The Heider balance (HB) is investigated in a fully connected graph of N nodes. The links are described by a real symmetric array r (i, j), i, j =1, …, N. In a social group, nodes represent group members and links represent relations between them, positive (friendly) or negative (hostile). At the balanced state, r (i, j) r (j, k) r (k, i) > 0 for all the triads (i, j, k). As follows from the structure theorem of Cartwright and Harary, at this state the group is divided into two subgroups, with friendly internal relations and hostile relations between the subgroups. Here the system dynamics is proposed to be determined by a set of differential equations, [Formula: see text]. The form of equations guarantees that once HB is reached, it persists. Also, for N =3 the dynamics reproduces properly the tendency of the system to the balanced state. The equations are solved numerically. Initially, r (i, j) are random numbers distributed around zero with a symmetric uniform distribution of unit width. Calculations up to N =500 show that HB is always reached. Time τ(N) to get the balanced state varies with the system size N as N-1/2. The spectrum of relations, initially narrow, gets very wide near HB. This means that the relations are strongly polarized. In our calculations, the relations are limited to a given range around zero. With this limitation, our results can be helpful in an interpretation of some statistical data.

Recent formulation of the Zaller model of mass opinion is generalized to include the interaction between agents. The mechanism of interaction is close to the bounded confidence model. The outcome of the simulation is the probability distribution of opinions on a given issue as dependent on the mental capacity of agents. Former result was that a small capacity leads to a strong belief. Here we show that an intensive interaction between agents also leads to a consensus, accepted without doubts.

The purpose of this study was to assess a wide range of physiological and performance variables and investigate whether and to what extent these variables are associated with each other in soccer. Twenty-five male soccer players (25.1 ± 4.56 years; body mass, 75.2 ± 5.92 kg; body height, 180.6 ± 5.45 cm) performed: 5- and 30-m sprints (T5m and T30m, respectively), 1-repetition-maximum (1RM) half squat, maximal voluntary isometric contraction (MVIC) of the knee extensors, countermovement jump (CMJ) to obtain vertical jump height (CMJheight) and power output (CMJpower), the 10-s Wingate Anaerobic Test (WAnT) to obtain peak power (Pmax), and the 20-m multi-stage shuttle run test (MST) to evaluate aerobic capacity. 1RM, MVIC, and Pmax were normalized to body mass. Large negative correlations were found between sprint times and 1RM half back squat/BM (r = -0.510 to -0.570, r2 = 0.260–0.325, both p < 0.01) and Pmax/BM (r = -0.501, r2 = 0.251, p < 0.01). T30m most strongly and negatively correlated with CMJheight (r = -0.744, r2 = 0.554, p < 0.001). WAnT-determined Pmax showed a very large correlation between absolute Pmax and knee-extensor MVIC (r = 0.827, r2 = 0.684, p < 0.001) and large correlations between absolute Pmax and 1RM half squat (r = 0.674, r2 = 0.454, p < 0.001) and CMJpower (r = 0.579, r2 = 0.335, p < 0.01). We also identified a large inverse relationship between CMJheight and T30m (r = -0.744, r2 = 0.554, p < 0.001) and large positive correlation between CMJheight and MVIC/BM (r = 0.702, p < 0.001). The results demonstrate that elite soccer players with greater lower body strength (quantified by the MVIC of the knee extensor and the 1RM half squat) show better sprint and CMJ performance, suggesting the incorporation of soccer-specific resistance training to develop lower body musculature and therefore maximize sprinting ability. The higher correlation coefficients found between T30m and the physiological and athletic measures compared with T5m promote the use of this sprint distance when assessing performance. The use of relative measures (normalized to body mass) is advisable when comparing strength variables with sprint and CMJ performance or anaerobic power. Considering the correlations of WAnT-determined Pmax versus CMJpower, coaches should administer tests that assess jumping and linear sprint performance rather than the cycling-specific WAnT.

Background: Physical inactivity and resultant lower energy expenditure contribute unequivocally to cardiovascular diseases, such as coronary artery disease and stroke, which are considered major causes of disability and mortality worldwide. Aim: The aim of the study was to investigate the influence of physical activity (PA) and exercise on different aspects of healthgenetics, endothelium function, blood pressure, lipid concentrations, glucose intolerance, thrombosis, and selfsatisfaction. Materials and Methods: In this article, we conducted a narrative review of the influence PA and exercise have on the cardiovascular system, risk factors of cardiovascular diseases, searching the online databases; Web of Science, PubMed and Google Scholar, and, subsequently, discuss possible mechanisms of this action. Results and Discussion: Based on our narrative review of literature, discussed the effects of PA on telomere length, nitric oxide synthesis, thrombosis risk, blood pressure, serum glucose, cholesterol and triglycerides levels, and indicated possible mechanisms by which physical training may lead to improvement in chronic cardiovascular diseases. Conclusion: PA is effective for the improvement of exercise tolerance, lipid concentrations, blood pressure, it may also reduce the serum glucose level and risk of thrombosis, thus should be advocated concomitant to, or in some cases instead of, traditional drug-therapy.

Although age is a dominant risk factor for Alzheimer’s disease (AD), epidemiological studies have shown that physical activity may significantly decrease age-related risks for AD, and indeed mitigate the impact in existing diagnosis. The aim of this study was to perform a narrative review on the preventative, and mitigating, effects of physical activity on AD onset, including genetic factors, mechanism of action and physical activity typology. In this article, we conducted a narrative review of the influence physical activity and exercise have on AD, utilising key terms related to AD, physical activity, mechanism and prevention, searching the online databases; Web of Science, PubMed and Google Scholar, and, subsequently, discuss possible mechanisms of this action. On the basis of this review, it is evident that physical activity and exercise may be incorporated in AD, notwithstanding, a greater number of high-quality randomised controlled trials are needed, moreover, physical activity typology must be acutely considered, primarily due to a dearth of research on the efficacy of physical activity types other than aerobic.