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This post is a more carefully thought out and peer reviewed version of a floating-point comparison article I wrote many years ago. This one gives solid advice and some surprising observations about the tricky subject of comparing floating-point numbers.
We've finally reached the point in this series that I've been waiting for. In this post I am going to share the most crucial piece of floating-point math knowledge that I have. Here it is:
[Floating-point] math is hard.
You just won't believe how vastly, hugely, mind-bogglingly hard it is. I mean, you may think it's difficult to calculate when trains from Chicago and Los Angeles will collide, but that's just peanuts to floating-point math.
Seriously. Each time I think that I've wrapped my head around the subtleties and implications of floating-point math I find that I'm wrong and that there is some extra confounding factor that I had failed to consider. So, the lesson to remember is that floating-point math is always more complex than you think it is. Keep that in mind through the rest of the post where we talk about the promised topic of comparing floats, and understand that this post gives some suggestions on techniques, but no silver bullets.
Previously on this channel…
This is the fifth chapter in a long series. The first couple in the series are particularly important for understanding this point. A (mostly) complete list of the other posts includes:
- 1: Tricks With the Floating-Point Format – an overview of the float format
- 2: Stupid Float Tricks – incrementing the integer representation
- 3: Don't Store That in a Float – a cautionary tale about time
- 3b: They sure look equal… – special bonus post (not on altdevblogaday), ranting about Visual Studio's float failings
- 4: Comparing Floating Point Numbers, 2012 Edition (return *this;)
- 5: Float Precision–From Zero to 100+ Digits
- 6: C++ 11 std::async for Fast Float Format Finding – running tests on all floats in just a few minutes
- 7: Intermediate Floating-Point Precision – the surprising complexities of how expressions can be evaluated
- 8: Floating-point complexities – some favorite quirks of floating-point math
- 9: Exceptional Floating Point – using floating point exceptions for fun and profit
- 10: That's Not Normal–the Performance of Odd Floats – the performance implications of infinities, NaNs, and denormals
- 11: Doubles are not floats, so don't compare them – a common type of float comparison mistake
- 12: Float Precision Revisited: Nine Digit Float Portability – moving floats between gcc and VC++ through text
Comparing for equality
Floating point math is not exact. Simple values like 0.1 cannot be precisely represented using binary floating point numbers, and the limited precision of floating point numbers means that slight changes in the order of operations or the precision of intermediates can change the result. That means that comparing two floats to see if they are equal is usually not what you want. GCC even has a warning for this: "warning: comparing floating point with == or != is unsafe".
Here's one example of the inexactness that can creep in:
float f = 0.1f; float sum; sum = 0; for (int i = 0; i < 10; ++i) sum += f; float product = f * 10; printf("sum = %1.15f, mul = %1.15f, mul2 = %1.15f\n", sum, product, f * 10);
This code shows two ancient and mystical techniques for calculating 'one'. I call these techniques "iterative-adding" and "multiplying". And, just to show how messy this stuff is I do the multiplication twice. That's three separate calculations of the same thing. Naturally we get three different results, and only one of them is the unity we were seeking:
sum=1.000000119209290, mul=1.000000000000000, mul2=1.000000014901161
Disclaimer: the results you get will depend on your compiler and your compiler settings, which actually helps make the point.
So what happened, and which one is correct?
What do you mean 'correct'?
Before we can continue I need to make clear the difference between 0.1, float(0.1), and double(0.1). In C/C++ 0.1 and double(0.1) are the same thing, but when I say "0.1" in text I mean the exact base-10 number, whereas float(0.1) and double(0.1) are rounded versions of 0.1. And, to be clear, float(0.1) and double(0.1) don't have the same value, because float(0.1) has fewer binary digits, and therefore has more error. Here are the values for 0.1, float(0.1), and double(0.1):
|0.1 (duh)
|0.10000000000000000555111512312578270211815834045 41015625
With that settled, let's look at the results of the code above:
- sum = 1.000000119209290: this calculation starts with a rounded value and then adds it ten times with potential rounding at each add, so there is lots of room for error to creep in. The final result is not 1.0, and it is not 10 * float(0.1). However it is the next representable float above 1.0, so it is very close.
- mul = 1.000000000000000: this calculation starts with a rounded value and then multiplies by ten, so there are fewer opportunities for error to creep in. It turns out that the conversion from 0.1 to float(0.1) rounds up, but the multiplication by ten happens to, in this case, round down, and sometimes two rounds make a right. So we get the right answer for the wrong reasons. Or maybe it's the wrong answer, since it isn't actually ten times float(0.1)
- mul2 = 1.000000014901161: this calculation starts with a rounded value and then does a double-precision multiply by ten, thus avoiding any subsequent rounding error. So we get a different right answer – the exact value of 10 * float(0.1) (which can be stored in a double but not in a float).
So, answer one is incorrect, but it is as close to 1.0 as a float can get without being there. Answer two is arguably correct, but so is answer three.
Now what?
Now we have a couple of different answers (I'm going to ignore the double precision answer), so what do we do? What if we are looking for results that are equal to one, but we also want to count any that are plausibly equal to one – results that are "close enough".
Epsilon comparisons
If comparing floats for equality is a bad idea then how about checking whether their difference is within some error bounds or epsilon value, like this:
bool isEqual = fabs(f1 – f2) <= epsilon;
With this calculation we can express the concept of two floats being close enough that we want to consider them to be equal. But what value should we use for epsilon?
Given our experimentation above we might be tempted to use the error in our sum, which was about 1.19e-7f. In fact, there's even a define in float.h with that exact value, and it's called FLT_EPSILON.
Clearly that's it. The header file gods have spoken and FLT_EPSILON is the one true epsilon!
Except that that is rubbish. For numbers between 1.0 and 2.0 FLT_EPSILON represents the difference between adjacent floats. For numbers smaller than 1.0 an epsilon of FLT_EPSILON quickly becomes too large, and with small enough numbers FLT_EPSILON may be bigger than the numbers you are comparing!
For numbers larger than 2.0 the gap between floats grows larger and if you compare floats using FLT_EPSILON then you are just doing a more-expensive and less-obvious equality check. For numbers above 16777216 the appropriate epsilon to use for floats is actually greater than one, and a comparison using FLT_EPSILON just makes you look foolish. We don't want that.
Relative epsilon comparisons
The idea of a relative epsilon comparison is to find the difference between the two numbers, and see how big it is compared to their magnitudes. In order to get consistent results you should always compare the difference to the larger of the two numbers. In English:
To compare f1 and f2 calculate diff = fabs(f1-f2). If diff is smaller than n% of max(abs(f1),abs(f2)) then f1 and f2 can be considered equal.
In code:
bool AlmostEqualRelative(float A, float B, float maxRelDiff) { // Calculate the difference. float diff = fabs(A - B); A = fabs(A); B = fabs(B); // Find the largest float largest = (B > A) ? B : A; if (diff <= largest * maxRelDiff) return true; return false; }
This function is not bad. It works. Mostly. I'll talk about the limitations later, but first I want to get to the point of this article – the technique that I first suggested many years ago.
When doing a relative comparison of floats it works pretty well to set maxRelDiff to FLT_EPSILON, or some small multiple of FLT_EPSILON. Anything smaller than that and it risks being equivalent to no epsilon. You can certainly make it larger, if greater error is expected, but don't go crazy. However selecting the correct value for maxRelativeError is a bit tweaky and non-obvious and the lack of a direct relationship to the floating point format being used makes me sad.
ULP, he said nervously
We already know that adjacent floats have integer representations that are adjacent. This means that if we subtract the integer representations of two numbers then the difference tells us how far apart the numbers are in float space. That brings us to:
Dawson's obvious-in-hindsight theorem:
If the integer representations of two same-sign floats are subtracted then the absolute value of the result is equal to one plus the number of representable floats between them.
In other words, if you subtract the integer representations and get one, then the two floats are as close as they can be without being equal. If you get two then they are still really close, with just one float between them. The difference between the integer representations tells us how many Units in the Last Place the numbers differ by. This is usually shortened to ULP, as in "these two floats differ by two ULPs."
So let's try that concept:
/* See https://randomascii.wordpress.com/2012/01/11/tricks-with-the-floating-point-format/ for the potential portability problems with the union and bit-fields below. */ union Float_t { Float_t(float num = 0.0f) : f(num) {} // Portable extraction of components. bool Negative() const { return (i >> 31) != 0; } int32_t RawMantissa() const { return i & ((1 << 23) - 1); } int32_t RawExponent() const { return (i >> 23) & 0xFF; } int32_t i; float f; #ifdef _DEBUG struct { // Bitfields for exploration. Do not use in production code. uint32_t mantissa : 23; uint32_t exponent : 8; uint32_t sign : 1; } parts; #endif }; bool AlmostEqualUlps(float A, float B, int maxUlpsDiff) { Float_t uA(A); Float_t uB(B); // Different signs means they do not match. if (uA.Negative() != uB.Negative()) { // Check for equality to make sure +0==-0 if (A == B) return true; return false; } // Find the difference in ULPs. int ulpsDiff = abs(uA.i - uB.i); if (ulpsDiff <= maxUlpsDiff) return true; return false; }
This is tricky and perhaps profound.
The check for different signs is necessary for several reasons. Subtracting the signed-magnitude representation of floats using twos-complement math isn't particularly meaningful, and the subtraction would produce a 33-bit result and overflow. Even if we deal with these technical issues it turns out that an ULPs based comparison of floats with different signs doesn't even make sense.
After the special cases are dealt with we simply subtract the integer representations, get the absolute value, and now we know how different the numbers are. The 'ulpsDiff' value gives us the number of floats between the two numbers (plus one) which is a wonderfully intuitive way of dealing with floating-point error.
One ULPs difference good (adjacent floats).
One million ULPs difference bad (kinda different).
Comparing numbers with ULPs is really just a way of doing relative comparisons. It has different characteristics at the extremes, but in the range of normal numbers it is quite well behaved. The concept is sufficiently 'normal' that boost has a function for calculating the difference in ULPs between two numbers.
A one ULP difference is the smallest possible difference between two numbers. One ULP between two floats is far larger than one ULP between two doubles, but the nomenclature remains terse and convenient. I like it.
ULP versus FLT_EPSILON
It turns out checking for adjacent floats using the ULPs based comparison is quite similar to using AlmostEqualRelative with epsilon set to FLT_EPSILON. For numbers that are slightly above a power of two the results are generally the same. For numbers that are slightly below a power of two the FLT_EPSILON technique is twice as lenient. In other words, if we compare 4.0 to 4.0 plus two ULPs then a one ULPs comparison and a FLT_EPSILON relative comparison will both say they are not equal. However if you compare 4.0 to 4.0 minus two ULPs then a one ULPs comparison will say they are not equal (of course) but a FLT_EPSILON relative comparison will say that they are equal.
This makes sense. Adding two ULPs to 4.0 changes its magnitude twice as much as subtracting two ULPs, because of the exponent change. Neither technique is better or worse because of this, but they are different.
If my explanation doesn't make sense then perhaps my programmer art will:
ULP based comparisons also have different performance characteristics. ULP based comparisons are more likely to be efficient on architectures such as SSE which encourage the reinterpreting of floats as integers. However ULPs based comparisons can cause horrible stalls on other architectures, due to the cost of moving float values to integer registers.
Normally a difference of one ULP means that the two numbers being compared have similar magnitudes – the larger one is usually no larger than 1.000000119 times larger than the smaller. But not always. Some notable exceptions are:
- FLT_MAX to infinity – one ULP, infinite ratio
- zero to the smallest denormal – one ULP, infinite ratio
- smallest denormal to the next smallest denormal – one ULP, two-to-one ratio
- NaNs – two NaNs could have very similar or even identical representations, but they are not supposed to compare as equal
- Positive and negative zero – two billion ULPs difference, but they should compare as equal
- One ULP above a power of two is twice as big a delta as one ULP below
That's a lot of notable exceptions. For many purposes you can ignore NaNs (you should be enabling illegal operation exceptions so that you find out when you generate them) and infinities (ditto for overflow exceptions) so that leaves denormals and zeros as the biggest possible problems. In other words, numbers at or near zero.
Infernal zero
It turns out that the entire idea of relative epsilons breaks down near zero. The reason is fairly straightforward. If you are expecting a result of zero then you are probably getting it by subtracting two numbers. In order to hit exactly zero the numbers you are subtracting need to be identical. If the numbers differ by one ULP then you will get an answer that is small compared to the numbers you are subtracting, but enormous compared to zero.
Consider the sample code at the very beginning. If we add float(0.1) ten times then we get a number that is obviously close to 1.0, and either of our relative comparisons will tell us that. However if we subtract 1.0 from the result then we get an answer of FLT_EPSILON, where we were hoping for zero. If we do a relative comparison between zero and FLT_EPSILON, or pretty much any number really, then the comparison will fail. In fact, FLT_EPSILON is 872,415,232 ULPs away from zero, despite being a number that most people would consider to be pretty small.
For another example, consider this calculation:
float someFloat = 67329.234; // arbitrarily chosen
float nextFloat = 67329.242; // exactly one ULP away from 'someFloat'
bool equal = AlmostEqualUlps( someFloat, nextFloat, 1); // returns true, numbers 1 ULP apart
Our test shows that someFloat and nextFloat are very close – they are neighbors. All is good. But consider what happens if we subtract them:
float diff = (nextFloat – someFloat); // .0078125000
bool equal = AlmostEqualUlps( diff, 0.0f, 1 ); // returns false, diff is 1,006,632,960 ULPs away from zero
While someFloat and nextFloat are very close, and their difference is small by many standards, 'diff' is a vast distance away from zero, and will dramatically and emphatically fail any ULPs or relative based test that compares it to zero.
There is no easy answer to this problem.
The most generic answer to this quandary is to use a mixture of absolute and relative epsilons. If the two numbers being compared are extremely close – whatever that means – then treat them as equal, regardless of their relative values. This technique is necessary any time you are expecting an answer of zero due to subtraction. The value of the absolute epsilon should be based on the magnitude of the numbers being subtracted – it should be something like maxInput * FLT_EPSILON. Unfortunately this means that it is dependent on the algorithm and the inputs. Charming.
The ULPs based technique also breaks down near zero for the technical reasons discussed just below the definition of AlmostEqualUlps.
Doing a floating-point absolute epsilon check first, and then treating all other different-signed numbers as being non-equal is the simpler and safer thing to do. Here is some possible code for doing this, both for relative epsilon and for ULPs based comparison, with an absolute epsilon 'safety net' to handle the near-zero case:
bool AlmostEqualUlpsAndAbs(float A, float B, float maxDiff, int maxUlpsDiff) { // Check if the numbers are really close -- needed // when comparing numbers near zero. float absDiff = fabs(A - B); if (absDiff <= maxDiff) return true; Float_t uA(A); Float_t uB(B); // Different signs means they do not match. if (uA.Negative() != uB.Negative()) return false; // Find the difference in ULPs. int ulpsDiff = abs(uA.i - uB.i); if (ulpsDiff <= maxUlpsDiff) return true; return false; } bool AlmostEqualRelativeAndAbs(float A, float B, float maxDiff, float maxRelDiff) { // Check if the numbers are really close -- needed // when comparing numbers near zero. float diff = fabs(A - B); if (diff <= maxDiff) return true; A = fabs(A); B = fabs(B); float largest = (B > A) ? B : A; if (diff <= largest * maxRelDiff) return true; return false; }
Catastrophic cancellation, hiding in plain sight
If we calculate f1 – f2 and then compare the result to zero then we know that we are dealing with catastrophic cancellation, and that we will only get zero if f1 and f2 are equal. However, sometimes the subtraction is not so obvious.
Consider this code:
It's straightforward enough. Trigonometry teaches us that the result should be zero. But that is not the answer you will get. For double-precision and float-precision values of pi the answers I get are:
sin(double(pi)) = +0.00000000000000012246467991473532
sin(float(pi)) = -0.000000087422776
If you do an ULPs or relative epsilon comparison to the correct value of zero then this looks pretty bad. It's a long way from zero. So what's going on? Is the calculation of sin() really that inaccurate?
Nope. The calculation of sin() is pretty close to perfect. The problem lies elsewhere. But to understand what's going on we have to invoke… calculus!
But first we have to acknowledge that we aren't asking the sin function to calculate sin(pi). Instead we are asking it to calculate sin(double(pi)) or sin(float(pi)). What with pi being a transcendental and irrational and all it should be no surprise that pi cannot be exactly represented in a float, or even in a double.
Therefore, what we are really calculating is sin(pi-theta), where theta is a small number representing the difference between 'pi' and float(pi) or double(pi).
Calculus teaches us that, for sufficiently small values of theta, sin(pi-theta) == theta. Therefore, if our sin function is sufficiently accurate we would expect sin(double(pi)) to be roughly equal to pi-double(pi). In other words, sin(double(pi)) actually calculates the error in double(pi)! This is best shown for sin(float(pi)) because then we can easily add float(pi) to sin(float(pi)) using double precision. Insert table here:
|float(pi) + sin(float(pi))
If you haven't memorized pi to 15+ digits then this may be lost on you, but the salient point is that float(pi) + sin(float(pi)) is a more accurate value of pi than float(pi). Or, alternately, sin(float(pi)) tells you nothing more than the error in float(pi).
Woah. Dude.
Again: sin(float(pi)) equals the error in float(pi).
I'm such a geek that I think that is the coolest thing I've discovered in quite a while.
Think about this. Because this is profound. Here are the results of comparing sin('pi') to the error in the value of 'pi' passed in:
sin(double(pi)) = +0.0000000000000001224646799147353207
pi-double(pi) = +0.0000000000000001224646799147353177
sin(float(pi)) = -0.000000087422776
pi-float(pi) = -0.000000087422780
Wow. Our predictions were correct. sin(double(pi)) is accurate to sixteen to seventeen significant figures as a measure of the error in double(pi), and sin(float(pi)) is accurate to six to seven significant figures. The main reason the sin(float(pi)) results are less accurate is because operator overloading translates this to (float)sin(float(pi)).
I think it is perversely wonderful that we can use double-precision math to precisely measure the error in a double precision constant. If VC++ would print the value of double(pi) to more digits then we could use this and some hand adding to calculate pi to over 30 digits of accuracy!
You can see this trick in action with a calculator. Just put it in radians mode, try these calculations, and note how the input plus the result add up to pi. Nerdiest bar trick ever:
pi =3.1415926535…
The point is, that sin(float(pi)) is actually calculating pi-float(pi), which means that it is classic catastrophic cancellation. We should expect an absolute error (from zero) of up to about 3.14*FLT_EPSILON/2, and in fact we get a bit less than that.
Know what you're doing
There is no silver bullet. You have to choose wisely.
- If you are comparing against zero, then relative epsilons and ULPs based comparisons are usually meaningless. You'll need to use an absolute epsilon, whose value might be some small multiple of FLT_EPSILON and the inputs to your calculation. Maybe.
- If you are comparing against a non-zero number then relative epsilons or ULPs based comparisons are probably what you want. You'll probably want some small multiple of FLT_EPSILON for your relative epsilon, or some small number of ULPs. An absolute epsilon could be used if you knew exactly what number you were comparing against.
- If you are comparing two arbitrary numbers that could be zero or non-zero then you need the kitchen sink. Good luck and God speed.
Above all you need to understand what you are calculating, how stable the algorithms are, and what you should do if the error is larger than expected. Floating-point math can be stunningly accurate but you also need to understand what it is that you are actually calculating. If you want to learn more about algorithm stability you should read up on condition numbers and consider getting Michael L Overton's excellent book Numerical Computing with IEEE Floating Point Arithmetic.
The true value of a float
In order to get the results shown above I used the same infinite precision math library I created for Fractal eXtreme to check all the math and to print numbers to high precision. I also wrote some simple code to print the true values of floats and doubles. Next time I'll share the techniques and code used for this extended precision printing – unlocking one more piece of the floating-point puzzle, and explaining why, depending on how you define it, floats have a decimal precision of anywhere from one to over a hundred digits.
Thanks to Florian Wobbe for his excellent error finding and many insights into this topic.
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Letter: Her record speaks volumes
Nick Carsillo, Naples
Her record speaks volumes
It's now time to re-elect Kathleen Passidomo for District 106.
Passidomo's track record speaks volumes as to why she should be re-elected. We are facing major challenges in this country, the state of Florida, and District 106. We need to have Passidomo lead the way to keep District 106 as one of the best managed districts in the state of Florida. Her integrity, creditability and response to all challenges has been proven over and over.
A vote for Passidomo will ensure our well-being moving on into the future.
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East Bay Water, Sewer Rates Headed Higher
June 11, 2014 5:53 PM
Anna Duckworth
Anna started her broadcasting career at KCBS in 1994, a few mont...Read More
OAKLAND (KPIX 5) — Water rates at the East Bay's largest water district are on the increase beginning next month.
Customers of the East Bay Municipal Utilities District will pay 9.5 percent more following a unanimous vote by the board.
Other customers in western Contra Costa and Alameda counties will also pay 8.5 percent higher sewer rates.
EBMUD said the hikes are needed to improve maintenance and for replacement of old pipes and equipment.
"We have an aging system and maintaining it is costing us more," said EBMUD spokeswoman Abby Figueroa. "So we're looking at having to replace more miles of pipelines every year."
The water rate increase is similar to one that took effect a year ago.


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The Blog
Romney on Chicago Teachers' Strike: 'I Am Disappointed'
12:06 PM, Sep 10, 2012 • By MICHAEL WARREN
Republican presidential candidate Mitt Romney issued a statement about Monday's teachers' strike in Chicago:
Romney's statement refers to Vice President Joe BIden's 2011 speech to the National Education Association's annual meeting. "One thing you should not have any doubt in your mind about is that Barack Obama, he is on your side," Biden said in his speech. "Make no mistake about it. He will and I will and we will, we will ‑‑ we will fight alongside you. We will fight for you."
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- Infowars - http://www.infowars.com -
Bikini Girl With Machine Gun Defends Liberty – Reporter Contest
Posted By aaron On April 26, 2012 @ 1:55 pm In Featured Stories,Old Infowars Posts Style,Tile | Comments Disabled
April 26, 2012
Reporter: Amanda Liberty
Video Production: Craig Boileau
The only way to defend our rights is by exercising them and that's exactly what Amanda Liberty is doing. The 20 year old from Florida displays her affection for the 2nd Amendment, heavy artillery, and ammunition in her video submission for the Infowars reporter contest. Don't be fooled by her youthful appearance! In the video she states, "I may only be 20 years old, but I can see what's going on in our country."
With the help of her producer Craig Boileau, she composed a video that positively sent shock waves throughout the Infowars compound. It has since been featured in opening segments of the Infowars Nightly News, as well as Alex's nationally syndicated talk show, broadcast visually through Prisonplanet.tv.
It's evident Amanda sees through the lies fed to us by our government and mainstream media with statements like, "You cannot get the truth from typical TV news. They are lying to us," and "There are precious few sources for current news that isn't propaganda."
Seen handling fully automatic firearms, she demonstrates she's definitely not afraid to take matters into her own hands: "I have one of these because the government won't and can't protect you." She also expresses her desire to seek the truth and her admiration of Alex and the information he puts forth stating, "Alex Jones is someone who we the people can trust…He always tells the truth."
It's people like Amanda who help keep our 2nd Amendment rights intact. The phrase "use it or lose it" applies; get to your local sporting goods store or gun show and purchase arms before your right gets revoked. Like the Granny who thwarted 2 would-be robbers with her own gun earlier this week, people need to stop being afraid of firearms and start learning that they are vital to ensure our personal security.
George Washington's infamous quote on bearing arms "bears" repeating: "Firearms stand next in importance to the constitution itself. They are the American people's liberty teeth…"
Amanda eloquently concludes,"If you don't have one of these, all you can do is throw rocks." Undoubtedly she would make our nation's Founding Fathers extremely happy.
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Montreal: A Market That is Performing Better Than You Think
Drawing upon the experience and the success of similar events in Vancouver, Calgary, Edmonton, and Toronto, the 17th annual Montreal Real Estate Forum will be a highly informative conference examining key challenges and opportunities in one of Canada's major markets.
Chaired by Sylvain Cossette, Executive Vice President & Chief Operating Officer, Cominar REIT, the Forum will feature a strong program, developed by a committee of industry executives. Over 890 real estate executives attended the 2014 conference which was sold out several weeks in advance.
The conference will offer over 60 speakers, presentations and panel discussions on the economic drivers responsible for the city's growth; the major trends in the office, industrial, retail, multi-unit residential, and land markets; how much development and renewal activity is underway; why investors are active in Montreal; and what municipal initiatives and strategies are facilitating growth.
UDI Québec, the leading real estate association in the province, is the principal sponsor of the Forum.
The annual UDI Real Estate Evening will be held on the night prior to the Montreal Real Estate Forum. Considered to be the Montreal real estate community's largest annual social event, the Real Estate evening is a very well attended and ideal networking opportunity for conference attendees.
The Forum will be targeted at the interests of real estate executives, brokers, developers, investors, asset managers, and other professionals active in the acquisition, leasing, financing, management, and marketing of office, industrial, retail, and multi-unit residential real estate.
The discussions will help you determine what strategies to follow for the remainder of 2015 and beyond in the Montreal market.
Note that the registration fee is significantly lower than other comparable events and fits virtually every organization's or individual's budget.
We sincerely hope you will take advantage of this very informative event.
Sylvain Cossette
Executive Vice President & Chief Operating Officer
Cominar REIT


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Advocate-on-record Amit Gupta puts forward the unfashionable opinion that, although Justice GS Singhvi's judgment in the section 377 gay sex case was not perfect and unpopular, he did in fact get the law right.
The severe criticism of the Supreme Court's judgment on constitutionality of Section 377 of the IPC raises a serious issue as to whether the judicial decision making ought to be guided by legal principles or prospective media trial? It would be a dangerous trend if the guiding factor for a Court to decide on constitutional matters were to be the criticism it may attract from liberals.
The judgment has been criticized on the ground that:
- It is regressive and a step backwards towards the LGBT (Lesbian, Gay, Bisexual and Transgender) equal rights and recognition. The Court should have taken a liberal view and legitimized homosexuality.
- It fails to meet the standards of decision making which is expected from the Supreme Court.
- It is legally wrong. Section 377 to the extent that it forbids sexual act of two consenting adults of the same gender is unconstitutional.
Regressive or judicial?
The first criticism suggests that there the Supreme Court ought to have taken only one view, i.e., to uphold the High Court judgment. This criticism fails to accept that a Court is free to uphold the view of either of the parties litigating before it. After having willingly subjected the issue to the judiciary, it is unusual, that one of the parties were so sure about the view that the Court ought to have taken.
This criticism also blurs the role of judiciary and the legislature. If allowing same sex intercourse is moral, legal, progressive and widely acceptable then it is the job of the legislature to amend the law. The changing notions of morality and sex, cannot by themselves be grounds for declaring a provision unconstitutional.
Weak analysis; Loose ends
The second criticism, though, is justified. After reserving the judgment for over 21 months, it was expected that the judgment would be more exhaustive. The judgment does not discuss the judicial developments in other parts of the world. A better analysis was certainly required.
It also contains invariably long extracts of the earlier reported judgments, without fully discussing the propositions. There is a contradiction, when the Supreme Court mentions that no incidents of discriminatory attitude exhibited by state agencies towards sexual minorities and consequential denial of basic human rights to them have been specifically stated, whereas the high court has extensively relied on the same.
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Para 43 of the judgment, treats with disdain the population of gays, lesbians, bisexuals or transgenders and was certainly uncalled for since ultimately those figures have no bearing while adjudicating on the validity of the Section. On a bare reading of the judgment, it appears that there are several loose ends left to be tied.
Lawrence vs Texas: Substantive due process
The main issue is, however, whether the Supreme Court has completely overlooked the Constitution and legal principles. Some critics have gone to the extent of stating that the court has abdicated its judicial function or has shown non-application of mind.
The criticism completely ignores few fundamental principles that evolved by our judiciary time to time. The courts presume any law to be validly enacted. Once it is presumed, the burden shifts on the party challenging the provision. The critics, however, argue the converse. The Indian Courts have never accepted the 'strict scrutiny' test, which has been used in the US in affirmative action cases. Even in Lawrence vs Texas, the US Supreme Court did not strike down the sodomy law in the State of Texas, by applying the test of 'strict scrutiny'.
In Lawrence vs Texas, the sodomy law was struck down since it was held that it violates substantive due process guaranteed under the Fourteenth Amendment of the US Constitution. It was held that the law did not further any legitimate state interest which can justify its intrusion into the personal and private life of the individual. Substantive Due Process allows the courts to test as to whether the enacted law is as such just, fair and reasonable.
In contrast, Article 14 of our Constitution does not recognise any concept of substantive due process. Article 14 has two limbs: the state is not to deny to any person (i) "equality before law" or (ii) "the equal protection of the laws." The second limb implies protection of equal laws for all similarly situated persons.
In this perspective, challenge to Section 377 is unfounded.
No such process here
First, it does not classify individuals into different categories. The criminality is attached to the act of "carnal intercourse against the order of nature". Such an act is criminal irrespective of the sexual tendencies of the person concerned. Thus, even a consensual heterosexual act which does not involve penile – vaginal intercourse is criminal.
Second, even if it is assumed that the section does create classification amongst persons, the court is correct to the extent it states in Para 42 that those who indulge in carnal intercourse in the ordinary course and those who do it against the order of nature constitute different class. Before the SC, the Union of India justified the classification on grounds of (a) strong societal disapproval and (b) health concerns.
A declaration from the court that sexual intercourse, apart from penile – vaginal intercourse is also an acceptable practice, is a concept borne out of "substantive due process", which has also not been accepted by the Indian courts.
It is asking the court to give a moral opinion or a value judgment on the issue.
Sex not equal to sexual orientation
The SC judgment does not carry any discussion on Article 15 of our Constitution, according to which no citizen should be discriminated only on the grounds of "sex". The SC clubs Article 14 and 15 together.
However, once it is understood that the Article criminalises the act and is applicable to both males and females, the argument of discrimination on grounds of Article 15 fails. Even the High Court did not hold that the section resulted in discriminatory behaviour because of sex of a person. Instead, the High Court equated "sexual orientation" to "sex."
If the logic of the High Court were carried further, then denying marriage to same sex couple or any kind of restriction whatsoever on same sex couples, would also be unconstitutional.
Right to privacy: Executive only
The argument that Section 377 violates "right to privacy" overlooks a basic principle. Article 21 states that no one can be deprived of his life or personal liberty except "according to procedure established by law." Certainly, it is a matter of one's personal choice and preference to have sexual intercourse either penile – vaginal or otherwise. Such a choice ought to be respected.
However, as pointed out by Professor MP Singh, in an article in NUJS Law Review, any state action would amount to infringement of right to privacy, if not backed by a competent law. In the present case, it is not the state action, which was being challenged, but the law itself. Most of the cases, involving "right to privacy" have been challenges to the executive action and not the statute itself.
The SC is correct to the extent that Section 377 does not mandate perpetrate harassment, blackmail and torture on certain persons. Furthermore, the proposition that merely because a law can be subjected to abuse or misuse, has also never been a ground to hold it unconstitutional is correct and unassailable.
LGBT window open
It is also not the case that the judgment leaves no window open for LGBT community. Para 38 of the judgment clearly provides the way ahead. While extensively dealing with the reported judgments, it has been held that in all the cases where the accused have been prosecuted on an offence under Section 377 IPC, there has been non-consensual and markedly coercive situations and the keenness of the Court in bringing justice to the victims who are either women or children cannot be discounted while analyzing the manner in which the section has been interpreted.
The judges clearly stated that they "are apprehensive of whether the Court would rule similarly in a case of proved consensual intercourse between the adults".
Last, those who have appeared in Justice Singhvi's court would vouch for his credentials, thoroughness, and his views on executive arbitrariness, environment, land acquisition and poor in general.
Amongst lawyers, it was perceived that he would take a conservative approach on the issue. Maybe for him, Section 377 does not merit the attention that it currently does. Even globally the issue attracts fierce debate.
However, on a proper analysis, the SC judgment is in line with the judicially evolved principles and the Constitution. It is doubtful if the judgment, even with all its current flaws, would have been so severely criticised if it had upheld the High Court judgment.
But it would be a sad day if media reactions become a factor in judicial decision making even on constitutional issues.
Amit Gupta is a Supreme Court advocate on record and partner at Delhi firm Mitter & Mitter & Co
Senior counsel and lawyer to the Naz Foundation, Anand Grover, argued a contrary view in the WSJ today.


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Winchcombe pottery ace dies
Posted: January 21, 2012|
One of the world's leading studio potters has died after a career in Winchcombe, Gloucestershire, spanning 76 years.
Ray Finch died on Wednesday at the age of 97, having first worked at Winchcombe Pottery in 1936. Although he handed the Broadway Road business over to his son Mike in 1979, he continued to work there and was making pottery until earlier this year.
In 1980, he was made an MBE for services to the arts and, in 1999, received a lifetime achievement award from the first international potters festival in Aberystwyth.
Ron Wheeler, who wrote a book about Mr Finch in 1998, said: "The world of studio pottery has lost one of its leading figures and practitioners. He was an outstanding artist and potter who also trained and influenced a large number of students from Britain and overseas."
Mr Wheeler said Mr Finch had been "a man of quiet dignity, modest with strong values". He seemed surprised that his work was collected by so many admirers. He said: "I've not really ever considered myself to be famous. We've always tended to use my pots at home but I don't keep many of them, just a few which I like."
Over seven decades, he worked in various forms, from slipware to the more robust stoneware, crafting water jugs, teapots and bowls for everyday use. His workshops were much sought after and many top potters, from home and abroad, expressed their gratitude to him for his guidance. Mr Finch kept one of the few remaining country potteries going against all the economic odds and its high quality products still attract a large number of customers from the UK and places such as Scandinavia, America and New Zealand.
Mr Finch's own work is represented in the collections of dozens of museums in Britain and overseas. He is survived by Mike, his daughter Marianne and four other sons – Anthony, Peter, Joe and Paul, as well as grandchildren and great grandchildren.
The funeral will be on Thursday at noon, at St Nicholas Roman Catholic Church in Winchcombe.


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"The Life And Times Of Prophecy"
Anthony Kiedis Watches The Lakers Game In Crutches posted by Garry "Prophecy" Sun on February 22, 2012
Gotta be rough for Anthony Kiedis.
To watch your favorite team, the Los Angeles Lakers playing your favorite sport, and stuck in crutches.
Who cares. He still rocks. Red Hot Chili Peppers 4 Lyfe.
Garry "Prophecy" Sun for SunOfHollywood.com
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Photos: SunOfHollywood.com
Photos: SunOfHollywood.com
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Katie Cleary continues her Beautiful Crusade to Restore Animal Rights and Bring about Awareness to Injustices all across the Globe that Threaten Thousands of Species ...Click Here For More
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Thursday, October 4, 2012
© Copyright 2015 Gwinnett Daily Post
Dacula Falcons (8-AAAAAA)
Coach: Jared Zito
Record: 0-5, 0-3 region
Last week: Lost to Archer 17-14
Brookwood Broncos (8-AAAAAA)
Coach: Mark Crews
Record: 2-2, 1-1 region
Last week: Lost to Parkview 21-14
These two teams may be coming off disappointing losses, but each have plenty of hope. For Brookwood, the hopes lay in the record. Sure losing to Parkview hits the Broncos in the gut, but the early date leaves plenty of time to re-assert themselves in the region.
At Dacula, the hope is less apparent. The Falcons dropped a three-point game to Archer, keeping them winless on the season. But for a team running in sophomores all across the field, head coach Jared Zito speaks optimistically.
"We feel encouraged because we are getting better," Zito said.
Receiver Josh Bullock is leading the improvement along with QB Brandon Goodson.
"The truth is our backs are against the wall if we have any hope of making the playoffs," Zito said.
And as luck would have it, the Falcons meet another playoff-caliber team in the Broncos. The run-first Broncos have a more balanced attack this year, including putting up more than 200 yards in the air in last week's loss to Parkview. For the year, 760 of Brookwood's 1,369 total yards have come on the ground and 609 have come through the air.
"They know exactly where they want to attack you and how they want to do it," Zito said of Brookwood.
Dacula will start the same five offensive linemen this week as it did last week, a first this season due to injuries. Senior David Flake will dress, but Zito does not expect him to play much.
Last meeting: Dacula won 20-6 last year.
Directions to Brookwood High School: From I-85, go east on Pleasant Hill Road and merge onto Ronald Reagan Parkway. Proceed to the Five Forks-Trickum Road exit. Turn right and the next left on Dogwood Road. School is on the right.
More like this story
- Dacula, Central want to build on wins ( November 1, 2012 )
- PREVIEW: Dacula at Berkmar ( November 8, 2012 )
- PREVIEW: Archer at Dacula ( September 27, 2012 )
- PREVIEW: Dacula at Shiloh ( October 25, 2012 )
- Dacula faces Parkview team following Falcons' script ( October 11, 2012 )


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Incredible fit and lightweight, weatherproof warmth are the hallmarks of Norrøna's Lofoten line.
The Norrøna Men's Lofoten Gore-Tex and Primaloft Jacket flew directly from Norway to stake its claim in the hyper-premium technical outerwear arena. Norrøna created the Lofoten freeride collection to meet the demands of expert skiers and boarders who redefine progression on the mountain, and the Gore-Tex PrimaLoft Jacket returns the favor.
- 2 Layer Gore-Tex Performance Shell will keep your under layers dry and wick away sweat and moisture
- PrimaLoft insulation adds tremendous warmth without sacrificing weight or flexibility
- Powder skirt and with wrist gaiters seal out unwanted snow
- Storm proof hood to hide from blizzard conditions
Share your thoughts
What do you think of the
Norrøna Lofoten Gore-Tex Primaloft Jacket - Men's
? Share a...
Good but not great.
- Gender: Male
- Familiarity: I've put it through the wringer
- Fit: True to size
Nice jacket but I was disappointed to see a lot of wear after just one season on the shoulder where I carry my skis. If you want a more durable product, pay up and get the 3layer goretex pro shell model. Also, one of the buttons on the powder skirt came off and I had to take it to a tailor to get it fixed. Everything else about the jacket I like, including ample pockets, goggle wipe, hood fits over my hemlet no problem, and comfortable against my face when zipped all the way up. Sizing is normal, I am 185lbs and 6ft tall, I wear a large and it fits great.
Great skiing jacket
- Familiarity: I've used it several times
- Fit: True to size
Needed to replace my 15yr old Rossignol and decided to give this one a shot. There are several great skiing jackets out there, I felt this one is a very good all-around jacket which kept me warm and dry even in blizzard and <-10F conditions while in the west fjords of Iceland recently as I was backcountry skiing there.
Great jacket. Skiing in Japan
- Familiarity: I've used it several times
- Fit: True to size
I've been skiing in Nozawa Onsen in -5 to -10 degs centigrade (-20 degs w wind chill). The jacket is warm and I haven't even thought about the conditions when skiing in it. It's materials make it as light as a feather making it superb to wear.
The jacket is highly functional with accessible pockets, easy to use zips and great features that make it practical.
It looks great. I often look like I'm wearing a sack as I wear larger sizes. But this is well shaped without being tight.
I am 6'5", 87kgs and wear the XL which fit great. Long enough and not too baggy.
Hand pocket pit zip
Hand pockets
Goggle pocket
Napoleon pocket
Hood adjuster
Very nice, slim, and over priced
- Familiarity: I've put it through the wringer
- Fit: Runs small
As a Norwegian I am happy to see that Norr�na has made a favorable impression on the US marked, and make NO mistake, they do make very nice, no-nonsense, delicate, outdoor cloths, in the best of my country�s tradition. Still the use of Gore-tex a rather old-fashion technology, and pricing makes them not the first choose for many of us, and we do spend a lot of time outside in bad weather (where i live at 65 N, the winter lasts for nine months..). Hence, looking for something using amore modern fabric but with the same good overall quality, look at Bergans.com. Still make no mistake, Norr�na is wonderful, especially this jacket !
On GorTex defense, Dermizax is a much newer material than the original GorTex XCR, but Gore Inc has produced many new products over the last decade. Dermizax technology owned by Toray is also a lot different than GorTex. Dermizax is a membrane like GorTex, but its waterproofness is determined by the DWR. Unlike GorTex, Dermizax is nonporous, and is a hydrophilic material relying on water soaking through the material at a slow rate. Rating GorTex breathability to Dermizax is kind of silly, being that they are different technologies. Dermizax again is nonporous, so it uses diffusive properties that act much slower than Gortex membranes. GorTex has 9 billion pores per square inch, which allows it to have a higher breathability than Dermizax, and it still does not breathe perfectly. Dermizax is actually not a new technology at all. Dermizax mimics technology that has been used in laboratories across the world for years. They use nonporous membranes in labs to demonstrate diffusion and how isotonic solutions work which mimics older technology (the cellular structure of the body). If you want something to breathe perfectly, then you would have to go with a soft-shell without a waterproofing membrane. Though many competitors of Gore Inc are working on different technologies, there is a reason why GorTex is still a staple in the outdoor community. Your right though, the original Goretex membrane was developed back in 1966 by John W. Cropper. Since the development of the 3L, they have since developed Paclite, Active , and Pro membrane materials offered in 3L, 2L and ZLiner.
All of these materials serve a different purposes and are becoming more advanced every season. Having lived in Embarrass Mn for several years and in the Kush mountains of Afghanistan for several years I know what the most extreme environments can feel like, and I do know what works. Mountaineering in these conditions, I never once had a problem using GorTex technology and believe me, I have used a lot of other products out there. I can honestly say, I LOVE and THRIVE on being outside during the bad to the worst weather. Because of materials like Gortex and their progressive technology I can continue to pursue my love affair with the outdoors in any condition. Oh and keep researching, because Gortex is set to launch a few new products in the next couple years to continue the journey
Great tech. info!
I worked in a Norwegian sports store for several years. I've seen and tested my fare share of both Norrona and Bergans products. I generally prefer Norrona. Short-version: less "fashionable" and more expensive, but better functionality and performance.
As for the price, yes Norrona is just as "overpriced" as arcteryx, and deliver the same quality. It is expensive equipment, that's why I personally buy these things on special offers, like right now... :)
Awesome Jacket
- Familiarity: I've put it through the wringer
- Fit: True to size
I have worn this jacket on super cold days for two years straight and I could not be more pleased. It is stupid warm and with the hood up, provides an amazing wind break. Skiing between 10 and 15 degrees F, I only wear a thin base layer underneath and I am fine. On 20 degrees F days, I only wear a tee shirt underneath it. This jacket really holds heat. It also has great vents to let the heat out and regulate.
The jacket has held up well with a few minor rips and tears from the trees. It is great to have a "go to" warm jacket for super cold days.
This was my first Norrona Jacket which I purchased for JH in January. I now own three total - I purchased two Norrona shells for spring skiing. They are that good.
Bottom line - this is a seriously warm jacket for cold conditions. It will not disappoint.
Everything you want/need in a jacket
- Familiarity: I've put it through the wringer
- Fit: True to size
I love this jacket. The Gore-Tex performance shell is extremely soft (read: no loud crinkling sound of typical Gore-Tex pro shell) and the 100g PrimaLoft Sport insulation makes the jacket super warm. I'm 5'11", 170 lbs and the Medium fits great. I'm a big fan of the slightly trimmer European cut.
I bought this for cold days as I was sick of adding a ton of layers under my Arc'teryx Rush Jacket (which is also a great shell BTW). This jacket keeps me plenty warm on most days with just a lightweight merino base layer on underneath. On really cold days, I'll add a light fleece. While this jacket can definitely serve as your only winter jacket, just know that it can almost get TOO warm on above average temp days, which is why I like to have a true pro shell that I can wear on those warmer days.
I own a handful of Norrona products and am a big fan of the brand. If you're concerned because Norrona is lesser known here in the U.S., don't be. Their products are top of the line (which unfortunately is reflected in the price) and come with a five year warranty.
Give it a shot. You'll be happy you did.
Amazingly warm and soft
- Familiarity: I've put it through the wringer
- Fit: True to size
Softer than any other technical shell I have had this jacket makes no noise when touring and or glissading down the mountain. Fit just like most Norrona jackets, it is an active fit with a little extra room for layering. The powderskirt is handy and the tons of pockets makes everything accessible. I literally do not need to carry a pack, because I can fit everything I need for a day on the slopes in this jacket. Built to the best of Norrona standards this is warm, sleek and efficient and a must buy for the park goer!
Great Coat
- Familiarity: I've put it through the wringer
- Fit: True to size
This has been an unbelievable coat. This Norrona fits true to size. I am 6-2, 185 and a Large fits perfectly. I am use to skiing and being in temps between -15 and 15 degrees Fahrenheit and this coat is good for all of it. The insulation is nice to have on those extremely cold days and it is still a very light coat. When it gets down to -15 I will usually wear a thermal long sleeve shirt and a fleece under this jacket and that is enough to stay warm. The coat is truly weatherproof. The powder skirt and wrist gaiters are also extremely nice to have to keep that snow out. I use this coat on the mountain just as much as I do on a daily basis commuting back and forth. In both situations the compliments keep rolling in. I would recommend this coat to anyone in search of an all-around coat that can be worn every skiing day along with those cold winter days.
Hi there !
I'm 5'10 and 150 lbs , will...
Hi there !
I'm 5'10 and 150 lbs , will a small or a medium the best fit for me? I like a slightly slimmer fitter than a baggier fit ... Thanks !
Geoff.... would be much easier to provide guidance if you could provide a chest size?
Chest size is 98 cm or 38,58 inches ! Thanks
Geoff, if you like a slightly slimmer fit, try the small. I'm typically between sizes in a lot of brands (5'11", 170 lbs) and the Medium is the way to go for me in Norrona so I assume the small would work well for you.
Pretty amazing jacket
- Familiarity: I've used it several times
- Fit: True to size
I started skiing 2 years ago and bought a Patagonia Powder Bowl jacket to get me started. It was great, but I got the itch to upgrade. I made a superb choice here. The warmth-to-bulk ratio is incredible. I love the small details -- the thumb-hole thingys in the sleeve, the goggle cleaning rag in the chest pocket, the low profile nature of the hood etc etc. And the fit is totally spot on. I'm 5'10"ish and 175lbs and the Medium is perfect. The arm length is solid, the shoulder room is great, and it's not too long or short in the waist, and not too tight or loose in the belly. I feel no buyers remorse, no curiosity to try other jackets, and I'm encouraged to check out other pieces of Norrona. This is the jacket you need!
What under layers/ how many? do you wear when wearing this jacket?
Ben, see my initial review above. I'll usually use a lightweight merino base layer and on colder days, I'll add a light fleece. I'm 5'11", 170 lbs and the Medium is perfect.
Backcountry Video, Employee
Norr?na Lofoten Gore-Tex Primaloft
Seth Hobby IFMGA Mountain Guide, Pro Athlete
This Jacket in use! In Lofoten!
- Familiarity: I've put it through the wringer
- Fit: True to size
Insulated Battle Armor for the extreme elements.
I'm 15 years old, 5'9" weighing 135lbs,...
I'm 15 years old, 5'9" weighing 135lbs, will a small or a medium be the best fit?
Since you're only 15 years of age, and already essentially on that fence split mark of whether to grab a Small or Medium, I would say go for the Medium.
If your size now is any prediction of future growth, I would say that a Medium would suit you just fine for at least a year or two before you possibly need to size up once again. In any case, I feel that, at least from the measurements you have provided, you will be much more satisfied (not to mention comfortable) if you go for the Medium.
One member, tra5609467, posted below a few reviews down from this about some firsthand experience he had with the jacket, so I would scour to see what others have said about the fit before you ultimately make a decision regarding a purchase though.
Ben, if you want the jacket to fit well now, the Small is the way to go. To James' point, if you're growing quickly, you'll grow into the Medium nicely in a year or two.
Seth Hobby IFMGA Mountain Guide, Pro Athlete
Ski guiding in Lofoten, with this jacket
Lexi Dowdall, Gearhead
Slobbering over here! Norway looks SO sick!
I'm ready to visit now!
Love the ending!
Matt A, Gearhead
The best insulated ski jacket out there
- Familiarity: I've put it through the wringer
You can't get any better than the Lofoten insulated for the price. It's got all the bells and whistles you expect from Norrona. Very warm, waterproof and has huge pit zips when you get back down to the lift. They've updated this jacket with embroidery of the Norrona logo where it used to be just a laminated logo so it's much more durable.


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An AUSL turnaround begins with new leaders, teachers, and staff, additional programs, and upgraded facilities resulting in more opportunities now and in the future for our students.
Turnaround Process
CPS Board of Education determines which schools will be turned around by AUSL.
During the summer, the school's facility is upgraded by CPS.
Before school starts, the principal, teachers and staff host events and participate in community walks to meet students and families.
Late Summer
Teachers and staff come together for several weeks during the summer to prepare for the coming school year.
All teachers at AUSL schools are CPS employees and Chicago Teachers Union members.
First Day of School
When the same students return to school in the fall, they enter an environment of high expectations and success.
AUSL's PASSAGE framework provides our school leadership teams with a roadmap for creating high-performing schools in high-poverty neighborhoods.
Positive School Culture
- Safe and orderly school and classroom environment
- Effective recruitment, attendance and discipline policies
Action Against Adversity
- Engaged parents and community partners
- Proactive social supports that meet student needs
Setting Goals and Getting it Done
- Aggressive, transparent goals for schools, teams, and individuals
- Performance management systems with cycles of inquiry
Shared Responsibility for Achievement
- Strong leadership with high-functioning teams
- Relentless efforts to recruit, retain, and motivate high-quality staff
Guaranteed and Viable Curriculum
- Standards-based, college prep K-12 curriculum
- Aligned assessment system that identifies student academic needs
Engaging and Personalized Instruction
- Focused professional development that ensures teacher effectiveness
- Deliberate use of Danielson framework and signature strategies


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Diamond OG Kush (Herbal Solutions)
Once again, when you call your variety of OG Kush "Diamond OG Kush", you better deliver. Take a look at these nugs and let me know what you think.
From: Herbal Solutions Compassionate Caregivers (Dispensary)
Grade: A-
Type: Indica
Price: $75/8th. Ounces are available.
Looks: I think the best word to describe the buds that were in my 1/8th is chunky.
Smell: Very pungent, very thick Kush smell. Had a bit of a menthol smell as well.
Taste: Strong. Even when filtered 3 times the smoke was very rich. Tasted like wood.
Buzz Type: Strong, hard hitting indica buzz that makes your forehead warm. Very similar to other strong OG Kush varieties I have smoked.
Buzz Length: Short. I have a feeling these buds were over handled or something and lost some of their trichomes/punch.
Overall: A strong OG Kush variety that I really liked. Unfortunately the 1/8th went quick as this bud just did not keep me stoned.
Buzz Report: I bought an 1/8th of Diamond OG Kush and literally went through the entire thing in about a day. It may be my tolerance is just really high. Who knows. –Chubbs
16 Comments | Add Yours
this stuff is pure fireeeeeeeeeeeee!!!!!!!!!!!!!!
lol dude JUST said he was disappointed, and then such enthusiasm???? lol seems like sounds like someone may have popped their trich cherry lately or something?? lolol, yeah man, again I gotta say, IMO any kush is just sooo over rated. I think its udder rubbish. Iv'e grown better on accident.
you're kidding right? i don't know what kind of kush you're smoking, but dank kush is a new paradigm.
Ok now Ive smoked alot of diferent strains but a good kush is definitely nice. However there are buds like realy good hazes or old school skunks that dont seem to exist anymore. So with that said I think I will go indulge in some sour bubba KUSH and topple that witrh some purple nepal hash.
This bud is some pretty good og. Sticky and pretty harsh.
Apparently I've been lucky with the two places that I've tried Diamond OG from, but the effects fit me so well, that I use it as my regular med (whenever possible). It might as well be a hybrid for me, because I use it for everything.
That said, the Platinum I like is similar to Diamond you reviewed in that it's often too short, but even with that I've been getting some that was blood red fire… I don't know if it's just me or not, but thankfully there's always others to try! =)
the og kush i had looked exactly like that and the taste was retarded.
Wow I had no idea there was even herb like that at herbal solutions..That is the real diamond og but I prefer to pay $45 so off to the Wilshire Clinic in Van Nuys when I want diamond og for a reasonable price; I usually go with the Private reserve, brandon, or skywalker sfv if they have it..They,re just a little bit better than the diamond… the diamond is THE SHIT tho..
Chubbs on your comment about going thru the 1/8th in a day. I too have had episodes like this and itll be odd because i can remember 1/8ths that werent as good lasting longer. I dunno just one of those things..
The Diamond OG I've been getting at the Green Light on Olive St. in Santa Barbara has been fire every single time.
im growing a "diamond cut" og also an indica dom. at 55/45
way more potent a completely diff. strand than this but all og is pretty decent as well as purps..i apreciate a good bud that was grown with care and cleanliness maybe if u fein too get major stoned everytime you smoke then i would understand you only get high to get fucked up or w.e
but iv'e had this as well not worth the price but if i was smoking it with somebody it's a very enjoyable bud really great aroma to it.


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Family of Ewa Beach homicide victim speaks outUPDATED 10:23 PM HST Mar 25, 2014
Hawaii police are on the hunt for three men who say they beat a man and left him to die in Ewa Beach. KITV's Brenton Awa spoke with witnesses and the victim's family.Video Transcript
they say beat a man and left him to die. Good evening, I'm Kenny Choi. And I'm Yunji de Nies...It all happened in the early hours of Sunday morning in Ewa Beach. KITV's Brenton Awa spoke with witnesses and the victim's family... in our top story tonight. Maria Gabriel can barely control her grief... Her sadness turns to anger... As she thinks of the men who killed her brother. 1314 "IN RETURN OF WHAT YOU DID TO HIM IT'S GOING TO BE BACK TO YOU BUT IT'S GOING TO BE TRIPLE TIMES FOR WHAT YOU DID SO YOU CAN RUN BUT YOU CANNOT HIDE, IN THE NAME OF JESUS, THEY WILL FIND YOU." John Melvin Howard was 38-years-old... This photo was taken when he was 20 ... He lived in this house near Campbell High School. And his sister still can't understand why why someone would murder him... 1240 "HE DOESN'T MAKE TROUBLE, THE ONLY TIME HE DID THAT IS WHEN HE WAS DRINKING BUT HE DOESN'T BOTHER NOBODY." Witnesses say a black sports car pulled up at this curb on Komana street where Howard was standing in the early hours of Sunday morning. After a brief exchange of words -- witnesses tell us the car drove off and Howard started walking in the middle of this road. That's when witnesses say three men walked up to Howard -- and one of them kicked him in the sternum -- causing him to fall to the ground. His sister heard the commotion from her bedroom. 936 "AS I LOOKED OUT I SAW MY BROTHER WENT FALL BACK AND I RUN OUT FROM MY BEDROOM." 947 "AND I HEARD SOMEBODY SAY HE KNOCKED OUT, GOOD FOR YOU." Gabriel says the suspects drove off in a faded black -- two door sports car. That's when she ran out to check on her brother. 1031 "HE WAS ALREADY LAYING DOWN, GASPING FOR AIR SO WHEN I TRIED TO CALL HIM, HE'S NOT EVEN RESPONDING." Howard was taken to the hospital with injuries to his head and body. The 38-year-old died on Monday. But as an organ donor -- his family says his kidney and liver became gifts that helped give life to two others. Another clue for the public to look out for might be floating somewhere on social media. Witnesses told us one of the suspects took a photo of the victim on the ground before they left the scene. The suspects face a charge of murder in the second degree. If you have any information on this case -- you're asked to call Crime-stoppers.
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Back to ECAR 2011 Identity Management Research Hub This chart reflects findings from the ECAR 2011 research of identity management (…
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Wood Lake Nature Center's Low Impact Scavenger Hunt
Most scavenger hunts ask you to find something and bring it back. This scavenger hunt is different; it asks you and your family to find things that can't necessarily be brought back. A sound, a sight, an experience-these are the things that you'll be hunting for. Scavenger Hunt List
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text: I told you on this site some time ago about the 14 year old girl he brought to my college campus (4 state lines and 550 miles away) in the spring of 1980. He was 20 then and if you ask me that's kidnapping. I made sure she was on a bus back to Georgetown that day (not headed to FL as he intended). Do you really need anymore? OK...I'm NOT going to give her name out but I will offer this...when they arrived he wanted two things from me. 1)Money and 2) use of my bed because ""I've only been able to do her in the backseat of my car". Kidnapping. Rape (of a child). Perversion.


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Sarasota, Florida - Jury selection proceedings took place today in the case of a North Port mother. Denise Amber Lee was found murdered after a 911 caller said she saw someone struggling in the back seat of a car. Jury selection could take some time in the first degree murder trial of Michael King.
Click here to read blog updates from Isabel Mascarenas today, who is reporting from the courthouse. Hundreds of people are in the pool of potential jurors, and because of the attention this case has gotten, many of those people may be dismissed because they already know a lot about it. Jurors also need to be okay with the idea that they may recommend Michael King be put to death if he's convicted.
It was January 17, 2008, three hours after Denise Amber Lee's husband reported her missing. North Port police were searching her neighborhood. And officers in Sarasota and Charlotte counties were looking for a dark green Camaro that may have been involved. A call came in to 911 from a driver, Jane Kowalski, who was stopped next to a Camaro at a red light on the county line. Someone in the car next to her "kept banging on the window," she told the dispatcher. She went on to say the person was "screaming... like 'get me out of here' screaming." Kowalski even followed the Camaro until it turned onto Toledo Blade Boulevard, and told dispatchers its location. At a memorial earlier this year, she told 10 Connects, "I knew something was wrong. You know when you have a gut instinct, make the call. Better to be safe than sorry. But Kowalski's information never made it to deputies out on the street. An internal affairs report says it was considered urgent, but somehow slipped through the cracks. Later that night, a state trooper spotted the Camaro on Toledo Blade Boulevard, and stopped Michael King. Police say he was soaking wet from the waist down and a wet shovel was in his car. Searchers later found Lee's body, buried in a swamp in southern Sarasota County. The jury will be allowed to see that green Camaro in person during this trial. They'll also be able to learn about the bodily fluids that were found in the car. Defense attorneys did not want that fluid evidence to be permitted. The defense had also argued against allowing jurors to hear the 911 calls in the case. But the judge has decided to allow them, including a call Denise Lee made while she was missing, where she pleads with someone to let her go.
Connect with 10 Connects multi-media journalist Grayson Kamm on Twitter as @graysonkamm, by e-mail at this link, or on AOL Instant Messenger as screen name GraysonConnects.
Grayson Kamm, 10 Connects


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WebMD Symptom Checker helps you find the most common medical conditions indicated by the symptoms bloating or fullness, missed or late menstrual period and upset stomach including Perimenopause, Ectopic pregnancy, and Irritable bowel syndrome.
There are 13 conditions associated with bloating or fullness, missed or late menstrual period and upset stomach. The links below will provide you with more detailed information on these medical conditions from the WebMD Symptom Checker and help provide a better understanding of causes and treatment of these related conditions.
Perimenopause is a transitional stage before menopause, causing irregular periods, hot flashes, and more.
An ectopic pregnancy can be life-threatening and causes severe pain, dizziness, fainting, and vaginal bleeding.
Irritable bowel syndrome is a common condition that causes painful spasms and cramping in the large intestine.
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JOHNSON CITY, Tenn. (Jan. 17, 2015) - Launched by the White House in September, the "It's On Us" campaign is an initiative aimed at ending sexual assaults on college campuses. Join the Buccaneers in taking the pledge by visiting itsonus.org.
JOHNSON CITY, Tenn. (Dec. 2, 2014) – A long-running ETSU Athletics tradition helped spread holiday cheer to local children Tuesday evening. As part of the 14th annual "A Buccaneer Christmas," around 70 children were treated to a special night full of activities.


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Treat or Treat: Halloween Freebies
As kids hope to eat their weight in candy this Halloween, parents are getting in on sweet deals from area restaurants, ABC News reported.
As a part of Chipotle's yearly "Boorito," anyone in costume after 4 p.m. Thursday can buy a burrito, bowl, salad or order of tacos for just $3. Proceeds up to $1 million will go to the Chipotle Cultivate Foundation, which supports sustainable agriculture organizations, family farmers, educators and programs that teach younger generations about sustainable food.
Kids 12 and younger -- no costume required -- will get a free Halloween "scary face" pancake Thursday (buttermilk pancake topped with whipped cream smile, glazed strawberry nose, mini-Oreo eyes and candy corn teeth).
Krispy Kreme
Don a costume on Halloween and get a free donut, regardless of your age. Click here for participating locations.
LongHorn Steakhouse/Olive Garden/Red Lobster
From now through Halloween (and through Nov. 7at Red Lobster), children get a free meal at LongHorn Steakhouse, Olive Garden and Red Lobster with the purchase of one adult entrée and the presence of a coupon. Click here to get a coupon.
Boston Market
Free kids meal with the purchase of any individual meal.
Buy a $1 Frosty coupon book filled with 10 coupons for a free Jr. Frosty. Proceeds go to the Dave Thomas Foundation for Adoption to help children in foster care.
Find more freebies at www.halloweenfreebies.net


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HiSITE Channel Manager is a leading Hotel Channel Manager connecting your property to all the major online Booking Channels such as Expedia and Booking.com via our easy to use, automatic channel management software. These channels have a high traffic flow and many consumers have become accustomed to making bookings through these websites. Creating an account on each of these websites and listing your rooms, rates and availability is a great way to increase your visitor numbers but it can also be very time consuming. HiSITE Channel Management Software becomes your Hotel Channel Manager, doing all of the maintenance work for you automatically, updating your availability seamlessly. Thanks to full two way integration to HiRUM Front Desk your Property Management System is automatically updated and you regain valuable time.
HiSITE Channel Manager will update your property's accommodation availability and real time rates to the leading Online Travel Agents (OTAs). With automatic and instant updating, it's easy to see why most HiRUM clients choose HiSITE as their Channel Manager!
HiSITE IP (Intuitive Pricing) takes automation to the next level by allowing you to set rate thresholds based on availability. When that threshold is met, HiSITE IP will automatically adjust your rates accordingly, and feed them out to your online channels via HiSITE Channel Manager.
Integration into your HiRUM Property Management Software enables automatic and instant updating of your availability so your website and third party accommodation channels mirror your real time availability.


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Edo Liberty, Founder and Advisor
Edo holds a PhD in computer science from Yale and has published many papers in applied mathematics. He currently teaches at Tel Aviv University and works in Yahoo! Research.
Ashley Swartz
Ashley's career has included manufacturing of components, electronics, entrepreneurial start-ups, and running a media practice, all coupled with over 10 years living and working in Europe, Asia and Central America. With a background in finance, she has landed in digital advertising due to her love of technology and ability to navigate and scale new channels to market. She most recently led the iTV practice at Digitas New York and the Global Samsung.com business. Leveraging her legacy building scalable advertising solutions in emerging channels like Mobile and Video Games, Ashley has recently founded Furious Minds, a collective of talent to provide, consulting, advisory and monetization strategies for companies whose revenue streams are advertising related or live within the converged ecosystem of iTV. Furious Minds is intended to be a platform to lead by example to get more women in technology, on boards and funded. She lives in NYC and practices what she preaches; in her living room is an HDMI hub, connected to 5 OTT devices and her Samsung Smart TV, having cut the cord earlier this year.


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Bach's spectacular choral masterpiece, the Magnificat, remains one of his most popular works. An elaborate ceremonial piece, featuring five soloists, a five-part choir and large orchestral forces, it is the setting for the Virgin Mary's praise to God on hearing news that she is to bear His son, taken from St Luke's gospel. It is accompanied by the Missae breves – Bach's quartet of short but beautiful Lutheran masses. These lively modern-instrument performances with the C.P.E. Bach Chamber Orchestra, recorded in 1993 at the Jesus-Christus-Kirche, Berlin, are led by the distinguished German conductor and former tenor Peter Schreier, a renowned performer of oratorio. He was the son of a church Kantor and a former member of the Dresden Kreuzchor, and the works of Bach are a major focus of his repertoire. The soloists include the fine lyric soprano Barbara Bonney, whose performance of 'Quia respexit' is described by Gramophone in their review as 'wonderfully intimate'. She is joined by the great German baritone Olaf Bär and his compatriots mezzo-soprano Birgit Remmert and tenor Rainer Trost, all notable concert artists.


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At Gentle Dental Care all children receive their first visit free when accompanying a paying adult.
Some procedures are expensive. These are not decisions that you will take lightly and we understand that you will need as much information as possible to help you make your choice. Complex and extensive treatments such as orthodontic, restorative surgeries, missing teeth requiring implants and some cosmetic procedures require a substantial commitment of time and money.
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Thank you again…"Lee Henry


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Tuesday's Knitting Tip – How to Add a Bead to a Knit StitchTuesday, April 3rd, 2012
This week's knitting tip comes from knitwear designer Laura Nelkin.
Ever wonder how to add beads to your knitting? In this video I teach you a trick for adding beads easily with either a crochet hook OR a piece of Super Floss!
Adding beads to your knitting gives it weight, flare and a bit of bling. You can take a simple design and really help it shine! I'll be coming to WEBS to teach for my first time later this month and look forward to sharing more of my beading techniques with you all…can't wait!
If you're interested in learning more about how to knit with beads, Laura will be teaching two classes in a couple weeks at our store. Follow the links below to find out more.
Advanced Lace with Beads April 21st
Butin: A Beaded Necklace April 20th


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Attleboro YMCA
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If you want to be a Jaguar and you want to learn more about this team, you are in the right place:
Welcome to the Attleboro YMCA Jaguars Track & Field Program. The mission of this program is to build character, courage and confidence in young people through their participation in track & field. Our practices provide young people with a variety of physical activities based on track & field events. With over fifteen events in track & field, there is a place for everyone in the Jaguar program. Although our practices provide young people with the knowledge and abilities to compete in youth track meets, there are no requirements to do so. Many young people find the Jaguars an ideal way to keep fit, improve their endurance, and to maintain a healthy lifestyle.
There are no minimum practices or track meets a participant has to attend. The more practices and track meets they attend the more fit they will get and the more fun they will have. There are no "bench sitters" in the Jaguar program. Everyone has an equal opportunity to participate in every event or activity we attend. Everyone will receive the same coaching attention and if requested will receive additional help from our expert coaching staff.
For the boy or girl using the Jaguars as a great fitness program we offer weekly group fun runs and walks of 1, 2, and 3 miles at a pace all children can participate in. Nutrition seminars, bike rides, and physical activities for parents and children are used to further encourage a healthy family lifestyle.
For those who want to compete our coaching staff has a no pressure, fun approach to coaching young athletes. The Jaguar program was never meant to be a highly competitive track team. Our young athletes have taken basic track & field skills taught in our program, added their own desire to excel, and made the Jaguars one of the top youth track & field teams in New England. Check out the trophy case at the Attleboro YMCA. As impressive as our participants are as athletes it is their exceptional sportsmanship, their willingness to help fellow participants, and the individual spirit of each Jaguar that makes the program unique in youth sports. I know you will enjoy the program. Please contact Coach Ed if you have any questions.
Early Years
The Jaguars started in the Summer of 1996 with 12 Athletes. Two of those athletes went on to get college scholarships for Track & Field.
This young Jaguar in the center is trying gain a win during a race at the Bishop Feehan High School Track
Now, the Jaguars roster is growing with 100 young althetes who enjoy track and field activities.
The current Jaguar program not only encourages track & field participation, it also includes activities focused on physical fitness. There are parent/child activities as well as non-competitive events.
The Jaguars, here shown in the white t-shirts, are ready to start their race at Brown University Indoor Track.
How old do you need to be? What do you need?
The ages of the Jaguars range from as young as 3 to college athletes. Jaguars are open to all and have at least some type of physical activity training 2 days a week 52 weeks a year.
Coaching Staff
Our coaching staff is comprised of highly qualified coaches who believe in the simple philosophy that youth athletics should be focused on having fun, learning new skills, and every athlete will get the same amount of playing time and coaching help.
Coach Ed (The Jaguars Head Coach) discusses strategy
before the race starts at Moses Brown Indoor track
Where is this team located?
This team is located at the Attleboro YMCA in Attleboro, Ma
What shoes are best for track meets and practices?
Youth Running Shoes: For all track meets and practice any pair of sneakers are fine.
There is two recommended of running shoes:
D&B Sports
Kelly Boulevard in North Attleboro. Ask for Kevin or Lou. Mentioned you are a member of the Jaguars. On non-sale items a discount may be available.
Rhode Runner Running & Walking
271 South Main Street Providence RI. Telephone: 401-831-6346. Ask for Bob. Mentioned you are a member of the Jaguars. On non-sale items a discount may be available.
How much does it cost to be a Jaguar?
$15 Y Family member
$25 for Attleboro Y members.
$40 for non-members.
Updated: August 22, 2006


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Enjoy 15% Off Upholstery & Entertainment Furniture With Code FALL2015. Exclusions Apply. Offer Ends 11/20.
Introducing the centerpiece of our Avant Garden Summer Bedding Collection - the Jardin Duvet Set. A hand-drawn garden of abstract botanicals set in a sun-washed color palette adds instant decorator style to the bedroom. This scenic pattern is inspired by antique hand painted wall murals.
Our design team modernized this sweeping print by simplifying the color palette and adding intricate hand-drawn elements. This duvet is an eye-catching centerpiece for the bedroom.


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Celebrity Cruising at Vinopolis
"Love. Exiciting and new. Come aboard. We're expecting youuuuu. The Looooooooove boat…." It's amazing but I can still remember the words to that cheesy 80's sitcom set on a cruise ship. And much like the 80's, cruise ships have always seemed a bit cheesy to me. That is until I was introduced to Celebrity X Cruises the other night at Vinopolis. If, like me, you've never bothered to find out more about a cruise experience, prepared to be surprised. Apparently, they are gigantic floating hotels/spas/world class restaurants with lux amenities. Celebrity now features fine wine and dining on all it's ships and gone are the days of shrimp cocktails and sausage cocktails. The ships are also looking pretty flash nowadays, too. I was invited to a dinner at Vinopolis to learn about Celebrity's new food and wine cruises that they are introducing in the Autumn. The cruises are going to be co-hosted by Oz Clarke and Vinopolis's Tom Forrest and will feature stops in various wine regions, including, Portugal, Spain and France. The dinner we had was representative of the kind of food and wine matching meals that would feature on the ship. We started off with an English Sparkling wine, the Ridgeview South Ridge 2008 traditional method, which was really good with the canapes. I was a bit surprised as I'd had it a few days previously and wasn't all that keen on it but it seems to go well with food. Served up with the starter of goat cheese tart and beetroot, we had a white Bordeaux, a 2004 Rioja reserva, Pagos de Tahola, was paired with a perfectly grilled steak and a 2007 LBV port with chocolate fondant was heavenly. Happily a cheese board was served up paired with a white wine from the the south of France, the Grand Reserve de Gassac blanc 2010. An interesting choice to have with the cheeses (Cheshire Blue, Brie de Meaux, Epoisse) and for me, they didn't match. While some people like the wine...read more


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Darwin, C. R. to Hindmarsh, Luke
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Thanks for information about natural increase of Chillingham cattle. Compares with case in Paraguay.
Summary Add
Down, Bromley, Kent, S.E.
May 12
Dear Sir
I thank you sincerely for your prompt and great kindness, and return the letter, which I have been very glad to see and have had copied. The increase is more rapid than I anticipated; but it seems rather conjectural; I had hoped that in so interesting a case some exact record had been kept. The number of births or calves reared till they followed their mothers would perhaps have been best datum. From Mr. Hardy's letter I infer then 10 must be annually born to make up the deaths from various causes. In Paraguay, Azara states that in a herd of 4000 from 1000 to 1300 are reared, but then though they do not kill calves, but castrate the young bulls, no doubt the oxen would be killed earlier than the cows, so that the herd would contain probably more of the female sex, than the herd at Chillingham.
There is not apparently any record, whether more young Bulls are killed than cows. If you should continue to keep notes on this interesting subject, which you have so well illustrated, it would be worth while to have the date of the last killed owing to the number exceeding 50, until one has to be killed from number exceeding 70. I am surprised that Lord Tankerville does not have exact record kept of deaths and sexes and Births, after a dozen years it would be an interesting statistical record to the naturalist and agriculturalist.
With my cordial thanks for your kindness, I beg leave to remain, Dear Sir, | Yours faithfully and obliged | Charles Darwin.
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- f1 3146.f1Dated by the relationship to the letter to Luke Hindmarsh, 3 May [1861], and to the letter from William Hardy to Luke Hindmarsh, [8 May 1861].
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- f2 3146.f2Letter from William Hardy to Luke Hindmarsh, [8 May 1861].
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- f3 3146.f3In Variation 2: 119, CD estimated the annual rate of increase of the Chillingham herd to be `about one in five'.
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- f4 3146.f4The reference is to F´elix d'Azara's descriptions of the fauna of Paraguay (Azara 1801). See CD's note, above. In Variation 2: 119, CD compared the rate of increase of the Chillingham herd with that of a half-wild South American breed, citing Azara's estimate of an annual rate of increase for the latter of `one in between three and four'. CD used the comparison to support his argument that cross-breeding leads to increased fertility.
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- f5 3146.f5The note is in DAR 46.1: 91; it refers to Azara 1801, an annotated copy of which is in the Darwin Library--CUL.


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|Written by Mike Kelly
|Sunday, 16 January 2011 00:59
Despite the wintry weather we had, the Northwestern 3A/4A Conference did get some games in this weekend.
Friday night:
Women: South Caldwell 50, Alexander Central 41
Men: Alexander Central 63, Souith Caldwell 38
Saturday night:
Women: Hickory 86, St. Stephens 17
WHS 67, Alexander Central 44
Men: Hickory 64, St. Stephens 55
Alexander Central 78, WHS 68
Fred T. Foard @ South Caldwell snowed out Tuesday has been rescheduled for January 31
Fred T. Foard @ Hibriten PPD Friday night, noi new date yet.
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