Projects

The aim of the project was to design and test a model based on recurrent neural networks for predicting sales of traded commodities. Another objective was to compare the accuracy of commodity sales estimates between autoregression-based models. The solution included the selection and analysis of input data, including data cleaning, and the design of a functional network architecture relative to the provided data. A series of competing models were sequentially tested, differing in input data length, regressors used, network architecture and topology, and their parameters. The models were compared in terms of their sales prediction performance for specified time periods. For each commodity sold in a given market, it was determined which model was the most suitable and whether it was competitive with the model currently in use.

Sample behavior of modeled time series for various products

The aim of the project was to design a linear regression model for modeling water table depth in boreholes. The project is based on provided meteorological and geophysical data. An integral part of the work is data consolidation and verification of its suitability for modeling. The model design includes the selection and construction of additional appropriate variables, such as aggregated precipitation over a specific period, average temperature, or the length of the time frame, for each borehole. These variables are subsequently used as regressors in the model. The expected outputs are not aimed at predicting future behavior, but at quantitatively assessing the influence of individual regressors on the water table depth.

Partial project outputs: model behavior (left) and model error behavior (right).

Nanogels are polymeric nanoparticles utilized in targeted therapy due to their high absorption capacity, controlled size during synthesis, and ability to alter their properties based on their surrounding environment. The capability to anchor functional groups onto the nanogel surface allows researchers to control its surface and mechanical properties. Mesoscale simulations were used to model the surface of a nanogel composed of polyethylene glycol and polyethylene imine (shown in gray in the figure), which was modified with alkyl-amine chains. The simulation results demonstrated that the grafting density and the alkyl-amine length play a crucial role in making the surface accessible to or shielded from the environment, thereby allowing control over the absorption capacity of the nanogel and the subsequent release of the encapsulated substance. The description and results are adapted from Posel et al., Nanomaterials 2019, 9, 1514.

During drug manufacturing in the pharmaceutical industry, chiral molecules enter into reactions, and the resulting product is very often a racemic mixture. While one component of the mixture is pharmaceutically active, the other is usually harmful or reduces the desired effect. For this reason, it is essential to separate these two chemically identical components. Currently, several methods for the separation of racemic mixtures exist, but their disadvantage is often low efficiency or high cost. Today, membrane separation methods appear to be the most promising. However, the selection of a suitable membrane is mostly based on intuition alone, without a full understanding of the separation process. Computer simulations represent a suitable tool for thoroughly investigating interactions between individual atoms, thereby providing complete insight into the studied system. In this topic, we focus on modeling the interactions of different enantiomers of pharmaceutically active substances with selected chiral selectors to describe the mechanism of chiral recognition.

Počítačová simulace chirální selekce ibuprofenu

Ibuprofen je typickým příkladem racemické směsi. Jeho dva enantiomery, označované jako (R)- a (S)-Ibuprofen, mají stejné termodynamické vlastnosti, avšak v organismu vykazují odlišné účinky. Zatímco (S)-Ibuprofen je v těle aktivní a ulevuje od bolesti, (R)-Ibuprofen nemá pozorovatelný účinek a snižuje výsledný efekt léku. Při pokusu o zachycení (R)-Ibuprofenu z racemické směsi byla jako chirální selektor použita molekula β-cyclodextrinu. Molekulárně dynamické simulace ukázaly, že (R)-Ibuprofen je schopen s chirálním selektorem vytvořit více vazeb než jeho (S)-forma, a je tedy možné ho tímto způsobem oddělit z racemické směsi. Efektivitu selekce ovšem silně ovlivňuje rozpouštědlo, které může zabrat dostupné vodíkové vazby a tím snížit účinnost dělení. Výběr vhodného rozpouštědla je předmětem dalšího výzkumu.

Výsledky a popis převzaty z Škvára et al., J. Mol. Liq. 2020, 302, 112575.

Pedestrian movement modeling is a complex, non-linear problem that involves crowd behavior and the self-organizing capability of the system. Pedestrian movement is influenced by a wide range of factors, including both social and psychological ones, as well as physical factors, such as environmental influences. One of the key applications is the simulation of crowd movement during panic situations, such as fires or floods. The results of such simulations can be utilized in the design of evacuation plans, for instance, for the optimal placement of exits.

In principle, we distinguish between two types of models: macroscopic and microscopic.

• From a macroscopic perspective, pedestrians can be perceived as an intelligent fluid, with their movement described by equations similar to those for compressible flow. However, it is also necessary to take into account non-physical factors, which can be modeled using the so-called social force. A pedestrian's movement is thus influenced by the proximity of other pedestrians and exits.
• Microscopic models focus on the individual pedestrian as a particle, with the crowd modeled as a system composed of these particles. Various modeling approaches can be utilized, such as description using ordinary differential equations, agent-based modeling, or cellular automata.

More detailed information can be found, for example, in Kubera et al., Mathematics 2021, 9, 1525, nebo v Felcman et al., Mathematical Modelling of Natural Phenomena 2021, 16, 11.