Related papers: Fermi-Dirac Statistics
The aim of this text is to provide a linguistically accessible, but comprehensive introduction into a variety of topics in dynamical systems and its applications. Whilst preliminary knowledge of dynamical systems is useful, it is not…
Statistical inference is the science of drawing conclusions about some system from data. In modern signal processing and machine learning, inference is done in very high dimension: very many unknown characteristics about the system have to…
Academic challenges comprise effective means for (i) advancing the state of the art, (ii) putting in the spotlight of a scientific community specific topics and problems, as well as (iii) closing the gap for under represented communities in…
In this talk I will describe the deep influence Planck had on the development of statistical mechanics. At this end I will first outline the theoretical situation of statistical mechanics before Planck. I will then describe his main…
These notes are based on a course for a general audience given at the Centro de Modeliamento Matem\'atico of the University of Chile, in December 2004. We study the mean convergence of multiple ergodic averages, that is, averages of a…
In this paper, the authors design a trial to count rational ratios on the interval [0, 1], and plot a normalized frequency statistical graph. Patterns, symmetry and co-linear properties reflected in the graph are confirmed. The main…
Statistics is one of the most valuable of disciplines. Science is based on proof and it alone produces results, other approaches are not, and do not. Statistics is the only acceptable language of proof in science. Yet statistics is…
This paper gives an introduction to some of the statistical physics problems which appear in the study of structural glasses. It is a shortened and updated version of a more detailed review paper which has appeared in cond-mat/0005173.
In our present investigation we propose to study and develop the I-function of two variables analogous to the I-function of one variable introduced and studied by one of the authors[24]. The conditions for convergence, series…
Data science is an emerging interdisciplinary field that combines elements of mathematics, statistics, computer science, and knowledge in a particular application domain for the purpose of extracting meaningful information from the…
The advent of artificial intelligence (AI) technologies has significantly changed many domains, including applied statistics. This review and vision paper explores the evolving role of applied statistics in the AI era, drawing from our…
The goal of this paper is to give some rigorous results, concerning high density behavior of Fermi systems.
In this short paper I consider relation between measurements, numbers and p-adic mathematical physics. p-Adic numbers are not result of measurements, but nevertheless they play significant role in description of some systems and phenomena.…
The purpose of this paper is to define statistically convergent sequences with respect to the metrics on generalized metric spaces (g-metric spaces) and investigate basic properties of this statistical form of convergence.
Research output and impact is currently the focus of serious debate worldwide. Quantitative analyses based on a wide spectrum of indices indicate a clear advantage of US institutions as compared to institutions in Europe and the rest of the…
There are several mathematical and physical reasons why Dirac's quantization must hold. How far one can go without it remains an open problem. The present work outlines a few steps in this direction.
The paper argues that a part of the current statistical discussion is not based on the standard firm foundations of the field. Among the examples we consider are prediction into the future, semi-supervised classification, and causality…
Without attempting to summarize the vast field of statistical mechanics, we briefly mention some of the progress that was made in areas which have enjoyed Barry Simon's interests. In particular, we focus on rigorous non-perturbative results…
Divergences often play important roles for study in information science so that it is indispensable to investigate their fundamental properties. There is also a mathematical significance of such results. In this paper, we introduce some…
The article surveys the known results and conjectures about the analytic properties of dispersion relations and Fermi surfaces for periodic equations of mathematical physics and their spectral incarnations.