Related papers: A method for testing the cosmic homogeneity with S…
This paper presents a systematic literature review focusing on the application of machine learning techniques for deriving observational constraints in cosmology. The goal is to evaluate and synthesize existing research to identify…
As an alternative to dark energy it has been suggested that we may be at the center of an inhomogeneous isotropic universe described by a Lemaitre-Tolman-Bondi (LTB) solution of Einstein's field equations. In order to test this hypothesis…
We propose a compression-based version of the empirical entropy of a finite string over a finite alphabet. Whereas previously one considers the naked entropy of (possibly higher order) Markov processes, we consider the sum of the…
We propose a new model-independent method to test the cosmic curvature by comparing the proper distance and transverse comoving distance. Using the measurements of Hubble parameter $H(z)$ and angular diameter distance $d_A$, the cosmic…
Global weak solutions to a chemotaxis model with local sensing and consumption are shown to converge to spatially homogeneous steady states in the large time limit, when the motility is assumed to be positive and $C^1$-smooth on…
For studies in reliability, biometry, and survival analysis, the length-biased distribution is often well-suited for certain natural sampling plans. In this paper, we study the strong uniform consistency of two nonparametric estimators for…
A wide variety of real random composites can be studied by means of prototypes of multiphase microstructures with a controllable spatial inhomogeneity. To create them, we propose a versatile model of randomly overlapping super-spheres of a…
We consider inference problems for high-dimensional (HD) functional data with a dense number (T) of repeated measurements taken for a large number of p variables from a small number of n experimental units. The spatial and temporal…
The purpose of the present work is based on two main observations: the tensions encountered by the standard $\Lambda$CDM model when confronted to precision small scale cosmological data and the finding that the matter distribution and the…
Many problems in materials science and biology involve particles interacting with strong, short-ranged bonds, that can break and form on experimental timescales. Treating such bonds as constraints can significantly speed up sampling their…
Standard cosmology is based on the assumption that the universe is spatially homogeneous. However the consensus on a homogeneous matter structure, even on very large scales, has never been complete. The advantage of correlation dimension…
A massive dataset often consists of a growing number of (potentially) heterogeneous sub-populations. This paper is concerned about testing various forms of heterogeneity arising from massive data. In a general nonparametric framework, a set…
The behavior of the Kozachenko - Leonenko estimates for the (differential) Shannon entropy is studied when the number of i.i.d. vector-valued observations tends to infinity. The asymptotic unbiasedness and L^2-consistency of the estimates…
We investigate the possibility of generating initial conditions for cosmological N-body simulations by simulating a system whose correlations at thermal equilibrium approximate well those of cosmological density perturbations. The system is…
Restricted path integral Monte Carlo simulations are used to calculate the equilibrium properties of hydrogen in the density and temperature range of $9.83 \times 10^{-4}\rm \leq \rho \leq 0.153 \rm gcm^{-3}$ and $5000 \leq T \leq 250 000…
The paper analyzes the probability distribution of the occupancy numbers and the entropy of a system at the equilibrium composed by an arbitrary number of non-interacting bosons. The probability distribution is derived both by tracing out…
Mouse-tracking of computer system users represents a less expensive, but also a far more applicable alternative to eye-tracking. The main disadvantage of mouse-tracking are errors manifested as discrepancies between the actual eye-gaze…
In statistical modeling of computer experiments sometimes prior information is available about the underlying function. For example, the physical system simulated by the computer code may be known to be monotone with respect to some or all…
We introduce a novel entropy-related function, \textit{non-repeatability}, designed to capture dynamical behaviors in complex systems. Its normalized form, \textit{mutability}, has been previously applied in statistical physics as a…
Convergence properties of Shannon Entropy are studied. In the differential setting, it is shown that weak convergence of probability measures, or convergence in distribution, is not enough for convergence of the associated differential…