Search

Hysteresis has been used to understand various social phenomena, such as political polarization, the persistence of the vaccination-compliance problem, or the delayed response of employees in a firm to wage incentives. The aim of this article is to show the insights that can be gained from using agent-based models (ABMs) to study hysteresis. To build up an intuition about hysteresis, we start with an illustrative example from physics that demonstrates how hysteresis manifests as collective memory. Next, we present examples of hysteresis in psychology and social systems. We then present two simple ABMs of binary decisions—the Ising model and the q -voter model—to explain how hysteresis can be observed in ABMs. Specifically, we show that hysteresis can result from the influence of various external factors present in social systems, such as organizational polices, governmental laws, or mass media campaigns, as well as internal noise associated with random changes in agent decisions. Finally, we clarify the relationship between several closely related concepts such as order–disorder transitions or bifurcation, and we conclude the article with a discussion of the advantages of ABMs. [ABSTRACT FROM AUTHOR]

We compare two versions of the nonlinear q -voter model: the original one, with annealed randomness, and the modified one, with quenched randomness. In the original model, each voter changes its opinion with a certain probability ϵ if the group of influence is not unanimous. In contrast, the modified version introduces two types of voters that act in a deterministic way in the case of disagreement in the influence group: the fraction ϵ of voters always change their current opinion, whereas the rest of them always maintain it. Although both concepts of randomness lead to the same average number of opinion changes in the system on the microscopic level, they cause qualitatively distinct results on the macroscopic level. We focus on the mean-field description of these models. Our approach relies on the stability analysis by the linearization technique developed within dynamical system theory. This approach allows us to derive complete, exact phase diagrams for both models. The results obtained in this paper indicate that quenched randomness promotes continuous phase transitions to a greater extent, whereas annealed randomness favors discontinuous ones. The quenched model also creates combinations of continuous and discontinuous phase transitions unobserved in the annealed model, in which the up–down symmetry may be spontaneously broken inside or outside the hysteresis loop. The analytical results are confirmed by Monte Carlo simulations carried out on a complete graph. [ABSTRACT FROM AUTHOR]

We present a short review based on the nonlinear q -voter model about problems and methods raised within statistical physics of opinion formation (SPOOF). We describe relations between models of opinion formation, developed by physicists, and theoretical models of social response, known in social psychology. We draw attention to issues that are interesting for social psychologists and physicists. We show examples of studies directly inspired by social psychology like: "independence vs. anticonformity" or "personality vs. situation". We summarize the results that have been already obtained and point out what else can be done, also with respect to other models in SPOOF. Finally, we demonstrate several analytical methods useful in SPOOF, such as the concept of effective force and potential, Landau's approach to phase transitions, or mean-field and pair approximations. [ABSTRACT FROM AUTHOR]

We investigate an agent-based model of opinion dynamics with two types of social response: conformity and independence. Conformity is introduced to the model analogously as in the Sznajd model or q -voter model, which means that only unanimous group exerts peer pressure on individuals. The novelty, in relation to previous versions of the q -voter model, is memory possessed by each agent and external noise T , which plays the role of social temperature. Each agent has its own memories of past experiences related to the social costs and benefits of being independent or conformist. If an agent was awarded in past more for being independent, it will have a greater tendency to be independent than conformist and vice versa. We will show that depending on the social temperature T the system spontaneously organizes into one of two regimes. Below a certain critical social temperature T c , all agents in the society acquire personal traits (so called person state ). Some of them become permanent conformists and others start to behave forever independently. This means that initially homogeneous population becomes heterogeneous, and agents respond differently to social influence. For T > T c , all agents with equal probabilities behave independently or conform to peer pressure (so called situation state ). This regime change between person and situation state, which reminds the idea of an annealed vs. quenched disorder, affects also public opinion. Particularly interesting results are obtained for individualistic societies, in which public opinion is non-monotonic function of T , which means that there is an optimal social temperature for which an agreement in the society is the highest. [ABSTRACT FROM AUTHOR]

We study the q-voter model driven by stochastic noise arising from one out of two types of nonconformity: anticonformity or independence. We compare two approaches that were inspired by the famous psychological controversy known as the person-situation debate. We relate the person approach with the quenched disorder and the situation approach with the annealed disorder, and investigate how these two approaches influence order-disorder phase transitions observed in the q-voter model with noise. We show that under a quenched disorder, differences between models with independence and anticonformity are weaker and only quantitative. In contrast, annealing has a much more profound impact on the system and leads to qualitative differences between models on a macroscopic level. Furthermore, only under an annealed disorder may the discontinuous phase transitions appear. It seems that freezing the agents' behavior at the beginning of simulation--introducing quenched disorder--supports second--order phase transitions, whereas allowing agents to reverse their attitude in time--incorporating annealed disorder--supports discontinuous ones. We show that anticonformity is insensitive to the type of disorder, and in all cases it gives the same result. We precede our study with a short insight from statistical physics into annealed vs. quenched disorder and a brief review of these two approaches in models of opinion dynamics. [ABSTRACT FROM AUTHOR]

We propose and compare six different ways of mapping the modified q -voter model to complex networks. Considering square lattices, Barabási–Albert, Watts–Strogatz and real Twitter networks, we ask the question if always a particular choice of the group of influence of a fixed size q leads to different behavior at the macroscopic level. Using Monte Carlo simulations we show that the answer depends on the relative average path length of the network and for real-life topologies the differences between the considered mappings may be negligible. [ABSTRACT FROM AUTHOR]

We study a nonlinear g-voter model with stochastic noise, interpreted in the social context as independence, on a duplex network. To study the role of the multilevelness in this model we propose three methods of transferring the model from a mono- to a multiplex network. They take into account two criteria: one related to the status of independence (LOCAL vs GLOBAL) and one related to peer pressure (AND vs OR). In order to examine the influence of the presence of more than one level in the social network, we perform simulations on a particularly simple multiplex: a duplex clique, which consists of two fully overlapped complete graphs (cliques). Solving numerically the rate equation and simultaneously conducting Monte Carlo simulations, we provide evidence that even a simple rearrangement into a duplex topology may lead to significant changes in the observed behavior. However, qualitative changes in the phase transitions can be observed for only one of the considered rules: L0CAL&AND. For this rule the phase transition becomes discontinuous for q = 5, whereas for a monoplex such behavior is observed for q = 6. Interestingly, only this rule admits construction of realistic variants of the model, in line with recent social experiments. [ABSTRACT FROM AUTHOR]

Background: Agent-based models (ABM) are believed to be a very powerful tool in the social sciences, sometimes even treated as a substitute for social experiments. When building an ABM we have to define the agents and the rules governing the artificial society. Given the complexity and our limited understanding of the human nature, we face the problem of assuming that either personal traits, the situation or both have impact on the social behavior of agents. However, as the long-standing person-situation debate in psychology shows, there is no consensus as to the underlying psychological mechanism and the important question that arises is whether the modeling assumptions we make will have a substantial influence on the simulated behavior of the system as a whole or not. Methodology/Principal Findings: Studying two variants of the same agent-based model of opinion formation, we show that the decision to choose either personal traits or the situation as the primary factor driving social interactions is of critical importance. Using Monte Carlo simulations (for Barabasi-Albert networks) and analytic calculations (for a complete graph) we provide evidence that assuming a person-specific response to social influence at the microscopic level generally leads to a completely different and less realistic aggregate or macroscopic behavior than an assumption of a situation-specific response; a result that has been reported by social psychologists for a range of experimental setups, but has been downplayed or ignored in the opinion dynamics literature. Significance: This sensitivity to modeling assumptions has far reaching consequences also beyond opinion dynamics, since agent-based models are becoming a popular tool among economists and policy makers and are often used as substitutes of real social experiments. [ABSTRACT FROM AUTHOR]

In this paper, we modify a two-dimensional variant of a two-state nonlinear voter model and apply it to understand how new ideas, products or behaviors spread throughout the society in time. In particular, we want to find answers to two important questions in the field of diffusion of innovation: Why does the diffusion of innovation take sometimes so long? and Why does it fail so often? Because these kind of questions cannot be answered within classical aggregate diffusion models, like the Bass model, we use an agent-based modeling approach. [ABSTRACT FROM AUTHOR]

The aim of this paper is to examine how different types of social influence, introduced on the microscopic (individual) level, manifest on the macroscopic level, i.e. in the society. The inspiration for this task came mainly from two sources-social psychology that recognize two different types of nonconformity (anticonformity and independence) and the observation related to the agent-based modeling that was verbalized in 2002 by Macy and Willer that there was a little effort to provide analysis of how results differ depending on the model designs. To achieve the goal, we propose a generalized model of opinion dynamics, that as a special cases reduces to the linear voter model, Sznajd model, q-voter model and the majority rule. We use the model to examine the differences, that appear at the macroscopic level, under the influence of two types of nonconformity, introduced on the microscopic level. We answer the question if the observed differences are universal or model dependent. [ABSTRACT FROM AUTHOR]

We propose a simple microscopic model of consumer behavior in which decisions are made solely on the basis of person to person communication. Within our model we determine which factors are important in word of mouth marketing. We provide both Monte Carlo simulations, as well as mean-field analytical calculations and show that both the average decision time and uncertainty of decision grow nonlinearly with the amount of information up to a certain threshold value. [ABSTRACT FROM AUTHOR]

We consider generalized zero-temperature Glauber dynamics under a partially synchronous updating mode for a one-dimensional system. Using Monte Carlo simulations, we calculate the phase diagram and show that the system exhibits phase transition between the ferromagnetic and active antiferromagnetic phases. Moreover, we provide analytical calculations that allow us to understand the origin of the phase transition and confirm simulation results obtained earlier for synchronous updates. [ABSTRACT FROM AUTHOR]

We study a nonlinear q-voter model with stochastic driving on a complete graph. We investigate two types of stochasticity that, using the language of social sciences, can be interpreted as different kinds of nonconformity. From a social point of view, it is very important to distinguish between two types nonconformity, so-called anticonformity and independence. A majority of work has suggested that these social differences may be completely irrelevant in terms of microscopic modeling that uses tools of statistical physics and that both types of nonconformity play the role of so-called social temperature. In this paper we clarify the concept of social temperature and show that different types of noise may lead to qualitatively different emergent properties. In particular, we show that in the model with anticonformity the critical value of noise increases with parameter q, whereas in the model with independence the critical value of noise decreases with q. Moreover, in the model with anticonformity the phase transition is continuous for any value of q, whereas in the model with independence the transition is continuous for q ⩽ 5 and discontinuous for q > 5. [ABSTRACT FROM AUTHOR]

We formulate and investigate the nonlinear q-voter model (which as a special case includes the linear voter and the Sznajd model) on a one-dimensional lattice. We derive an analytical formula for the exit probability and show that it agrees perfectly with Monte Carlo simulations. The puzzle that we deal with here may be summarized by a simple question: Why does the mean-field approach give the exact formula for the exit probability in the one-dimensional nonlinear q-voter model? To answer this question, we test several hypotheses proposed recently for the Sznajd model, including the finite size effects, the influence of the range of interactions, and the importance of the initial step of the evolution. On the one hand, our work is part of a trend of the current debate on the form of the exit probability in the one-dimensional Sznajd model, but on the other hand, it concerns the much broader problem of the nonlinear q-voter model. [ABSTRACT FROM AUTHOR]

In this paper we investigate a model (based on the idea of the outflow dynamics), in which only conformity and anticonformity can lead to the opinion change. We show that for low level of anticonformity the consensus is still reachable but spontaneous reorientations between two types of consensus ("all say yes" or "all say no") appear. [ABSTRACT FROM AUTHOR]

In this paper we compare the relaxation in several versions of the Sznajd model (SM) with random sequential updating on the chain and square lattice. We start by reviewing briefly all proposed one-dimensional versions of SM. Next, we compare the results obtained from Monte Carlo simulations with the mean field results obtained by Slanina and Lavicka. Finally, we investigate the relaxation on the square lattice and compare two generalizations of SM, one suggested by Stauffer et al. and another by Galam. We show that there are no qualitative differences between these two approaches, although the relaxation within the Galam rule is faster than within the well known Stauffer et al. rule. [ABSTRACT FROM AUTHOR]

Abstract: We propose a model to simulate the process of opinion formation in a society where the traditional division into leftists and rightists is not enough any longer. The model is based on the Ashkin–Teller idea to assign two Ising spins to each site (agent). The two states (up and down) of the first spin represent two possible opinions on any question in an economic area, and the two states of the second spin in a personal area. We assume that the mechanisms of opinion formation in both of these areas are different. The interaction between them is introduced in the form of a tolerance factor. It has been found, among others, that the formation of consensus between groups of agents which differ only in the economic area is quite simple, whereas if they differ in the personal area no consensus is possible. [Copyright &y& Elsevier]

A simple Ising spin model which can describe a mechanism of making a decision in a closed community is proposed. It is shown via standard Monte Carlo simulations that very simple rules lead to rather complicated dynamics and to a power law in the decision time distribution. It is found that a closed community has to evolve either to a dictatorship or a stalemate state (inability to take any common decision). A common decision can be taken in a "democratic way" only by an open community. [ABSTRACT FROM AUTHOR]

In honor of professor Dietrich Stauffer we review the literature on the Sznajd model, which probably owes him not only the name and popularity, but perhaps even the fact that it was published in a scientific journal at all. We start the review with the personal memories on the origin of the model and on Stauffer's role throughout the story. Then, we describe the original model and propose the new generalization that captures all versions of the model described in the original paper from 2000. In consecutive sections we review the existing literature that was published over last 20 years. [ABSTRACT FROM AUTHOR]

In this work, we address the question of the role of the influence of group size on the emergence of various collective social phenomena, such as consensus, polarization and social hysteresis. To answer this question, we study the three-state noisy q-voter model with bounded confidence, in which agents can be in one of three states: two extremes (leftist and rightist) and centrist. We study the model on a complete graph within the mean-field approach and show that, depending on the size q of the influence group, saddle-node bifurcation cascades of different length appear and different collective phenomena are possible. In particular, for all values of q > 1 , social hysteresis is observed. Furthermore, for small values of q ∈ (1 , 4) , disagreement, polarization and domination of centrists (a consensus understood as the general agreement, not unanimity) can be achieved but not the domination of extremists. The latter is possible only for larger groups of influence. Finally, by comparing our model to others, we discuss how a small change in the rules at the microscopic level can dramatically change the macroscopic behavior of the model. [ABSTRACT FROM AUTHOR]

We study the homogeneous symmetrical threshold model with independence (noise) by pair approximation and Monte Carlo simulations on Erdős-Rényi and Watts-Strogatz graphs. The model is a modified version of the famous Granovetter's threshold model: with probability p a voter acts independently, i.e., takes randomly one of two states ±1; with complementary probability 1-p, a voter takes a given state, if a sufficiently large fraction (above a given threshold r) of individuals in its neighborhood is in this state. We show that the character of the phase transition, induced by the noise parameter p, depends on the threshold r, as well as graph's parameters. For r=0.5 only continuous phase transitions are observed, whereas for r>0.5 discontinuous phase transitions also are possible. The hysteresis increases with the average degree ⟨k⟩ and the rewriting parameter β. On the other hand, the dependence between the width of the hysteresis and the threshold r is nonmonotonic. The value of r, for which the maximum hysteresis is observed, overlaps pretty well with the size of the majority used for the descriptive norms in order to manipulate people within social experiments. We put the results obtained within this paper into a broader picture and discuss them in the context of two other models of binary opinions: the majority-vote and the q-voter model. Finally, we discuss why the appearance of social hysteresis in models of opinion dynamics is desirable. [ABSTRACT FROM AUTHOR]

We study the q-voter model with flexibility, which allows for describing a broad spectrum of independence from zealots, inflexibility, or stubbornness through noisy voters to self-anticonformity. Analyzing the model within the pair approximation allows us to derive the analytical formula for the critical point, below which an ordered (agreement) phase is stable. We determine the role of flexibility, which can be understood as an amount of variability associated with an independent behavior, as well as the role of the average network degree in shaping the character of the phase transition. We check the existence of the scaling relation, which previously was derived for the Sznajd model. We show that the scaling is universal, in a sense that it does not depend neither on the size of the group of influence nor on the average network degree. Analyzing the model in terms of the rescaled parameter, we determine the critical point, the jump of the order parameter, as well as the width of the hysteresis as a function of the average network degree 〈 k 〉 and the size of the group of influence q. [ABSTRACT FROM AUTHOR]

We introduce a generalized version of the noisy q-voter model, one of the most popular opinion dynamics models, in which voters can be in one of s ≥ 2 states. As in the original binary q-voter model, which corresponds to s = 2 , at each update randomly selected voter can conform to its q randomly chosen neighbors only if they are all in the same state. Additionally, a voter can act independently, taking a randomly chosen state, which introduces disorder to the system. We consider two types of disorder: (1) annealed, which means that each voter can act independently with probability p and with complementary probability 1 - p conform to others, and (2) quenched, which means that there is a fraction p of all voters, which are permanently independent and the rest of them are conformists. We analyze the model on the complete graph analytically and via Monte Carlo simulations. We show that for the number of states s > 2 the model displays discontinuous phase transitions for any q > 1 , on contrary to the model with binary opinions, in which discontinuous phase transitions are observed only for q > 5 . Moreover, unlike the case of s = 2 , for s > 2 discontinuous phase transitions survive under the quenched disorder, although they are less sharp than under the annealed one. [ABSTRACT FROM AUTHOR]

Despite the very positive – as measured by market surveys – attitude towards eco-innovations and sustainability in general, the actual market penetration of green products and practices generally falls behind the expectations. In this paper we argue that considering difficulty of engagement , as used in the Campbell Paradigm, is of critical importance when modeling diffusion of eco-innovations. Such a notion of difficulty possesses three desired properties: (i) parsimony – it is represented by a single value, (ii) interpretability – it can be regarded as an estimator of the otherwise complex notion of behavioral cost , and (iii) applicability – it can be easily measured through market surveys. In an extensive simulation and analytical study involving empirically measured difficulty and an agent-based model spanned on different social network structures, we show that innovation adoption may exhibit abrupt changes in market penetration as a result of even small changes in difficulty. The latter may be of particular interest to policy makers who have to make strategic decisions when introducing socially – but not necessarily individually – desired products and practices, like dynamic or green electricity tariffs. [ABSTRACT FROM AUTHOR]

We modify the kinetic Ising model with Metropolis dynamics, allowing each spin to interact only with q spins randomly chosen from the whole system, which corresponds to the topology of a complete graph. We show that the model with q ≥ 3 exhibits a phase transition between ferromagnetic and paramagnetic phases at temperature T*, which linearly increases with q. Moreover, we show that for q = 3 the phase transition is continuous and that it is discontinuous for larger values of q. For q ≥ 3, the hysteresis exhibits oscillatory behavior--expanding for even values of q and shrinking for odd values of q. Due to the mean-field-like nature of the model, we are able to derive the analytical form of transition probabilities and, therefore, calculate not only the probability density function of the order parameter but also precisely determine the hysteresis and the effective potential showing stable, unstable, and metastable steady states. Our results show that a seemingly small modification of the kinetic Ising model leads not only to the switch from a continuous to a discontinuous phase transition, but also to an unexpected oscillating behavior of the hysteresis and a puzzling phenomenon for q = 5, which might be taken as evidence for the so-called mixed-order phase transition. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we investigate the Sznajd model of opinion dynamics with anticonformity on a complete graph. We show that below some threshold value of anticonformal behavior spontaneous reorientations occur between two stable states. Dealing with a complete graph allows us also for an analytical treatment. We provide analytical calculations both for the infinite and finite systems. We show that opinion dynamics can be understood as a movement of a public opinion in a symmetric bistable effective potential. We focus also on the spontaneous transitions between stable states in the case of the finite system and show that a typical waiting time can be observed. [Copyright &y& Elsevier]

We study the binary q-voter model with generalized anticonformity on random Erdős–Rényi graphs. In such a model, two types of social responses, conformity and anticonformity, occur with complementary probabilities and the size of the source of influence q c in case of conformity is independent from the size of the source of influence q a in case of anticonformity. For q c = q a = q the model reduces to the original q-voter model with anticonformity. Previously, such a generalized model was studied only on the complete graph, which corresponds to the mean-field approach. It was shown that it can display discontinuous phase transitions for q c ≥ q a + Δ q , where Δ q = 4 for q a ≤ 3 and Δ q = 3 for q a > 3 . In this paper, we pose the question if discontinuous phase transitions survive on random graphs with an average node degree ⟨ k ⟩ ≤ 150 observed empirically in social networks. Using the pair approximation, as well as Monte Carlo simulations, we show that discontinuous phase transitions indeed can survive, even for relatively small values of ⟨ k ⟩ . Moreover, we show that for q a < q c - 1 pair approximation results overlap the Monte Carlo ones. On the other hand, for q a ≥ q c - 1 pair approximation gives qualitatively wrong results indicating discontinuous phase transitions neither observed in the simulations nor within the mean-field approach. Finally, we report an intriguing result showing that the difference between the spinodals obtained within the pair approximation and the mean-field approach follows a power law with respect to ⟨ k ⟩ , as long as the pair approximation indicates correctly the type of the phase transition. [ABSTRACT FROM AUTHOR]

Motivated by the empirical study that identifies a correlation between particular social responses and different interaction ranges, we study the q -voter model with various combinations of local and global sources of conformity and anticonformity. The models are investigated by means of the pair approximation and Monte Carlo simulations on Watts–Strogatz and Barabási–Albert networks. We show that within the model with local conformity and global anticonformity, the agreement in the system is the most difficult one to achieve and the role of the network structure is the most significant. Interestingly, the model with swapped interaction ranges, namely, with global conformity and local anticonformity, becomes almost insensitive to the changes in the network structure. The obtained results may have far reaching consequences for marketing strategies conducted via social media channels. [ABSTRACT FROM AUTHOR]

We ask a question about the possibility of a discontinuous phase transition and the related social hysteresis within the q-voter model with anticonformity. Previously, it was claimed that within the q-voter model the social hysteresis can emerge only because of an independent behavior, and for the model with anticonformity only continuous phase transitions are possible. However, this claim was derived from the model, in which the size of the influence group needed for the conformity was the same as the size of the group needed for the anticonformity. Here, we abandon this assumption on the equality of two types of social response and introduce the generalized model, in which the size of the influence group needed for the conformity q c and the size of the influence group needed for the anticonformity q a are independent variables and in general q c ≠ q a . We investigate the model on the complete graph, similarly as it was done for the original q-voter model with anticonformity, and we show that such a generalized model displays both types of phase transitions depending on parameters q c and q a . [ABSTRACT FROM AUTHOR]

Within this paper we explore the idea of a critical value representing the proportion of majority members within a group that affects dramatic changes in influence targets’ conformity. We consider the threshold q-voter model when the responses of the Willis-Nail model, a well-established two-dimensional model of social response, are used as a foundation. Specifically, we study a generalized threshold q-voter model when all basic types of social response described by Willis-Nail model are considered, i.e. conformity, anticonformity, independence, and uniformity/congruence. These responses occur in our model with complementary probabilities. We introduce independently two thresholds: one needed for conformity, as well as a second one for anticonformity. In the case of conformity, at least r individuals among q neighbors have to share the same opinion in order to persuade a voter to follow majority’s opinion, whereas in the case of anticonformity, at least w individuals among q neighbors have to share the same opinion in order to influence voters to take an opinion that goes against that of their own reference group. We solve the model on a complete graph and show that the threshold for conformity significantly influences the results. For example, there is a critical threshold for conformity above which the system behaves as in the case of unanimity, i.e. displays continuous and discontinuous phase transitions. On the other hand, the threshold for anticonformity is almost irrelevant. We discuss our results from the perspective of theories of social psychology, as well as the philosophy of agent-based modeling. [ABSTRACT FROM AUTHOR]

We analyze a modified kinetic Ising model, a so-called q-neighbor Ising model, with Metropolis dynamics [Phys. Rev. E 92, 052105 (2015)] on a duplex clique and a partially duplex clique. In the q-neighbor Ising model each spin interacts only with q spins randomly chosen from its whole neighborhood. In the case of a duplex clique the change of a spin is allowed only if both levels simultaneously induce this change. Due to the mean-field-like nature of the model we are able to derive the analytic form of transition probabilities and solve the corresponding master equation. The existence of the second level changes dramatically the character of the phase transition. In the case of the monoplex clique, the q-neighbor Ising model exhibits a continuous phase transition for q=3, discontinuous phase transition for q≥4, and for q=1 and q=2 the phase transition is not observed. On the other hand, in the case of the duplex clique continuous phase transitions are observed for all values of q, even for q=1 and q=2. Subsequently we introduce a partially duplex clique, parametrized by r∈[0,1], which allows us to tune the network from monoplex (r=0) to duplex (r=1). Such a generalized topology, in which a fraction r of all nodes appear on both levels, allows us to obtain the critical value of r=r∗(q) at which a tricriticality (switch from continuous to discontinuous phase transition) appears. [ABSTRACT FROM AUTHOR]

We introduce a new agent-based model of opinion dynamics in which binary opinions of each agent can be measured and described regarding both pre- and post-influence at both of two levels, public and private, vis-à-vis the influence source. The model combines ideas introduced within the q-voter model with noise, proposed by physicists, with the descriptive, four-dimensional model of social response, formulated by social psychologists. We investigate two versions of the same model that differ only by the updating order: an opinion on the public level is updated before an opinion on the private level or vice versa. We show how the results on the macroscopic scale depend on this order. The main finding of this paper is that both models produce the same outcome if one looks only at such a macroscopic variable as the total number of the individuals with positive opinions. However, if also the level of internal harmony (viz., dissonance) is measured, then significant, qualitative differences are seen between these two versions of the model. All results were obtained simultaneously within Monte Carlo simulations and analytical calculations. We discuss the importance of our studies and findings from three points of view: the theory of phase transitions, agent-based modeling of social systems, and social psychology. [ABSTRACT FROM AUTHOR]

We investigate a kinetic Ising model with several single-spin-flip dynamics (including Metropolis and heat bath) on quenched and annealed random regular graphs. As expected, on the quenched structures all proposed algorithms reproduce the same results since the conditions for the detailed balance and the Boltzmann distribution in an equilibrium are satisfied. However, on the annealed graphs the situation is far less clear--the network annealing disturbs the equilibrium moving the system away from it. Consequently, distinct dynamics lead to different steady states. We show that some algorithms are more resistant to the annealed disorder, which causes only small quantitative changes in the model behavior. On the other hand, there are dynamics for which the influence of annealing on the system is significant, and qualitative changes arise like switching the type of phase transition from a continuous to a discontinuous one. We try to identify features of the proposed dynamics which are responsible for the above phenomenon. [ABSTRACT FROM AUTHOR]

We study a simple agent-based model of the recurring fashion cycles in the society that consists of two interacting communities: “snobs” and “followers” (or “opinion hunters”, hence the name of the model). Followers conform to all other individuals, whereas snobs conform only to their own group and anticonform to the other. The model allows to examine the role of the social structure, i.e. the influence of the number of inter-links between the two communities, as well as the role of the stability of links. The latter is accomplished by considering two versions of the same model—quenched (parameterized by fraction L of fixed inter-links) and annealed (parameterized by probability p that a given inter-link exists). Using Monte Carlo simulations and analytical treatment (the latter only for the annealed model), we show that there is a critical fraction of inter-links, above which recurring cycles occur. For p ≤ 0.5 we derive a relation between parameters L and p that allows to compare both models and show that the critical value of inter-connections, p*, is the same for both versions of the model (annealed and quenched) but the period of a fashion cycle is shorter for the quenched model. Near the critical point, the cycles are irregular and a change of fashion is difficult to predict. For the annealed model we also provide a deeper theoretical analysis. We conjecture on topological grounds that the so-called saddle node heteroclinic bifurcation appears at p*. For p ≥ 0.5 we show analytically the existence of the second critical value of p, for which the system undergoes Hopf’s bifurcation. [ABSTRACT FROM AUTHOR]

Abstract: Introduction: Anatomical proximity of the eye and the intracranial space is a fact but the existence of physiological and pathophysiological relationships between them is elusive. The objective of this study was to explore anatomical and pathophysiological interactions between the eye and the intracranial space and to assess clinical utility of intraocular pressure measurement in estimation of intracranial pressure in patients with brain injuries and to discover how haemodynamic instability could influence these interactions. Controversy surrounds the recent literature concerning this problem and the consensus has not been achieved. Materials and methods: We evaluated the correlation between intracranial pressure and intraocular pressure, intracranial pressure and mean arterial pressure, intraocular pressure and mean arterial pressure in 40 patients with brain injuries initially comatose, admitted to our hospital. All patients required the intracranial pressure monitoring on clinical grounds. Simultaneous recordings of intracranial pressure, intraocular pressure and mean arterial pressure were performed. Results: We calculated both the linear correlation coefficient and the Spearman rank-order correlation coefficient for all three relations. We found significant correlation between intraocular pressure and mean arterial pressure in 63% of the tested population. When the power of the test was increased, by considering only patients with 11 or more observations, this ratio increased to 76%. However, the correlation between intraocular pressure and intracranial pressure, as well as, between intracranial pressure and mean arterial pressure was not significant. Conclusions: There is no anatomical and pathophysiological basis for the statement that intraocular pressure can be used as an indirect estimator of intracranial pressure. [Copyright &y& Elsevier]

We study a q-voter model with stochastic driving on a complete graph with q being a random variable described by probability density function P(q), instead of a constant value. We investigate two types of P(q): (1) artificial with the fixed expected value ⟨q⟩, but a changing variance and (2) empirical of freely forming groups in informal places. We investigate also two types of stochasticity that can be interpreted as different kinds of nonconformity (anticonformity or independence) to answer the question about differences observed at the macroscopic level between these two types of nonconformity in real social systems. Moreover, we ask the question if the behavior of a system depends on the average value of the group size q or rather on probability distribution function P(q). [ABSTRACT FROM AUTHOR]