The Heider balance and the looking-glass self: modelling dynamics of social relations

Proper network randomization is key to assessing social balance

Social ties, either positive or negative, lead to signed network patterns, the subject of balance theory. For example, strong balance introduces cycles with even numbers of negative edges. The statistical significance of such patterns is routinely assessed by comparisons to null models. Yet, results in signed networks remain controversial. Here, we show that even if a network exhibits strong balance by construction, current null models can fail to identify it. Our results indicate that matching the signed degree preferences of the nodes is a critical step and so is the preservation of network topology in the null model. As a solution, we propose the STP null model, which integrates both constraints within a maximum entropy framework. STP randomization leads to qualitatively different results, with most social networks consistently demonstrating strong balance in three- and four-node patterns. On the basis our results, we present a potential wiring mechanism behind the observed signed patterns and outline further applications of STP randomization.

Multidimensional attributes expose Heider balance dynamics to measurements

Most of studied social interactions arise from dyadic relations. An exception is Heider Balance Theory that postulates the existence of triad dynamics, which however has been elusive to observe. Here, we discover a sufficient condition for the Heider dynamics observability: assigning the edge signs according to multiple opinions of connected agents. Using longitudinal records of university student mutual contacts and opinions, we create a coevolving network on which we introduce models of student interactions. These models account for: multiple topics of individual student opinions, influence of such opinions on dyadic relations, and influence of triadic relations on opinions. We show that the triadic influence is empirically measurable for static and dynamic observables when signs of edges are defined by multidimensional differences between opinions on all topics. Yet, when these signs are defined by a difference between opinions on each topic separately, the triadic interactions' influence is indistinguishable from noise.

Mean-field approximation for structural balance dynamics in heat bath

A critical temperature for a complete signed graph of N agents where the time-dependent polarization of links tends towards the Heider (structural) balance is found analytically using the heat-bath approach and the mean-field approximation as T^{c}=(N-2)/a^{c}, where a^{c}≈1.71649. The result is in perfect agreement with numerical simulations starting from the paradise state where all links are positively polarized as well as with the estimation of this temperature received earlier with much more sophisticated methods. When heating the system, one observes a discontinuous and irreversible phase transition at T^{c} from a nearly balanced state when the mean link polarization is about x_{c}=0.796388 to a disordered and unbalanced state where the polarization vanishes. When the initial conditions for the polarization of links are random, then at low temperatures a balanced bipolar state of two mutually hostile cliques exists that decays towards the disorder and there is a discontinuous phase transition at a temperature T^{d} that is lower than T^{c}. The system phase diagram corresponds to the so-called fold catastrophe when a stable solution of the mean-field equation collides with a separatrix, and as a result a hysteresislike loop is observed.

Modified Heider balance on Erdös-Rényi networks

The lack of signed random networks in standard balance studies has prompted us to extend the Hamiltonian of the standard balance model. Random networks with tunable parameters are suitable for better understanding the behavior of standard balance as an underlying dynamics. Moreover, the standard balance model in its original form does not allow preserving tensed triads in the network. Therefore, the thermal behavior of the balance model has been investigated on a fully connected signed network recently. It has been shown that the model undergoes an abrupt phase transition with temperature. Considering these two issues, we examine the thermal behavior of the structural balance model defined on Erdös-Rényi random networks within the range of their connected regime. We provide a mean-field solution for the model. We observe a first-order phase transition with temperature for a wide range of connection probabilities. We detect two transition temperatures, T_{cold} and T_{hot}, characterizing a hysteresis loop. We find that with decreasing the connection probability, both T_{cold} and T_{hot} decrease. However, the slope of decreasing T_{hot} with decreasing connection probability is larger than the slope of decreasing T_{cold}. Hence, the hysteresis region gets narrower until it disappears in a certain connection probability. We provide a phase diagram in the temperature-tie density plane to accurately observe the metastable or coexistence region behavior. Then we justify our mean-field results with a series of Monte Carlo simulations.

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.

The Spread of Ideas in a Network-The Garbage-Can Model

The main goal of our work is to show how ideas change in social networks. Our analysis is based on three concepts: (i) temporal networks, (ii) the Axelrod model of culture dissemination, (iii) the garbage can model of organizational choice. The use of the concept of temporal networks allows us to show the dynamics of ideas spreading processes in networks, thanks to the analysis of contacts between agents in networks. The Axelrod culture dissemination model allows us to use the importance of cooperative behavior for the dynamics of ideas disseminated in networks. In the third model decisions on solutions of problems are made as an outcome of sequences of pseudorandom numbers. The origin of this model is the Herbert Simon’s view on bounded rationality. In the Axelrod model, ideas are conveyed by strings of symbols. The outcome of the model should be the diversity of evolving ideas as dependent on the chain length, on the number of possible values of symbols and on the threshold value of Hamming distance which enables the combination.

Towards the Heider balance: Cellular automaton with a global neighborhood

We study a simple deterministic map that leads a fully connected network to the Heider balance. The map is realized by an algorithm that updates all links synchronously in a way depending on the state of the entire network. We observe that the probability of reaching a balanced state increases with the system size N. Jammed states become less frequent for larger N. The algorithm generates also limit cycles, mostly of length 2, but also of length 3, 4, 6, 12, or 14. We give a simple argument to estimate the mean size of basins of attraction of balanced states, and we discuss the symmetries of the system including the automorphism group as well as gauge invariance of triad configurations. We argue that both symmetries play an essential role in the occurrence of cycles observed in the synchronous dynamics realized by the algorithm.

Mean-field solution for critical behavior of signed networks in competitive balance theory

The competitive balance model has been proposed as an extension to the balance model to address the conflict of interests in signed networks. In this model, two different paradigms or interests compete with each other to dominate the network's relations and impose their own values. In this paper, using the mean-field method, we examine the thermal behavior of the competitive balance model. Our results show that under a certain temperature, the symmetry between two competing interests will spontaneously break which leads to a discrete phase transition. So, starting with a heterogeneous signed network, if agents aim to decrease tension stemming from competitive balance theory, evolution ultimately chooses only one of the existing interests and stability arises where one paradigm dominates the system. The critical temperature depends linearly on the number of nodes, which is a linear dependence in the thermal balance theory as well. Finally, the results obtained through the mean-field method are verified by a series of simulations.

Risk of Substance Use Disorder and Its Associations With Comorbidities and Psychotropic Agents in Patients With Autism

IMPORTANCE

The risk of substance use disorder (SUD) in patients with autism spectrum disorder (ASD) remains unclear.

OBJECTIVE

To investigate the risk of SUD in patients with ASD and its associations with comorbidities, psychotropic agents (PAs), and mortality.

DESIGN, SETTING, AND PARTICIPANTS

This retrospective, population-based, cohort study of 1 936 512 participants used data from the Taiwan National Health Insurance Research Database and was conducted from January 1, 2000, to December 31, 2015. Included participants attended at least 3 outpatient visits within the 1-year study period for symptomatic ASD as determined by the International Classification of Diseases, Ninth Revision, Clinical Modification (ICD-9-CM) diagnostic codes. Individuals diagnosed with ASD before 2000, those diagnosed with SUD before the first visit for ASD, and those with missing data were excluded from the analysis. Patients with ASD and non-ASD controls were matched 1:4 by age, sex, and index date.

EXPOSURES

Symptomatic ASD evaluated for at least 3 outpatient visits within the 1-year study period.

MAIN OUTCOMES AND MEASURES

Adjusted hazard ratios (aHRs) with 95% CIs for SUD, including alcohol use disorder (AUD) and drug use disorder (DUD), and the risk of mortality were calculated. Data were analyzed from March 1 to July 13, 2020.

RESULTS

A total of 6599 individuals with ASD (mean [SD] age, 11.9 [5.1] years; 5094 boys [77.2%]; mean [SD] follow-up period, 8.1 [8.3] years; median follow-up period, 4.3 [interquartile range [IQR], 2.3-5.3] years) and 26 396 controls (mean [SD] age, 12.1 [5.8] years; 20 376 boys [77.2%]; mean [SD] follow-up period, 8.6 [8.9] years; median follow-up period, 4.4 [IQR, 2.4-5.4] years) were enrolled in the study. According to multivariable-adjusted analysis, the aHRs for SUD (2.33; 95% CI, 1.89-2.87), AUD (2.07; 95% CI, 1.60-2.63), and DUD (3.00; 95% CI, 2.15-4.58) were significantly higher in the ASD group than in the non-ASD controls. The aHRs for SUD in the ASD subgroups with 1 PA (0.60; 95% CI, 0.43-0.66) and with multiple PAs (0.37; 95% CI, 0.28-0.49) were significantly lower than those in the ASD subgroup with no PAs. Comparisons between patients with ASD and non-ASD controls with the same comorbidities showed higher aHRs for SUD among patients with ASD (range, 1.17-2.55); moreover, the ASD subgroup not receiving any PAs had an aHR of 6.39 (95% CI, 5.11-7.87) for SUD when they had comorbid tic disorder and aHRs of 5.48 (95% CI, 5.12-5.70) for AUD and 5.42 (95% CI, 5.12-5.80) for DUD when they had comorbid impulse control disorder. The mortality risk was significantly higher in patients with ASD and concomitant SUD than in non-ASD controls without SUD (aHR, 3.17; 95% CI, 2.69-3.89).

CONCLUSIONS AND RELEVANCE

These findings suggest that patients with ASD are vulnerable to the development of SUD. Comorbid ASD and SUD were associated with an increase in mortality risk.

Altered structural balance of resting-state networks in autism

What makes a network complex, in addition to its size, is the interconnected interactions between elements, disruption of which inevitably results in dysfunction. Likewise, the brain networks' complexity arises from interactions beyond pair connections, as it is simplistic to assume that in complex networks state of a link is independently determined only according to its two constituting nodes. This is particularly of note in genetically complex brain impairments, such as the autism spectrum disorder (ASD), which has a surprising heterogeneity in manifestations with no clear-cut neuropathology. Accordingly, structural balance theory (SBT) affirms that in real-world signed networks, a link is remarkably influenced by each of its two nodes' interactions with the third node within a triadic interrelationship. Thus, it is plausible to ask whether ASD is associated with altered structural balance resulting from atypical triadic interactions. In other words, it is the abnormal interplay of positive and negative interactions that matters in ASD, besides and beyond hypo (hyper) pair connectivity. To address this question, we explore triadic interactions based on SBT in the weighted signed resting-state functional magnetic resonance imaging networks of participants with ASD relative to healthy controls (CON). We demonstrate that balanced triads are overrepresented in the ASD and CON networks while unbalanced triads are underrepresented, providing first-time empirical evidence for the strong notion of structural balance on the brain networks. We further analyze the frequency and energy distributions of different triads and suggest an alternative description for the reduced functional integration and segregation in the ASD brain networks. Moreover, results reveal that the scale of change in the whole-brain networks' energy is more narrow in the ASD networks during development. Last but not least, we observe that energy of the salience network and the default mode network are lower in ASD, which may be a reflection of the difficulty in dynamic switching and flexible behaviors. Altogether, these results provide insight into the atypical structural balance of the ASD brain (sub) networks. It also highlights the potential value of SBT as a new perspective in functional connectivity studies, especially in the case of neurodevelopmental disorders.

Stability of Imbalanced Triangles in Gene Regulatory Networks of Cancerous and Normal Cells

Genes communicate with each other through different regulatory effects, which lead to the emergence of complex network structures in cells, and such structures are expected to be different for normal and cancerous cells. To study these differences, we have investigated the Gene Regulatory Network (GRN) of cells as inferred from RNA-sequencing data. The GRN is a signed weighted network corresponding to the inductive or inhibitory interactions. Here we focus on a particular of motifs in the GRN, the triangles, which are imbalanced if the number of negative interactions is odd. By studying the stability of imbalanced triangles in the GRN, we show that the network of cancerous cells has fewer imbalanced triangles compared to normal cells. Moreover, in the normal cells, imbalanced triangles are isolated from the main part of the network, while such motifs are part of the network's giant component in cancerous cells. Our result demonstrates that due to genes' collective behavior the structure of the complex networks is different in cancerous cells from those in normal ones.

Expulsion from structurally balanced paradise

We perform simulations of structural balance evolution on a triangular lattice using the heat-bath algorithm. In contrast to similar approaches-but applied to the analysis of complete graphs-the triangular lattice topology successfully prevents the occurrence of even partial Heider balance. Starting with the state of Heider's paradise, it is just a matter of time when the evolution of the system leads to an unbalanced and disordered state. The time of the system relaxation does not depend on the system size. The lack of any signs of a balanced state was not observed in earlier investigated systems dealing with the structural balance.