Department of Numerical Methods
The primary area of research conducted in the Department is the development of the mathematical foundations of an innovative method published under the name Parametric Integral Equation System (PIES).
This method constitutes an analytical modification of the classic Boundary Integral Equations (BIE). It is used to more efficiently solve boundary value problems modeled by various partial differential equations, based on the developed algorithms for their numerical solution. Furthermore, research is carried out on the efficiency and computational complexity of the aforementioned algorithms.
Department of Bioinformatics
The research conducted by the Department's staff focuses primarily on the development of machine learning algorithms and their potential applications in the analysis of various biological and medical problems. In particular, the Department of Bioinformatics staff is interested in identifying important variables in decision-making systems and using these methods to identify factors responsible for biological effects - disease development, drug resistance, odor recognition mechanisms, and many others. The Department’s staff participate in international research experiments conducted in a challenge-based approach, including those conducted within the DREAM consortium and the CAMDA community. They also conduct interdisciplinary research in collaboration with numerous diverse domestic and international research teams representing biological, medical, chemical, and agricultural sciences.
Department of Artificial Intelligence and Multimedia
The research conducted by the Department's staff focuses on the following topics: data representation and processing in Semantic Web and Linked Data environments; streaming data; RDF graph stores; databases; structure discovery in music information; syntax and semantics of music information; biometrics and pattern recognition; granular computing; rough sets; and intelligent systems.
Department of Programming and Formal Methods
The research conducted by the Department's staff focuses primarily on the computer formalization and verification of mathematical proofs, as well as on expanding the database of computer-verified formal mathematics. Currently, the Faculty of Computer Science is home to a team of developers of the Mizar system, one of the world's most well-known and respected systems for computer-verified proofs and the collection of such proven theorems (Mizar Mathematical Library).
Department of Discrete Processes
The research focuses on discrete processes, i.e., processes in which we can distinguish a finite number of events/states. In particular, the research topics concern the qualitative theory of difference equations. It involves problems related to the asymptotics of solutions and their classification for various types of discrete equations, which are also algorithms ready for computer implementation.