On the cardinality of unique range sets with weight one
July 19, 2018
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Mathematics
Complex Variables
Two meromorphic functions f and g are said to share the set S⊂C∪{∞} with weight l∈N∪{0}∪{∞},
if Ef​(S,l)=Eg​(S,l) where $$E_{f}(S,l)=\bigcup\limits_{a \in S}\{(z,t)
\in \math...
First-Passage Duality
July 19, 2018
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Physics
Statistical Mechanics
We show that the distribution of times for a diffusing particle to first hit
an absorber is \emph{independent} of the direction of an external flow field,
when we condition on the event that the particle reaches the target for flow
away fro...
On the L-polynomials of curves over finite fields
July 19, 2018
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Mathematics
Algebraic Geometry
Number Theory
We discuss, in a non-archimedean setting, the distribution of the
coefficients of L-polynomials of curves of genus g over Fq​. This
allows us to prove, among other things, that the Q-vector space
spanned by such char...
Convergence of martingale solutions to the hybrid slow-fast system
July 18, 2018
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Mathematics
Dynamical Systems
Analysis of PDEs
This paper is devoted to studying the weak convergence for a slow-fast system
with jumps modulated by Markovian switching regimes with the martingale method.
However, due to the coexistence of fast component and Markovian switching
regimes,...
Topological and nonlinearity-induced thermalization in a PT-symmetric
split-Langevin bath
July 17, 2018
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Physics
Statistical Mechanics
Pattern Formation and Solitons
Statistical Mechanics
Pattern Formation and Solitons
Open classical systems with balanced, separated gain and loss, called
PT-symmetric systems, have been extensively studied over the past decade. Here,
we investigate the properties of a uniform, harmonic chain with spatially
separated viscou...
Near-Optimal Bootstrapping of Hitting Sets for Algebraic Models
July 17, 2018
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Computer Science
Computational Complexity
Computational Complexity
The Polynomial Identity Lemma (also called
the "Schwartz--Zippel lemma") states ...
Timed Discrete-Event Systems are Synchronous Product Structures
July 17, 2018
Electrical Engineering and Systems Science
Computer Science
Systems and Control
Systems and Control
Timed discrete-event systems (TDES), which is a modelling formalism proposed
by Brandin and Wonham, can be used for modelling scheduling and production
planning problems. This paper aims to show that TDES are essentially
synchronous product...
Pattern Synthesis via Complex-Coefficient Weight Vector Orthogonal
Decomposition
July 17, 2018
Electrical Engineering and Systems Science
Signal Processing
This paper presents a new array response control scheme named
complex-coefficient weight vector orthogonal decomposition (C2-WORD) and its application to pattern synthesis. The
proposed C2-WORD ...
Classification of homogeneous functors in manifold calculus
July 16, 2018
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Mathematics
Algebraic Topology
Algebraic Topology
For any object A in a simplicial model category M, we construct a topological
space \^A which classifies homogeneous functors whose value on k open balls is
equivalent to A. This extends a classification result of Weiss for homogeneous
func...
Lectures on Statistics in Theory: Prelude to Statistics in Practice
July 16, 2018
Physics
Data Analysis, Statistics and Probability
This is a writeup of lectures on "statistics" that have evolved from the
initial version for the 2009 Hadron Collider Physics Summer School at CERN to
versions for other venues and, most recently, for the African School of
Fundamental Physi...