Mathematics Seminar

Department of Mathematics, University of Ostrava

Organized by Pasha Zusmanovich.

For speakers: For participants:

Planned talks
April 2023   12:00   L031
Dmitry Gromov
(University of Latvia)
Ranking nodes in signed networks: an algebraic perspective
This study is devoted to the problem of network ranking, which consists in determining the node hierarchy in a network. A number of algorithms have been proposed for the unsigned networks, i.e., networks whose edges have only positive weights. We mention the eigenvector centrality, the PageRank, and HITS, as well as their variants such as the weighted PageRank and others. These algorithms typically admit a neat algebraic formulation and can be studied using the methods from linear algebra and matrix analysis. We are particularly interested in the convergence properties of the algorithms, the existence of invariants, and the qualitative behavior of the solutions under the (structured) variation of parameters.
The situation becomes more involved if we wish to rank the nodes in a signed network, i.e., the network, whose edges can have both positive and negative weights taken from a finite set. The most common case is the binary set {-1,1}. Such networks describe not only the structure of interactions between different agents, but they also reflect the positive or negative relations between them. Because of this additional feature, signed networks are indispensable for analyzing social interactions in politically, religiously, racially or otherwise divided societies, the voting processes, and the competition/cooperation relations between companies, to mention just a few.
In the presentation, an overview of the previously obtained results will be given, and the novel results will be presented. In doing so, a main emphasis will be put on the algebraic structure of the considered methods.
April 2023   12:00   L031
Dmitry Gromov
(University of Latvia)
Optimal control and value of information: theory and applications
Optimal control theory is an indispensable tool for the computation and analysis of optimal strategies in various applications, ranging from economics to technics. However, the optimal control methods can lead to wrong conclusions when applied to uncertain models. This particularly concerns the models that describe natural, social, or economical processes. In contrast to models built upon physical laws, the former models unavoidably incorporate uncertainties. These uncertainties result from the incomplete knowledge of the underlying dynamics of natural processes, the simplifying assumptions we have to make when describing complex phenomena, and our inability to measure the parameters of the considered models. Understanding and quantifying the model uncertainty is vital for making well-informed decisions.
Value of information (VoI) is a quantitative tool to analyze decision-making in the face of uncertainty. The first step of VoI analysis consists of formalizing the process of obtaining new information about the structure of the model, resp. values of parameters and quantifying the contribution of this new information toward obtaining better prediction of the model behavior. In the second stage, we carry out a qualitative and quantitative analysis of the profit acquired through the use of the new information. The estimation of the potential gain in profit is thus used to make an informed decision about the need for procuring more information.
In the presentation, a formal overview of different approaches aimed toward formalizing the value of information will be given. We will consider formal properties of the value of information and present several examples of the practical application of VoI.

Past talks:   2023   2022

The previous incarnation of the seminar was running in 2016-2021. It was founded by Olga Rossi as "Ostrava Seminar on Mathematical Physics", and continued as "Ostrava Mathematical Seminar". Archive of talks:   2021   2020   2019   2018   2017   2016

Index of speakers:
Balaki:   2023
Barrett:   2016
Boronski:   2018
Burde:   2017
Burdík:   2017
Do:   2016
Galaev:   2016
Gładki:   2022/1,2
Górska:   2022
Goyeneche:   2017
Gubarev:   2018
Hai:   [2020] [2022]
Hlaváč:   2017
Hołubowski:   2017
Hynek:   [2016/1] [2016/2]
Ibrogimov:   2019
Ivanov:   2019
Iwanow:   2019
Jedlička:   [2019] [2022]
Kaygorodov:   2019
Khavkine:   2019
Khrabustovskyi:   [2016] [2017] [2018/1] [2018/2] [2018/3-7]
Kondej:   2016
Krejčiřík:   2016
Krutov:   [2017/1] [2017/2] [2017/3]
Kučera: 2022
Kycia:   [2017] [2019]
Lachowicz:   [2016] [2017]
Lang:   2018
Leite Freire: 2018
Lipovský:   [2016] [2018] [2019]
Lopatkin:   [2018/1] [2018/2] [2019]
Lotoreichik:   [2016] [2017]
Lytova:   [2017] [2018]
Markl:   2017
Mišík:   2022
Moens:   2019
Morozov:   2017
Novák:   2022
Nurzhauov:   2022
Pietrzak:   2022
Popovych:   2017
Prince:   [2016] [2017]
Prykarpatsky:   2022
Saunders:   [2016] [2017] [2019]
Schneider:   [2019] [2022]
Sergyeyev:   [2017] [2021]
Šostak:   2022
Štampach:   2018
Stepanov:   [2019] [2021]
Taghavi-Chabert:   2017
Tomovski:   2022
Truong:   2020
Turek:   [2018] [2022]
Tušek:   2017
Wolak:   2017
Zuevsky:   2022
Zusmanovich:   [2019] [2022/1] [2022/2] [2022/3]

Created: Mon Jan 25 2016
Last modified: Tue Mar 7 11:45:16 CET 2023