Introduction to Nonsmooth Analysis and Optimization
January 1, 2020
|
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
| | |
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
|
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 \...
Infrared structure of SU(N)×U(1) gauge theory to three loops
December 31, 2019
| |
Physics
High Energy Physics - Phenomenology
We study the infrared (IR) structure of SU(N)×U(1) (QCD ×
QED) gauge theory with nf quarks and nl leptons within the framework of
perturbation theory. In particular, we unravel the IR structure of the form
factors and ...
Spectral analysis on standard locally homogeneous spaces
December 29, 2019
|
Mathematics
Representation Theory
Differential Geometry
Spectral Theory
Let X=G/H be a reductive homogeneous space with H noncompact, endowed
with a G-invariant pseudo-Riemannian structure. Let L be a reductive
subgroup of G acting properly on X and Γ a torsion-free discrete
subgroup of L. ...
Approximating intractable short ratemodel distribution with neural
network
December 29, 2019
|
Quantitative Finance
Computer Science
Statistics
Mathematical Finance
Machine Learning
Machine Learning
We propose an algorithm which predicts each subsequent time step relative to
the previous timestep of intractable short rate model (when adjusted for drift
and overall distribution of previous percentile result) and show that the
method ach...
Vinogradov three prime theorem with Piatetski-Shapiro primes
December 28, 2019
| |
Mathematics
Number Theory
Combinatorics
We prove that, for any c1,c2,c3∈(1,41/35), every sufficiently large
odd number N can be represented as the sum of three primes N=p1+p2+p3 such that pi=⌊nici⌋ for some ni∈N for each...
Scaled Relative Graph of Normal Matrices
December 27, 2019
| | | | |
Mathematics
Computer Science
Numerical Analysis
Numerical Analysis
Optimization and Control
Numerical Analysis
Numerical Analysis
Optimization and Control
The Scaled Relative Graph (SRG) is a geometric tool that maps the action of a
multi-valued nonlinear operator onto the 2D plane, used to analyze the
convergence of a wide range of iterative methods. As the SRG includes the
spectrum for line...