An elementary formula for the von Neumann and Rényi entropies describing quantum correlations in two-fermionic systems having four single-particle states is presented. An interesting geometric structure of fermionic entanglement is revealed. A connection with the generalized Pauli principle is established.

A highly economic prediction method for fine resolution wavelet coefficients of wave functions and energy expectation values is presented.

Depth mapping can be carried out by ultrasound measuring devices using the time of flight method. Ultrasound measurements are favorable in such environments, where the light or radio frequency measurements can not be applied due to the noise level, calculation complexity, reaction time, size and price of the device, accuracy or electromagnetic compatibility. It is also usual to apply and fusion ultrasound sensors with other types of sensors to increase the precision and reliability. In the case of visually impaired people, an echolocation based aid for determining the distance and the direction of obstacles in the surroundings can improve the life quality by giving the possibility to move alone and individually in unlearnt or rapidly changing environments. In the following considerations, a model system is presented which can provide rather reliable position and distance to multiple objects. The mathematical model based on the time of flight method with a correction: it uses the measured analog sensor signals, which represent the probability of the presence of an obstacle. The device consists of multiple receivers, but only one source. The sensor fusion algorithm for this setup and the results of indoor experiments are presented. The mathematical model allows the usage, processing, and fusion of the signals of up to an infinite number of sensors. In addition, the positions of the sensors can be arbitrary, and the mathematical model does not restrict them to be placed in regular formations.

Correlation was detected between the thermal treatment parameters of the AuGe–GaAs system and surface fractal structure. Structural entropic calculations were used to confirm the results obtained by fractal calculations.

This study explores existing research on neural networks, fuzzy logic-based models, and genetic algorithms applied to brain tumor classification. A systematic review of 53 studies was conducted following PRISMA guidelines, covering search strategy, selection criteria, quality assessment, and data extraction. Articles were collected from three scientific databases: Web of Science, Scopus, and IEEE. The review primarily focuses on practical contributions, with most studies emphasizing applications over conceptual insights. Key methods in the field demonstrate significant impact and innovation. Commonly used training and testing mechanisms include dataset splitting, augmentation, and validation techniques, highlighting their widespread adoption for performance evaluation. The analysis of evaluation metrics shows that accuracy and the DICE score are the most frequently used, alongside sensitivity, specificity, recall, and other domain-specific measures. The variety of metrics underscores the need for tailored approaches based on dataset characteristics and research objectives. By highlighting trends, challenges, and research gaps, this review provides actionable insights for advancing BTC research. It offers a comprehensive overview of techniques and evaluation methods to guide future developments in this critical domain.