Seminar for
DECISION MAKING – THEORY, TECHNOLOGY AND PRACTICE

 

PROGRAM

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Plan rada Seminara Odlučivanje - teorija, tehnologija, praksa za OKTOBAR 2022.

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ČETVRTAK, 13.10.2022. u 13:00, Live stream Niš
Dragan Stevanović, Mathematical Institute SANU
APPROXIMATING ENERGY OF WINE GLASS PATHS AND CYCLES
The energy E of a graph G is the sum of absolute values of the eigenvalues of its adjacency matrix. Akbari, Alazemi and Anđelić [App. Anal. Discrete Math. 15 (2021), 444-459] recently proved that for the connected graph G with the maximum vertex degree D≥6 and the matching number m one has E≤2m\sqrt(D). Despite the fact that the proof relied extensively on the condition D≥6, they conjectured that the same inequality is also valid when 2≤D≤5. We use this conjecture here to first showcase the process of searching for small counterexamples by reinforcement learning. The small counterexamples identified by this artificial intelligence technique provide the motivation to define two aptly named infinite families—wine glass cycles and paths, for which we then illustrate an elegant use of elementary calculus for approximating their energy and showing that almost all wine glass paths and cycles are indeed the counterexamples for this conjecture.

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PONEDELJAK, 17.10.2022. u 13:00, Live stream Niš
Dušan Džamić, University of Belgrade, Faculty of Organizational Sciences
NOVEL METHODS FOR CLUSTERING IN COMPLEX NETWORKS
The theory of complex networks has proven to be very important in the study of the characteristics and structure of various complex systems. In 2012, Center for Discrete Mathematics and Theoretical Computer Science (DIMACS), which is a well-known consortium of prestigious academic institutions (Rutgers University, Princeton, Colombia) and research laboratories (Microsoft, IBM, AT & T, NEC), included the problem of clustering in complex networks on the list of the most important problems and challenges in computer science. Clustering in complex networks can be applied in a variety of contexts to achieve different goals, and therefore, there is no generally accepted definition of a cluster. For this reason, different approaches are used in developing clustering methods. An approach that has attracted the most attention of researchers involves two subproblems: (1) defining a function to determine the quality of a partition and (2) constructing methods to find a partition that has the maximum value of the defined quality function. In this lecture we will consider both subproblems, a new E-function for measuring the quality of a partition, and a new method for optimization modularity (one of the most commonly used quality function).

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ČETVRTAK, 27.10.2022. u 13:00, Live stream Niš
Andjelka N. Hedrih, Mathematical Institute SANU
ENERGY DISSIPATION IN OSCILLATORY MOVEMENTS OF SISTER CHROMATIDS IN ANAPHASE OF MITOSIS
The arrangement of chromosomes in metaphase plate is considered stochastic. Biophysical laws that govern the arrangement and movements of sister chromatids still remain unclear. However, sister chromatids have to move through cytoplasm that can be considered a viscous fluid with a low Reynolds number. Using a modified oscillatory model of mitotic spindle, forced oscillations of moving chromosomes during anaphase are analysed. Dissipative forces will reduce the total energy of moving sister chromosomes. The position of a chromosome in the system of the mitotic spindle will affect its total energy. A mitotic spindle is considered a system of coupled oscillators. Rayleigh function of energy dissipation and a system of coupled ordinary differential equations were used to analyse the total energy of each pair of sister chromatids in the anaphase. Numerical analyses were done for masses of mouse chromosomes, for different arrangements of pairs of sister chromatids and different frequencies of centrosome excitations. Results are discussed in the light of its biological implications. We proposed that the mitotic spindle is a complex system that uses the principle of minimum energy consumption in the process of cell division in movements of sister chromatids in metha- and anaphases. A new mechanism of movement of sister chromatids is proposed.

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Predavanja su namenjena sirokom krugu slusalaca, ukljucujuci studente redovnih i doktorskih studija. Seminar će se održavati svakog drugog četvrtka od 13:00 - 14:00^h, CIITLAB, Elektronski fakultet Niš, Aleksandra Medvedeva 14, Niš

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