Monday, August 21, 2017
Wednesday, August 16, 2017
(Tip of the cap to several people for this news. I got the tweet from Cathy O'Neil.)
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.