On constructions of spherical codes Докладчик: д-р Константин Воробьов, ИМИ - БАН Дата: 27.03.2024 г. Час: 16:00 ч. Място: зала 503 Резюме: 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 Докладчик: проф. Огнян Кунчев, ИМИ - БАН Дата: 31.01.2024 г. Час: 15:00 ч. Място: ... Резюме: 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 [...]

How log-concavity fought lottery frauds in Florida and what it did after winning Докладчик: Дмитри Карп Дата: 14.11.2023 г. Час: 14:00 ч. Място: Зала 503 на ИМИ-БАН Резюме: 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. Фейсбук страница на семинара: Семинар по Приложна математика

Крайни автомати и невронни мрежи за езиково моделиране Докладчик: проф. Стоян Михов Дата: 25.10.2023 г. Час: 15:00 ч. Място: Зала 503 на ИМИ-БАН Резюме: Езиковите модели са основен инструмент за решаването на редица сложни задачи като извличане на информация, генерация на естествен език, машинен превод, речева комуникация и много други. Традиционно езиковите модели се представят с крайни преобразуватели. През последните години обаче езиковите модели, базирани на невронни мрежи, извършиха значителен скок в качеството на езиковото моделиране, с което се постигнаха близки до човешки способности в много задачи за разбиране на естествен език. В предстоящата лекция ще направим първо кратък преглед на традиционните представяния на езикови модели, базирани на крайни преобразуватели. След това ще покажем често използвани архитектури на невронни мрежи за езиково моделиране и ще [...]

Minimax problems and results for sum of translates functions Автори: Bálint Farkas, Béla Nagy and Szilárd Révész, Alfréd Rényi Institute of Mathematics Дата: 06.06.2023 г. Час: 17:30 ч. Място: Зала 503 на ИМИ-БАН Резюме: 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 generality while proving precise [...]

NUMERICAL SOLUTION OF MULTIDIMENSIONAL SPECTRAL FRACTIONAL DIFFUSION PROBLEMS: FROM CAFFARELLI TO BURA Лектор: чл.-кор. Св. Маргенов (ИИКТ-БАН) Час: 15:00 Дата: 23.05.2023 г. Място: Зала 503 на ИМИ-БАН Резюме: 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 multidimensional case and domains with general geometry, [...]

A New Walk on Equations Monte Carlo Method for Linear Algebraic Problems Лектор: проф. Иван Димов Час: 16:00 Дата: 14.02.2023 Място: Зала 503 на ИМИ-БАН Резюме: A new Walk on Equations (WE) Monte Carlo algorithm for Linear Algebra (LA) problem, namely, functionals of the solution, eigenvalue problems, etc., is proposed and studied. This algorithm relies on a non-discounted sum of an absorbed random walk. It can be applied for either real or complex matrices. Several techniques like simultaneous scoring or the sequential Monte Carlo method are applied to improve the basic algorithm. Numerical tests are performed on examples with matrices of different size and on systems coming from various important applications. Comparisons with standard deterministic, including unimprovable Conjugate Gradient Method (CGM) or Monte Carlo [...]

Втората сбирка на новоучредения Семинар по приложна математика, който е част от дейностите на програма ПИКОМ, ще се състои на 07.12.2022 от 15:00 в Заседателната зала на ИМИ. Доклад на тема: Introduction to Steiner Trees ще изнесе д-р Данила Черкашин, пост-докторант в ИМИ - БАН.  Фейсбук страница на семинара: Семинар по Приложна математика