相关论文: Theoretical analysis of a discrete population bala…
In this study, we describe different modeling approaches for ovarian follicle population dynamics, based on either ordinary (ODE), partial (PDE) or stochastic (SDE) differential equations, and accounting for interactions between follicles.…
We present a self-contained investigation on the local and global well-posedness for a system of nonlocal advection--diffusion equations for a heterogeneous population over $\mathbb{R}^d$, $d \in \mathbb{N}$. Each convolution kernel…
Statistical machine learning plays an important role in modern statistics and computer science. One main goal of statistical machine learning is to provide universally consistent algorithms, i.e., the estimator converges in probability or…
This article is concerned with the mathematical analysis of the perturbation method for extended Kohn-Sham models, in which fractional occupation numbers are allowed. All our results are established in the framework of the reduced…
This work is devoted to studying the dynamics of a structured population that is subject to the combined effects of environmental stochasticity, competition for resources, spatio-temporal heterogeneity and dispersal. The population is…
Optimal transport (OT) defines a powerful framework to compare probability distributions in a geometrically faithful way. However, the practical impact of OT is still limited because of its computational burden. We propose a new class of…
In this article, discrete and stochastic changes in (effective) population size are incorporated into the spectral representation of a biallelic diffusion process for drift and small mutation rates. A forward algorithm inspired by…
A class of models of biological population and communities with a singular equilibrium at the origin is analyzed; it is shown that these models can possess a dynamical regime of deterministic extinction, which is crucially important from…
In this paper, we introduce the convergence analysis of the fixed pivot technique given by S.Kumar and Ramkrishna \cite{Kumar:1996-1} for the nonlinear aggregation population balance equations which are of substantial interest in many areas…
We study reproducing kernels, and associated reproducing kernel Hilbert spaces (RKHSs) $\mathscr{H}$ over infinite, discrete and countable sets $V$. In this setting we analyze in detail the distributions of the corresponding Dirac…
The Cahn-Hilliard equation has a wide range of applications in many areas of physics and chemistry. To describe the short-range interaction between the solution and the boundary, scientists have constructed dynamical boundary conditions by…
We analyze a differential equation with a state-dependent delay that is implicitly defined via the solution of an ODE. The equation describes an established though little analyzed cell population model. Based on theoretical results of…
A class of parabolic cross-diffusion systems modeling the interaction of an arbitrary number of population species is analyzed in a bounded domain with no-flux boundary conditions. The equations are formally derived from a random-walk…
The Schelling model of segregation looks to explain the way in which a population of agents or particles of two types may come to organise itself into large homogeneous clusters, and can be seen as a variant of the Ising model in which the…
The conserved Kuramoto-Sivashinsky (CKS) equation, u_t = -(u+u_xx+u_x^2)_xx, has recently been derived in the context of crystal growth, and it is also strictly related to a similar equation appearing, e.g., in sand-ripple dynamics. We show…
This article is devoted to a generalized version of Smoluchowski's coagulation equation. This model describes the time evolution of a system of aggregating particles under the effect of external input and output particles. We show that for…
We investigate one-dimensional scalar balance laws with singular convolution-type source terms. Under appropriate convexity and kernel assumptions, we establish the global existence of entropy weak solutions in ${\bf L}^2(\mathbb{R})$,…
For the class of stochastic partial differential equations studied in [Conus-Dalang,2008], we prove the existence of density of the probability law of the solution at a given point $(t,x)$, and that the density belongs to some Besov space.…
The notion of reproducing kernel Hilbert space (RKHS) has emerged in system identification during the past decade. In the resulting framework, the impulse response estimation problem is formulated as a regularized optimization defined on an…
We demonstrate an approach to solving the coagulation equation that involves using a finite number of moments of the particle size distribution. This approach is particularly useful when only general properties of the distribution, and…