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."
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.
"I have discovered a truly remarkable proof of this theorem which a Twitter post is too small to contain."— Mason Porter (@masonporter) March 25, 2017
In retrospect, I should have written "this tweet" instead of "a Twitter post" to make the parallel even stronger.
Thursday, March 23, 2017
(Tip of the cap to Rachael Rosenthal.)
Update (3/27/17): This article in The Washington Post includes several more spectacular examples of GOP D & D. By the way, the hashtag is #GOPDnD. (Tip of the cap to Mohi Kumar for this article.)
Title: The Multilayer Nature of Ecological Networks
Authors: Shai Pilosof, Mason A. Porter, Mercedes Pascual, and Sonia Kéfi
Abstract: Although networks provide a powerful approach to study a large variety of ecological systems, their formulation does not typically account for multiple interaction types, interactions that vary in space and time, and interconnected systems such as networks of networks. The emergent field of ‘multilayer networks’ provides a natural framework for extending analyses of ecological systems to include such multiple layers of complexity, as it specifically allows one to differentiate and model 'intralayer' and 'interlayer' connectivity. The framework provides a set of concepts and tools that can be adapted and applied to ecology, facilitating research on high-dimensional, heterogeneous systems in nature. Here, we formally define ecological multilayer networks based on a review of previous, related approaches; illustrate their application and potential with analyses of existing data; and discuss limitations, challenges, and future applications. The integration of multilayer network theory into ecology offers largely untapped potential to investigate ecological complexity and provide new theoretical and empirical insights into the architecture and dynamics of ecological systems.
Wednesday, March 22, 2017
I'm pretty sure that this is the official definition that you'll find in many mathematics books.
In case you're interested in these objects, see Todd Kapitula's primer. And here is a new article by Chris Jones that reminded me of the above definition.
Actually, I'm pretty sure I once heard someone — maybe even Chris? — joking call an Evans function "a Wronskian on steroids" during a seminar. I remember thinking that 'on steroids' probably wasn't doing justice to the function.
Tuesday, March 21, 2017
I am puzzled as to why Ingrid Daubechies didn't share this prize.
Update: Terry Tao has written a short blog post about the prize. Among other things (and I hadn't caught this), note the following text from Tao: Daubechies also made extremely important contributions to the theory of wavelets, but my understanding is that due to a conflict of interest arising from Daubechies’ presidency of the International Mathematical Union (which nominates members of the Abel prize committee) from 2011 to 2014, she was not eligible for the prize this year, and so I do not think this prize should be necessarily construed as a judgement on the relative contributions of Meyer and Daubechies to this field.
Wednesday, March 15, 2017
Also see previous blog entries of mine, such as this one, this one, and this one.
Vindication is mine!
(Tip of the cap to Jaideep Taggart Singh.)
Update: Aaron Clements pointed me to this Washington Post article.
Also see my Facebook post about this for witty repartee, other suggested names, and possible prequels (e.g., "The Vector").
(Tip of the cap to Sammy Kline for the information about the reboot.)
As a twist on this, I decided to look at the first sentence of the preface of one of my books. This yields the following sentence: "Traditionally, much of the study of networks has focused on structural features, and then the murders began."
Unfortunately, the tense of the sentence hurts things, so I am going to change one letter ("s" to "d" in the word "has") to produce the following sentence: "Traditionally, much of the study of networks had focused on structural features, and then the murders began."
Much better! (And highly amusing.)
(Tip of the cap to Keith Fraser.)
I would move "cherry" way over to the right.
I did recently have an experience with eating a pink Starburst and expecting strawberry but getting watermelon instead. It was unpleasant.
Even more unpleasant are past experiences of eating red with the hope that it's cherry but then getting cinnamon instead.
Tuesday, March 14, 2017
(Tip of the cap to Jeremy Stell.)
Update (3/19/17): I forgot to mention that I found out a few days ago that there was some Photoshopping in the above picture. It's still very cool, though not quite as cool as before.
Well, Martin Gould is CEO of Sonalytic, which was just acquired by Spotify! Very well done!
Saturday, March 11, 2017
This article, which has lots of great pictures of mathematical art, is a review of the exhibit Picturing Math at the Metropolitan Museum of Art in New York City.
(Tip of the cap to James Tanton.)
Thursday, March 09, 2017
Wednesday, March 08, 2017
Spicer: "I wish he'd have an affair. That'd be better than defending the stupid s*** he says in Twitter."— Rogue POTUS Staff (@RoguePOTUSStaff) March 8, 2017
Here is an older blog entry about the rogue government Twitter accounts.
Tuesday, March 07, 2017
It should say "specializes" (present tense), by the way, as Karin is still research-active, even though she's retired. In fact, no doubt, she is now more active in her research, as that is how it often works.
As I write this, the tumblr has gotten up to 'M' so far, and there are many great mathematicians profiled (including, thankfully, people besides the same ones that often show up over and over again in such lists).
(Tip of the cap to Association for Women in Mathematics.)
Monday, March 06, 2017
Sunday, March 05, 2017
Saturday, March 04, 2017
Thursday, March 02, 2017
After proposing party affiliation quotas for faculty, lawmaker grilled about business degree from Sizzler Steakhouse https://t.co/9ycYTISAm1— Carl T. Bergstrom (@CT_Bergstrom) March 3, 2017
In his tweet, Carl Bergstrom links to a Boing Boing article, but the article to which it links gives a clearer explanation.
It's not quite as surreal as a National Park Service Twitter account going rogue (initially by simply tweeting basic facts about climate science), but it's still odd.
Garfield contributed a lot to the study of scientific productivity and output, and for better or for worse (often for worse), he gave us the impact factor (which of course has led to many variants).