We introduce Cayley transform ellipsoid fitting (CTEF), an algorithm that uses the Cayley transform to fit ellipsoids to noisy data in any dimension. Unlike many ellipsoid fitting methods, CTEF is ellipsoid specific, meaning it always returns elliptic solutions, and can fit arbitrary ellipsoids. It… read more about this publication »
We study the mixing time of a random walk on the torus, alternated with a Lebesgue measure preserving Bernoulli map. Without the Bernoulli map, the mixing time of the random walk alone is O(1/ε2), where ε is the step size. Our main results show that for a class of Bernoulli maps, when the random… read more about this publication »
A lubrication model can be used to describe the dynamics of a weakly volatile viscous fluid layer on a hydrophobic substrate. Thin layers of the fluid are unstable to perturbations and break up into slowly evolving interacting droplets. A reduced-order dynamical system is derived from the… read more about this publication »
We study the convergences of three projected Sobolev gradient flows to the ground state of the Gross-Pitaevskii eigenvalue problem. They are constructed as the gradient flows of the Gross-Pitaevskii energy functional with respect to the H1 0 -metric and two other equivalent metrics on H1 0 ,… read more about this publication »
Let K be a rationally null-homologous knot in a 3-manifold Y, equipped with a non-zero framing λ, and let Yλ(K) denote the result of λ-framed surgery on Y. Ozsváth and Szabó gave a formula for the Heegaard Floer homology groups of Yλ (K) in terms of the knot Floer complex of (Y, K). We strengthen… read more about this publication »
This paper explores the expressive power of deep neural networks for a diverse range of activation functions. An activation function set A is defined to encompass the majority of commonly used activation functions, such as ReLU, LeakyReLU, ReLU2, ELU, CELU, SELU, Softplus, GELU, SiLU, Swish, Mish,… read more about this publication »
We consider a stochastic version of the point vortex system, in which the fluid velocity advects single vortices intermittently for small random times. Such system converges to the deterministic point vortex dynamics as the rate at which single components of the vector field are randomly switched… read more about this publication »
Flow-based generative models enjoy certain advantages in computing the data generation and the likelihood, and have recently shown competitive empirical performance. Compared to the accumulating theoretical studies on related score-based diffusion models, analysis of flow-based models, which are… read more about this publication »
We present a computationally efficient framework, called FlowDRO, for solving flow-based distributionally robust optimization (DRO) problems with Wasserstein uncertainty sets while aiming to find continuous worst-case distribution (also called the Least Favorable Distribution, LFD) and sample from… read more about this publication »
We show that certain singular structures (Hölderian cusps and mild divergences) are transported by the flow of homeomorphisms generated by an Osgood velocity field. The structure of these singularities is related to the modulus of continuity of the velocity and the results are shown to be sharp in… read more about this publication »
OBJECTIVES: To characterize and quantify accumulating immunologic alterations, pre and postoperatively in patients undergoing elective surgical procedures. BACKGROUND: Elective surgery is an anticipatable, controlled human injury. Although the human response to injury is generally stereotyped,… read more about this publication »
Chemotaxis is a directed cell movement in response to external chemical stimuli. In this paper, we propose a simple model for the origin of chemotaxis - namely how a directed movement in response to an external chemical signal may occur based on purely reaction-diffusion equations reflecting inner… read more about this publication »
In volume transmission (or neuromodulation) neurons do not make one-to-one connections to other neurons, but instead simply release neurotransmitter into the extracellular space from numerous varicosities. Many well-known neurotransmitters including serotonin (5HT), dopamine (DA), histamine (HA),… read more about this publication »
Race-based inequity in federal criminal sentencing is widely acknowledged, and yet our understanding of it is far from complete. Inequity may arise from several sources, including direct bias of courtroom actors and structural bias that produces racially disparate impacts. Irrespective of these… read more about this publication »
Let TtP2f(x) denote the solution to the linear Schrödinger equation at time t, with initial value function f, where P 2(ξ) = ∣ξ∣2. In 1980, Carleson asked for the minimal regularity of f that is required for the pointwise a.e. convergence of TtP2f(x) to f(x) as t → 0. This was recently resolved by… read more about this publication »
We study a prototypical example in nonlinear dynamics where transition to self-similarity in a singular limit is fundamentally changed as a parameter is varied. Here, we focus on the complicated dynamics that occur in a generalised unstable thin-film equation that yields finite-time rupture. A… read more about this publication »
We study the one‐dimensional KPZ equation on a large torus, started at equilibrium. The main results are optimal variance bounds in the super‐relaxation regime and part of the relaxation regime. read more about this publication »
Learning to differentiate model distributions from observed data is a fundamental problem in statistics and machine learning, and high-dimensional data remains a challenging setting for such problems. Metrics that quantify the disparity in probability distributions, such as the Stein discrepancy,… read more about this publication »
We provide a refined explicit estimate of the exponential decay rate of underdamped Langevin dynamics in the L2 distance, based on a framework developed in Albritton et al. (Variational methods for the kinetic Fokker–Planck equation, arXiv arXiv:1902.04037 , 2019). To achieve this, we first prove a… read more about this publication »
This paper proposes a novel kernel-based optimization scheme to handle tasks in the analysis, e.g., signal spectral estimation and single-channel source separation of 1D non-stationary oscillatory data. The key insight of our optimization scheme for reconstructing the time-frequency information is… read more about this publication »
We consider a stochastic conservation law on the line with solution-dependent diffusivity, a super-linear, sub-quadratic Hamiltonian, and smooth, spatially-homogeneous kick-type random forcing. We show that this Markov process admits a unique ergodic spatially-homogeneous invariant measure for each… read more about this publication »
We introduce a family of stochastic models motivated by the study of nonequilibrium steady states of fluid equations. These models decompose the deterministic dynamics of interest into fundamental building blocks, i.e., minimal vector fields preserving some fundamental aspects of the original… read more about this publication »