Search for New Physics with rare decays at LHCb

We discuss the potential of the LHCb experiment to study rare B decays and their impact on various scenarios for New Physics. Some possible experimental strategies are presented

Categorial analysis of A. Kurpatov's "Methodology of thought" in context of perspective AGI development

In this article we apply language of category theory in order to formalize core methodological principles that structure the methodology of thought elaborated by Russian modern psychiatrist and philosopher A. Kurpatov. According to the author such formalization could be useful both from the standpoint of unification of ways of thinking about brain functioning and reasoning in particular, and from the standpoint of search of uniform language of scientific thought in general

Tropical Determinant of Integer Doubly-Stochastic Matrices

Let D(m,n) be the set of all the integer points in the m-dilate of the Birkhoff polytope of doubly-stochastic n by n matrices. In this paper we find the sharp upper bound on the tropical determinant over the set D(m,n). We define a version of the tropical determinant where the maximum over all the transversals in a matrix is replaced with the minimum and then find the sharp lower bound on thus defined tropical determinant over D(m,n).Comment: 18 page

Intercalates and Discrepancy in Random Latin Squares

An intercalate in a Latin square is a $2\times2$ Latin subsquare. Let $N$ be the number of intercalates in a uniformly random $n\times n$ Latin square. We prove that asymptotically almost surely $N\ge\left(1-o\left(1\right)\right)\,n^{2}/4$, and that $\mathbb{E}N\le\left(1+o\left(1\right)\right)\,n^{2}/2$ (therefore asymptotically almost surely $N\le fn^{2}$ for any $f\to\infty$). This significantly improves the previous best lower and upper bounds. We also give an upper tail bound for the number of intercalates in two fixed rows of a random Latin square. In addition, we discuss a problem of Linial and Luria on low-discrepancy Latin squares

Space of thought: categorial structure and gluing axiom

In his article the author attempts to investigate a logic model of space of thought with formal means of category theory. Concept of space of thought was elaborated by modern Russian psychologist A. Kurpatov. According to the author of the article, it would be appropriate to use a category of complete Heyting-valued sets as a model of space of thought, provided that certain methodological assumptions will be accepted. Same model could be used in a number of approaches in the area of perspective AGI developement