The combinatorics of splittability

Marion Scheepers, in his studies of the combinatorics of open covers, introduced the property Split(U,V) asserting that a cover of type U can be split into two covers of type V. In the first part of this paper we give an almost complete classification of all properties of this form where U and V are significant families of covers which appear in the literature (namely, large covers, omega-covers, tau-covers, and gamma-covers), using combinatorial characterizations of these properties in terms related to ultrafilters on N. In the second part of the paper we consider the questions whether, given U and V, the property Split(U,V) is preserved under taking finite unions, arbitrary subsets, powers or products. Several interesting problems remain open.Comment: Small update

Association study of the Taq1D rs1800498 polymorphism of the DRD2 gene with personality traits in a group of athletes

Introduction: This study investigates an association between the human dopamine receptor 2 gene DRD2 Taq1D rs1800498 polymorphism and personality traits among athletes, exploring the genetic underpinnings of sports performance and psychological characteristics. It aims to understand how genetic factors related to dopamine reception influence athletic predispositions and behaviors. Materials and Methods: An association study was conducted with 391 male participants, comparing 159 sports subjects with 232 non-trained controls. Personality traits were assessed using the NEO Five-Factor Inventory, while the DRD2 Taq1D rs1800498 polymorphism was genotyped through real-time PCR. Results: Significant differences in the DRD2 Taq1D rs1800498 genotype and allele frequencies were found between athletes and controls, with athletes displaying higher scores in extraversion and conscientiousness on the NEO-FFI scales. These findings suggest a genetic influence on certain personality traits relevant to sports performance. Conclusions: The study supports the notion that genetic factors, specifically the DRD2 Taq1D rs1800498 polymorphism, are associated with personality traits that may influence athletic performance. This insight contributes to the field of psychogenetics in sports, offering a deeper understanding of how genetics and personality interact to shape athletic capabilities

The combinatorics of the Baer-Specker group

Denote the integers by Z and the positive integers by N. The groups Z^k (k a natural number) are discrete, and the classification up to isomorphism of their (topological) subgroups is trivial. But already for the countably infinite power Z^N of Z, the situation is different. Here the product topology is nontrivial, and the subgroups of Z^N make a rich source of examples of non-isomorphic topological groups. Z^N is the Baer-Specker group. We study subgroups of the Baer-Specker group which possess group theoretic properties analogous to properties introduced by Menger (1924), Hurewicz (1925), Rothberger (1938), and Scheepers (1996). The studied properties were introduced independently by Ko\v{c}inac and Okunev. We obtain purely combinatorial characterizations of these properties, and combine them with other techniques to solve several questions of Babinkostova, Ko\v{c}inac, and Scheepers.Comment: To appear in IJ

Association analysis of the dopaminergic receptor 2 gene Tag1B rs1079597 and personality traits among a cohort of professional athletes

Research into sports participation has increasingly pointed to inherent biological mechanisms as influential factors alongside psychosocial and environmental elements. The dopaminergic D2 receptor is a strong candidate gene for physical activity behaviour, given its role in locomotor control and reward mechanisms. Hence, this study aimed to analyse the association of the DRD2 gene Tag1B rs1079597 polymorphism with personality traits in elite athletes. The study group consisted of 395 volunteers. Of these, 163 were professional athletes (22.56±5.9; M = 114, F = 49), and 232 were controls (22.07±4.3; M = 150, F = 82). The MINI-International Neuropsychiatric Interview and the NEO Five-Factor Inventory were administered in both groups. Genotyping was performed using the real-time PCR method. Statistical analysis was performed: genotypes and alleles frequencies were compared using the chi-square test and the relations between DRD2 Tag1B rs1079597 variants, professional athletes and control participants and the NEO Five-Factor Inventory were analysed with the factorial ANOVA. Statistically significant differences were found in the frequency of DRD2 Tag1B rs1079597 genotypes and alleles in the group of professional athletes group compared to the control group. The GG genotype and G allele were significantly more frequent in the group of professional athletes (G/G 0.79 vs G/G 0.66; A/A 0.04 vs A/A 0.03; A/G 0.17 vs A/G 0.31, p = 0.0056; G 0.87 vs. G 0.81; A 0.13 vs. A 0.19, p = 0.0281) compared to the control group. The professional athletes’ participants, compared to the controls, obtained significantly higher scores in the assessment of NEO-FFI Extraversion (p = 0.0369) and Conscientiousness (p < 0.0001) scales. Additionally, there was a statistically significant effect of DRD2 rs1079597 genotype association with being a professional athlete on the Openness scale (F2.3389 = 3.07; p = 0.0475; η2 = 0.015) and on the Conscientiousness scale (F2.3389 = 3.23; p = 0.0406; η2 = 0.016). This study highlights the significant associations between the DRD2 Taq1B polymorphicsite and personality traitsin a group of professional athletes. It also demonstratesthe association of Taq1B polymorphism and professional sportsmanship with personality traits measured by NEO-FFI. The results suggest that genetic factors and professional sportsmanship both shape an athlete’s personality traits

Some new directions in infinite-combinatorial topology

We give a light introduction to selection principles in topology, a young subfield of infinite-combinatorial topology. Emphasis is put on the modern approach to the problems it deals with. Recent results are described, and open problems are stated. Some results which do not appear elsewhere are also included, with proofs.Comment: Small update