Communications on Pure and Applied Mathematics

Journal: Communications on Pure and Applied Mathematics

Abbreviation

Comm. Pure Appl. Math.

Publisher

Wiley

ISSN

0010-3640
1097-0312

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Publications 1 - 10 of 38

Continuity of optimal transport maps and convexity of injectivity domains on small deformations of S^2
Figalli, Alessio; Rifford, Ludovic (2009)
Communications on Pure and Applied Mathematics
Normalized Harmonic Map Heat Flow
Struwe, Michael (2020)
Communications on Pure and Applied Mathematics
Partial regularity for harmonic maps and related problems
Struwe, Michael; Rivière, Tristan (2008)
Communications on Pure and Applied Mathematics
Semiclassical limit of quantum dynamics with rough potentials and well posedness of transport equations with measure initial data
Ambrosio, Luigi; Figalli, Alessio; Friesecke, Gero; et al. (2011)
Communications on Pure and Applied Mathematics
Integrability of SLE via conformal welding of random surfaces
Ang, Morris; Holden, Nina; Sun, Xin (2024)
Communications on Pure and Applied Mathematics
We demonstrate how to obtain integrability results for the Schramm-Loewner evolution (SLE) from Liouville conformal field theory (LCFT) and the mating-of-trees framework for Liouville quantum gravity (LQG). In particular, we prove an exact formula for the law of a conformal derivative of a classical variant of SLE called SLE kappa(rho(-); rho(+)). Our proof is built on two connections between SLE, LCFT, and mating-of-trees. Firstly, LCFT and mating-of-trees provide equivalent but complementary methods to describe natural random surfaces in LQG. Using a novel tool that we call the uniform embedding of an LQG surface, we extend earlier equivalence results by allowing fewer marked points and more generic singularities. Secondly, the conformal welding of these random surfaces produces SLE curves as their interfaces. In particular, we rely on the conformal welding results proved in our companion paper Ang, Holden and Sun (2023). Our paper is an essential part of a program proving integrability results for SLE, LCFT, and mating-of-trees based on these two connections.
Likelihood Maximization and Moment Matching in Low SNR Gaussian Mixture Models
Katsevich, Anya; Bandeira, Afonso S. (2023)
Communications on Pure and Applied Mathematics
We derive an asymptotic expansion for the log-likelihood of Gaussian mixture models (GMMs) with equal covariance matrices in the low signal-to-noise regime. The expansion reveals an intimate connection between two types of algorithms for parameter estimation: the method of moments and likelihood optimizing algorithms such as Expectation-Maximization (EM). We show that likelihood optimization in the low SNR regime reduces to a sequence of least squares optimization problems that match the moments of the estimate to the ground truth moments one by one. This connection is a stepping stone towards the analysis of EM and maximum likelihood estimation in a wide range of models. A motivating application for the study of low SNR mixture models is cryo-electron microscopy data, which can be modeled as a GMM with algebraic constraints imposed on the mixture centers. We discuss the application of our expansion to algebraically constrained GMMs, among other example models of interest.
Free boundary partial regularity in the thin obstacle problem
Franceschini, Federico; Serra, Joaquim (2024)
Communications on Pure and Applied Mathematics
Deterministic Guarantees for Burer‐Monteiro Factorizations of Smooth Semidefinite Programs
Boumal, Nicolas; Voroninski, Vladislav; Bandeira, Afonso S. (2020)
Communications on Pure and Applied Mathematics
Adiabatic charge pumping in open quantum systems
Avron, Joseph E.; Elgart, Alexander; Graf, Gian Michele; et al. (2004)
Communications on Pure and Applied Mathematics
Infinite speed of propagation and regularity of solutions to the fractional porous medium equation in general domains
Bonforte, Matteo; Figalli, Alessio; Ros-Oton, Xavier (2017)
Communications on Pure and Applied Mathematics

Publications 1 - 10 of 38

Journal: Communications on Pure and Applied Mathematics

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