Related papers: Comparison of continuity equation and Gaussian mix…
Gaussian distribution is commonly used as a good approximation to study the trapped one-component Bose-condensed atoms with relatively small nonlinear effect. It is not adequate in dealing with the one-component system of large nonlinear…
Graphical models are commonly used tools for modeling multivariate random variables. While there exist many convenient multivariate distributions such as Gaussian distribution for continuous data, mixed data with the presence of discrete…
Diffusion models have become a standard approach for generative modeling in continuous domains, yet their application to discrete data remains challenging. We investigate why Gaussian diffusion models with the DDPM solver struggle to sample…
With the aim of generalizing histogram statistics to higher dimensional cases, density estimation via discrepancy based sequential partition (DSP) has been proposed to learn an adaptive piecewise constant approximation defined on a binary…
Finite mixture such as the Gaussian mixture is a flexible and powerful probabilistic modeling tool for representing the multimodal distribution widely involved in many estimation and learning problems. The core of it is representing the…
We study the quasilinear evolution of the one-point probability density functions (PDFs) of the smoothed density and velocity fields in a cosmological gravitating system beginning with Gaussian initial fluctuations. Our analytic results are…
Clustering mixtures of Gaussian distributions is a fundamental and challenging problem that is ubiquitous in various high-dimensional data processing tasks. While state-of-the-art work on learning Gaussian mixture models has focused…
A method for the quantification of acoustophoretic separation and dispersion for microparticle populations featuring continuously distributed physical parameters is presented. The derivation of the method starts by (i)~considering the…
The entropy computation of Gaussian mixture distributions with a large number of components has a prohibitive computational complexity. In this paper, we propose a novel approach exploiting the sphere decoding concept to bound and…
Continuum dislocation dynamics (CDD) represents the evolution of systems of curved and connected dislocation lines in terms of density-like field variables which include the volume density of loops (or 'curvature density') as an additional…
This thesis investigates the evolution of galaxies in diverse environments, utilizing Sloan Digital Sky Survey (SDSS) data to explore the impact of environmental richness on central and satellite galaxies across stellar mass ranges,…
Considerable efforts have been devoted to statistical modeling and the characterization of channels in a range of statistical models for fading channels. In this paper, we consider a unified approach to model wireless channels by the…
The mass fraction of hot gas in clusters is a basic quantity whose level and dependence on the cluster mass and redshift are intimately linked to all cluster X-ray and SZ measures. Modeling the evolution of the gas fraction is clearly a…
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…
In this paper, we are interested in a generalised Vlasov equation, which describes the evolution of the probability density of a particle evolving according to a generalised Vlasov dynamic. The achievement of the paper is twofold. Firstly,…
Although the theory of density evolution in maps and ordinary differential equations is well developed, the situation is far from satisfactory in continuous time systems with delay. This paper reviews some of the work that has been done…
We study the dependence on configuration in momentum space of the primordial 3-point function of density perturbations in several different scenarios: standard slow-roll inflation, curvaton and variable decay models, ghost inflation, models…
Explaining the formation and evolution of galaxies is one of the most challenging problems in observational cosmology. Many observations suggest that galaxies we see today could have evolved from the merging of smaller subsystems. Evolution…
In this paper, we propose a nonparametric Bayesian approach for Lindsey and penalized Gaussian mixtures methods. We compare these methods with the Dirichlet process mixture model. Our approach is a Bayesian nonparametric method not based…
Heterogeneity in dynamics in the form of non-Gaussian molecular displacement distributions appears ubiquitously in soft matter. We address the quantification of such heterogeneity using an information-theoretic measure of the distance…