Computational Mathematics, Probabilistic and Statistical Methods

Description
The scientific activity of the team focuses on computational mathematics, statistics, and probability in the broadest sense, as well as their applications. Problems currently under consideration include: - the construction of new resampling methods and proofs of their consistency for the parameters of nonstationary processes, - choice of the optimal block length for various bootstrap methods in the case of non-stationary signals, - concentration inequalities in the nonstationary case, - analysis of nonstationary signals, - analysis of biomedical signals, - numerical methods for ordinary and delay differential equations in the time domain, - construction of new numerical methods for stochastic differential equations, - Monte Carlo methods, - quantum algorithms, and stochastic simulations on GPU graphics cards, - numerical linear algebra, - robust stability of polynomials and matrices, and incomplete systems, - multi-criteria decision-making, - computational complexity of deterministic and stochastic differential problems. The results obtained have applications, among others, in economics, finance, insurance biostatistics, medicine, neurology, mechanics, vibroacoustics, telecommunications, metallurgy.
Cooperation:
University of Udine (Italy)
Paris Nanterre University (France)
Université d'Aix-Marseille (France)
University of Cambridge (Great Britain)
King Abdullah University of Science and Technology (Saudi Arabia)
University of Naples Parthenope (Italy)
Università degli Studi di Napoli Federico II (Italy)
Tabriz University (Iran)
University of Klagenfurt (Austria)
Montanuniversität Loeben (Austria)
University of Strathclyde (Great Britain)
Università degli Studi di Bari Aldo Moro (Italy)
Silesian University in Opava (Czech Republic)
Laurentian University (Canada)
Mathematical and Physical Science Foundation (Denmark)

Contact

Dr hab. Anna Dudek
30-059 Kraków, al. Mickiewicza 30, pawilon A3-A4. 3. piętro, pok. 307a
12 617 39 96

Leading unit

Faculty of Applied Mathematics - Department of Mathematical Analysis, Computational Mathematics, and Probabilistic Methods

Team leader

Dudek Anna

Team members

  • Bochacik Tomasz
  • Bożek Bogusław
  • Braś Michał
  • Ćmiel Adam
  • Ćmiel Bogdan
  • Goćwin Maciej
  • Kałuża Andrzej
  • Majewski Bartosz
  • Morkisz Paweł M.
  • Przybyłowicz Paweł
  • Rydlewski Jerzy Piotr
  • Szkutnik Zbigniew
  • Szybowski Jacek

IDUB research areas

  • Sustainable energy technologies, renewable sources of energy, energy storage, and resource management. Design, production, application, synergy, and process integration
  • Water-energy-climate: interdisciplinary approach to sustainable development
  • Technical solutions: from fundamental research, through modelling and design, to prototypes. The application of mathematical, information technology, and electronics tools to macro-, micro-, and nanoscale problems
  • Materials, technologies, and processes inspired by nature: biotechnology, bioinspirations in engineering and materials science, biosensors, bioenergetics, biocatalysis, biocomputers, and biocomputation
  • Intelligent information, telecommunication, computer, and control and operation technologies

Keywords

stochastic processestime seriesnon-stationarityresampling methodslarge data setscomputational complexitystochastic differential equationsquantum algorithmsmulti-criteria decision-makingsignal analysis