good Clinical Practice (ICH GCP) and all applicable patient privacy requirements, and the ethical principles that are outlined in the Declaration of Helsinki. This study is registered at <http://www.clinicaltrials.gov> (NCT00358540).
All participants provided informed consent prior to performance of any study-specific procedures. All patients were scheduled to receive 10 days of eltrombopag dosing starting in Cycle 2, either continuously for 10 days following AI chemotherapy (Days 5 to 14) or for 5 days before (Days -5 to -1) and 5 days after (Days 5 to 9) AI chemotherapy (Days 1 to 4). Each cycle consisted of 21 days. Doxorubicin was administered as a 75 mg/m^2^ intravenous (IV) bolus (Day 1) or as 3 consecutive 25 mg/m^2^ IV boluses (Days 1 to 3); ifosfamide was administered as a 2.5 g/m^2^ IV infusion for 4 days (Days 1 to 4). Mesna and dexrazoxane were administered as per the current standard of care.
The original study design included 2 components: a dose-escalation phase to determine the OBD of eltrombopag in combination with AI, with a daily starting dose of 75 mg eltrombopag and escalating in a stepwise fashion to 100 mg, 150 mg, 200 mg, 250 mg, and 300 mg daily; and an expansion phase to enroll additional patients at the OBD to a maximum of 48 total patients, in order to further explore the efficacy of eltrombopag in this patient population. Due to slow recruitment, dose escalation was halted at the 150-mg dose level prior to identification of an OBD, the expansion phase was not initiated, and the study was closed prior to completion.
Study completion was defined as receiving ≥ 1 dose of eltrombopag starting from Cycle 2 and completing all visits through to the end of Cycle 2. Patients were permitted to stay on study for up to 6 cycles of chemotherapy (5 cycles of eltrombopag dosing).
Patient selection
-----------------
Eligible patients were age 18 or older with histologically confirmed, locally advanced or metastatic STS; an Eastern Cooperative Oncology Group (ECOG)-Zubrod performance status of 0 or 1; adequate hematologic, hepatic, and renal function; a life expectancy of ≥ 3 months; no history of platelet disorders or dysfunction, or bleeding disorders; and were otherwise candidates for AI chemotherapy.
Study enrollment was initially limited to chemotherapy-naïve patients. A protocol amendment (January 2008) during the active enrollment period allowed enrollment of patients with 0 or 1 previous chemotherapy regimens and required that all patients had developed ≥ Grade 2 thrombocytopenia (platelet nadir ≤ 75,000/μL) in a previous chemotherapy treatment setting. Alternatively, patients with no previous chemotherapy treatment should have developed ≥ Grade 2 thrombocytopenia during a previous AI chemotherapy cycle, with AI at the same dose and schedule planned in the 2 cycles following enrollment into the study. An additional change in this amendment allowed enrollment for patients with thromboembolic events (TEEs) \> 6 months previously; prior to this amendment patients with a history of TEEs were excluded from the study. A subsequent (July 2009) protocol amendment required that patients have adequate cardiac function at baseline, as measured by echocardiogram (ECHO) or multiple gated acquisition (MUGA) scan, as newly available in vitro data demonstrated that eltrombopag was an inhibitor of breast cancer resistance protein (BCRP) efflux transporter, for which doxorubicin and potentially its metabolite, doxorubicinol, are substrates. As these findings suggested that eltrombopag had the potential to increase doxorubicin(ol) plasma concentrations, the protocol was amended to implement additional cardiac monitoring and PK sampling for doxorubicin(ol).
Patients were excluded if they had \> 1 previous chemotherapy regimens in any disease setting; preexisting cardiovascular disease; any known clotting disorder associated with hypercoagulability; prior treatment that affected platelet function or anticoagulants for \> 3 consecutive days within 2 weeks of the study start and until the end of the study; recent history of drug-induced thrombocytopenia; history of prior radiotherapy (RT) to more than 20% bone marrow bearing sites; planned cataract surgery; or any clinical abnormality or laboratory parameters that interfered with study treatment or conferred a risk for participation in the study.
Study assessments, procedures, and analyses
-------------------------------------------
Assessments performed at screening (within 14 days prior to the first cycle of treatment) included evaluation of eligibility criteria; medical history; routine physical examination; ECOG performance status; risk factors for kidney impairment and cataracts; 12-lead electrocardiogram (ECG); laboratory assessments (hematology with complete blood count, serum chemistries, urinalysis, and renal assessments); and ophthalmologic examination. The July 2009 amendment required cardiac monitoring using ECHO or MUGA scans at baseline and every 3 cycles.
Physical examinations were performed on study Day 1 of each cycle and on the last day of Cycle 6 or upon withdrawal from study. Ophthalmic assessment was performed at study completion/withdrawal and also at the 6-month follow-up visit. Bleeding events, AE/toxicity assessment, and concomitant medications were assessed at each study visit and on the last day of Cycle 6 or upon withdrawal from the study. Additional safety assessments (renal assessments, ECG recordings, hematology assessments, and chemistry assessments) were completed throughout the study at protocol-specified time points.
Safety and efficacy analyses were summarized by descriptive statistics. Safety analyses were reported using the safety population, comprising all patients who received ≥ 1 dose of AI chemotherapy. Efficacy analyses were reported using the efficacy population, comprising all patients who received ≥ 1 dose of eltrombopag and had at least 1 platelet count measurement in each of Cycles 1 and 2. Eltrombopag PK was analyzed and will be reported elsewhere.
Results
=======
Patient demographics and disposition
------------------------------------
Due to slow patient recruitment over a 4-year period, enrollment into the study was ended prior to achieving sufficient patients to meet all predetermined study objectives, including identification of OBD and enrollment into an expansion phase. In addition, no evaluable doxorubicin PK samples were collected for assessment of the potential doxorubicin-eltrombopag PK interaction. A total of 18 patients were enrolled into the study. Three patients withdrew prior to receiving any chemotherapy and 15 patients received at least 1 dose of chemotherapy (safety population, Table [1](#T1){ref-type="table"}). Of these 15 patients, 12 received at least 1 dose of eltrombopag: 7, 4, and 1 patients received 75 mg, 100 mg, and 150 mg eltrombopag daily, respectively (Figure [1](#F1){ref-type="fig"}). Two of the 7 patients who received 75 mg eltrombopag were treated for 10 days post AI chemotherapy; the remainder of patients received eltrombopag for 5 days prior to and 5 days post AI chemotherapy. Three patients within the safety population withdrew prior to eltrombopag dosing: 1 due to a serious AE (SAE, Grade 3 pulmonary embolism), 1 due to disease progression, and 1 due to patient decision. The median age (range) was 44 (20--65) years and 53% were male.
######
Patient demographics and baseline clinical characteristics (safety population)
**Demographics** **No** **Eltrombopag** **Eltrombopag** **Eltrombopag** **Total**
------------------------------------------------- --------------- ----------------- ----------------- ----------------- ---------------
Median age, y (range) 56.0 (20--65) 48.0 (38--62) 30.5 (23--44) 59.0 44.0 (20--65)
Gender, n (%)
Female 1 (33) 4 (57) 2 (50) 1 (100) 8 (53)
Male 2 (67) 3 (43) 2 (50) 0 (0) 7 (47)
Race, n (%)
Hispanic or Latino 1 (33) 0 (0) 2 (50) 0 (0) 3 (20)
Not Hispanic or Latino 2 (67) 7 (100) 2 (50) 1 (100) 12 (80)
**Baseline clinical characteristics**
Median baseline platelet count, 1000/μL (range) 256.0 300.0 264.0 388.0 281.0
(218--371) (197--368) (180--595) (180--595)
ECOG PS
ECOG 0, n (%) 0 (0) 6 (86) 0 (0) 1 (100) 7 (47)
ECOG 1, n (%) 3 (100) 1 (14) 4 (100) 0 (0) 8 (53)
^a^Patients were withdrawn prior to receiving eltrombopag during the second cycle.
ECOG PS, Eastern Cooperative Oncology Group Performance Status.
{#F1}
During Cycle 2, 12 patients received a median (range) of 8.5 (2--17) days of treatment with eltrombopag; 7 (2--17), 8.5 (6--10), and 10.0 days for the 75-mg, 100-mg, and 150-mg dose groups, respectively. During Cycle 3, 9 patients received a median (range) of 10 (3--12) days of treatment with eltrombopag; 10.0 (3--12), 10.0 (7--10), and 10.0 days for the eltrombopag 75 mg, 100-mg, and 150-mg dose groups, respectively. During Cycle 4, 5 patients received a median (range) of 10 (3--10) days of treatment with eltrombopag; 10.0 (3--10) and 10.0 days for the eltrombopag 75 mg and 100 mg dose groups, respectively. During Cycle 5, 2 patients received a median (range) of 6 (2--10) days of treatment with eltrombopag; 2 and 10.0 days for the eltrombopag 75-mg and 100-mg dose groups, respectively.
Safety
------
Since the study did not complete as planned, analyses of safety are limited. Five patients who received eltrombopag completed the study (ie, received at least 1 dose of eltrombopag and underwent all visits through to completion of Cycle 2). The majority of patients in the safety population (10/15, 67%) withdrew prior to study completion. Reasons for study withdrawal included AEs; loss to follow-up; disease progression; patient decision; poor tumor response to AI therapy; evaluation for surgical amputation; and inability to continue AI therapy.
All patients experienced at least 1 AE while enrolled in the study. Thrombocytopenia (12 patients, 80%), neutropenia (11 patients, 73%), and anemia (10 patients, 67%) were the most common hematologic AEs; and fatigue (8 patients, 53%), alanine aminotransferase (ALT) increased, constipation, and nausea (7 patients each, 47%) were the most common nonhematologic AEs (Table [2](#T2){ref-type="table"}). Grade 3 and 4 toxicities occurring in each group are listed in Table [3](#T3){ref-type="table"}.
######
Adverse events of any grade (≥ 15% of patients, safety population)
**Treatment-emergent** **No** **Eltrombopag** **Eltrombopag** **Eltrombopag** **Total**
--------------------------- -------- ----------------- ----------------- ----------------- -----------
Hematologic AEs, n (%)
Thrombocytopenia 2 (67) 5 (71) 4 (100) 1 (100) 12 (80)
Neutropenia 2 (67) 5 (71) 4 (100) 0 11 (73)
Anemia 1 (33) 6 (86) 3 (75) 0 10 (67)
Leukopenia 0 3 (43) 2 (50) 0 5 (33)
Febrile neutropenia 0 2 (29) 1 (25) 1 (100) 4 (27)
Thrombocytosis 0 4 (57) 0 0 4 (27)
Nonhematologic AEs, n (%)
Fatigue 0 6 (86) 2 (50) 0 8 (53)
ALT increased 0 5 (71) 2 (50) 0 7 (47)
Constipation 0 6 (86) 1 (25) 0 7 (47)
Nausea 1 (33) 5 (71) 1 (25) 0 7 (47)
Alopecia 0 5 (71) 1 (25) 0 6 (40)
Pyrexia 1 (33) 3 (43) 2 (50) 0 6 (40)
Vomiting 1 (33) 3 (43) 2 (50) 0 6 (40)
AST increased 0 3 (43) 2 (50) 0 5 (33)
Hypokalemia 0 3 (43) 2 (50) 0 5 (33)
Confusional state 1 (33) 2 (29) 0 0 3 (20)
Hemorrhoids 0 3 (43) 0 0 3 (20)
Hypocalcemia 0 1 (14) 2 (50) 0 3 (20)
Headache 0 3 (43) 0 0 3 (20)
Edema peripheral 1 (33) 1 (14) 1 (25) 0 3 (20)
Proteinuria 0 3 (43) 0 0 3 (20)
Vitamin B12 increased 0 3 (43) 0 0 3 (20)
^a^Patients were withdrawn prior to receiving eltrombopag during the second cycle.
AE, adverse events; ALT, alanine aminotransferase; AST, aspartate aminotransferase.
######
Grade 3 or 4 adverse events (safety population)
**Treatment-emergent** **No** **Eltrombopag** **Eltrombopag** **Eltrombopag**
----------------------------- -------- ----------------- ----------------- -----------------
Hematologic AEs, n (%)
Thrombocytopenia 0 3 (43) 2 (50) 1 (100)
Neutropenia 2 (67) 4 (57) 4 (100) 0
Anemia 0 3 (43) 2 (50) 0
Leukopenia 0 3 (43) 0 0
Febrile neutropenia 0 2 (29) 0 0
Nonhematologic AEs, n (%)
Pulmonary embolism 1 (33) 0 0 0
Abdominal abscess 1 (33) 0 0 0
Abdominal pain 0 1 (14) 0 0
Mucosal inflammation 0 1 (14) 0 0
Dehydration 0 1 (14) 0 0
Subclavian vein thrombosis 0 1 (14) 0 0
Sepsis 0 0 1 (25) 0
^a^Patients were withdrawn prior to receiving eltrombopag during the second cycle.
AE, adverse events.
No AEs considered related to study treatment were reported for patients receiving 100 mg and 150 mg dosages of eltrombopag. Five patients in the 75-mg group had 20 AEs reported as related to eltrombopag dosing. Eltrombopag-related AEs occurring in ≥ 2 patients were thrombocytosis (3 patients), anemia, fatigue, and thrombocytopenia (2 patients each).
Overall, 11 SAEs were reported in 7 patients. The 2 patients who withdrew prior to receiving any eltrombopag experienced 3 SAEs. Four patients in the 75-mg group experienced 7 SAEs, 1 of which (subclavian venous thrombosis) was reported as related to eltrombopag dosing. One patient in the 100-mg group experienced 1 SAE (sepsis), which was reported as unrelated to eltrombopag. No SAEs were reported for the 1 patient who received 150 mg eltrombopag. No deaths were reported in this study.
Three patients reported 1 SAE each leading to permanent discontinuation or withdrawal: 2 patients in the 75-mg group and 1 patient who never received eltrombopag. One of these SAEs, the Grade 3 subclavian venous thrombosis described above, occurred in a patient in the 75-mg group with no prior history of TEEs; further details are included below.
Ten patients reached a platelet count \> 400,000/μL on at least 1 occasion, requiring temporary interruption of eltrombopag per protocol; none of these platelet count increases were associated with sequelae. Platelet count increases occurred at various points throughout the cycle; no pattern was observed.
Three patients in the 75-mg group reported 6 bleeding AEs, all Grade 1. The 1 patient who received 150 mg eltrombopag experienced Grade 3 epistaxis (Cycle 3; proximal platelets 15,000/μL). No bleeding events led to discontinuation of eltrombopag dosing or study withdrawal, and none were considered by the investigator to be related to eltrombopag dosing. An additional patient who did not receive eltrombopag reported three Grade 2 bleeding AEs during Cycle 1 of AI chemotherapy: hematemesis (proximal platelets 371,000/μL), hematuria (proximal platelets 126,000/μL), and hemoptysis (proximal platelets 126,000/μL).
Two patients who received 75 mg eltrombopag and 1 patient who never received eltrombopag experienced TEEs during the study. One patient who did not receive eltrombopag experienced a Grade 3 pulmonary embolism 3 days after completion of the first cycle of chemotherapy; proximal platelet counts were 126,000/μL. The event resolved 18 days later. The 2 patients who received 75 mg eltrombopag both experienced a Grade 3 subclavian venous thrombosis at proximal platelet counts of 193,000/μL and 284,000/μL. The former event, as described above, was considered by the investigator to be possibly related to eltrombopag dosing. The investigator also considered that the event may have been due to a port insertion that was located on the same side as the event. The TEE resolved 6 months later. The latter patient had concurrent estrogen use and a prior history of a TEE (deep vein thrombosis \[DVT\]); the patient had been enrolled under a prior protocol amendment that excluded patients with prior TEEs. The patient was withdrawn from the study after 2 days of eltrombopag dosing and the TEE resolved 11 days later. This event was considered by the investigator to be unrelated to eltrombopag.
All hepatobiliary laboratory abnormalities (HBLAs) were Grade 1 or Grade 2, none were considered related to eltrombopag dosing, and none required permanent discontinuation of eltrombopag or study withdrawal.
No patient experienced renal events with onset during eltrombopag dosing or within 6 months post-treatment. All creatinine values were reported as normal at all assessments.
Four cardiac-related AEs (palpitations, 2 events; tachycardia, 2 events) were reported for 3 patients who received 75 mg of eltrombopag. All were Grade 1 in severity and all were considered unrelated to eltrombopag dosing. All but one event (tachycardia) resolved. No clinically significant ECG results were observed. All QTc values were ≤ 500 msec throughout the study. No clinically meaningful decrease in ejection fraction was reported for the 1 patient (in the 150-mg group) who completed MUGA/ECHO assessment.
No new cataracts or progression of existing cataracts was reported.
Efficacy
--------
Since the study did not complete as planned due to poor enrollment, analyses of efficacy are also necessarily limited. Of the 12 patients who received at least 1 dose of eltrombopag 75 mg, 100 mg, or 150 mg, 11 patients had at least 1 platelet count measurement in each of Cycles 1 and 2 while on study and were evaluable for efficacy. Available data demonstrated increased pre-chemotherapy platelet counts on Day 1 of Cycle 2 (cycle with eltrombopag) compared to Day 1 of Cycle 1 (cycle without eltrombopag) in all 11 of these patients (Figure [2](#F2){ref-type="fig"}). Ten of these 11 patients received additional cycles of therapy (including eltrombopag) beyond Cycle 2; of these 10, 6 showed increased pre-chemotherapy platelet counts in all treatment cycles compared to Cycle 1 (5 in the 75-mg group and 1 in the 100-mg group). Two patients who were chemotherapy naïve (patients 1 and 2), and who did not have thrombocytopenia prior to study entry (ie, prior to the protocol change), had higher platelet counts on Day 1 of Cycle 2 than during Cycle 1. This is most likely due to natural rebound or recovery of hematopoiesis at the end of Cycle 1.
{#F2}
Platelet nadirs for these 11 patients are shown in Figure [3](#F3){ref-type="fig"}. Two of 4 patients who received 100 mg eltrombopag daily demonstrated improved platelet nadirs in Cycle 2 (cycle with eltrombopag) compared to Cycle 1 (cycle without eltrombopag). The other 2 patients who received 100 mg eltrombopag daily did not receive their full 5 days of post-chemotherapy eltrombopag dosing.
{#F3}
Discussion
==========
Thrombocytopenia is a common side effect of chemotherapy, and multiple studies have suggested that CIT is a dose-limiting AE in the treatment of cancer, and can necessitate dose delays and/or dose reductions \[[@B23],[@B24]\]. For example, a database analysis of 47,159 patients with both solid tumors and hematologic malignancies showed that TCP increased from 11% at baseline to 22-64% following chemotherapy treatment \[[@B24]\]. Grade 3/4 TCP has been reported in 63% of patients with advanced STS treated with AI chemotherapy \[[@B6]\]. An effective agent for the treatment of CIT may allow chemotherapy administration according to schedule and without dose delays and/or reductions.
This study evaluated the safety and efficacy of eltrombopag in patients with advanced STS and CIT due to receiving AI chemotherapy. Enrollment into this study was challenging as the target study population dwindled due to the emergence of novel standards of care for advanced STS during the 4-year course of the study. Despite implementation of several strategies to boost enrollment, patient recruitment remained slow and the study closed prior to recruitment of the planned number of patients.
Although data are limited, repeated treatment cycles of eltrombopag appeared to be generally well tolerated and the safety profile was consistent with the known safety profile of eltrombopag and with what is expected for patients with advanced STS receiving treatment with the AI chemotherapy regimen. TEEs were observed in this study in 1 patient who did not receive eltrombopag and 2 patients who received eltrombopag, consistent with the known propensity for TEEs in cancer patients. Both eltrombopag-treated patients had known risk factors for TEEs (a port insertion on the same side for one patient, and prior DVT with concurrent estrogen for the other). Renal and cardiac events were examined thoroughly and no eltrombopag-related renal or cardiac events of concern were reported. After this study was initiated, in vitro data showed eltrombopag was an inhibitor of the BCRP-mediated transport of cimetidine. Extensive cardiac safety assessments were subsequently implemented through a study amendment. More recent in vitro studies have shown the BCRP-mediated transport of doxorubicin is not inhibited by eltrombopag at concentrations up to 30 μM, the highest concentration that can be tested in vitro (unpublished data). This concentration is 3- to 4-fold higher than the Day 1 plasma eltrombopag concentration after administration of 100 mg eltrombopag on Days -5 to -1 (unpublished data). These observations suggest that the risk of a clinical eltrombopag-doxorubicin interaction may be far less than originally anticipated.
As shown in Table [2](#T2){ref-type="table"}, 100% of patients treated at the 100 mg and 150 mg doses experienced TCP of any grade, whereas only in 71% of patients treated at the 75 mg experienced TCP. The main reason for this difference was that the protocol had no requirement for patients to have thrombocytopenia for study entry when patients were enrolling at the 75-mg dose level, and the patients enrolled at this eltrombopag dose were also chemotherapy naïve. The protocol was amended for patients enrolled at the 100-mg and 150-mg dose levels to require that the patient experience at least Grade 2 thrombocytopenia (platelets \< 75,000/μL) prior to study entry. This resulted in patients who had previously received chemotherapy having a greater degree of thrombocytopenia at study entry, and explains the increased rate of TCP observed at the higher doses.
Although there was insufficient enrollment for identification of an OBD, no dose-limiting toxicities were observed that limited eltrombopag dose escalation to 150 mg daily in the study. The 75 mg eltrombopag dose demonstrated increased platelet counts at Day 1 of Cycle 2; however, this dose may be inadequate since it did not also improve platelet nadirs. Determination of the OBD for eltrombopag for patients with CIT requires further study.
Limited data were available to explore the efficacy of eltrombopag in this patient population. The study protocol required temporary interruption of eltrombopag dosing when a patient's platelet counts were \> 400,000/μL. Ten patients had platelet counts \> 400,000/μL on at least one occasion, requiring temporary eltrombopag interruption; this may have decreased efficacy for these patients. Available platelet data showed that all patients receiving eltrombopag demonstrated increased pre-chemotherapy platelet counts during Cycle 2 (eltrombopag dosing cycle) compared to Cycle 1 (cycle prior to eltrombopag dosing); additionally, 6 of 10 patients who received \> 2 cycles of therapy showed increased pre-chemotherapy platelet counts in each cycle compared to Cycle 1. Finally, 2 of 4 patients receiving 100 mg eltrombopag had improved platelet nadirs in Cycle 2 compared to Cycle 1. Both of these patients received eltrombopag 5 days pre- and 5 days post-chemotherapy, suggesting that this schedule might improve platelet nadirs as well as pre-chemotherapy platelet count, allowing patients to complete subsequent chemotherapy cycles at the planned dose and schedule.
Further studies are needed to better assess the effects of this pre- and post-chemotherapy schedule of eltrombopag administration in combination with other chemotherapy regimens. In an ongoing, randomized Phase I/II study of eltrombopag versus placebo in patients with solid tumors receiving gemcitabine alone or in combination with cisplatin or carboplatin (NCT01147809), eltrombopag 100 mg daily is being administered according to a pre- and post-chemotherapy schedule (5 days before and 5 days following Day 1 of chemotherapy). The results of this study will further clarify the safety and efficacy of this eltrombopag dosing schedule in combination with chemotherapy.
Conclusions
===========
Although data are limited, the safety profile was consistent with the known safety profile of eltrombopag and the AI chemotherapy regimen. These preliminary data suggest a potential pre- and post-chemotherapy dosing scheme for eltrombopag when administered with AI chemotherapy, and support further investigation of eltrombopag treatment in patients with CIT.
Competing interests
===================
Sant P Chawla receives honoraria and research funding/grants from, and provides consultancy for Merck, Ariad, Amgen, Threshold, Cytrax, and Berg. Arthur P Staddon and Andrew E Hendifar have no relevant financial relationships to disclose. Conrad Messam, Rita Patwardhan, and Yasser Mostafa Kamel are employees of and have equity ownership in GlaxoSmithKline (GSK).
Authors' contributions
======================
SC and AH participated in the acquisition of and analyzed the clinical data. AS participated in the acquisition and interpretation of and analyzed the clinical data. He also contributed to the design of the amendments. CM contributed to the design of the study, and acquired, analyzed, and interpreted the data. RP is the statistician responsible for the design, analysis, and interpretation of the data. YMK is the medical monitor for the study; he has led amendments of the protocol, reviewed the data, and led the development of the clinical study report. All authors contributed to the writing and reviewing of the manuscript, and approved the final draft for publication.
Pre-publication history
=======================
The pre-publication history for this paper can be accessed here:
<http://www.biomedcentral.com/1471-2407/13/121/prepub>
Acknowledgment
==============
Funding for this study was provided by GlaxoSmithKline (GSK) (NCT00358540). All listed authors meet the criteria for authorship set forth by the International Committee for Medical Journal Editors. The authors wish to acknowledge the following individuals for their contributions and critical review during the development of this manuscript: Sandra J Saouaf, PhD, and Ted Everson, PhD, of AOI Communications, L.P., for writing and editorial assistance; and Kimberly Marino and Rosanna Tedesco of GSK, for critical review.
|
You may apply On The Spot to the whole face. Leave on for 10 to 15 minutes. Helps with acne, clogged pores, and many skin concerns. Use once per week as a mask.
On the Spot! Solution is an excellent overnight fix for problematic skin. A unique combination of natural drying agents, such as Sulfur, Camphor and Zinc Oxide, dries up those pesky problem areas and balances excessive oiliness, while minimizing the appearance of redness on the skin. No harmful acids or chemicals; effective usage on all skin types & conditions; safe & effective on delicate skin, as well as problem skin conditions such as acne. Single daily use controls break-outs & normalizes problematic skin while minimizing the appearance of redness on the skin; most effective when used with The Vanishing Act Soap.
The container has enough product to last approximately 8 weeks.
FEATURE
ADVANTAGE
BENEFIT
Suitable for sensitive skin
FDA designation
No harmful acids or chemicals; effective
usage on all skin types & conditions; safe & effective on
delicate skin, as well as problem skin conditions such as acne
Effective treatment for oily/acneic skin
Provides customized moisture treatment for oily/acneic skin by
naturally drying skin abnormalities such as pustules & papules, as
well as occasional blemishes
Single daily use controls break-outs & normalizes problematic
skin while minimizing the appearance of redness on the skin; most
effective when used with complementary RLSC products such as The Vanishing Act Soap & The Vanishing Act Light Moisture Creme |
Hair restoration surgeons of Theni Skin Clinic have pioneered the lateral slit technique, recognized as the single most important surgical breakthrough in hair transplant surgery since the follicular unit. Lateral slit technique provides natural results, mimicking nature, and minimizing scarring. This revolutionary surgical method for recipient site creation is now used by leading hair transplant clinics around the world.
Results of Natural Hair Transplant
The lateral slit technique is the only surgical method that is able to duplicate the alignment and distribution of hair as it occurs in nature, maximizing coverage, and eliminating the pluggy results of older hair transplantation methods. The angle and direction of hair growth can be precisely controlled, allowing transplantation of areas previously regarded as too difficult or unsuitable for hair transplant surgery, i.e. the temple and sideburn zones. In the donor area, follicular units appear to be lined up alongside one another in a plane perpendicular to the direction of hair growth. Lateral slit technique mimics nature's arrangement of hair follicles providing the patient with the most natural possible results. In other methods of creating the recipient site, incisions are made sagitally, parallel to the direction of hair growth. In such methods, maximum possible density in a given area cannot be achieved, hairs grow randomly and often atop one another, producing redundant coverage and unnatural results..
Lateral Slits Minimize Shock Loss
Hair shock usually results from trauma of incisions made in the skin close to preexisting hair. Lateral Slit Technique minimizes trauma to the recipient area, thus dramatically reducing incidents of hair shock. In addition to trauma caused by recipient site creation another cause of shock loss is the repeated manipulation and tugging on preexisting hair in order to expose surrounding bald scalp and to assess the angle of the hair shaft with regard to the scalp. This angle must be exactly copied when making the recipient site incision. This cause of hair shock can be virtually eliminated by having the hair on the scalp approximately 1/2 cm long so that the surrounding scalp can be visualized without moving the adjacent hair, and the hair angle can be copied with precision. At our clinic we encourage our patients to allow us to trim their hair. This will make the first 2-3 weeks post transplant difficult to conceal but will otherwise be of significant benefit to the patient (and surgical team). |
In John 5, Jesus showed his enemies that He was God’s son. The testimony came from various sources, such as John the Baptist, the miracles Jesus performed, the Father in Heaven, and Moses and the Prophets. This testimony is true and sure!
There are consequences to men who do not understand their place in relation to God. Too often men seek their own counsel, and pay no respect to the One who made them. “Woe to those who seek deep to hide their counsel far from the Lord, and their works are in the dark; they say, ‘Who sees us?’ and, ‘Who knows us?’ Surely you have things turned around! Shall the potter be esteemed as the clay; for shall the thing made say of him who made it, ‘He did not make me’? Or shall the thing formed say of him who formed it, ‘He has no understanding’?” (Isaiah, 29:15-16).
Bible believers have long defended the text of Scripture against the attacks of skeptics. For a long while this defense, specifically regarding the text of the Old Testament, was made more difficult by relatively recent manuscript evidence that formed the basis of the Hebrew text.
“These were more fair- minded than those in Thessalonica, in that they received the word with all readiness, and searched the Scriptures daily to find out whether these things were so” (Acts 17:11).
The Bereans were fair-minded. Why? It is because they had the right attitude toward the Scriptures. For us to emulate their example, we must as well.
First, realize that the truth is the truth. That is, it is revealed, absolute and unchanging. While men’s perceptions may vacillate, the truth remains inviolate.
Our approach to truth should be a desire for conformity. We do not go to the Scriptures to rationalize and validate our settled practice or teaching. We use the Scriptures as a standard to which we compare our practice and teaching. If we find the two to be identical, we are vindicated; if we do not, we must change our practice or teaching.
We make a mistake if we go to the Scriptures with settled convictions regarding our practice or teaching. If that is so, and the two do not agree, our tendency will be to twist the Scriptures to our practice rather than to conform our practice to the Scriptures.
The question must be, what do the Scriptures teach? We then compare our own practice and teaching to the light of that divine standard, with the purpose of conforming our practice and teaching to it.
Josh Cox discusses attitudes toward the Bible, expressed by those who are not Christians; the inspiration and sufficiency of the scriptures as God’s word; and the proper attitude that Christians should have toward the Bible.
Sermon by Jeremiah Cox (Note: His first time preaching a full sermon, Age 19).
The scriptures are profitable to complete a man, and equip him for every good work (cf. 2 Timothy 3:16-17). Jeremiah identifies and applies the truths found in four verses designated by the Holy Spirit as “faithful sayings.”
In 2 Timothy 3 the apostle Paul encourages the young evangelist Timothy to be faithful in Doctrine and in his manner of living. He shows the key to a faithful life is preparedness by a study and application of the word of God.
I recently came across a wonderful quote from Nelson Mandela, a Nobel Prize winner, an former President of South Africa. He wrote or said:
There is nothing like returning to a place that remains unchanged to find the ways in which you yourself have altered.
This has a wonderful spiritual application. God’s word is unchanging. The epistle of Jude states that it has been “once for all delivered to the Saints” (verse 3). As such, it serves as a standard by which we can examine and compare ourselves.
One of the great dangers of any Christian is to, with time, begin to drift away from God. Societal influences, changes in circumstances and the passage of time can lead to subtle changes that may not even be noticed by the careless Christian. He may believe himself to be every bit as faithful to God as in the past, not recognizing that he has left the moorings, and has changed the profession of his faith.
However, a careful and frequent comparison between his faith and God’s word will catch any drift, thus saving him from an unfortunate apostasy! “Examine yourselves as to whether you are in the faith. Test yourselves. Do you not know yourselves, that Jesus Christ is in you? — unless indeed you are disqualified” (2 Corinthians 13:5).
I have put on the back table in the foyer a very good daily Bible reading schedule that will help you read through the entire Bible in a year’s time. Best of all, you only read on the weekdays, so you aren’t behind! It starts tomorrow.
I do not know of a better habit to form than daily Bible reading. The commitment is no more than 30 minutes a day. Those who have a fast reading rate can finish the reading in 20 minutes or less each day.
Remember the words of the apostle Paul, written to his son in the faith, Timothy. “Be diligent to present yourself approved to God, a workman who does not need to be ashamed, rightly dividing the word of truth” (2 Timothy 2:15).
In 1 Chronicles 28, King David called all of the leaders of Israel, (captains, stewards and men of valor), to himself, and explained to them that Solomon had been chosen by God to follow him on his throne, and to build the temple. He told them that God had promised to establish Solomon’s kingdom “forever”, “if he is steadfast to observe My judgments and My commandments, as it is this day” (vs. 7).
In verses 8-10, he first addressed the leaders of Israel, and then Solomon, enjoining them to seek God and His will. Notice the passage:
Now therefore, in the sight of all Israel, the assembly of the LORD, and in the hearing of our God, be careful to seek out all the commandments of the LORD your God, that you may possess this good land, and leave it as an inheritance for your children after you forever. 9 As for you, my son Solomon, know the God of your father, and serve Him with a loyal heart and with a willing mind; for the LORD searches all hearts and understands all the intent of the thoughts. If you seek Him, He will be found by you; but if you forsake Him, He will cast you off forever. 10 Consider now, for the LORD has chosen you to build a house for the sanctuary; be strong, and do it.
The phrase “be careful to seek out all the commandments of the Lord your God” is especially instructive to us.
The Catholic church contends that it, as an institution, is the final arbiter and authority for all matters pertaining to the spiritual welfare and condition of man. A careful reading of the scriptures shows this claim to be invalid. God intended His word to be the final standard man must submit to religiously. |
Q:
avoid repeating of result using JavaScript or jQuery
Hi guys I have been wondering how can I avoid displaying of the same result on JavaScript or jQuery using for loop
Here is my code:
function displayData(e)
{
var html = '';
var html2 = '';
var x = '';
var mapDiv = document.getElementById('mapContainer'), i = 0,
dataIndex, tooltipDiv, key
mapMarkers = $(mapDiv).find('.e-mapMarker'), index = 0;
var divCont = $(mapDiv).find('#rightdiv'), index = 0;
for (i = 0; i < mapMarkers.length; i++)
{
if (e.target.parentNode.parentNode == mapMarkers[i])
{
index = i;
}
}
html += '<div id="infocontainer">';
html += '<div class="p-image"><img src="src/images/retrofit.png"/></div>';
html += '<div class="popupdetail">';
html += '<div class="p-name"> Site Name: ' + flsSites[index].site_name + '</div>';
html += '<div class="p-name"> Site Status: ' + flsSites[index].status + '</div>';
html += '<div class="p-name"> Country: ' + flsSites[index].country_name + '</div>';
html += '</div>';
html += '</div>';
html2 += '<div class="rightcontainer">';
html2 += '<img id="productimage" src="src/images/retrofit.png" onclick="DisplayProfileCard();"/>';
html2 += '<div id="imagedetail">';
html2 + '<input type="hidden" value='+ flsSites[index].serial_number +'/>';
html2 += '<span class="details">Product Type:' + flsSites[index].serial_number +'</span>';
html2 += '<span class="details">Version / Size <img class="row_one_icon lightbulb_icon" id="lightbulb" src="src/images/lightbulb1.png" onClick="LightBulb()" /><img id="convert" class="row_one_icon arrow_icon" src="src/images/arrow_Off.png" onClick="Conversion()"/><img id="lightning" class="row_one_icon" src="src/images/lightningOff.png" onClick="Lightning()"/><img id="bullseye" class="row_one_icon bullseye" src="src/images/bullseye_off.png" onClick="BullsEye()"/></span>';
html2 += '<span class="details">Estimated annual Spend <img class="row_one_icon ribbon" src="src/images/ribbon1.png"/><img class="row_one_icon map" src="src/images/map1.png"/><img class="row_one_icon paper_stack" id="paper" src="src/images/paper_stack_Off.png" onclick="PaperStack()"/><img class="row_one_icon chain" id="chain" src="src/images/chain_Off.png" onClick="ChainLink()"/></span>';
html2 += '<span class="details">Site name / manufacturer</span>';
html2 += '<span class="details">Selling Sales Eng</span>';
html2 += '</div>'
html2 += '</div>';
if (!document.getElementById('map_tooltip'))
{
tooltipdiv = $("<div></div>").attr('id', "map_tooltip");
$(document.body).append(tooltipdiv);
$(tooltipdiv).css({
"display": "none", "padding": "5px",
"position": "absolute",
"z-index": "13000",
"cursor": "default",
"font-family": "Segoe UI",
"color": "#707070",
"font-size": "12px", "pointer-events": "none",
"background-color": "#FFFFFF",
"border": "1px solid #707070"
});
}
else
{
tooltipdiv = $("#map_tooltip");
$(tooltipdiv).css({
"left": (e.pageX + 5),
"top": (e.pageY + 5)
});
$(tooltipdiv).html(html).show("slow");
//$('#defaulttext').hide();
//$('#searchcontainer').append(html2);
//$('.rightcontainer').eq($(this).index()).addClass('background');
$(html2).appendTo("#searchcontainer");
}
Now in this code I was able to display my result on a div by hovering on a marker on the map but if I return on my previous hovered marker instead of highlighting its corresponding result, it will just make another rendering of the same result below in which I dont need
A:
You can use a Set object to store each result you renderer and check if it is already there before to render each one.
Unfortunately that Set objects aren't supported in older browsers.
But you can emulate it by simply using the keys of a regular object. For example:
var Idx = {};
function renderOne(flsSite) {
if (Idx[flsSite.name]) return; // Here I suppose same name => same result.
Idx[flsSite.name] = true; // Mark as rendered.
// Do render...
};
Hope it helps...
|
//
// AccessTokenFactorytests.swift
// UberRides
//
// Copyright © 2015 Uber Technologies, Inc. All rights reserved.
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
// THE SOFTWARE.
import XCTest
@testable import UberCore
class AccessTokenFactoryTests: XCTestCase {
private let redirectURI = "http://localhost:1234/"
private let tokenString = "token"
private let tokenTypeString = "type"
private let refreshTokenString = "refreshToken"
private let expirationTime = 10030.23
private let allowedScopesString = "profile history"
private let errorString = "invalid_parameters"
override func setUp() {
super.setUp()
// Put setup code here. This method is called before the invocation of each test method in the class.
}
override func tearDown() {
// Put teardown code here. This method is called after the invocation of each test method in the class.
super.tearDown()
}
func testParseTokenFromURL_withSuccess() {
var components = URLComponents()
components.fragment = "access_token=\(tokenString)&refresh_token=\(refreshTokenString)&token_type=\(tokenTypeString)&expires_in=\(expirationTime)&scope=\(allowedScopesString)"
components.host = redirectURI
guard let url = components.url else {
XCTAssert(false)
return
}
do {
let token : AccessToken = try AccessTokenFactory.createAccessToken(fromRedirectURL: url)
XCTAssertNotNil(token)
XCTAssertEqual(token.tokenString, tokenString)
XCTAssertEqual(token.refreshToken, refreshTokenString)
XCTAssertEqual(token.tokenType, tokenTypeString)
XCTAssertEqual(token.grantedScopes.toUberScopeString(), allowedScopesString)
UBSDKAssert(date: token.expirationDate!, approximatelyIn: expirationTime)
} catch _ as NSError {
XCTAssert(false)
} catch {
XCTAssert(false)
}
}
func testParseTokenFromURL_withError() {
var components = URLComponents()
components.fragment = "access_token=\(tokenString)&refresh_token=\(refreshTokenString)&token_type=\(tokenTypeString)&expires_in=\(expirationTime)&scope=\(allowedScopesString)&error=\(errorString)"
components.host = redirectURI
guard let url = components.url else {
XCTAssert(false)
return
}
do {
_ = try AccessTokenFactory.createAccessToken(fromRedirectURL: url)
XCTFail("Didn't parse out error")
} catch let error as NSError {
XCTAssertEqual(error.code, UberAuthenticationErrorType.invalidRequest.rawValue)
XCTAssertEqual(error.domain, UberAuthenticationErrorFactory.errorDomain)
} catch {
XCTAssert(false)
}
}
func testParseTokenFromURL_withOnlyError() {
var components = URLComponents()
components.fragment = "error=\(errorString)"
components.host = redirectURI
guard let url = components.url else {
XCTAssert(false)
return
}
do {
_ = try AccessTokenFactory.createAccessToken(fromRedirectURL: url)
XCTFail("Didn't parse out error")
} catch let error as NSError {
XCTAssertEqual(error.code, UberAuthenticationErrorType.invalidRequest.rawValue)
XCTAssertEqual(error.domain, UberAuthenticationErrorFactory.errorDomain)
} catch {
XCTAssert(false)
}
}
func testParseTokenFromURL_withPartialParameters() {
var components = URLComponents()
components.fragment = "access_token=\(tokenString)"
components.host = redirectURI
guard let url = components.url else {
XCTAssert(false)
return
}
do {
let token : AccessToken = try AccessTokenFactory.createAccessToken(fromRedirectURL: url)
XCTAssertNotNil(token)
XCTAssertEqual(token.tokenString, tokenString)
XCTAssertNil(token.refreshToken)
XCTAssertNil(token.tokenType)
XCTAssertNil(token.expirationDate)
XCTAssertEqual(token.grantedScopes, [UberScope]())
} catch _ as NSError {
XCTAssert(false)
} catch {
XCTAssert(false)
}
}
func testParseTokenFromURL_withFragmentAndQuery_withError() {
var components = URLComponents()
components.fragment = "access_token=\(tokenString)"
components.query = "error=\(errorString)"
components.host = redirectURI
guard let url = components.url else {
XCTAssert(false)
return
}
do {
_ = try AccessTokenFactory.createAccessToken(fromRedirectURL: url)
XCTFail("Didn't parse out error")
} catch let error as NSError {
XCTAssertEqual(error.code, UberAuthenticationErrorType.invalidRequest.rawValue)
XCTAssertEqual(error.domain, UberAuthenticationErrorFactory.errorDomain)
} catch {
XCTAssert(false)
}
}
func testParseTokenFromURL_withFragmentAndQuery_withSuccess() {
var components = URLComponents(string: redirectURI)!
components.fragment = "access_token=\(tokenString)&refresh_token=\(refreshTokenString)&token_type=\(tokenTypeString)"
components.query = "expires_in=\(expirationTime)&scope=\(allowedScopesString)"
guard let url = components.url else {
XCTAssert(false)
return
}
do {
let token : AccessToken = try AccessTokenFactory.createAccessToken(fromRedirectURL: url)
XCTAssertNotNil(token)
XCTAssertEqual(token.tokenString, tokenString)
XCTAssertEqual(token.tokenType, tokenTypeString)
XCTAssertEqual(token.refreshToken, refreshTokenString)
XCTAssertEqual(token.grantedScopes.toUberScopeString(), allowedScopesString)
UBSDKAssert(date: token.expirationDate!, approximatelyIn: expirationTime)
} catch {
XCTAssert(false)
}
}
func testParseTokenFromURL_withInvalidFragment() {
var components = URLComponents()
components.fragment = "access_token=\(tokenString)&refresh_token"
components.host = redirectURI
guard let url = components.url else {
XCTAssert(false)
return
}
do {
let token : AccessToken = try AccessTokenFactory.createAccessToken(fromRedirectURL: url)
XCTAssertNotNil(token)
XCTAssertEqual(token.tokenString, tokenString)
XCTAssertNil(token.tokenType)
XCTAssertNil(token.refreshToken)
XCTAssertNil(token.expirationDate)
XCTAssertEqual(token.grantedScopes, [UberScope]())
} catch _ as NSError {
XCTAssert(false)
} catch {
XCTAssert(false)
}
}
func testParseValidJsonStringToAccessToken() {
let jsonString = "{\"access_token\": \"\(tokenString)\", \"refresh_token\": \"\(refreshTokenString)\", \"token_type\": \"\(tokenTypeString)\", \"expires_in\": \"\(expirationTime)\", \"scope\": \"\(allowedScopesString)\"}"
guard let accessToken = try? AccessTokenFactory.createAccessToken(fromJSONData: jsonString.data(using: .utf8)!) else {
XCTFail()
return
}
XCTAssertEqual(accessToken.tokenString, tokenString)
XCTAssertEqual(accessToken.refreshToken, refreshTokenString)
XCTAssertEqual(accessToken.tokenType, tokenTypeString)
UBSDKAssert(date: accessToken.expirationDate!, approximatelyIn: expirationTime)
XCTAssert(accessToken.grantedScopes.contains(UberScope.profile))
XCTAssert(accessToken.grantedScopes.contains(UberScope.history))
}
func testParseInvalidJsonStringToAccessToken() {
let tokenString = "tokenString1234"
let jsonString = "{\"access_token\": \"\(tokenString)\""
let accessToken = try? AccessTokenFactory.createAccessToken(fromJSONData: jsonString.data(using: .utf8)!)
XCTAssertNil(accessToken)
}
}
|
Signal perception during performance of an activity under the influence of noise.
Usually the perception of acoustic signals is investigated under conditions where the subjects pay full attention to the signals. It can be assumed that the threshold of signal perception is much higher if the attention has simultaneously to be focused on the execution of any kind of other activity. In the following experiment subjects have to perceive acoustic signals while solving different arithmetical tasks at the same time. The results (number of perceived signals, number of arithmetical tasks solved, reaction time, and solving time) show that the threshold of signal perception rises while other tasks are being performed simultaneously. Consequences for the recognition of warning signals in occupational safety and in traffic conditions are discussed. |
Ceylon Railway Engineer Corps
Ceylon Railway Engineer Corps was a (reserve) regiment of the Ceylon Army. Raised in 1955 with staff from the Ceylon Government Railway. The government hoped to minimized the effects to the Post and Telegraph services in the event of trade union action (strikes were common) by mobilizing the personnel attached to this unit. However it was disbanded in 1956 when the leftist S.W.R.D. Bandaranaike became prime minister.
Category:Disbanded regiments of the Sri Lankan Army
Category:Military units and formations established in 1955
Category:Military units and formations disestablished in 1956
Category:1955 establishments in Ceylon
Category:1956 disestablishments in Ceylon |
Surface relief holograms have been made in the past by several methods. It is standard practice to record an original hologram in a relief medium such as photoresist or hardened gelatin. It is also standard practice to replicate surface relief holograms by preparing a durable master in the form of a nickel electroform as an embossing die for thermally embossing the original hologram into PVC or other thermoformable plastics. Solvent casting has been demonstrated wherein a clear plastic dissolved in a solvent is coated onto a master hologram and allowed to dry by evaporation, and the resulting dry layer of plastic is peeled off the master.
Hot-foil stamping is a well-established printing technique and a well-established method of transferring pre-printed images to a substrate. A holographic hot-stamping foil was demonstrated in 1982, without disclosure of its method of manufacture. The foil was used to transfer pre-made holographic images onto a plastic substrate. |
Cloverdale Elem School
What do students and teachers say about Cloverdale Elem School?
In 2017,
students and teachers
in The State of Illinois
participated in the 2017 Illinois 5Essentials Survey, which asked questions about their school’s culture and climate. Cloverdale Elem School’s performance on the 5Essentials (fig. 1) summarizes the participants’ answers to those survey questions as they relate to the 5Essentials.
Cloverdale Elem School is partially organized for improvement
The 5Essentials can identify the ways in which a school is organized for school improvement. In fact, over two decades of research on Chicago Public Schools has shown that schools strong on three or more of these essentials were 10 times more likely to improve student learning than schools weak in three or more.
Explore the Survey Reports to see Cloverdale Elem School's performance on the 5Essentials, the main concepts underlying the 5Essentials (measures), and individual survey questions underlying each measure. |
Studies on the effect of serine protease inhibitors on activated contact factors. Application in amidolytic assays for factor XIIa, plasma kallikrein and factor XIa.
Amidolytic assays have been developed to determine factor XIIa, factor XIa and plasma kallikrein in mixtures containing variable amounts of each enzyme. The commercially available chromogenic p-nitroanilide substrates Pro-Phe-Arg-NH-Np (S2302 or chromozym PK), Glp-Pro-Arg-NH-Np (S2366), Ile-Glu-(piperidyl)-Gly-Arg-NH-Np (S2337), and Ile-Glu-Gly-Arg-NH-Np (S2222) were tested for their suitability as substrates in these assays. The kinetic parameters for the conversion of S2302, S2222, S2337 and S2366 by beta factor XIIa, factor XIa and plasma kallikrein indicate that each active enzyme exhibits considerable activity towards a number of these substrates. This precludes direct quantification of the individual enzymes when large amounts of other activated contact factors are present. Several serine protease inhibitors have been tested for their ability to inhibit those contact factors selectively that may interfere with the factor tested for. Soybean trypsin inhibitor very efficiently inhibited kallikrein, inhibited factor XIa at moderate concentrations, but did not affect the amidolytic activity of factor XIIa. Therefore, this inhibitor can be used to abolish a kallikrein and factor XIa contribution in a factor XIIa assay. We also report the rate constants of inhibition of contact activation factors by three different chloromethyl ketones. D-Phe-Pro-Arg-CH2Cl was moderately active against contact factors (k = 2.2 X 10(3) M-1 s-1 at pH 8.3) but showed no differences in specifity. D-Phe-Phe-Arg-CH2Cl was a very efficient inhibitor of plasma kallikrein (k = 1.2 X 10(5) M-1 s-1 at pH 8.3) whereas it slowly inhibited factor XIIa (k = 1.4 X 10(3) M-1 s-1) and factor XIa (k = 0.11 X 10(3) M-1 s-1). Also Dns-Glu-Gly-Arg-CH2Cl was more reactive towards kallikrein (k = 1.6 X 10(4) M-1 s-1) than towards factor XIIa (k = 4.6 X 10(2) M-1 s-1) and factor XIa (k = 0.6 X 10(2) M-1 s-1). Since Phe-Phe-Arg-CH2Cl is highly specific for plasma kallikrein it can be used in a factor XIa assay selectively to inhibit kallikrein. Based on the catalytic efficiencies of chromogenic substrate conversion and the inhibition characteristics of serine protease inhibitors and chloromethyl ketones we were able to develop quantitative assays for factor XIIa, factor XIa and kallikrein in mixtures of contact activation factors. |
Q:
Does the browser de-duplicate HTML imports if the unresolved paths are different?
If I have two HTML imports of the same file, but the unresolved paths are different, will the browser figure out that the imports are from the same location or will it import the element twice?
For example:
<!--If I am in a random folder: -->
<link rel="import" href="/bower_components/paper-ripple/paper-ripple.html">
<!-- If I am at the root: -->
<link rel="import" href="bower_components/paper-ripple/paper-ripple.html">
<!-- If I am in a sub folder in bower_components: -->
<link rel="import" href="../paper-ripple/paper-ripple.html">
A:
Yes, it will work.
You can observe it by means of the F12 / DevTools in your favorite browser.
|
Q:
Ordering: Identity
Given a unital C*-algebra $1\in\mathcal{A}$.
Denote selfadjoints:
$$\mathcal{S}(\mathcal{H}):=\{A\in\mathcal{B}(\mathcal{H}):A=A^*\}$$
Introduce an order:
$$A\leq A':\iff\sigma(A'-A)\geq0$$
Consider projections:
$$P\in\mathcal{A}:\quad P^2=P=P^*$$
Then one has:
$$P\leq A\leq 1\implies P=PA=AP$$
And equivalently:
$$0\leq A\leq P\implies A=PA=AP$$
How can I check this?
A:
You don't need the square, which gives you the additional step of justifying that $(1-A)^2\leq 1-A$. You can simply do, since $0\leq A\leq 1$ (because $P\leq A\leq Q$),
$$
0\leq P(1-A)P=P-PAP=0,
$$
so
$$
0=P(1-A)P=[(1-A)^{1/2}P](1-A)^{1/2}P,
$$
from where $(1-A)^{1/2}P=0$, and then $(1-A)P=0$.
|
US Home Building Regulations
Building your home in the United States can present you with a number of unique regulatory and zoning hurdles that can be difficult to navigate through. When you don't know where to look, it can become very difficult to know what you're getting yourself into. While there are many things for all home builders to keep in mind, the truth is that it's not impossible to navigate these waters if you have the right type of help. In truth, trying to gain a proper understanding of general US home building regulations is much easier when you start out with the right type of information.
Special Certifications for Contractors
The first thing that you should learn about will be the certification and licensing requirements. For many projects in certain states, you won't need to worry about licensing or certification guidelines. Some states have few if any guidelines of this nature. However, most states have some form of contractor certification and licensing requirement that they rely on. The requirements will generally circle around training and insurance standards, meaning the state is ensuring that only reasonably-qualified contractors are populating the market. However, there are some contractors who will need specialized certifications beyond a simple license.
This is especially apparent with contractors who work with home wiring and other major electrical projects. It's almost universally agreed that contractors who work with home wiring need to go through a more stringent amount of certifications. This means that you should only work with electricians who have the proper certifications. If you work with an electrician who is not properly certified to work in your state, then you are opening yourself up to the potential for massive fire damage and other serious issues.
Zoning Regulations Vary State to State
All state and local governments have zoning regulations that you need to abide by if you're going to be building anything on your property that is permanent. It's important to recognize that the vast majority of these regulations will only apply to permanent additions to your property. Permanent additions can be a new shed or any other type of out building on your property. These additions can even be pools or other non-structural changes to the property that impact municipal resource use and public easement boundaries. In some cases, you will be required to get a zoning permit for a garden in the front of your home. Certain municipal governments have zoning regulations that prohibit front-lawn gardens and these laws are enforced on a regular basis.
Habitability Laws are Important to Understand
Habitability laws are designed to protect people from living in environments that are considered squalid or otherwise unfit for human habitability. In many cases, people don't recognize the dangers that associated with certain habitability issues in their home. The problem is that these dangers extend beyond the person who owns the home and into the public sphere as well. Due to the public health risk that uninhabitable homes cause, you may have to have your building inspected before you're even allowed to live in it. This is something that varies wildly from one state or municipality to another. Not all states engage in these types of very strict habitability concerns, but it is something that comes up from time to time. Be sure you work with a qualified contractor who understands these habitability issues and can guide you through the process of eliminating them. This is the best way to ensure you won't have to worry about running afoul of any of these important laws.
Permitting Issues
When you're building in a city, suburb or other area that uses the public grid, you'll need to gain permits to connect your home to water and electricity lines. The permitting process can be a very long one, so it's important to get the process started well in advance of your home being finished. In some cases, the local government will require you to bring out a government-employed utility worker to make the connection. In states with deregulated utilities, the utility company would send someone out to do the hook up. In either case, it's smart to get started on the permitting process sooner rather than later.
There are a lot of things to keep in mind when you're planning on building a home. While many regulations may seem like they're intrusive or overbearing, the truth is that they are truly designed to be in the public good. Poorly-installed home wiring is not just a danger to the person living in the house. It's a danger to everyone in the area. To keep up with the regulations in your area surrounding contractors and building, take some time to visit your local city hall. The best information you'll get on building regulations can be found through your local zoning board. |
Herbs for osteoporosis
There are 5 products.
What is osteoporosis?
Osteoporosis is a disease that weakens bones, making them more likely to break, especially those in the hip, spine, and wrist. After skeletal mass peaks (between 30 and 40), bones begin to lose calcium faster than they can replace it. For women, the loss of bone density speeds up during the first three to seven years after ...
What is osteoporosis?
Osteoporosis is a disease that weakens bones, making them more likely to break, especially those in the hip, spine, and wrist. After skeletal mass peaks (between 30 and 40), bones begin to lose calcium faster than they can replace it. For women, the loss of bone density speeds up during the first three to seven years after menopause.
Herbs for osteoporosis
Herbs and supplements cannot eliminate osteoporosis, but they can slow the process. Let see how herbs can help below:
Nettle is high in calcium, so if you do not want to take a calcium supplements, drinking nettle infusion or taking a capsule can be an interesting solution to prevent osteoporosis or reduce its progression.
Dandelion contains a compound called boron. This seems to boost the production of estrogen by the body. Therefore, it can be a good solution, notably for menopause women.
Anti-inflammatory herbs can help to the pain associated with osteoporosis. You can try Borage, Mallow or Rosemary for example.
Main properties: for irritation of the mouth and throat, dry cough, and bronchitis for stomach and bladder complaints. for insect bites, pimples, acne and swellingsQuality guarantee: All herbs are grown in Chile Botica del Alma has a SEREMI agreement to package the herbs The company is also supported by CORFO
Main properties: for treating rheumatism (rheumatoid arthritis). tonic effect on the liver and digestive system gentle laxativeQuality guarantee: All herbs are grown in Chile Botica del Alma has a SEREMI agreement to package the herbs The company is also supported by CORFO
Main properties: stimulates blood circulation for low blood pressure to calm nerves, ease pain and reduce tension in the body tonic for hairQuality guarantee: All herbs are grown in Chile Botica del Alma has a SEREMI agreement to package the herbs The company is also supported by CORFO
Main properties: re-hydrates and revitalizes aged skin, or skin damaged by sun for skin disorders such as psoriasis and eczema for women: it contains high levels of calcium and ironQuality guarantee: All herbs are grown in Chile Botica del Alma has a SEREMI agreement to package the herbs The company is also supported by CORFO
Main properties: for arthritis, rheumatoid arthritis, and gout to reduce sneezing and itching a good general tonic for women for men suffering from baldnessQuality guarantee: All herbs are grown in Chile Botica del Alma has a SEREMI agreement to package the herbs The company is also supported by CORFO |
248 P.2d 311 (1952)
126 Colo. 265
CITY OF COLORADO SPRINGS
v.
PUBLIC UTILITIES COMMISSION et al.
No. 16741.
Supreme Court of Colorado, en Banc.
September 8, 1952.
F. T. Henry, Louis Johnson, Colorado Springs, for plaintiff in error.
Duke W. Dunbar, Atty. Gen., H. Lawrence Hinkley, Deputy Atty. Gen., Ralph Sargent, Jr., Asst. Atty. Gen., for defendants in error.
PER CURIAM.
This cause is pending on a writ of error directed to a judgment of the district court rendered on September 11, 1950, in which the trial court determined that the city of Colorado Springs, a home-rule city, in furnishing water to customers outside its municipal boundaries is a public utility and subject to the jurisdiction of the Public Utilities Commission of Colorado. Subsequent thereto and on February 19, 1951, our court, by a unanimous decision to which no petition for rehearing was filed, in the case of City of Englewood v. City and County of Denver, 123 Colo. 290, 229 P.2d 667, determined that the City and County of Denver, in supplying water outside of its corporate limits, under generally similar circumstances as in the case at bar, was not a public utility and not subject to the jurisdiction of the Public Utilities Commission as to such service. It is our opinion that the decision in City of Englewood v. City and County of Denver, supra, is controlling in the present case in every respect. This view is shared by counsel for plaintiff in error as well as the Attorney General, appearing for defendants in error, who has filed a confession of error and joins with counsel for plaintiff in error in his request for a reversal of the judgment.
Accordingly, the judgment is reversed and the cause remanded with directions to the trial court to dismiss the action and remand the case to the Public Utilities Commission with instructions that it dismiss the complaint.
|
Tom Willighan
Tom (Thomas) Willighan (22 March 1903 - 7 July 1936) was an Irish full-back football player. He was capped twice for the Ireland national football team (Northern Ireland), played five seasons for Burnley FC and won leagues and cups during his early days in his hometown of Belfast.
Early Days
Tom Willighan began his playing career in Belfast for Forth River FC, St Mary's FC and Willowfield FC.
He was captain of the St. Mary's team that won the Steel and Sons Cup in the 1925-26 season, beating Summerfield 4-0 in the final.
After moving to Willowfield FC, he again tasted victory in the Steel and Sons in 1927-28, beating Ormiston 2-1 in a final replay. This was a remarkable season for the club as they won the Irish Cup that year, becoming the first from outside the Irish League to win the Irish Cup since the League's formation in 1890. They defeated Larne 1-0 in the final at Windsor Park. Also that season, Willowfield won the Irish Intermediate League and Irish Intermediate Cup. Four trophies, including the Irish Cup, in one season - an amazing achievement.
Burnley
He moved to English First Division side Burnley in 1929 and made his debut against Manchester United in March 1930. However, the team finished in 21st place and were relegated down to the Second Division. He was a strong, robust defender and made sixty-one appearances over a further four seasons for the Lancashire club. His career ended in late 1933 after suffering a serious leg injury playing against Manchester United at Old Trafford. Tom never recovered from the injury and returned home to Belfast.
International
Willighan twice represented Ireland (now known as Northern Ireland). On 7 December 1932, he was a defender in the 4-1 defeat to Wales at Wrexham and on 16 September 1933 he was in the starting XI that beat Scotland 2-1 in Glasgow.
Personal Life
Tom Willighan was the third of ten children born in Cambrai Street, Belfast. He married Alice Bradshaw in Burnley in 1934 and witness to their wedding were Burnley team-mate and best friend George Waterfield, along with wife Nellie.
Tragedy struck two years later when Tom died from cancer on 7 July 1936 at the age of 33. His son Thomas Waterfield Willighan was just 5 months old. Thomas Jnr still lives in Burnley with his family.
External links
Clarets Mad - Tom Willighan's caps
Willighan Family History
Category:1903 births
Category:1936 deaths
Category:Irish association footballers (before 1923)
Category:Pre-1950 IFA international footballers
Category:Burnley F.C. players
Category:Linfield F.C. players
Category:Sportspeople from Belfast
Category:Association football fullbacks |
Contact Us
The LED high bay is available
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The LED high bay lighting offers numerous installation options: It can be surface mounted easily and also has the ability to be pendant mounted, ideally to be used in a variety of areas such as warehouses, production and logistics workshops, retails stores, amusement parks, stadiums and other industrial and outdoor lighting purposes.
To help you secure more projects with our LED high bay, 3N LED® offers 3 year warranty. |
About Liam
Hi, I’m Liam O’Mara, and I’m running for Congress. I may not look like your average politician, but let me tell you who I am and what I can do for you.
I’m a working class kid from a union family. My great-grandfather helped found the ILWU and my father is retiring after fifty years on the waterfront. My mother runs a daycare and is in SEIU. I never expected to go to college, and didn’t until I was thirty years old. Before that I worked as a fry cook, a longshoreman, and a computer nerd. But I saved my money, took on student loans, and I finished a Ph.D. in history. I’ve been teaching college now for ten years, and my students have taught me a lot about where we are as a society.
My story is the American story – an up-from-the-bootstraps success. But it is much harder than it used to be, and getting harder. Wages have been stagnant for forty years even as costs have risen. Decent housing and a good job are out of reach for ever more people. Health care costs have exploded. And all while productivity climbs and corporations make record profits. The American Dream is dying, and our politicians have been killing it.
But it doesn’t have to be this way. Washington used to understand how to balance sustainable growth and the interests of society. I’m running to make sure it gets back to work. I want Medicare for all, so people can move jobs without losing benefits, and millions of people can stop relying on emergency rooms to get the care they need. I want paid sick and family leave for all, like every other developed country offers, so people don’t have to choose between their health and their rent. I want a $15 an hour minimum wage, so that people working full time can afford a dignified and independent life, and so their spending can drive growth. I want tuition-free public colleges, so that our young people can pick up the skills they need for a 21st century economy.
Together we can build an America that works for all of us, not just the lucky few. My loyalty is to the American people, not the special interests, so I won’t be taking Super PAC money. Help us make real change possible. For the price of a coffee each month, you can support my campaign and other folks like me, and change the direction in Washington. The American Dream is for all of us. Help me fight to restore that promise. |
Michael Flynn and George Papadopoulos, two of President Trump’s former aides, are billed as speaking at an upcoming conference hosted by a supporter of the QAnon conspiracy theory.
Flynn and Papadopoulos are both advertised online as speaking at the Digital Soldiers Conference scheduled to take place Sept. 14 in Atlanta, Mother Jones first reported Tuesday.
The event is being organized by Rich Granville, a Florida tech executive who has repeatedly posted online about the fringe QAnon conspiracy theory that purports the president is the target of a “deep state” coup, the report noted. An image used to promote the event online depicts the American flag so that its stars are arranged to resemble the letter Q.
Papadopoulos, a former foreign policy adviser for Mr. Trump’s election campaign, announced on Twitter that he will be speaking at the conference with Flynn, a retired Army general who briefly served as the president’s former national security adviser. Both were criminally charged as a result of the special counsel’s investigation into Russian election interference and have pleaded guilty to counts of lying to the FBI.
Flynn could not immediately be reached for comment. Mr. Granville said that Flynn’s lawyer, Sidney Powell, authorized him to speak at the event, Mother Jones reported.
Other speakers scheduled to appear at the conference include conservative personalities Joy Villa and Bill Mitchell, according to the event’s website.
“Conservative voices are increasingly being banned from the digital public square,” reads a message posted on the “About” section of the event’s website. “Patriotic social media warriors will not raise the white flag of surrender in the face of this onslaught. Together we will unite for freedom at the inaugural Digital Soldiers Conference.”
Mr. Granville admittedly “espouses QAnon views,” Mother Jones reported.
“Do I think it’s good for America? Absolutely,” he said. “Do I think it’s a conspiracy theory? I doubt that.”
Tickets for the event are being sold online starting at $49, with the “majority” of proceeds going toward Flynn’s defense fund, the site says.
Details about the conference emerged less than two weeks since an FBI intelligence bulletin surfaced in which the bureau’s Phoenix field office mentioned QAnon while describing “conspiracy theory-driven domestic extremists” as a growing threat.
“The FBI assesses these conspiracy theories very likely will emerge, spread, and evolve in the modern information marketplace, occasionally driving both groups and individual extremists to carry out criminal or violent acts,” said the document.
Mr. Granville, the chief executive of the Yippy search engine, has referenced QAnon several times on his personal Twitter account, including a July 23 tweet about Flynn.
Flynn, 60, resigned as the president’s national security adviser in early 2017 after it emerged that he misled the FBI about his contacts with the former Russian ambassador. He was subsequently charged with lying to the FBI, pleaded guilty and is awaiting sentencing.
Papadopoulos, 31, similarly pleaded guilty to lying to the FBI about contacts he had with Russians during the 2016 race. He accordingly spent 12 days in federal prison and is currently on supervised released.
Copyright © 2020 The Washington Times, LLC. Click here for reprint permission. |
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fixes:
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Fixes compatability with some hardware that requires the file name of
any virtual media to end with the suffix ".iso" when Ironic generates
a virtual media image. We recommend operators generating their own
virtual media files to name the files with proper extensions.
|
227 Pa. Superior Ct. 172 (1974)
Commonwealth
v.
Lewis, Appellant.
Superior Court of Pennsylvania.
Argued November 12, 1973.
April 3, 1974.
*173 Before WRIGHT, P.J., WATKINS, JACOBS, HOFFMAN, CERCONE, and SPAETH, JJ. (SPAULDING, J., absent.)
James M. Keller, for appellant.
R. Banks, Assistant District Attorney, with him Joseph J. Nelson, District Attorney, for Commonwealth, appellee.
*174 OPINION BY HOFFMAN, J., April 3, 1974:
Appellant contends that the Commonwealth did not present sufficient evidence to sustain his conviction of larceny.[1]
At 5:30 p.m. on August 11, 1972, John Kasbee left his backhoe with the keys hidden under the hood in the Sunset Mobile Park in Transfer, Mercer County, Pennsylvania. The next morning when he returned at 7:20 a.m. the backhoe was gone. Kasbee testified that on August 18th, the appellant told him he could retrieve his backhoe for one thousand dollars,[2] and that he wanted no repercussions or names mentioned.
On August 19th at 10:05 a.m., Mr. Kasbee and two State Troopers came back to talk to the appellant. Trooper Leskovak testified that he overheard the conversation *175 between Kasbee and the appellant. He said that appellant indicated he knew where the backhoe was and "that he would take us there and if the backhoe wasn't Mr. Kasbee's he would get his $1000 back and if it was damaged Mr. Kasbee would get $1000 back." Kasbee said that he returned again on the 19th at 11:00 a.m. with $1000. The appellant told him to leave the money and come back in an hour after the appellant had made a phone call. Kasbee refused and left. On October 6th, 1972 the backhoe was found fifteen to eighteen miles from where it had been stolen.
The issue then crystallizes to whether, without direct evidence of the theft of the backhoe, and without any evidence placing the appellant at the scene of the crime at the time of the theft, there was sufficient circumstantial evidence on the basis of the conversations to sustain a conviction of larceny.
In order to sustain a conviction for larceny, there must be proof beyond a reasonable doubt that the accused took and carried away the personal property of another with the specific intent of depriving the owner permanently of that property. Commonwealth v. Lyons, 219 Pa. Superior Ct. 18, 280 A. 2d 458 (1971); Commonwealth v. Whitner, 444 Pa. 556, 281 A. 2d 870 (1971). While it is true that the evidence must be read in the light most favorable to the Commonwealth, which, by reason of the verdict, is entitled to all reasonable inferences arising therefrom the record fails to disclose any evidence of a taking and carrying away on the part of the appellant. Our Court said in Commonwealth v. Zimmerman, 214 Pa. Superior Ct. 61, 67, 251 A. 2d 819 (1969) that: "`It must be remembered that the guilt must be proved and not conjectured. The reasonable inference of guilt must be based on facts and conditions proved; it cannot rest solely on suspicion or surmise. These do not take the place of testimony. The *176 facts and circumstances proved must, in order to warrant a conviction, be such as to establish the guilt of the defendant, not necessarily beyond a moral certainty, nor as being absolutely incompatible with his innocence, but at least beyond a reasonable doubt.'"
A close reading of the record and the testimony fails to persuade us that the Commonwealth has met its burden in proving beyond a reasonable doubt that the appellant, Donald Lewis, was guilty of larceny of the backhoe. The backhoe was found a great distance from appellant's land. Witnesses, who saw the backhoe driven away, could not identify the appellant as the driver. The appellant who testified in his own behalf, denied being anywhere near the scene of the theft on the night in question producing a turnpike receipt corroborating his alibi that he was in Michigan at the time.
We, therefore, reverse the judgment of sentence, and order the appellant discharged.
WATKINS, P.J., dissents.
NOTES
[1] Appellant also contends that the charge of larceny was improperly added to his indictment without the benefit of a preliminary hearing. Appellant was arrested and charged with conspiracy and compounding a crime. After a preliminary hearing on these two charges, the Grand Jury added the charge of larceny to the Bills of Indictment. In our opinion Commonwealth v. Brabham, 225 Pa. Superior Ct. 331, 309 A. 2d 824 (1973) we fully discussed all aspects of preliminary hearings. Our Court pointed out that a preliminary hearing is a matter of right only if "the person accused shall so demand." Here there is no indication in the record that the appellant ever objected to the charge of larceny being added to the Bills of Indictment without a preliminary hearing being held. Absent a timely objection the appellant cannot raise this issue now as it is not one of basic and fundamental error. See Commonwealth v. Sampson, 454 Pa. 215, 311 A. 2d 624 (1973); Commonwealth v. Agie, 449 Pa. 187, 296 A. 2d 741 (1972).
[2] Kasbee stated that appellant said that $900 was for the person that took the backhoe and $100 for the appellant. Appellant testified, however, that an unknown man had called him and said, "I've got your backhoe." Lewis said he told the unknown caller that he didn't own a backhoe. The caller then asked him if the owner would want it back, and could Lewis try to locate him and tell the owner he could have it back for $1000. The appellant further testified that he was just trying to do a favor for Kasbee.
|
How the Effective Executive Spends Time
by Laura Stack
Doing the right things right requires leaders to manage the intersection of efficiency and effectiveness and follow 12 related practices outlined by Stack. Each of the 12 practices belongs to one of the 3T categories of strategic thinking, team focus, and tactical work, ultimately disclosing how to improve profitability and productivity.
How Hypergrowth Companies Create Predictable Revenue
by Aaron Ross, Jason Lemkin
The world’s fastest growing companies share seven ingredients in their recipes for hypergrowth. Ross and Lemkin break these down into steps that leaders can easily use as a guide for growing their businesses and increasing revenue.
Know Your Talent Better Than You Know Your Customers
by Aaron Goldstein, Rahaf Harfoush, Leerom Segal, Jay Goldman
The authors present an actionable plan for any company that wants the best from its people and isn’t afraid of radical approaches to achieve it. Six proven principles are offered that can be used to decode work and unlock the potential of employees.
The 360° Leader is a concept designed to teach participants how to lead from any position in an organization. Important concepts, such as how to lead down as you manage your team are foundational — while unprecedented concepts such as how to lead across with those who are your organizational peers, and how to lead upward to those to whom you report — will be revolutionary to your leadership. It's these behaviors, leading across and leading up that revolutionize this century’s leaders.
What Companies and Individuals Can Do to Go Beyond Making a Profit to Making a Difference
by Tim Sanders
A "Responsibility Revolution" is shaking up corporate America. In this provocative and insightful book, bestselling author Tim Sanders reveals why companies must go beyond making a profit and start making a difference and offers concrete suggestions on how all of us can help our companies join the Responsibility Revolution.
How to Identify the Sources of Growth and Drive Enduring Company Performance
by Patrick Viguerie, Sven Smit, Mehrdad Baghai
While growth is a top priority for companies of all sizes, it can be extremely difficult to maintain — especially in today's competitive business environment. In order to achieve this goal, you need to think through the growth challenges your organization faces and follow a detailed approach to uncover, understand and capture potential growth opportunities.
Developing Effective Leadership Through Managerial Accountability
by Brian Dive
Centered around three themes — leadership, accountability and organizational structure — this book explores what it means for managers to be held accountable at every level and argues that most leadership-related problems arise from the ineffectiveness of organizational structures that lack accountable jobs.
The Credit Crisis of 2008 and What It Means
by George Soros
In the midst of the most serious financial upheaval in decades, legendary financier George Soros explores the origins of the crisis and its implications for the future. Soros, whose breadth of experience in financial markets is unrivaled, places the current crisis in the context of decades of study of how individuals and institutions handle the boom-and-bust cycles and dominate global economic activity. The prevailing paradigm for financial markets — that markets tend toward equilibrium an
Leadership Communication that Drives Results
by Bob Matha, Macy Boehm
Leadership communications experts Bob Matha and Macy Boehm offer a strategic plan for addressing one of the most difficult challenges any business leader can face: engaging employees to take action. Written for all those who lead groups — including supervisors, managers, HR and communications professionals, executives and CEOs — this practical resource describes how to put in place proven communication principles that do just that. |
General News
By editor - 11.1 2018
From the Governing Body Commission of the International Society for Krishna Consciousness
[Guideline]
Whereas numerous websites of ISKCON temples currently do not prominently feature the personality and teachings of His Divine Grace A. C. Bhaktivedanta Swami...Read more...
BY: SUN STAFF - 10.1 2018
Orukal Mandapam, Tirukkalukkunram
A serial exploration of places of Lord Brahma's worship.
Lord Brahma at Tirukkalukkunram
From the time of King Mahendravarman I through the next century, there were quite a number of rock-cut temples...Read more...
By Urmila Dasi (Dr. Edith Best, Professor of ISKCON History and The Sociology of ISKCON at Bhaktivedanta College, Durbuy, Belgium; Associate Editor of Back to Godhead magazine; member of the Sastric Advisory Council to the GBC)
Understanding ISKCON through the lens of social development...Read more...
By Lokanatha Swami - 10.1 2018
From Back to Godhead
The unseen merciful hand of Lord Krsna helps a determined young science student become one of Srila Prabhupada’s first Indian disciples.
I was born in Aravade, a small village in the Indian state of Maharashtra that differs little...Read more...
By editor - 9.1 2018
Andree Marie Dussault, a Canadian journalist in Delhi feels women are now really free. Times of India (2nd May’ 2010) carries her view that modern India and the Western society can be proud of the way the status of women has matured in the past fifty...Read more...
By Dr. David Frawley - 9.1 2018
Yoga means unification, which is first the unity of all the dualities and contraries that constitute the energies of life. Yoga philosophy teaches us to understand and transcend duality, but this rests upon harmonizing the dualities within us in a...Read more...
BY: MAYESVARA DASA - 8.1 2018
The following is a continuation of the discussion from our previous paper entitled, "Does the Earth Float in Space?" In sections 1.1 and 1.2 of the previous paper we discussed how the Srimad Bhagavatam describes the planets floating in space by...Read more...
By Adikarta Das - 8.1 2018
Veganism is a very fast growing diet. In the US there was a 500% increase in Veganism in the last 3 years; up from 1% in 2014 to 6% now. In the UK over half a million follow the diet, up from 150000 in 2007.
There are 3 main reasons. Health, ethics and...Read more...
By Sitalatma das - 8.1 2018
Monks of Mount Athos – is there something we should learn from them?
January 7 is the date of Orthodox Christmas but most of our devotees are not familiar with that tradition though there are quite a few useful things we can learn from it.
Srila Rupa...Read more...
By Dr David Frawley - 5.1 2018
The following article by Dr David Frawley was first published by Daily
For the practice of yoga, Krishna is the Yogavatara, the incarnation of yoga in all its aspects of knowledge, devotion and action.
If there is any single figure who represents India...Read more...
BY: SUN STAFF - 4.1 2018
Lord Brahma does Tapas on Agni
A serial exploration of places of Lord Brahma's worship.
Lord Brahma at Pancheshti
The temple town of Pancheshti (Pancheti) is located in the far northeastern corner of Tamil Nadu, well north of Chennai....Read more...
BY: SUN STAFF - 3.1 2018
By HDG A.C. Bhaktivedanta Swami Prabhuada, from 'Back To Godhead', Apr 5, 1956, Vol. 03, No. 03.
Sri Chaitanya Charitamrita is the record of immortal activities of the Lord. In the first part 9th chapter of the book the welfare activities of the Lord is...Read more...
BY: BHAKTA TORBEN - 3.1 2018
I cannot do anything, even if I become president
The politics is so corrupted that as soon as you are prepared to do something actually, you will be killed
Prabhupāda: So the rascal scientist is responsible for giving such things in the hands of the...Read more...
BY: SUN STAFF - 3.1 2018
On the purnima of the month of pausa (Narayana - December - January), (Srimad Bhagavatam, 2:10:4, 'posanam tad-anugrahah."), the last day of the astrological month (Pushyami nakshatra), one should bath the Deity in five seers (or pounds - 2.5 kg approx...Read more...
By Nikunja Vilasini Dasi - 3.1 2017
Nick Vujicic was born without arms and legs. “Why me?” he always asked until he discovered that God had chosen him for a purpose. Because of his disability, he was able to reach out to people and give them courage. Nick’s zest for life...Read more...
BY: SUN STAFF - 2.1 2018
We conclude the "India Through the Eyes of Europe" series with a final comparative study. Again, we have an engraving done by Barlow around 1790, and another piece done by Sourindro Mohun Tagore in 1880.
At first glance these appear to be completely...Read more...
By Sesa Dasa - 2.1 2018
From Back to Godhead
Lord Caitanya launched His mission of mercy in
West Bengal. Five hundred years later, Srila Prabhupada
took that mission to heart and to the entire world.
The flat, verdant ricelands of West Bengal’s district of Nadia appear...Read more...
BY: SUN STAFF - 29.12 2017
Today we will compare three examples of work: engravings and illustrations of Lord Nrsimhadev. Viewing them side-by-side, we see a fascinating progression of transcendental imagery that was borrowed from India by a European artist, re-drawn 70 years later by...Read more...
By Madhumati Pushkarini Devi Dasi - 29.12 2017
Yes I hold back. There is every reason to surrender to You, every reason to hold on to You. Yet I hold back. This is my precarious condition, dear Lord. While I keep trying to coax my mind to understand what is good for me and what’s in it...Read more...
BY: SUN STAFF - 28.12 2017
Today's image is another of the copper plate engravings by Barlow, c. 1790's, from his Dasavatara series. The image depicts the pastimes of Lord Vamanadev, the Dwarf Avatar.
The background of this picture is quite different than other images in...Read more...
By editor - 27.12 2017
Christmas trees are a central part of Christmas celebrations around the world. Families gather around them to exchange gifts, cities put them up in squares and town halls, you'll find them in nearly every hotel and shopping mall...
But where did the "...Read more...
BY: SUN STAFF - 27.121 2017
Mother Mary and Baby Jesus
Excerpt from a lecture by Srila Prabhupada on Srimad-Bhagavatam - December 02, 1968, Los Angeles.
It is said that this Krsna consciousness movement is not an artificial thing that we have manufactured something, ideal thing,...Read more...
By editor - 17.12 2017
I sent a telegram to Prabhupada saying, “Can I get out of here?”
Brahmananda: In 1971 Prabhupada was having big public programs in India, and one evening an Arya Samajist challenged Prabhupada. He said, “Oh, Swamiji, you have come to India with your...Read more...
By Murari Gupta Dasa - 27.12 2017
From Back to Godhead
Not getting what you want? Perhaps that’s good for you.
“Please cancel my tickets,” I said to my friend on the phone. “I won’t be able to go.”
I hung up the phone and sank down onto my bed, my...Read more...
All articles, books, pictures, and audio files in this site are the property of Radha.name or their respective owners.
Opinions expressed in articles are not necessarily reflecting the opinion of Radha.name. |
BOB FAW, correspondent: This is “coming out day” at Georgetown University in Washington, DC. At this Jesuit institution, three dozen students celebrate homosexual and lesbian lifestyles even though the Catholic Church considers them immoral. Thomas Lloyd is president of Georgetown’s Gay Pride.
THOMAS LLOYD (Student, Georgetown University): By recognizing pride, Georgetown has become more true to its Jesuit values. Commitments to social justice are some of the most important and historically grounded parts of Catholic doctrine.
FAW: But what is sanctioned at one Catholic university is anathema at another: Florida’s Ave Maria University.
JIM TOWEY (President, Ave Maria University): This is a university that’s founded on biblical truth, on scripture, and on the sacramental richness of the Catholic Church.
FAW: At Ave Maria, ninety percent of the one-thousand-member student body are Catholic. Professors pledge to uphold Catholic beliefs. There are worship sites in every dorm, and mass is held three times a day. Its president, Jim Towey, who worked for the Bush administration as director of its faith-based and community initiatives office, also served as legal advisor for the late Mother Teresa. Ave Maria is determined to stay a course from which its president says other Catholic institutions have strayed.
TOWEY: In an age where modernity has attacked the whole idea of objective truth and the whole relativism that you see that’s pervasive in our culture, I guess this university’s not going to be here to be popular; it’s not here to try to please everyone. It’s here to try to be true to itself and its own Catholic identity.
FAW: Georgetown University, renowned for its academic excellence, has a different view of its Catholic identity. All students, though only half of the 7,000 undergraduates are Catholic, are required to take two theology and two philosophy courses.
Mass at Georgetown: “Lord, you are the giver of all good gifts.” “Lord, have mercy.”
FAW: Though students are not required to go to mass, there are many to choose from, and Catholic priests live in each dorm acting as mentors and friends. But Georgetown, which boasts “the largest campus ministry in the world,” also fiercely champions unfettered dialogue.
REV. KEVIN O’BRIEN (Vice President for Mission and Ministry, Georgetown University): What we did 50 years ago to promote our identity does not suffice today because the world is different, and our students and faculty are different. To quote something Father Hesburgh from Notre Dame would often say, “The Catholic university is a place where the church does its thinking.” And if that is to be the case, then we have to permit this free exchange of ideas.
FAW: Georgetown insists that welcoming groups like Gay Pride, even hosting a gay and lesbian center on campus, is part of the Jesuit’s priestly mission.
O’BRIEN: The purpose of the center is not to undermine the church’s teaching. It is a center for education. We try to teach our students and faculty and our alumni about issues of sexuality, of sexual identity and gender. That’s an expression of our Jesuit tradition of cura personalis, caring for each person mind, body, and spirit, in their unique individuality.
FAW: It’s an openness, a kind of tolerance Ave Maria’s president disdains.
TOWEY: They become bastions of relativism where your truth is your truth, my truth is my truth, the Catholic teaching is just one path. That’s not our view, and I feel sorry for those universities. I think they’ve lost their moral bearings, and I think they’ve lost their Catholic identity when they water it down to the point where everything’s true.
FAW: Still, many Georgetown students argue that this Catholic university has found the right mix of scholarship and religious character.
KEVIN SULLIVAN (Student, Georgetown University): I think it’s reaching a great number of students, non-Catholic and Catholic, and helping them to develop, grow in their own faith and figure out really how they can bring their faith into public life.
FAW: On Georgetown’s campus there are, of course, dissenting voices which contend that this university has strayed.
LOUIS CONA (Student, Georgetown University): Is it Catholic enough? I would say no. We have the Knights of Columbus, the Catholic Daughters, there’s all student-run organizations, but the university is not promoting this stuff. We have a mass, but are they teaching you about this stuff? Are they promoting this as an ideal, as a good?
FAW: And you would say no.
CONA: I would say they are a little passive on that.
FAW: Senior Andrew Schilling lives at the Knights of Columbus house just off campus. His letter to the student newspaper opposing same-sex marriage provoked withering criticism of him. Schilling says when Georgetown lets gays and lesbians advocate, Georgetown’s Catholic identity is diluted.
ANDREW SCHILLING (Student, Georgetown University): It’s not so much that Georgetown can’t support homosexuals and treat them with respect and the dignity that they deserve, but it’s rather that the university remains silent about the church’s teaching and position with regard to homosexuality, with regard to human sexuality in general.
FAW: But gay pride activist Thomas Lloyd counters that his faith has been affirmed precisely because Georgetown is Catholic.
LLOYD: I wouldn’t even think about how to reconcile my queer identity with my Catholic faith identity if I hadn’t come to Georgetown. What does it mean to be gay and Catholic? Can those two go together? And my experience at Georgetown with Jesuits and with other people who are Catholic and identify as queer on campus show me that you can.
FAW: On the campus of Ave Maria, a debate on the role about groups opposed to Catholic teachings seems unlikely.
CHRIS AUDINO (Student, Ave Maria University): Take what you want, leave what you don’t: as Catholics we believe that’s not the way faith is meant to be lived.
FAW: Nor do students here feel they’ve been short-changed because they don’t have direct exposure to gay and pro-choice groups permitted on the Georgetown campus.
PAIGE PILARSKI (Student, Ave Maria University): Even though our campus does not have such groups as that, within the classroom, you're talking about these topics in a way that presents, I think, both why do people believe what we believe with regards to abortion or homosexuality, and why do we believe what we believe?
MIKE WATKINS (Student, Ave Maria University): The professors represent their views well, and they present the argument in such a way that is challenging for us as Catholics to engage the argument and try and prove it false.
TOWEY: If a group wanted to be pro-choice, pro-abortion Catholics we would not want to try to endow that group with legitimacy. That’s not in some way curtailing academic freedom. It’s recognizing that academic freedom has limits.
FAW: And many Ave Maria students agree their faith has been strengthened largely because the Catholic identity here is so pervasive.
ELIZABETH ALTOMARI (Student, Ave Maria University): It’s definitely grown. Being able to experience it every day only makes you appreciate it and come to understand it more. Being able to go to mass every day, and being able to go to the chapel only allows you to grow deeper in your faith.
FAW: And fostering that, says Ave Maria’s president, is the true role of a Catholic university.
TOWEY: What’s needed now is a Catholicism rooted in scripture, sacramental in nature, that’s open to engagement with the world without losing its own identity.
FAW: It isn’t easy. Ave Maria to get more students recently slashed tuition. Georgetown policies have prompted harsh criticism and loss of financial support from some alumni; and if the debate now underway at many of the country’s nearly 270 Catholic colleges and universities seems a bit untidy, that’s precisely because it is.
O’BRIEN: That’s where there’s a creative tension to be Catholic and university, and it is. Yes, is it messy sometimes? And is it challenging? Yes. Those same questions that play out in parishes and around family dinner tables, they play out in a university, because we’re all asking the question: what does it mean to be Catholic today?
FAW: Questions reverberating in the world at large and on Catholic campuses.
For Religion & Ethics NewsWeekly this is Bob Faw in Ave Maria, Florida. |
"""
Python Interchangeable Virtual Instrument Library
Copyright (c) 2012-2017 Alex Forencich
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.
"""
from .agilent90000 import *
class agilentDSA90254A(agilent90000):
"Agilent Infiniium DSA90254A IVI oscilloscope driver"
def __init__(self, *args, **kwargs):
self.__dict__.setdefault('_instrument_id', 'DSO90254A')
super(agilentDSA90254A, self).__init__(*args, **kwargs)
self._analog_channel_count = 4
self._digital_channel_count = 0
self._channel_count = self._analog_channel_count + self._digital_channel_count
self._bandwidth = 2.5e9
self._init_channels()
|
Q:
Type conversion with bit shift (in C)
I'm trying to get how memory allocation works, what happens with addresses and memory while changing types, etc.
I stacked with this string and can't understand what exactly is happening here:
(uint32_t)(((uint64_t)addr) >> 32)
There is no pointers so I have no guesses how memory allocation is changed here.
Could you explain me, please? Let's imagine that variable "addr" has type DWORD.
A:
addr is casted to uint64_t; its content shifted 32 bits to the right (with zeros pushed from the left) and the results is cast to uint32_t. It does not seems to make much sense a part of returning zero of type uint32_t in a complex way.
Besides, it has nothing to do with memory allocation, a part of possibly few temporaries on the stack.
|
Noon Meem Rashid
Not to be confused with Noon Meem Danish.
Nazar Muhammad Rashed (), (1 August 1910 – 9 October 1975) commonly known as Noon Meem Rashed (Urdu: ن۔ م۔ راشد) or N.M. Rashed, was an influential Pakistani poet of modern Urdu poetry.
Early years
Rashed was born as Nazar Muhammad in a Janjua family in the village of Kot Bhaaga, Akaal Garh (now Alipur Chatha), Wazirabad, Gujranwala District, Punjab, and earned a master's degree in economics from the Government College Lahore.
Career
He served for a short time in the Royal Indian Army during the Second World War, attaining the rank of Captain. Before independence of Pakistan in 1947, he worked with All India Radio in New Delhi and Lucknow starting in 1942. He was transferred to Peshawar in 1947 where he worked until 1953. Later he was hired by Voice of America and had to move to New York City for this job. Then, for a short while, he lived in Iran. Later on, he worked for the United Nations in New York.
Rashed served the UN and worked in many countries. He is considered to be the 'father of Modernism' in Urdu Literature. Along with Faiz Ahmed Faiz, he is one of the great progressive poets in Pakistani literature.
His themes run from the struggle against oppression to the relationship between words and meanings, between language and awareness and the creative process that produces poetry and other arts. Though intellectually deep, he is often attacked for his unconventional views and life-style. In an age when Pakistani literature and culture acknowledge their Middle Eastern roots, Rashed highlighted the Persian element in the making of his nation's history and psyche. Rashed edited an anthology of modern Iranian poetry which contained not only his own translations of the selected works but also a detailed introductory essay. He rebelled against the traditional form of 'ghazal' and became the first major exponent of 'free verse' in Urdu literature. While his first book, Mavra, introduced free verse and is more technically accomplished and lyrical. Urdu literary world was shocked when he used the theme of sex in his poems. Any discussion of sex was still considered a taboo back then. His main intellectual and political ideals reached maturity in his last two books.
His readership is limited and recent social changes have further hurt his stature and there seems to be a concerted effort to not to promote his poetry. His first book of free verse, Mavra, was published in 1940 and established him as a pioneering figure in 'free form' Urdu poetry.
He retired to England in 1973 and died in a London hospital in 1975. His body was cremated, though no such request appears in his will. This created an outcry in conservative Pakistani circles and he was branded an infidel. Anyhow, he is considered a great figure in progressive Urdu literature.
Poetry
N M Rashed was often attacked for his unconventional views and life style. According to Zia Mohyeddin, a friend of Rashed, "In the time when everybody was in quest of learning English, which was a must for getting some decent job, Rashed was busy in making paintings or poetry."
The themes of Rashed's poetry run from the struggle against domination to the relationship between words and meanings, between language and awareness and the creative process that produces poetry and other arts.
Initially his poetry appeared to have the influence of John Keats, Robert Browning and Matthew Arnold and he wrote many sonnets on their pattern, but later on he managed to maintain his own style. These were his initial exercises of poetry, which could not last for a longer period of time, and so ultimately he developed and maintained his own style.
He rebelled against the traditional form of the 'ghazal' and became the first major exponent of free verse in Urdu Literature. His first book, 'Mavra', introduced free verse and is technically accomplished and lyrical.
Family and children
Rashed's first wife Safia died in 1961 at the age of 46, of an incorrectly administered B-complex injection in Karachi. His second marriage, to Sheila Angelini, an Italian, took place in 1964.
Rashed had several children. His eldest Nasrin Rashed lives in Islamabad and is retired from her work with the Pakistan Broadcasting Corporation. The second daughter Yasmin Hassan resides in Montreal, and has two children, Ali and Nauroz. His nephew (sister's son) and son-in-law (Yasmin Hassan's husband) Faruq Hassan was a teacher at Dawson College and McGill University. Faruq Hassan died on 11 November 2011. The third daughter, Shahin Sheikh, now deceased, lived in Washington and worked for the Voice of America. She has two children in the US. Rashed's youngest daughter, Tamzin Rashed Jans, lives in Belgium and has two sons.
His eldest son Shahryar Rashed died on 7 December 1998, serving as the Pakistani Ambassador to Uzbekistan. The younger son, Nazeil, lives in New York.
Bollywood
His poem "Zindagi sey dartey ho" was set to music in the 2010 Bollywood movie, Peepli Live. It was performed by the Indian music band, Indian Ocean, and received critical appreciation as "hard-hitting" and "a gem of a track" that "everyone is meant to sing, and mean, at some point in life".
Bibliography
Mavraa (Beyond)-1940
Iran Main Ajnabi (A stranger in Iran)
La Musawi Insaan (Unequal man)- 1969
Gumaan ka Mumkin (Speculations) was published after his death in 1976
Maqalat (Essays)- Ed. Shima Majeed, 2002.
College hall named after him
At Government College Lahore., a hall is named after him as "Noon Meem Rashid Hall" at Postgraduate Block Basement.
References
External links
Selected Poetry of N.M. Rashid Translated in English
Kuliyat e Noon Meem Rashid
Category:1910 births
Category:1975 deaths
Category:Punjabi people
Category:People from Wazirabad
Category:Pakistani poets
Category:Urdu poets
Category:Government College University, Lahore alumni
Category:People of British India
Category:20th-century poets
Category:Urdu scholars |
[Elective radiotherapy in breast carcinoma].
From March 1972 to November 1979 a total of 157 patients with stage I to III primary breast cancers have been irradiated after segmental resection (12 cases), tilectomy (89 cases) or biopsy (56 cases). Complete local control was achieved in all Stage I lesions, in 97% of Stage II lesions and in 68% of Stage III lesions. Non recurrence has been observed in patients previously operated by segmental resections, while local failures occurred in 6/89 and in 16/56 patients operated by tilectomy or biopsy, respectively. Of the 28 Stage I patients, 24 (86%) are alive, one with distant metastases. Four patients of this group are dead, 2 of intercurrent disease and 2 of breast cancer. Of the 61 (Stage II) patients, 38 (62%) are alive, 5 of these with distant metastases. Twenty-three patients are dead, 15 with active disease, and 8 suffered intercurrent death. Of the 68 Stage III patients, 21 (31%) are alive, 6 of these with distant metastases. Fourty-seven patients are dead, 43 of breast cancer and 4 of intercurrent disease. The high probability of initial subclinical deposits is evidenced by the fact that 49 of the 68 patients in this group developed distant metastases. The patients with T1 lesions appear to comprise the most favourable group with a relapse free survival at five years of 76%. The 5 years relapse free survival was 62% for T2 lesions and 25% for T3 and T4 lesions. N0 status does not confer the same favourable prognosis as T1 status. N+ status, however, resulted in a definitely negative prognostic factor. Cosmetic results after our treatment approach appear to be extremely good. A marked difference between the irradiated and controlateral breast occurred only in 10 of the 125 patients after a minimum of 2 years observation. |
/*
* Copyright (C) 2015 - present Instructure, Inc.
*
* This file is part of Canvas.
*
* Canvas is free software: you can redistribute it and/or modify it under
* the terms of the GNU Affero General Public License as published by the Free
* Software Foundation, version 3 of the License.
*
* Canvas is distributed in the hope that it will be useful, but WITHOUT ANY
* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
* A PARTICULAR PURPOSE. See the GNU Affero General Public License for more
* details.
*
* You should have received a copy of the GNU Affero General Public License along
* with this program. If not, see <http://www.gnu.org/licenses/>.
*/
import React from 'react'
import {string, shape, arrayOf, func} from 'prop-types'
import I18n from 'i18n!account_course_user_search'
import CoursesListRow from './CoursesListRow'
import CoursesListHeader from './CoursesListHeader'
import {Table} from '@instructure/ui-table'
import {ScreenReaderContent} from '@instructure/ui-a11y'
export default function CoursesList(props) {
// The 'sis_course_id' field is only included in the api response if the user has
// permission to view SIS information. So if it isn't, we can hide that column
const showSISIds = !props.courses || props.courses.some(c => 'sis_course_id' in c)
return (
<Table margin="small 0" caption={I18n.t('Courses')}>
<Table.Head>
<Table.Row>
<Table.ColHeader id="header-published" width="1">
{I18n.t('Published')}
</Table.ColHeader>
<Table.ColHeader id="header-course-name">
<CoursesListHeader
{...props}
id="course_name"
label={I18n.t('Course')}
tipDesc={I18n.t('Click to sort by name ascending')}
tipAsc={I18n.t('Click to sort by name descending')}
/>
</Table.ColHeader>
{showSISIds && (
<Table.ColHeader id="header-sis-id">
<CoursesListHeader
{...props}
id="sis_course_id"
label={I18n.t('SIS ID')}
tipDesc={I18n.t('Click to sort by SIS ID ascending')}
tipAsc={I18n.t('Click to sort by SIS ID descending')}
/>
</Table.ColHeader>
)}
<Table.ColHeader id="header-term">
<CoursesListHeader
{...props}
id="term"
label={I18n.t('Term')}
tipDesc={I18n.t('Click to sort by term ascending')}
tipAsc={I18n.t('Click to sort by term descending')}
/>
</Table.ColHeader>
<Table.ColHeader id="header-teacher">
<CoursesListHeader
{...props}
id="teacher"
label={I18n.t('Teacher')}
tipDesc={I18n.t('Click to sort by teacher ascending')}
tipAsc={I18n.t('Click to sort by teacher descending')}
/>
</Table.ColHeader>
<Table.ColHeader id="header-sub-account">
<CoursesListHeader
{...props}
id="subaccount"
label={I18n.t('Sub-Account')}
tipDesc={I18n.t('Click to sort by sub-account ascending')}
tipAsc={I18n.t('Click to sort by sub-account descending')}
/>
</Table.ColHeader>
<Table.ColHeader id="header-students" width="1">
{I18n.t('Students')}
</Table.ColHeader>
<Table.ColHeader id="header-option-links" width="1">
<ScreenReaderContent>{I18n.t('Course option links')}</ScreenReaderContent>
</Table.ColHeader>
</Table.Row>
</Table.Head>
<Table.Body data-automation="courses list">
{(props.courses || []).map(course => (
<CoursesListRow
key={course.id}
courseModel={props.courses}
roles={props.roles}
showSISIds={showSISIds}
{...course}
/>
))}
</Table.Body>
</Table>
)
}
CoursesList.propTypes = {
courses: arrayOf(shape(CoursesListRow.propTypes)).isRequired,
onChangeSort: func.isRequired,
roles: arrayOf(shape({id: string.isRequired})),
sort: string,
order: string
}
CoursesList.defaultProps = {
sort: 'sis_course_id',
order: 'asc',
roles: []
}
|
Q:
Standard location for external web (Grails) application config files on linux
Is there a standard location on Linux (Ubuntu) to place external config files that a web application (Grails) uses?
UPDATE: Apparently, there is some confusion to my question. The way Grails handles config files is fine. I just want to know if there is a standard location on linux to place configuration files. Similar to how there is a standard for log files (/var/log). If it matters, I'm talking about a production system.
A:
Linux configuration files typically reside in /etc. For example, apache configuration files live in /etc/httpd. Configuration file not associated with standard system packages often live in /usr/local/etc.
So I'd suggest /usr/local/etc/my-grails-app-name/. Beware that this means you can't run two different configurations of the same app on the same server.
|
Fundus microvascular flow monitoring during retrograde cerebral perfusion: an experimental study.
Retrograde cerebral perfusion (RCP) through the superior vena cava was clinically introduced as a supportive technique to protect the brain during deep hypothermic circulatory arrest. This study searched for a direct monitor of cerebral blood flow to evaluate the effect of cerebral perfusion. Retinal microvascular perfusions were studied in six piglets using fundus fluorescein angiography (FFA) and color Doppler sonography before cardiopulmonary bypass and retrograde cerebral perfusion during deep hypothermic circulatory arrest. FFA showed initial filling of the fundus venae in 2.5 minutes, and complete filling in 4.5 minutes with partial filling of the arteriae. Arteriae completely filled in 8 minutes, and all of the arteriae and venae filled from 15 to 17 minutes. Color Doppler sonography showed that flow signals were detected in all of the fundus vessels during RCP. FFA and color Doppler sonography are direct and sensitive methods for observing cerebral blood flow and assessing the effect of cerebral perfusion. |
// ---------------------------------------------------------------------
// THIS FILE IS AUTO-GENERATED BY BEHAVIAC DESIGNER, SO PLEASE DON'T MODIFY IT BY YOURSELF!
// ---------------------------------------------------------------------
#include "../types/behaviac_types.h"
namespace behaviac
{
class bt_node_test_PreconditionEffectorTest_PreconditionEffectorTest_3
{
public:
static bool Create(BehaviorTree* pBT);
};
class bt_node_test_repeat_repeat_ut_0
{
public:
static bool Create(BehaviorTree* pBT);
};
class bt_node_test_repeat_repeat_ut_1
{
public:
static bool Create(BehaviorTree* pBT);
};
class bt_node_test_action_child_agent_0
{
public:
static bool Create(BehaviorTree* pBT);
};
class bt_node_test_action_noop_ut_0
{
public:
static bool Create(BehaviorTree* pBT);
};
class bt_node_test_action_ut_0
{
public:
static bool Create(BehaviorTree* pBT);
};
class bt_node_test_action_ut_1
{
public:
static bool Create(BehaviorTree* pBT);
};
class bt_node_test_action_ut_2
{
public:
static bool Create(BehaviorTree* pBT);
};
class bt_node_test_action_ut_3
{
public:
static bool Create(BehaviorTree* pBT);
};
class bt_node_test_action_ut_waitforsignal_0
{
public:
static bool Create(BehaviorTree* pBT);
};
class bt_node_test_action_ut_waitforsignal_1
{
public:
static bool Create(BehaviorTree* pBT);
};
class bt_node_test_action_ut_waitforsignal_2
{
public:
static bool Create(BehaviorTree* pBT);
};
class bt_node_test_action_waitframes_ut_0
{
public:
static bool Create(BehaviorTree* pBT);
};
class bt_node_test_circular_ut_0
{
public:
static bool Create(BehaviorTree* pBT);
};
class bt_node_test_condition_ut_0
{
public:
static bool Create(BehaviorTree* pBT);
};
}
|
User login
PATRIOTS?
Sat, 01/24/2015 - 00:49 — ub
Other
A patriot is someone who defends the rules and the enumeration of certain rights, which shall not be construed to deny or disparage others retained by the public.
The NFL once again finds itself involved in yet another controversy and says they've been conducting an investigation as to whether the footballs used in last Sunday's AFC Championship Game complied with the specifications that are set forth in the playing rules. The investigation began based on information that suggested that the game balls used by the New England Patriots were not properly inflated to levels required by the playing rules, specifically Playing Rule 2, Section 1, which requires that the ball be inflated to between 12.5 and 13.5 pounds per square inch. Prior to the game, the game officials inspect the footballs to be used by each team and confirm that this standard is satisfied, which was done before last Sunday's game.
The investigation is being led jointly by NFL Executive Vice President Jeff Pash and Ted Wells of the law firm of Paul Weiss. Mr. Wells and his firm bring additional expertise and a valuable independent perspective. The investigation began promptly on Sunday night. Over the past several days, nearly 40 interviews have been conducted, including of Patriots personnel, game officials, and third parties with relevant information and expertise. We have obtained and are continuing to obtain additional information, including video and other electronic information and physical evidence. We have retained Renaissance Associates, an investigatory firm with sophisticated forensic expertise to assist in reviewing electronic and video information.
The playing rules are intended to protect the fairness and integrity of our games. We take seriously claims that those rules have been violated and will fully investigate this matter without compromise or delay. The investigation is ongoing, will be thorough and objective, and is being pursued expeditiously. In the coming days, we expect to conduct numerous additional interviews, examine video and other forensic evidence, as well as relevant physical evidence. While the evidence thus far supports the conclusion that footballs that were under-inflated were used by the Patriots in the first half, the footballs were properly inflated for the second half and confirmed at the conclusion of the game to have remained properly inflated. The goals of the investigation will be to determine the explanation for why footballs used in the game were not in compliance with the playing rules and specifically whether any noncompliance was the result of deliberate action. We have not made any judgments on these points and will not do so until we have concluded our investigation and considered all of the relevant evidence.
Upon being advised of the investigation, the Patriots promptly pledged their full cooperation and have made their personnel and other information available to us upon request. Our investigation will seek information from any and all relevant sources and we expect full cooperation from other clubs as well. As we develop more information and are in a position to reach conclusions, we will share them publicly.
The National Football League's statement of an investigation into the footballs used by the New England Patriots during last Sunday's 45-7 win over the Indianapolis Colts appears to be more hot air... Blah, blah, blah...etc.
Comments
City Island Images is proud to offer "Front Pages" from newspapers all over the globe. They are today's chosen front pages from many cities and countries. For copyright protection, watermarks are occasionally placed on front pages that cover news events of historic significance.
Through a special agreement with more than 800 newspapers worldwide, the Newseum displays these front pages each day on its website. The front pages are in their original, unedited form, and some may contain material that is deemed objectionable to some visitors. Discretion is advised.
Anyone seeking permission to use a front page must credit the Newseum and contact the newspaper directly for permission. U.S. copyright laws apply. |
1. Field of the Invention
The present invention relates to a lock mechanism and a related electronic device, and more particularly, to a lock mechanism and a related electronic device capable of releasing lock constraint and ejecting an electronic component simultaneously by one touch.
2. Description of the Prior Art
The electronic component applied to the notebook computer, such as the battery or the portable hard disk, is installed on the bottom of the notebook computer. The notebook computer is rotated to assemble and to disassemble the electronic component from the bottom of the notebook computer. Generally, the conventional latch mechanism, which is disposed on the bottom of the notebook computer, is utilized to assemble and disassemble the electronic component from a casing of the notebook computer. Operating procedure of the conventional latch mechanism is complicated and inconvenient, so quality impression and satisfaction of the notebook computer with the conventional latch mechanism are accordingly decreased. Thus, design of a lock mechanism capable of rapidly and conveniently assembling/disassembling the electronic component is an important issue of the mechanical industry. |
The suspect in last month’s shooting at a California synagogue has been charged with federal hate crimes in a 113-count indictment returned by a grand jury in southern California on Tuesday.
John Earnest, 19, has been charged with murder and attempted murder of 53 other people by the grand jury in the U.S. District Court for the Southern District of California, the Justice Department announced.
Earnest has been charged with 54 counts of obstruction of free exercise of religious beliefs using a dangerous weapon resulting in death, bodily injury, and attempts to kill as well as related firearm offenses, authorities said. He is also accused of 54 hate-crime charges.
The suspect was initially charged earlier this month with 109 federal counts and he pleaded not guilty to the hate crimes charges last week. The latest indictment adds four charges for discharging a firearm during crimes of violence.
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Authorities say Earnest shot four people using an AR-15 rifle at the Chabad of Poway Synagogue on April 27, killing one person. Several congregants, including an off-duty Border Patrol Agent, eventually chased Earnest as he fled the synagogue to his car, where he was subsequently detained by authorities who found the weapon and additional ammunition.
The shooting took place on the last day of Passover.
Authorities later found a manifesto they say belonged to Earnest that included many anti-Semitic and anti-Muslim statements, including comments from Earnest saying he regretted he was unable to kill more people.
According to the affidavit of the criminal complaint, Earnest also admitted in the manifesto to the arson of the nearby Dar-ul-Arqam Mosque in March.
Earnest wrote in his manifesto that he was inspired by the Tree of Life synagogue shooting in Pittsburgh and the recent shootings at two mosques in New Zealand, according to the Justice Department.
He faces a possible death sentence or life without parole. He is currently in state custody pending state criminal charges. |
81-86 Jeep CJ5, 6, 7 PaceSetter Headers w/ARMOR*Coat
Part #
72C1135
$ 861.87
In Stock
QuantityIn Stock
PaceSetter Performance Products is a manufacturer. We only sell to automotive resellers and do not sell directly to the public. The best way to find a reseller is to click either Google or Bing. Or search your favorite search engine using the part # 72C1135 and our name pacesetter. This will return a list of current local stocking resellers and online stores
DescriptionFitment - NotesWarranty
Unleash the power under your hood!
PaceSetter Shorty Headers are custom engineered for racetrack performance and sound, a combination of ease of installation & superior fitment while achieving maximum performance gains. All Pacesetter products combine over 45 years of commitment to provide quality-made, affordably priced American-made auto-parts to the automobile enthusiast.
Ensure a perfect seal every time with plasma cut, CNC-machined, 3/8 in. thick head flanges
ARMORCoat- Lower Underhood Temperatures
Armor*Coat: Keep underhood temperatures to a minimum and protect your investment! Pacesetter's ARMOR*Coat finish, a polished, 2000 F metallic ceramic coating. ARMOR*Coat won't discolor like paint, chrome or even stainless steel, reduces underhood temperatures, helps the header resist rust and corrosion and is easy to keep clean. The coating itself is guaranteed not to chip, peel or flake for three years.
NOTE: Unless Design Note 11 appears on the information page for the application you are searching, it is NOT legal for sale or use in California or for sale or use in NY on vehicles with CA Emissions.
These headers are a modification to your vehicle altering your vehicle from stock.. If your vehicle is using additional aftermarket components, parts from other applications, or custom altered parts, it is the installer's responsibility to verify fitment.
Do not use HEADER WRAP, it traps moisture and begins the immediate RAPID deterioration of your headers. The use of Header Wrap voids all warranties
Making America great again, one vehicle at a time, right here in the USA
Year
Model
Engine
Location/Notes
Part#
PaceSetter Performance Products warrants this part free from defects in workmanship and materials for 3 years from date of purchase by the original end user.
Exceptions set forth below:
1st year of the warranty, PaceSetter will repair or replace products with defects in workmanship and materials.
2nd and 3rd years product will be replaced with a pro-rated fee charged. Amount of the fee will be determined of the claim and will be based on the Suggested Retail Price of the product at the time of claim and the amount of time the product was used during warranty period. PaceSetter will not be responsible for freight, labor, other expense incurred, or inconveniences or damages caused by failure of the product, or for breach of any expressed or implied warranty with respect to the product other than as set forth herein.
Implied warranties on PaceSetter products shall be in effect only for the duration of the expressed warranty (with exceptions set forth below). This limited warranty is void if the product shows evidence of mishandling, externally-applied heat, welding, bending, or mutilating of parts, burn-out or blowout resulting from improper tuning, visual rust or rust-through as the result of an external wrap or coating not applied by PaceSetter. Also voiding the warranty are uses contrary to applicable instruction sheets, shipping damage, header wrap or repair performed by other than PaceSetter. Paint, gaskets, bolts, external (visual) rust, rust-through, and cosmetic appearance are not covered under the terms of
this warranty. Plating on a product, once the product is installed, is not covered under the terms of this warranty. For service under the terms of this warranty the end user must be able to prove date of purchase. Shipping to PaceSetter is responsibility of customer. Contact dealer from which the product was purchased or PaceSetter Performance Products in Phoenix, AZ. Written permission must be obtained on all warranty claims.
**This product is sold "for racing use only" and it is not legal for street or off-road use.
10.
Fits cylinder heads with evenly spaced exhaust ports
11.
50 States legal (C.A.R.B. legal, E.O. available upon request)
12.
Replaces stock exhaust manifold
13.
Long tube header
14,
Shorty header
15,
Retains catalytic converter in stock location
16,
Y-pipe available to connect to stock system
17,
X-pipe available to connect to stock system
18,
H-pipe available to connect to stock system
19,
Extensions available to hook to stock system
20,
Will not fit angle plug heads
22,
Y-pipes 82-1176, 82-1177 will not fit 6
30,
Includes catalytic converters
Not legal for use on catalyst-equipped vehicles except for racing vehicles which may not be operated on a highway except headers with Design Note #11. Pre-catalyst vehicles must use original emission control devices. It is the responsibility of the customer to reinstall these devices on the vehicle. |
Development of cutaneous sarcoidosis in a patient with chronic hepatitis C treated with interferon alpha 2b.
Sarcoidosis is a multisystemic granulomatous disorder of unknown etiology that most commonly affects young adults. A probable induction of sarcoidosis by interferons (IFN) has been published. To this date, few cases of cutaneous sarcoidosis inpatients with chronic hepatitis C under interferon treatment have been reported. We describe a 50-year-old woman with chronic hepatitis C who developed lesions of cutaneous sarcoidosis three months after IFN treatment. The possible role of INF therapy in the development of cutaneous sarcoidosis in a patient with chronic hepatitis C should be considered. |
REDISCOVERING ZEN’S ROOTS IN ANCIENT CHINA
Join us Apr 6 - 8 for Rediscovering Zen's Roots in Ancient China with philosopher David Hinton who teaches at Columbia University. His books include Existence: A Story, The Wilds of Poetry, and his translation of the Ch'an classic No-Gate Gateway (Wu-men Kuan) is forthcoming.
Wendy Johnson: 06-16-2012: The Four Elements Return to Their True Nature (Part 2 of 2)
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This retreat is an exploration in environmental chaplaincy: Healing the Earth, Healing Ourselves. During this highly experiential retreat, we will use our embodied experience of the four elements — Earth, Water, Fire, and Air — to deepen our understanding of some of the most pressing environmental issues of our time. This talk takes up the elements of water and fire.
Wendy Johnson is a Buddhist meditation teacher and organic gardening mentor who lives in the San Francisco Bay Area. She has been practicing Zen meditation for thirty-five years and has led meditation retreats nationwide since 1992 as an ordained lay dharma teacher in the traditions of Vietnamese teacher Thich Nhat Hanh and the San Francisco Zen Center. Wendy is one of the founders of the organic Farm and Garden Program at Green Gulch Farm Zen Center in Marin County, where she lived with her family from 1975 to 2000. She has been teaching gardening and environmental education to the public since the early 1980s.
Wendy Johnson is a Buddhist meditation teacher and organic gardening mentor who lives in the San Francisco Bay Area. Wendy has been practicing Zen meditation for thirty-five years and has led meditation retreats nationwide since 1992 as an ordained lay dharma teacher in the traditions of Vietnamese teacher Thich Nhat Hanh and the San Francisco Zen Center. Wendy is one of the founders of the organic Farm and Garden Program at Green Gulch Farm Zen Center in Marin County, where she lived with her family from 1975 to 2000. She has been teaching gardening and environmental education to the public since the early 1980s.
In 2000 Wendy and her husband, Peter Rudnick, received the annual Sustainable Agriculture Award from the National Ecological Farming Association. Since 1995 Wendy has written a quarterly column, “On Gardening,” for Tricycle Magazine, a Buddhist Review. She was honored in The Best Science and Nature Writing 2000, published by Houghton Mifflin. Wendy is a mentor and advisor to the Edible Schoolyard program of the Chez Panisse Foundation, a project that she has been involved in since in its inception in 1995. This is her first book.
One Response to Wendy Johnson: 06-16-2012: The Four Elements Return to Their True Nature (Part 2 of 2)
Good talk. the quote from the girl at the Earth Summit was very powerful. One of the true hopes we collectively have would be to heal the Earth together and in so doing move away from the prison of a self seeking competive nature. How to do this? |
Abstract : Amazonian tree communities have already been seriously impacted by extreme natural droughts, and intense droughts are predicted to increase in frequency. However, our current knowledge of Amazonian tree species- responses to water stress remains limited, as plant trait databases include few drought tolerance traits, impeding the application and predictive power of models. Here we explored how leaf water potential at turgor loss point π tlp, a determinant of leaf drought tolerance, varies with species life history, season, tree size and irradiance within a forest in French Guiana. First, we provided a further direct validation of a rapid method of π tlp determination based on osmometer measurements of leaf osmotic potential at full hydration for five Amazonian tree species. Next, we analysed a dataset of 131 π tlp values for a range of species, seasons, size including saplings, and leaf exposure. We found that early-successional species had less drought-tolerant leaves than late-successional species. Species identity was the major driver of π tlp variation, whereas season, canopy tree size and leaf exposure explained little variation. Shifts in π tlp from saplings to canopy trees varied across species, and sapling leaf drought tolerance was a moderate predictor of canopy tree leaf drought tolerance. Given its low within-species variability, we propose that π tlp is a robust trait, and is useful as one index of species- drought tolerance. We also suggest that measuring this trait would considerably advance our knowledge on leaf drought tolerance in hyperdiverse communities and would thus likely shed light on the resilience of such vulnerable species-rich ecosystem. |
Industry Expert Validates Unprecedented Effectiveness in Removing Contaminants From Water
SANTA ANA, CA--(Marketwired - Sep 29, 2014) - BioLargo, Inc. (OTCQB: BLGO) announced that scientists at the University of Alberta Department of Agricultural, Food and Nutritional Science tested and validated its Advanced Oxidation System (AOS) Filter for use in food and agriculture. This work follows on the heels of validation work by the University of Alberta's Department of Engineering for its use in eliminating soluble organic contaminants like those found in oil sands tailings ponds.
The tests validated unprecedented effectiveness in destroying highly concentrated contaminants in sample water, including Listeria and Salmonella. Although the testing is applicable in many areas, food safety was a primary concern of this most recent work. Professor Lynn McMullen evaluated the results and commented, "The AOS Filter technology could be highly efficient in solving food safety problems and may be applied to improve food quality with the potential to improve storage life. The potential applications of the BioLargo AOS filter in the food industry could be endless -- from primary commodities to finished food products."
She further explained, "At the foundation of the AOS Filter is its efficiency in generating a highly oxidative state. The data supports its potential to accomplish high-level disinfection that can be useful in multiple markets including food processing and agriculture production. Extremely high levels of performance [disinfection] were achieved during testing and we are excited to expand the work with BioLargo to other applications targeting food safety concerns."
The company intends to expand its focus to include commercial opportunities for its AOS Filter within the agriculture and food processing industry. Its commercial success will depend upon commercial scale testing, finalizing design and engineering, refining target markets and proving efficacy, as well as general business sales, distribution and/or licensing resources, and appropriate regulatory approvals where needed.
Dennis Calvert, President of BioLargo, stated: "This validation further demonstrates the effectiveness of our AOS Filter technology and it points to the growing excitement for our significant commercial opportunity across multiple industries. We have already demonstrated the AOS Filter's ability to dismantle organic molecules commonly trapped in water, in 'seconds vs. hours' and at extremely low power levels. It is believed to offer a low cost solution when compared to all other technologies. Now, by expanding the work to include high-level disinfection within the food and agriculture industry, we can confidently point to the expanded scope of our future commercial markets. We believe the AOS Filter will dramatically impact every segment of the $350 billion water industry. We believe that many market opportunities will include strategic alliances and joint venture partners to exploit such a large opportunity as ours. We look forward to sharing additional scientific results as the various researcher teams publish them. We are very excited about this milestone, the expanding work within the Department of Agricultural, Food and Nutritional Science at the University of Alberta, and the massive commercial future for our AOS Filter."
About BioLargo, Inc. BioLargo, Inc. (OTCQB: BLGO) makes life better by delivering technology-based products that help solve some of the world's most important problems that threaten water, food, agriculture, healthcare and energy. More information can be found about the company and its subsidiaries at www.BioLargo.com. The subsidiary BioLargo Water, Inc. (www.BioLargoWater.com) showcases the Advanced Oxidation Systems, including its AOS Filter, a product in development specifically designed to eliminate common, troublesome, and dangerous (toxic) contaminants in water in a fraction of the time and cost of current technologies. BioLargo also owns a 50% interest in the Isan System, which was honored with a "Top 50 Water Company for the 21st Century" award by the Artemis Project. The subsidiary Odor-No-More Inc., features award-winning products serving the pet, equine, and consumer markets, including the Nature's Best Solution® and Deodorall® brands. (www.OdorNoMore.com). The subsidiary Clyra Medical Technologies, Inc. (www.ClyraMedical.com), focuses on advanced wound care management and is preparing to make FDA 510(k) applications in 2015.
Safe Harbor StatementThe statements contained herein, which are not historical, are forward-looking statements that are subject to risks and uncertainties that could cause actual results to differ materially from those expressed in the forward-looking statements, including, but not limited to, the risks and uncertainties included in BioLargo's current and future filings with the Securities and Exchange Commission, including those set forth in BioLargo's Annual Report on Form 10-K for the year ended December 31, 2013. |
Filex Kiprotich
Filex Kipchirchir Kiprotich (born 1988) is a Kenyan long-distance runner. In 2019 he won the Sydney Marathon and he set a new course record of 2:09:49. In this year he also won the Daegu Marathon held in Daegu, South Korea setting a new course record of 2:05:33.
In 2015 he won the Honolulu Marathon. In 2016 and 2017 he won the Gyeongju International Marathon.
Achievements
References
External links
Category:Living people
Category:1988 births
Category:Place of birth missing (living people)
Category:Kenyan male marathon runners
Category:Kenyan male long-distance runners |
A small Amsterdam startup called Medicinal Genomics, has analyzed the marijuana plant down to its strands of DNA, and the company's CEO says some analysis of the data will be available as an iPad app next fall.
For now, they've released the estimated 400 million base pairs that make up the Cannabis sativa genome on Amazon's EC2 public cloud.
The company hopes to grow marijuana plants tailored to have specific medicinal properties.
Advertisement
Kevin McKernan, Medicinal Genomics' CEO has been in biotech since 2000 when he cofounded Agencourt Bioscience. Cannabis caught his fancy after reading a 2003 study that outlined anticancer properties in cannabinoids. He told UPI that the medical marijuana market is growing by 50 percent every year, and having a detailed genome sequence will help with regulation.
"It's going to have to be a fairly regulated market," he said, "and regulation is going to come through genetics and fingerprinting of which strains are approved." |
Extra Outbuildings And Land Available By Separate NegotiationSituated in an idyllic location in Wigfair just outside the Cathedral City of St Asaph is Pen Y Bryn, a charming character filled farmhouse with exposed stone features, inglenook fireplaces and exposed...
Asking Price £595,000
An 18th century semi-detached converted farmhouse with original features in an idyllic rural location. Situated in Cefn Meiriadog on the outskirts of the cathedral city of St. Asaph. In the village there is a church and primary school and approximately 2 miles into St.
Offers in the region of £350,000
Beresford Adams are pleased to market this well presented four bedroom semi detached house situated in the popular city of St Asaph within close proximity of the A55 expressway and allows easy access for the commuters along the North Wales Coast. In brief the...
Asking Price £185,000
A spacious five bedroom, two reception room property with off road parking in the Cathedral City of St Asaph close to local amenities and the A55 North Wales Expressway giving access to motorway links towards Liverpool and Manchester. The accommodation comprises; hall ,
Offers Over £160,000
Beresford Adams are pleased to announce for sale this recently redecorated property that has also recently has a gas central heating boiler fitted. The property briefly comprises of entrance hall, kitchen diner, utility room, lounge, three spacious bedrooms and a wet...
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Very Aggressive Grinding Pad
Diamonds Offer Longer Life
The CRL 3M® Diamond Disc offers tremendous life compared to a standard silicon carbide disc. In addition, the edge quality is consistent throughout the life of the disc. This is because diamonds wear much slower than silicon carbide. Since diamonds cut rather than scratch like sandpaper, less pressure is required to accomplish the same material removal. Disc life and finish will always be improved when used with water. Supply the water by using a spray bottle or spray delivery system for best results. If used dry, wear appropriate dust protection equipment to guard against health hazards.
When working on clean cut (sharp edge) glass, use light pressure on first pass to remove sharp edges. Then increase pressure to suit desired grinding rate. Disc backing material is impervious to water, which help to aid the aggressive pressure adhesive in a positive grip on the disc pad. Although considerably more expensive, diamond discs can offer savings in situations where disc changing time or consistency of edge finish is critical.
Always wear the proper safety gear including eye protection and a respirator before grinding or sanding glass. Rotary tools of any kind will always pose a serious risk to the operator and anybody nearby. Serious injury and/or irreversible health hazards can occur if these warnings are disregarded.
Most shipping weights are approximate and have not been verified. If the exact weight is needed in order to determine shipping costs, and shipping costs are required in order for you to complete your order, please request this prior to submitting your order by contacting CRL Customer Service. Product images shown are of the actual product or a close representation. ColorsColours can vary depending on your computer's video card and on how your monitor's colorcolour is adjusted. |
Welcome to the Liberal Studies Major!
Startled and pleased when information and ideas overlap, when you see relationships?
Interested in a wide range of subjects and ways of inquiring about the world?
Curious to see how studies fit together, how one subject illuminates another?
Uneasy with the prospect of choosing just one major field of study or even choosing a double major?
If so, the Liberal Studies Major may be for you.
The Liberal Studies Major is a broad, multi-disciplinary major in the humanities and social sciences. Its core characteristic is flexibility and freedom, letting students tailor their college work toward exploration and broad cultural grounding for the bachelor’s degree, for teaching and other aspects of education, for those heading to graduate school, and for those contemplating careers in law, business, social service agencies like adult and family services, health and welfare organizations, criminal justice, research enterprises, or governmental service.
The wide range of careers depend on the skills and abilities cultivated by the major, such as the ability to gather, categorize, and implement approaches to difficult problems; the ability to understand and analyze complex concepts and to arrive at sound, defensible judgments and decisions regarding them; and the ability to organize information, draw inferences, write persuasively, and fashion memorable presentations.
The Liberal Studies Major, above all, allows students to cultivate their particular and developing interests. |
In the News
Marathon Drugs Increases Price 70-Fold – 2/10/17 More predation by pharma. Marathon has gotten a decades old muscular dystrophy drug, deflazacort, approved and is charging $89,000 a year for it. It’s price in Europe is under $1500/year. Where are the free market forces? Why aren’t our elected officials protecting us from this egregious practice?
Promising New Prostate Cancer Treatment – 2/2/17 A new and very effective prostate cancer treatment, reported here, has a two-year relapse rate of around 25%. Though clearly not a cure, it has a major benefit in that, unlike all other treatments, it has no. Light fibres are inserted in the prostate, rather like a biopsy, and a light-sensitive drug is administered. The cancerous tissue is killed, and all else left alone. Would certainly be worth a try.
Hypertension Developing Late in Life Halves Onset of Dementia – 1/21/17 Research here indicate that people who develop hypertension in late in life has almost half the reate of dementia. Yet more proof that hypertension has a purpose and unless it is off the charts, is best left alone.
Lowest Stroke Rates in Older Baby Boomers; Younger People Rising– 9/12/16 reports the American Heart Association, here. There could be numerous factors at work. Less smoking among the baby boomers and less healthy diet among the young would be our guess.
Sugar Lobby Promotes Sugar– 11/13/16 Surreal. JAMA reports here that the sugar lobby has been systematically attempting to put the blame for heart diseases on something other than sugar. What were they supposed to do? They’re the sugar lobby. The real question is, “Why did Standard Medicine buy it?”
Zika Breakthrough– 8/30/16 Reported here and elsewhere, two existing (already approved) drugs appear to be effective against Zika. If this pans out, it will speed things up immeasurably.
AHA Limits Added Sugar– 8/17/16 A sensible recommendation from the American Heart Association limits sugar for children aged 2-18 to fewer than 6 teaspoons a day. Paper here. A better recommendation: Fewer than 0 teaspoons added sugar per day for all children aged 0-110.
Calcium Supplements Linked to Dementia– 8/17/16 A report in the journal Neurology, here, links calcium supplements to dementia in some groups of women. The risk, alarmingly, is double for this group.
Suppression of Antioxidants Kills Pancreatic Cancer cells– 7/28/16 Researchers at Cold Springs Harbor Labs find that antioxidants are, in some cases, aiding cancer, and by suppressing the antioxidants, the oxidants are then able to kill the cancer. Link here.
High Cholesterol Found to be Cancer Protective– 7/9/16 A study presented at a British Cardiovascular Society Conference, link here, finds that high cholesterol is significantly protective for four common cancers: breast, prostate, lung, and colorectal. Reasons for this are unknown.
Zinc Acetate Lozenges Reduce Length of Common Cold– 7/6/16 Zinc for a cold is a Dr. Mike favorite. Here’s some science to back it up. A study published here finds that Zinc Acetate Lozenges shorten common colds by three days.
BMJ Article: Bad Cholesterol Isn’t Bad After All– 6/13/16 This is huge. In BMJ Open, here, a peer reviewed study finds that high “bad” cholesterol, aka LDL-cholesterol, is inversely associated with mortality. Higher levels=less death. The stuff is good for you. This is heresy of the first water. Expect a huge blow-back. The lipid hypothysis—that high LDL cholesterol causes heart disease—is ingrained in the medical community like an eleventh commandment. It has never been proven, and kudos to BMJ for daring to run this article. (We would crow that we have repeatedly posted that the dangers of LDL cholesterol were nonexistent, but we will be nice and refrain.)
Stem Cell Injection Reversed Strokes– 6/6/16 At Stanford, reported here, stroke patients receiving injection of mesenchymal stem cells directly into the brain experienced, in some cases, dramatic improvement. If this research holds up, this is an astounding result. “This wasn’t just, ‘They couldn’t move their thumb, and now they can.’ Patients who were in wheelchairs are walking now,” said lead researcher Steinberg.
Bariactric Surgery Now Recommended for Diabetes– 5/26/16 The American Diabetes Association (ADA), and other groups, have now endorsed bariactric surgery (stomach stapling) as a treatment for adult onset or type 2 diabetes (ADOM). We are not making this up. Report here. Of course the ADA dietary recommendations are almost guaranteed to prolong AODM, so we suppose some sort of strange logic is at work here. For the surgery-free, drug-free Quantitative Medicine method, click here.
Low Salt May Be Dangerous – 5/20/16 The prestigious British journal Lancet reports here that low salt intake is more dangerous than high intake. This is heresy, of course, and the article, the magazine, and the authors have already been condemned and will be burnt at the stake. The QM view is that high salt intake is a fairly minor factor. In this article, high intake is worse only for those with high blood pressure, whereas low salt intake is dangerous to those with high blood pressure, and those with normal blood pressure. Again, standard-practice medicine has been making things worse.
JAMA Discovers QM – 5/19/16 The prestigious Journal of the American Medical Association (JAMA) reports here that secession of of smoking, non-heavy drinking, and exercise reduce cancer. Now while it’s wonderful that they have now seen the light, or at least are circling around it, hasn’t this been obvious for the last 50 years? They studied only white males. Are they setting us up for a sequel? Let’s spoil that one: it works for everybody.
Calcium/Vitamin D Causes a Stroke or Heart Attack for Each Fracture prevented – 5/12/16 From a Norwegian study reported here, “Our analysis shows that if 100,000 65-year-old women take 1000 mg calcium every day, 5890 hip fractures and 3820 other fractures would be prevented. On the other hand, as many as 5917 heart attacks and 4373 strokes could be caused.” A horrid tradeoff made worse by the fact that osteoporosis is easily prevented and reversed with no supplements needed. See posts here, here, and here
Medical Error Third Leading Cause of Death in U.S. – 5/3/16 This is not news. As a leading cause of death in hospitals,medical error has been a focal area for almost 20 years. However, findings published here in the British Medical Journal.indicate the the problem is far from solved. Deaths due to medical error represent around 10% of deaths, some 250,000. One problem, according to the article, is that adequate records aren’t kept: the deaths are often attributed to something else. Best strategy: stay out of hospitals.
Big Pharma to World: Take Something! – 4/21/16 From JAMA, here, a trial was conducted for patients who couldn’t tolerate stains.(42%, in fact). The “solution” was to give them ezetimibe, a drug with no known benefit and some probably harm, a drug currently approved for a very, very narrow cohort of off-the-charts high cholesterol. Only 27% could not stand this drug, so the trial was considered a success. The drug industry seems insistent on cramming ezetimibe down our throats. To even embark on this strange experiment shows a callousness and disregard for patient benefit that surprises even us.
Is Fructose Highly Dangerous? – 4/21/16 Maybe. From UCLA we have a finding that fructose is linked to detrimental changes to hundreds of brain genes. Press release here. Scary stuff, and it makes some sense. The body goes to a lot of trouble to keep dietary fructose out of circulation, converting most of it to a concentrated form of glucose called glycogen, and rapidly removing any excess that does get into circulation. The reason for this aversion to fructose is not known, but the research sited above may provide a significant clue. Besides a major sugar component of fruit, table sugar is a 50-50 mix of fructose and glucose, as is high-fructose corn syrup, a ubiquitous food additive.
Are Proton Pump Inhibitors Overprescribed? – 4/15/16 A new report In the Journal of the American Society of Nephrolog seems to indicate that long term use of proton pump inhibitors, which significant reduce stomach acidity, causes increased kidney disease. Such drugs are widely prescribed and are also available over-the-counter. Though likely safe for short-term use, longer term consumption seems to have problems.
FDA Pulls Plug on Combo Drug – 4/15/16 In a rare glimmer of sanity, the FDA has withdrawn approval on a drug called Niaspan, which is a combination of statins and niacin. The approval was made in 1997. Given that is know that statins are practically useless, and that niacin actually increases heart problems, you may wonder what they were waiting for. So do we.Might they now consider the rest of the dangerous drugs out there? Details here.
Interesting Alzheimer’s-Insulin Result – 4/13/16 An NYU business school researcher has connected some interesting dots. It is well know that high insulin is involved in Alzheimers, but the connection wasn’t clear. It seems that the enzyme that breaks down insulin is the same one that breaks down amyloid-beta plaque, the tangled mess that is a hallmark of Alzheimer’s. Schiller’s idea is that perhaps the all the enzyme resources are spent on the high insulin, and the amyoid-beta doesn’t get removed. Details here.
Another Early Cancer Detection Breakthrough – 4/8/16 Researchers at Case Western Reserve University in Cleveland, OH, have created an optical biosensor for cancer detection that is a million times more sensitive than previous versions, pointing the way toward an effective early detection system for cancer and other illnesses.This might greatly improve early detection, which is ket to fighting cancer.Details here.
Choral Singing May Reduce Cancer – 4/5/16Researchers in Wales have determined that choral group singing improves levels of several anti-cancer hormones and biochemicals. Paper can be found here. In view of the next news item, the song Java Jive should probably be included in the repertoire.
Coffee Reduces Colorectal Cancer 50% – 4/1/16 Researchers at USC report “We found that drinking coffee is associated with lower risk of colorectal cancer, and the more coffee consumed, the lower the risk.” The press release is here. Dramatics reductions of up to 50% were seen. This area has been controversial for 20 years. The mechanism of cancer prevention is unknown, though it doesn’t seem to be caffeine, as decaf works as well.
Early Cancer Detection Breakthrough – 3/29/16Researchers at UCLA have developed a PET probe capable of producing far better images in certain types of cancers. With cancer, early detection is key. Clinical trials of the procedure may begin this year. Further info here.
Blonds Found to Be Non-Dumb – 3/23/16 A study here has found that blonds have a slightly higher IQ that non-blond people.Quoting,”Blonde women have a higher mean IQ than women with brown, red and black hair. Blondes are more likely classified as geniuses and less likely to have extremely low IQ.” It is hard to predict what researchers will think of to do research on. How about: “Do Blonds Have More Fun?”
Meal Time More Important Than Previously Thought – 3/17/16 Every traveler know that disrupting the circadian rhythm—the sleep cycle— is no picnic. New research from the Weizmann Institute indicates that not only is the body locked into this cycle, but even our mitochondria are. Mitochondria are tiny bacterial like cells found within almost all our own cells that convert the food we eat to energy. They apparently have time-driven hungry states, wherein they are ready and willing to convert the food to energy, and sleepy state as well. This means having meals at a regular time is more critical than previously thought.
Alzheimer’s and Brain Research – 3/17/16 There are almost daily reports of discoveries or possible breakthroughs involving Alzheimer’s and the brain. Just today, there are three such reports, all on mice, and so it is unknown if the results would carry over. There are reports of new neurons grown from stem cells, lost memories reactivate through light flashes, and increasing available neural energy by injecting pyruvate, an intermediate of glucose metabolism. A very active area.
Antidepressants Increase Mortality – 3/16/16 A study from Auburn and University of Alabama show a slight increase in mortality with uses of second generation anti-depressants.Report here. Knowledge of this will likely offset any anti-depression benefit as well. I much stronger anti-depressant that features a very strong reduction of mortality is exercise.
Canadian Medicine Discovers Exercise – 3/14/16 Canadian Medical Association announces: “Many doctors and their patients aren’t aware that exercise is a treatment for these chronic conditions and can provide as much benefit as drugs or surgery, and typically with fewer harms.” Not really. It actually provides A LOT MORE benefit. Bit it’s a step for organized medicine. Next week: hot water.
Exercise Reduces Alzheimer’s 50% – 3/11/16 No surprise at our end. But here, another study demonstrates the most effect way to prevent Alzheimer’s.
Alzheimer’s Caused By Microbes? – 3/10/16 Researchers have reported that a virus and two types of bacteria are a major cause of Alzheimers. A microbial connection has been (and probably will remain) controversial. However, the causes of Alzheimer’s are not known.
Magic Pill Announced – 3/4/16 Drug companies adore lifelong drugs, and the latest “breakthrough” combines statins, blood pressure reducers, aspirin, and adult onset diabetes medication, and is called a Polypill. However none of these four have shown any mortality benefit, and all of them have serious side effects. But in combination, they are suddenly magical? The idea seems to be to get rid of screening and blood testa altogether, and put everyone over 50 on this pill. This idea is so bad, it would be praising it to call it crazy.
Breast Cancer Breakthrough – 3/3/16 A new drug combo is very effective against the HER-2 variant of breast cancer. A fourth of those treated saw dramatic reduction in tumor size, while in an additional 11% the tumor completely disappeared, in under two weeks. Details here.
Television Exposure Directly Linked To A Thin Body Ideal In Women – 2/22/16 The only real question here is: Are they paying grown-ups to come up with this? It’s a real study. Details here. What will they study next? How about: Driving Blindfolded May Increase Accident Risk.
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Are SGLT2 Inhibitors a Bad Idea?
SGLT2 Inhibitors are the Latest Treatment for Adult Onset Diabetes. However, Many Treatment, Like Insulin, Have Done More Harm Than Good. Caution is Advised.
Brilliant basic science research continues its quest to understand human physiology. Pharmaceutical science continues its quest to cash in on the latest basic science discoveries. I want to illustrate this specifically with SGLT2 inhibitors. In that setting I also want to ask what is the ethical duty of the medical profession towards those suffering with Adult Onset Diabetes Mellitus (AODM)?
SGLT2 inhibitors block the type 2 sodium-glucose-transport system in the kidneys. What the heck is that?
The kidneys serve as a passive filter, somewhat like cheesecloth, as an active pump emitting undesired chemicals in the urine and as an active pump holding onto presumably desirable chemicals. The kidneys are very good at actively holding onto glucose; it exchanges, spits out, sodium, in order to hold onto glucose. There are two such known systems, I bet you guessed, called SGLT1 and SGLT2.
In diabetes blood glucose can become high enough to exceed the capacity of the kidneys to hold onto glucose and then it escapes into the urine; called glycosuria. In Type I the threshold is about 150 mg/dl before the glucose escapes into the urine. In AODM the threshold can be even higher, much higher, so by using the SGLT2 inhibitors those with AODM more or less urinate out a lot of their glucose. It does seem odd, another blog post to discuss this, that the kidneys try even harder to hold onto glucose in AODM than in health or even Type I DM.
Those advocating the use of SGLT2 inhibitors point to water-weight loss, consequent, though temporary, lower blood pressure and other virtues. They minimize currently known side effects like ‘yeast’ infections in both men and women and confess that we don’t really know anything about long term consequences. What we do know is that blood glucose goes down. Analogies are made to mice models without, called ‘knock out mice,’ SGLT2 who seem to be doing alright; I mention this to give them their due for clever work looking at SGLT2 inhibitors. All and all from the basic science, pharmaceutical and clinical science perspective this is all very elegant work.
But is it a good idea for every doc on the block to be handing out SGLT2 inhibitors? At first blush it might seem that giving someone with AODM a new drug that lowers their glucose can only be helpful. In fact the argument goes something like this, taken from Medscape, a largely doc portal:
“According to the Center for Disease Control and Prevention, diabetes presents features of an epidemic: it is common, disabling and deadly. Approximately 25.8 million people in the USA (8.3% of the population) have been diagnosed with diabetes. It is the leading cause of blindness, kidney failure and non-traumatic foot amputation, and it has been reported as the seventh leading cause of death as listed on the US death certificates in 2007. It has been estimated that incase the current trend continue, one of three US adults will have diabetes by 2050. From the financial point of view, the total cost (direct and indirect) of diabetes in 2007 was $174 billion of which $116 billion was direct medical cost.”
OK, with that ringing in your ears, it seems urgent to find every single drug that ameliorates AODM and docs should be writing prescriptions for those drugs at the drop of the proverbial ‘hat.’
But wait. It is still common to prescribe injectable insulin for AODM even though, given alone, this has been shown to increase the risk of cancer by nearly 50%. It took years and the lives of many people before this was known and still it is common practice.
So, caution is in order with any new approach to an old disease. However even this is not my objection to using the SGLT2 inhibitors. I have an even more broadly-based objection.
In the words of a better, more persuasive writer, my objection would lead you to this conclusion: it is the ethical duty of the medical profession to always and everywhere advocate personal behavior and cultural trends which support people in overcoming AODM by the simple, powerful and effective expedients of better diet, better sleep and more, and more effective, exercise. My claim is few do this not merely from lack of will power but from the continuing misdirection of the medical and pharmaceutical communities that such a simple cure is impossible but for the supermen and women among us. This is not so; with the conviction that it is possible, and quantitative and reliable guidance, anyone can do it.
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New App
We have created a free iPhone shopping list app for the book Eat Real Vietnamese Food. It contains ingredient list for all the recipes and will populate the shopping list with the desired serving amount. It is also usable as a general purpose shopping app. Search “Eat Real Food Vietnam” in the App store. Similar app under development for Eat Real Food or Else.
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Use code ERVF50 for 50% discount
Why does Quantitative Medicine work?
Many sites offer nice-sounding advice about nutrition and exercise, but almost none have actually put this advice to work in a large-scale clinical setting. Starting in the late 90s, Dr. Mike Nichols operated a clinic wherein each patient was quantified with blood tests and other measurements, and an optimum diet and exercise regime suggested.
This became a continual process and Dr. Mike has accumulated data on hundreds of people for almost 20 years. At this point in the process, he knows what works, what doesn’t, how to restore health, slow aging, and block degenerative disease. But the formula is different for everyone, and without measurement, lifestyle recommendations are just a medical guessing game. Is Paleo best? For some, sure. But without measurement, there is no way to tell.
But more importantly, when the optimum lifestyle is determined, implemented, and actually achieved, almost all people get well, and life’s chronic diseases are slowed, often reversed.
This is no idle claim or hopeful promise. This has already worked in a clinical setting, long-term and with real people. Given how different people are, it is folly to try to apply a one-size-fits-all set of recommendations. The sooner this is realized, the faster the planet will get well. Quantitative Medicine is the future.
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Email Address
Mike Nichols, M.D.
Charles Davis, Ph.D.
What Is Quantitative Medicine?
Quantitative medicine is the practice of determining and modifying your health guided by direct measurement of meaningful biological markers. Everyone is different. The best diet is unique to each of us. Diet markers must be directly and precisely measured.
Why Are We Doing This?
My practice has been highly successful. Many many people have gotten well, have avoided degenerative diseases, have extended their lives. But my practice is full.
By starting this blog, I am taking the first steps to make Quantitative Medicine available to everyone. You, the patient, supply the self-discipline, physical, mental, and spiritual perseverance, and we will supply the information and resources you need to realize the full benefits of Quantitative Medicine.
By measurement, an optimally healthy lifestyle can be determined for anyone. The results are profound and pervasive. Degenerative disease is prevented or rolled back. Longevity – healthy active longevity – is increased. This has worked for over 2000 patients.
This blog is just starting. There will be videos, books, ebooks, ebooklets, on-line analysis tools, in short, everything you will need. Some will be free, and some will not. None of it, though, will be expensive.
For now we are just getting started. A lot more information is coming, so please stay tuned. |
Q:
.addClass() where data-id equals data-category?
Here I have constructed a fiddle, I cant think of how to .addClass where the clicked data-id equals the data-category. Take a look at the fiddle, you will understand much better.
Fiddle
Here I just .addClass to all the .item classes, Im not sure how to write it so that it adds class to the data-category that matches the data-id.
Uncompleted jQuery Snippet:
$(".breadcrumb-cell .breadcrumb").click(function () {
var theID = $(this).data("id"),
theCAT = $('.item').attr("data-category"),
item = $('.item')
//This just shows you that when you click the element it returns the data-id each click
alert(theID);
// Here I gave it a few shots but no success, so I just add .active to all
item.addClass('active');
});
This feels kinda noobish but I havent messed with this kind of write up (matching data attributes) so a little bump of knowledge would be stupendous.
Answer: by: Sushanth --
$(".breadcrumb-cell .breadcrumb").click(function () {
var theID = $(this).data("id"),
$allItem = $('.item'),
$currItem = $('.item[data-category=' + theID + ']')
$currItem.addClass('active');
$allItem.not($currItem).removeClass('active');
});
A:
You can use this selector
$('.item[data-category=' + theID + ']').addClass('active');
This selector matches all the items that has a specific data-category
Code
$(".breadcrumb-cell .breadcrumb").click(function () {
// This will have the category
var theID = $(this).data("id"),
// All items
$allItem = $('.item');
// Current item is should be active
var $currItem = $('.item[data-category=' + theID + ']');
$('.item[data-category=' + theID + ']').addClass('active');
// Remove the active class for other items
$allItem.not($currItem).removeClass('active');
});
Check Demo
A:
fiddle
var items = $('.item');
$(".breadcrumb-cell .breadcrumb").click(function () {
var theID = $(this).data("id");
items.filter(function() {
return $(this).data('category') === theID;
}).addClass('active');
});
You can use the filter method. This is useful if you're going to be using items elsewhere as well as for this.
|
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