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Recently, a number of statistical problems have found an unexpected solution by inspecting them through a "modal point of view". These include classical tasks such as clustering or regression. This has led to a renewed interest in…
As long as people have studied mathematics, they have wanted to know how many primes there are. Getting precise answers is a notoriously difficult problem, and the first suitable technique, due to Riemann, inspired an enormous amount of…
It turns out that some empirical facts in Big Data are the effects of properties of large numbers. Zipf's law 'noise' is an example of such an artefact. We expose several properties of the power law distributions and of similar distribution…
Convergent sequences of real numbers play a fundamental role in many different problems in system theory, e.g., in Lyapunov stability analysis, as well as in optimization theory and computational game theory. In this survey, we provide an…
We present another interpretation of the data by P.Markos and give a lot of new illustrations for our conception. All existing numerical data look perfectly compatible with predictions of the self-consistent theory of localization.
We give new proofs of some well-known results from Invariant Theorey using the Kempf-Ness theorem.
These notes aim at presenting an overview of Bayesian statistics, the underlying concepts and application methodology that will be useful to astronomers seeking to analyse and interpret a wide variety of data about the Universe. The level…
Math is widely considered as a powerful tool and its strong appeal depends on the high level of abstraction it allows in modelling a huge number of heterogeneous phenomena and problems, spanning from the static of buildings to the flight of…
Statistics has made tremendous advances since the times of Fisher, Neyman, Jeffreys, and others, but the fundamental and practically relevant questions about probability and inference that puzzled our founding fathers remain unanswered. To…
In statistics education, the concept of population is widely felt hard to grasp, as a result of vague explanations in textbooks. Some textbook authors therefore chose not to mention it. This paper offers a new explanation by proposing a new…
Statistical learning theory provides the theoretical basis for many of today's machine learning algorithms. In this article we attempt to give a gentle, non-technical overview over the key ideas and insights of statistical learning theory.…
Frieze patterns of numbers, introduced in the early 70's by Coxeter, are currently attracting much interest due to connections with the recent theory of cluster algebras. The present paper aims to review the original work of Coxeter and the…
Numerical study of the distribution of the Riemann zeros differences following the work [1] shows the significance of the function for which the prime sum expression is proposed. Computational results related to this definition explored…
The law of large numbers for the empirical density for the pairs of uniformly distributed integers with a given greatest common divisor is a classic result in number theory. In this paper, we study the large deviations of the empirical…
In the paper based on the question of Zhang and L\"{u}[15], we present one theorem which will improve and extend the results of Banerjee-Majumder [2] and a recent result of Li-Huang [9].
In this article, we discuss the remarkable connection between two very different fields, number theory and nuclear physics. We describe the essential aspects of these fields, the quantities studied, and how insights in one have been…
A new general and unified method of summation, which is both regular and consistent, is invented. It is based on the idea concerning a way of integers reordering. The resulting theory includes a number of explicit and closed form summation…
Green, Tao and Ziegler prove ``Dense Model Theorems'' of the following form: if R is a (possibly very sparse) pseudorandom subset of set X, and D is a dense subset of R, then D may be modeled by a set M whose density inside X is…
From the viewpoint of mutation, we will give a brief survey of tilting theory and cluster-tilting theory together with a motivation from cluster algebras. Then we will give an introdution to \tau-tilting theory which was recently developed…
Social networks are increasingly being used to conduct polls. We introduce a simple model of such social polling. We suppose agents vote sequentially, but the order in which agents choose to vote is not necessarily fixed. We also suppose…