Projects and Grants

Team members in this broader project provide mathematical and informatics support for research on topics related to the energy transition in the Ostrava metropolitan area. In addition to developing our own methods, we also collaborate with other teams, including the development of a mathematical model for PEDs (Positive Energy Districts) and data analysis of large datasets to answer questions related to the study of energy poverty.

The main goal of the team’s involvement in this broad strategic project focused on regional transformation is to conduct research on current trends in data analysis and the development of methods for artificial intelligence applications. These methods are designed for use across a wide range of fields, including social science research and industrial applications. The objective is not only to develop data analytics methods but also to apply them in collaboration with other work packages and research labs.

Team members focus on research, development, and implementation of computational intelligence methods for the analysis of uncertain information, such as biosensor and social science data with systematic errors. In the analytical part, they focus on hypothesis generation, non-statistical processing of time series with detection and prediction of structural changes, and machine learning, including deep neural networks. Research on knowledge systems aims at expert knowledge bases using Explainable AI (XAI) principles in combination with data-driven and compositional models. This is crucial for personalized digital interventions and mHealth, where data-driven approaches are insufficient to determine the appropriate intervention, which requires expert knowledge and logical methods of interpretation.

Fractional calculus is a valuable tool for modeling physical dynamics with internal memory, especially when the memory is related to the power of time. A relatively new branch in fractional calculus is fuzzy fractional calculus based on fuzzy numbers and dealing with quantities with imprecise numerical values. The goal is to develop a unified mathematical framework that combines formal methods developed separately for both cases of fractional calculus to identify and classify models of random walks in continuous time. Fractional generalization will then be used to estimate moments for selected physical diffusion processes. Another goal is to analyze the suitability of this generalization for modeling physical, biological, and financial processes.

The project focuses on the development of new methods for creating transparent models of financial time series that can reveal hidden relationships both within individual series and in the complex structure of multiple series. These models provide valuable information about the future development of financial quantities thanks to an integrated probabilistic approach. The project combines tools from fuzzy transformation theory, fuzzy GUHA methods, fuzzy natural logic, and probability theory with financial modeling methods, creating an innovative approach to processing and analyzing financial data.

The goal of the project was to develop international cooperation between 4 universities by conducting joint research in the field of neural networks, resulting in the design of new neural networks based on the theory of complex, hypercomplex, and fuzzy numbers, including the investigation of their mathematical properties. The aim is to create a framework for permanent solutions in the field of scientific cooperation among those included in the Strategic Partnership. The result will be ongoing cooperation, joint projects, and research. Activities within the international cooperation of the 4 partner universities in the field of scientific research will involve conducting joint research work on an international scale and disseminating the effects of this research: advancing the state of knowledge about hypercomplex neural networks, designing neural networks based on hypercomplex number structures, researching mathematical aspects and numerical experiments, and their applications. The assumption was dissemination of results on an international scale (articles, conferences, materials/lectures/info seminars for students).