We prove that the half-integer valued local index of an isolated umbilic
point on a C3+α-smooth convex surface in Euclidean 3-space is less
than two. The approach is to study the co-kernel of an associated
Riemann-Hilbert boundary...
Yet Another Table of Integrals
July 24, 2012
Mathematics
Classical Analysis and ODEs
This collection of sums and integrals has been harvested from the
mathematical and physical literature in unstructured ways. Its main use is
backtracking the original sources whenever an integral of the reader's
application resembles one of...
The Supernova of 1054AD, the Armenian chronicle of Hetum, and Cronaca
Rampona
July 16, 2012
Physics
History and Philosophy of Physics
Solar and Stellar Astrophysics
The rareness of nearby supernovae ensures particular value to the historic
records for determination of their light curves. We provide the translation of
13th century Armenian chronicle of Hetum, which by its unexpected association
to Crona...
Meyers inequality and strong stability for stable-like operators
July 11, 2012
|
Mathematics
Functional Analysis
Let α∈(0,2), let E(u,u)=∫Rd∫Rd(u(y)−u(x))2∣x−y∣d+αA(x,y)dydx be the Dirichlet form
for a stable-like operator, let $$\Gamma u(x)=\int_{\Bbb R^d}
(u(y)-u(x))^2\frac{A(x,y)...
Control of Probability Flow in Markov Chain Monte Carlo --
Nonreversibility and Lifting
July 1, 2012
|
Physics
Computer Science
Mathematics
Statistics
Statistical Mechanics
Numerical Analysis
Mathematical Physics
Mathematical Physics
Numerical Analysis
Data Analysis, Statistics and Probability
Computation
Methodology
The Markov Chain Monte Carlo (MCMC) method is widely used in various fields
as a powerful numerical integration technique for systems with many degrees of
freedom. In MCMC methods, probabilistic state transitions can be considered as
a rand...
Factorization homology of topological manifolds
June 24, 2012
|
Mathematics
Algebraic Topology
Geometric Topology
Quantum Algebra
Factorization homology theories of topological manifolds, after Beilinson,
Drinfeld and Lurie, are homology-type theories for topological n-manifolds
whose coefficient systems are n-disk algebras or n-disk stacks. In this
work we prov...
Perfect taxon sampling and fixing taxon traceability: Introducing a
class of phylogenetically decisive taxon sets
June 15, 2012
|
Quantitative Biology
Mathematics
Populations and Evolution
Combinatorics
Phylogenetically decisive sets of taxon sets have the property that if trees
are chosen for each of their elements, as long as these trees are compatible,
the resulting supertree is unique. This means that as long as the trees
describing th...
Tilings of an Isosceles Triangle
June 9, 2012
Mathematics
Metric Geometry
An N-tiling of triangle ABC by triangle T is a way of writing ABC as a union
of N triangles congruent to T, overlapping only at their boundaries. The
triangle T is the "tile". The tile may or may not be similar to ABC. In this
paper we stud...
Random matrices: Universality of local spectral statistics of
non-Hermitian matrices
June 8, 2012
|
Mathematics
Probability
It is a result of Ginibre that the normalized bulk k-point correlation
functions of a complex n×n Gaussian matrix with independent entries of
mean zero and unit variance are asymptotically given by the determinantal point
process ...
Triangle Tiling V: Tilings by a tile with integer sides
June 4, 2012
Mathematics
Metric Geometry
An N-tiling of triangle ABC by triangle T is a way of writing ABC as a union
of N triangles congruent to T, overlapping only at their boundaries. The
triangle T is the "tile". The tile may or may not be similar to ABC. We wish to
understand...