Topological Crystals
July 26, 2016
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Mathematics
Algebraic Topology
Combinatorics
Algebraic Topology
Combinatorics
Sunada's work on crystallography emphasizes the role of the "maximal abelian
cover" of a graph . This is a covering space of for which the group of
deck transformations is the first homology group . An
embedding of...
On some Lie groups containing spin group in Clifford algebra
July 25, 2016
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Physics
Mathematics
Mathematical Physics
Mathematical Physics
Mathematical Physics
Mathematical Physics
In this paper we consider some Lie groups in complexified Clifford algebras.
Using relations between operations of conjugation in Clifford algebras and
matrix operations we prove isomorphisms between these groups and classical
matrix groups...
Relaxed Highest Weight Modules from -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
, 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 and that any planar graph admits the same even in
. For a graph and , let 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 . 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 be a 4-regular graph. Each circuit partition of has a
corresponding touch-graph ; the circuits in correspond to vertices
of , and the vertices of correspond to edges of . We
discuss the connec...
The denominators of harmonic numbers (Revised)
July 11, 2016
Mathematics
Number Theory
The denominators of the harmonic number
do not increase monotonically with~. It
is conjectured that infinitely often. For an
odd prime , 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...