Wednesday, August 16, 2017
Monday, August 14, 2017
Sunday, August 13, 2017
The first calculator to be able to perform all 4 operations automatically was invented by Anton Braun, a German optician, in 1727 pic.twitter.com/j8tj7LTUIA— Fermat's Library (@fermatslibrary) August 13, 2017
(Tip of the cap to Daniele Avitabile.)
Saturday, August 12, 2017
The journey is turning into a book tour in itself: signed Beyond Infinity at O'Hare and How to Bake Pi at LAX...in self-improvement!! pic.twitter.com/KqhdGnvoCR— Dr Eugenia Cheng (@DrEugeniaCheng) August 13, 2017
Thursday, August 10, 2017
Update (8/11/17): Initially I described the Tetris window as a "stained-glass window". As Aaron Clements pointed out on my Facebook post, a correct description is actually "colored glass blocks with mortar".
(Tip of the cap to Rachel Simmons Carter.)
Wednesday, August 09, 2017
Title: Core-Periphery Structure in Networks (Revisited)
Authors: Puck Rombach, Mason A. Porter, James H. Fowler, and Peter J. Mucha
Abstract: Intermediate-scale (or “meso-scale”) structures in networks have received considerable attention, as the algorithmic detection of such structures makes it possible to discover network features that are not apparent either at the local scale of nodes and edges or at the global scale of summary statistics. Numerous types of meso-scale structures can occur in networks, but investigations of such features have focused predominantly on the identification and study of community structure. In this paper, we develop a new method to investigate the meso-scale feature known as
core-periphery structure, which entails identifying densely connected core nodes and sparsely connected peripheral nodes. In contrast to communities, the nodes in a core are also reasonably well-connected to those in a network’s periphery. Our new method of computing core-periphery structure can identify multiple cores in a network and takes into account different possible core structures. We illustrate the differences between our method and several existing methods for identifying which nodes belong to a core, and we use our technique to examine core-periphery structure in examples of friendship, collaboration, transportation, and voting networks. For this new SIGEST version of our paper, we also discuss our work’s relevance in the context of recent developments in the study of core-periphery structure.
Title: A Roadmap for the Computation of Persistent Homology
Authors: Nina Otter, Mason A. Porter, Ulrike Tillmann, Peter Grindrod, and Heather A. Harrington
Abstract: Persistent homology (PH) is a method used in topological data analysis (TDA) to study qualitative features of data that persist across multiple scales. It is robust to perturbations of input data, independent of dimensions and coordinates, and provides a compact representation of the qualitative features of the input. The computation of PH is an open area with numerous important and fascinating challenges. The field of PH computation is evolving rapidly, and new algorithms and software implementations are being updated and released at a rapid pace. The purposes of our article are to (1) introduce theory and computational methods for PH to a broad range of computational scientists and (2) provide benchmarks of state-of-the-art implementations for the computation of PH. We give a friendly introduction to PH, navigate the pipeline for the computation of PH with an eye towards applications, and use a range of synthetic and real-world data sets to evaluate currently available open-source implementations for the computation of PH. Based on our benchmarking, we indicate which algorithms and implementations are best suited to different types of data sets. In an accompanying tutorial, we provide guidelines for the computation of PH. We make publicly available all scripts that we wrote for the tutorial, and we make available the processed version of the data sets used in the benchmarking.
Tuesday, August 08, 2017
According to this, the most different job from "mathematician" is "mine shuttle car operator".
Naturally, the first thing that came to my mind that Sam mentioned Cassandra was not the prophet, but rather the ABBA song (which turns out to be a B-side). And checking the lyrics, the song does indeed refer to the prophet.
Monday, August 07, 2017
Saturday, August 05, 2017
Friday, August 04, 2017
(There are quite a few comments on the tweet. I haven't looked at them, but I wonder if people are picking apart inaccuracies? I haven't spent the time to vet this diagram, but I really like the idea!)
how probability distributions are related pic.twitter.com/1i8VHEHdy5— hardmaru (@hardmaru) August 2, 2017
(Tip of the cap to Michael Stumpf.)
Thursday, August 03, 2017
I saw this yesterday, but I didn't post it because the embedded tweet wasn't showing the original question. I should have taken a screenshot and posted it. :)
Publish in journals. https://t.co/U2Oiin9Hu3— Michael Hendricks (@MHendr1cks) August 2, 2017
Tuesday, August 01, 2017
Here is a list of physicists on Twitter with 1000+ followers. I am not on this list either, though it can be argued that I am also a physicist (in addition to being a mathematician).
Update (8/03/17): My account is now on the list of mathematicians.
Monday, July 31, 2017
In separate deals, we also traded for left-handed relief pitchers Tony Watson of the Pirates and Tony Cingrani of the Reds.
Sunday, July 30, 2017
This team is so amazing.
We now have an astounding 74–31 record (after our 8th win in a row, and recently we had 10-game and 11-game winning streaks).
We also now have a 14-game lead!
Next stop, Cooperstown! And it will be on the first ballot.
Beltré has been appreciated more in recent years as his counting numbers approach 'magic' milestones, but I still don't think most people truly appreciate just how excellent his career has been. I can't remember who wrote this — was it 538.com? — but I recently saw an estimate that put him in the top-5 third basemen of all time.
There is also a discussion at 538.com about future members of the 3000-hit club. The next member will be Albert Pujols, who will become the second person from the Dominican Republic (Beltré is the first) in the 3000-hit club. I believe that the next person after that will be Miguel Cabrera and then Robinson Canó. (Here are the active leaders in career hits.)
Update: Here's a new article in 538.com about Beltré's greatness as both an offensive player and defensive player.
Saturday, July 29, 2017
This is one of the most brilliant political cartoons of all time. pic.twitter.com/6FG4Wsg5pb— David Moser (@david__moser) July 28, 2017
(Tip of the cap to Melanie Mitchell.)
Friday, July 28, 2017
(Tip of the cap to multiple people.)
30 years ago today I said I was Never Gonna Give You Up. I am a man of my word - Rick x pic.twitter.com/VmbMQA6tQB— Rick Astley (@rickastley) July 27, 2017
Thursday, July 27, 2017
(I don't normally care about gratuitous apps, but I am seriously geeking out over this one! I want to try this out.)
P.S. The video for "Take on Me" is the best music video of all time! And this is one of the best songs all time — definitely in my top 5.
It's too bad that he won't continue pursuing both careers, but I have to say that I feel warm and fuzzy about passion for mathematics being such an important facet of his decision. (And his publication record for somebody at his career stage is very impressive even before considering the fact that he's simultaneously been playing pro football, which then makes it astounding.)
"I think it hurt my ability to think well mathematically," Urschel said. "It took me about three weeks before I was football-ready. It took me a little bit longer before my high-level visualizations ability came back."
(Tip of the cap to Eric Eager.
Sunday, July 23, 2017
(Tip of the cap to Manlio De Domenico, who retweeted Valids Krebs.)
Friday, July 21, 2017
You can see from this data analysis that math professors appear to be the least boring among all professors (yay!) and there are some expected (and perhaps more surprising) gender gaps (boo!) in the reviews.
(Tip of the cap to Nicholas Christakis.)
Wednesday, July 19, 2017
(The things I learn when listening to a baseball game... The context, unsurprisingly, is all of the rather specific days there are — several of them each day — and most of them seem rather pointless. For example, tomorrow is National Lollypop Day.)
That will make 11 wins in a row and a 31–4 record in our last 35 games!
Entering today, with our record of 65–29, we were more games above .500 than we have been any day since the last day of the 1974 season (so before I was born), when we won 102 games.
Also, based on current records (or perhaps All-Star break records?), 30 out of our first 36 games after the break are slated to be against teams that are under .500.
OMG OMG. Edward Teller tried a run as a television show host in 1955. How did I not know this? These photos are AMAZING. This is so bonkers. pic.twitter.com/lGsPPpQkbz— Alex Wellerstein (@wellerstein) July 19, 2017
Tuesday, July 18, 2017
''Turkey tail mushrooms,'' an actual thing, not a painting pic.twitter.com/l7I4Yha34A— Life on Earth (@planetepics) July 17, 2017
(Tip of the cap to GrrlScientist.
Monday, July 17, 2017
This, by the way, was a very natural mistake to make. I hope that the song "Atomic" is in the film, at least.
Sunday, July 16, 2017
Just about* every time that I got into trouble at school was an instance of rebelling against this (which was already the case when I was in elementary school and high school).
* Most other instances involved a radio and a baseball game.
Modern day education pic.twitter.com/yq47iDdfUE— banksy (@thereaIbanksy) July 17, 2017
(Tip of the cap to Nalini Joshi.)
Saturday, July 15, 2017
Here is the BBC's obituary.
(Tip of the cap to Nalini Joshi.)
Update: The Stanford obituary was written nicely. (Tip of the cap to Leslie Sheppard.)
Update: Here is Terry Tao's tribute.
Update (7/18/17): Here is the AMS's brief obituary, which includes links to some other tributes as well as prior articles.
Update (8/15/17): Here is a blog entry by Anna Haensch with links to various articles about Mirzakhani and other prominent women mathematicians who died recently.
Friday, July 14, 2017
Good luck with that one.
Thursday, July 13, 2017
I'm pretty sure that one can also use a modification of the "diagonal argument" to prove that the set is uncountable. :)
Wednesday, July 12, 2017
Tuesday, July 11, 2017
Monday, July 10, 2017
Sunday, July 09, 2017
Wednesday, July 05, 2017
"Mean-Field Approach to Evolving Spatial Networks, with an Application to Osteocyte Network Formation"
Title: Mean-Field Approach to Evolving Spatial Networks, with an Application to Osteocyte Network Formation
Authors: Jake P. Taylor-King, David Basanta, S. Jonathan Chapman, and Mason A. Porter
Abstract: We consider evolving networks in which each node can have various associated properties (a state) in addition to those that arise from network structure. For example, each node can have a spatial location and a velocity, or it can have some more abstract internal property that describes something like a social trait. Edges between nodes are created and destroyed, and new nodes enter the system.We introduce a "local state degree distribution" (LSDD) as the degree distribution at a particular point in state space. We then make a mean-field assumption and thereby derive an integro-partial differential equation that is satisfied by the LSDD. We perform numerical experiments and find good agreement between solutions of the integro-differential equation and the LSDD from stochastic simulations of the full model. To illustrate our theory, we apply it to a simple model for osteocyte network formation within bones, with a view to understanding changes that may take place during cancer. Our results suggest that increased rates of differentiation lead to higher densities of osteocytes, but with a smaller number of dendrites. To help provide biological context, we also include an introduction to osteocytes, the formation of osteocyte networks, and the role of osteocytes in bone metastasis.
Tuesday, July 04, 2017
This is quite the erratum from the 1983 edition of Bogoliubov and Shirkov's "Quantum Fields." (Shirkov did pass away last year.) pic.twitter.com/btMCHACu6I— Robert McNees (@mcnees) July 3, 2017
Sunday, July 02, 2017
Wednesday, June 28, 2017
Tuesday, June 27, 2017
Monday, June 26, 2017
I found this out via the follow tweet.
(Tip of the cap to Sydney Padua.)
Sunday, June 25, 2017
(Tip of the cap to Meghan Duffy.)
Friday, June 23, 2017
While I am based in Oxford for a bit, I'll spend a couple days in London as part of the Mathematics for the Modern Economy workshop (where I will also be giving a talk), will spend a weekend visiting friends in Newcastle, and will head to Nottingham for a day for a collaboration that is just starting up.
Tuesday, June 20, 2017
Title: Modeling the Lowest-Cost Splitting of a Herd of Cows by Optimizing a Cost Function
Authors: Kelum Gajamannage, Erik M. Bollt, Mason A. Porter, and Marian S. Dawkins
Abstract: Animals live in groups to defend against predation and to obtain food. However, for some animals—especially ones that spend long periods of time feeding—there are costs if a group chooses to move on before their nutritional needs are satisfied. If the conflict between feeding and keeping up with a group becomes too large, it may be advantageous for some groups of animals to split into subgroups with similar nutritional needs. We model the costs and benefits of splitting in a herd of cows using a cost function that quantifies individual variation in hunger, desire to lie down, and predation risk. We model the costs associated with hunger and lying desire as the standard deviations of individuals within a group, and we model predation risk as an inverse exponential function of the group size. We minimize the cost function over all plausible groups that can arise from a given herd and study the dynamics of group splitting. We examine how the cow dynamics and cost function depend on the parameters in the model and consider two biologically-motivated examples: (1) group switching and group fission in a herd of relatively homogeneous cows, and (2) a herd with an equal number of adult males (larger animals) and adult females (smaller animals).
Chaos, the journal in which we published our paper, decided to write a press release. Thus far, our work has been covered by Wired.
Back in my undergrad era, Hall Daily was also the advisor for The California Tech (our student newspaper), of which I was a writer and co-editor. I learned a ton about journalism from Hall. He too someone who was someone who Autumn Looijen and I purposely earmarked as getting one of our free copies of Legends of Caltech III. He was an awesome advisor, and I owe a lot to him for my communication and journalistic skills. My experience with The Tech was probably more important for my career than any math or science class I ever took.
Friday, June 16, 2017
I was once — well, at least once — told in elementary school that I was drawing circles the wrong way (because I was using the wrong sense around the clock). I think I responded with the definition of a circle and that the definition doesn't depend on the sense in which one draws it, and I think my teacher did not appreciate that.
On a similar note, in high school, I once lost 50% of the point total on an answer for misspelling ellipse (by using one 'l' instead of two), which was the correct answer. I called bullshit (on the grounds that it was my mathematics knowledge that was being tested), but unfortunately I lost.
More closely related to the article, one thing I noticed in the UK is that the most common way to write an 'x' there is with two arcs, so that they won't always cross if one writes quickly. In contrast, I write two attempts at lines that explicitly cross. (I haven't checked if this is US versus UK convention.)
And, indeed, most Americans drew their circles counterclockwise in this data set, and I draw mine clockwise.
(Tip of the cap to Improbable Research for their Facebook post.)
Update: Here is a lovely quote from the article: In a 1977 paper Theodore Blau, then-president of the American Psychological Association and creator of the torque test, argued that drawing clockwise circles was a sign of learning and behavioral aberrance.
Thursday, June 15, 2017
During the Faculty Recession of the commencement ceremony, as professors started marching off the stage, the organist started things off with the theme to Star Wars.
I contend, however, that the Imperial March would have been far more appropriate.
Wednesday, June 14, 2017
At the local deli. What could have happened to make them put up that sign?? pic.twitter.com/7BzPNjFm1L— Anna Haensch (@extremefriday) June 14, 2017
Monday, June 12, 2017
A couple of years ago, I blogged about playing cards of Women in Computing.
Title: A Local Perspective on Community Structure in Multilayer Networks
Authors: Lucas G. S. Jeub, Michael W. Mahoney, Peter J. Mucha, and Mason A. Porter
Abstract: The analysis of multilayer networks is among the most active areas of network science, and there are several methods to detect dense “communities” of nodes in multilayer networks. One way to define a community is as a set of nodes that trap a diffusion-like dynamical process (usually a random walk) for a long time. In this view, communities are sets of nodes that create bottlenecks to the spreading of a dynamical process on a network. We analyze the local behavior of different random walks on multiplex networks (which are multilayer networks in which different layers correspond to different types of edges) and show that they have very different bottlenecks, which correspond to rather different notions of what it means for a set of nodes to be a good community. This has direct implications for the behavior of community-detection methods that are based on these random walks.
Thursday, June 08, 2017
(My Ph.D. students get awesome powers, of course! What kind of advisor do you think I am?)
Saturday, June 03, 2017
From the website, I see that "foundational to" is just over twice as common as "foundational for".
And if you want to learn about the amount of information to navigate such things, you may be interested in this paper.
(Tip of the cap to Marta González.)
Tuesday, May 30, 2017
There are several other amusing ones, as you can see in this map.
(Tip of the cap to George Takei.)
Monday, May 29, 2017
(Tip of the cap to Noelle Beckman.)
Sunday, May 28, 2017
I hadn't noticed the author's infamous "name" until today. Also, Ms. Pac-Man seems to alternate during the article between being Pac-Man's girlfriend and being his wife. I didn't remember that part either.
This description of a cursed magic rock from an ancient (1981) issue of DRAGON magazine is basically just a cell phone. pic.twitter.com/EmyrWqcpNb— Robert McNees (@mcnees) May 29, 2017
(Tip of the cap to Sean Carroll.
Friday, May 26, 2017
Friday, May 19, 2017
"Apparently, it’s a common practice in Russia for Orthodox priests to bless server rooms and other technology equipment. So, it won’t be wrong to assume that priests might be really called in upcoming days to bless the computers once again. I just hope that priests would be careful enough to not get the water inside the PCs; I’m sure that computer suppliers won’t be enthusiastic to replace damage due to water."
I am amused.
Also, our printers could use some holy water.
Thursday, May 18, 2017
This review of work by , who was famous for his work in population dynamics, is both harsh and astounding.
Mathematic biology, alternative perpsective pic.twitter.com/HdskKTFazX— Hong Qin (@hongqin) May 17, 2017
(Tip of the cap to Kit Yates.)
Wednesday, May 17, 2017
You have walks on networks, you have different ones that you can compare to each other, and you also have descriptions from the authors of these different places.
(Tip of the cap to Bonnie Harland.)
Tuesday, May 16, 2017
(Tip of the cap to James Gleick.)
Clever display at Barnes and Noble. Check out top titles... pic.twitter.com/pCB7alkxnk— Amy Wilentz (@amywilentz) May 16, 2017
Title: Quasi-Centralized Limit Order Books
Authors: Martin D. Gould, Mason A. Porter, and Sam D. Howison
Abstract: A quasi-centralized limit order book (QCLOB) is a limit order book (LOB) in which financial institutions can only access the trading opportunities offered by counterpartieswithwhomthey possess sufficient bilateral credit. In this paper, we perform an empirical analysis of a recent, high-quality data set from a large electronic trading platform that utilizes QCLOBs to facilitate trade. We argue that the quote-relative framework often used to study other LOBs is not a sensible reference frame for QCLOBs, so we instead introduce an alternative, trade-relative framework, which we use to study the statistical properties of order flow and LOB state in our data. We also uncover an empirical universality: although the distributions that describe order flow and LOB state vary considerably across days, a simple, linear rescaling causes them to collapse onto a single curve. Motivated by this finding, we propose a semi-parametric model of order flow and LOB state for a single trading day. Our model provides similar performance to that of parametric curve-fitting techniques but is simpler to compute and faster to implement.
They wrote: "If you can tell us in a sentence or two why you chose to be a member of APS, and we use your quote in the APS membership brochure, we will send you one item of your choice from the APS store."
Here is what I decided to write: I chose to join APS because my research as an applied mathematician also interfaces with numerous areas of physics (and I publish much of my work in physics journals), and I wanted to make sure that I am also part of the physics community. I was already playing ultimate frisbee with physicists in grad school, and this was the natural next step.
Do you think they'll use my quote?
Sunday, May 14, 2017
Patent Application (from 2012): "Devices and Implements for Deterring Monsters, Specters, Demons, and the Like"
Here is a choice excerpt: Devices and implements for staving off monsters, specters, demons and the like as imagined by a child at bedtime. A hand-held controller unit is provided having a user interface, which is capable of being used by the child under the bed covers of a bed. The hand-held controller unit may include any of a walkie-talkie capability, a flashlight capability, a nightlight capability, the capability to activate an external device, and other capabilities. At least one external device may be provided which is capable of being placed beneath the bed and is configured to be activated by the hand-held controller unit. At least one substantially hollow air-through member may be provided which is configured to facilitate airflow between underneath the bed covers of the bed and above the bed covers of the bed. A supplemental bed cover may be provided that is configured to be placed on the bed.
Personally, I am most afraid of "the like".
Also, the Google Patent listing says the patent was granted.
(Tip of the cap to the Improbable Research Blog.)
Saturday, May 13, 2017
Credit where it is due on two counts:
(1) Sandy is a very good member of support staff! I have interacted with support staff at many places, and good ones versus bad ones make a huge difference in academic experience. Sandy always stood out during my time at Oxford as one of the really good ones. The number of times I have told my students to 'Go ask Sandy Patel." (and similar) is very numerous indeed.
(2) And credit to my former employer (the Oxford Mathematical Institute) for publishing Sandy's award on their website and circulating it on Twitter. This type of recognition is almost always in the background and it shouldn't be. (I learned this from grad school, where we had the awesome Dolores Pendell, versus nearly everywhere else I have been.) We spend a lot of time bragging about the scientific accomplishments of faculty (and occasionally also their teaching accomplishments, though not enough), but we almost never publicize things when our support staff are excellent (though we do complain loudly when they're not), and we should!
The typewriter in the picture below is part of a current exhibit in terminal 2 of SFO airport.
A coin-operated typewriter. pic.twitter.com/dTibdbEtZc— Harry McCracken 🇺🇸 (@harrymccracken) May 13, 2017
Among the things I enjoyed when on sabbatical at Stanford were the really cool exhibitions at SFO. Among other things, this included one of classic boardgames.
Harry McCracken also posted pictures of several other typewriters from the exhibit on his Twitter feed. Take a look at this one, this one, this one, this one, and this one. This should be all of the typewriter pictures that he posted as part of this thread.
(Tip of the cap to Sydney Padua.)
Friday, May 12, 2017
I of course decided to look at how Depeche Mode stacks up, and I zoomed up on them as an individual artist.
From the song and artist library they used, Depeche Mode is listed as the band from the 1990s with the least repetitive lyrics, though it does only use a subset of their songs and it listed them in the 1990s instead of the 1980s. (Naturally, the employed songs span multiple decades.)
The most lyrically repetitive Depeche Mode song is very obvious.
(Tip of the cap to Taha Yasseri and I Fucking Love Data.)
I had already heard that Cédric Villani is one of the candidates standing for Macron (and that itself is awesome!), but I really like the article title in this case.
Also, the second sentence in the article's description of Villani is amusing: Cédric Villani, 43, who in 2010 won the Fields medal, the equivalent of the Nobel prize in mathematics, will stand for Macron in a suburban Paris district. The mathematician is known for his dandy-ish looks, long hair and collection of floppy bow ties.
(Tip of the cap to Yves van Gennip for this specific article.)
Thursday, May 11, 2017
This reminds me of a game called Balloon Fight that I played many moons ago on my NES. This game was very underrated. (It is an excellent game!)
(Tip of the cap to Guillermo Valle Pérez.)
I think I could make this BWAAAAARP from Organist a bit bigger come to think of it pic.twitter.com/mDr0yv9rFX— SydneyPadua (@sydneypadua) May 11, 2017
Wednesday, May 10, 2017
Here is a choice quote from the Washington Post article above: "White House press secretary Sean Spicer wrapped up his brief interview with Fox Business from the White House grounds late Tuesday night and then disappeared into the shadows, huddling with his staff near a clump of bushes and then behind a tall hedge. To get back to his office, Spicer would have to pass a swarm of reporters wanting to know why President Trump suddenly decided to fire the FBI director."
Her clearly did not play enough Zelda games as a child. Here is how to properly sneak past people while hiding in a barrel.
We continue to live in a Coen Brothers movie. It's like watching a train wreck in slow motion (from a seat on the train, unfortunately).
Update: I just noticed the following tweet.
Spicer on phone to WaPo: 😡— Prof Dynarski (@dynarski) May 11, 2017
"I was not IN the bushes!
I was AMONG the bushes!"
Social media manager: 😎 pic.twitter.com/o8TJUsEPRy
Update (5/11/17): And then there's this beauty.
found this photo of sean spicer hiding between the bushes pic.twitter.com/YZOMCOvHZC— David Mack (@davidmackau) May 10, 2017
Update (5/12/17): This Garden Spicer is pretty damn funny. (Tip of the cap to Maria Satterwhite, though I believe she shared a different article about the same item.)
Monday, May 08, 2017
Friday, May 05, 2017
Here is an example.
(Tip of the cap to Esteban Moro.)
Wednesday, May 03, 2017
The complicated border between Belgium and the Netherlands at Baarle-Nassau pic.twitter.com/2eSmkF9xuh— Amazing Maps (@Amazing_Maps) May 3, 2017
Monday, May 01, 2017
There is a primitive cell in reciprocal space beyond that which is known to undergraduates. It is a fundamental unit into which that space is divided. It can tile lattices as vast as space and as timeless as infinity. It leads to a sequence of disjoint equal-volume regions at increasing distances from the origin, and it lies between the pit of physicists' fears and the summit of their knowledge. This is the region of imagination. It is an area which we call THE BRILLOUIN ZONE.
Update: Joshua Bodyfelt produced a really nice picture after seeing my quote above on Facebook. Here it is.
Saturday, April 29, 2017
Friday, April 28, 2017
I had never heard of Lego Grad Student before, but this brilliantly fills a gap in the online world. I'll include one of LGS's tweets in this blog entry.
Running into a paywall for yet another article, the grad student is pummeled anew by the academic-industrial complex. pic.twitter.com/QnvFhjszPk— Lego Grad Student (@legogradstudent) April 18, 2017
Title: Persistent Homology of Time-Dependent Functional Networks Constructed from Coupled Time Series
Authors: Bernadette J. Stolz, Heather A. Harrington, and Mason A. Porter
Abstract: We use topological data analysis to study "functional networks" that we construct from time-series data from both experimental and synthetic sources. We use persistent homology with a weight rank clique filtration to gain insights into these functional networks, and we use persistence landscapes to interpret our results. Our first example uses time-series output from networks of coupled Kuramoto oscillators. Our second example consists of biological data in the form of functional magnetic resonance imaging data that were acquired from human subjects during a simple motor-learning task in which subjects were monitored for three days during a five-day period. With these examples, we demonstrate that (1) using persistent homology to study functional networks provides fascinating insights into their properties and (2) the position of the features in a filtration can sometimes play a more vital role than persistence in the interpretation of topological features, even though conventionally the latter is used to distinguish between signal and noise. We find that persistent homology can detect differences in synchronization patterns in our data sets over time, giving insight both on changes in community structure in the networks and on increased synchronization between brain regions that form loops in a functional network during motor learning. For the motor-learning data, persistence landscapes also reveal that on average the majority of changes in the network loops take place on the second of the three days of the learning process.
Thursday, April 27, 2017
Tuesday, April 25, 2017
(More seriously, I really like this visualization.)
Here is the blurb on the Facebook post that goes with the Physics Today article (though I added the hyperlink): The ocellated lizard develops an intricate, ever-changing pattern of black and green spots when it matures. Now researchers have determined that the patterns on the animals' backs update according to a well-defined algorithm: Over a period of a month or so, a given scale will change color—from green to black or black to green—with a probability that depends on the colors of the scales around it. In essence, the reptile is the embodiment of a cellular automaton, a type of discretized model made popular by John Conway’s Game of Life and used to simulate the spread of wildfires, the firing of neurons, and other phenomena.
Physics Today's article is about a recent article in Nature called "A living mesoscopic cellular automaton made of skin scales".
Monday, April 24, 2017
As one of my friends pointed out on Facebook, I should perhaps be careful about using the terms "quick trip" and "Berkeley" in the same sentence. :)
Sunday, April 23, 2017
We gave away tons of AMS Mathematical Moments, in particular. We brought English, Spanish, and Korean versions of the Mathematical Moments. We also gave away a bunch of SIAM's Math Matters, Apply It!. We also had copies of our networks literacy handbook in each of the 19 languages in which it is available, and we brought copies of our networks outreach materials for school students and talked to a lot of teachers about it. We mostly discussed the outreach efforts themselves, but we also brought copies of the teaching materials with us.
I wonder how much mathematics ending up photobombing the pictures from the LA March?
Also, several people came and took pictures of a differential equation that I wrote down on a flip chart to explain to someone the difference between linear and nonlinear equations.
At different times, our booth also had a comedian and a Fields Medalist show up.
I was really exhausted after the event. An almost-8-hour teaching marathon in the heat is very tiring. (Having a tent and some shade was very helpful, though. Paying for a booth was a very good idea.)
An amusing incident: Yesterday morning, the first person who came to our booth asked us about buying our tangerine juice. Math, damnit! Not tangerine juice. That's for us!
Another amusing incident: One person I know recognized my handwriting on our flip chart before he saw me at our booth.
And some pictures of the action at our booth: one, another one, setting up, and setting up (and a view of one of our neighboring booths)
Update (4/25/17): And here are some pictures from the LA March from Los Angeles Magazine.
(Tip of the cap to Craig Montuori.)
Saturday, April 22, 2017
I'll try to post some more links later. I have been seeing fantastic signs on the March for Science Facebook page for the past several weeks (and I saw some great signs in LA today).
(Tip of the cap to Maria Satterwhite.)
P.S. Some Thomas Dolby got played at the LA March, of course. :) This was the first song blasted as the gathering started on their march after a series of short speeches. Allusions to Thomas Dolby also showed up yesterday on signs, of course.
Update (4/23/17): Here are some more signs. (Tip of the cap to Peter Mucha.)
Update (4/23/17): Naturally, and as expected, people nerded out quite a bit yesterday (just like we people do in venues like Dragon*Con). In some ways, it was also like Coachella for scientists and friends. You can see some more signs in this Motherboard article and this Vox article. (The so-called "Laplace equation" in one of the pictures actually shows a Laplace transform.) Spock, Data, Beaker, and other scientifically-themed fictional characters were also very well represented.
Update (4/23/17): According to this Washington post article, the March for Science was unprecedented. (Tip of the cap to Karen Daniels.)
Update (4/23/17): Here are some signs from the New York march. I am partial to the Oregon Trail one, of course. (I have seen variants of it posted on the Facebook page for March for Science.)
Update (4/25/17): Here are some pictures from the LA March.
Update (4/26/17): Linda Hall Library is developing a digital archive of the March for Science. Very cool! (Tip of the cap to Laci Gerhart-Barley.)
Friday, April 21, 2017
We'll be drawing from materials here (and hence here) and will also have booklets on essential concepts and core ideas about networks.
Thursday, April 20, 2017
Graph Alignment is a major open problem in mathematics and computer science. pic.twitter.com/Q8EJDSYLge— Mason Porter (@masonporter) April 20, 2017
Wednesday, April 19, 2017
In case you don't remember and don't want to follow a chain of links on Wikipedia, go to this page.
Tuesday, April 18, 2017
Sunday, April 16, 2017
A must for every library: eighteenth-century rotating table allowing readers to view multiple volumes at once. pic.twitter.com/p18X8LRpPo— NSCM (@LitteraCarolina) April 14, 2017
(Tip of the cap to Gabrielle Birkman.)
Saturday, April 15, 2017
The article includes a reprint of a cartoon from The New Yorker that reminds me of this song. (The song is relevant to the whole article, actually.)
(Tip of the cap to Ben Rogers.)
Friday, April 14, 2017
This is the first time in Major League Baseball history that a team started an outfield where all three outfielders have the same last name. Nice! (The Alous were in an outfield together, but they didn't all start a game together.)
My favorite starting outfield, however, is when the Cincinnati Reds started an outfield of Young, Frank, and Stynes. (It consisted of Dmitri Young in left field, Mike Frank in center field, and Chris Stynes in right field.)
Also see this recent blog entry.
(Tip of the cap to Sam Scarpino.O
Tuesday, April 11, 2017
I gave up on shoelaces very early in life (important life hack!). Of course, I never could tie the damn things in the first place, and I still can't.
The authors of this research may well have Ig Nobel prizes in their future (perhaps awarded jointly in physics and in fashion).
Quoting Steve from this article: "So many of the things that we do in math education—and maybe more generally in education—are giving students answers to questions that they would never think of asking. By definition, that's what it is to be boring."
Conversely, this also speaks to why so many students find networks exciting from the start. They're already asking many of these questions! They just need the words and concepts to make the questions more precise to be able to answer them in a better way.
Saturday, April 08, 2017
(I got this from a post on the Dragon*Con Facebook page.)
Friday, April 07, 2017
At first, I accidentally, introduced the typo "rouge", but I managed to change the tweet before anybody could reply with "What's a rouge wave?" Naturally, this inspired the title of this post.
Rogue Wave Hunters: Wind-generated waves in ring-shaped water tanks can spontaneously yield behemoth waves: https://t.co/4QSaR0MsSl— DynamicalSystemsSIAM (@DynamicsSIAM) April 7, 2017
I have an important question, though: What does "The Ride of the Valkyries" look like?
(Tip of the cap to Chris Gong.)
Thursday, April 06, 2017
(And, apropos, I received an e-mail called "What is Reality?", from a group of people working on a crazy idea, while I was reading this article.)
P.S. David Stevenson is a great classroom lecturer. I had him for half of AMa 95 at Caltech.
Tuesday, April 04, 2017
Monday, April 03, 2017
I wasn't aware of the historical path. I can't wait to see what results from some of the grades I give! Also, never underestimate the power of being bloody-minded...
(Tip of the cap to Nicholas Christakis and others.)
Sunday, April 02, 2017
Saturday, April 01, 2017
Rock 'n' Roll Physics Sing-Along. Thanks to Walter Smith for contacting me about doing this after he found my blog entry with my lyrics. Take a look at his physics-song webpage.
Friday, March 31, 2017
(And I am looking forward to the stories on ESPN and other venues.)
I got the news from Greg Fricke's post:
BEAVERS WIN! BEAVERS WIN! BEAVERS WIN! BEAVERS WIN! BEAVERS WIN! BEAVERS WIN! BEAVERS WIN! BEAVERS WIN! BEAVERS WIN! BEAVERS WIN!
After 586 (est, including 83 I played in) straight losses in SCIAC, dating back to 1988:
Caltech Beavers DEFEAT Pomona-Pitzer 4-3 on WALKOFF single.
No one on this team had yet been born the last time Caltech registered a SCIAC win in baseball.
1988... such a magical year for baseball...
Update: And here are some details: Caltech baseball has just won its first SCIAC game since 1988! Trailing 3-2 headed to the 9th inning, the Beavers got a two-out single from David Watson, who was replaced on the base paths by Schaffer Reed. Senior Kai Kirk then smacked a double to left center to tie the game, bringing freshman Alex Corado came up to bat. The rookie got ahead 3-0 before facing a full count and slashed a single to left field to plate the historic walk-off run.
Update: Also take a look at the video and the ensuing victory celebration.
Update (4/01/17): This is not an April Fool's Day joke. (I know it sounds like one.)
Thursday, March 30, 2017
(The arXiv doesn't have 1 April as a mailing day this year, so we get it early.)
The last sentence of the abstract is amusing: "Over-training is also discussed, although the linear algebra teacher assures us that in Barry’s case this is not possible."
As things catch my eye, I will post links to more April Fool's Day shenanigans.
Here are various past posts related to April Fool's Day (and a couple of other posts that show up in the search but aren't particularly related).
Update: Here is another joke arXiv paper. It is called: Schrodinger's Cat and World History: The Many Worlds Interpretation of Alternative Facts
Update: This article seems to purposely be dated April 1st, but it has a rather different flavor from the other two.
Update: According to an April 1st article in The Guardian, former British chancellor (more formally, "Chancellor of the Exchequer") George Osborne has become a fashion designer. (Tip of the cap to Dominic Vella.)
Update (4/01/17) Here is a screenshot of my April Fool's Day prank of 2006, for which I was able to convince a member of Caltech's public-relations department to post my article (actual fake news, which of course is an April 1st tradition) on the Caltech web page and include a link to it in an e-mail circular.
Update (4/01/17): Cherwell, a student publication from University of Oxford, published an interesting story about possible cancellation of the Cancer Research UK Boat Races. Here is another one from Cherwell.
Update (4/01/17): There's also the matter of the Spaced X rocket launch out of Santa Monica, California. (Tip of the cap to Andrea Bertozzi.)
Update (4/01/17): In other news, an ancient particle accelerator was discovered on Mars. (Tip of the cap to Jean Bellissard.)
Update (4/01/17): George Takei played an amusing prank.
Update (4/01/17): Also, the American Physical Society is launching a new journal called Physical Review Tweets. Awesome!
Update (4/02/17): Google remixed an old (but awesome) prank by letting people play Ms. Pac-Man on Google Maps. (Tip of the cap to Myah Evers.) Google also played a few other pranks.
Update (4/02/17): And here are various other pranks that you may have encountered yesterday.
Update (4/08/17): Well, the Reddit prank appears to have resulted in a rather interesting example of self-organization (and of astounding art, with some "This is why we can't have nice things." thrown in). (Tip of the cap to Kevin Hickerson, Maria Satterwhite, and others.)
Wednesday, March 29, 2017
Here's a nice (and topical) one to start us off: "Get your facts first, and then you can distort them as much as you please."
Update (3/30/17): Here is another, of many, great quotes that you can find on the above page: "Whenever you find that you are on the side of the majority, it is time to reform."
I recently saw this awesome license plate that does so as well.
I really enjoy alluding to the characters Boris and Natasha. I did that recently in my winning entry in a caption content, and I did it in 2006 in an Aprils Fool's Day prank.
This is my first ever trip to Missouri.
A little while ago, after I went through the x-ray machine, the TSA agents wanted to check my hair to make sure I wasn't hiding something in there. (This happens a couple of times every year.)
Monday, March 27, 2017
Update: This is an episode of a mathematics show called "Infinite Series". The above episode refers to an episode about Markov chains. Take a look at their YouTube channel and Twitter feed.
Saturday, March 25, 2017
Title: Eigenvector-Based Centrality Measures for Temporal Networks
Authors: Dane Taylor, Sean A. Myers, Aaron Clauset, Mason A. Porter, and Peter J. Mucha
Abstract: Numerous centrality measures have been developed to quantify the importances of nodes in time-independent networks, and many of them can be expressed as the leading eigenvector of some matrix. With the increasing availability of network data that changes in time, it is important to extend such eigenvector-based centrality measures to time-dependent networks. In this paper, we introduce a principled generalization of network centrality measures that is valid for any eigenvector-based centrality. We consider a temporal network with N nodes as a sequence of T layers that describe the network during diff erent time windows, and we couple centrality matrices for the layers into a supracentrality matrix of size NT x NT whose dominant eigenvector gives the centrality of each node i at each time t. We refer to this eigenvector and its components as a joint centrality, as it reflects the importances of both the node i and the time layer t. We also introduce the concepts of marginal and conditional centralities, which facilitate the study of centrality trajectories over time. We find that the strength of coupling between layers is important for determining multiscale properties of centrality, such as localization phenomena and the time scale of centrality changes. In the strong-coupling regime, we derive expressions for time-averaged centralities, which are given by the zeroth-order terms of a singular perturbation expansion. We also study first-order terms to obtain fi rst-order-mover scores, which concisely describe the magnitude of the nodes' centrality changes over time. As examples, we apply our method to three empirical temporal networks: the United States Ph.D. exchange in mathematics, costarring relationships among top-billed actors during the Golden Age of Hollywood, and citations of decisions from the United States Supreme Court.