相关论文: Numerical Simulation of Non-Gaussian Random Fields…

The definition and the properties of a Gaussian point distribution, in contrast to the well-known properties of a Gaussian random field are discussed. Constraints for the number density and the two-point correlation function arise. A simple…

The growing field of large-scale time domain astronomy requires methods for probabilistic data analysis that are computationally tractable, even with large datasets. Gaussian Processes are a popular class of models used for this purpose…

We propose efficient classical algorithms which (strongly) simulate the action of bosonic linear optics circuits applied to superpositions of Gaussian states. Our approach relies on an augmented covariance matrix formalism to keep track of…

We present some nonparametric methods for graphical modeling. In the discrete case, where the data are binary or drawn from a finite alphabet, Markov random fields are already essentially nonparametric, since the cliques can take only a…

As a statistical measure to quantify the topological structure of the large-scale structure in the universe, the genus number is calculated for a number of non-Gaussian distributions in which the density field is characterized by a…

The dynamic emulation of non-linear deterministic computer codes where the output is a time series, possibly multivariate, is examined. Such computer models simulate the evolution of some real-world phenomenon over time, for example models…

Random fields are useful mathematical tools for representing natural phenomena with complex dependence structures in space and/or time. In particular, the Gaussian random field is commonly used due to its attractive properties and…

In this work we present a model for computation of random processes in digital computers which solves the problem of periodic sequences and hidden errors produced by correlations. We show that systems with non-invertible non-linearities can…

We consider Gaussian quantum circuits supplemented with non-Gaussian input states and derive sufficient conditions for efficient classical strong simulation of these circuits. In particular, we generalise the stellar representation of…

This paper covers some of the current techniques and issues involved in performing numerical simulations of the formation of singularities.

We propose a new method to numerically calculate higher-order correlation functions of primordial fluctuations generated from any early-universe scenario. Our key-starting point is the realization that the tree-level In-In formalism is…

We compute probabilistic controlled invariant sets for nonlinear systems using Gaussian process state space models, which are data-driven models that account for unmodeled and unknown nonlinear dynamics. We propose a semidefinite…

We report a technique to calculate the impact of distinct physical processes inducing non-Gaussianity on the cosmological density field. A natural decomposition of the cosmic genus statistic into an orthogonal polynomial sequence allows…

Given a Gaussian Markov random field, we consider the problem of selecting a subset of variables to observe which minimizes the total expected squared prediction error of the unobserved variables. We first show that finding an exact…

Established techniques for simulation and prediction with Gaussian process (GP) dynamics often implicitly make use of an independence assumption on successive function evaluations of the dynamics model. This can result in significant error…

This paper presents a new framework for oriented texture modeling. We introduce a new class of Gaussian fields, called Locally Anisotropic Fractional Brownian Fields, with prescribed local orientation at any point. These fields are a local…

As a complementary tool to laboratory experiments, discrete numerical simulation, applied to granular materials, provides valuable information on the grain and contact scale microstructure, thereby enabling one to better understand the…

All discretized numerical models contain modelling errors - this reality is amplified when reduced-order models are used. The ability to accurately approximate modelling errors informs statistics on model confidence and improves…

In the present paper we are concerned with a numerical algorithm for the approximation of the two-dimensional neural field equation with delay. We consider three numerical examples that have been analysed before by other authors and are…

Numerical simulations of the evolution of a global topological defect field have two characteristic length scales --- one macrophysical, of order the field correlation length, and the other microphysical, of order the field width. The…