This study explores the geospatial relationship between the invasive crayfish species Faxonius limosus and the native Austropotamobius bihariensis and A. torrentium crayfish populations in Eastern Europe, identifying the environmental factors which influence the invasion. We used species distribution modelling based on several climatic, geophysical and water quality variables and crayfish distributional data to predict sectors suitable for each species within the river network. Thus, we identified the sectors potentially connecting invasive and native population clusters and quantified the degree of proximity between competing species. These sectors were then extensively surveyed with trapping and hand searching, doubled by eDNA methods, in order to assess whether any crayfish or the crayfish plague pathogen Aphanomyces astaci are present. The predictive models exhibited excellent performance and successfully distinguished between the analysed crayfish species. The expansion of F. limosus in streams was found to be limited by flash-flood potential, resulting in a range that is constrained to lowland rivers. Field surveys found neither crayfish nor pathogen presence in the connective sectors. Another interesting finding derived from the screening efforts, which are among the most extensive carried out across native, apparently healthy crayfish populations, was the existence of a latent infection with an A. astaci strain identified as A-haplogroup. Our results provide realistic insights for the long-term conservation of native Austropotamobius species, which appear to be naturally protected from F. limosus expansion. Conservation efforts can thus focus on other relevant aspects, such as ark-sites establishment for preventing the spread of more dangerous invasive crayfish species and of virulent crayfish plague pathogen strains, even in locations without direct contact between crayfish hosts.

Caddisflies are often used in studies on freshwater ecosystem ecology because of their aquatic-dependent larvae. The present study addresses the ecological affinities of larvae of Hydropsyche incognita in terms of the pattern of distribution of this species in the Romanian Carpathians using a boosted regression trees (BRT) model. A population cluster located in the western Romanian Carpathians was identified by the spatial analysis. The statistical model revealed that this species prefers a neutral to low-alkaline pH, high levels of dissolved oxygen, low conductivity, fast flowing water, moderate sized rivers at an altitude below 600 m a.s.l. and low concentrations of organic pollutants. An eastward decrease in the frequency of H. incognita populations was recorded along rivers in the Carpathians. The predictions derived from the BRT model on sites outside the population cluster suggest that many locations in the central and eastern Romanian Carpathians are suitable for H. incognita. However, this species was found at only a few of these locations. In contrast, some populations in this area were found in habitats predicted as unsuitable. There are several possible explanations of this, one of which is random dispersion of the species by flying adults.

By using the fixed point method, we obtain a version of a stability result of Baker in probabilistic metric and quasimetric spaces under triangular norms of Hadžić type. As an application, we prove a theorem regarding the stability of the additive Cauchy functional equation in random normed spaces.

The rapid integration of large language models into higher education creates opportunities for mathematics instruction, but also raises the need for structured interaction strategies that support reflective learning rather than passive answer consumption. This study, conducted within the Erasmus+ MAESTRO-AI project, examines how selected AI prompt patterns can be implemented in concrete university mathematics activities and how students evaluate these AI-supported experiences. Two experimental modules were compared: complex numbers for first-semester Applied Mathematics students in Poland ($n=100$) and conditional probability for second-year Computer Science students in Romania ($n=213$). After completing AI-assisted learning activities with ChatGPT and/or Gemini, students completed a common evaluation questionnaire assessing engagement, perceived usefulness, and reflections on AI as a tutor. Group comparisons and experience-based analyses were performed using the Mann–Whitney test. Results indicate that students who reported regular prior use of AI tools evaluated AI-supported learning significantly more positively than those with occasional or no prior experience. They gave higher ratings across most questionnaire items as well as for the overall score. The findings suggest that prompt-pattern-based designs can support engaging AI-assisted mathematics activities. They also indicate that such designs can provide a structured learning experience, while introductory guidance may be important to ensure comparable benefits for less experienced students.