Related papers: Statistical Topology and the Random Interstellar M…
In this paper, we show how to use the framework of mod-Gaussian convergence in order to study the fluctuations of certain models of random graphs, of random permutations and of random integer partitions. We prove that, in these three…
Using very long baseline interferometry data for the sources that comprise the third International Celestial Reference Frame (ICRF3), we examine the quality of the formal source position uncertainties of ICRF3 by determining the excess…
The article studies non-Gaussian extensions of a recently discovered link between certain Gaussian random fields, expressed as solutions to stochastic partial differential equations (SPDEs), and Gaussian Markov random fields. The focus is…
Autonomous robots are increasingly deployed to estimate spatiotemporal fields (e.g., wind, temperature, gas concentration) that vary across space and time. We consider environments divided into non-overlapping regions with distinct spatial…
We present a class of diffusion-based algorithms to draw samples from high-dimensional probability distributions given their unnormalized densities. Ideally, our methods can transport samples from a Gaussian distribution to a specified…
Three dimensional topological field theories associated with the three dimensional version of Abelian and non-Abelian Seiberg-Witten monopoles are presented. These three dimensional monopole equations are obtained by a dimensional reduction…
The spatial averaging used for the splitting of the local scale factor on the homogeneous background and small inhomogeneous perturbation leads to a non-local relationship between locally and globally defined comoving curvature…
Three methods for detecting and characterizing structure in point data, such as that generated by redshift surveys, are described: classification using self-organizing maps, segmentation using Bayesian blocks, and density estimation using…
We propose a new test for distinguishing observationally cosmological models based on seed-like primordial perturbations (like cosmic strings or textures), from models based on Gaussian fluctuations. We investigate analytically the {\it…
We present a generic algorithm for generating Gaussian random initial conditions for cosmological simulations on periodic rectangular lattices. We show that imposing periodic boundary conditions on the real-space correlator and choosing…
Universe models with compact spatial sections smaller than the observable universe produce a topological lens effect. Given a catalog of cosmic sources, we estimate the number of topological images in locally hyperbolic and locally elliptic…
A stationary spatial model is an idealization and we expect that the true dependence structures of physical phenomena are spatially varying, but how should we handle this non-stationarity in practice? We study the challenges involved in…
A number of recent studies have estimated the inter-galactic void probability function and investigated its departure from various random models. We study a family of parametric statistical models based on gamma distributions, which do give…
Obtaining high-resolution maps of precipitation data can provide key insights to stakeholders to assess a sustainable access to water resources at urban scale. Mapping a nonstationary, sparse process such as precipitation at very high…
We study Spatial Logistic Gaussian Process (SLGP) models for non-parametric estimation of probability density fields using scattered samples of heterogeneous sizes. SLGPs are examined from the perspective of random measures and their…
Gaussian graphical models, where it is assumed that the variables of interest jointly follow a multivariate normal distribution with a sparse precision matrix, have been used to study intrinsic dependence among variables, but the normality…
Reliable prediction of large chaotic sytems in the short to middle time range is of interest in a number of fields, including climate, ecology, seismology, and economics. In this paper, results from chaos theory, and statistical theory are…
Persistent homology probes topological properties from point clouds and functions. By looking at multiple scales simultaneously, one can record the births and deaths of topological features as the scale varies. In this paper we use a…
Scalar perturbations of Friedmann-Lemaitre cosmologies can be analyzed in a variety of ways using Einstein's field equations, the Ricci and Bianchi identities, or the conservation equations for the stress-energy tensor, and possibly…
Non-Gaussian shapes, despite a linear form of the mean-squared displacement, have been observed for the displacement distribution in a large range of diffusive systems. Stochastic models for such "Brownian yet non-Gaussian" diffusion will…