Related papers: Homogeneous and nonlinear generalized master equat…
Predictive linear and nonlinear models based on kernel machines or deep neural networks have been used to discover dependencies among time series. This paper proposes an efficient nonlinear modeling approach for multiple time series, with a…
Similarity-based approaches represent a promising direction for time series analysis. However, many such methods rely on parameter tuning, and some have shortcomings if the time series are multivariate (MTS), due to dependencies between…
We investigate the accuracy of the second-order time-convolutionless (TCL2) quantum master equation for the calculation of linear and nonlinear spectroscopies of multichromophore systems. We show that, even for systems with non-adiabatic…
Growth curve models are popular tools for studying the development of a response variable within subjects over time. Heterogeneity between subjects is common in such models, and researchers are typically interested in explaining or…
Traffic forecasting is one of the most fundamental problems in transportation science and artificial intelligence. The key challenge is to effectively model complex spatial-temporal dependencies and correlations in modern traffic data.…
The homogeneous Boltzmann equation for inelastic Maxwell mixtures is considered to study the dynamics of tracer particles or impurities (solvent) immersed in a uniform granular gas (solute). The analysis is based on exact results derived…
In many complex applications, data heterogeneity and homogeneity exist simultaneously. Ignoring either one will result in incorrect statistical inference. In addition, coping with complex data that are non-Euclidean becomes more common. To…
We introduce graph gamma process (GGP) linear dynamical systems to model real-valued multivariate time series. For temporal pattern discovery, the latent representation under the model is used to decompose the time series into a…
Consider learning a generative model for time-series data. The sequential setting poses a unique challenge: Not only should the generator capture the conditional dynamics of (stepwise) transitions, but its open-loop rollouts should also…
Mixed linear regression (MLR) has attracted increasing attention because of its great theoretical and practical importance in capturing nonlinear relationships by utilizing a mixture of linear regression sub-models. Although considerable…
In numerical relativity simulations with non-trivial matter configurations, one must solve the Hamiltonian and momentum constraints of the ADM formulation for the metric variables in the initial data. We introduce a new scheme based on the…
We develop a new tool, the time inhomogeneous Poisson equation in the whole space and with a terminal condition at infinity, to study the asymptotic behavior of the non-autonomous multi-scale stochastic system with irregular coefficients,…
Efficient sampling from the Boltzmann distribution given its energy function is a key challenge for modeling complex physical systems such as molecules. Boltzmann Generators address this problem by leveraging continuous normalizing flows to…
Biological systems are typically highly open, non-equilibrium systems that are very challenging to understand from a statistical mechanics perspective. While statistical treatments of evolutionary biological systems have a long and rich…
Non-homogeneous renewal processes are not yet well established. One of the tools necessary for studying these processes is the non-homogeneous time convolution. Renewal theory has great relevance in general in economics and in particular in…
In this note we study the convergence of monotone P1 finite element methods on unstructured meshes for fully non-linear Hamilton-Jacobi-Bellman equations arising from stochastic optimal control problems with possibly degenerate, isotropic…
In the framework of the ab-initio no-core shell model (NCSM), we describe the longitudinal-longitudinal distribution function, part of the inclusive (e,e') longitudinal response. In the two-body cluster approximation, we compute the…
This study proposes a high-order multi-scale method tailored for time-dependent nonlinear thermo-electro-mechanical coupling problems of composite structures with highly spatial heterogeneity, which incorporate temperature-dependent…
We introduce a notion of chain of evolution algebras. The sequence of matrices of the structural constants for this chain of evolution algebras satisfies an analogue of Chapman-Kolmogorov equation. We give several examples (time homogenous,…
We present a new strategy for learning the functional relation between a pair of variables, while addressing inhomogeneities in the correlation structure of the available data, by modelling the sought function as a sample function of a…