Research articles

Amplitude determination for $M M \to M M$ , $M = \pi, K$ and cross-sections for $\gamma \gamma \to \pi^+ \pi^-, \pi^0 \pi^0, \pi^0 \eta$ in a chiral model

July 28, 2016

| |

Physics

High Energy Physics - Phenomenology

Dai and Pennington have performed a comprehensive analysis of essentially all pion and kaon pair production data from two-photon collisions below 1.5 GeV, including all high statistics results from Belle, as well as the older data from Mark...

Topological Crystals

July 26, 2016

Mathematics

Algebraic Topology

Combinatorics

Algebraic Topology

Combinatorics

Sunada's work on crystallography emphasizes the role of the "maximal abelian cover" of a graph

X

. This is a covering space of

X

for which the group of deck transformations is the first homology group

H_1(X,\mathbb{Z})

. An embedding of...

On some Lie groups containing spin group in Clifford algebra

July 25, 2016

Physics

Mathematics

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 $\mathcal{D}$ -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

\hat{\mathfrak{sl}_2}

, 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

| | | | |

Computer Science

Computational Geometry

Computational Complexity

It is well known that any graph admits a crossing-free straight-line drawing in

\mathbb{R}^3

and that any planar graph admits the same even in

\mathbb{R}^2

. For a graph

G

and

d \in \{2,3\}

, let

\rho^1_d(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

\mathbb{Z}^d

. 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

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

d_n

of the harmonic number

1+\frac12+\frac13+\cdots+\frac1n

do not increase monotonically with~

n

. It is conjectured that

d_n=D_n={\rm LCM}(1,2,\ldots,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

| |

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...

Amplitude determination for $M M \to M M$ , $M = \pi, K$ and cross-sections for $\gamma \gamma \to \pi^+ \pi^-, \pi^0 \pi^0, \pi^0 \eta$ in a chiral model

July 28, 2016

| |

Physics

High Energy Physics - Phenomenology

Topological Crystals

July 26, 2016

Mathematics

Algebraic Topology

Combinatorics

Algebraic Topology

Combinatorics

Sunada's work on crystallography emphasizes the role of the "maximal abelian cover" of a graph

X

. This is a covering space of

X

for which the group of deck transformations is the first homology group

H_1(X,\mathbb{Z})

. An embedding of...

On some Lie groups containing spin group in Clifford algebra

July 25, 2016

Physics

Mathematics

Mathematical Physics

Relaxed Highest Weight Modules from $\mathcal{D}$ -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

\hat{\mathfrak{sl}_2}

, 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

| | | | |

Computer Science

Computational Geometry

Computational Complexity

It is well known that any graph admits a crossing-free straight-line drawing in

\mathbb{R}^3

and that any planar graph admits the same even in

\mathbb{R}^2

. For a graph

G

and

d \in \{2,3\}

, let

\rho^1_d(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

\mathbb{Z}^d

. 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

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

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

d_n

of the harmonic number

1+\frac12+\frac13+\cdots+\frac1n

do not increase monotonically with~

n

. It is conjectured that

d_n=D_n={\rm LCM}(1,2,\ldots,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

| |

Physics

Chaotic Dynamics

Amplitude determination for MM→MMM M \to M MMM→MM, M=π,KM = \pi, KM=π,K and cross-sections for γγ→π+π−,π0π0,π0η\gamma \gamma \to \pi^+ \pi^-, \pi^0 \pi^0, \pi^0 \etaγγ→π+π−,π0π0,π0η in a chiral model

Topological Crystals

On some Lie groups containing spin group in Clifford algebra

Relaxed Highest Weight Modules from D\mathcal{D}D-Modules on the Kashiwara Flag Scheme

The Complexity of Drawing Graphs on Few Lines and Few Planes

Large Deviations of a Network of Neurons with Dynamic Sparse Random Connections

Multiparameter Fuss--Catalan numbers with application to algebraic equations

Circuit partitions and signed interlacement in 4-regular graphs

The denominators of harmonic numbers (Revised)

Minimal cover of high-dimensional chaotic attractors by embedded recurrent patterns

Amplitude determination for MM→MMM M \to M MMM→MM, M=π,KM = \pi, KM=π,K and cross-sections for γγ→π+π−,π0π0,π0η\gamma \gamma \to \pi^+ \pi^-, \pi^0 \pi^0, \pi^0 \etaγγ→π+π−,π0π0,π0η in a chiral model

Topological Crystals

On some Lie groups containing spin group in Clifford algebra

Relaxed Highest Weight Modules from D\mathcal{D}D-Modules on the Kashiwara Flag Scheme

The Complexity of Drawing Graphs on Few Lines and Few Planes

Large Deviations of a Network of Neurons with Dynamic Sparse Random Connections

Multiparameter Fuss--Catalan numbers with application to algebraic equations

Circuit partitions and signed interlacement in 4-regular graphs

The denominators of harmonic numbers (Revised)

Minimal cover of high-dimensional chaotic attractors by embedded recurrent patterns

Amplitude determination for $M M \to M M$ , $M = \pi, K$ and cross-sections for $\gamma \gamma \to \pi^+ \pi^-, \pi^0 \pi^0, \pi^0 \eta$ in a chiral model

Relaxed Highest Weight Modules from $\mathcal{D}$ -Modules on the Kashiwara Flag Scheme

Amplitude determination for $M M \to M M$ , $M = \pi, K$ and cross-sections for $\gamma \gamma \to \pi^+ \pi^-, \pi^0 \pi^0, \pi^0 \eta$ in a chiral model

Relaxed Highest Weight Modules from $\mathcal{D}$ -Modules on the Kashiwara Flag Scheme