相关论文: Discrete fragmentation systems in weighted $\ell^1…
The Cauchy problem for a scalar conservation laws admits a unique entropy solution when the data $u_0$ is a bounded measurable function (Kruzhkov). The semi-group $(S_t)_{t\ge0}$ is contracting in the $L^1$-distance. For the…
The Bayesian approach to inference stands out for naturally allowing borrowing information across heterogeneous populations, with different samples possibly sharing the same distribution. A popular Bayesian nonparametric model for…
Inspired by rational canonical forms, we introduce and analyze two decompositions of dynamic programming (DP) problems for systems with linear dynamics. Specifically, we consider both finite and infinite horizon DP problems in which the…
The Cluster Variation Method known in statistical mechanics and condensed matter is revived for weighted bipartite networks. The decomposition of a Hamiltonian through a finite number of components, whence serving to define variable…
Our focus is on the fast diffusion equation driven by the $p$-Laplacian operator, that is $\partial_t u=\Delta_p u$ with $1<p<2$, posed in the whole space $\mathbb{R}^N$, $N\geq 2$. The nonnegative solutions are expected to converge in time…
Numerical methods of approximate solution of the Cauchy problem for coupled systems of evolution equations are considered. Separating simpler subproblems for individual components of the solution achieves simplification of the problem at a…
A simple model of ballistic aggregation and fragmentation is proposed. The model is characterized by two energy thresholds, Eagg and Efrag, which demarcate different types of impacts: If the kinetic energy of the relative motion of a…
We extend the single-site coherent potential approximation (CPA) to include the effects of non-local disorder correlations (alloy short-range order) on the electronic structure of random alloy systems. This is achieved by mapping the…
In this paper, we provide a systematic way of finding explicit solutions for a class of continuous fragmentation equations with growth or decay in the state space and derive explicit solutions in the cases of constant and linear…
We develop an unconditionally energy-stable tensor-product space-time discretization framework for the solution of a linear kinetic transport equation in one space dimension. The kinetic equation is a simplified model of radiative transfer…
We study classical asymmetric binary perceptron (ABP) and associated \emph{local entropy} (LE) as potential source of its algorithmic hardness. Isolation of \emph{typical} ABP solutions in SAT phase seemingly suggests a universal…
Given the ubiquity of non-separable optimization problems in real worlds, in this paper we analyze and extend the large-scale version of the well-known cooperative coevolution (CC), a divide-and-conquer black-box optimization framework, on…
We study a linear-quadratic optimal control problem involving a parabolic equation with fractional diffusion and Caputo fractional time derivative of orders $s \in (0,1)$ and $\gamma \in (0,1]$, respectively. The spatial fractional…
We study the problem of clustering sequences of unlabeled point sets taken from a common metric space. Such scenarios arise naturally in applications where a system or process is observed in distinct time intervals, such as biological…
The solution space of many classical optimization problems breaks up into clusters which are extensively distant from one another in the Hamming metric. Here, we show that an analogous quantum clustering phenomenon takes place in the ground…
A computational theory for clustering and a semi-supervised clustering algorithm is presented. Clustering is defined to be the obtainment of groupings of data such that each group contains no anomalies with respect to a chosen grouping…
We investigate the well-posedness of the fast diffusion equation (FDE) in a wide class of noncompact Riemannian manifolds. Existence and uniqueness of solutions for globally integrable initial data was established in [5]. However, in the…
In this paper we prove the existence of global classical solutions to continuous coagulation-fragmentation equations with unbounded coefficients under the sole assumption that the coagulation rate is dominated by a power of the…
We report surprising steady oscillations in aggregation-fragmentation processes. Oscillating solutions are observed for the class of aggregation kernels $K_{i,j} = i^{\nu}j^{\mu} + j^{\nu}i^{\mu}$ homogeneous in masses $i$ and $j$ of…
We consider the entanglement marginal problem, which consists of deciding whether a number of reduced density matrices are compatible with an overall separable quantum state. To tackle this problem, we propose hierarchies of semidefinite…