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During the recent school holidays in June, 80 Nalanda Dhamma School students from Sri Serdang and Johor Bahru were privileged to embark on a study tour to Kelantan. The teenagers enjoyed many teachings by Bro. Tan while visiting Buddhist temples such as Wat Machimaram, Wat Photivihan, and Wat Mai Suwankhiri.Read more
During the recent June holidays, 80 teenage Nalanda Dhamma School students from Sri Serdang and Johor Bahru embarked on a journey of discovery to Kelantan – the most north-easterly state of Peninsular Malaysia – and an important centre of Buddhism centuries ago.Read more
Nalanda founder will be returning to his home-state of Kelantan for a 4-day Dhammaduta tour from 3 to 6 June 2017. 80 Dhamma School students from Serdang and Johor Bahru will participate in the tour, and receive teachings at well-known Buddhist landmarks such as Wat Machimaram, Wat Photivihan, and Wat Mai Suwankhiri.Read more
From 19 to 22 March, 70 Nalanda Dhamma School students from Sri Serdang and Johor Bahru Branches spent their school holidays meaningfully by participating in the Stay-in Programme. The 4-day camp was aimed at fostering friendship among students, and to inculcate a sense of gratitude and appreciation.Read more
On 18 March, 160 youths participated joyfully in the Bhāvanā Day meditation retreat on loving-acceptance, conducted by Bro Tan. In this third installment of one-day meditation retreats organised by Nalanda Youth Centre, participants learned how to better cope with the vicissitudes and vagaries of life with by accepting and enduring them.Read more
On Sunday 19 February, Nalanda Dhamma School organised an outing for facilitators and students to Taman Putra Perdana in Putrajaya. 104 teenagers and children from Sri Serdang and Kuala Lumpur branches spent a healthy and fun day out with their Dhamma friends, while learning the important values of good friendship and loving-kindness.Read more
On Sunday 12 February, Nalanda Dhamma School held its annual tea-offering ceremony in conjunction with the Lunar New Year. The purpose of the tea ceremony was for children to express their love and gratitude towards parents and teachers who have cared for, and supported them unconditionally.Read more
On Saturday 4 February, Nalandians were delighted to host a study tour by 80 students from SMK Gajah Berang, Malacca, and 40 students from SMK USJ 13, Selangor. The young visitors and their teachers were warmly received in the morning, and they proceeded on a tour of Nalanda Centre.Read more
On the last day of 2016, Nalanda Dhamma School Facilitators, students and their parents, alumni, volunteers and guests gathered at Nalanda Centre for the annual School Appreciation and Honours Day. It was an important event to celebrate the learning and progress of students throughout the year, and also to give thanks to teachers and parents who supported their learning.Read more
From 16 to 18 December 2016, Nalanda Dhamma School organized another wonderful teenagers' learning camp themed 'Inspector Me'. 74 youngsters ranging from 13 to 17 years old took part in the programme held at Nalanda Centre, Sri Serdang.Read more

subset: commoncrawl


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Discover... Comment only Updates 12 Aug 2011 1.2 Now accounts for the fact that if x-values are also supplied, they may not be in ascending order. 24 Oct 2011 1.3 This version LikeLike Reply 'With the great power of graphs comes great responsibility' « neuroscience and medecine says: August 7, 2014 at 5:39 pm […] Grouped bar plots with errorbars […] LikeLike Reply ERRORBAR_GROUPS allows transmitting optional input property-value pairs to both the BAR and ERRORBAR functions, making it quite versatile. Check This Out
MathWorks does not warrant, and disclaims all liability for, the accuracy, suitability, or fitness for purpose of the translation. For an intermediate user, this function provides the handles to the BAR and ERRORBAR lines for further modification. [b,e] = errorbarbar(y,e); % or ... [b,e] = errorbarbar(x,y,e); % where x is Comment only 24 Mar 2015 Jatin Gera Jatin Gera (view profile) 0 files 0 downloads 0.0 12 Mar 2015 Martina Callaghan Martina Callaghan (view profile) 1 file 171 downloads 4.875 If you do, feel free to post how you get on.
With tha, you should also add an "end" after, the hold off being non longer the termination. Comment only Updates 22 Jul 2014 1.1 Added a line at the end to adjust the limits of the X axis to the plot. 22 Jul 2014 1.2 (this time with Play games and win prizes! » Learn more 4.42857 4.4 | 7 ratings Rate this file 110 Downloads (last 30 days) File Size: 5.8 KB File ID: #47250 Version: 1.6 Grouped
The newsgroups are a worldwide forum that is open to everyone. Thanks. Example: errorbar(x,y,err,'CapSize',10) 'LineWidth' -- Line width0.5 (default) | positive value Line width, specified as a positive value in points. Error Bars Matlab Scatter Plot Messages are exchanged and managed using open-standard protocols.
You can also add a tag to your watch list by searching for the tag with the directive "tag:tag_name" where tag_name is the name of the tag you would like to Error Bars Matlab Bar Graph Is the standard Canon 18-55 lens the same as 5 years ago? Comment only 01 Nov 2013 Beate Beate (view profile) 0 files 0 downloads 0.0 25 Sep 2013 Matt Matt (view profile) 0 files 0 downloads 0.0 Fantastic. 18 Jul 2013 The function can pass PropertyName - PropertyValue pairs of input arguments to both the BAR and ERRORBAR functions, which allows for considerable customization!
I've tried both solutions in this thread >> with no success. ... Barwitherr Matlab Tags for This File Please login to tag files. It is related to the "reshape" function: Also, would you know how to draw the error bar differently for each bar? LikeLike Reply pierremegevand says: July 22, 2014 at 2:04 am Merci Markus!
I had to also add a drawnow after line 115: handles.bar = bar(varargin{:}); This is a bit weird, but the handles.bar wasn't properly initialised (XOffset used later would be 0) until I tried to figure it out, but I couldn't. Barplot With Error Bars Matlab IF you find a way to deal with the issue on your side, please keep me posted and I'll happily update the code. Error Bars Matlab Scatter Not the answer you're looking for?
How do I add an item to my watch list? http://waspsoft.com/error-bars/barplot-with-error-bars-in-matlab.html Click the button below to return to the English verison of the page. They were too complex for what I wanted. What it DOESN'T do: 1. Horizontal Error Bars Matlab
Specify the values in data units. Unfortunately, I do not have R2015a and am therefore unable to debug the graphical display problems that cropped up in the function following the R2014b update and its overhaul of graphical e.g., > > mu=rand(2,3); > sigma=randn(2,3); > h = bar(mu); > hold on > errorbar(mu, sigma, '.') > hold off The main reason of your trouble is that you do not this contact form Comment only 28 May 2015 Liviu Liviu (view profile) 0 files 0 downloads 0.0 Hi Pierre.
I understand the point of using that dependency but just using builtin colormap as jet or hsv(N_grps) would make this package be more robust. Matlab Errorbar No Line for i = 1:5 j = 1:6; x = -0.5 + i + 1/7 * j; errorbar(x, ff(j,i), ee(j,i), '.'); end Results in: (Leaving out the labels, but otherwise this seems This can be solved by removing this part, and adding the following argument when you call the errorbar function: 'LineWidth', errorbar_width, ...
Fill in your details below or click an icon to log in: Email (required) (Address never made public) Name (required) Website You are commenting using your WordPress.com account. (LogOut/Change) You are But, I tried your codes (see below) and get a error message saying "Index exceeds matrix dimensions". When I use your code, it works for the first bar graph, but for the second and third functions it creates figures with just the error bars and bar plots. Matlab Grouped Bar Graph No apparent adverse consequences of commenting out that block.
Comment only 23 Jul 2014 Elizabeth Elizabeth (view profile) 0 files 0 downloads 0.0 Thank you! The symbols can appear in any order. Error in applyhatch_plusC (line 82) oldppmode = get(h,'paperpositionmode'); ...which I presume arises because of the way barwitherr generates the plot associated with the handle h. navigate here Commenting it out solved it.
In R2015a, the bar's x-positions for the last group are wrong. It also removes my first figure complete. bardata visualizationerrorbargui Cancel Please login to add a comment or rating. Examplescollapse allPlot Vertical Error Bars of Equal LengthOpen ScriptCreate vectors x and y.
For instance, both the width of the bars themselves and that of the error bars can be adjusted. All rights reserved. So I've made my own wrapper function that successively calls BAR, then ERRORBAR, taking care to overlay the error bars right on top of the corresponding bars.
© Copyright 2017 waspsoft.com. All rights reserved.


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Students travel from Grove City College to spruce up Roaring Run Trail in Kiski Township
A group of more than 80 students from Grove City College occupied the Roaring Run Watershed in Kiskiminetas Township on Saturday.
Only they weren't there to protest or to make a statement.
On a nearly perfect spring day with no scheduled classes, they were there to work.
For the second year in a row, members of the college's Orientation Board, the group of students tasked with welcoming incoming freshmen to their first semester, volunteered one of their weekend days to help police the miles of trails at Roaring Run Watershed.
The main Roaring Run Trail is about 6.5 miles long, extending from Third Street in Apollo to the Edmon section of Kiski Township along the path of the 1800s Pennsylvania Main Line Canal. There also is the 1.5-mile Rock Furnace Trail that branches off the main trail and follows the Roaring Run creek to Brownstown Road.
The 650-acre Roaring Run Watershed property includes 15 miles of fairly rugged mountain bike and hiking trails, all maintained mostly by the volunteers of the Roaring Run Watershed Association.
But every now and then the association gets an offer it can't refuse.
Like when Emily Fankulewski, senior chair of the Orientation Board, reached out to association board member John Linkes and asked, "would Roaring Run be willing to have approximately 90 volunteers help out around the site on Saturday?"
Linkes said, "come on down!"
The students spent the day clearing the trails of trees downed by winter weather and dredging leaves and debris from trailside drainage ditches. Despite the down-and-dirty work, Fankulewski described the day's labors as an ideal situation.
"It's a huge opportunity for us," she said.
Fankulewski said the Orientation Board's members schedule a service project every year and that the projects serve two purposes, both as a means of giving back to area communities and as a way to grow closer as a group before they meet next year's freshmen.
"We really get to know each other as an organization, to connect on a deeper level," she said. "We've found this model is conducive to us being better able to connect with the freshmen."
Bob Bowman, a member of the Roaring Run Watershed Association's board of directors, praised the students for their hard work.
"They are just an amazing group of hardworking young adults," he said. "They really represent their college well and they really do work very hard. You can put it into your own words, but I think they are superstars."
Linkes noted that the students drove for more than an hour and a half to get to Roaring Run, and he said they seemed to really enjoy the work.
Fankulewski said that she fell in love with the Roaring Run Watershed during last year's service project.
"We came here last year with a group of about 40 and I just loved it. These people are great; they are just so great to work with and so friendly," she said.
According to Roaring Run Watershed Association Vice President Tom Iseman, all of the work the students accomplished couldn't have been done at a better time. Iseman said the association doesn't do much to take in money throughout the year, but one of its biggest events, a 15K run and a 5K run/walk, is less than a month away.
"We get lots of people that offer to help. Some do a little, some do more. These kids do a lot," Iseman said. "If we didn't get in here and clean out these drainage ditches, the running trails would wash away."
The Roaring Run Trail Association also sells yearly memberships to help cover the cost of maintaining the park. Individual memberships are $10, and family memberships are $25. A lifetime membership can be purchased for $100, but no membership is required to use the park.
Matthew Medsger is a Tribune-Review staff writer. Reach him at 724-226-4675 or email@example.com.


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Being an oily skin gal i am very familiar with my makeup sliding off my face come lunch time, separating, setting into fine lines, changing colour.. you name it, ive experienced it. And now summer is starting to come around (of what summer england gets), my face would resemble the shine of a disco ball if i didn't have the Benefit The POREfessional Primer. The difference in staying power of my makeup when i use this is that insane that this is my fourth purchase of this primer.
What they say:
"Quickly minimizes the appearance of pores and fine lines for a smoother-than-smooth skin! Apply this silky, lightweight balm alone, under or over makeup. Translucent, oil-free formula complements all skintones and helps makeup stay put. Contains a vitamin E derivative, known to protect skin from free radicals."
£24.50 debenhams
What i say:
As many of you probably already are aware that this primer has had alot of hype on beauty blogs, i was so excited to get to try it out and see if it really lived up to my expectations. The POREfessional is designed to minimise the appearance of pores and fine lines, which for us oily skin guys and gals is music to our ears.
Just like every other primer it is intended for use after moisturizer but before foundation, however this primer can be used over your makeup also to diminish the look of pores and fine lines.
Alongside minimizing the appearance of large pores, this primer helps to smooth out any imperfections on the skin to create an even canvas and good base for makeup application as well as increasing the staying power. The POREfessional primer can also be used on its own without foundation to mattify the skin slightly and smooth out pores and imperfections; i sometimes do this if i'm just running errands.
This primer comes with 22ml of product for £24.50, at first this seemed a little pricey for a primer, but then i thought you can use all the products you want but without a good base the makeup wont last very well on this skin. It comes in a retro-esk tube with a screw lid, the actual primer has a pale beige tint but once applied to the skin is 100% transparent, so great for every skin tone.
The pale beige tint of the primer
The tube appears small for £24.50 but such a small amount of product is needed so it lasts such a long time.
I am so impressed with the POREfessional primer, i can instantly see the difference when i have not used this product. Even without makeup my skin looks really even, smooth, poreless.. the perfect canvas for makeup. This primer was a life saver when working on the wards as it made my makeup last all day and i was still able to leave my shift with my foundation in tact.
I have always had confidence issues with my skin as i have some acne scaring, large pores and some redness and i really feel with this primer my skin looks the best it ever has. No sliding, no fading, no separating. Flawless!
When using the POREfessional primer, i find that my skin needs less foundation and concealer and i do not need to touch up throughout the day. I am not completely sure why this is but it is a great time saver for me with my early morning starts.
I 100% recommend this primer to anyone who wants their makeup to last all day, minimise pores, keep shine at bay, the list is endless.
Have you guys tried this? What did you think?
Do you have another primer you recommend instead?
Let me know.


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Park backs Kagawa to shine
Manchester United midfielder Ji-Sung Park has backed new signing Shinji Kagawa to shine at Old Trafford.
Last Updated: 14/06/12 6:33pm
Manchester United midfielder Ji-Sung Park has backed new signing Shinji Kagawa to shine at Old Trafford.
Kagawa is joining from Borussia Dortmund in a £17million deal and will become United's first Japanese player in their history.
Park was the Red Devils' first South Korean player seven years ago and although he was a relative unknown in England when he first signed, he has since gone on to become one of the club's most reliable squad members.
The 31-year-old believes Kagawa can go on and make a similar impact when he pulls on a United shirt next season.
"I know United have agreed a deal for Kagawa and I'm happy because we're signing a good player," Park told the club's official website.
"Manchester United is a huge club and every season we sign new, world-class names.
"I hope Kagawa shows how good he is next season and I think he will do."
Park made just 17 appearances last season and the arrival of Kagawa and Crewe youngster Nick Powell has increased the competition for places in midfield ahead of the new campaign.
However, the former PSV man insists he is happy at Old Trafford and believes the competition will spur him on.
"There is a lot of competition in the squad but it doesn't matter who I'm competing with," he added.
"We're a team and I just want to concentrate on producing better performances.
"We're starting our pre-season tour next month and those matches will help me to prepare for the new season.
"As always, when I begin a new season I am determined to improve."


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Many of you have met Michelle and/or have been to one of the many classes she has taught for our meet up group - even when she was very pregnant!
Baby Zachary has arrived and he is an amazing little guy. I am sure that you agree that a party is in order to celebrate mother and babe.
Let's meet at Michelle's house for a potluck brunch. Btw. Michelle,the unstoppable teacher, will show us grafting on her Apricot tree and how to propagate pomegranates. Who knows, you might come home with a brand new baby tree.
Michelle is registered at diaper.com and babies r us.
You can always contact her through meet up for questions on what to get. Hint: Zachary is growing fast! No tiny little newborn things are needed.
Such a cute baby!!
0 · February 16, 2014
If you use your GPS tomorrow, remember to set it to not use toll roads or bring $2 for the 125 toll road from the 54 to H street exit, the machines take credit cards as well if you get trapped on it
0 · February 15, 2014
previous commitment
0 · January 22, 2014
Meetup members, Log in
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Coffman Named J&C Big School Player of the Year6-2 Sophomore Kaylan Coffman was recently honored by Lafayette's Journal & Courier newspaper as Big School Player of the Year. Kaylan averaged 18 pts, More…
IF-Bradford Off to Strong StartCongratulations to 16U IF-Bradford for finishing Runner-Up in the 11th grade Gold Division of Shamrock Classic! The girls will now take their talents to More…
Check out Indiana's Finest East Team player videos!Check out these videos of the IF East Team players! Alexis Fussnecker Class 2015, 5-6 PG (summer 2012 ) Ashlee Miller Class 2015, 5-8 More…
Indiana's Finest Resurrects a Proud Tradition
Indiana's Finest, the powerhouse of girl's basketball of the 90's and early 2000's and one the foundations of Indiana's grassroots basketball, resurrects with the More…
News & Updates
Tryouts for both Boys and Girls teams
Will be Sunday 10/11/15 at Decatur Central HS Armstrong Pavillion from 1-3pm. Contact Coach Fry 317-675-8508
Indiana Finest Tryouts 2015-2016
Indiana Finest will host 1st round of tryouts this Sunday at Traders Point Christian Academy 6601 S. Indianapolis Rd More….
New highlight video for Mount Vernon's Ariana Sandefur
Check out the latest video for 5-9 Guard Ariana Sandefur, 2016. Ariana plays for IF Bradford-East
Check Out Jessica Wagers' Video! (IF-East Bradford)
CLICK HERE to view latest video from Jessica Wagers. Jess plays for IF – East, Bradford 17U's. Graduating in 2015 More…
Coffman Named J&C Big School Player of the Year
6-2 Sophomore Kaylan Coffman was recently honored by Lafayette's Journal & Courier newspaper as Big School Player of the More…
Ariana Sandefur named HHC player of the week
Ariana Sandefur, Mt. Vernon. Scored career-high 22 points in Marauders' 72-56 victory over Hamilton Heights. Ariana was named HHC player More…
Indiana's Finest 2014 Workout/Tryout
NEW!! 2nd Workouts/Tryouts for the 2014 Season will be Sunday September 8th Southport Middle School – 5715 S Keystone More…
AAU National Runner up 7th Grade 13u
Cincinnati Spring Jam 13U Champions
Great Plains Chicago 15U Tourney Champs


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Miss Utah flubs answerJune 17th, 2013 | Posted by in Perspectives
So it seems that Miss Utah totally flubbed her answer at the Miss USA pageant on Sunday night. While it's a shame (and I do feel bad for her) the question still merits an answer.
The question she was asked:
"A recent report shows that in 40 percent of American families with children, women are the primary earners, yet they continue to earn less than men. What does this say about society?"
This is a serious issue, one which deserves attention.
What she should have said:
Number 1. In order to answer that question, the type of jobs reported must be assessed. For example, a waitress will never earn as much money as a CEO–it doesn't matter how many hours are clocked. The report must be analysed to see what jobs women are working in.
Number 2. Education is required for high paying jobs. Credentials are not optional. Women who expect to earn a high wage must put in the same amount of preparation as a male counterpart. Which brings us to the next point.
Number 3. Society does not respect motherhood. For that matter, it does not respect children. Women who choose to stay at home to raise a family are seen as skill-less. And yet, the skills necessary to raise a family are all consuming. No one ever put on their job resume, "Three children raised to perfection." That may sound like a bit of a joke, but the truth is, raising children forces the development of vital skills, including an understanding of computers, child development, and the education system. Furthermore, it is impossible to run a household without an understanding of management. Even so, a resume outlining these skills–learned on the job as a mother–would be scoffed at by an employer. Instead society prefers to think of mothers as women who sit at home eating bon bons while their children run amuck.
So what does this say about society? It says that we have a long way to go. We need to educate, prepare, and respect women. We need to stop glorifying the way women "look" and appreciate them for who they are: our mothers who taught us to read and write, our sisters who helped us with our geometry homework, our daughters who look to us for education, our coworkers, and possibly even our boss.
You can follow any responses to this entry through the RSS 2.0 You can leave a response, or trackback.


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Corner+Fence+Landscaping+Ideas | Dr. Dan's Garden Tips: Getting Creative in the Garden
Chakra mosaic pattern by Brett Campbell Mosaics535 x 535 | 30.7KB | www.mosaics.com.au
Google Image Result for http://www.theophilia-mosaic-art.com/mosaic/14_mosaic_pink%2520plumeria%2520rubra.JPG
mandalas em mosaico - Pesquisa Google..............Wonderful color-combo!
Mosaic Window Panel Beautiful reds golds and by lowlightcreations,
Mosaic SPR104x by JulieEdmunds-Mosaic.deviantart.com on @deviantART
Beautiful Blue Circles Mosaic Window Panel by lowlightcreations, $350.00
20 Budget Friendly DIY Home Decor Projects...I'm not interested in rolling little birdies on the walls, lol, but another oller sounds interesting, assuming there are other designs available.
stenciled wall...
Great Idea!


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19 Useful Nail Tips & Tricks
Here are 19 useful nail tips and tricks to help you take care of your nails, help you with some pesky polish problems and help you get stunning looking painted nails!
1. Moisturize your hands after washing them
2. Always keep a hand moisturizer nearby
3. No not pick off your nail polish as this can damage your nails and make them weaker
4. Line your nails with petroleum jelly (Vaseline) before painting them so that the clean-up is easier
5. Using a white colour as a base coat will make your nail polish colour pop
6. Use tape to do two-tone designs with
7. Dry your nail polish faster by soaking your nails in icewater
8. Roll your nail polish bottle instead of shaking it. Shaking can create air bubbles
9. Add nail polish thinner to thick polishes
10. Use a bobby pin to create larger polkadots
11. Pushing cuticles are always easier to do if your fingers are wet or damp
12. A base coat is great to help prevent stainng your nails
13. To remove stains from your nails, mix a tablespoon of lemon juice in a cup of water and soak your nails for a few minutes
14. Sharpies work great for nailart! If you happen to make a mistake, use a wipe with rubbing alcohol to take it off
15. Fix a smudge by licking it. The saliva reacts with your nail polish and helps to soften and blend the surface
16. Is your nail polish lid stuck? Run it under hot water or wrap a rubber band around the top, gripping the rubber band and twisting it off
17. Dont use a blowdryer to dry your nails
18. A top coat can provide a shine, prevent chipping and prevent colour fade
19. Apply your nail polish in thin layers. Apply in 2 thin coats as it will dry faster with less smudgemarks and it will help prevent chipping


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or make 4 interest-free payments of $4.86 AUD fortnightly with More info
Funky and Vibrant Drop Earrings - Colourful Circles of Silk Organza on Sterling Silver Posts
Made in Cambodia
Ships from Australia
Category: blue, Blue Earrings, Cambodia, Drop Earrings, Green, Green Earrings, Purple, Purple Earrings, Recycling, Red, Red Earrings, Shopforgood, Silk, Silver Earrings, Social Enterprise, Teal, Teal Earrings
Type: jewellery
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Showcasing designer fashion accessories and homewares from South East Asia. Temples and Markets brings you virtual travelling and browsing without the need to step on a plane.
Evoke the senses, bring back the memories.


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Love in Bloom Address Labels
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Love in Bloom Address Labels
Elegant yellow and white floral wedding design by Shelby Allison. Click the Love in Bloom Collection to view matching items including invitations, rsvp cards, stickers and more.
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text: Homework Help > American Psycho what is psycho chemistry? and pharmacologyaside from meanings, i need to know the explanation about these two topics. thank you... print Print document PDF list Cite like 0 dislike 0 1 Answer User Comments bocateacher322 | Middle School Teacher | (Level 1) Salutatorian Posted on February 25, 2009 at 2:27 AM The actual definition of psychochemistry is the study of chemicals that have psychological effects. And psychopharmocology is the study of drugs that affect the mind. It is the branch of pharmacology that deals with the study of the actions, effects, and development of psychoactive drugs. Psychopharmacology is different than regular pharmacology in that it focuses mainly on drugs that affect psychiatric disorders. This includes, but is not limited to the four main groups of disorders which are schizophrenia, anxiety, mania and depression. Psychopharmacology deals with the drugs to treat mental and psychological disorders.


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Our Starburst Fan Light Shade will update the look of your ceiling fan while adding traditional style to your home. Expertly made, the glass fan shade is composed of many pieces of colorful glass, all radiating from the central star. Complement your home's decor with Tiffany-style lighting; order now.
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Epilepsy is a complex neurological disorder characterized by recurring seizures. In 30% of patients, seizures are insufficiently reduced by anti-epileptic drugs. In the case where seizures originate from a relatively circumscribed region of the brain, epilepsy is said to be partial and surgery can be indicated. The success of epilepsy surgery depends on the accurate localization and delineation of the epileptogenic zone (which often involves several structures), responsible for seizures. It requires a comprehensive pre-surgical evaluation of patients that includes not only imaging data but also long-term monitoring of electrophysiological signals (scalp and intracerebral EEG). During the past decades, considerable effort has been devoted to the development of signal analysis techniques aimed at characterizing the functional connectivity among spatially distributed regions over interictal (outside seizures) or ictal (during seizures) periods from EEG data. Most of these methods rely on the measurement of statistical couplings among signals recorded from distinct brain sites. However, methods differ with respect to underlying theoretical principles (mostly coming from the field of statistics or the field of non-linear physics). The objectives of this paper are: (i) to provide an brief overview of methods aimed at characterizing functional brain connectivity from electrophysiological data, (ii) to provide concrete application examples in the context of drug-refractory partial epilepsies, and iii) to highlight some key points emerging from results obtained both on real intracerebral EEG signals and on signals simulated from physiologically plausible models in which the underlying connectivity patterns are known a priori (ground truth).
Epilepsies constitute a common neurological disorder that affects about 1% of the world population (Engel et al., 1993). Epilepsies are characterized by the repetitive seizures (called ictal periods), the frequency and duration of which is variable. In 20–30% of the cases, seizures remain drug-resistant and considerably affect the patient's quality of life. Drug-resistant epilepsies are often partial or focal, with an origin located in relatively circumscribed brain regions. For patients with partial epilepsy, a surgical treatment can be considered. The problem is then to determine which brain areas which must be removed such that seizures are suppressed under the constraint that post-surgical deficits (sensory-motor or cognitive) induced by surgery are limited. In other words, the epileptogenic zone (EZ) that is responsible for seizures must be defined from anatomo-functional observations acquired during pre-surgical evaluation (Bartolomei et al., 2002).
The delineation of the EZ is the essential diagnostic step, prior to surgery. As the epileptic seizure is a dynamic phenomenon, imaging techniques providing "static" images of the brain (MRI, PET scan) are frequently not the best tools to identify the EZ. About 20–30% of patients have either no lesion or some lesions but without any clear link with their epilepsy.
Electroencephalography is the technique most suited to capture the dynamical properties of a seizure. In some specialized Epilepsy Surgery Units, direct exploration of brain regions using intracerebral depth-electrodes is performed (Bancaud and Talairach, 1973; Chauvel et al., 1993, 1996; Guenot et al., 2001; Cossu et al., 2005; McGonigal et al., 2007). These depth-EEG recordings have long been considered as the "gold standard" for EZ identification. Although they allow for better definition of the EZ, the complete delineation of the EZ may remain elusive, such that suppression of seizures is not always obtained. The reason is that in most of the cases the organization of the EZ is quite complex. This organization corresponds to that of a network of neuronal populations (showing "hyperexcitabilty" and "hypersynchronization" properties) distributed in distinct and distant brain structures. This network is often referred to as the epileptogenic network (Spencer, 2002; Bartolomei et al., 2008b). Accurate identification of epileptogenic networks is the thus the central problem in drug-resistant epilepsies and novel methods have to be proposed to achieve this goal (Wendling et al., 2009). In particular, the demand is high for diagnostic methods allowing for better characterization and interpretation of depth-EEG signals, in terms of underlying neuronal networks and pathophysiological mechanisms taking place in these networks (Rampp and Stefan, 2006).
In this context, signal analysis techniques have considerably developed since the middle of the last century (Brazier and Casby, 1952; Barlow and Brazier, 1954). It is now admitted that signal analysis can provide relevant information regarding epileptic processes (either during interictal or ictal periods) when three conditions are met, at least: (i) signal processing methods are specifically adapted to phenomena under study, (ii) methods have been successfully evaluated on "control" datasets and (iii) the information conveyed by computed quantities is appropriately interpreted.
More specifically, methods aimed at quantifying interactions between recorded structures are of particular interest for identifying functional networks involving spatially distributed brain regions. Over the past decades, considerable effort has been devoted to the development of such methods allowing for characterization of functional and/or effective brain connectivity (Friston, 1994; Jirsa and McIntosh, 2007; Sporns, 2010). A consequence of this increasing interest is that now a plethora of methods is available, each method being based on specific assumptions about the underlying model of relationship between analyzed signals. The objective of this paper is not to provide a comprehensive review of all these methods but rather to focus on those aimed at quantifying functional connectivity from EEG signals. A particular attention is paid to a well-established method in the field of EEG signal processing, namely non-linear regression analysis. Over the past decade, this method has been extensively used in our group to analyze EEG signals recorded in epileptic patients. In this paper, its behavior is illustrated on a typical activity that has long been considered as a hallmark of the EZ: low-voltage rapid discharges observed in depth-EEG signals at the onset of partial seizures. Based on realistic models of coupled neuronal populations, it is showed that this method can provide relevant information on connectivity and can thus be used to interpret the behavior of brain structures involved at the onset of seizures. Finally, the advantages and the limitations of brain connectivity methods will be discussed in the context of the identification of epileptogenic networks from electrophysiological signals, which remains a difficult and still unsolved issue.
The idea of extracting, from EEG recordings, some information about brain connectivity is not new. Research in this domain has been – and is still – very active (Uhlhaas and Singer, 2006) and novel methods (or improvement of existing ones) are continuously reported. The underlying assumption is quite simple: the temporal evolution of the cross-correlation (in a wide sense) between electrophysiological signals recorded (with appropriate time resolution) from spatially distributed brain regions is a reflection of the functional connectivity among these regions. The word "functional" here is important as it marks a difference with the concept of "anatomic connectivity" (the actual brain circuitry) and the concept of "effective connectivity" (the actual influence of one region over another one). Regarding functional connectivity, the first methods (Barlow and Brazier, 1954) were developed in the 50s, just after fast Fourier transform (FFT) algorithms were introduced (Cooley and Tukey, 1965). Authors made use of either the cross-correlation function in the time domain or the coherence function in the frequency domain. The first results about the propagation of interictal events as observed in human intracerebral EEG data were reported by Brazier (1972). A few years later, quantitative analysis of these events was performed on scalp-EEG data (Lopes da Silva et al., 1977). From 1980, with the fast development of computers and EEG digital systems, signal processing methods spread more and more rapidly in the field of neurophysiology (for both clinical and research purpose). In the context of epilepsy, Gotman (1987) made use of the averaged coherence function computed on signals recorded from both hemispheres to study the evolution of inter-hemispheric interactions over the entire duration of partial seizures. This coherence function was also used to reveal the possible existence of activities propagating over short- or long-range connection fibers (Thatcher et al., 1986) as well as synchronization mechanisms particularly at the onset of seizures (Duckrow and Spencer, 1992). A corollary study was the estimation of time delays from coherence values (Avoli et al., 1983; Ktonas and Mallart, 1991) as measured "latencies" can be related to the propagation of activity among distant structures. In this category of coherence-based methods, some attempts to use time-varying linear models (autoregressive models) were also reported. These parametric methods were used to measure the degree of synchronization of interictal and ictal EEG signals and to characterize the relationship between brain oscillations in the time and/or frequency domain (Haykin et al., 1996; Franaszczuk and Bergey, 1999).
It is noteworthy that the aforementioned methods are said to be linear. This means that they can only capture the linear component of the relationship between analyzed time series. However, it is commonly admitted that most of the mechanisms at the origin of the generation of EEG signals are non-linear. Therefore, research effort was also devoted to the development of so-called non-linear methods (Pikovsky et al., 2001). A first family of non-linear methods was introduced in the field of EEG about twenty years ago. It included mutual information (Mars and Lopes da Silva, 1983) and non-linear regression analysis (Pijn and Lopes da silva, 1993b; Wendling et al., 2001b). A second family developed later on, based on works related to the analysis of non-linear dynamical systems and chaos (Iasemidis, 2003; Lehnertz, 1999). Regarding this second family of methods, the number of variants is high. Basically, two groups have emerged: (i) phase synchronization methods (Bhattacharya, 2001; Rosenblum et al., 2004) which first estimate the instantaneous phase of each signal and then compute a quantity based on co-variation of extracted phases to determine the degree of relationship and (ii) generalized synchronization methods (Arnhold et al., 1999; Stam et al., 2002, 2003) which also proceed according to two steps. Firstly, state space trajectories are reconstructed from scalar time series signals. Secondly, a similarity index is computed to quantify the similarity between these trajectories.
As shown by this brief literature review the panel of methods that can be used to estimate functional connectivity is wide. In a recent comparative study, we have analyzed the performances of ten methods aimed at characterizing functional connectivity from EEG signals. These methods belonged to three families (linear and non-linear regression, phase synchronization, and generalized synchronization) and were evaluated according to a model-based methodology. In considered simulations, the underlying relationship was known a priori (ground truth). It could be controlled using a parameter representing a degree of coupling in the three types of models (coupled stochastic signals, coupled non-linear dynamical systems, and coupled neuronal populations) that were used to generate output signals. Readers may refer to (Ansari-Asl et al., 2006; Wendling et al., 2009) for detailed results. In brief, the most salient findings of this study can be summarized as follows. First, we could demonstrate that some methods are insensitive to the coupling parameter in considered models (for instance, phase synchronization methods when the relationship between simulated signals only involves their envelope). Second, results showed strong dependence on the frequency distribution of signals (broad band versus narrow band). Third, we found that there is no "universal" method, i.e., none of the studied methods performed better than the other ones whatever the considered situation. Nevertheless, results revealed that methods belonging to the family of linear and non-linear regression analyses showed to be always sensitive to the coupling parameter in considered models. In particular, in the context of ictal activity simulated from coupled populations of neurons, the non-linear correlation coefficient h2 showed good performances. The behavior of this method on simulated and on real depth-EEG signals is illustrated in section Application to the identification of epileptogenic networks in partial epilepsies. Theoretical aspects as well as basic principles of the modeling approach are summarized in the next two sections.
Non-linear regression analysis was first introduced in the field of EEG analysis by Lopes da Silva et al. (1989) as a non-parametric method for characterizing the dependency of a signal Y on a signal X, from signal samples only and independently of the type of relation between the two signals. Readers may refer to (Pijn, 1990; Pijn et al., 1992; Pijn and Lopes Da Silva, 1993a; Kalitzin et al., 2007) for theoretical aspects of this method and to (Bartolomei et al., 2001; Wendling and Bartolomei, 2001; Wendling et al., 2001b) for practical application of this method in the context of epileptic activity analysis. In short, the dependency between considered signals is quantified by a normalized non-linear correlation coefficient given by
and where h is a non-linear fitting curve which approximates the statistical relationship between X and Y. In practice, this function h can be obtained from the piece-wise linear approximation between the samples of the two time series. Conceptually, quantifies the reduction of variance of signal Y that is obtained when Y samples are predicted for X samples. Indeed, as depicted from Eq. (1), when there exists no relationship between X and Y (i.e., the conditional variance VAR[Y(t+τ)/X(t)] is equal to the marginal variance VAR[Y(t+τ)). Conversely, signal Y is fully determined by signal X, the conditional variance VAR[Y(t+τ)/X(t)] =0 and .
The h2 coefficient is asymmetric ( is different from the quantity ). This asymmetry property was shown to provide insight into causality (Arnhold et al., 1999): if signals X and Y are of the same order of complexity and if Y is (at least partially) driven by X then the difference is positive. Finally, in Eq. (1), parameter τ corresponds to the time shift that maximizes the value of the h2 coefficient. Due to the asymmetry property, this time shift can take two values (either τXY or τYX) depending on the way the computation of the h2 coefficient is performed (from X to Y or vice versa). As a notation convention, we will consider that τYX>0 (resp. τYX<0) in the case where signal Y is delayed (resp. in advance) with respect to X. The time delay information corresponds to the notion of latency classically used in neurophysiology. It can also be related to causality as the delayed activity is more likely – caused by – rather than – causing – the preceding activity.
To end with this section on non-linear regression analysis, it is noteworthy that the asymmetry information and the time delay information were combined in single quantity named "direction index" D (Wendling and Bartolomei, 2001; Wendling et al., 2001a). This quantity allows for more reliable estimation of the direction of coupling between systems that generate signals, compared to the case where asymmetry information and time delay are considered separately. Briefly, the direction index D starts from the fact that the difference and the difference Δτ=τYX−τXY are both positive when signal Y is dependent on – and is delayed with respect to – signal X. The idea is thus to make a conjoint use of the sign of Δh2 and Δτ in order to provide a probabilistic information on the direction of coupling. A possible formula is when the same weighting coefficient is used for the asymmetry and delay information. In this case, D=+1 (respectively −1) denotes that Y (respectively X) is dependant on – and delayed with respect to – X (respectively Y). Conversely, D=0 denotes either (i) a situation where there is a constant discrepancy between the information provided by the asymmetry (Δh2) and by the time delay (Δτ) or (ii) a situation where the sign of Δh2 and the sign of Δτ continuously fluctuates, over the considered time window.
A general scientific approach that has proven useful in the study of complex systems is to capture some essential properties in a formal description – a model – which allows for thorough analysis of possible behaviors based on parameters considered in the model. More particularly, in the field of epilepsy, computational neuroscience has developed quite rapidly over the three past decades (Soltesz and Staley, 2008). Besides experimental models, computational models have gained maturity. They are now considered as an efficient way of structuring the tremendous amount of data coming from neurobiological and neurophysiological research in order to interpret experimental findings and, in some cases, to generate hypotheses that can be tested experimentally (Suffczynski et al., 2006). Basically, two complementary approaches developed since the 1970s and led to either detailed (i.e., microscopic) or lumped (i.e., mesoscopic) models of neural systems involved in the generation of epileptic activity. Readers may refer to (Bartolomei et al., 2008b; Lytton, 2008; Ullah and Schiff, 2009) for recent reviews on this topic. In this section, we focus on a mesoscopic model of coupled neuronal populations, illustrated in Figure Figure1A.1A. This type of model has been described in previous reports (Wendling et al., 2000, 2002, 2005). It is intended to reproduce the activity of two (or more) populations of neurons interacting through excitatory synaptic connections. Each population contains different subsets of neurons, typically main cells, and local interneurons. Figure Figure1A1A shows a model of two bi-directionally coupled neuronal populations. Each population comprises a subset of excitatory pyramidal neurons (with collateral glutamatergic excitation) and two subsets of inhibitory interneurons which receive excitatory input (glutamatergic) from pyramidal cells and which, in turn, provide inhibition (GABAergic) to pyramidal cells. It is noteworthy that the mesoscopic approach provides a description of the "average" activity in the considered populations of neurons. This means that it does not require an explicit representation of single units and that it leads to "much smaller" sets of ordinary differential equations, especially when compared to high-dimensional networks in which each neuron is described using a multicompartmental model. Two main input–output functions are used at the level of each subset in order to describe the whole population activity. The first function transforms the average density of incoming action potentials (APs) into an average post-synaptic potential (PSP). This average PSP can be either excitatory (EPSP) or inhibitory (IPSP) depending on the nature of the considered subset of cells. The kinetics of PSPs (rise and decay times) are adjusted to match experimentally recorded PSPs. The second function changes the average PSP into an average density of APs fired by the subset. This function is non-linear and accounts for threshold and saturation effects classically observed in neuronal physiology. In addition to the specific input from population P2 (resp. P1), an input noise p1(t) (resp. p2(t)) is used to describe the influence of non-specific afferences to population P1 (resp. P2). Both signals p1(t) and p2(t) represent a density of action potentials. They were chosen to have a Gaussian distribution (mean=90, SD=30). Finally, the model output that is usually chosen is the summation of EPSPs and IPSPs generated at the level of pyramidal cells. Indeed, it can be shown that these summated PSPs are the principal contribution to the local field potential (LFP, the signal that would be recorded by an extracellular electrode positioned in the vicinity of the neuronal population). Note that this output can be directly used as an estimate of the temporal dynamics of the LFP if one neglects the source-sensor transfer function (quasi-static assumption).
In the particular context of this study, two important aspects must be underlined. Firstly, this model corresponds to a network of coupled non-linear dynamical systems. Coupling parameters (degree, direction) corresponding to "inter-population" excitatory connections can be tuned. Second, in this network, the behavior of each "node" is governed by "intra-population" parameters, typically the efficacy of excitatory and inhibitory synaptic transmission among local subsets of neurons comprised in the population. These two aspects are illustrated in Figure Figure1B.1B. In this example, two coupled populations are considered. Inside each population, the scenario is as follows: the excitatory synaptic efficacy is constant but has been augmented with respect to "normal" value while the average IPSP on pyramidal cells is progressively decreased with time. This gradual disinhibition leads to dynamical changes in the system as reflected by simulated signals. Indeed, a first transition from background activity (interictal phase) to spikes (pre-ictal phase) is observed in this simulation. Spikes occur synchronously, they become more frequent and then an abrupt change to higher frequency activity happens (onset phase). This fast activity finally changes into higher-amplitude lower-frequency activity (ictal phase). Such dynamics and transitions match those occurring in depth-EEG signals recorded from limbic structures in temporal lobe epilepsy (TLE) as already reported in (Wendling et al., 2002, 2005) and as briefly described in the next section.
Among pre-surgical evaluation methods, stereoelectroencephalography (SEEG) permits direct recording of electrical activity from brain structures that are potentially part of the epileptogenic zone. It provides electrophysiological markers of epileptic activities (interictal and ictal) in the form of time series signals with excellent temporal resolution (about 1ms). The term "stereoelectroencephalography" was introduced by Bancaud et al. (1965) to emphasize the fact that recording of electrical activity is performed within the intracranial space (rather than from the surface) and that stereotaxic determination of the anatomical structures is necessary to "strategically" position intracerebral multi-contact electrodes (Figure (Figure2).2). The positioning of electrodes is determined in each patient from available non-invasive information and hypotheses about the localization of his/her epileptogenic zone. Implantation accuracy is per-operatively controlled by telemetric X-ray imaging. A post-operative CT scan without contrast product is then used to verify both the absence of bleeding and the precise 3D location of each electrode contact. After SEEG exploration, intracerebral electrodes are removed and an MRI is performed on which the trajectory of each electrode remains visible. Finally, a CT scan/MRI data fusion is performed to anatomically locate each contact along each electrode trajectory. In practice, SEEG is carried out as part of normal clinical care of patients who give their informed consent about the use of data for research purposes.
An example of intracerebral SEEG recording is given in Figure Figure3.3. In this example, the patient had mesial TLE. Signals were recorded on a 128-channel Deltamed™ system and were sampled at 256Hz. The only filter present in the acquisition procedure is a hardware analog high-pass filter (cut-off frequency equal to 0.16Hz) used to remove very low frequency variations of the baseline. For simplicity, only signals recorded from contacts located in the hippocampus (anterior and posterior parts), in the entorhinal cortex, in the amygdala and in the lateral temporal cortex (middle temporal gyrus) are represented in Figure Figure3.3. This electrophysiological pattern is very typical in TLE and reproducible in the various ictal episodes of a given patient (Wendling et al., 1996, 1997). Interictal and pre-ictal spikes (generally of higher amplitude) are usually observed in limbic structures (Figure (Figure3A,3A, before seizure onset). They are also observed in lateral structures of the temporal lobe relatively frequently (Wendling et al., 2003). Of particular interest is the activity observed at the onset of seizures. Indeed, in TLE (but not only), the onset of seizures is very often characterized by the appearance of a fast activity (also referred to as rapid discharge) in mesial structures (Figure (Figure3A,3A, seizure onset). This fast onset activity dramatically differs from interictal background activity recorded far from seizure (in time). The salient feature is a re-distribution of the energy of intracerebral EEG signals into higher frequency bands. Typically, in the temporal lobe, the dominant frequency ranges from 20 to 30Hz (Figure (Figure3B)3B) which corresponds to the low gamma frequency band. The duration of the rapid discharge may vary from patient to patient. Generally, it lasts for 5 to 10s. Then, as the seizure develops, the signal frequency gradually slows down and the amplitude progressively increases. The activity becomes more rhythmic and more synchronous across the recorded regions. Clinical symptoms generally occur during this "clonic" phase. Finally, seizure termination occurs after a few tens of seconds with respect to onset. A striking and reproducible feature is the "abrupt stop" of the ictal activity simultaneously observed on all channels.
The diversity of dynamics (and transitions of dynamics) observed at the level of depth-EEG signals shows that the epileptic seizure is a complex dynamical process. The seizure onset is particularly important in this dynamical process as it conveys key information about the EZ: what are the involved structures? Why and how are these structures engaged into the fast activity? What is the underlying network and how is it organized? Which "nodes" in this network should be removed in the aim to suppress ictal activity? These are typical questions faced by epileptologists as they analyze EEG recordings. From the signal processing viewpoint, these are particularly difficult questions. Indeed, the seizure onset phase is relatively short (a few seconds) and the number of seizures, in a given patient, is usually limited (typically in the order of 5–10s). Therefore, statistical significance of computed quantities (whatever the quantity) is always a delicate issue. The close analysis of rapid discharges reveals that they often start quasi-synchronously (Figure (Figure3A).3A). As far as limbic structures are concerned, their frequency content is quite similar, as depicted in Figure Figure3B3B which shows the power spectral density (PSD) of signals recorded from the amygdala, the hippocampus, and the entorhinal cortex during the fast onset activity. This PSD reveals that rapid discharges are quite narrow band (15–30Hz) which is confirmed by the plot in Figure Figure3C3C where the "sinusoidal" nature and amplitude modulation of recorded signals can be easily observed. This plot also shows a striking feature of recorded signals: a jitter is present as shown by the alternation of epochs where signals are either in phase or out of phase. By "jitter," we mean a "phase shift" (between analyzed quasi-sinusoidal depth-EEG signals) that is continuously and randomly changing over the duration of the fast activity. This jitter makes the problem of interpreting the propagation of epileptic activity quite complicated. Indeed, from visual inspection, it cannot be determined whether one signal is in advance – or is delayed – with respect to the other signal.
This section illustrates the behavior of non-linear regression analysis as applied on the fast activity recorded at the onset of seizures (as described above). The non-linear correlation coefficient h2, the time delay, and the direction index were computed on signals recorded from the amygdala (AMY), the anterior hippocampus (HIP, ant.) and the entorhinal cortex where rapid discharges could be observed (Figure (Figure3).3). The three pair-wise combinations (AMY vs. HIP, AMY vs. EC, and AMY vs. HIP) were considered.
In order to assess the statistical significance of measured quantities, we compared the statistical distributions of the h2 values, as computed over the seizure onset period and over the interictal period that precedes the seizure. As these distributions are not normal, a possible approach is to compare the means of Z-transformed variables via t-tests. Indeed, it can be shown that the variable w=1/2× log((1+ r)/(1− r)) (Eq. 3, where r denotes the linear correlation coefficient) follows a Gaussian distribution. However, it is worth to mention that this transformation cannot be readily applied in the case of non-linear correlation values, as those computed in the example shown in Figures Figures33 and and4.4. Indeed, the r quantity takes values in the interval [−1, 1] and is therefore mapped into the interval ]−∞, +∞[. Conversely, the non-linear correlation coefficient h2 is strictly positive (see Eq. 1). Therefore, using Eq. 3, it will be mapped into the R+=]0, +∞[ interval and theoretically can never follow a normal distribution. To deal with this issue a solution is to set the variable r equal to (2×h2−1) in Eq. 3. This transformation is such that r takes values in the interval [−1, 1] and that w=1/2× log (h2/(1− h2)) takes values in ]−∞, +∞[ with a distribution that can be assumed to be Gaussian (verified on empirical histograms). In addition, it worth mentioning that the time delay and direction index can only be interpreted in the situations where the h2 coefficient is significantly high. Indeed, analyzing those quantities is meaningless when there is no relationship between recorded brain sites.
Results are summarized in Figure Figure44 which shows the behavior of estimated quantities. Note that the h2 coefficient and the time delay were computed according to the two possibilities: dependence of the first signal on the second one (Figure (Figure4,4, solid line) and vice versa (Figure (Figure4,4, dash line). First, results showed that for the two first pairs (AMY vs. EC, Figure Figure4A)4A) and (HIP vs. EC, Figure Figure4B),4B), the behavior of computed quantities is similar. First, the h2 values averaged over the duration of the fast discharge were found to be significantly higher (AMY vs. EC: p=5.706e−3, HIP vs. EC: p=8.743e−3) than those computed on interictal activity. Second, time delays were found to be relatively stable over this seizure onset period as the direction index that is negative in both cases, indicating that the direction of coupling was more likely to be from the EC toward the AMY (Figure (Figure4A,4A, fourth plot) and from the EC toward the HIP (Figure (Figure4B,4B, fourth plot). Results were quite different regarding the third pair (AMY vs. HIP, Figure Figure4C).4C). The average h2 values were not found to be different from those computed during interictal activity (AMY vs. HIP: p=0.215). Second, time delays were found to be unstable as continuously varying from positive to negative value. This resulted in a direction index which stayed close to 0 and which was more difficult to interpret in term of effective connectivity.
This example (typical of mesial TLE) shows the difficulty of interpreting connectivity measures performed on intracerebral EEG data. Indeed, we are facing situations where computed quantities exhibit different behaviors. As described in the next section, data simulated from models in which (i) the excitability of neuronal populations and (ii) the underlying connectivity among these populations are known a priori may help this interpretation.
In this section, we report results about the behavior of non-linear regression analysis (h2, time delay and direction index measures) as applied on signals simulated from two coupled neuronal populations. Simulations were performed under two constraints: (i) the spectral content of simulated signals matches that of real signals and (ii) a jitter similar to that observed in real data is also present in simulated signals.
Results are reported in Figure Figure5.5. A first general result is that the model could generate a fast activity (about 25Hz, as observed) at the level of both populations if, and only if, the ratio between excitation and inhibition was increased such that the populations of neurons become "more excitable." Note that this result is not new. It was already shown (Wendling et al., 2002, 2005) that decreased inhibition (at the level of GABAa,slow receptors on pyramidal cells) leads to a dramatic change in the model: the fast feedback inhibitory loop (involving GABAa,fast receptors on pyramidal cells) becomes very active and leads to the generation of fast IPSPs on pyramidal cells (GABAa,fast receptors). These IPSPs dramatically affect the LFP by adding higher-frequency components.
Starting from this "increased excitability" condition at both populations, we found three situations where the model could generate signals with the aforementioned constraints.
The first situation is displayed in Figure Figure5B5B where excitability was strongly increased in population 1 (thick red rectangle) and less strongly in population 2 (thin green rectangle) and where population 2 received excitatory input from population 1 (unidirectional arrow). Note that without this excitatory drive, population 2 did not generate a fast activity, as shown in Figure Figure5A.5A. In other words, the fast discharge in population 2"is caused by" the input from population 1. In this situation (Figure (Figure5B),5B), a significant increase of the h2 value could be measured with respect to the uncoupled situation (Figure (Figure5A).5A). Time delays were found to be quite stable and symmetric. Finally, the direction index was strictly positive, clearly indicating an influence of population 1 on population 2.
The second situation is displayed in Figure Figure5C.5C. Here, populations were uncoupled but excitability was strongly increased in both populations such that they both generated a fast activity "intrinsically". It can be depicted that the behavior of measured quantities is different compared to the previous situation. The h2 values were lower and the variance strongly increased. Time delays were found to be very unstable, continuously reversing as time goes on. Conversely, the direction index D was more stable and centered around 0. It did not indicate a preferred direction in the coupling between population 1 and population 2.
The third situation is illustrated in Figure Figure5D.5D. Here, excitability was increased and both populations mutually interacted. For each population, the excitatory input from the other population was such that it generated a fast activity. Again, and as the underlying scenario changed, measured quantities behaved in a different manner compared to previous situations. Strikingly, the h2 values measured in a situation where neuronal populations are bi-directionally coupled were even lower compared to the previous uncoupled situation (Figure (Figure5C).5C). Time delays were also found to be very unstable. Finally, the direction index was also close to 0 but the variance was higher compared to the uncoupled situation. In order to assess the statistical significance of results, we generated long-duration simulated signals (400s) from which we could evaluate the asymptotic behavior (mean and standard deviation) of measured quantities. Results are summarized in Figure Figure6.6. They corroborated those obtained on shorter duration segments. The most salient finding is that there was only one situation, among the three analyzed situations, for which measured quantities provided a non-ambiguous result. This situation is that presented in Figure Figure5B5B and corresponds to the case where population 2 generated a rapid discharge, due to the excitatory drive from population 1.
Therefore, according to the above simulation results, a possible interpretation of the underlying network organization in the example of real data show in Figure Figure33 is as follows. In the three recorded structures (AMY, HIP, and EC), excitability would be increased with respect to normal condition. The disinhibition in the entorhinal cortex would lead to the generation of a fast activity. Then, measured h2 values (functional connectivity), time delay and direction index (effective connectivity) would indicate that the EC is driving the fast activity observed in the two other structures (AMY and HIP).
High frequency oscillations occurring at the onset of epileptic seizures have long been considered as a potentially valuable marker of the epileptogenic zone (EZ), usually defined as the subset of brain structures involved in the generation of seizures. These oscillations, also referred to as "fast onset activity" or "rapid discharges" (Allen et al., 1992; Alarcon et al., 1995; Wendling et al., 2003) have been recognized to be one of the most characteristic electrophysiological patterns of the EZ in focal epilepsy (Bancaud et al., 1965). Several experimental (Traub et al., 2001; Uva et al., 2005; Gnatkovsky et al., 2008; de Curtis and Gnatkovsky, 2009) and computational modeling (Wendling et al., 2005) studies demonstrated the existence of a relationship between the epileptogenicity of the neuronal tissue and its propensity to generate fast oscillations at seizure onset. From clinical viewpoint, resection of regions with rapid discharges has also been found to favorably influence the surgical prognosis (Alarcon et al., 1995). A striking feature of rapid discharges is that they always involve distinct – and possibly distant – brain structures, either in a quasi-synchronous or a more delayed manner. Based on these observations, an index, called epileptogenicity index, was recently proposed (Bartolomei et al., 2008a). This index accounts for both spectral (occurrence of fast oscillations) and temporal (delay of occurrence with respect to seizure onset) properties of intracerebral EEG signals to quantify the epileptogenic nature of recorded neuronal systems.
However, the mechanisms of seizure generation and propagation remain elusive. A number of studies have used signal processing techniques (in particular those able to characterize the underlying connectivity) in order to characterize the seizure dynamics from intracerebral EEG data (Gotman, 1987; Lieb et al., 1987; Mormann et al., 2003; Schindler et al., 2007; Bartolomei and Wendling, 2009). The intent of this paper was to also address this issue with a particular focus on the mechanisms involved in the generation of fast activity at the onset of seizures. We assumed that the epileptogenic zone is organized as a network of distributed neuronal populations with altered excitability properties and then study how a simple computational model (two (un)coupled populations) could help us to better interpret connectivity (functional and effective) measures performed on real signals (intracerebral EEG). The main findings of this study are discussed hereafter.
First, what do we learn from this apparently simple model? This question is always raised in any study involving modeling aspects. In the present work, the first insight is that rapid discharges with properties that are similar to those observed in real signals can be generated from different model configurations, in terms of level of excitability (moderate vs. major increase) in the two considered populations and connectivity pattern (no coupling, unidirectional coupling or bidirectional coupling). Indeed, we managed to generate signals that not only have a realistic spectral content but also in which a random phase jitter (instability of the phase difference between signals) is observed. The second insight is that the level of excitability is a crucial parameter. In the network, only the "nodes" with decreased inhibition (i.e., increased excitability) can be involved in the fast onset activity. The tricky question is then related to the mode of involvement of neuronal populations into the fast run. This question leads to the third insight. Our model shows that there are basically two situations. According to the first situation, the level of excitability in one population is so high that this population "autonomously" generates a fast activity. Of course, this population can have excitatory connections to distant populations (typically on the sub-population of pyramidal cells). When the excitability in these "remote" populations is altered (i.e., also increased), the model shows that they can be "driven" into the fast activity mode. Formally, this "entrainment" would correspond to an external perturbation that continuously drives the target dynamical system away from its "normal" behavior. It is noteworthy that the driven neuronal population does not become unstable as the removal of the external input leads it to return back to "normal background activity". According to the second situation, the level of excitability in considered populations is such that they autonomously generate a fast activity. In this case, the influence of couplings is much more difficult to determine and would deserve, in itself, a detailed analysis.
Second, what do we learn from signal analysis methods aimed at characterizing the connectivity? It is difficult to answer this question as only one method, among the many methods presented in section "From EEG signals to brain functional connectivity: a brief overview", was applied on real and simulated signals. In the following we will thus emphasize results we obtained regarding non-linear regression analysis which could provide interpretable results in the first studied situation. A first interesting aspect in this method is that it does not require strong assumptions about the properties of analyzed signals (broadband vs. narrow band, for instance) nor about the nature of the relationship between these signals (linear, non-linear, phase, or amplitude). The only restriction is that the duration of the sliding window (which defines the number of independent (X,Y) pairs of amplitude values) is large enough to correctly estimate the non-linear fitting curve h in Eq. 2. A second interesting aspect is that this method was able to provide reliable results in a complicated situation where the phase difference between signals is continuously varying. On simulated signals, we could obtain statistically significant results regarding the mean non-linear correlation coefficient, time delays (as measured in both directions) and direction index values. Indeed, measured quantities could be related, without ambiguity, to the underlying organization (population 2 receives excitatory input from population 1). Nevertheless, this result also means that there exist some situations where this method cannot provide univocal interpretation of recorded signals. Two examples were presented in this study corresponding to two situations where both neuronal populations generate a fast activity. In this case, we could not determine, from measured quantities, whether or not the two populations are coupled. Therefore, these results show that one should be cautious with the interpretation of connectivity measures, as already mentioned in several studies (Horwitz, 2003; Wendling et al., 2009). In particular, they show that deriving relevant information regarding the underlying effective connectivity is particularly difficult in the situations where the non-linear correlation coefficient is low.
From the physiological viewpoint, these results also show that the notion of "propagation of rapid discharges" should be clarified. Indeed, in some cases, the fact that rapid discharges are observed at different brain sites, is not due to propagation but, instead, to quasi-synchronous involvement of neuronal populations. According to this view, an epileptogenic network would include two types of "nodes," both having a capacity to generate fast activity due to altered excitation- and/or inhibition-related mechanisms. Some nodes could spontaneously generate rapid discharges and could "drive" some other nodes which would act as "relays" of those rapid discharges. For instance, in real signals shown in this study, the entorhinal cortex would belong to the first category whereas the hippocampus and amygdala would go in the second. This latter point leads us to a frequently asked question: how are functional, effective and anatomical connectivity related one with another? This is still a challenging question that cannot be answered in this study. However, it can be noticed, in the chosen example, that the entorhinal cortex has direct anatomical projections (temporo-amonic pathway) to the hippocampus (see, for instance, Witter and Wouterlood, 2002 for detailed description). Projections to the amygdala are less clear. Some detailed studies were performed in the cat using tract-tracing techniques (Russchen, 1982a,b; Witter and Groenewegen, 1986; Witter et al., 1986). As in the rat (Brothers and Finch, 1985; McDonald and Mascagni, 1997), results showed entorhinal–amygdala projections arising primarily from deep layers of the lateral entorhinal cortex. Although little is known about details of the projection of the entorhinal cortex to the amygdala in primates, such a pathway has been hypothesized in human based on neuronal responses evoked by electrical stimulation (Wilson et al., 1990, 1991). Besides these in vivo studies, functional connections as well as spread of epileptic activity were also studied in vitro, using slice preparations (rat brain) which preserve the connectivity between the hippocampus and the entorhinal cortex (Rafiq et al., 1993) and also with the amygdala (Stoop and Pralong, 2000). These studies confirmed the existence of reciprocal connections between hippocampus and entorhinal cortex. In addition, it was found that bursting epileptic activity could spread via two different pathways, either from entorhinal cortex or hippocampus and both toward the amygdala.
To end with this discussion, one should also mention the limitations of this study that lead, in fact, to open issues that should be addressed in the future. First, scenarios involving more than two coupled neuronal populations should be investigated, keeping in mind that the number of combinations becomes rapidly high with the number of populations and with the various ways of inter-connecting populations. Second, an interesting issue would be to compare results obtained from "classical" methods (as used here) with those obtained with methods "dedicated" to the analysis of causality among time series like Granger causality, directed transfer function and partial directed coherence on simulated signals (Blinowska et al., 2004; Kus et al., 2004). One advantage of these methods is that they make use of multichannel estimates conversely to the method used in this study that proceeds according to a bivariate approach, often considered as less powerful. Nevertheless, for simulated data, most of the studies which analyze the performances of multivariate versus bivariate methods make us of a multivariate autoregressive model which may not be the most relevant model for epileptic ictal-like activity. It would therefore be very informative to test aforementioned methods on signals generated with more "physiologically plausible" models of EEG (or LFP) generation, as the one used in this study and which can easily extended to multiple populations of neurons. A similar approach based on neural mass models was used to examine linear and non-linear methods for assessing functional connectivity (David et al., 2004). Finally, in the context of drug-resistant epilepsy, a nice – but difficult – perspective would be to investigate brain connectivity from both scalp-EEG and depth-EEG signals. This would allow us to assess the relationship between connectivity measures as obtained from global field potentials and from LFPs and to determine whether "finer" hypotheses about the epileptogenic zone could be establish on the basis on non-invasive electrophysiological data.
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
PubMed Central Canada is a service of the Canadian Institutes of Health Research (CIHR) working in partnership with the National Research Council's national science library in cooperation with the National Center for Biotechnology Information at the U.S. National Library of Medicine(NCBI/NLM). It includes content provided to the PubMed Central International archive by participating publishers.


text:
Re: Newspaper in 1930?
In reply to:
Re: Newspaper in 1930?
Danielle aaron zuber 10/02/12
More family info -
008771-74 (Perth Co) Thadeus JONES, 28, farmer, Beverly, Usborne, s/o John JONES & Ann GILBERT married Mary Ann KELLAND, 17, London Twp, Usborne, d/o Mathew KELLAND & Elizabeth HEAMAN, witn: John Kelland BAKER & Sarah Jane KELLAND (no residence given), 3 February 1874 in St. Marys
006345-77 (Middlesex), Robert KELLAND, 21, farmer, London, Usborne Twp, s/o Mathew and Elizabeth KELLAND, mar Elizabeth Ann HERBERT, 20, Usborne Twp, Biddulph Twp, d/o John and Charlotte HERBERT, witn William SKINNER and Sarah Jane KELLAND both of Usborne, 15 Jan 1877 Lucan
Father remarried??
003932-78 (Huron Co): Matthew KELLAND, 48, widower, farmer, England, Usborne, s/o John & Mary married Emma CARSON, 49, widow, England, Stephen, d/o John & Elizabeth BROWN. Wit: James CAVES of Usborne and Kate RYAN of Exeter. October 10, 1875 at Exeter
1881 Census... possible Parsons should be Carson??
name: Mathew Kelland
gender: Male
age: 52y
calculated birth year: 1829
birthplace: England
marital status: Married
occupation: Hotel Keeper
ethnic origin: English
religion: Ch of Eng
head of household: Mathew Kelland
born during last year:
census place: Usborne, Huron South, Ontario, Canada
district number: 173
sub district: C
division: 1
page number: 5
house number: 830865
family number: 24
digital folder number: 4467153
image number: 00422
film number: 1375908
library and archives canada film number: C-13272
Mathew KellandM52yEngland
Emma KellandF53yEngland
Hannah ParsonsF10yOntario
James ParsonsM12yOntario
Frederick ParsonsM9yOntario
Frances KellandF9yOntario
1871 Census -
name: Metthew Kelland
gender: Male
age: 42
calculated birth year: 1829
country or province of birth: England
marital status: Married
ethnic origin: English
religion: C Of England
census place: 01, Usborne c, South Huron 25, Ontario
page number: 8
line number: 17
house number: 33
family number: 33
film number: 4396748
library and archives canada film number: C-9929
digital folder number: 4396748
image number: 00033
Metthew KellandM42England
Elizabeth KellandF44England
Robert KellandM15O
Mary Ann KellandF14O


text:
a feast _Dominic
The glowing blue trail ended at the base of a ladder, deep within the royal castle of the Kingdom of Humanity. According to Dominic's internal mapping software, the prison cell was in the forward-most ring of shaft three, four levels out from the central area Sera had called the Spine. Dominic slipped down the ladder and waited inside the panel for a moment, allowing his enhanced senses to scan through the thin wallboard and take in the empty room beyond. Once he was sure that the space was unoccupied, Dominic palmed the switch set into the wall above the access panel. He slipped through the opening and stepped aside, making room for Max and Natalia to follow him through.
>> We'll go through the hallways from here, Dominic sent to the others. He opened a connection back to the Spider and asked, Can you open the door for us?
There was a short pause, then the reply came scrolling across his vision. > I'm a little busy. Later.
Dominic nodded. The Spider must have finished its preparations and begun working to infiltrate the Captain's secure partitions. He sent another message, this time to Raven in the monitoring station. >> Can you find us on the video feeds from the monitoring station?
> Yes, she replied, speaking over an audio link. But the coverage in here is spotty. Nearly all of the wireless network relays have been destroyed, so I'm working on what bleeds through to the relays here in the monitoring station. It's patchy at best.
>> Tell me about it. Kamon and I spent months watching those video feeds, trying to understand how these Luddites lived.
> Nobody is in the hall outside.
>> See if you can locate the king. If it isn't obvious, pull him up in the visual search.
Dominic turned to Natalia. He could see her in his thermal imaging overlay, but in the visible spectrum her camouflaged skin was blended perfectly with the background. >> Once we are out of the cell I want you to take point. Scout the passage in either direction and let us know if you find a way up.
> And we are going to get out of here how? Natalia asked.
Max stepped up to the door and glanced at Dominic. He nodded. She braced her feet against the floor, pulled a hand back, and slammed her hand into the thin metal of the door. Her rigid fingers pierced the door and she twisted her fingers around the lock assembly, then jerked her arm back, ripping the lock out of the door with a squeal of twisting metal.
> Oh, yes. Completely in stealth mode tonight aren't we, Natalia sent to both of them before pushing the twisted metal aside and slipping through the gap.
> Good call on going up, Dominic, Raven sent.
>> Go on.
> The king is holding court right now four levels up, almost directly above your position. I'm uploading the chamber identification code to you now, but don't trust the mapping tools from here out. I'm sure you already know that they've hacked this place to bits.