text:
Win the Super Bowl? Face a Big Tax Bill
February 6, 2015
There's another aspect to the Super Bowl that Americans might not have thought about -- taxes. Americans for Tax Reform have analyzed quarterback Tom Brady's tax bill after the Super Bowl, and it's not small. According to their analysis:
- Brady won a 2015 Chevy Colorado truck for being MVP. The truck is taxable and has a fair market value of $34,000. Brady faces a 39.6 percent income tax rate, meaning he must pony up $13,500 to the IRS in taxes.
- Brady plans to give the truck to his teammate, so he's also subject to a gift tax. Under the U.S. tax code, a person can give up to $14,000 before he faces taxes. Because the truck is worth $34,000, Brady will probably be taxed 40 percent on the $20,000 ($34,000 minus the $14,000 exclusion) -- $5,000 for giving a gift to a friend.
- Each player on a winning Super Bowl team receives $97,000 from the NFL. That income will be taxed at the 39.6 percent rate. His winnings will also be taxed by a 3.8 percent Medicare tax.
In all, Americans for Tax Reform put Brady's tax bill at $42,000 for winning the Super Bowl.
Source: Ryan Ellis, "IRS to Steal Tom Brady's Superbowl MVP Truck," Americans for Tax Reform, February 4, 2015.
Browse more articles on Tax and Spending Issues


text:
Or a relative of mine maybe?
rabbit stew any 1?
Easter is cancelled!
....and the winner is......
'Loftie Wiseman's Road Kill '? Poor Bunny Good photo though
Here's a link to this photo. Just copy and paste!
Here is direct link of this photo
Copy and paste the code below (HTML):
Copy and paste the code below (BBCode):
[URL=https://www.arrse.co.uk/community/gallery/photos/1400/]1400[/URL] by [URL=https://www.arrse.co.uk/community/gallery/authors/hodge.9054/]Hodge[/URL] on Army Rumour Service
Separate names with a comma.

subset: commoncrawl


text:
Real Estate Executive, Marketing Managar, Sales, Business Development ( 1 - 5 yrs)
RS 1,25,000 To 3,00,000 Bhagalpur, Gaya, Muzaffarpur, Patna, Purnia, Siwan, Bokaro, Dhanbad, Jamshedpur, Ranchi, Kolkata
Real Estate Executive, Marketing Managar, Sales, Business Development
Key Skills : real estate executive,marketing managar,sales,business development
Business Development manager ( 0 - 2 yrs)
Redefine Loyala Group
RS 1,50,000 To 4,00,000 Aurangabad - Bihar, Gaya, Jehanabad, Sasaram, Bokaro, Daltonganj, Dhanbad, Gumia, Gumla, Kodarma, Ranchi
We have opening for the position of "Business Manager" and "Business Associates" Their Role & Responsibilities are: -Sell the plots on company's behalf -Prospecting, meet & convert associates to consistently achieve direct sales. -Recruitme...
Key Skills : real estate agent,real estate consultant,business associate,business advisors,business development manager,business development...
Sales Manager - Real Estate ( 2 - 5 yrs)
Lalima Jobs
RS 1,75,000 To 3,50,000 Patna, Bokaro, Ranchi
Must have hands on customer relation building. Develop and Implement the Marketing strategy. Build client relation and brief them about our various projects along with arrangements of site visits. Establish and manage new brokers, alliances and pa...
Key Skills : real estate sales manager,marketing,business development


text:
ZAGREB, Croatia, Feb. 3 (UPI) -- Second-seeded Ivan Ljubicic won 60 percent of the points Thursday in advancing to the quarterfinals of the Zagreb Indoors tennis tournament in Croatia.
Ljubicic, playing in his home country, took more than three-quarters of the points on serve and nearly half when receiving in a 6-2, 6-3 victory over Daniel Brands. He was good on only 51 percent of his first serves but still didn't face a break point.
Qualifier Alex Bogomolov Jr. was even more efficient in defeating No. 7-seeded Philipp Petzschner 6-1, 6-2. The match took just 53 minutes as Bogomolov dropped only 12 points in eight games on serve. Bogomolov's first-round match took nearly three hours.
Ivan Dodig had four service breaks in a 6-2, 6-3 win over Illya Marchenko and fourth-seeded Richard Gasquet advanced in a walkover when Arnaud Clement was unable to play Thursday because of a shoulder injury.
A quarterfinal match pitting top-seeded Marin Cilic and No. 5 Florian Mayer was determined Wednesday. Thursday's results set up the rest of the quarters with Gasquet playing eighth-seeded Michael Berrer, Bogomolov meeting No. 3-seeded Guillermo Garcia-Lopez and Dodig paired against Ljubicic.


text:
The President noted that both lawsuits of Ukraine recognized suitable under the jurisdiction of the international court of justice.
President Petro Poroshenko called an interim decision of the Hague court on the claim of Ukraine against Russia promising.
"I think it's very promising today's decision in the Hague, as both lawsuits were found suitable under the jurisdiction of the international court of justice", – he told reporters in London.
"We are confident that we are on the right track, and we hope for a successful outcome of these lawsuits," the President added.
Корреспондент.net allocated the main tezisy the decision of the court in the Hague.


text:
Tripura Tourism Recruitment/ Admit Card 2016 for 20 Marketing Manager, Computer Programmer, Manager (Tourist Lodge) & Receptionist: Tripura Tourism Development Corporation Limited has released a recruitment notification for filling up 20 vacant posts of Marketing Manager, Computer Programmer, Manager (Tourist Lodge) & Receptionist on contract basis. Eligible permanent residents of Tripura state can apply in prescribed application format latest by 30.07.2016. Other details like age limit, educational qualification, selection process, application fee and how to apply are given below..…
Total No. of Posts: 20
Name of the Post:
- For S.N. 2: Master Degree in Computer Application (MCA).
- For Other Posts: Degree in Management/ Catering Technology and Applied Nutrition/ Hotel Management.
Age Limit:
- For General: Born not earlier than 01.06.1976 and not later than 31.05.1998.
- For SC: Born not earlier than 01.06.1971 and not later than 31.05.1998.
Fees: There will be no application fee for this recruitment.
Selection Process: Selection will be based on Written Exam and/ or Interview.
How to Apply: Eligible candidates have to complete prescribed format as given in official detail and send it to the Managing Director, Tripura Tourism Development Ltd., Swetmahal, Palace Compund, Agartala, Pin-799001 as it should reach on or before 30.07.2016.
Important Dates:
Start Date for Submission of Application: 15.07.2016
Last Date for Submission of Application: 30.07.2016
Admit Card: Admit cards will be sent through post to candidate address by department.


text:
Yesterday before hopping on special guest interview with the Elite Marketing Pro guys (you can actually checkout the replay right here… It's pretty badass if I do say so myself ;)), I spent a while listening to last weeks replay, and once again, was SOLD on why I love Solo Ads so much for traffic generation.
See… Last week they featured someone who has built an extremely large following, but used Facebook ads to do so.
As I listened to the Interview, I realized something that was kind of funny.
Literally, 1/2 of the interview (and it was about an hour and a half long) was her talking about all the various changes that Facebook has made, and how every single time they made a change, she had to change her ENTIRE traffic strategy, start from scratch with a new method, and "re-figure out" (is that proper english? lol) the big bad Facebook.
Now, I don't know about you, but to me, that sounds completely and totally crazy, and it's something that would keep me up at night tossing and turning (not knowing when the next Facebook slap would come, and not knowing whether or not I'd be able to get traffic again once it occurred).
See, there's one lesson I learned a long time ago from my main man Daegan Smith about traffic generation that has served me greatly… And now, I want to pass it on to you…
When it comes to picking a traffic source to tap into, you want to make sure of 2 things…
1. The traffic source that your tapping into should be easily accessible.
You shouldn't have to go write a thousand blog posts, shoot 500 youtube videos, write 38,000 articles, ect. You should be able to go out and get traffic within a 24 hour time period whenever you want, and you should be able to get LOTS of it when you do.
Solo Ads… VERY accessible (people are selling ad-space in there newsletters every single day).
Facebook Ads… They're still pretty accessible (you can setup an ad in a matter of minutes, and have traffic flowing to your site almost immediately, very similar to a Solo Ad, but, they're getting harder).
Getting traffic off of Organic search, Youtube videos, social media posts and so on and so forth… Not very easily accessible.
2. The traffic source that you're tapping into should be controllable.
I'm sure you've heard nightmare stories about the Google slap of 2008. About how people had there #1 (and only) traffic strategy pulled out from underneath them overnight, and how many seven figure business's got shut down almost overnight.
Why? Well, there traffic wasn't controllable.
YES, it was easily accessible, but they were at the mercy of the platform (google), and when the big bad Googly decided they didn't like Home Biz owners, well, there traffic disappeared instantly.
How you make sure your traffic is controllable is simple. You build relationships with the people that you're getting your traffic from. Whether it be an ad network, a solo ad provider, or a JV partner, when you build a relationship with your traffic providers (and diversify), there's much less of a chance that you'll run out of places to get traffic.
Example… In my own business, we have nearly 100 relationships built with top notch Solo Ad providers that we can tap into at any time. If one of them decides they don't like me anymore, well, I can still go to the 99 others and get near unlimited traffic whenever I want (VERY controllable).
On the flip-side, if you're putting all your eggs in one basket (what people do with Facebook in many cases), right when they decide to make an adjustment (or worse, that they don't like you), they'll shut you down, and your traffic flow is DONE.
I literally can't count how many people I know who have had there ad accounts shutdown, and as a result, have been left with ZERO traffic running to their sites.
Facebook ads… NOT CONTROLLABLE AT ALL… (and the interview that I listened to yesterday should be a perfect illustration of the battle that you WILL be facing if you decide to tap into a source of traffic that you can't control).
Now I don't know about you, but I love what I do, and I'm in this thing for the long haul. I want to build a business that's not only profitable, but which is also very stable and sustainable. I like to sleep well at night, and I don't want to wake up tomorrow and realize that my entire business's foundation has been taken out from underneath me due to some adjustment that a big company which I have ZERO influence over decided they don't like me.
…And well, that's why I use Solo Ads for 100% of my traffic generation (all $300,000+ worth of revenue last month came in as a DIRECT result of using Solo Ads). Getting traffic through Solo Ads is very fast and very easy, and at the same time, VERY controllable and very sustainable.
If used correctly, they're literally the ULTIMATE shortcut that will have you tapping into potentially thousands of leads starting as soon as tomorrow.
Click here right now for the ULTIMATE Solo Ad Success Formula. 🙂
Either way, remember… Whenever you tap into any source of traffic, focus on traffic sources that are easily accessible, and ultra controllable. If you do that, you can't fail.
To the top,
Misha Wilson
P.S. Did you happen to catch the insane result that my student Zane White got from implementing my Solo Ad strategies (over 1,000 leads in a day)?
If not, click here and checkout this video right now.
If were not connected, find me on social media here…
Add me on Facebook right here…
Subscribe to my Youtube channel right here…
And follow me on Twitter right here…
Latest posts by Misha (see all)
- Marketing With Misha Q&A: How To Find Success When You Leave An Event Without Falling Back Into The Same Struggles - November 17, 2017
- Marketing With Misha Q&A: How To Get Started Online And Into Profit As Quickly As Humanly Possible… - November 17, 2017
- Marketing With Misha Q&A… Which Activities Should I Focus On When I'm Brand New Online? - November 11, 2017


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THE Takeover Panel has turned down C3D Transport's request to freeze the timetable on its 650p-a-share hostile bid for Go-Ahead, the bus and rail group.
The ruling means C3D has until Wednesday to decide whether to raise its offer, a situation complicated by the fact that the outcome of Go-Ahead's bid for the Connex South Central rail franchise is not yet known.
The panel has allowed a one-month extension to the timetable after day 81 to deal with any competition issues raised by the British government's intervention on Tuesday.
Euro pressure
inttext: 29 September 2000: [International] Blow to euro as Danes vote No
inttext: 29 September 2000: Euro firm as Danes say No
FURTHER intervention by the G7 industrialised nations loomed closer last night as the euro tottered below 87 cents in London, closing at 86.98. Pressure on the currency is thought to be caused by jitters over the wider European picture rather than a concerted attack on the euro itself.
Houses divide
THE increase in house prices continues to slow, but there remains a distinct north-south divide, according to Halifax's regional survey for the third quarter. Overall, UK house prices increased by 1.1pc, while annual inflation was 8.1pc, down from 11.3pc in the second quarter. London saw the greatest decline, down to 13.2pc from 29.5pc in the first quarter.
Oftel net check
OFTEL, the telephone regulator, is to review the dial-up internet access market. It will consider whether consumers are getting the best deal before deciding on the appropriate level of regulation.
Eidos departure
EIDOS, the computer games company which has put itself up for sale, has lost its chief financial officer, Jeremy Lewis. Mike McGarvey, the chief operating officer, said Mr Lewis resigned because Eidos was no longer interested in making acquisitions.
Tomkins sale
inttext: 30 September 2000: Tomkins sells jets as figures weaken
TOMKINS has sold its bicycle and lawnmower businesses, Murray and Hayter to Summersong Investments for $221m (£150m). Tomkins bought Murray in 1988 for $232m and Hayter for £4m in 1984.
Output rises
MANUFACTURING output rose by a stronger-than-expected 0.8pc in August, taking year-on-year growth to 1.1pc, driven largely by the boom in mobile phones and computer equipment.


text:
Statistics New Zealand (SNZ) has sought submissions on the content for the 2006 Census. A number of submissions have been received asking for the inclusion of questions on sexual orientation.
Currently, in New Zealand information on sexual orientation is sparse and is generally restricted to studies on heath research in general and AIDS research in particular. Some regional multi-disciplinary studies amongst particular age groups have been conducted, but there is a question as to how generalisable these would be to the total population.
The availability of data on sexual orientation internationally is also limited. While some countries include questions on sexual orientation in sample surveys, to date no western country has included questions on sexual orientation in their population Census.
Statistics New Zealand sought to undertake focus group research amongst the New Zealand public to gauge public attitudes on the inclusion of sexual orientation questions in the 2006 Census. The research will help to inform decisions on the final content for the 2006 Census.
The downloadable file is in Adobe Acrobat format. If you do not have the Adobe Acrobat Reader you may download the reader to view or print the contents of this file.


text:
When it's hard to find any story idea
But write anything down, anything at all.
Test what you come up with, let your mind free fall.
Tell yourself you're fighting imaginary fear.
Writing can be like driving in that you need enough confidence to do it well but not so much you come across as an arrogant tit. I don't believe in writers' block but do accept there are days when the words simply refuse to flow well. I think that's a normal part of being a writer. We're not robots - there are bound to be times when life, difficult circumstances or whatever prey on our minds and that's bound to affect the writing. What matters is you keep writing - anything at all, seriously, it does work - and remember every writer has had their day when they felt like packing it in. The world would've been poorer had they done so.


text:
This might not be relevant to this site, but hopefully you guys can
point me in the right direction, or even have experience with the something
We have an app that we can't put registration on
because apple want's their cut in the profits, i.e. they want their
But the markup we have on the item for sale is so low that
if we give apple 30% we will actually be
I am working on restoring purchases, So I have few doubts
How to show restore button
I have shown it on top left corner,
and on click of it I call this function
(IBAction)restorePurchases:(id)sender {
[[SKPaymentQueue defaultQueue] addTransactionObserver:self];
[[SKPaymentQueue defaultQueue]restoreCompletedTransactio
Each User has many Purchases. I want to find
the sum for each of the previous 28 days.
t1 = Time.now -
(28.days)t2 = Time.now@dailysum = Array.new(29)(0..29).each do |i| @dailysum[i] =
@user.purchases.where(:created_at =>
This works, but I
Our In-App Purchases are "Waiting for Review" for a long time. We forgot
to connect them with the correct binary. So the binary was rejected. Is it
possible to reject In-App purchases? Or what is the solution to connect
I'm developing an update to an application. The application was
originally free but I want to add in-app purchases.
Of course,
I would like to test the application and make sure that the in-app purchase
work well before submitting it to the AppStore.
I'm able to
test the in-app purchases and they work well. However, I can only do that
if I remove the previous version (wh
I am looking into the iPhone in app purchased models and need to
implement a subscription. Ex content will be available for 24 hours. Now
the most important thing is that it needs to be available on all the other
devices, so bought on the iPhone, viewable on the iPad. I'm not sure how
this works ? I need to store some information on the developer server but
is this the transaction id and curren
I need to implement in-app purchases.


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Internet Explorer Running Slow or Crashing
If your Internet Explorer is really acting up on you, and it is not a virus, it could be a bad or corrupted add in.
You can reset Internet Explorer to the factory defaults by going to the "Tools" menu, "Internet Options" menu and then "Advanced". From here you can click "Reset".
After doing this, you will get the "Welcome to Internet Explorer" screen and it will ask you to pick some startup options, just like when you first used IE. When this is done, you should be good to go.
* Note: The first time you put in a password for a site, it will ask if you want IE to save it. The best security option is NOT to let IE save your passwords.
One Response to "Internet Explorer Running Slow or Crashing"
All the above is good advice all I would add is that once you get IE working,
Don't touch it
Leave it alone so that it can do updates
If you try to upgrade it, downgrade it or even use it for browsing it will probably break and then you can't do any updates.
Use a different browser for everyday use and leave IE to do updates only
There are lots of browsers to choose from
If you are really keen on using IE then at least download another browser SOON so that when IE stops working you can get some online help.


text:
Arsenal summer transfer addition Shkodran Mustafi has said he had the option of playing for German champions Bayern Munich as a teenager but he chose to play for Hamburg.
"I had trials at Hamburg, Eintracht, Frankfurt, Werder Bremen and even FC Bayern. My father asked me where it suited me best, so I opted for HSV."


text:
I've recently started using Chrome at work, and noticed some issues when attempting to post to or browse Chowhounds boards.
replying to an existing thread - the Post button is active, but does nothing. same with starting a new thread.
browsing - boards or topics. I find that clicking the name or topic link does not work, however changing the URL will bring up the topic or board.


text:
Product Description
Online Shopping Description:This is a brand new 2 button remote key case fob.It fits with cars of VauxhallSignumAstra 2005-2009Vectra 2002-2008Zafira 2006-2009Meriva 2005-OnwardsA perfect replacement for broken buttons.You can literally put your immobiliser and away you go.Inner remote is not included in this auction. You can use your old remote.If you use your old remote then there is no programming require.This remote case also does not come with any logos or emblem.The image is of the real product. Not downloaded from internet.Important Note:This remote shell functions exactly like the original. It MUST be glued together… There are no 'snaps'. There is no way around this.Please kindly check mental part and the bottom location of the key, if your key have same profile, this will fit your car.Please compare carefully before placing order.Package Included:1 x remote key fob case amazon 60% off Shopping | Glasses, cameras, dress, cloth, watches, shoes, baby dress party dress


text:
At 07:27 -0800 1998-12-02, Nathan Myers wrote:
The next release of Egcs, 1.1.1 is due out "soon". It's supposed to be mainly a bug-fix release (i.e. there's a separate "new features" development line). Is it possible to get this into Slink?
Considering that the pre-releases are already there, my guess would be yes. In general, pure bug fix releases are allowed into frozen until "deep freeze".
-- Joel Klecker (aka Espy) <URL:http://web.espy.org/> <URL:mailto:firstname.lastname@example.com> <URL:mailto:email@example.com> Debian GNU/Linux PowerPC -- <URL:http://www.debian.org/ports/powerpc/>


text:
Category: Stock Graphic, Patterns
Stock Graphic >> Pattern - Seamless pattern with glamour access 51780 by Lian-art @ CreativeMarket
File Size: 3.7 MB; Tileable: Yes; Requirements: Adobe CS1+; Vector: Yes.
Seamless pattern with glamour accessories, furniture, girl portrait and dogs (Dalmatian, dachshund, terrier, poodle, chihuahua) - black silhouettes on pink background. Ready to use as swatch.
Click on the preview to see what you get.
Zip includes.
- 1 EPS 8 + 1 Hi res JPEGs files
This image is a vector illustration and can be scaled to any size without loss of resolution. All parts of the image are editable. Watermarks will not appear on your purchased files.
Note: This images are NOT for sale and are NOT included in the sales package.
Best regards, Elena
Keywords: dalmatian, chair, vogue, orchid, clothes, dachshund, glamour, terrier, chic, accessories, boudoir, poodle, black, female, vintage, style, background, royal, seamless, pattern.


text:
Rikku's Eyes
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- 4.52 / 5.00
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Author Comments
Rated 5 / 5 stars
Eyes? What Eyes? I see no eyes...
Oh there they are... Still not sure those are eyes though. Anyway great pic very very very good, you've got some serious talent up in here. Ever think about going like for the big time comics and stuff, I think these kinda of things would just show off your talent big time.
Rated 5 / 5 stars
Well done!
It's really well done. It must be hard drawing from that perspective. I mean having the lower body smaller than the top and stuff. Very good. 10/10
Rated 3.5 / 5 stars
I know I have seen this one somewhere else but I can´t seem to remember from where though.
It is a very nicely done sketch of Rikku from FFX.
Hey, cool!
Glad it's been getting noticed in other places over the internet. C:
It's one of my slightly more popular pictures.
I've got it posted on my DeviantART and CGHub account too. :)
I think gamesradar.com featured it at some point as well.
Thanks for the review!
Rated 4.5 / 5 stars
In my opinion this is by far the best piece in your gallery, it reflects a strong sense of proportions and foreshortening. Colouring is good, but i cant help but feel like the lineart needs a tad more attention. For example it looks a bit too rough for the style you were going for, mainly around the clothing. I dont really know how to explain it though...meh ignore it, looks awesome.
Rated 5 / 5 stars
Very good art
You have a gift


text:
Separate names with a comma.
Discussion in 'Lawn Mowing' started by ranger520, Oct 28, 2003.
I bought a walker ghs.
ouch! that was short and to the point!
Now that you've solved your blowout problem, How are you going to be able to pay your mechanic? His bill will be going up in direct proportion to your productivity going down.
HAHAHA, not funny
Well exmark didnt seem to want to solve the problemso I did. Besides, it is fun to start a little bit of trouble on a rainy day.
Well I hope all that rain makes it fun when you try to use your walker and blower to clean the wet soggy leaves. I am just feeding your fire.
Scott, where did you buy your walker at? Not that Im going to run out and get one but the blowout defineatly makes me use more Q-tips.
Better buy a box of rubber gloves, You will not only have wet leaves in the blower but WET GRASS TOO.
Why not just get the blow out baffel?
new walker $10,000, blow out baffel $50.00
I had blowout problem on t.t.hp 17/48 until I put on curvy mulching blades and set deck at 2/34 inches.(made spacers for quarter inch intervals) tried it in dry conditions, no blowout at all,picked up every leaf. At 3" with high lifts I chased leaves all over the place. hope this helps, Rich


text:
Albarn speaks over Gorillaz replacing U2 at Glastonbury
Damon Albarn says he's "surprised and nervous" after Gorillaz were offered U2's Friday night headlining slot at this year's Glastonbury Festival.
It'll be the virtual band's only UK festival appearance this year.
Albarn, who headlined Glastonbury in 2009 with Blur, says it will be a privilege to appear at the festival and they won't let anyone down.
He said: "I was surprised and a bit nervous. I appreciate that it's a big deal but I think we can pull it off."
U2 were forced to pull out of Glastonbury and cancel their US tour after Bono had back surgery.
The singer said he was "heartbroken" at having to take the decision.
It means Damon Albarn, 42, will be headlining his second Glastonbury in a row.
But speaking on Zane Lowe's Radio 1 show, he says it will be completely different to playing with Blur.
He admitted: "I'm not thinking for one second that I can compete with that kind of thing.
"This is something very separate and I wouldn't try to compare the two at all.
"Obviously it's a great shame for U2 that they can't do that. I know that they were really looking forward to playing that gig. They've never done Glastonbury.
"It's magic, Glastonbury. It's definitely magic in so many ways."
Gorillaz released their third album, Plastic Beach, in March and unveiled their new set at the Coachella Music Festival in America in April.
Damon Albarn says he hopes some of the stars who appeared on the record can sing with them at Glastonbury on Friday 25 June.
"I just hope we can convince Lou Reed and he grasps that it's a real privilege to get the chance to do it.
"Then we'd have a complete house and that really would be amazing."
Albarn also says he's never had the chance to spend any time experiencing Glastonbury as a punter.
He said: "It's nice being at the beginning because [Blur] was right at the end and we had to get off stage and get in our bus and drive straight off, which was really strange.
"I didn't get a chance to experience it. I'd quite like this time to be able to do my thing and hang out for a while."


text:
December 31, 2014
Friends and family mourn father and son with 'a unique bond'
A family member says Gus and Casey Cloutier, who died in a crash in Leeds on Tuesday, 'were the most wonderful father and son that anyone could ever imagine.'
December 31, 2014
Tsarnaev's attorneys file appeal over trial venue
They ask a federal appeals court to overturn a judge's decision that would keep the trial in Massachusetts.
December 31, 2014
Maine's Riverview Psychiatric Center gets grant for doctoral interns
The state's only psychiatric hospital has been working to rebuild its image in the wake of problems related to patient and staff safety
December 31, 2014
Police aim to find out whether one gun was used in two drive-by shootings
Investigators in Portland and Westbrook hope the state police crime lab will determine the answer.
December 31, 2014
Pirates' victory deserving of good cheer
The year ends on a resolute note as Portland beats Hartford convincingly.
December 31, 2014
Bruins lose to Toronto in shootout after erasing two-goal deficit
Boston misses on three scoring chances in overtime before falling, 4-3.
December 31, 2014
State prison populations at lowest point in a decade; Maine's rate lowest in U.S.
According to the Bureau of Justice Statistics, just 980 adults per 100,000 in Maine were under some form of supervision at the end of 2013.
December 31, 2014
Obama's kid diplomacy – photos from 2014
President Obama had an up-and-down year when dealing with grown-ups, but he usually hit it off with kids.
December 31, 2014
Red Claws rain down threes on Texas
Maine wins 122-106 in a record-setting performance.
December 31, 2014
Two Saco hikers safe after getting lost in New Hampshire
The 19-year-olds call 911 after losing their way on Mount Garfield and may be billed for the rescue effort.
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In this week's stellar issue of the Mercury, I examined whether Portland's Drug Impact Area's will be doomed by city budget cuts.
City Council opted not to continue funding a deputy district attorney dedicated to the program in this year's budget. The county, which has been willing to backfill some of the city's cuts, is apparently not budging on this one. So it falls to Multnomah County District Attorney Rod Underhill to decide whether he'll use existing resources to continue staffing what was a city-initiated project.
A quick rundown: The DIAs are used to keep drug offenders out of the city's narcotics hotspots. Depending on the substance they're caught with, people are ordered to stay out of certain areas— Old Town, downtown, the Lloyd District—as a condition of probation. Businesses love it.
Anyway, I was unable to get the most recent tally of exclusions by press time. It came through today, though. Since their inception roughly two years ago, the impact areas have resulted in 1,047 exclusions, according to the DA's office.
That's not to say 1,047 individuals have been excluded. According to Deputy District Attorney Shawn Overstreet—the guy who, depending on Underhill's decision, could be snatched from DIA duty in coming days—some offenders have multiple exclusions. One person has five.
Still, the number reflects how much the tool has been used in its two years.
Other figures [PDF] the DA's office provided aren't as fresh—they're current as of December 31—but show nearly one third of the county's drug distribution and possession cases from June 2011 to December 2012 originated in one of the drug impact areas. In that same period, police made 113 arrests for violations of orders to steer clear of an impact area. Nearly 55 percent of those arrested were Black.
Race has been a touchy subject in the impact areas. The program's predecessor, Drug Exclusion Zones, were discontinued in 2007 amid criticism they unfairly targeted minorities. But while the DA's report does a good job breaking down the criminal cases issued by race, it doesn't go the extra step to break down exclusions.


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President Dmitry Medvedev will lay out his vision for joint missile defence with the West when he addresses the weekend NATO summit, a top Kremlin official said in comments released Friday.
Despite a lukewarm response from Europe, Medvedev has pushed for a common European security strategy uniting the continent that was long split between the West and the Soviet bloc.
"During his address, President Medvedev will voice a number of ideas about how we shall build cooperation in the missile defense sphere in the coming years," said his top foreign policy aide Sergei Prikhodko.
"We believe that the Euro-Atlantic process has indeed been set in motion and we have a good opportunity to work to finally remove dividing lines, move towards a common indivisible security space," he told reporters in the Kremlin.
"Decisions will be taken in the next few years but the consequences will influence the nature of cooperation for decades to come."
At the summit, Russia would like NATO to put its declared willingness to cooperate with Russia on missile defence on paper, Prikhodko said.
"We would like the importance of joint participation in missile defence, which would ensure security, to be reflected in the documents in one way or another," he said.
Moscow, however, will not expect too much too early. "We are realists, we will not ask for the impossible."
US President Barack Obama, who will also attend the gathering, has shelved an initiative by his predecessor George W. Bush to place an anti-missile radar facility in the Czech Republic and interceptors in Poland, opting for what he says is more a flexible system.
Russia and NATO are also expected to agree on a number of documents, including on "reverse transit", which would allow NATO to ship non-lethal cargo from Afghanistan, and common threats, the Kremlin said.
The NATO-Russia summit will mark the highest-level meeting between the two sides since the war between Russia and the pro-Western former Soviet state of Georgia in August 2008 severely strained relations.


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In this goofy comedy, Mark Ruffalo (ETERNAL SUNSHINE OF THE SPOTLESS MIND) stars as Alex, a struggling painter going through a particularly bad patch. Dumped by his girlfriend and unable to get work, Alex finds his life taking a rare upswing when he moves into a new apartment and falls for his neighbor, Lori (Beth Ulrich). But when things start to go wrong between Alex and Lori, their close proximity to each another proves to have an enormous downside, leading to further amusing antics as Ruffalo proves his comedic chops.
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How Hollywood bowed to Hitler: Film studios showed Nazi Germany in positive light historian claims
George Lucas' Wedding Party: Hollywood Heads to Chicago The historian found a letter from January 1938 in which a 20th Century Fox worker was asking Hitler about his views on films. The letter was signed 'Heil Hitler'. Studios were also … Continue reading
Healthy Hollywood: Get Movin' Monday – Train With Madonna!
Hollywood "boiler room" sold $2 million in fake precious metals; two arrested The iconic superstar is offering fitness fanatics a chance to work out with her. Yup; that's right, workout alongside Madonna herself. Madonna certainly knows the secrets to an … Continue reading
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Takayama Jinya
Takayama Travel Blog› entry 9 of 34 › view all entries
March 15th, 2008 – by: portia
The rain was gone, and the sun was out. We packed our luggage but left them at the guest house and went for another walk around town. We walked toward the river and saw the morning market in front of the Takayama Jinya. To be honest the market wasn't that interesting, it had stalls selling some fruits and spices, vegetables and some knick knacks. But the Takayama Jima turned out to be much better than I had imagined. Takayama Jinya was the local government building for administration, finance/tax, police and courts.
We toured the jinya which consisted of the Entrance Hall, many offices, guardroom, lounge, kitchen, living room of the head official, maids' room, tea house, large hall, a courtroom and torture devices, storehouses for rice, kitchen utensils and books. You can easily spend 2 hours looking at everything.
We next visited the Hida Kokubunji Temple, with its 3-tiered pagoda. Then we walked along the river, crossed it at Yayobashi bridge, where a couple of real tall and odd looking statues were installed on its railings. Then we went into the Kusakabe Folk Museum right next to the Yoshijima Hertiage House we visited yesterday. The folk museum used to be a money lender's house, its structure was similar to the Yoshijima Hertiage House. The special thing it had was the folk museum and display of dolls, furniture, combs, money boxes etc.
There were still a lot to see in Takayama, if we had stayed 2 nights, we could have seen a lot more. Takayama is real popular during the festivals (once in spring, another in the fall) because of all the floats would be decked out and paraded around town. I quite liked the Edo era housing with the latticed windows and mostly wood construction. Some people named Takayama as the place where time forgot, staneding on one of the old preserved streets, you could use your imaginiation and see if you were living some 200 years ago.
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AMMAN (Reuters) - Syrian authorities on Monday blamed Islamist militants for the massacre of 108 men, women and children in the town of Houla and denied U.N. and witness accounts that army tanks were in the area at the time.
In a letter to the U.N. Security Council published by state media, the Foreign Ministry said the Syrian army had clashed with hundreds of armed men who it said committed Friday's massacre. The ministry said the killers used knives, which it called a "signature" of Islamist militant attacks.
"Not a single tank entered the region and the Syrian army was in a state of self-defense using the utmost degree of self control and appropriate response, and anything other than this is pure lies," the ministry's letter said.
"The terrorist armed groups ... entered with the purpose of killing and the best proof of that is the killing by knives, which is the signature of terrorist groups who massacre according to the Islamist way."
It said three Syrian soldiers were killed and 16 wounded.
United Nations Secretary-General Ban Ki-Moon said in a letter to the Security Council on Sunday that U.N. observers who visited the site after the massacre "saw artillery and tank shells and as well as fresh tank tracks", adding that many buildings had been destroyed by heavy weapons.
Witnesses and opposition activists said Assad's forces, the only side with artillery and tanks during the 14-month-old uprising against his rule, carried out the massacre of the Sunni Muslim civilians. They said the 108 were mostly killed by bullets and knives but that at least 15 also died from shelling.
Houla is mostly populated by Sunni Muslims - from Syria's majority community which has led the revolt - while many of the surrounding villages are dominated by Alawites, the offshoot of Shi'ite Islam that provides most of Assad's ruling cadre.
Reporting by Khaled Yacoub Oweis; Editing by Mark Heinrich


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Single neurons carry out important sensory and motor functions related to the larger networks in which they are embedded. Understanding the relationships between single-neuron spiking and network activity is therefore of great importance and the latter can be readily estimated from low-frequency brain signals known as local field potentials (LFPs). In this work we examine a number of issues related to the estimation of spike and LFP signals. We show that spike trains and individual spikes contain power at the frequencies that are typically thought to be exclusively related to LFPs, such that simple frequency-domain filtering cannot be effectively used to separate the two signals. Ground-truth simulations indicate that the commonly used method of estimating the LFP signal by low-pass filtering the raw voltage signal leads to artifactual correlations between spikes and LFPs and that these correlations exert a powerful influence on popular metrics of spike–LFP synchronization. Similar artifactual results were seen in data obtained from electrophysiological recordings in macaque visual cortex, when low-pass filtering was used to estimate LFP signals. In contrast LFP tuning curves in response to sensory stimuli do not appear to be affected by spike contamination, either in simulations or in real data. To address the issue of spike contamination, we devised a novel Bayesian spike removal algorithm and confirmed its effectiveness in simulations and by applying it to the electrophysiological data. The algorithm, based on a rigorous mathematical framework, outperforms other methods of spike removal on most metrics of spike–LFP correlations. Following application of this spike removal algorithm, many of our electrophysiological recordings continued to exhibit spike–LFP correlations, confirming previous reports that such relationships are a genuine aspect of neuronal activity. Overall, these results show that careful preprocessing is necessary to remove spikes from LFP signals, but that when effective spike removal is used, spike–LFP correlations can potentially yield novel insights about brain function.
Much of our mechanistic understanding of brain function comes from extracellular recordings, which provide a direct measure of electrical activity near the tip of the recording electrode. The resulting voltage signal is composed of the spikes emitted by one or more neurons and the local field potentials (LFPs), which represent the total synaptic current in the neuronal circuit from which the recordings are obtained. Typically, the LFP is extracted by low-pass filtering the wideband voltage signal, whereas spikes are identified by high-pass filtering, thresholding, and subsequent sorting. The possibility of isolating both signals from the same electrode is of great interest because it allows the experimenter to relate the responses of individual neurons to those of the larger-scale circuits in which they are embedded.
Popular methods for studying spike–LFP relationships in the time domain include the spike-triggered average (STA) of the LFP, the spike-field coherence (SFC), spike–LFP phase-locking histograms, and the prediction of spike timing from LFP features. These types of analysis have proven useful for inferring the role of feedforward and feedback circuitry in functions as diverse as perception, attention, memory, and motor control (Andersen et al. 2004; Chalk et al. 2010; Destexhe et al. 1999; Fries et al. 2008; Jacobs et al. 2007; Pesaran et al. 2002; Saleh et al. 2010). Similar methods applied to the space domain permit comparisons of single-neuron activity to columnar systems in the cortex (Nauhaus et al. 2008; Xing et al. 2009). More generally, comparisons of spiking and LFP activity facilitate comparison with other signals, such as blood oxygenation level dependent (BOLD) and electroencephalographic (EEG) activity, that can be obtained noninvasively (Goense and Logothetis 2008).
Of course, before attempting to analyze the relationship between two types of signals, one must ensure that they can be estimated independently. LFP estimation often relies on the fact that the frequency content of LFPs and individual spike waveforms differ substantially, such that LFPs can be isolated by simply low-pass filtering the voltage signal. However, to the extent that the LFPs and spikes contain overlapping frequencies, this approach will fail to completely separate the two signals. The resulting spectral contamination is of particular concern when estimating the causal relationships between LFPs and spikes because contamination of one signal by the other will result in spurious correlations. Spectral contamination is most problematic when spikes and LFPs are estimated from the same electrode recordings, but it can also affect recordings obtained from separate electrodes, particularly when the corresponding spike density functions are highly correlated. Although various algorithms for efficient removal of spikes from LFPs have been proposed (David et al. 2010; Galindo-Leon and Liu 2010), a systematic appraisal of the consequences of this contamination in common analytical settings has not yet been attempted.
In this work we use simulations to estimate the extent of the spectral contamination of LFPs by individual spikes and spike trains, under conditions similar to those of typical extracellular recordings. We show that such contamination introduces artifactual spike–LFP relationships into many of the popular time-domain metrics mentioned earlier. In particular, strong spike–LFP coherence and spike-triggered LFPs can be obtained from random combinations of spikes and LFPs, if the former are not removed properly. We confirm these simulation results with real recordings from the primate visual system.
To address the issues associated with spike contamination we develop a novel Bayesian method that estimates veridical LFPs by removing action potential signatures from raw voltage signals. We show that application of this method to both simulations and real data has a substantial impact on measures of the relationships between spikes and LFPs. We also test two other spike removal methods and show that the Bayesian algorithm performs better in most cases. Overall, these results show that the way in which electrode signals are processed can significantly affect the conclusions drawn about the nature of spikes, LFPs, and interactions between these two signals.
Electrophysiological recordings
Two rhesus macaque monkeys took part in the experiments. Both underwent a sterile surgical procedure to implant a headpost and recording cylinder and, after recovery, monkeys were seated comfortably in a primate chair (Crist Instruments) and trained to fixate a small spot on a computer monitor in return for a liquid reward. Eye position was monitored at 200 Hz with an infrared camera (SR Research) and required to be within 3° of the fixation point for the reward to be dispensed. Recordings were obtained from well-isolated single units in areas MT/V5 and V6, both of which were identified based on anatomical magnetic resonance imaging scans and the physiological properties of the neurons (Fattori et al. 2009; Maunsell and Newsome 1987). All aspects of the experiments were approved by the Animal Care Committee of the Montreal Neurological Institute and were conducted in compliance with regulations established by the Canadian Council of Animal Care.
On each trial, the animal acquired fixation, after which the stimulus appeared and remained stationary for 200 ms. The stimulus then moved at a constant direction and speed for 500 ms. Stimuli were displayed at 85 Hz at a resolution of 1,920 × 1,200 pixels and the viewing area subtended 70 × 42° of visual angle at a distance of 42 cm. Stimuli consisted of sinusoidal gratings of optimal spatiotemporal frequency or random-dot patches displayed on a gray background (luminance of 70.3 cd/m2). Stimulus size was optimized for each cell. Motion direction was sampled in 30° steps and each stimulus was repeated five times in blockwise random order.
Signal processing
Electrophysiological signals were recorded with a standard data acquisition system (Plexon Multichannel Acquisition Processor [MAP] System). Specifications of this system typically include a dedicated low-pass filter for LFP signals (four-pole high cut at 170 Hz) followed by digitization at 1 kHz. As we show in the following text, this type of filtering invariably introduces spurious correlations into measures of spike–LFP coherence. We therefore obtained custom hardware modifications to the MAP system that included wideband analog filters (two-pole high cut at 2.5 kHz) and a higher digitization rate (10 kHz). These modifications allowed us to detect spectral contamination of the LFPs by spikes; subsequent spike sorting and LFP analysis were performed through off-line digital filtering.
To remove line noise at 60 Hz, we assumed that the underlying signal had equal power in a small range of frequencies around 60 Hz and filtered the signal so that the power at 60 Hz was similar to that of surrounding frequencies. We transformed the wideband signal into the Fourier domain and minimized the squared error between the absolute value of the Fourier coefficients between 55 and 65 Hz and the function (1) Here f is frequency, f0 is the peak frequency (nominally 60 Hz), a is the height of the 60 Hz peak, b controls its width, c adjusts the shape of the peak, and d is the baseline frequency content. This functional form provides a parsimonious parameterization of the frequency content around 60 Hz. We then corrected the 60 Hz artifact by filtering the signal in the Fourier domain with the function's inverse (2) The power spectrum of the corrected signal showed no apparent discontinuity around 60 Hz, in contrast to a simpler notch filter. A similar operation was performed around 180 Hz.
To assess the likely contribution of spectral contamination to various measures of spike–LFP coherence, we analyzed a signal that, by construction, contained no temporal relationship between spikes and LFPs. This composite signal was obtained by taking the frequency content of the wideband signal obtained from our electrophysiological recordings, after removing the spikes using the spike removal algorithm presented in the following text, and shuffling the phases (Fig. 1A). To this signal we added back waveforms taken at random from the original electrophysiological signal, preserving the timing of each spike while scaling the waveforms to achieve a desired signal-to-noise ratio (SNR). To obtain reliable estimates of the underlying spike waveforms, we first selected typical waveforms that were within 3SDs of the mean waveform at all times. We then projected this ensemble of waveforms onto their first five principal components, obtaining a bank of denoised waveforms. To achieve a desired mean firing rate, Poisson distributed spurious spikes were added to the signal.
The LFP components of this signal thus had the same amplitude spectra as those of a real neural signal, but lacked any consistent relationship between spike times and LFP phases. Consequently, any apparent relationship between the two signals would necessarily be artifactual.
Data analysis
In an initial preprocessing step, we corrected the phase distortions introduced by analog filters by filtering the wideband signal backward in time with a digital Bessel filter that closely modeled the phase response of the analog filters used in the preamplifier (Nelson et al. 2008). We then filtered the wideband signal with digital filters similar to those used conventionally to estimate LFPs. The filters used were a fourth-order 170-Hz low-pass causal Butterworth filter (digital version of the filter used on the Plexon PreAmp separation for the LFP board) and a fourth-order two-pass Butterworth (same filter with zero phase delay). Filtering was implemented with Matlab software (The MathWorks).
For some analyses, we divided the LFP frequency spectrum into the following bands, similar to those used in previous studies (Khawaja et al. 2009; Ray et al. 2008): θ (4–8 Hz), α (8–12 Hz), β (16–24 Hz), low γ (25–55 Hz), and high γ (65–140 Hz). Since the θ, α, and β bands did not show significant spike contamination in any of our metrics, in both simulations and real data, for reasons of compactness we combined all three bands into a single "low-frequency" band (4–24 Hz).
Spike detection and sorting based on the high-pass filtered wideband signal were performed off-line using established methods (Quiroga et al. 2004). These results were compared for consistency with results from Plexon's Off-line Sorter software, which uses spike waveforms sampled at 40 kHz. Spike timing information was considered accurate if agreement between the results of the two spike sorting methods was above a criterion level of 95%; otherwise, the sorting parameters were altered until the agreement exceeded the criterion. In three cases where this level could not be reached, the data were rejected from further analysis.
SNRs were computed for each isolated unit as the peak-to-trough voltage of the mean spike waveform, divided by the square root of the mean power of the complete raw signal. We obtained the STA of the LFP by averaging local field potentials centered around the time of spikes (Dayan and Abbot 2001). We subsequently filtered the LFP with complex Morlet wavelets and used the magnitude of the coefficients as an estimate of the instantaneous power of the LFP at given frequencies (Goupillaud et al. 1984). We averaged the magnitude of the coefficients around the time of spikes, normalized by the average magnitude of the coefficients of the whole LFP signal, to obtain a normalized wavelet STA, which can reveal transient increases or decreases in the magnitude of oscillations at given frequencies around the time of spikes.
To test whether spikes preferred certain phases of the LFP, the instantaneous phase and amplitude of the LFP at 35 different frequencies (log spaced from 4 to 150 Hz) were first calculated with the Hilbert transform of different filtered versions of an LFP recording. A single phase value was then assigned at each frequency for every spike in a recording (Jacobs et al. 2007). By convention, a phase value of 180° corresponds to the positive (hyperpolarizing) peak of the cycle. Finally, histograms of the distributions of spike phase for different LFP frequencies across all spikes were compiled; 50 phase bins, ranging from 0 to 360° were used. The uniformity of the distribution of spike phase values for our frequency ranges was assessed for each case, using the Rayleigh statistical test, corrected for the number of frequency ranges (Rutishauser et al. 2010). A cell was considered phase-locked at a specific frequency range if the null hypothesis of uniformity of the phase distribution could be rejected at a corrected P < 0.01.
Spike-field coherence (SFC) was calculated as the power spectrum of the LFP STA divided pointwise by the sum of the power spectra of all LFP segments used to compute the STA (Fries et al. 2001). This measure can reveal phase-locking at high frequencies that is otherwise obscured in the STA of the LFP by low-frequency noise. A value of 1 at a given frequency of the SFC means that all spikes appear at the same phase for this frequency, whereas a value of 0 indicates no consistent relationship between the phase of the LFP at a given frequency and spikes.
Tuning curves were quantified for single units (spike count) and LFPs (normalized LFP band power), in the three frequency bands described earlier. We used Morlet wavelets to measure the instantaneous power at different frequencies of the LFP across time, as in the wavelet STA analysis. LFP tuning curves were derived by normalizing the mean magnitude of the Morlet coefficients over a time period that spanned 100–500 ms after the onset of stimulus motion against that in a baseline period consisting of 150 ms of spontaneous activity before the stimulus presentation. Average tuning vectors for each band were also computed for both single units and LFPs.
Spike removal algorithm
The purpose of the algorithm is to estimate the local field potential based on a measured wideband voltage trace of length n. We assume that this wideband signal y is the superposition of a low-frequency local field potential w, high-frequency spike components ηk, an offset μ, and white noise ε (Fig. 1B). (3) Here m is the number of sorted neurons emitting spikes. The high-frequency component of the kth neuron ηk is created by the convolution of the neuron's spike train sk, assumed known (see Fig. 1B), and the neuron's spike waveform ϕk (4) Importantly, waveforms ϕk are not set to the mean waveforms determined by spike sorting or by spike-triggered averaging the wideband signal, as in previously proposed methods of eliminating spike remnants (Pesaran et al. 2002). Rather, the waveforms ϕk are considered as free parameters and are estimated optimally as a part of the algorithm. The offset μ is introduced to compensate for the fact the mean of ηk is likely to be negative.
The generative model (Eq. 3) contains more unknowns (w, ϕk, and μ) than knowns. Thus assumptions must be introduced to make the estimation of the local field potential w well-posed. We first assume that the local field potential is smooth or, equivalently, that most of its power lies in the low frequencies (5) Here N(a, Σ) represents a multivariate Gaussian with mean a and covariance Σ. Capital gamma (Γ) is a matrix that embodies our assumption of smoothness. Multiplication of a vector x by this matrix (Γx) produces a low-pass filtered version of the target x. The matrix was chosen to be circulant, a property necessary to make estimation of the local field potential tractable; definitions and properties of circulant matrices are discussed at length in the Supplemental appendix.1 Gamma (γ) controls the strength of the prior. Our second assumption is that ε is generated by a white noise process, p(ε) = N(0, σ2I). Finally, we assume that spike waveforms ϕk lie in a subspace B (6) We chose B so that spike waveforms were described by one parameter per time sample in the interval from −1 to +2 ms relative to the peak depolarization. This duration of 3 ms was chosen based on the traditional length of snippets used in spike sorting, generally ranging from 1.5 to 3 ms.
To estimate the local field potential w, the spike waveforms ϕk, and the offset μ, we used Bayesian inference to obtain maximum a posteriori (MAP) model parameters. By Bayes' theorem, the log-posterior of the model is (7)
Here k is a constant factor. By taking the log of this expression and setting partial derivatives with respect to the parameters to 0, we obtain the MAP estimates of the parameters Here A+ = (A′A)−1A′ denotes the Penrose–Moore pseudoinverse. These equations can be understood as follows. First, the optimal offset of the model μ̄ is simply the mean of the wideband signal with the LFP and spike contributions removed. Second, the optimal local field potential w̄ is related to the spike-free, mean-corrected wideband signal z = y − ∑k sk*(Bφ̄k) − μ̄ by matrix multiplication with (γ2Γ + σ2I)−1γ2Γ. Multiplying a vector by this matrix low-pass filters the vector and thus the model tells us that the optimal LFP is obtained by low-pass filtering the wideband signal after removing spike waveforms around the time of every spike.
The key equation is the second in the series, which governs the spike waveforms. By the properties of the pseudoinverse, (sk*B)+(sk*B)a = a. Now to recover a waveform a from a train of waveforms (sk*B)a, one simply needs to take the spike-triggered average of this signal normalized by the autocorrelation of the spike train. Thus the optimal spike waveform for the kth neuron is given by the decorrelated STA of the wideband signal minus the LFP, the spike contributions from other neurons, and the offset. However, since the optimal LFP is mostly determined by low-pass filtering the wideband signal, the overlap between spikes from different neurons is often negligible and spike trains are uncorrelated at short time lags due to the absolute refractory period, it follows that to a first approximation the optimal waveform for a given neuron is equal to the STA of the high-pass filtered wideband signal.
In practice, the optimal spike waveform determined by the model can vary substantially from the STA of the high-pass filtered wideband signal because of the various corrections it applies. A fast and effective model-based spike removal algorithm can be derived by decoupling the Eq. 8 system and applying the conjugate gradient descent to solve the resulting equations, as shown in the appendix. An implementation of this algorithm in Matlab is available from our website (http://apps.mni.mcgill.ca/research/cpack/lfpcode.zip). For the model to be fully specified, the strength of the prior relative to the noise γ2/σ2 must be estimated because this determines what the model considers as signal and what it discounts as noise. In the appendix, we show how marginal likelihood (or evidence) optimization is used to estimate prior and noise levels. We also detail in the appendix how to choose an appropriate form for the prior matrix Γ and how to optimize performance for long recordings.
Other spike removal algorithms
Two methods to remove spike waveforms from wideband signals were also tested in both simulated and real data. The first method, known as mean spike removal, simply subtracts the mean spike waveform from the wideband signal at the corresponding spike times. Here we used a 3-ms window (1 ms before the spike and 2 ms after) to recover the mean spike waveform. This was chosen for comparison with our Bayesian algorithm, which used a window of the same size. A second method uses linear interpolation to replace the wideband signal around the time of each spike, using the same time window as that in the other methods (3 ms).
Spectral composition of spike waveforms
Spikes are by definition fast events that are dominated by temporal frequencies far higher than those that make up the LFP signals. Thus it is natural to assume that low-pass filtering the raw voltage signal will remove the spikes and that what remains will be a pure estimate of the LFPs. This assumption can be examined by computing the power spectrum of a typical spike waveform and Fig. 2A shows one such waveform recorded extracellularly in our laboratory. As is typical in such recordings, the duration of the action potential is on the order of 1 ms and the corresponding waveform contains both a peak and a trough. Consequently, the power spectrum (Fig. 2B, top) is dominated by high frequencies. However, closer inspection of the power spectrum shows that there is a small amount of power at low frequencies in this fast waveform (as shown in Fig. 2B, bottom), particularly in some of the frequencies (100–200 Hz) that are often examined in LFP studies (Gold et al. 2006).
The bottom panel of Fig. 2A shows the result of applying a low-pass filter to the spike waveform shown in the top panel. Although this filtering reduces the amplitude of the waveform, some residual signal remains and this residual retains the basic shape of the original waveform. Moreover, the residual signal is stretched in time over an interval determined by the cutoff frequency of the low-pass filter (here on the order of 10 ms).
Beyond the low-frequency content of individual spike waveforms, the temporal structure of spike trains can contain additional power at low frequencies (Bair et al. 1994). Consequently, if spikes are not properly removed, a succession of spikes can contain more power at low frequencies than an individual waveform would indicate. These considerations suggest that the commonly used technique of low-pass filtering the raw voltage signal is not entirely sufficient to isolate the LFP signals. To estimate the magnitude of this problem, we developed a set of ground-truth simulations that allowed us to quantify the effects of spike contamination in a context where the veridical LFP signal is known.
Spectral contamination in simulated data
The basis of the simulations was a phase-randomized wideband signal with the same frequency content as that of a real wideband signal (see methods and Fig. 1A for details). By combining this signal with spike waveforms taken from electrophysiological recordings (see following text), we obtained a composite signal similar to that typically recorded with electrophysiological methods but in which the LFPs and spike times were completely dissociated. This allowed us to perform ground-truth simulations in which any temporal relationship between spikes and LFPs was necessarily an artifact of the method of analysis. The duration of the phase-randomized signal in all our simulations was 3 min.
Figure 3 shows a short segment of the signals used in our ground-truth simulations. The top panel shows a phase-randomized wideband signal before (red line) and after the addition of spikes with a mean amplitude of 2 dB (blue line, offset downward to facilitate reading). The middle panel shows these same signals after low-pass filtering. Here the difference between the signals is much less visible, which suggests that in some analysis scenarios low-pass filtering may be sufficient to remove spike traces. The bottom panel, however, reveals that the deviations between the two signals (green line, scaled by a factor 3 to facilitate reading) are centered around the time of spikes (gray lines) and are highly stereotyped. These small spike remnants can bias analyses of LFPs, as we show in the next sections.
Spike-triggered average (STA) of the LFP
As shown in Fig. 2, a typical spike waveform contains power at low frequencies, which can potentially complicate the isolation of the LFP component of the raw voltage signal. In particular, although the magnitude of the low-frequency component is relatively small (Fig. 3, bottom), its importance could be amplified by analytical techniques aimed at finding the components of the LFP that are correlated with spikes. One common example of such an analysis is the STA of the LFP.
The STA of the LFP is obtained by averaging the LFP signals recorded around the time of each spike. In principle this method is useful for inferring causal relationships between the two signals and it is commonly used to study local neuronal synchronization related to the discharge of a specific neuron and to compute the average spike-related modulation in specific LFP bands. The shape of the STA reveals the nature of such correlations, whereas a flat STA suggests that the two signals are unrelated.
We first examined the STA of a composite signal in which the SNR of the spike relative to the LFP was set to 2 dB and the mean spike rate was 9 spikes/s. Prior to calculation of the STA the raw composite signal was low-pass filtered to remove frequencies ≥170 Hz. However, inspection of the resulting STA in Fig. 4A (top) reveals clear residual structure, indicating that low-pass filtering is insufficient to separate spikes from LFPs. The artifact has a shape similar to that of the mean waveform, but has a longer duration, as expected from Fig. 2A (bottom). The exact shape of the artifact is determined by the properties of the low-pass filter.
For comparison we also computed the STA associated with a signal that was filtered with a single-pass Butterworth filter (Fig. 4A, middle), which is commonly implemented in analog circuits that are part of LFP recording hardware. In addition to the spurious STA, this filter also introduces frequency-dependent phase shifts, as reported previously (Nelson et al. 2008). Thus the commonly used approach of low-pass filtering the raw voltage signal appears to alter both the magnitude and timing of spike–LFP correlations.
The effects of this contamination are decomposed into different frequency bands in Fig. 4B. Here the STAs affected by spike contamination are shown in blue, whereas STAs obtained after the application of the spike removal algorithm introduced in the next section are shown for reference in red. The residual influence of spikes is present in all frequency bands and is particularly strong at low- and high-gamma frequencies.
Although the STA can detect linear relationships between spikes and LFPs, it is insensitive to higher-order correlations between these signals. The wavelet STA, however, can reveal transient changes in the relative instantaneous power in different frequency bands around the time of spikes, the signature of a more complex relationship between LFPs and spikes (Burns et al. 2010; also see methods). Figure 4C (top) shows that the wavelet STA is also sensitive to contamination by spikes. Here contamination is restricted to LFP frequencies ≥100 Hz at 0 ms time lag (deep red color). Note that the stripe pattern visible at low frequencies is due to chance fluctuations in the power at these frequencies and is not significant.
Bayesian spike removal algorithm
To address the contamination issues illustrated in Fig. 4, we developed an algorithm that removes spikes from raw voltage traces. The algorithm assumes that the wideband voltage signal is generated by the sum of a low-frequency LFP component, spikes of limited duration occurring at known times, an offset, and white noise (see Fig. 1B, bottom diagram, and methods). These assumptions are embedded in a probabilistic model and the most likely LFP is then determined through Bayesian inference. The optimal parameters of the model have straightforward interpretations (see methods and the appendix): spike waveforms are essentially STAs of the high-pass filtered wideband signal, whereas the LFP is given by the low-pass filtered wideband signal after the subtraction of the contribution of spikes.
Figure 4A shows that the magnitude of the STA of the LFP when the composite signal is preprocessed through different methods. As mentioned earlier, a spurious STA is obtained following standard low-pass filtering (top two panels), whereas our spike removal algorithm greatly reduces this artifact (bottom). Figure 4B shows the STAs at different frequencies, with the LFP derived through standard low-pass filtering indicated in blue. The red lines show the STAs at different frequencies following application of our spike removal algorithm. The magnitude of the spurious correlation is now much smaller, particularly at high frequencies. Because the spike removal method removes the mean spike only at spike times, and thus will not remove all spike remnants when spike shapes for a given neuron are not completely stereotyped, some residual second-order correlations between spikes and LFPs could remain. Nevertheless, the method is effective at attenuating spurious correlations in the wavelet STA, as shown in Fig. 4C. Additional details on the derivation and implementation of the spike removal algorithm are given in the appendix, which also covers more challenging conditions, such as long recordings or nonstationary spike shapes that result from electrode drift.
Phase synchronization
Another quantity commonly used to assess spike–LFP relationships is the synchronization between spikes and LFPs at different frequencies. This is typically manifested as a preference for spikes to occur at specific phases of the LFP oscillation cycle and such preferences may reveal synchronization of the local presynaptic activity. This synchronization can be an alternative way of encoding behaviorally relevant signals, particularly those related to visual attention (Fries et al. 2008), motor planning (Denker et al. 2007), motor output (Baker et al. 1999), and memory consolidation (Paz et al. 2008; Siapas et al. 2005). The frequency at which spikes are locked can also provide hints about the spatial and dynamic properties of the neural circuitry driving the neuron (Liu and Newsome 2006).
One method that is commonly used to assess the synchronization between spikes and LFPs is the spike-field coherence (SFC), obtained from the power spectrum of the STA. Figure 5A shows the SFC as a function of frequency for simulations in which the composite signal was preprocessed with low-pass filtering (blue) and our spike removal algorithm (red). When spikes are removed by low-pass filtering alone, prominent phase synchronization is seen at the higher frequencies and this artifactual relationship disappears following spike removal.
Figure 5B shows the phase-locking histogram, which measures the distribution of the instantaneous phase of the LFP at different frequencies at the time of spikes. Here it is clear that this measure is particularly sensitive to spectral contamination of the LFP. Note that the slant visible in the phase–frequency relationship is due to frequency-dependent phase shifts induced by the causal low-pass filter.
LFP tuning curves
A final quantity of interest is the tuning curve, which captures the magnitude of the spike or LFP response as a function of an experimentally manipulated sensory or motor variable. Comparison of tuning curves obtained from the two signals provides additional insight into local cortical processing, the architecture of such neuronal circuits (Liu and Newsome 2006), the spatial extent of the LFP (Katzner et al. 2009), and links of LFP features to synaptic inputs and neuronal outputs (Khawaja et al. 2009). We therefore examined the tuning of a composite signal in which untuned LFPs were combined with the waveforms of well-tuned spikes. For the latter both the waveforms and the tuning curves were taken from a single-unit recording of a neuron found in the middle temporal area (MT) of a macaque monkey. The tuning curve for the spiking responses of this neuron for the motion direction of a visual stimulus is shown in Fig. 6A.
Figure 6 shows the LFP tuning curve for the high gamma band, with low-pass filtering of the raw signal and after our spike removal algorithm was applied (Fig. 6B). Because the LFP signal is untuned by construction, successful spike removal should yield responses that respond roughly equally to all motion directions, whereas spike contamination will manifest itself as tuning for the downward-rightward motion shown in Fig. 6A. The results show that both LFP tuning curves are untuned for visual motion direction, suggesting that the spikes do not introduce spurious tuning into the LFPs, even at higher frequencies (high gamma band).
Summary of spike contamination in simulated data
Our simulation results reveal that spike contamination can introduce strong artifactual correlations between spikes and LFPs. In further stimulations we found that both spike amplitude and the firing rate of a neuron affect the magnitude of spike contamination in LFPs, with larger firing rates and spike amplitudes leading to greater contamination. Supplemental Figs. S1 and S2 and Table 1 provide summaries of the magnitude of spike contamination for different spike amplitudes and firing rates. As shown in Supplemental Fig. S1, the normalized amplitude of the STA of the LFP rises linearly as spike amplitude increases. Similarly, higher values of SNR give higher artifactual values of the SFC and raise the probability of a neuron being considered phase-locked to specific frequency ranges (Table 1). A weaker effect is observed for high neuronal firing rates (Table 1).
Other spike removal approaches
As an alternative to simple low-pass filtering, one might attempt to estimate LFPs by removing individual spikes from the wideband signal. This has traditionally been accomplished using one of two methods. The first method involves subtracting each neuron's mean action potential waveform from the raw signal at the corresponding spike times. A second approach involves removing each action potential and interpolating the wideband signal across the resulting gap. Figure 7 compares the performance of these approaches with the Bayesian algorithm, for three of the metrics discussed earlier (LFP STAs, wavelet STAs, and phase-locking histograms). Here the simulated data are the same as those used in the previous figures.
The top panel of Fig. 7A shows that the mean spike removal method did not completely remove the residual spike correlation from the STA [a difference of 0.48 dB or 16% more residual compared with the Bayesian spike removal (green line)]. By contrast, the interpolation method (Fig. 7A, middle panel) seems to perform overly aggressive spike removal, in the process introducing an artificial positive deflection of the LFP STA around the moment of the spike (a difference of 1.68 dB or 44% more residual compared with the Bayesian spike removal). For the wavelet STA (Fig. 7B), the mean spike removal method (top panel) succeeds in attenuating the spurious correlations, as does the interpolation method (middle panel). Indeed the latter method slightly outperforms our Bayesian algorithm (bottom panel) for this particular measure (SD of the wavelet coefficients for the interpolation method is 0.0013, for the mean spike removal and the Bayesian algorithm 0.0015 and for the low-pass filter 0.0036). However, as shown in Fig. 7C (middle panel), interpolation can introduce significant spurious correlations into the phase locking histogram. For this measure mean spike removal (Fig. 7C, top panel) also fails to remove the spurious phase locking correlations, while the Bayesian algorithm shows little residual structure (bottom panel). These results are confirmed by the P values of Rayleigh statistical tests (0.008 for the mean spike removal, 0.004 for the interpolation method and 0.74 for the Bayesian algorithm, with the hypothesis of phase-locking for a value of P < 0.01).
Thus we find that removal of individual spikes is generally preferable to low-pass filtering the wideband signal. Of the methods for removing individual spikes, removal of the mean spike waveform most often leaves residual, artifactual spike–LFP correlations. Interpolation methods perform better by aggressively removing all signals related to each spike, but in the process they can introduce other types of spurious correlations. In most cases our Bayesian algorithm outperformed both previous approaches. Furthermore, as we show in the discussion and the appendix, the Bayesian algorithm generalizes the advantages of these previous approaches, while casting the problem in a rigorous mathematical framework within which key assumptions can be made explicit.
Real recordings
The previous sections showed that low-pass filtering cannot completely remove spike waveforms from composite signals constructed to have no correlation between spikes and LFPs. The resulting spectral contamination of the LFP can introduce significant bias into such measures as the STA, the wavelet STA, the SFC, and phase-locking histograms, especially for higher-frequency bands. By comparison, we found that the tuning of the LFP to stimulus features as measured by tuning curves is not significantly affected by spikes, even when spike responses are strongly tuned. We introduced a new spike removal algorithm that performs better than low-pass filtering.
To examine the consequences of these findings for signals obtained in vivo, we recorded single-unit activity and LFPs from two alert macaque monkeys. A total of 26 isolated neurons in areas V6 (19) and MT (7) neurons were analyzed. Both areas are specialized for the processing of visual motion (Fattori et al. 2009; Maunsell and Newsome 1987). In each case, we determined the selectivity of the single-unit activity for visual motion by drifting a sinusoidal grating or a random-dot stimulus in 12 different directions spaced evenly around the circle. Cells that failed to respond to the stimulus or that lacked direction selectivity (defined in methods) were excluded from the analysis.
As shown for a typical cell in Figs. 8 and 9, the trends in the real data qualitatively match those in our simulations. In several cases, including the one illustrated in Fig. 8, the LFP was correlated with the timing of spikes and this was apparent in both STA analysis and phase synchronization. These correlations were not removed by the spike removal algorithm. Thus our results are consistent with previous findings (Gregoriou et al. 2009; Whittingstall and Logothetis 2009) that indicate a relationship between spike timing and LFP phase. However, both the range of frequencies over which this relationship is found and the magnitude of the correlations are affected by the method of preprocessing the raw signals. For example, inspection of the spike-triggered coherence before spike removal (Fig. 9A, blue line) would lead one to conclude that high frequencies of the LFP are robustly correlated with spikes, whereas application of the spike removal algorithm shows that in fact only low frequencies of the LFP are modulated with spikes (Fig. 9A, red line).
Figure 10B shows LFP tuning curves before and after removal of the spikes of a robustly tuned neuron (Fig. 10A). As expected from our simulations, LFP tuning curves were essentially unaffected by spike removal. The next section quantifies the extent of this contamination for our population of cells.
Population results.
We assessed the level of spectral contamination for different coherence metrics for all our neuronal recordings and these results are shown in Fig. 11. Figure 11A shows that the normalized amplitude of the LFP STA (SNR) for various frequency bands, measured around the time of spikes (10 ms before to 10 ms after peak depolarization), drops significantly after the removal of spikes [average of 5 dB (68%) drop for high gamma and 1 dB (20%) decrease for low gamma]. The wideband signal, which contains both high and low frequencies, is similarly affected [average of 7 dB (80%) decrease]. In contrast, the STA at low frequencies is only weakly affected by the spike removal algorithm. A similar pattern was observed for the SFC, as shown in Fig. 11B. There is on average a 66% decrease of SFC values for the high gamma and a 30% decrease for the low gamma frequencies.
The effect of spike removal on phase-locking histograms follows a similar pattern across frequencies, as shown in Table 2. The phase-locking metric is dramatically affected by spike remnants, with the proportion of cells classified as phase-locked to high gamma frequencies dropping by half after spike removal.
In contrast to these results, Fig. 11C shows the correlation between the LFP and spike tuning curves, both before and after spike removal. For both high and low frequencies, the difference in the correlation coefficient of the two tuning curves is very small (average reduction of 0.06 and 0.03, respectively), indicating that spike contamination has little effect on LFP tuning curves. This conclusion is further supported by the fact that the points are clustered along the unity line, despite wide variation in the extent to which the tuning of the two signals is correlated. These results are consistent with our simulations (Supplemental Figs. S1 and S2).
Other approaches of spike removal on real data
For comparison with previous approaches, we also estimated the effects of mean spike removal and interpolation methods on our real data and the results are shown for an example recording in Fig. 12 (same example as that in Figs. 8 and 9). As in the simulated data, mean spike removal leads to larger LFP STAs and more structure in the phase-locking histogram (Fig. 12, A and C). In this specific example, linear interpolation performs very similarly to the Bayesian spike removal algorithm. However, across the population, both mean spike removal and interpolation yield larger estimates of spike–LFP relationships than our Bayesian algorithm (summary in Table 2). Although ground-truth is not available in the real data, our simulations from the preceding sections suggest that the greater synchronization found with other algorithms is likely to be artifactual.
In recent years there has been an increase in the sophistication of analytical methods for interpreting neuronal activity. Although these advances are important for understanding brain circuitry, they are also easily influenced by particular assumptions about the way in which the raw signals should be processed. In this study, we have explored one issue related to such signal processing by quantifying the contamination of the LFP from action potential waveforms in both simulated and real data.
Our results show that estimates of the relationship between LFPs and spikes can be considerably affected by spike contamination. This results simply from the spectral characteristics of spike trains and individual spike waveforms: both have power at the frequencies used to study LFPs (Fig. 2B). Consequently, spikes and LFPs cannot be isolated from a raw voltage signal with simple frequency-domain filtering. To estimate the extent of this problem we performed simulations in which spike waveforms were added to phase-randomized LFP signals, such that the spectral profile of the LFP was maintained but there was no actual LFP–spike relationship. Nevertheless, when LFPs were estimated by low-pass filtering, our analysis showed artifactual spike–LFP STAs (Fig. 4) and spurious phase-locking of spikes to LFPs (Fig. 5). This effect was particularly strong at high frequencies. In contrast, tuning curves in response to visual stimuli were not strongly affected by spike contamination (Fig. 6), even at high frequencies (≤140 Hz), unless the spike-to-LFP power ratio was unnaturally high (>5 dB). Similar results were obtained using real recordings with direction-tuned neurons from the primate visual system (Figs. 8⇑⇑–11). To address these issues we developed a novel Bayesian spike removal algorithm and demonstrated that it is capable of removing artifactual spike–LFP correlations.
Comparison with previous studies
Although the existence and potential importance of spectral contamination of LFPs by spikes has been recognized for some time (Pesaran et al. 2002), the issue has been addressed only rarely in recent studies. One common approach in previous work is to subtract the mean spike waveform from the raw signal at each spike time (Pesaran et al. 2002; Zanos et al. 2006).
The generative model underlying our spike removal algorithm was constructed to generalize this spike subtraction method. In fact, we show in the appendix that our spike removal method reduces to the spike subtraction method when spike waveforms do not overlap, no assumptions are made on the smoothness of the LFP, and an offset term is not included in the model. The full spike removal algorithm thus works similarly to the spike subtraction method, but corrects for spike train autocorrelations and reduces low-frequency components in spike waveforms attributable to LFPs. Each of these adjustments corrects for artifacts introduced by spike subtraction, thus enabling more effective spike removal, as we show in detail in Figs. 7 and 12 and the appendix.
Another proposed method of spike removal is to replace time samples around each spike with samples interpolated from the LFP before and after the spike (Galindo-Leon and Liu 2010; Jacobs et al. 2007; Okun et al. 2010). This approach, although again being superior to low-pass filtering, introduces the difficulty of selecting the method of interpolation, including the function used to interpolate and the length of its support on either side of spikes, without a firm theoretical foundation to justify these choices. Linear interpolation, which is commonly used on wideband signals for this purpose, not only does not completely remove spurious correlations but also introduces new ones, as shown in detail in Fig. 7. The difficulty of selecting a proper method could be alleviated by casting the interpolation as a Bayesian inference problem similar to the one considered here. Within this framework, the functional form of the interpolation would be adjusted by the statistics of the local field potential. A more fundamental issue is that when recording in areas with high transient firing rates, interpolation must sometimes be done over intervals several times longer than a single spike waveform. This is likely to introduce additional artifacts into the estimated LFP.
A recent method (David et al. 2010) uses a more sophisticated linear filtering approach to remove all spike–LFP correlations from the raw signal. In the appendix, we show that our proposed spike removal algorithm reduces to this method in the limit of very long spikes. When very long spikes are assumed, however, the method essentially removes all linear relationships between spikes and LFPs, including legitimate correlations, and thus cannot provide an estimate of the degree to which spikes and LFPs are actually correlated. In contrast, our method focuses on removing the purely artifactual parts of the LFP signal that are introduced by spike waveforms of short duration (≤3 ms), while preserving legitimate correlations that occur at longer timescales. Although the method of David et al. (2010) can be modified to accommodate the assumption of finite spikes, we show in the appendix that this leads to residual artifacts around the time of spikes due to the way that the method handles edges.
Practical considerations for effective spike removal
Our spike removal algorithm assumes that the wideband signal derived from extracellular recordings is the sum of a low-frequency LFP signal, stereotyped spikes of finite length occurring at known times, noise, and an offset (Fig. 1B). For the spike removal process to be most effective, it is important that careful preprocessing be done so that the signal closely matches the assumptions of the generative model.
The form of the prior assumed on the LFP signal should be adjusted so that it closely matches the empirical autocorrelation properties of the observed signal; a practical procedure to choose the form of the prior is detailed in the appendix. Line noise should be removed before spike removal because this effect is not dealt with by the generative model (see methods). Furthermore, analog filters in the recording hardware can cause frequency-dependent phase shifts in the wideband signal (Nelson et al. 2008), which may artificially lengthen the duration of the observed spike waveforms. This issue can be avoided by compensating for phase distortions by digital filtering (Nelson et al. 2008).
Our spike removal algorithm will remove artifactual linear correlations between spikes and LFPs regardless of whether the spikes in the wideband signal are completely stereotyped. In the latter case, however, residual high-frequency artifacts of random phase will be visible around the time of spikes. These artifacts may be picked up by second-order methods such as the wavelet STA and Volterra methods (Zanos et al. 2006, 2008). It is therefore crucial to perform careful spike sorting before removing spikes. It is also important that spike timings be accurate because spike timings that are inaccurate by as little as one or two samples will cause observed waveforms to shift appreciably (Sahani 1999). Spike timings that are obtained by thresholding a high-passed signal can be inaccurate; more accurate timings can be obtained by aligning spikes to their peak depolarization (Quiroga et al. 2004; Sahani 1999). Additionally, if spike waveforms shift over time, for example because of electrode drift, the algorithm should be applied on short segments of the data to obtain the best results; we show in the appendix how to perform spike removal in chunks.
Many of these prescriptions are equally applicable to other methods of spike removal and, of course, they do not guarantee complete removal of spike artifacts from the wideband signal. Nonetheless, we found empirically that the spike removal algorithm diminished artifactual correlations to a great extent. When an interesting finding relies crucially on the quality of spike removal, it may be worthwhile to back up claims with ground-truth simulations, similar to those of Fig. 1A.
Hardware considerations
Several manufacturers offer products designed to record local field potentials (often designated LFP boards). These boards typically low-pass filter the wideband signal from a headstage, with a cutoff usually ranging from 150 to 300 Hz, and sample the resulting signal at a typical rate of 1 kHz. Our results indicate that the signals derived from these boards are at all frequencies appropriate for analyses that are insensitive to the relative timing of spikes and LFPs, for example to derive tuning curves (Figs. 6 and 10). However, our results also imply that analyses that are sensitive to temporal relationships between spikes and LFP, including the STA, spike-triggered coherence, phase-locking histograms, and predictions of spikes from LFPs, can be corrupted by the presence of spike remnants in LFPs derived from these boards. This contamination is especially strong at gamma frequencies >60 Hz.
It may be possible to work around this contamination, either by limiting analyses to frequencies <60 Hz, removing all linear correlation between spikes and LFPs using the methods of David et al. (2010), or by recording spikes and LFPs on different electrodes. However, a safer approach is to acquire the complete wideband signal during electrophysiological recording and to perform careful postprocessing using methods similar to those outlined here. For data that have already been recorded with LFP boards, it may be possible to recover the spike-free LFP by extending our algorithm to include a model of the processing performed by the boards, but this has not yet been attempted.
Numerous studies examining the relationship between spikes and LFPs have reported convincing and significant results. Important examples include studies using spikes and LFPs recorded from different electrodes (Gregoriou et al. 2009; Whittingstall and Logothetis 2009), spikes and cortical EEGs (Whittingstall and Logothetis 2009), or spikes, LFPs, and BOLD signals (Goense and Logothetis 2008) and results like those shown in Figs. 8 and 9 are consistent with some of these studies. However, our results indicate that commonly used methods of preprocessing may lead to overestimation of the association between spikes and LFPs. This is particularly the case when low-pass filtering is used as the only preprocessing step of the LFP, as has often been done in past work (e.g., Chalk et al. 2010; Litaudon et al. 2008; Rasch et al. 2008). The existence and magnitude of spurious correlations in such cases will depend on the nature of the data and the types of analyses applied. Particularly when higher frequencies of the LFP are analyzed with sophisticated nonlinear methods, the effect of even modest contaminations on the results can be significantly magnified (Zanos et al. 2006). On the other hand, successfully removing the spike waveforms from the raw recordings can reveal significant spike–LFP relationships that might otherwise have been masked (as in Fig. 9B).
We have introduced a spike removal algorithm that is designed to remove specific spike waveform(s) from the raw voltage signal, without affecting real spike–LFP correlations that are of great interest to the study of neural circuitry. In simulations, where ground-truth is available, our algorithm removed virtually all spike artifacts and the results of all subsequent analyses on the "spike-free" LFP did not show significant correlations between spike timing and any frequency band of the LFP. Similarly, when applied to real data the algorithm often eliminated artifactual spike–LFP relationships that would have emerged from LFPs obtained by low-pass filtering the raw voltage signal (Fig. 9). However, in other cases (Figs. 8 and 9) strong spike–LFP correlations remained after application of the spike removal algorithm and such synchronization will be an important topic for further study. Indeed, with accurate spike removal one can in principle study spike–LFP relationships at higher LFP frequencies (>150 Hz), despite their overlap with the spectral content of the spike waveforms.
This work was supported by a Canadian Institutes of Health Research Grant MOP-79352 to C. C. Pack and a Montreal Neurological Institute Centre for Commercialization and Research fellowship to T. P. Zanos.
No conflicts of interest, financial or otherwise, are declared by the authors.
We thank Dr. Stavros Zanos for indicating the issue of spike contamination in previous local field potential studies and for providing analysis ideas, R. Cipriani for assistance in data collection, J. Coursol and C. Hunt for assistance with animal care and training, and N. Jabakhanji for help with computer programming.
↵1 The online version of this article contains supplemental data.
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