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 »
In this paper, we study the localization length of the continuum directed polymer, defined as the distance between the endpoints of two paths sampled independently from the quenched polymer measure. We show that the localization length converges in distribution in the thermodynamic limit, and… read more about this publication »
Alloreactivity can drive autoimmune syndromes. After allogeneic hematopoietic stem cell transplantation (allo-HCT), chronic graft-versus-host disease (cGVHD), a B cell-associated autoimmune-like syndrome, commonly occurs. Because donor-derived B cells continually develop under selective pressure… read more about this publication »
BACKGROUND: Due to intrinsic differences in data formatting, data structure, and underlying semantic information, the integration of imaging data with clinical data can be non-trivial. Optimal integration requires robust data fusion, that is, the process of integrating multiple data sources to… read more about this publication »
It is well known that vortex patches are wellposed in C1,α if 0 < α< 1 . In this paper, we prove the illposedness of C2 vortex patches. The setup is to consider the vortex patches in Sobolev spaces W2,p where the curvature of the boundary is Lp integrable. In this setting, we show the… read more about this publication »
The true sensitivity of a cancer screening test, defined as the frequency with which the test returns a positive result if the cancer is present, is a key indicator of diagnostic performance. Given the challenges of directly assessing test sensitivity in a prospective screening program, proxy… read more about this publication »
In 1980 Carleson posed a question on the minimal regularity of an initial data function in a Sobolev space that implies pointwise convergence for the solution of the linear Schrödinger equation. After progress by many authors, this was recently resolved (up to the endpoint) by Bourgain, whose… read more about this publication »
We use bordered Floer theory to study properties of twisted Mazur pattern satellite knots Qn(K). We prove that Qn(K) is not Floer homologically thin, with two exceptions. We calculate the 3-genus of Qn(K) in terms of the twisting parameter n and the 3-genus of the companion K, and we determine when… read more about this publication »
We give a new proof of a recent resolution [18] by Michelen and Sahasrabudhe of a conjecture of Shepp and Vanderbei [19] that the moduli of roots of Gaussian Kac polynomials of degree $n$, centered at $1$ and rescaled by $n^2$, should form a Poisson point process. We use this new approach to verify… read more about this publication »
Background Guidelines recommend annual surveillance imaging after diagnosis of ductal carcinoma in situ (DCIS). Guideline adherence has not been characterized in a contemporary cohort. Purpose To identify uptake and determinants of surveillance imaging in women who underwent treatment for DCIS.… read more about this publication »
In this paper, we consider patch solutions to the α-SQG equation and derive new criteria for the absence of splash singularity where different patches or parts of the same patch collide in finite time. Our criterion refines a result due to Gancedo and Strain Gancedo and Strain (2014), providing a… read more about this publication »
We equate various Euler classes of algebraic vector bundles, including those of [12] and one suggested by M. J. Hopkins, A. Raksit, and J.-P. Serre. We establish integrality results for this Euler class and give formulas for local indices at isolated zeros, both in terms of the six-functors… read more about this publication »
In this paper, we propose a tumor growth model to incorporate and investigate the spatial effects of autophagy. The cells are classified into two phases: normal cells and autophagic cells, whose dynamics are also coupled with the nutrients. First, we construct a reaction-(cross-)diffusion system… read more about this publication »
We exhibit a non-hyperelliptic curve C of genus 3 such that the class of the Ceresa cycle [C]-[C-] in JC modulo algebraic equivalence is torsion. read more about this publication »
We consider the porous medium equation subject to zero-Dirichlet conditions on a variety of two-dimensional domains, namely strips, slender domains and sectors, allowing us to capture a number of different classes of behaviours. Our focus is on intermediate-asymptotic descriptions, derived by… read more about this publication »
We present a data-driven point of view for rare events, which represent conformational transitions in biochemical reactions modeled by overdamped Langevin dynamics on manifolds in high dimensions. We first reinterpret the transition state theory and the transition path theory from the optimal… read more about this publication »