Smooth subsolutions of the discounted Hamilton-Jacobi equations
July 21, 2020
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Mathematics
Dynamical Systems
Analysis of PDEs
Dynamical Systems
Analysis of PDEs
For the discounted Hamilton-Jacobi equation,λu+H(x,dxu)=0,x∈M,we construct C1,1 subsolutions which are indeed solutions on the
projected Aubry set. The smoothness of such subsolutions can be improved under
addition...
Models of Jacobians of curves
July 21, 2020
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Mathematics
Algebraic Geometry
We show that the Jacobians of prestable curves over toroidal varieties always
admit N\'eron models. These models are rarely quasi-compact or separated, but
we also give a complete classification of quasi-compact separated group-models
of su...
Outer approximations of core points for integer programming
July 21, 2020
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Mathematics
Computer Science
Optimization and Control
Computational Geometry
For several decades the dominant techniques for integer linear programming
have been branching and cutting planes. Recently, several authors have
developed core point methods for solving symmetric integer linear programs
(ILPs). An integer ...
SUBPLEX: Towards a Better Understanding of Black Box Model Explanations
at the Subpopulation Level
July 21, 2020
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Computer Science
Human-Computer Interaction
Understanding the interpretation of machine learning (ML) models has been of
paramount importance when making decisions with societal impacts such as
transport control, financial activities, and medical diagnosis. While current
model interp...
Rationality of representation zeta functions of compact p-adic
analytic groups
July 21, 2020
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Mathematics
Group Theory
We prove that for any FAb compact p-adic analytic group G, its
representation zeta function is a finite sum of terms
ni−sfi(p−s), where ni are natural numbers and
fi(t)∈Q(t) are rational functions. Mer...
A Deep Ordinal Distortion Estimation Approach for Distortion
Rectification
July 21, 2020
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Computer Science
Computer Vision and Pattern Recognition
Distortion is widely existed in the images captured by popular wide-angle
cameras and fisheye cameras. Despite the long history of distortion
rectification, accurately estimating the distortion parameters from a single
distorted image is st...
Treatment Effects with Targeting Instruments
July 20, 2020
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Economics
Statistics
Econometrics
Methodology
Econometrics
Methodology
Multivalued treatments are commonplace in applications. We explore the use of
discrete-valued instruments to control for selection bias in this setting. Our
discussion revolves around the concept of targeting: which instruments target
which...
Optical quantum memory for noble-gas spins based on spin-exchange
collisions
July 20, 2020
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Physics
Quantum Physics
Atomic Physics
Optical quantum memories, which store and preserve the quantum state of
photons, rely on a coherent mapping of the photonic state onto matter states
that are optically accessible. Here we outline and characterize schemes to map
the state of...
Competing Bandits: The Perils of Exploration Under Competition
July 20, 2020
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Computer Science
Economics
Computer Science and Game Theory
Machine Learning
Theoretical Economics
Most online platforms strive to learn from interactions with users, and many
engage in exploration: making potentially suboptimal choices for the sake of
acquiring new information. We study the interplay between exploration and
competition:...
Geometric analysis of a truncated Galerkin discretization of fast-slow
PDEs with transcritical singularities
July 20, 2020
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Mathematics
Dynamical Systems
We consider a fast-slow partial differential equation (PDE) with
reaction-diffusion dynamics in the fast variable and the slow variable driven
by a differential operator on a bounded domain. Assuming a transcritical normal
form for the reac...