The roundtable: an abstract model of conversation dynamics

Is it possible to abstract a formal mechanism originating schisms and governing the size evolution of social conversations? In this work a constructive solution to such problem is proposed: an abstract model of a generic N-party turn-taking conversation. The model develops from simple yet realistic assumptions derived from experimental evidence, abstracts from conversation content and semantics while including topological information, and is driven by stochastic dynamics. We find that a single mechanism - namely the dynamics of conversational party's individual fitness, as related to conversation size - controls the development of the self-organized schisming phenomenon. Potential generalizations of the model - including individual traits and preferences, memory effects and more elaborated conversational topologies - may find important applications also in other fields of research, where dynamically-interacting and networked agents play a fundamental role.Comment: 18 pages, 4 figures, to be published in Journal of Artificial Societies and Social Simulatio

The Roundtable: An Abstract Model of Conversation Dynamics

Is it possible to abstract a formal mechanism originating schisms and governing the size evolution of social conversations? In this work we propose a constructive solution to this problem: an abstract model of a generic N-party turn-taking conversation. The model develops from simple yet realistic assumptions derived from experimental evidence, abstracts from conversation content and semantics while including topological information, and is driven by stochastic dynamics. We find that a single mechanism, namely the dynamics of conversational party\'s individual fitness as related to conversation size, controls the development of the self-organized schisming phenomenon. Potential generalizations of the model - including individual traits and preferences, memory effects and more elaborated conversational topologies - may find important applications also in other fields of research, where dynamically-interacting and networked agents play a fundamental role.ABM, Complexity, Turn-Taking Dynamics, Schism, Stochastic Dynamics

Approximate entropy of network parameters

We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We firstly define a purely structural entropy obtained by computing the approximate entropy of the so called slide sequence. This is a surrogate of the degree sequence and it is suggested by the frequency partition of a graph. We examine this quantity for standard scale-free and Erd\H{o}s-R\'enyi networks. By using classical results of Pincus, we show that our entropy measure converges with network size to a certain binary Shannon entropy. On a second step, with specific attention to networks generated by dynamical processes, we investigate approximate entropy of horizontal visibility graphs. Visibility graphs permit to naturally associate to a network the notion of temporal correlations, therefore providing the measure a dynamical garment. We show that approximate entropy distinguishes visibility graphs generated by processes with different complexity. The result probes to a greater extent these networks for the study of dynamical systems. Applications to certain biological data arising in cancer genomics are finally considered in the light of both approaches.Comment: 11 pages, 5 EPS figure

Comment on the existence of a long range correlation in the geomagnetic disturbance storm time (Dst) index

Very recently (Banerjee et al. in Astrophys. Space, doi:1007/s10509-011-0836-1, 2011) the statistics of geomagnetic Disturbance storm (Dst) index have been addressed, and the conclusion from this analysis suggests that the underlying dynamical process can be modeled as a fractional Brownian motion with persistent long-range correlations. In this comment we expose several misconceptions and flaws in the statistical analysis of that work. On the basis of these arguments, the former conclusion should be revisited

Irreversibility of symbolic time series: a cautionary tale

Many empirical time series are genuinely symbolic: examples range from link activation patterns in network science, DNA coding or firing patterns in neuroscience to cryptography or combinatorics on words. In some other contexts, the underlying time series is actually real-valued, and symbolization is applied subsequently, as in symbolic dynamics of chaotic systems. Among several time series quantifiers, time series irreversibility (the difference between forward and backward statistics in stationary time series) is of great relevance. However, the irreversible character of symbolized time series is not always equivalent to the one of the underlying real-valued signal, leading to some misconceptions and confusion on interpretability. Such confusion is even bigger for binary time series (a classical way to encode chaotic trajectories via symbolic dynamics). In this article we aim to clarify some usual misconceptions and provide theoretical grounding for the practical analysis -- and interpretation -- of time irreversibility in symbolic time series. We outline sources of irreversibility in stationary symbolic sequences coming from frequency asymmetries of non-palindromic pairs which we enumerate, and prove that binary time series cannot show any irreversibility based on words of length m < 4, thus discussing the implications and sources of confusion. We also study irreversibility in the context of symbolic dynamics, and clarify why these can be reversible even when the underlying dynamical system is not, such as the case of the fully chaotic logistic map