Related papers: Copula methods for modeling pair densities in dens…
A frequent task in exploratory data analysis consists in examining pairwise dependencies between data variables. Popular approaches include visualizing correlation or scatter plot matrices. However, both methods can be misleading. The…
Multivariate datasets are common in various real-world applications. Recently, copulas have received significant attention for modeling dependencies among random variables. A copula-based information measure is required to quantify the…
A random packing of hard particles represents a fundamental model for granular matter. Despite its importance, analytical modeling of random packings remains difficult due to the existence of strong correlations which preclude the…
A new method for constructing absolutely continuous two--dimensional copulas by differential equations is presented. The copulas are symmetric with respect to reflection in the opposite diagonal. The support of the copula density may be…
Copula-based modeling has seen rapid advances in recent years. However, in big data applications, the lengthy computation time for estimating copula parameters is a major difficulty. Here, we develop a novel method to speed computation time…
As an alternative to solving of Poisson equation in Particle-in-Cell methods, a new construction of current density exactly satisfying continuity equation in finite differences is developed. This procedure called density decomposition is…
This work is concerned with a simple model for a polar fluid, a Gaussian field model based on the excess density and on the polarization. It is a convenient framework to implement the dielectric properties of correlated liquids that stem…
Motivated by experiments on cell segregation, we present a two-species model of interacting particles, aiming at a quantitative description of this phenomenon. Under precise scaling hypothesis, we derive from the microscopic model a…
In order to quantify the error budget in the measured probability distribution functions of cell densities, the two-point statistics of cosmic densities in concentric spheres is investigated. Bias functions are introduced as the ratio of…
Non-Gaussianity of the cosmological matter density field can be largely reduced by a local Gaussianization transformation (and its approximations such as the logrithmic transformation). Such behavior can be recasted as the Gaussian copula…
The Sutherland approximation to the van der Waals forces is applied to the derivation of a self-consistent Vlasov-type field in a liquid filling a half space, bordering vacuum. The ensuing Vlasov equation is then derived, and solved to…
Fluids made of two-dimensional hard particles with polygonal shapes may stabilize symmetries which do not result directly from the particle shape. This is due to the formation of clusters in the fluid. Entropy alone can drive these effects,…
We present a simple density functional theory for the solid phases of systems of particles interacting via soft-core potentials. In particular, we apply the theory to particles interacting via repulsive point Yukawa and Gaussian pair…
We derive a unified stochastic picture for the duality of a resampling-selection model with a branching-coalescing particle process (cf. http://www.ams.org/mathscinet-getitem?mr=MR2123250) and for the self-duality of Feller's branching…
We define a general method for finding a quasi-best approximant in sup-norm to a target density belonging to a given model, based on independent samples drawn from distributions which average to the target (which does not necessarily belong…
We explicitly describe the possible pairs of triangle and square densities for r-regular finite simple graphs. We also prove that every r-regular unimodular random graph can be approximated by r-regular finite graphs with respect to these…
We propose the use of two point Pade approximants to find expressions valid uniformly in coupling constant for theories with both weak and strong coupling expansions. In particular, one can use these approximants in models with a…
Sklar's theorem is an important tool that connects bidimensional distribution functions with their marginals by means of a copula. When there is imprecision about the marginals, we can model the available information by means of p-boxes,…
Bayes spaces were initially designed to provide a geometric framework for the modeling and analysis of distributional data. It has recently come to light that this methodology can be exploited to provide an orthogonal decomposition of…
We study a classical system of identically charged counter-ions near a planar wall carrying a uniform surface charge density. The equilibrium statistical mechanics of the system depends on a single dimensionless coupling parameter. A new…