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Philippe Beaudoin
Works at Google
Attended University of British Columbia
Lives in Ville Mont-Royal
5,277 followers|796,535 views


Philippe Beaudoin

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I love simple-to-state-but-impossible-to-prove math problems.

/cc +Yannick Delbecque 
The Lonely Runner Conjecture

Suppose that six runners are running around and around a circular track, each running at a different constant speed, but in the same direction. Will each runner eventually be in a situation where each of the other five runners is at least 1/6 of a lap away? According to the Lonely Runner Conjecture, the answer is yes.

This animation from Wikipedia by Claudio Rocchini illustrates the situation for six runners. The runners are initially represented by black dots, which turn to yellow as soon as the corresponding runner has 1/6 of a lap of empty track both ahead of and behind them. Eventually, all the runners have had the experience of being in this state.

In general if the number of runners on the circular track is k, a runner is said to be lonely if each of the other runners is at least 1/k of a lap away. The conjecture is that if k is at least 2 and each runner runs at a different speed, then each runner will be “lonely” at some point.

The conjecture was originally made by J.M. Wills in 1967. Although it is easy to state, the conjecture is even now only known to be true in general for small values of k. The case k=2 is trivial, the case k=3 is not too hard, and the case k=4 was proved in 1972. A proof of the case k=5 involving a computer check was found in 1984, and a more elegant proof was found in 1998. The case k=6 was proved in 2001, with a shorter proof being found in 2004. The case k=7 was proved by Barajas and Serra in 2008, but the problem is still open if k is 8 or more.

The Lonely Runner Conjecture has points of contact with other areas of mathematics. As Barajas and Serra explain in the introduction to their paper (, the positive solution of the conjecture would prove a theorem about nowhere zero flows in regular matroids. The known results about the conjecture have also been used to compute chromatic numbers of distance graphs.

If all the runners' speeds are irrational multiples of each other, the problem becomes easy and the conjecture is known to be true. For this reason, attacks on the problem focus on the most difficult case, where all the speeds are rational multiples of each other. This case quickly reduces to the case where all the runners' speeds are integers with no common factor greater than one. We may also assume that one of the speeds is zero, meaning that one of the “runners” is stationary. 

In the case of six runners, the stationary runner will be lonely when the other five runners are bunched in the 4/6 of the track centred at the point diametrically opposite the stationary runner. This point of view can be used to recast the conjecture in terms of a line of sight problem in Euclidean space. My previous post on this topic goes into more detail about this aspect of the problem ( and provides a link to another relevant paper.

Picture source:

#mathematics #scienceeveryday #spnetwork arXiv:0710.4495
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“If I get another volunteer I am going to go out of business.”

The rise of "bullshit jobs" linked to the rise of people's desire to volunteer.

(via +Esther Wojcicki)
Corporate day jobs can provide meaningful, purpose-driven work.
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Also, this screams of a big potential opportunity to make voluteering "scale". Someone should take on that challenge. /cc +Seb Paquet 
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Greatest sport ever?
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Nice. I'd like to see the hockey version 
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Philippe Beaudoin

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I, for one, welcome our tiny robot builder overlords.

More details on the full video:
Magnetically Actuated Micro-Robots for Advanced Manipulation Applications

/cc +Michiel van de Panne 
Micro Robots
SRI International have developed incredibly small and fast robots that are capable of following building instructions.
More Here:
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Oh my thats so cool
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Philippe Beaudoin

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Nice super creative "juggling".
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Ray Cromwell's profile photoSeb Paquet's profile photoPatrick Allaert's profile photoPhilippe Beaudoin's profile photo
Best comment I've read on this one: I'd hire this guy to make a loading screen. :)
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Computational photography continuing its steady march to the mainstream...

/cc +Michiel van de Panne
Google on its new Lens Blur effect now in KitKat.
Here’s how we do it. First, we pick out visual features in the scene and track them over time, across the series of images. Using computer vision algorithms known as Structure-from-Motion (SfM) and bundle adjustment, we compute the camera’s 3D position and orientation and the 3D positions of all those image features throughout the series.

Once we’ve got the 3D pose of each photo, we compute the depth of each pixel in the reference photo using Multi-View Stereo (MVS) algorithms. MVS works the way human stereo vision does: given the location of the same object in two different images, we can triangulate the 3D position of the object and compute the distance to it. How do we figure out which pixel in one image corresponds to a pixel in another image? MVS measures how similar they are -- on mobile devices, one particularly simple and efficient way is computing the Sum of Absolute Differences (SAD) of the RGB colors of the two pixels.

Now it’s an optimization problem: we try to build a depth map where all the corresponding pixels are most similar to each other. But that’s typically not a well-posed optimization problem -- you can get the same similarity score for different depth maps. To address this ambiguity, the optimization also incorporates assumptions about the 3D geometry of a scene, called a "prior,” that favors reasonable solutions. For example, you can often assume two pixels near each other are at a similar depth. Finally, we use Markov Random Field inference methods to solve the optimization problem.

Having computed the depth map, we can re-render the photo, blurring pixels by differing amounts depending on the pixel’s depth, aperture and location relative to the focal plane. The focal plane determines which pixels to blur, with the amount of blur increasing proportionally with the distance of each pixel to that focal plane. This is all achieved by simulating a physical lens using the thin lensapproximation.
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Have him in circles
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Philippe Beaudoin

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If Dalí had known GIFs...
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loll good job!!
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Philippe Beaudoin

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On being a good friend...
Still relevant 2 years later. :-[
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Beautiful campaing by the Berliner Philharmoniker, a strange blend of musical instruments and architecture.

(I wish I could find the original, but it doesn't seem to be on the orchestra's website. This site gives credit to the artists behind the concept, as opposed to some others that use superlative titles... Consider this is my small contribution at trying to make the web suck less. :))
This print campaign for the Berlin Philharmonic orchestra uses macro photographs taken inside the cramped spaces of instruments making the inner workings of a violin, cello, flute, and pipe organ appear vast and spacious, almost as if you could walk around inside them. So wonderfully done. A
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Philippe Beaudoin

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That little real-time regex golf game is a bit too nerdy. I have to play it.

h/t +SP Gingras (I gave up at Triples... :))
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Software developer
programming, boardgame design
  • Google
    Software developer, 2011 - present
  • BookedIn
    Lead developer, 2010 - 2011
  • ArcBees
    CTO, 2010 - 2011
  • University of British Columbia
    Postdoc, 2008 - 2010
  • Digital Fiction
    Software developer, 2001 - 2003
  • Matrox
    ASIC Architect, 2000 - 2001
  • Neo Dimensions
    CEO, 1999 - 2000
  • Université de Montréal
    Research and teching assistant, 1997 - 1998
  • Nortel
    Intern, 1996 - 1996
  • NetCorp
    Intern, 1995 - 1995
  • Teleglobe Canada
    Intern, 1993 - 1993
Map of the places this user has livedMap of the places this user has livedMap of the places this user has lived
Ville Mont-Royal
Trois-Rivières - Montréal - Vancouver
Code + Boardgames
I stayed in school too long, they gave me a PhD for it. Then I created two popular open source projects, gwt-platform and jukito. In June 2011 I joined Google as a software developer on Chrome.

I also play and design boardgames, Quebec is my first published design.

Moderation style
I like Google+ more than any other social network because the discussions I have here are more substantial, more polite, and more interesting than anywhere else on the Net. However, to maintain that level of quality, I will sometimes (very rarely) delete comments that I feel throw the conversation in undesirable directions. It does not mean I do not welcome opinions that differ from mine. However, if:
  • you attack someone else personally,
  • you propose an outrageous claim without any backing evidence,
  • you are too agressive,
it is very likely that I will delete your comment.

Fortunately, this happens so seldom that I can take the time to contact people whose comments I delete. You're always welcome to come back and voice your opinion in a more polite way, or with stronger evidence. Naturally, you're also welcome to reshare my post and comment in any way you like on your own stream.

Disclaimer! Although I work for Google, I use Google+ to publish my personal opinions. Any views I express here are mine alone and do not necessarily reflect those of my employer.

Bragging rights
Gave a talk at Google I/O before I was a googler.
  • University of British Columbia
  • Université de Montréal
  • École Polytechnique
Basic Information
In a relationship
Philippe Beaudoin's +1's are the things they like, agree with, or want to recommend.

Port of the DOS game Tyrian - classical arcade-style vertical scrolling shooter.4 full episodes, ship upgrades, storyline, powerful enemies,


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Philippe Beaudoin

The CircleRank of Philippe Beaudoin is 22718! In Canada the CircleRank is even 386! Philippe Beaudoin says 'Code + Boardgames' and has 4801


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Nicest guys ever. Repaired my punctured tire right away. Very best service and nice people too.
Public - 8 months ago
reviewed 8 months ago
The burgers are good but overpriced. Fries were OK. Nice decor.
Public - 9 months ago
reviewed 9 months ago
We went there three times: once for breakfast and twice for the amazing desserts. Breakfast was OK, but the desserts are really good. Everything we tried was delicious, save maybe for the cannolis that were a bit disappointing. The kids just love the place and they make you feel welcome every time you step in.
Food: Very goodDecor: ExcellentService: Excellent
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Miniature cookies in an hipsterish decor. Not bad if you're into that kind of thing. I did not try enough variety, so take my rating with a grain of salt.
Quality: Very goodAppeal: GoodService: Very good
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reviewed 9 months ago
50 reviews
Whenever I travel to the US I like to get at least one "diner" experience. I was looking at doing the famous Broadway Diner but it was a bit further away from home so we opted for Amsterdam. It did not disappoint: all the breakfast were excellent. Kids loved their pancakes. Try the sausages they are different than regular breakfast sausages but delicious!
Food: Very goodDecor: GoodService: Excellent
Public - 9 months ago
reviewed 9 months ago
Rating is for the shop, as we did not eat there. Lovely place, great and original selection of sweets, beautiful chocolates. Absolutely worth stopping at.
Food: Very goodDecor: ExcellentService: Excellent
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reviewed 9 months ago
No way I was going to do Grimaldi's line up with the heat and two kids, so we opted for Ignazio's, half-expecting sub-par pizza. We were pleasantly surprised: best pie I've had in NYC. Admittedly, I'm not an expert, but this is definitely a valid alternative if you find yourself in that area.
Food: Very goodDecor: Poor to fairService: Good
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reviewed 9 months ago