Quantum Advantages in (n,d)->1 Random Access Codes
October 11, 2015
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Physics
Computer Science
Mathematics
Quantum Physics
Computational Complexity
Information Theory
Information Theory
A random access code (RAC), corresponding to a communication primitive with
various applications in quantum information theory, is an instance of a
preparation-and-measurement scenario. In this work, we consider (n,d)-RACs
constituting an "...
Plug-in error bounds for a mixing density estimate in Rd, and for its
derivatives
October 7, 2015
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Mathematics
Statistics
Statistics Theory
Statistics Theory
Statistics Theory
Statistics Theory
A mixture density, fp​, is estimable in Rd, d≥1, but an estimate
for the mixing density, p, is usually obtained only when d is unity; h is
the mixture's kernel. When fp​'s estimate has form fp^​n​​ and p is
$\til...
Smith Normal Form of Matrices Associated with Differential Posets
October 2, 2015
Mathematics
Combinatorics
We prove a conjecture of Miller and Reiner on the existence of Smith normal
form for the DU-operators for a certain class of r-differential posets....
Parabolic and near-parabolic renormalizations for local degree three
September 30, 2015
Mathematics
Dynamical Systems
The invariant class under parabolic and near-parabolic renormalizations
constructed by Inou and Shishikura has been proved to be extremely useful in
recent years. It leads to several important progresses on the dynamics of
certain holomorph...
Properties of Eventually Positive Linear Input-Output Systems
September 28, 2015
Mathematics
Computer Science
Optimization and Control
Systems and Control
In this paper, we consider the systems with trajectories originating in the
nonnegative orthant becoming nonnegative after some finite time transient.
First we consider dynamical systems (i.e., fully observable systems with no
inputs), whic...
Analytical Methods for Squaring the Disc
September 21, 2015
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Mathematics
History and Overview
Differential Geometry
History and Overview
Differential Geometry
We present and discuss several old and new methods for mapping a circular
disc to a square. In particular, we present analytical expressions for mapping
each point (u,v) inside the circular disc to a point (x,y) inside a square
region. Idea...
A guide to tropical modifications
September 11, 2015
Mathematics
Algebraic Geometry
This paper surveys {\it tropical modifications}, which have already become a
folklore in tropical geometry. Tropical modifications are used in tropical
intersection theory, tropical Hodge theory, and in the study of singularities.
They admi...
Asymptotic Differential Algebra and Model Theory of Transseries
September 8, 2015
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Mathematics
Logic
Commutative Algebra
Classical Analysis and ODEs
Logic
Commutative Algebra
Classical Analysis and ODEs
We develop here the algebra of the differential field of transseries and of
related valued differential fields. This book contains in particular our
recently obtained decisive positive results on the model theory of these
structures....
The complex structure on the six dimensional sphere
September 8, 2015
Mathematics
Differential Geometry
Algebraic Geometry
Proof of existence of a complex structure on the six-sphere, followed by an
explicit computation of its underlying integrable almost complex tensor by the
aid of inner automorphisms of the octonions, is exhibited. Both are elementary
and se...
The six operations in equivariant motivic homotopy theory
September 7, 2015
Mathematics
Algebraic Geometry
Algebraic Topology
K-Theory and Homology
We introduce and study the homotopy theory of motivic spaces and spectra
parametrized by quotient stacks [X/G], where G is a linearly reductive linear
algebraic group. We extend to this equivariant setting the main foundational
results of m...