Related papers: An algorithm for series expansions based on hierar…

The aggregation of particles in the free molecular regime is determined approximately for situations with a high degree of translational energy equilibration. The mean particle sizes develop linearly in time. Scaling relations are used to…

This paper develops a general asymptotic theory of series estimators for spatial data collected at irregularly spaced locations within a sampling region $R_n \subset \mathbb{R}^d$. We employ a stochastic sampling design that can flexibly…

In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…

In this paper we present a method to generate independent samples for a general random variable, either continuous or discrete. The algorithm is an extension of the acceptance-rejection method, and it is particularly useful for kinetic…

We propose a new algorithm for classical statistical simulations in scalar and gauge theories undergoing a one dimensional expansion, which allows simulations to study boxes of larger transverse extent and to continue for longer times,…

This paper considers approximate smoothing for discretely observed non-linear stochastic differential equations. The problem is tackled by developing methods for linearising stochastic differential equations with respect to an arbitrary…

In this short note, we discuss the basic approach to computational modeling of dynamical systems. If a dynamical system contains multiple time scales, ranging from very fast to slow, computational solution of the dynamical system can be…

In applications of nonlinear and complex dynamical systems, a common situation is that the system can be measured but its structure and the detailed rules of dynamical evolution are unknown. The inverse problem is to determine the system…

We develop a novel algorithm for feature extraction in time series data by leveraging tools from topological data analysis. Our algorithm provides a simple, efficient way to successfully harness topological features of the attractor of the…

We present an algorithm for finding the probabilities of rare events in nonequilibrium processes. The algorithm consists of evolving the system with a modified dynamics for which the required event occurs more frequently. By keeping track…

We develop a classical microscopic model of a dielectric. The model features nonlinear interaction terms between polarizable dipoles and lattice vibrations. The lattice vibrations are found to act as a pseudo-reservoir, giving broadband…

For a two-dimensional quantum mechanical problem, we obtain a generalized power-series expansion of the S-matrix that can be done near an arbitrary point on the Riemann surface of the energy, similarly to the standard effective range…

Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…

We develop and implement new probabilistic strategy for proving basic results about long time behaviour for interacting diffusion processes on unbounded lattice. The concept of the solution used is rather weak as we construct the process as…

We show that by means of connected-graph expansions one can effectively generate exact high-order series expansions which are informative of low-lying excited states for quantum many-body systems defined on a lattice. In particular, the…

In this paper we extend the hierarchical model reduction framework based on reduced basis techniques for the application to nonlinear partial differential equations. The major new ingredient to accomplish this goal is the introduction of…

Lattice Green functions appear in lattice gauge theories, in lattice models of statistical physics and in random walks. Here, space coordinates are treated as parameters and series expansions in the mass are obtained. The singular points in…

We propose a dynamical mechanism for a scale dependent error growth rate, by the introduction of a class of hierarchical models. The coupling of time scales and length scales is motivated by atmospheric dynamics. This model class can be…

Modern applications have made ubiquitous high-dimensional data, especially time-dependent data, with more and more complicated structures, and it also has become more frequent to encounter the scenario of hierarchical relationships among…

Gradient algorithms are classical in adaptive control and parameter estimation. For instantaneous quadratic cost functions they lead to a linear time-varying dynamic system that converges exponentially under persistence of excitation…