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Register a new userMarkov Chain Aggregation for Simple Agent-Based Models on Symmetric Networks: The Voter Model
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For Agent Based Models, in particular the Voter Model (VM), a general framework of aggregation is developed which exploits the symmetries of the agent network $G$. Depending on the symmetry group $Aut_{omega} (N)$ of the weighted agent network, certain ensembles of agent configurations can be interchanged without affecting the dynamical properties of the VM. These configurations can be aggregated into the same macro state and the dynamical process projected onto these states is, contrary to the general case, still a Markov chain. The method facilitates the analysis of the relation between microscopic processes and a their aggregation to a macroscopic level of description and informs about the complexity of a system introduced by heterogeneous interaction relations. In some cases the macro chain is solvable.
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(shortened version) Religions and languages are social variables, like age, sex, wealth or political opinions, to be studied like any other organizational parameter. In fact, religiosity is one of the most important sociological aspects of populations. Languages are also a characteristics of the human kind. New religions, new languages appear though others disappear. All religions and languages evolve when they adapt to the society developments. On the other hand, the number of adherents of a given religion, the number of persons speaking a language is not fixed. Several questions can be raised. E.g. from a macroscopic point of view : How many religions/languages exist at a given time? What is their distribution? What is their life time? How do they evolve?. From a microscopic view point: can one invent agent based models to describe macroscopic aspects? Does it exist simple evolution equations? It is intuitively accepted, but also found through from statistical analysis of the frequency distribution that an attachment process is the primary cause of the distribution evolution : usually the initial religion/language is that of the mother. Later on, changes can occur either due to heterogeneous agent interaction processes or due to external field constraints, - or both. Such cases can be illustrated with historical facts and data. It is stressed that characteristic time scales are different, and recalled that external fields are very relevant in the case of religions, rending the study more interesting within a mechanistic approach
The voter model has been studied extensively as a paradigmatic opinion dynamics model. However, its ability for modeling real opinion dynamics has not been addressed. We introduce a noisy voter model (accounting for social influence) with agents recurrent mobility (as a proxy for social context), where the spatial and population diversity are taken as inputs to the model. We show that the dynamics can be described as a noisy diffusive process that contains the proper anysotropic coupling topology given by population and mobility heterogeneity. The model captures statistical features of the US presidential elections as the stationary vote-share fluctuations across counties, and the long-range spatial correlations that decay logarithmically with the distance. Furthermore, it recovers the behavior of these properties when a real-space renormalization is performed by coarse-graining the geographical scale from county level through congressional districts and up to states. Finally, we analyze the role of the mobility range and the randomness in decision making which are consistent with the empirical observations.
Spreading processes are ubiquitous in natural and artificial systems. They can be studied via a plethora of models, depending on the specific details of the phenomena under study. Disease contagion and rumor spreading are among the most important of these processes due to their practical relevance. However, despite the similarities between them, current models address both spreading dynamics separately. In this paper, we propose a general information spreading model that is based on discrete time Markov chains. The model includes all the transitions that are plausible for both a disease contagion process and rumor propagation. We show that our model not only covers the traditional spreading schemes, but that it also contains some features relevant in social dynamics, such as apathy, forgetting, and lost/recovering of interest. The model is evaluated analytically to obtain the spreading thresholds and the early time dynamical behavior for the contact and reactive processes in several scenarios. Comparison with Monte Carlo simulations shows that the Markov chain formalism is highly accurate while it excels in computational efficiency. We round off our work by showing how the proposed framework can be applied to the study of spreading processes occurring on social networks.
Complex systems made of interacting elements are commonly abstracted as networks, in which nodes are associated with dynamic state variables, whose evolution is driven by interactions mediated by the edges. Markov processes have been the prevailing paradigm to model such a network-based dynamics, for instance in the form of random walks or other types of diffusions. Despite the success of this modelling perspective for numerous applications, it represents an over-simplification of several real-world systems. Importantly, simple Markov models lack memory in their dynamics, an assumption often not realistic in practice. Here, we explore possibilities to enrich the system description by means of second-order Markov models, exploiting empirical pathway information. We focus on the problem of community detection and show that standard network algorithms can be generalized in order to extract novel temporal information about the system under investigation. We also apply our methodology to temporal networks, where we can uncover communities shaped by the temporal correlations in the system. Finally, we discuss relations of the framework of second order Markov processes and the recently proposed formalism of using non-backtracking matrices for community detection.
Collective or group intelligence is manifested in the fact that a team of cooperating agents can solve problems more efficiently than when those agents work in isolation. Although cooperation is, in general, a successful problem solving strategy, it is not clear whether it merely speeds up the time to find the solution, or whether it alters qualitatively the statistical signature of the search for the solution. Here we review and offer insights on two agent-based models of distributed cooperative problem-solving systems, whose task is to solve a cryptarithmetic puzzle. The first model is the imitative learning search in which the agents exchange information on the quality of their partial solutions to the puzzle and imitate the most successful agent in the group. This scenario predicts a very poor performance in the case imitation is too frequent or the group is too large, a phenomenon akin to Groupthink of social psychology. The second model is the blackboard organization in which agents read and post hints on a public blackboard. This brainstorming scenario performs the best when there is a stringent limit to the amount of information that is exhibited on the board. Both cooperative scenarios produce a substantial speed up of the time to solve the puzzle as compared with the situation where the agents work in isolation. The statistical signature of the search, however, is the same as that of the independent search.
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