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In this paper, we prove a Talagrand's T2 transportation cost-information inequality for the law of a stochastic wave equation in spatial dimension d=3 driven by the Gaussian random field, white in time and correlated in space, on the…
This paper studies the traffic state estimation (TSE) problem using sparse observations from mobile sensors. Most existing TSE methods either rely on well-defined physical traffic flow models or require large amounts of simulation data as…
Tensor train (TT) representation has achieved tremendous success in visual data completion tasks, especially when it is combined with tensor folding. However, folding an image or video tensor breaks the original data structure, leading to…
Higher-order data with high dimensionality arise in a diverse set of application areas such as computer vision, video analytics and medical imaging. Tensors provide a natural tool for representing these types of data. Although there has…
In recent years, the application of tensors has become more widespread in fields that involve data analytics and numerical computation. Due to the explosive growth of data, low-rank tensor decompositions have become a powerful tool to…
In this paper, we present an efficient fully spectral approximation scheme for exploring the one-dimensional steady-state neutron transport equation. Our methodology integrates the spectral-(Petrov-)Galerkin scheme in the spatial dimension…
Routing problems are optimization problems that consider a set of goals in a graph to be visited by a vehicle (or a fleet of them) in an optimal way, while numerous constraints have to be satisfied. We present a solution based on…
We present version 2 of the DRAGON code designed for computing realistic predictions of the CR densities in the Galaxy. The code numerically solves the interstellar CR transport equation (including inhomogeneous and anisotropic diffusion,…
We consider the transport equation on $[0,T]\times \mathbb{R}^n$ in the situation where the vector field is $BV$ off a set $S\subset [0,T]\times \mathbb{R}^n$. We demonstrate that solutions exist and are unique provided that the set of…
The problem of non-linear transport near a quantum phase transition is solved within the Landau theory for the dissipative insulator-superconductor phase transition in two dimensions. Using the non-equilibrium Schwinger round-trip Green…
In optimal transport, quadratic regularization is an alternative to entropic regularization when sparse couplings or small regularization parameters are desired. Quadratic regularization penalizes transport couplings by the squared $L^2$…
Sparsity and missing data problems are very common in spatiotemporal traffic data collected from various sensing systems. Making accurate imputation is critical to many applications in intelligent transportation systems. In this paper, we…
The (4,4) null superstring equations of motions and constraints on de Sitter space are given by using the harmonic superspace. These are solved explicitly by performing a perturbative expansion of the (4,4) superstring coordinates in powers…
We discuss transport equations resulting from relativistic diffusions in the proper time. We show that a solution of the transport equation can be obtained from the solution of the diffusion equation by means of an integration over the…
Following seminal work in the early 1980s that established the existence and representations of the homogenized transport coefficients for two phase random media, we develop a mathematical framework that provides Stieltjes integral…
This paper proposes a novel formulation of the tensor completion problem to impute missing entries of data represented by tensors. The formulation is introduced in terms of tensor train (TT) rank which can effectively capture global…
Tensor networks, particularly the tensor train (TT) format, have emerged as powerful tools for high-dimensional computations in physics and computer science. In solving coupled differential equations, such as those arising from stochastic…
Disordered systems have grown in importance in the past decades, with similar phenomena manifesting themselves in many different physical systems. Because of the difficulty of the topic, theoretical progress has mostly emerged from…
The dynamics of a tracer particle in a glassy matrix of obstacles displays slow complex transport as the free volume approaches a critical value and the void space falls apart. We investigate the emerging subdiffusive motion of the test…
Tensor train is a hierarchical tensor network structure that helps alleviate the curse of dimensionality by parameterizing large-scale multidimensional data via a set of network of low-rank tensors. Associated with such a construction is a…