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Recent Activity on SelectedPapers.net

#homologicalalgebra new topic created (6 days ago)
#graphtheory new topic created (6 days ago)
David Roberts commented on Categorifying the magnitude of a graph (6 days ago)
With blog post and discussion at https://golem.ph.utexas.edu/category/2015/05/categorifying_the_magnitude_of.html There's some interesting remarks about spectral sequences in the comments.

http://arxiv.org/abs/1505.04125

Title: Categorifying the magnitude of a graph
Authors: +Richard Hepworth , +Simon Willerton

Abstract: The magnitude of a graph can be thought of as an integer power series associated to a graph; Leinster introduced it using his idea of magnitude of a metric space. Here we introduce a bigraded homology theory for graphs which has the magnitude as its graded Euler characteristic. This is a categorification of the magnitude in the same spirit as Khovanov homology is a categorification of the Jones polynomial. We show how properties of magnitude proved by Leinster categorify to properties such as a Kunneth Theorem and a Mayer-Vietoris Theorem. We prove that joins of graphs have their homology supported on the diagonal. Finally, we give various computer calculated examples.


#arXiv #spnetwork arXiv:1505.04125 #homologicalalgebra #graphtheory  
John Baez replied RE: Bounded intervals containing many primes (May 8, 2015)
It'll be interesting to see if #spnetwork does its job if you don't include arXiv:1505.01815 next to it. 

(Unfortunately my putting it in a comment won't help.)
David Roberts commented on Bounded intervals containing many primes (May 8, 2015)
An improvement on the #primegaps  work for the case of bunches of primes. There are infinitely many collections of m+1 successive primes with gap < exp(3.815m). In the Polymath project this bound was m exp( [4-28/157]m )

http://arxiv.org/abs/1505.01815

Title: Bounded intervals containing many primes
Authors: R. C. Baker, A. J. Irving

Abstract: By combining a sieve method of Harman with the work of Maynard and Tao we show that

\liminf_{n\rightarrow \infty}(p_{n+m}-p_n)\ll \exp(3.815m).

#arXiv   #spnetwork   #numbertheory  
David Roberts replied RE: A first-order logic for string diagrams (May 6, 2015)
+Philip Thrift ah, of course!
Philip Thrift replied RE: A first-order logic for string diagrams (May 6, 2015)
! could be pronounced as Victor Borge defined it:
Victor Borge: Phonetic punctuation
https://www.youtube.com/watch?v=6bpIbdZhrzA
David Roberts replied RE: A first-order logic for string diagrams (May 6, 2015)
+Philip Thrift but about as practical as iTeX* from a pronunciation point of view (see Knuth explain here: https://www.youtube.com/watch?v=eKaI78K_rgA)
Philip Thrift replied RE: A first-order logic for string diagrams (May 6, 2015)
To have a programming language named ! does sound cool.
#diagrammaticcalculus new topic created (May 6, 2015)
David Roberts commented on A first-order logic for string diagrams (May 6, 2015)
No doubt related to Quantomatic (http://quantomatic.github.io/)

http://arxiv.org/abs/1505.00343

Title: A first-order logic for string diagrams
Authors: +Aleks Kissinger , +David Quick

Abstract: Equational reasoning with string diagrams provides an intuitive means of proving equations between morphisms in a symmetric monoidal category. This can be extended to proofs of infinite families of equations using a simple graphical syntax called !-box notation. While this does greatly increase the proving power of string diagrams, previous attempts to go beyond equational reasoning have been largely ad hoc, owing to the lack of a suitable logical framework for diagrammatic proofs involving !-boxes. In this paper, we extend equational reasoning with !-boxes to a fully-fledged first order logic called with conjunction, implication, and universal quantification over !-boxes. This logic, called !L, is then rich enough to properly formalise an induction principle for !-boxes. We then build a standard model for !L and give an example proof of a theorem for non-commutative bialgebras using !L, which is unobtainable by equational reasoning alone.

#arXiv #spnetwork arXiv:1505.00343 #categorytheory #logic #diagrammaticcalculus  
Holden Lee commented on Efficiently learning Ising models on arbitrary graphs (May 1, 2015)
Notes on Bresler's paper "Learning Ising models on arbitrary graphs": https://holdenlee.wordpress.com/2015/05/01/efficiently-learning-ising-models/  #spnetwork  arxiv:1411.6156
#impactfactor new topic created (May 1, 2015)
#bibliometrics new topic created (May 1, 2015)
#dora new topic created (May 1, 2015)
#if new topic created (May 1, 2015)
David Roberts commented on Cited Half-Life of the Journal Literature (May 1, 2015)
The mean cited half-life of journals in the Thompson-Reuters Journal Citation Reports classed under 'Mathematics' is 9.9 years. Makes a mockery of even mentioning impact factors for maths journals. As Stephen Curry said: "If you use impact factors you are statistically illiterate" [1]. If you are on an editorial board, push for the publisher etc to sign DORA [2].

http://arxiv.org/abs/1504.07479

[1] http://occamstypewriter.org/scurry/2012/08/13/sick-of-impact-factors/
[2] http://en.wikipedia.org/wiki/San_Francisco_Declaration_on_Research_Assessment
#dora   #impactfactor #spnetwork arXiv:1504.07479 #bibliometrics #if
Harold Hausman replied RE: Decompositions of a polygon into centrally symmetric pieces (Apr. 29, 2015)
Mondrian did seem to have a refined sense of proportion that those developing automated imitations of his work have so-far sorely lacked.
Richard Green replied RE: Decompositions of a polygon into centrally symmetric pieces (Apr. 29, 2015)
They do have a lot of potential as an art form, +Mark Hurn. More so than computer-generated simulations of Mondrian-style art, which don't seem to work very well.
Mark Hurn replied RE: Decompositions of a polygon into centrally symmetric pieces (Apr. 29, 2015)
Taking the stained glass idea a stretch further, they would make a rather fetching set of coasters.