Response of the competitive balance model to the external field.

The competitive balance model was proposed as an extension of the structural balance theory, aiming to account for heterogeneities observed in real-world networks. In this model, different paradigms lead to form different friendship and enmity. As an example, friendship or enmity between countries can have a political or religious basis. The suggested Hamiltonian is symmetrical between paradigms. Our analyses show that a balanced state can be achieved if just one paradigm prevails in the network and the paradigm shift is possible only by imposing an external field. In this paper, we investigate the influence of the external field on the evolution of the network. We drive the mean-field solutions of the model and verify the accuracy of our analytical solutions by performing Monte-Carlo simulations. We observe that the external field breaks the symmetry of the system. The response of the system to this external field, contingent upon temperature, can be either paramagnetic or ferromagnetic. We observed a hysteresis behavior in the ferromagnetic regime. Once communities are formed based on a certain paradigm, then they resist change. We found that to avoid wasting energy we need to know the level of stochastic behavior in the network. Analogous to magnetic systems, we observe that susceptibility adheres to Curie's law.

The structure balance of gene-gene networks beyond pairwise interactions.

Despite its high and direct impact on nearly all biological processes, the underlying structure of gene-gene interaction networks is investigated so far according to pair connections. To address this, we explore the gene interaction networks of the yeast Saccharomyces cerevisiae beyond pairwise interaction using the structural balance theory (SBT). Specifically, we ask whether essential and nonessential gene interaction networks are structurally balanced. We study triadic interactions in the weighted signed undirected gene networks and observe that balanced and unbalanced triads are over and underrepresented in both networks, thus beautifully in line with the strong notion of balance. Moreover, we note that the energy distribution of triads is significantly different in both essential and nonessential networks compared to the shuffled networks. Yet, this difference is greater in the essential network regarding the frequency as well as the energy of triads. Additionally, results demonstrate that triads in the essential gene network are more interconnected through sharing common links, while in the nonessential network they tend to be isolated. Last but not least, we investigate the contribution of all-length signed walks and its impact on the degree of balance. Our findings reveal that interestingly when considering longer cycles, not only, both essential and nonessential gene networks are more balanced compared to their corresponding shuffled networks, but also, the nonessential gene network is more balanced compared to the essential network.

Effects of dual-task training with blood flow restriction on cognitive functions, muscle quality, and circulatory biomarkers in elderly women.

This study investigated the effects of an eight-week dual-task training with and without blood flow restriction (BFR) on muscle quality (MQ) biomarkers, physical and cognitive functions in older women. Twenty-four healthy volunteers (62.9 ± 3.1years) were randomly assigned into either dual-task (DT), DT with blood flow restriction (DTBFR), or control (C) group. The experimental groups performed cognitive tasks while walked on a treadmill at 45% of heart rate reserve (HRR), 20 min per session, three sessions per week for eight weeks. The cuff pressure for the DTBFR group was 50% of the calculated arterial blood occlusion and was increased by 10% every 2 weeks. Pre and post-training intervention, biomarkers of MQ and cognitive functions, body composition, maximal strength, and psychological status were measured. There was a significant interaction effect on BDNF, CAF, P3NP, body mass, BMI, fat percentage, visceral fat mass, and total fat mass (p<0.05). Furthermore, a significant interaction effect on knee extension, 30-s stand-up test, 6-min walk test, timed up&go test, and QOL was observed. There was a significant effect of time on MMSE, sleep quality, and mood score. These findings suggested that including BFR to DT training result in greater physiological and psychological responses and should be considered a training method to combat undesired changes associated with increasing age.