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 footprint of campaign strategies in Farsi Twitter: A case for 2021 Iranian presidential election.

The rise of social media accompanied by the Covid-19 Pandemic has instigated a shift in paradigm in the presidential campaigns in Iran from the real world to social media. Unlike previous presidential elections, there was a decrease in physical events and advertisements for the candidates; in turn, the online presence of presidential candidates is significantly increased. Farsi Twitter played a specific role in this matter, as it became the platform for creating political content. In this study, we found traces of organizational activities in Farsi Twitter, and our investigations reveal that the discussion network of the 2021 election is heterogeneous and highly polarized. However, unlike many other documented election cases in Iran and around the globe, communities of candidates' supporters are very close in one pole, and the other pole is for "Anti-voters" who endorse boycotting the election. With almost no reciprocal ties, these two poles form two echo chambers, one favoring the election and the other for voter suppression. Furthermore, a high presence of bot activity is observed among the most influential users in all of the involved communities.

Pattern of frustration formation in the functional brain network.

The brain is a frustrated system that contains conflictual link arrangements named frustration. The frustration as a source of disorder prevents the system from settling into low-energy states and provides flexibility for brain network organization. In this research, we tried to identify the pattern of frustration formation in the brain at the levels of region, connection, canonical network, and hemisphere. We found that frustration formation has no uniform pattern. Some subcortical elements have an active role in frustration formation, despite low contributions from many cortical elements. Frustrating connections are mostly between-network connections, and triadic frustrations are mainly formed between three regions from three distinct canonical networks. We did not find any significant differences between brain hemispheres or any robust differences between the frustration formation patterns of various life-span stages. Our results may be interesting for those who study the organization of brain links and promising for those who want to manipulate brain networks.

Brain network analysis approaches commonly ignore the signs of links. Frustration is a fascinating phenomenon referring to the conflictual arrangements of signed links. As a source of instability, it can give valuable information on altering components of a network. It can specify which brain network elements intend to drive brain network alterations. Accordingly, we tried to identify the pattern of frustration formation in the brain network, which brain network elements are more frustrated and which ones are less frustrated. We provided some maps for frustration formation in the levels of region, connection, canonical network, and hemisphere. The introduced concept of frustration and our results may be interesting for brain network scientists.

Requirement to change of functional brain network across the lifespan.

Many studies have focused on neural changes and neuroplasticity, while the signaling demand for neural modification needs to be explored. In this study, we traced this issue in the organization of brain functional links where the conflictual arrangement of signed links makes a request to change. We introduced the number of frustrations (unsatisfied closed triadic interactions) as a measure for assessing "requirement to change" of functional brain network. We revealed that the requirement to change of the resting-state network has a u-shape functionality over the lifespan with a minimum in early adulthood, and it's correlated with the presence of negative links. Also, we discovered that brain negative subnetwork has a special topology with a log-normal degree distribution in all stages, however, its global measures are altered by adulthood. Our results highlight the study of collective behavior of functional negative links as the source of the brain's between-regions conflicts and we propose exploring the attribute of the requirement to change besides other neural change factors.

Using the Quantum Potential in Elementary Portfolio Management: Some Initial Ideas.

Owing to the globalization of the economy, the concept of entangled markets started to form, and this occurrence has smoothed the entrance of quantum mechanics into behavioral finance. In this manuscript, we introduce quantum risk and perform an analysis on portfolio optimization by controlling the quantum potential. We apply this method to eight major indices and construct a portfolio with a minimum quantum risk. The results show quantum risk has a power law behavior with a time-scale just as a standard deviation with different exponents.

Topological impact of negative links on the stability of resting-state brain network.

Stability is a physical attribute that stands opposite the change. However, it is still unclear how the arrangement of links called topology affects network stability. In this study, we tackled this issue in the resting-state brain network using structural balance. Structural balance theory employs the quality of triadic associations between signed links to determine the network stability. In this study, we showed that negative links of the resting-state network make hubs to reduce balance-energy and push the network into a more stable state compared to null-networks with trivial topologies. In this regard, we created a global measure entitled 'tendency to make hub' to assess the hubness of the network. Besides, we revealed nodal degrees of negative links have an exponential distribution that confirms the existence of negative hubs. Our findings indicate that the arrangement of negative links plays an important role in the balance (stability) of the resting-state brain network.

Coupled Criticality Analysis of Inflation and Unemployment.

In this paper, we focus on the critical periods in the economy that are characterized by unusual and large fluctuations in macroeconomic indicators, like those measuring inflation and unemployment. We analyze U.S. data for 70 years from 1948 until 2018. To capture their fluctuation essence, we concentrate on the non-Gaussianity of their distributions. We investigate how the non-Gaussianity of these variables affects the coupling structure of them. We distinguish "regular" from "rare" events, in calculating the correlation coefficient, emphasizing that both cases might lead to a different response of the economy. Through the "multifractal random wall" model, one can see that the non-Gaussianity depends on time scales. The non-Gaussianity of unemployment is noticeable only for periods shorter than one year; for longer periods, the fluctuation distribution tends to a Gaussian behavior. In contrast, the non-Gaussianities of inflation fluctuations persist for all time scales. We observe through the "bivariate multifractal random walk" that despite the inflation features, the non-Gaussianity of the coupled structure is finite for scales less than one year, drops for periods larger than one year, and becomes small for scales greater than two years. This means that the footprint of the monetary policies intentionally influencing the inflation and unemployment couple is observed only for time horizons smaller than two years. Finally, to improve some understanding of the effect of rare events, we calculate high moments of the variables' increments for various q orders and various time scales. The results show that coupling with high moments sharply increases during crises.

Fractional Dynamics of Network Growth Constrained by Aging Node Interactions.

In many social complex systems, in which agents are linked by non-linear interactions, the history of events strongly influences the whole network dynamics. However, a class of "commonly accepted beliefs" seems rarely studied. In this paper, we examine how the growth process of a (social) network is influenced by past circumstances. In order to tackle this cause, we simply modify the well known preferential attachment mechanism by imposing a time dependent kernel function in the network evolution equation. This approach leads to a fractional order Barabási-Albert (BA) differential equation, generalizing the BA model. Our results show that, with passing time, an aging process is observed for the network dynamics. The aging process leads to a decay for the node degree values, thereby creating an opposing process to the preferential attachment mechanism. On one hand, based on the preferential attachment mechanism, nodes with a high degree are more likely to absorb links; but, on the other hand, a node's age has a reduced chance for new connections. This competitive scenario allows an increased chance for younger members to become a hub. Simulations of such a network growth with aging constraint confirm the results found from solving the fractional BA equation. We also report, as an exemplary application, an investigation of the collaboration network between Hollywood movie actors. It is undubiously shown that a decay in the dynamics of their collaboration rate is found, even including a sex difference. Such findings suggest a widely universal application of the so generalized BA model.

Aging scaled Brownian motion.

Scaled Brownian motion (SBM) is widely used to model anomalous diffusion of passive tracers in complex and biological systems. It is a highly nonstationary process governed by the Langevin equation for Brownian motion, however, with a power-law time dependence of the noise strength. Here we study the aging properties of SBM for both unconfined and confined motion. Specifically, we derive the ensemble and time averaged mean squared displacements and analyze their behavior in the regimes of weak, intermediate, and strong aging. A very rich behavior is revealed for confined aging SBM depending on different aging times and whether the process is sub- or superdiffusive. We demonstrate that the information on the aging factorizes with respect to the lag time and exhibits a functional form that is identical to the aging behavior of scale-free continuous time random walk processes. While SBM exhibits a disparity between ensemble and time averaged observables and is thus weakly nonergodic, strong aging is shown to effect a convergence of the ensemble and time averaged mean squared displacement. Finally, we derive the density of first passage times in the semi-infinite domain that features a crossover defined by the aging time.