Informatics

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Research Topic Summary.

Human-computer interface is the form of communication between a user and computer, when the user issues commands for computer in natural form. Such an interface can be implemented using various forms depending on the purpose and user requirements. Natural and user-friendly forms of the implementation shorten time of the user learning to use the implemented tool. Brain – Computer interface is a system that converts the brain activity into the control signals for a computer or some other electronic device. Such a system has large field of application ranging from the disabled persons to playing games. The clear relationship between the brain activity and the commands to muscles is not disclosed yet. Nevertheless, it is possible using mathematical methods to analyse the brain activity and to form the control signals for the external electronic devices. For this purpose, the method is needed to scan and to save the brain activity. The formation of electroencephalogram (EEG) is one of such methods. This is a non-invasive investigation of bioelectrical brain activity. The measured signals of brain activity are non-stationary and non-linear and they are directly dependent of the particular person. Consequently, it is difficult to distinguish the effective control signals. For this purpose, the feature extraction and classification methods are used. The methods of neural networks are dominant among classification methods. The deep neural networks present very good results for image recognition and classification. The signals of brain activity can be presented in the form of image. The research in this filed is carried out worldwide, however, there is always room for the improvement of the obtained results. The purpose of the investigation is to apply the deep neural networks to recognize and classify the signals of brain-computer interface.

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Research Topic Summary.

Transparent and reflective surfaces often mislead vision systems: boundaries overlap with reflections and depth becomes unreliable. This project aims to build a rigorous theoretical basis and methods that fuse color, depth, and polarization cues while adhering to the physical laws of refraction and reflection. We will develop mathematical models, uncertainty estimation and calibration procedures, and a clear evaluation protocol using public datasets. The expected outcome is segmentation that remains accurate and stable under varied conditions, validated by standard metrics, with open-access method descriptions and a reference implementation. The resulting knowledge will advance reliable computer vision for industrial inspection, robotics, and quality assurance.

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Research Topic Summary.

This research focuses on developing high-performance and AI-enhanced computational methods to accelerate subsurface flow simulations for CCS, hydrogen storage, and geothermal energy systems. Traditional numerical solvers for multiphase, thermal, and reactive flow are computationally expensive, limiting real-time analysis and large-scale optimization. The project will integrate advanced numerical algorithms, reduced-order modelling, high-performance computing, and machine-learning techniques—including physics-informed neural networks and AI surrogate models—to achieve fast, accurate, and scalable simulations. Agentic AI systems will support automated workflow optimization and adaptive model refinement. The resulting hybrid physics-AI framework will enable rapid reservoir characterization, improved injection strategies, and reliable long-term performance assessment, supporting the deployment of next-generation sustainable energy technologies.

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Research Topic Summary.

Image reconstruction (inpainting) covers cases where it is necessary to restore missing parts of an image, anonymize a part of an image, restore damaged parts of an image or similar tasks. Such problems are solved in satellite image analysis, medical image analysis, virtual reality scene creation and other application areas. The object of research is the integration of signal processing methods with deep neural networks for image reconstruction.

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Research Topic Summary.

Optimization methods and algorithms are an important constitutive part of the computer science and also artificial intelligence. In particular, the heuristic algorithms play a very significant role, just to mention local search, tabu search, genetic algorithms, (evolutionary) population-based algorithms and their numerous combinations. The high efficiency of the combined heuristic algorithms was empirically confirmed several decades ago. The further demand of such algorithms was stimulated by the growth of research and development (R&D) along with the newly arising tasks. This has become even more actual in recent years. The current development of heuristic algorithms is continued by not only combining different algorithms, but also by exploiting the inner architecture of the algorithms. One of the promising directions in this area is the use of so-called hierarchically-structured (hierarchicity-based) (or simply hierarchical) heuristic (HH) algorithms. The central idea behind the HH algorithms is the multiple adoption (reuse) of the well-known heuristics. This in connection with what is known as self-similarity ? this means that an object (in our case, algorithm) is exactly or approximately similar to constituent parts of itself. The principle of self-similarity is the universal principle; so, we conjecture that for both the computational algorithms, this principle may also be deeply inherent and important. This idea is not very new, and some examples of hierarchical-like algorithms have been already investigated. Still, this is an area of active and progressing research. Further computational studies are required for accelerating research and to reveal higher potential of the HH algorithms. The following are the particular stages of the research process: - analysis of design and computational implementation of the HH algorithms; - empirical testing and comparison of different variants of the HH algorithms; - applications to real-world problems.

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Research Topic Summary.

This project introduces a new generation of map-based neuron models in which traditional scalar variables are replaced by nxn matrices, creating matrix neurons and matrix neural networks. This extension allows the models to capture richer, higher-dimensional dynamics than classical approaches, but it also leads to unexplored computational challenges. A central focus of the project is understanding divergence dynamics - rapid growth, instability, or chaotic transitions that arise in these high-dimensional nonlinear systems. Such behaviors can significantly affect model accuracy, numerical stability, and computational cost. The project will therefore examine how divergence emerges in individual matrix neurons and how it propagates across networks, while also studying numerical error amplification and the computational complexity of simulating these processes. To ensure the practical use of matrix neuron models, the project will also develop new algorithms for stability analysis and control, enabling researchers to manage transient phenomena such as divergence and chaos. By establishing the theoretical and computational foundations of matrix neuron models, this project aims to open new directions in computational neuroscience, nonlinear systems research, and high-dimensional neural network modeling.

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Research Topic Summary.

Maximally diverse grouping problems (MDGPs) consist of finding a partition of a set of elements into a given number of mutually disjoint groups, while respecting the requirements of group size constraints and diversity. The MDGP models a variety of real-world situations. It is possible to formulate MDGPs with different objective functions and constraints. The purpose is to introduce MDGPs with the Max-Min objective function. Such a variation of the MDGP has several important applications. There is a clear need to develop metaheuristic-based algorithms for solving the Max-Min MDGPs.

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Research Topic Summary.

We will investigate how finger optical signals can be used to non-invasively assess glucose changes and detect high-risk episodes, thereby reducing the need for frequent finger pricks. The aim is to develop a personalized methodology that learns from each individual’s reference measurements (e.g., self-monitoring or continuous glucose monitoring) and integrates multi-wavelength optical measurements with auxiliary parameters (temperature, contact pressure). The models will be grounded in the principles of light propagation in tissue and in quality-control procedures, so that artifacts are recognized and uncertainty is quantified in a principled manner. Expected results include open-access methods and a data-collection protocol demonstrating improvements in change estimation and episode detection, as well as publications in the field of computer science. The study will be conducted with volunteers in compliance with ethical requirements; the methodology will not be intended for medical diagnosis.

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Research Topic Summary.

The heartbeat is generated by electrical excitation and coordinated Ca2+ release. These processes depend on ion channels that regulate membrane voltage and intracellular Ca2+. Gap junction (GJ) channels, formed by two docked connexin (Cx) hemichannels, are essential for electrical conduction, while undocked hemichannels also influence cellular signalling. Because membrane voltage, Ca2+ levels, and Cx (hemi)channel gating interact strongly, their combined impact on cardiac excitation remains insufficiently understood. Mathematical and computational models, supported by experiments, provide an effective way to study these mechanisms. The aim of this thesis is to develop models describing permeation and gating of Cx channels and hemichannels and to assess their effects on cardiac excitation. It will include the following interrelated tasks: 1) Permeation modelling GJ channels and hemichannels conduct ions and small molecules, producing mixed-charge fluxes not captured by classical models such as the Goldman-Hodgkin-Katz equation. We will develop ion-hopping models based on transition-state theory, using analytical and numerical approaches. Model predictions will be compared with electrophysiological data. 2) Voltage- and Ca2+-dependent gating We will construct models describing how GJ channels and hemichannels respond to voltage and Ca2+ via mechanisms such as binding and surface-charge effects. Parameter identifiability will be analysed using sensitivity methods, global optimisation, and Markov chain Monte Carlo sampling. 3) Integrated cardiac excitation model The developed models of GJ (hemi)channel gating and permeation will be incorporated into a cardiomyocyte excitation model to evaluate how Cx (hemi)channels influence action potential propagation and Ca2+ handling. Simulations will be validated by cardiac optical mapping data.

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Research Topic Summary.

Dissertation topic: Post-Quantum Cryptographic (PQC) algorithms integration and investigation in blockchain technologies. Since quantum computers are under the rapid development, there is a threat of classical cryptographic methods security. Therefore appeared a new trend in cryptography named as Post-Quantum Cryptography (PQC) which must ensure the security of cryptographic methods realized by classical computers against quantum cryptanalysis. Since in this time PQC functionality is insufficient it is required to integrate classical cryptographic methods with PQC methods. This integration is also and in particular actual in blockchain technologies.

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Research Topic Summary.

Blockchain technology enables recording of business transactions online in a secure, transparent, efficient and auditable way. This technology makes it possible to create truly autonomous smart devices that can exchange data (including business data) without the help of a centralized intermediary. Eliminating intermediaries would reduce the costs of many public services, increase the efficiency of the sharing economy and e-government, and could contribute to the implementation of a smart city vision. Blockchain technology allows the creation of chains of value, i.e. a complete sequence of business processes that enable an enterprise to bring a particular service or product to market and receive remuneration in a safe, efficient, and undeniable manner. An essential element of such chains of value is Smart Contracts, i.e. autonomous agents (programs) operating in blockchains and ensuring that business rules are followed in business transactions. Smart contracts can scan data, perform the necessary calculations according to a specified algorithm and protocol, and pass the results further down to smart contracts in blockchains without human intervention. The practical implementation of blockchain technologies would allow for an innovative transformation of the public services and management sector. One of the small particles of the public sector is university students. After graduation, students obtain a diploma. However, the diploma does not reflect the course of studies and does not provide the employer with enough information about the prospective employee. Therefore, the employer cannot properly evaluate the prospective employee. In the course of the study process, it would be possible to gather information about students' behavior and achievements. Students could supervise the students. The blockchain technology is perfect one for this purpose. The aim of the research is to apply the blockchain technology to the development of a student’s reputation model.