After initially meeting with fierce resistance, "branes", p-dimensional
extended objects which go beyond particles (p=0) and strings (p=1), now occupy
centre stage in theoretical physics as microscopic components of M-theory, as
the seeds o...
Relationship between quandle shadow cocycle invariants and Vassiliev
invariants of links
December 30, 2018
Mathematics
Geometric Topology
We prove that there exist links and quandle (shadow) cocycle invariants by
using Alexander quandles such that quandle (shadow) cocycle invariants by using
Alexander quandles induce Vassiliev invariants. It is natural to try to relate
quandl...
Exponential convergence in Wasserstein Distance for Diffusion Semigroups
with Irregular Drifts
December 25, 2018
Mathematics
Probability
The exponential contraction in L1-Wasserstein distance and exponential
convergence in Lq-Wasserstein distance (q≥1) are considered for
stochastic differential equations with irregular drift. When the irregular
drift drift is loc...
On the It\^o-Alekseev-Gr\"obner formula for stochastic differential
equations
December 24, 2018
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Mathematics
Probability
In this article we establish a new formula for the difference of a test
function of the solution of a stochastic differential equation and of the test
function of an It\^o process. The introduced formula essentially generalizes
both the cla...
Pauli-type coupling between spinors and curved spacetime
December 23, 2018
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Physics
General Relativity and Quantum Cosmology
Classical Physics
General Relativity and Quantum Cosmology
Classical Physics
In this study we prove that the Pauli interaction -- which is associated with
a length parameter -- emerges when the minimal coupling recipe is applied to
the non-degenerate version of the Dirac Lagrangian. The conventional Dirac
Lagrangian...
Asymptotic distribution and convergence rates of stochastic algorithms
for entropic optimal transportation between probability measures
December 21, 2018
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Mathematics
Statistics
Statistics Theory
Statistics Theory
Statistics Theory
Statistics Theory
This paper is devoted to the stochastic approximation of entropically
regularized Wasserstein distances between two probability measures, also known
as Sinkhorn divergences. The semi-dual formulation of such regularized optimal
transportati...
Boson Sampling with Gaussian input states: toward efficient scaling and
certification
December 21, 2018
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Physics
Quantum Physics
A universal quantum computer of large scale is not available yet, however,
intermediate models of quantum computation would still permit demonstrations of
a quantum computational advantage over classical computing and could challenge
the Ex...
Parton distribution functions from scalar light-front parton gas model
December 21, 2018
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Physics
Nuclear Theory
We model the structure of hadrons by a confined parton gas with light-front
kinematics. These partons are treated as classical spin-zero particles confined
inside the hadron with inter-parton collisions as their only interaction. The
microc...
Lectures on 4d N=1 dynamics and related topics
December 21, 2018
Physics
High Energy Physics - Theory
This lecture series consists of mostly independent three parts: Part 1: a
tour of basic 4d N=1 supersymmetric dynamics, covering the pure super
Yang-Mills, the Seiberg duality for classical groups, the supersymmetric index
on S^3, and the a...
First-order invariants of differential 2-forms
December 18, 2018
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Mathematics
Differential Geometry
Differential Geometry
Let M be a smooth manifold of dimension 2n, and let OM be the dense
open subbundle in ∧2T∗M of 2-covectors of maximal rank. The
algebra of DiffM-invariant smooth functions of first order on
$O_{M...