The next meeting of the Applied Mathematics Seminar will be held online on June 3, 2025, at 3:00 pm: Join Zoom Meeting https://us02web.zoom.us/j/87588684853?pwd=4xPgBSVfxBwjV4P8hrsHn2rN9gWQGB.1 Meeting ID: 875 8868 4853 Passcode: 711528 A generalization of Meijer's G function motivated by probability Speaker: Dmitrii Karp Abstract: Meijer's G function appeared in probability in 1930-ies even before Meijer's work as the density of the product of independent beta variables and as the density of the likelihood ratio test for samples drawn from many classical probability distributions. It is defined by a contour integral of the appropriate ratio of gamma products (sometimes reducible to the inverse Mellin transform). Replacing the Euler gamma function by the Barnes double gamma function in this contour integral, we introduce a new family of special [...]

About m-ary Gray codes Speaker: Maria Pashinska, IMI - BAS Date: March 27, 2025 Time: 2:00 pm Place: Room 503, IMI - BAS Abstract: We present several systemized implementations of the Gray code over an alphabet with m ≥ 2 elements. Gray codes are widely used in digital communications and effective generation of combinatorial objects. We consider two variants - reflected and modular m-ary Gray codes. We present algorithms for their generation and other important functions such as ranking and unranking and functions for generation of a maximal set of non-proportional vectors of length n over the given alphabet. Some applications of the m-ary Gray codes are also considered. This talk is based on joined work with Stefka Bouyuklieva , Iliya Bouyukliev and Valentin [...]

Subdiffusion-reaction systems: from microscopic random walk to the mesoscopic fractional PDE's Speaker: Yana Teplitskaya Date: September 3, 2024 Time: 2:00 pm Place: Room 256, IMI - BAS Abstract

Subdiffusion-reaction systems: from microscopic random walk to the mesoscopic fractional PDE's Speaker: Prof. Sergei Fedotov, head of the applied group of the Mathematics Department of the University of Manchester Date: September 11, 2024 Time: 2:00 pm Place: Room 403, IMI - BAS Abstract: An interesting feature of subdiffusion-reaction systems is the lack of a universal model for reactions in subdiffusive media. Consequently, the coarse-grained fractional subdiffusion-reaction equations depend on the specific details of the underlying microscopic random walk models. This complexity arises from the memory effects inherent in subdiffusive transport systems. Simply adding a reaction term to the transport equation can be physically inconsistent. Due to the memory effect, the subdiffusion process depends on the entire history of the system’s evolution making the diffusion and [...]

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 [...]