RDSP 2023: Recent Developments in Stochastic Processes
2023-03-27 - 2023-03-29 | Българска академия на науките, ул. „15 ноември“ №1, София, София-град, 1040, Bulgaria
Мини-конференцията
Recent Developments in Stochastic Processes
ще се проведе между 27.03.2023 и 29.03.2023 в Големия Салон на БАН.
Съорганизатори са Института по математика и информатика и Факултета по математика и информатика.
Поканени са изследователи от различни области на вероятностите като е поставен фокус върху стохастичните процеси.
Има възможност за подаване на заглавие и резюме за contributed talk (срокът за приемане ще бъде удължен).
Студенти, докторанти, членове на Българското статистическо дружество участват без такса правоучастие.
Сайта на конференцията: https://icms.bg/recent-developments-in-stochastic-processes/
За повече информация: rdsp2023@icms.bg.

Семинар по Приложна математика
2023-05-23 16:00 - 17:30 (Europe/Sofia) | Институт по математика и информатика – БАН, Block 8, 1113 БАН IV км., София, Bulgaria
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, the considered problems are extremely expensive from a computational point of view. Over the past decade, several different techniques have been proposed to localize the nonlocal operator, thereby increasing the spatial dimension of the computational domain.
We have developed an alternative approach. Let A be a SPD sparse matrix arising from finite element method (FEM) or finite difference method (FDM) discretization of the initial (local) problem.
Based on the best uniform rational approximations (BURA) of degree k of zα, 0 ≤ z ≤ 1, a class of efficient solution methods for algebraic systems involving Aα, 0 < α < 1, is proposed and analysed. Robust error estimates with respect to the condition number κ(A) are derived, showing the exponential convergence of the BURA methods with respect to the degree of rational approximation.
Although the fractional power of A is a dense matrix, the algorithm has complexity of order O(N log2N), where N is the number of unknowns. At this point, we assume that some solver of optimal complexity (say multigrid or multilevel) is used for the auxiliary systems with matrices A + djI, dj ≥ 0, j = 1, . . . , k.
The presented (up to 3D) numerical tests are focussed on problems with low regularity of the solutions, including cases of adaptive mesh refinement. The comparative analysis demonstrates the superiority of the BURA methods provided with rigorous theoretical results. Some recent works about BURA based preconditioning of coupled problems and non-overlapping domain decomposition methods are discussed at the end.
Фейсбук страница на семинара: Семинар по Приложна математика

SPCSC 2023: Sphere packings, coverings, and spherical codes
2023-05-28 09:00 - 2023-05-31 17:00 | Семинар по Приложна математика
Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences
Faculty of Mathematics and Informatics, Sofia University “St. Kliment Ohridski”
organize
International Workshop

Sphere packings, coverings, and spherical codes
SPCSC 2023

May 28 – 31, 2023,
Sofia, Bulgaria

The workshop will bring together leading experts from the fields of Sphere packings, sphere coverings and spherical codes to present new results and developments, open problems and new directions.
For more information visit SPCSC 2023 web page.

Колоквиум на МЦМН
2023-06-06 15:00 - 16:30 | Институт по математика и информатика – БАН, Block 8, 1113 БАН IV км., София, Bulgaria
Във вторник, 06.06.2023 г., от 15:00 часа в зала 403 ще състои поредната сбирка на колоквиума на
Международния център за математически науки.
Доклад на тема:
Arc spaces and partition identities
ще изнесе Hussein Mourtada (Institut de Mathématiques de Jussieu-Paris Rive Gauche).

Абстракт

Семинар по Приложна математика
2023-06-06 17:30 - 19:00 | Институт по математика и информатика – БАН, Block 8, 1113 БАН IV км., София, Bulgaria
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 results for minimax, maximin and equioscillating node systems, and the behavior of the local (interval) maxima. One of our main motivations is to generalize Bojanov’s theorem about the variant of the Chebyshev problem with prescribed zero multiplicities. In particular, we derive a weighted generalization with surprisingly general weights.
Фейсбук страница на семинара: Семинар по Приложна математика

Семинар по Приложна математика
2023-10-25 15:00 - 16:30 | Институт по математика и информатика – БАН, Block 8, 1113 БАН IV км., София, Bulgaria
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 обсъдим техните предимства спрямо моделите, базирани на крайни преобразуватели.
В третата част на лекцията ще представим нашия подход за конструиране на ансамбли от крайни автомати, използвайки методите на дълбокото машинно обучение. По този начин ще комбинираме високото качество на невронните езикови модели с изчислителната ефективност на крайните автомати. Ще покажем, че клас от архитектури на невронни мрежи е изчислително изоморфен на клас от ансамбли от крайни автомати.
В заключение, ще представим емпирични резултати, показващи, че с помощта на нашия подход достигаме до перплексия (качество) на езиковите модели, реализирани с ансамбли от крайни автомати, конкурентна с перплексията на невронните езикови модели.
Фейсбук страница на семинара: Семинар по Приложна математика

Семинар по Приложна математика
2023-11-14 14:00 - 15:30 | Институт по математика и информатика – БАН, Block 8, 1113 БАН IV км., София, Bulgaria
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

Семинар по Приложна математика
2024-01-31 15:00 - 16:30 | Институт по математика и информатика – БАН, Block 8, 1113 БАН IV км., София, Bulgaria
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 brings a reconsideration of the notion of Fiedler vector for temporal networks. Depending on the time, some discussion about the recent history of Tensors (mathematical sense) and their application in ML may be presented.
Фейсбук страница на семинара: Семинар по Приложна математика
Семинарът ще бъде излъчен и по Zoom:
https://us02web.zoom.us/j/85916659659?pwd=[REDACTED]

Семинар по Приложна математика
2024-03-27 16:00 - 17:30 | Институт по математика и информатика – БАН, Block 8, 1113 БАН IV км., София, Bulgaria
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.

Семинар по Приложна математика
2024-05-28 15:00 - 16:30 | Институт по математика и информатика – БАН, Block 8, 1113 БАН IV км., София, Bulgaria
An efficient approach for searching three-body periodic orbits passing through Euler configuration
Докладчик: Иван Христов (ФМИ-СУ)
Дата: 28.05.2024 г.
Час: 15:00 ч.
Място: зала 503
Резюме: 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 (one or two points in the search domain). A high precision numerical search based on Newton-Raphson method on a relatively coarse search grid for solutions with relatively short scale-invariant periods is conducted. The results of the search clearly demonstrate the efficiency of the approach. More than 12,000 initial conditions for periodic collisionless orbits (most of which new ones) are found. The extensive high precision computations are performed in Nestum cluster, Sofia Tech Park.
[1] Ivan Hristov, Radoslava Hristova. “An efficient approach for searching three-body periodic orbits passing through Eulerian configuration.” arXiv preprint arXiv:2404.16526 (2024).

Семинар по Приложна математика
2024-09-03 14:00 - 15:30 | Институт по математика и информатика – БАН, Block 8, 1113 БАН IV км., София, Bulgaria
About maximal distance minimizers. What is it and why they are so good?
Докладчик: Яна Теплицкая
Дата: 03.09.2024 г.
Час: 14:00 ч.
Място: зала 256
Резюме

Семинар по Приложна математика
2024-09-11 14:00 - 15:30 | Институт по математика и информатика – БАН, Block 8, 1113 БАН IV км., София, Bulgaria
Subdiffusion-reaction systems: from microscopic random walk to the mesoscopic fractional PDE’s
Докладчик: проф. Сергей Федотов, ръководител на групата по приложна математика в университета на Манчестър
Дата: 11.09.2024 г.
Час: 14:00 ч.
Място: зала 403
Резюме: 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 reaction processes inseparable.

Семинар по Приложна математика
2025-03-27 14:00 - 15:30 | Институт по математика и информатика – БАН, Block 8, 1113 БАН IV км., София, Bulgaria
About m-ary Gray codes
Докладчик: д-р Мария Пашинска, ИМИ – БАН
Дата: 27.03.2025 г.
Час: 14:00 ч.
Място: зала 503
Резюме: 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 Bakoev.

Семинар по Приложна математика
2025-06-03 15:00 - 16:30 | Zoom
Следващата сбирка на Семинара по приложна математика ще се проведе на 03.06.2025 г. от 15:00 в онлайн среда:
Join Zoom Meeting
https://us02web.zoom.us/j/87588684853?pwd=[REDACTED]
Meeting ID: 875 8868 4853
Passcode: [REDACTED]
A generalization of Meijer’s G function motivated by probability
Докладчик: Dmitrii Karp
Резюме: 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 functions which we call Mellin-Barnes’ K function. It is a quite general family which contains Meijer’s G function (thus also all classical hypergeometric functions pFq), as well as several new functions that appeared recently in the study of random processes and the fractional fenomena. For example, the running supremum of an alpha-stable Levy process has density expressible by K function as well as does the exponential functionals of the hypergeometric process. In the talk, we will discuss the definition of the new function, its basic analytic and transformation properties and relations to the functions found in the literature. We further define a generalization of the Kilbas-Saigo function introduced earlier to solve in closed form certain classes of integral and differential equations of fractional order and observe that both the original and the generalized Kilbas-Saigo functions are special cases of our new function.
The talk is based on a joint work with Alexey Kuznetsov (York University, Toronto, Canada).
