Wednesday, February 21, 2018

Mathematical Haiku


(Thanks to Paul Glendinning for the Twitter 'mention', from which I learned that my haiku made it into the article.)

What Happens in Knoxville Stays in Knoxville

I'll be heading to my first visit to Tennessee to participate in a NIMBioS working group at University of Tennessee.

I'd try to link to a relevant website, except that my internet connection at the airport is glacially slow, so I'm not going to even try for now. We'll be formulating some forward-looking big problems in network neuroscience to think about together and then hopefully start thinking deeply about and trying to solve.

Update: Here is the link to our working group.

Tuesday, February 20, 2018

Danger in the Nth Dimension: A 1950s Comic with N = 4

The cover of this 1950s comic book is adorable.

And this was with only a 4th dimension!

This will be great fodder for some math and physics talks... "NO! Don't enter that manifold!"

(Tip of the cap to James Gleick.)

Monday, February 19, 2018

Tales from the ArXiv: Building on "Seminal but Laconic" Findings

I am highly amused by one of the sentences in the abstract of this paper, which is called "Systematic elimination of Stokes divergences emanating from complex phase space caustics".

The sentence in the abstract reads as follows: Building on the seminal but laconic findings of Adachi, we show that the deviation from second order can be used to rigorously determine the Stokes lines and therefore the region of the space that should be removed.

I think I need to steal the first part of that sentence, and I know that I have felt that way on many occasions (e.g., with respect to work by Nesterenko) in my career.

"Neither Global nor Local: Heterogeneous Connectivity in Spatial Network Structures of World Migration"

One of my papers, which has had a DOI for about half a year, finally has its final publication coordinates. Notably, this is my first paper in a sociology journal. Here are some details.

Title: Neither Global nor Local: Heterogeneous Connectivity in Spatial Network Structures of World Migration

Authors: Valentin Danchev and Mason A. Porterc

Abstract: For a long time, geographic regions were considered the dominant spatial arbiter of international migration of people. However, since the late 1970s, many scholars have argued that movements reach beyond contiguous regions to connect distant, dispersed, and previously disconnected countries across the globe. The precise structure of world migration, however, remains an open question. We apply network analysis that incorporates spatial information to international migration-stock data to examine what multilateral structures of world migration have emerged from the interplay of regional concentration (local cohesion)and global interconnectedness (global cohesion) for the period 1960–2000. In the world migration network (WMN), nodes represent countries located in geographic space, and edges represent migrants froman origin country who live in a destination country during each decade. We characterize the large-scale structure and evolution of the WMN by algorithmically detecting international migration communities (i.e., sets of countries that are densely connected via migration) using a generalized modularity function for spatial, temporal, and directed networks. Our findings for the whole network suggest that movements in the WMN deviate significantly from the regional boundaries of the world and that international migration communities have become globally interconnected over time. However, we observe a strong variability in the distribution of strengths, neighborhood overlaps, and lengths of migration edges in the WMN. This manifests as three types of communities: global, local, and glocal. We find that long-distance movements in global communities bridge multiple non-contiguous countries, whereas local (and, to a lesser extent, glocal) communities remain trapped in contiguous geographic regions (or neighboring regions) for almost the whole period, contributing to a spatially fragmented WMN. Our findings demonstrate that world migration is neither regionally concentrated nor globally interconnected, but instead exhibits a heterogeneous connectivity pattern that channels unequal migration opportunities across the world.

Wednesday, February 14, 2018

Tales from the ArXiv: "The Random Walk of Cars and Their Collision Probabilities with Planets"

Well, the title of this paper pretty much says it all.

However, there are also some choice quotes in the paper. For example, I really like this deadpan sentence: We now turn to the long-term dynamical evolution for which we integrate 240 realizations of the Tesla for 3.5 Myr into the future.

The final part of the abstract is also nice: By running a large ensemble of simulations with slightly perturbed initial conditions, we estimate the probability of a collision with Earth and Venus over the next one million years to be 6% and 2.5%, respectively. We estimate the dynamical lifetime of the Tesla to be a few tens of millions of years. (I guess the simulation of 3.5 million years wasn't long enough.)

(Tip of the cap to Predrag Cvitanovic.)

Physics Fashion Police: Save the Pocket Protector

Well, this is a bit awkward.


(Tip of the cap to John Dudley.)

Tuesday, February 13, 2018

"Direct Measurement of Superdiffusive Energy Transport in Disordered Granular Chains"

Our paper in which we — after many years of effort — showed strongly nonlinear Anderson phenomena in experiments is finally out in published form!

Here are some details.

Title: Direct Measurement of Superdiffusive Energy Transport in Disordered Granular Chains

Authors: Eunho Kim, Alejandro J. Martínez, Sean E. Phenisee, Panayotis G. Kevrekidis, Mason A. Porter, and Jinkyu Yang

Teaser: Wave propagation is often nonlinear in character, yet the interplay between disorder and nonlinearity remains elusive. Kim et al. use experiments and corroborating numerical simulations to investigate this phenomenon and demonstrate superdiffusive energy transport in disordered granular chains.

Abstract: Energy transport properties in heterogeneous materials have attracted scientific interest for more than half of a century, and they continue to offer fundamental and rich questions. One of the outstanding challenges is to extend Anderson theory for uncorrelated and fully disordered lattices in condensed-matter systems to physical settings in which additional effects compete with disorder. Here we present the first systematic experimental study of energy transport and localization properties in simultaneously disordered and nonlinear granular crystals. In line with prior theoretical studies, we observe in our experiments that disorder and nonlinearity—which individually favor energy localization—can effectively cancel each other out, resulting in the destruction of wave localization. We also show that the combined effect of disorder and nonlinearity can enable manipulation of energy transport speed in granular crystals. Specifically, we experimentally demonstrate superdiffusive transport. Furthermore, our numerical computations suggest that subdiffusive transport should be attainable by controlling the strength of the system’s external precompression force.

Thursday, February 08, 2018

Beware of "Echolocating Insectivorous Hats"

Seriously.


(Tip of the cap to Jennifer Ouelette.)

Sunday, February 04, 2018

Tolkienesque Maps of National Parks

I approve!

Please, please, please can we do this for university campus maps? That would be so awesome!


(Tip of the cap to Peter Dodds.)

Friday, February 02, 2018

An ASCII Soliton Collision

I promised this to some of my Ph.D. students, so I drew it, and I'm posting it here as well.

Thursday, February 01, 2018

"Surprise!"

I still love the result of this ‘emotion analysis’ of the profile pictures of mathematicians on Twitter.

In addition to these three categories, no face is detected in 24 images.

A Dozen Ways to Divide the United Kingdom

There is some great snark in here!

(Tip of the cap to Melina Freitag.)