Related papers: Revisiting a Number-Theoretic Puzzle: The Census-T…
We study the problem of reconstructing the probability measure of the Curie-Weiss model from a sample of the voting behaviour of a subset of the population. While originally used to study phase transitions in statistical mechanics, the…
Theory of Probability is distinguished by several high-level philosophical attitudes, some stressed by Jeffreys, some implicit. By reviewing these we may recognize the importance in this work in the historical development of statistics.…
An essay on Model Theory: Why am I interested in model theory? What are, in my opinion, the most challenging problems in model theory?
This Ph.D. thesis concerns the version of the classical coupon collector's problem, when a collector samples with replacement a set of $n\ge 2$ distinct coupons so that at each time any one of the $n$ coupons is drawn with the same…
We consider the problem of counting the number of answers to a first-order formula on a finite structure. We present and study an extension of first-order logic in which algorithms for this counting problem can be naturally and conveniently…
We develop large sample theory for merged data from multiple sources. Main statistical issues treated in this paper are (1) the same unit potentially appears in multiple datasets from overlapping data sources, (2) duplicated items are not…
For any particularly interesting theorem one proof is never enough. Instead, the first proof sets the challenge to find a more elegant method that illuminates subtle features of the math, is simpler to understand, or even avoids using…
The problem of how mathematics and physics are related at a foundational level is of much interest. One approach is to work towards a coherent theory of physics and mathematics together. Here steps are taken in this direction by first…
The $abc$ conjecture is a very deep concept in number theory with wide application to many areas of number theory. In this article we introduce the conjecture and give examples of its applications. In particular we apply the $abc$…
This is an attempt at an elementary exposition, with examples, of the theory of motivic integration developed by R. Cluckers and F. Loeser, with the view towards applications in representation theory of p-adic groups.
"Ever since the advent of modern quantum mechanics in the late 1920's, the idea has been prevalent that the classical laws of probability cease, in some sense, to be valid in the new theory. [...] The primary object of this presentation is…
In which a review of the concept of countability is done in mathematics, subjecting review some of the theorems so far accepted, showing their inconsistency and also taking concrete elements on the countability of all the powers of the set…
Not long ago primary census data became available to publicity. It opened qualitatively new perspectives not only for researchers in demography and sociology, but also for those people, who somehow face processes occurring in society. In…
The notion of two-numbers of connected Riemannian manifolds was introduced about 35 years ago in [Un invariant geometrique riemannien, C. R. Acad. Sci. Paris Math. 295 (1982), 389--391] by B.-Y. Chen and T. Nagano. Later, two-numbers have…
The theory of random real numbers is exceedingly well-developed, and fascinating from many points of view. It is also quite challenging mathematically. The present notes are intended as no more than a gateway to the larger theory. They…
The motivation of this paper originates from rethinking an essential characteristic of crowd counting: individuals (heads of humans) in the crowd counting task typically occupy a very small portion of the image. This characteristic has…
The Hoover index H, derived from the distribution of population density, has a long history in population geography. But it is prone to misinterpretation and serious measurement artifacts, some of which have been recognized for years. Here…
In the summer of 2013 Marcus, Spielman, and Srivastava gave a surprising and beautiful solution to the Kadison--Singer problem. The current presentation is slightly more didactical than other versions that have appeared since; it hopes to…
The aim of the present article is to explore the possibilities of representing positive integers as sums of other positive integers and highlight certain fundamental connections between their multiplicative and additive properties. In…
It is proposed that to the usual probability theory, three definitions and a new theorem are added, the resulting theory allows one to displace the central role usually given to the notion of conditional probability. When a mapping $\phi$…