On constructions of spherical codes Speaker: Ivan Hristov, FMI, Sofia University Date: May 28, 2024 Time: 3:00 pm Place: Room 503, IMI - BAS Abstract: The classic gravitational three-body problem is considered. The motion of the bodies is determined by Newton’s second law and Newton’s law of universal gravitation. We are interested in a special case of planar periodic orbits – those that pass through Euler configuration. In this talk a new efficient approach for searching three-body periodic equal-mass collisionless orbits passing through Euler configuration is presented [1]. The approach is based on a symmetry property of the solutions at the half period. Depending on two previously established symmetry types on the shape sphere, each solution is presented by one or two distinct initial conditions [...]

On constructions of spherical codes Speaker: Dr. Konstantin Vorob'ev Date: March 27, 2024 Time: 4:00 pm Place: Room 503 Abstract: In this talk, we review various approaches to construct spherical codes with a given coding distance. We also propose a new approach that allows us to find new codes on spheres in small dimensions. In particular, we find a previously unknown kissing arrangement of 40 spheres in R^5.

Temporal networks, Tensors, and applications to ML Speaker: Prof. Ognyan Kounchev Date: January 31, 2024 Time: 3:00 pm Place: ... Abstract: Recently, temporal networks got an increasing interest, related to their numerous applications in real-life data analysis. The temporal networks (more mathematically, “graphs depending on time”) are a typical example of a Tensor – the adjacency matrix depends on several parameters and is a tensor (in the mathematical sense of the word). We present some recent results about the structure of the spectrum of the normalized Laplacian in the case of “slowly varying temporal networks”. The detailed structure of the spectrum gives rise of the notion of “constant block Jacobi model”, which has closed-form solution for the spectrum and the eigenfunctions. This brings a [...]

How log-concavity fought lottery frauds in Florida and what it did after winning Speaker: Dmitri Karp Date: November 14, 2023 Time: 2:00 pm Place: Room 503 of IMI - BAS Abstract: In the talk I will first discuss the log-concavity in parameters of the normalized beta function (which represents the cumulative distribution function of beta distributed random variable) that has been used recently in an investigation of lottery frauds in Florida.  I will then present some related  properties of incomplete beta function and proceed to general log-concavity problems and their particular cases motivated by various problems in statistics, probability and analysis. Facebook page of the seminar: Семинар по Приложна математика

Finite automata and neural networks for language modeling Speaker: Prof. Stoyan Mihov Date: October 25, 2023 Time: 3:00 pm Place: Room 503 of IMI - BAS Facebook page of the seminar: Семинар по Приложна математика

NUMERICAL SOLUTION OF MULTIDIMENSIONAL SPECTRAL FRACTIONAL DIFFUSION PROBLEMS: FROM CAFFARELLI TO BURA Authors: Bálint Farkas, Béla Nagy and Szilárd Révész, Alfréd Rényi Institute of Mathematics Date: June 6, 2023 Time: 5:30 pm Place: Room 503 of IMI - BAS Abstract: We introduce a general framework to investigate minimax problems for sum of translates functions F(x,t)=\sum_k K(t-x_j) or F(x,t)=J(t)+\sum_k K(t-x_j), where K is a general concave "kernel function" and J is an "outer field" function, t runs [0,1], and x=(x_1,...,x_n) is a set of nodes which are used to translate the kernel. Our setup is very close to logarithmic potential theory, but fixing n and focusing on a more detailed analysis, we obtain new results even for very classical problems. Extending a method of P. Fenton, we reach considerable [...]

NUMERICAL SOLUTION OF MULTIDIMENSIONAL SPECTRAL FRACTIONAL DIFFUSION PROBLEMS: FROM CAFFARELLI TO BURA Lecturer: Prof. Sv. Margenov (IICT - BAS) Time: 3:00 pm Date: May 23, 2023 Place: Room 503 of IMI - BAS Abstract: Fractional diffusion operators appear naturally in many areas in mathematics, physics, ect. The most important property of the related b.v. problems is that they are nonlocal. Let us consider the fractional power of a self-adjoint elliptic operator introduced through its spectral decomposition. It is also self-adjoint but nonlocal. Advanced numerical methods in this area have been heavily influenced by the pioneering work in differential operator theory by Caffarelli and Silvestre, "An Extension Problem Associated with the Fractional Laplacian", 2007. After discretization, nonlocal problems lead to linear systems with dense matrices. In the [...]