Zobrazeno 1 - 10
of 112
pro vyhledávání: '"Jacobs, Matt"'
Motivated by recent work on approximation of diffusion equations by deterministic interacting particle systems, we develop a nonlocal approximation for a range of linear and nonlinear diffusion equations and prove convergence of the method in the slo
Externí odkaz:
http://arxiv.org/abs/2312.11438
Autor:
Elamvazhuthi, Karthik, Jacobs, Matt
We consider the optimal transport problem over convex costs arising from optimal control of linear time-invariant(LTI) systems when the initial and target measures are assumed to be supported on the set of equilibrium points of the LTI system. In thi
Externí odkaz:
http://arxiv.org/abs/2312.10197
In this paper, we study a tumor growth model where the growth is driven by nutrient availability and the tumor expands according to Darcy's law with a mechanical pressure resulting from the incompressibility of the cells. Our focus is on the free bou
Externí odkaz:
http://arxiv.org/abs/2309.05971
Autor:
Bungert, Leon, Trillos, Nicolás García, Jacobs, Matt, McKenzie, Daniel, Nikolić, Đorđe, Wang, Qingsong
Although deep neural networks have achieved super-human performance on many classification tasks, they often exhibit a worrying lack of robustness towards adversarially generated examples. Thus, considerable effort has been invested into reformulatin
Externí odkaz:
http://arxiv.org/abs/2305.18779
We study three models of the problem of adversarial training in multiclass classification designed to construct robust classifiers against adversarial perturbations of data in the agnostic-classifier setting. We prove the existence of Borel measurabl
Externí odkaz:
http://arxiv.org/abs/2305.00075
Autor:
Jacobs, Matt
In this paper, we construct global-in-time forward and backward Lagrangian flow maps along the pressure gradient generated by weak solutions of the Porous Media Equation. The main difficulty is that when the initial data has compact support, it is we
Externí odkaz:
http://arxiv.org/abs/2208.01792
We study a family of adversarial multiclass classification problems and provide equivalent reformulations in terms of: 1) a family of generalized barycenter problems introduced in the paper and 2) a family of multimarginal optimal transport problems
Externí odkaz:
http://arxiv.org/abs/2204.12676
In this paper we study a tumor growth model with nutrients. The model presents dynamic patch solutions due to the contact inhibition among the tumor cells. We show that when the nutrients do not diffuse and the cells do not die, the tumor density exh
Externí odkaz:
http://arxiv.org/abs/2204.07572
Autor:
Jacobs, Matt
Reaction cross diffusion systems are a two species generalization of the porous media equation. These systems play an important role in the mechanical modeling of living tissues and tumor growth. Due to their mixed parabolic-hyperbolic structure, eve
Externí odkaz:
http://arxiv.org/abs/2107.12412
One of the most important aims of grain boundary modeling is to predict the evolution of a large collection of grains in phenomena such as abnormal grain growth, coupled grain boundary motion, and recrystallization that occur under extreme thermomech
Externí odkaz:
http://arxiv.org/abs/2102.02773