Relaxed Highest Weight Modules from D-Modules on the
Kashiwara Flag Scheme
July 21, 2016
Mathematics
Representation Theory
Algebraic Geometry
The relaxed highest weight representations introduced by Feigin et al. are a
class of representations of the affine Kac-Moody algebra
sl2^, which do not have a highest (or lowest) weight. We
formulate a generalization of ...
The Complexity of Drawing Graphs on Few Lines and Few Planes
July 21, 2016
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Computer Science
Computational Geometry
Computational Complexity
It is well known that any graph admits a crossing-free straight-line drawing
in R3 and that any planar graph admits the same even in
R2. For a graph G and d∈{2,3}, let ρd1(G) denote
the smallest numb...
Large Deviations of a Network of Neurons with Dynamic Sparse Random
Connections
July 19, 2016
Mathematics
Probability
In this work we determine a process-level Large Deviation Principle (LDP) for
a model of interacting particles indexed by a lattice Zd. The
connections are random, sparse and unscaled, so that the system converges in
the large s...
Multiparameter Fuss--Catalan numbers with application to algebraic
equations
July 14, 2016
Mathematics
Combinatorics
We present an exposition on the Fuss--Catalan numbers, which are a
generalization of the well known Catalan numbers. The literature on the subject
is scattered (especially for the case of multiple independent parameters, as
will be explaine...
Circuit partitions and signed interlacement in 4-regular graphs
July 14, 2016
Mathematics
Combinatorics
Let F be a 4-regular graph. Each circuit partition P of F has a
corresponding touch-graph Tch(P); the circuits in P correspond to vertices
of Tch(P), and the vertices of F correspond to edges of Tch(P). We
discuss the connec...
The denominators of harmonic numbers (Revised)
July 11, 2016
Mathematics
Number Theory
The denominators dn of the harmonic number
1+21+31+⋯+n1 do not increase monotonically with~n. It
is conjectured that dn=Dn=LCM(1,2,…,n) infinitely often. For an
odd prime p, the set $\{n:pd_n|D_n\...
Minimal cover of high-dimensional chaotic attractors by embedded
recurrent patterns
July 7, 2016
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Physics
Chaotic Dynamics
We propose a general method for constructing a minimal cover of
high-dimensional chaotic attractors by embedded unstable recurrent patterns. By
minimal cover we mean a subset of available patterns such that the
approximation of chaotic dyna...
Feature Selection Library (MATLAB Toolbox)
July 5, 2016
Computer Science
Computer Vision and Pattern Recognition
The Feature Selection Library (FSLib) signifies a notable progression in
machine learning and data mining for MATLAB users, emphasizing the critical
role of Feature Selection (FS) in enhancing model efficiency and effectiveness
by pinpointi...
Dual Cheeger Constants, Signless 1-Laplacians and Maxcut
July 2, 2016
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Mathematics
Spectral Theory
Combinatorics
Optimization and Control
Spectral Theory
Combinatorics
Optimization and Control
The first nontrivial lower bound of the worst-case approximation ratio for
the maxcut problem was achieved via the dual Cheeger problem, whose optimal
value is referred to the dual Cheeger constant h+, and later improved
through its modi...
Polyhedral Horofunction Compactification as a Polyhedral Ball
July 2, 2016
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Mathematics
Geometric Topology
Metric Geometry
In this paper we answer positively a question raised by Kapovich and Leeb in
a paper titled "Finsler bordifications of symmetric and certain locally
symmetric spaces". Specifically, we show that for a finite-dimensional vector
space with a ...