Mathematics Days in Sofia – 2026

Section “Numerical Analysis, Operations Research, Probability and Statistics”

Participants

Invited Speakers

  • Andrew Belmonte, Pennsylvania State University, USA

Contributors

  • Alexandr Varipaev, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria
  • Dmitrii Karp, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria
  • Higinio Serrano Garcia, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria

  • Hristo Sariev, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria

  • Ioannis Triantafyllou, University of Piraeus, Greece
  • Jordan Stoyanov, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria
  • Malvina Bozhidarova, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria
  • Nikolai I. Nikolov, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria
  • Nikos Stylianopoulos, University of Cyprus, Cyprus
  • Pavlina Jordanova, University of Shumen “Konstantin Preslavsky”, Bulgaria
  • Petar Evgeniev, Sofia University “St. Kliment Ohridski”, Bulgaria
  • Plamen Koev, San Jose State University, USA

  • Raquel Viaña, University of Alcalá, Spain

  • Svetoslav Vasilev, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria
  • Turgay Akyar, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria

Program and Abstracts

Dominated strategies in classical game theory usually lead to similar results in evolutionary games, via the common norm of instantaneous payoff (winning). Motived by real-world interactions based on secondary characteristics, we investigate the consequences of an imitation dynamics using each player’s status, a secondary attribute defined to be the sum of all previous payoffs in a cache or bank, similar to stored body fat or other carryover effects in ecology. This results in persistent patterns of Cooperation in the Prisoner’s Dilemma, and even the loss of Defection as an Evolutionarily Stable Strategy (ESS). We also study the Rock-Paper-Scissors game using a similar approach, determining conditions for the formation of stable strategic communities.

This is joint work with Alex Galvin, Connor Olson, and Christopher Griffin.

Apparent slowness estimation of coherent seismic wavefields is a fundamental inverse and parameter estimation problem in array seismology, with applications to event localization, phase identification, and source characterization. Classical frequency–wavenumber (f–k) analysis remains one of the standard approaches for this task; however, its performance may deteriorate in the presence of low signal-to-noise ratios, waveform distortions, and imperfect coherence across the array. We investigate the applicability of the Steered Response Power with Phase Transform (SRP-PHAT) method to apparent slowness estimation using small-aperture seismic arrays. Originally developed for acoustic source localization, SRP-PHAT employs phase-normalized cross-spectral information and has been reported to exhibit increased robustness to noise and model mismatch in acoustic localization applications. We show that the method can be interpreted within the framework of broadband beamforming as a phase-weighted extension of conventional f–k analysis, providing an alternative objective function for slowness vector estimation. The study focuses on the robustness properties of the resulting estimator under realistic observational conditions. A plane-wave observation model is adopted, and the sensitivity of the beamforming response to incoherent noise, waveform distortions, and reduced signal coherence is investigated through numerical experiments and real-data case studies. Since the true source parameters are unavailable for observational data, the performance of the method is assessed using RMSD-based consistency measures derived from repeated slowness estimates, providing a quantitative framework for inter-event and inter-method comparison. The proposed approach is evaluated on multiple seismic events recorded by a small-aperture array during October 2000. The results indicate that SRP-PHAT yields more stable slowness estimates than conventional broadband f–k analysis, particularly for weak and emergent signals. These findings indicate that phase-based beamforming constitutes a robust alternative to conventional broadband f–k analysis for slowness estimation in challenging seismic monitoring scenarios.

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We propose a novel framework for modelling the spread of financial crises in complex networks, combining financial data, Extreme Value Theory and an epidemiological transmission model. We accommodate two key aspects of contagion modelling: fundamentals-based contagion, where the transmission is due to direct financial linkages, and pure contagion, where a crisis might trigger additional crises due to global effects. We use stock price, geographical location and economic sector data for a set of companies to construct multiplex networks of four layers, on which a Susceptible-Infected-Recovered transmission model is defined, in order to model the spread of financial shocks between companies by accounting for their interconnected nature. By utilizing stock price data for the 2008 and 2020 financial crises, we investigate and assess the effectiveness of our model in forecasting the propagation of financial shocks through the network, where a shock is detected by measuring stock price volatility. The results suggest that the proposed framework is effective in predicting the spread of financial crises. Our findings demonstrate the significance of each layer of the multiplex network structure, which differentiates between various transmission pathways, for predicting the number of affected companies, as well as for company-, sector or location-specific predictions.

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We will present new algorithms for performing virtually all computations with totally nonnegative matrices to high relative accuracy regardless of whether the matrix is singular generalizing the results of [3] for nonsingular totally nonnegative matrices.

The algorithms achieve high relative accuracy by avoiding subtractions and thus preserving the high relative accuracy. The matrix computations include the inverse, the eigenvalues, the SVD [2], the Schur complement, a submatrix, as well as any minor.

The new algorithms also include for the first time the computation of the singular vectors to high relative accuracy. It also completes computations in the nonsingular case, such as submatrices (and the properties thereof) which can be singular even when the initial matrix isn’t.

Joint work with J. Delgado, A. Marco, J.M. Pena, J.J. Martines.

References

[1] J. Delgado, P. Koev, A. Marco, J.M. Peña, J.J. Martines, R. Viaña, Accurate Computations with Totally Nonnegative Matrices of Any Rank. Numerische Mathematik (2026) submitted.

[2] Koev, P. Accurate eigenvalues and exact zero Jordan blocks of totally nonnegative matrices. Numer. Math. 141, 693–713 (2019).

[3] Plamen Koev Accurate Computations with Totally Nonnegative Matrices SIAM Journal on Matrix Analysis and Applications, 2007, 29:3, 731-75

The moment problem fascinates researchers for more than a hundred years. There have been many advances in formulation conditions for the moment determinacy and moment indeterminacy. It may be the case that two different random variables share the same moments and then they are moment indeterminate. However, a further natural question is if one of the variables is from certain class, in our case infinitely divisible, then can it share the same moments with another random variable from the same class. In this talk we discuss this problem in the context of Levy processes.

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