Children's Drawings and the Riemann-Hilbert Problem
October 25, 2019
Mathematics
History and Overview
Dessin d'enfants (French for children's drawings) serve as a unique
standpoint of studying classical complex analysis under the lens of
combinatorial constructs. A thorough development of the background of this
theory is developed with an e...
Higher-categorical combinatorics of configuration spaces of Euclidean
space
October 25, 2019
Mathematics
Algebraic Topology
We examine configurations of finite subsets of manifolds within the
homotopy-theoretic context of ∞-categories by way of stratified spaces.
Through these higher categorical means, we identify the homotopy types of such
configuration ...
Augmented virtual double categories
October 24, 2019
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Mathematics
Category Theory
Category Theory
In this article the notion of virtual double category (also known as
fc-multicategory) is extended as follows. While cells in a virtual double
category classically have a horizontal multi-source and single horizontal
target, the notion of a...
The Persuasion Duality
October 24, 2019
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Economics
Theoretical Economics
We present a unified duality approach to Bayesian persuasion. The optimal
dual variable, interpreted as a price function on the state space, is shown to
be a supergradient of the concave closure of the objective function at the
prior belief...
Hierarchical Representation Learning in Graph Neural Networks with Node
Decimation Pooling
October 24, 2019
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Computer Science
Mathematics
Statistics
Machine Learning
Spectral Theory
Machine Learning
In graph neural networks (GNNs), pooling operators compute local summaries of
input graphs to capture their global properties, and they are fundamental for
building deep GNNs that learn hierarchical representations. In this work, we
propose...
Non-locally modular regular types in classifiable theories
October 24, 2019
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Mathematics
Logic
We introduce the notion of strong p-semi-regularity and show that if p is
a regular type which is not locally modular then any p-semi-regular type is
strongly p-semi-regular. Moreover, for any such p-semi-regular type,
"domination...
Q-GADMM: Quantized Group ADMM for Communication Efficient Decentralized
Machine Learning
October 23, 2019
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Computer Science
Mathematics
Statistics
Machine Learning
Distributed, Parallel, and Cluster Computing
Information Theory
Networking and Internet Architecture
Information Theory
Machine Learning
Machine Learning
Distributed, Parallel, and Cluster Computing
Information Theory
Networking and Internet Architecture
Information Theory
Machine Learning
In this article, we propose a communication-efficient decentralized machine
learning (ML) algorithm, coined quantized group ADMM (Q-GADMM). To reduce the
number of communication links, every worker in Q-GADMM communicates only with
two neig...
Symmetry multi-reduction method for partial differential equations with
conservation laws
October 23, 2019
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Physics
Mathematics
Mathematical Physics
Mathematical Physics
For partial differential equations (PDEs) that have n≥2 independent
variables and a symmetry algebra of dimension at least n−1, an explicit
algorithmic method is presented for finding all symmetry-invariant conservation
laws that wil...
Continuous K-Theory and Cohomology of Rigid Spaces
October 23, 2019
Mathematics
Algebraic Geometry
K-Theory and Homology
We establish a connection between continuous K-theory and integral cohomology
of rigid spaces. Given a rigid analytic space over a complete discretely valued
field, its continuous K-groups vanish in degrees below the negative of the
dimensi...
Nonsmooth Analysis of Doubly Nonlinear Second-Order Evolution Equations
with Non-Convex Energy Functionals
October 22, 2019
Mathematics
Physics
Analysis of PDEs
Mathematical Physics
Mathematical Physics
We investigate the existence of strong solutions to a general class of doubly
multivalued and nonlinear evolution equations of second order. The multivalued
operators are generated by the subdifferential of nonsmooth potentials that
live in...