The Neumann Problem for Parabolic Hessian Quotient Equations
January 6, 2020
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Mathematics
Analysis of PDEs
In this paper, we consider the Neumann problem for parabolic Hessian quotient
equations. We show that the k-admissible solution of the parabolic Hessian
quotient equation exists for all time and converges to the smooth solution of
ellipti...
Sharp bounds on the Nusselt number in Rayleigh-B\'enard convection and a
bilinear estimate via Carleson measures
January 6, 2020
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Mathematics
Analysis of PDEs
We prove a conjecture in fluid dynamics concerning optimal bounds for heat
transportation in the infinite Prandtl number limit. Due to a maximum principle
property for the temperature exploited by Constantin-Doering and Otto-Seis,
this amou...
The troublesome kernel -- On hallucinations, no free lunches and the
accuracy-stability trade-off in inverse problems
January 5, 2020
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Computer Science
Machine Learning
Computer Vision and Pattern Recognition
Methods inspired by Artificial Intelligence (AI) are starting to
fundamentally change computational science and engineering through breakthrough
performances on challenging problems. However, reliability and trustworthiness
of such techniqu...
Normal crossing immersions, cobordisms and flips
January 4, 2020
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Mathematics
Geometric Topology
Combinatorics
We study various analogues of theorems from PL topology for cubical
complexes. In particular, we characterize when two PL homeomorphic cubulations
are equivalent by Pachner moves by showing the question to be equivalent to the
existence of ...
The Initial Value Problem for Singular SPDEs via Rough Paths
January 2, 2020
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Mathematics
Analysis of PDEs
In this contribution we develop a solution theory for singular quasilinear
stochastic partial differential equations subject to an initial condition. We
obtain our solution theory as a perturbation of the rough path approach
developed to ha...
Introduction to Nonsmooth Analysis and Optimization
January 1, 2020
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Mathematics
Optimization and Control
This book aims to give an introduction to generalized derivative concepts
useful in deriving necessary optimality conditions and numerical algorithms for
infinite-dimensional nondifferentiable optimization problems that arise in
inverse pro...
Errata and Addenda to Mathematical Constants
January 1, 2020
Mathematics
History and Overview
Number Theory
We humbly and briefly offer corrections and supplements to Mathematical
Constants (2003) and Mathematical Constants II (2019), both published by
Cambridge University Press. Comments are always welcome....
On the Limits of Topological Data Analysis for Statistical Inference
January 1, 2020
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Statistics
Mathematics
Statistics Theory
Statistics Theory
Algebraic Topology
Probability
Topological data analysis has emerged as a powerful tool for extracting the
metric, geometric and topological features underlying the data as a
multi-resolution summary statistic, and has found applications in several areas
where data arise...
Distributed Stochastic Block Coordinate Descent for Time-Varying
Multi-Agent Optimization
December 31, 2019
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Mathematics
Optimization and Control
In this paper, a class of large-scale distributed nonsmooth convex
optimization problem over time-varying multi-agent network is investigated.
Specifically, the decision space which can be split into several blocks of
convex set is consider...
Kerr Black Hole Evaporation and Page Curve
December 31, 2019
Physics
High Energy Physics - Theory
General Relativity and Quantum Cosmology
We compute the black hole entropy and the entanglement entropy of Hawking
radiations due to photons during the evaporation of a 4d asymptotically flat
Kerr black hole. The Page curve for the Kerr black hole is obtained in the
original way \...