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In this paper we consider kinetic and associated macroscopic models for chemotaxis on a network. Coupling conditions at the nodes of the network for the kinetic problem are presented and used to derive coupling conditions for the…

Analysis of PDEs · Mathematics 2015-12-29 Raul Borsche , Axel Klar , Ha T. N. Pham

Change-point models are widely used by statisticians to model drastic changes in the pattern of observed data. Least squares/maximum likelihood based estimation of change-points leads to curious asymptotic phenomena. When the change-point…

Statistics Theory · Mathematics 2015-10-20 Rui Song , Moulinath Banerjee , Michael R. Kosorok

We consider a system of two coupled parabolic PDEs introduced in [1] to model motility of eukaryotic cells. We study the asymptotic behavior of solutions in the limit of a small parameter related to the width of the interface in phase field…

Analysis of PDEs · Mathematics 2016-02-05 Leonid Berlyand , Mykhailo Potomkin , Volodymyr Rybalko

Reliability evaluation and fault tolerance of an interconnection network of some parallel and distributed systems are discussed separately under various link-faulty hypotheses in terms of different $\mathcal{P}$-conditional…

Combinatorics · Mathematics 2022-03-25 Mingzu Zhang , Zhaoxia Tian , Lianzhu Zhang

These lecture notes represent supplementary material for a short course on time series econometrics and network econometrics. We give emphasis on limit theory for time series regression models as well as the use of the local-to-unity…

Econometrics · Economics 2023-08-15 Christis Katsouris

We model the Knudsen layer in Kramers' problem by linearized high order hyperbolic moment system. Due to the hyperbolicity, the boundary conditions of the moment system is properly reduced from the kinetic boundary condition. For Kramers'…

Numerical Analysis · Mathematics 2017-04-20 Yuwei Fan , Jun Li , Ruo Li , Zhonghua Qiao

In this work, we prove rigorous convergence properties for a semi-discrete, moment-based approximation of a model kinetic equation in one dimension. This approximation is equivalent to a standard spectral method in the velocity variable of…

Numerical Analysis · Mathematics 2017-12-25 Zheng Chen , Cory D. Hauck

We investigate various versions of multi-dimensional systems involving many species, modeling aggregation phenomena through nonlocal interaction terms. We establish a rigorous connection between kinetic and macroscopic descriptions by…

Analysis of PDEs · Mathematics 2024-02-06 Young-Pil Choi , Simone Fagioli , Valeria Iorio

We study the full class of kinetically constrained models in arbitrary dimension and out of equilibrium, in the regime where the density $q$ of facilitating sites in the equilibrium measure (but not necessarily in the initial measure) is…

Probability · Mathematics 2024-05-29 Ivailo Hartarsky , Fabio Toninelli

We determine the large size limit of a network of interacting Hawkes Processes on an adaptive network. The flipping of the node variables is taken to have an intensity given by the mean-field of the afferent edges and nodes. The flipping of…

Probability · Mathematics 2024-11-15 James MacLaurin

In cosmology an important role is played by homogeneous and isotropic solutions of the Einstein-Euler equations and linearized perturbations of these. This paper proves results on the asymptotic behaviour of scalar perturbations both in the…

Analysis of PDEs · Mathematics 2009-06-16 Paul T. Allen , Alan D. Rendall

A main challenge in numerical simulations of moving contact line problems is that the adherence, or no-slip boundary condition leads to a non-integrable stress singularity at the contact line. In this report we perform the first steps in…

Fluid Dynamics · Physics 2015-10-23 Hanna Holmgren , Gunilla Kreiss

We provide an asymptotic expansion of the value function of a multidimensional utility maximization problem from consumption with small non-linear price impact. In our model cross-impacts between assets are allowed. In the limit for small…

Analysis of PDEs · Mathematics 2020-06-25 Erhan Bayraktar , Thomas Caye , Ibrahim Ekren

The coefficients of elastic and dissipative operators in a linear hyperbolic SPDE are jointly estimated using multiple spatially localised measurements. As the resolution level of the observations tends to zero, we establish the asymptotic…

Statistics Theory · Mathematics 2025-02-24 Anton Tiepner , Eric Ziebell

We study a high-dimensional generalized linear model and penalized empirical risk minimization with $\ell_1$ penalty. Our aim is to provide a non-trivial illustration that non-asymptotic bounds for the estimator can be obtained without…

Statistics Theory · Mathematics 2007-09-12 Sara A. van de Geer

We prove the well posedness of a class of non linear and non local mixed hyperbolic-parabolic systems in bounded domains, with Dirichlet boundary conditions. In view of control problems, stability estimates on the dependence of solutions on…

Analysis of PDEs · Mathematics 2023-09-13 Rinaldo M. Colombo , Elena Rossi

We are interested in numerical schemes for the simulation of large scale gas networks. Typical models are based on the isentropic Euler equations with realistic gas constant. The numerical scheme is based on transformation of conservative…

Numerical Analysis · Mathematics 2020-05-26 Sara Grundel , Michael Herty

In this paper we consider the hyperbolic formulation of the constraints introduced by R\'acz. Using the numerical framework recently developed by us we construct initial data sets which can be interpreted as nonlinear perturbations of…

General Relativity and Quantum Cosmology · Physics 2017-10-02 Florian Beyer , Leon Escobar , Jörg Frauendiener

We propose an optimistic estimate to evaluate the best possible fitting performance of nonlinear models. It yields an optimistic sample size that quantifies the smallest possible sample size to fit/recover a target function using a…

Machine Learning · Computer Science 2023-07-19 Yaoyu Zhang , Zhongwang Zhang , Leyang Zhang , Zhiwei Bai , Tao Luo , Zhi-Qin John Xu

We consider networks for isentropic gas and prove existence of weak solutions for a large class of coupling conditions. First, we construct approximate solutions by a vector-valued BGK model with a kinetic coupling function. Introducing…

Analysis of PDEs · Mathematics 2020-04-21 Yannick Holle