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SUMMERSOLSTICE2014: Discrete Models of Complex Systems

Short Abstracts of Invited Talks

• Anna Carbone, Detrending Moving Average Algorithm: a Non-Random Walk through ComplexSystems Science
Time series are a tool to describe biological, social and economic systems in one dimension, such as stock market indexes and genomic sequences. Extended systems evolving over space, such as urban textures, World Wide Web and firms are described in terms of high-dimensional random structures. A short review of the Detrending Moving Average (DMA) algorithm is presented. The DMA has the ability to quantify temporal and spatial long-range dependence of fractal sets with arbitrary dimension. Time series, profiles and surfaces can be characterized by the fractal dimension D, a measure of roughness, and by the Hurst exponent H, a measure of long-memory dependence. The method, in addition to accomplish accurate and fast estimates of the fractal dimension D and Hurst exponent H, can provide interesting clues between fractal properties, self-organized criticality and entropy of long-range correlated sequences. Further readings \'a0and tips about the DMA algorithm at www.polito.it/noiselab


• Álvaro Corral, Zipf's law and a scaling law, in texts and in music
Zipf's law is considered one of the key statistical regularities of human language. We show that, in general, Zipf's power law does not hold for the whole domain of word frequencies, but only for the upper tail, i.e., for the most common words. On the other hand, the distribution of word frequencies changes with the size of the text in such a way that if scales with the size of the text and the size of the vocabulary; this means that the shape of the distribution does not change with system size, only its scale changes, providing a recipe for the proper comparison of texts of different size [1]. The distinction between power law and scaling law is fundamental here.
A second part of the talk will be devoted to the extension of Zipf's law to music, drawing parallelisms and differences with texts. The construction of music code-words from the chords defining the pitch in modern popular music reveals the validity of Zipf's law in this case. This law has kept stability for the last 50 years, although other characteristics of music have shown an evolution that seems to indicate a decrease of the complexity of music with time [2]. References: [1] F. Font-Clos, G. Boleda, and A. Corral (2013). A scaling law beyond Zipf’s law and its relation to Heaps’ law. New J. Phys., 15, 093033. [2] J. Serra, A. Corral, M. Boguna, M. Haro, and J. Ll. Arcos (2012). Measuring the evolution of contemporary western popular music. Sci. Rep., 2, 521.


• Andrea Guazzini, Sociophysics of Virtual Dynamics
The Human Virtual Dynamics (HVD) have assumed a crucial role in modern societies, well beyond the expectations, at least of politicians around the world. HVD relies on every interaction network over different, and typical, timescales, mediated by technological environments (i.e. web base systems, ICT devices, etc). The social networks are rapidly becoming the principal autoritas even for the "ethical" and "moral" education of people, as well as the places where the "opinions", the "credencies", the "beliefs", and sometimes the "whishes" are shaped and managed. In the latest decades disciplines as sociophysics and econophysics developed models to describe the behaviour of humans, and human groups, in interaction. Nowadays the modern tools developed within the Information and Communication Technology domain (ICT) allow a new and very effective setting to both, standardized and validate the sociophysical and sociopsychologycal models, and to develop a radically new approach to study the human social dynamics. Moreover a "sociophysics of virtual human dynamics" would allow to investigate the relation between the dynamics of cultures, societies and generally big communities (i.e. big data analysis), with respect to the small group dynamics (e.g. families, work and friends communities, etc.), assessing the role of mesoscopic entities on the overall dynamics interwined in social phenomena. In order to fill such a gap recent sociophysical studies introduced cognitive elements and mechanisms. Such kind of model to characterize the node's dynamics, and to keep into account explicitly the evolution of the relations among people, coupled with the standard evolution of the state variable (e.g. opinion). To validate such approach we built an experimental framework to investigate the small group dynamics, exploiting a web based application in order to reach an optimal control of the experimental conditions and artefacts.


• Jian Yuan, Understanding the Large-Scale Urban Vehicular Mobility by Discrete Models
Currently, urban traffic congestion is an increasingly serious problem that is significantly affecting many aspects of the quality of metropolis life around the world. Scientific mobility modeling and traffic engineering, which aims to achieve efficient management of the resource of networks of the urban systems, become an important problem that attracts broad interests from many scientific communities. In this talk, I will first introduce our proposed microscopic-level discrete models to describe the individual mobility behavior precisely, and macroscopic-level discrete models to characterize the gross quantities or metrics, by treating the traffic according to fluid dynamics and, therefore, can reveal the large-scale overall vehicular mobility behaviors and traffic patterns. Then, focusing on investigating how much the vehicular mobility can be predicted, we talk about the prediction limitations described by discrete entropy model, to answer the fundamental questions of what is the role of the randomness playing in the human/vehicular mobility, is there any regularity in the daily vehicular movement, and to what degree is the mobility predictable.


• Anna T. Lawniczak, Model Of A Population Of Autonomous Simple Cognitive Agents And Their Performance In Various Environments
Autonomous robots are intelligent machines exhibiting a predefined behaviour, such that, once they are deployed, they can performed tasks by themselves (autonomously), without human innervation, or if required with minimal human intervention. For the purpose of modeling and simulation, structurally and architecturally simple autonomous robots can be identified with autonomous cognitive agents. A cognitive agent is an abstraction of an autonomous entity capable of interacting with its environment and other agents. With the goal in mind of possible hardware implementation, there is an obvious interest in dentifying the simplest possible architecture still capable of producing meaningful results for the desire ask. In this context we study a problem of defining autonomous cognitive agents capable of learning from and adapting to their environment and providing results in a multi-agent setting. In the presented work we develop cognitive agents, which we call naïve creatures, able to operate in a multi-agent and multi-species agent reality and capable of surviving by learning the dangers of the universe of the experiment and of developing a simple strategy of survival, as a species. We present an extension of the works. We describe our model of a population of autonomous simple naive creatures experiencing fear and/or desire earning to cross a highway, and their experimental virtual universe. We investigate how these feelings and creature mobility along a highway may affect the creatures' ability to learn to successfully cross the highway. We present selected simulation results and their analysis for various types of highways and densities of car traffic.


• Zoran Levnajic, Reconstructing network structure from dynamical signals
A method of network reconstruction from the dynamical time series is introduced, relying on the concept of derivative-variable correlation. Using a tunable observable as a parameter, the reconstruction of any network with known interaction functions is formulated via simple matrix equation. We suggest a procedure aimed at optimizing the reconstruction from the time series of length comparable to the characteristic dynamical time scale. Our method also provides a reliable precision estimate. We illustrate the method's implementation via elementary dynamical models, and demonstrate its robustness to both model and observation errors.


• Joaquin Marro, Non-equilibrium Phase Transitions in the Brain
I shall briefly describe recent studies in our group of mathematical models for brain cooperative functions and network structure--which focus on phenomenology such as the propagation of weak signals competing with noise and the spontaneous process of synaptic pruning during early human growth--to show how the combination of familiar concepts in physics such as those of chaos, non-equilibrium, phase transitions and criticality provides a coherent understanding of some of the brain complex behaviour.


• Roderick Melnik, Interacting Scales and Coupled Phenomena in Nature and Models (IJS Colloquium)
Interacting time and space scales are universal. They frequently go hand in hand with coupled phenomena which can be observed in nature and man-made systems. Such mutiscale coupled phenomena are fundamental to our knowledge about all the systems surrounding us, ranging rom such global systems as the climate of our planet, to such tiny ones as quantum dots, and all he way down to the building blocks of life such as nucleic acid biological molecules. In this talk I will provide an overview of some coupled multiscale problems that we face in studying physical, engineering, and biological systems. I will start from considering tiny objects, known as low dimensional nanostructures, and will give examples on why the nanoscale is becoming increasingly important in the applications affecting our everyday lives. By using fully coupled mathematical models, I will show how to build on the previous results in developing a new theory, while analyzing the influence of coupled multiscale effects on properties of these tiny objects. In the remaining time, I'll talk about coupled multiscale problems in studying biological structures constructed from ribonucleic acid (RNA). As compared to deoxyribonucleic acid (DNA) and some other bio-molecules, RNA offers not only a much greater variety of interactions but also great conformational flexibility, making it an important functional material in many bioengineering and medical applications. Examples of numerical simulations of such biological structures will be shown, based on our developed coarse-grained methodologies.


• Jose Fernando Mendes, Structural properties of complex networks
Many complex systems, both natural, and man-made, can be represented as multiplex or interdependent networks. Multiple dependencies make a system more fragile: damage to one element can lead to avalanches of failures throughout the system. Recent theoretical investigation of two or more networks in which vertices in each network mutually depend on vertices in other networks has shown that indeed small initial failures can cascade back and forth through the networks, leading to a discontinuous collapse of the whole system. Damage in one network propagates along edges and leads to damage in the other network. This is an individual stage of a cascade in back-and-forth damage propagation. In this talk I will revisit a number of well-studied problems concerning structural properties of complex networks. Some concepts like percolation, k-core organization, bootstrap percolation are well well-known to the audience but I will present them in a different perspective showing the recent analytical advances from a network theory point of view. I will show that however different problems they share some common features like a hybrid phase transition.


• Marija Mitrovic, Agent-Based Modeling and Social Structure in Bloggers' Dynamics
Emotions play pivotal role in both offline and online social dynamics. Although, collective emotional behavior of users is frequently observed in online societies, the role of emotions in online communication and their connection with emerging social structure of online communities are still not thoroughly understood. In this paper, we study mechanisms underlying the collective emotional behavior of Bloggers by using the agent-based modeling and the parameters inferred from the empirical data of popular BBC Blogs and discussion-driven Diggs. Agents, whose individual emotional states are described by their valence and arousal, are embedded in bipartite network of users and posts. This bipartite network evolves trough the addition of agents and their actions on posts; agents transfer their current emotional state to post by posting an emotional comment. Emotional state of agent fluctuates in time as a direct consequence of indirect interaction with other agents trough its ego-network of posts. We show that the indirect communication of the emotion in the model rules, combined with the action-delay time and the circadian rhythm extracted from the empirical data, can explain the genesis of emotional bursts by users on popular Blogs and similar Web portals. Our results show that the emotion-driven dynamics leads to long-range correlations and emergent networks with community structure, also observed in analysis of empirical data. We show that the size and activity of evolving agents communities correlates with the expression of negative emotions (critique). more...


• Matjaz Perc, Bargaining with discrete strategies
Imagine two players having to share a sum of money. One proposes a split, and the other can either agree with it or not. No haggling is allowed. If there is an agreement, the sum is shared according to the proposal. If not, both players remain empty handed. This is the blueprint of the ultimatum game. Experiments on the ultimatum game have revealed that humans are remarkably fond of fair play. When asked to share something, unfair offers are rare and their acceptance rate is small. Traditionally, the ultimatum game has been studied with continuous strategies, and it has been shown that empathy and spatiality may lead to the evolution of fairness. However, evolutionary games with continuous strategies often hide the true complexity of the problem, because solutions that would be driven by pattern formation are unstable. Discrete strategies in the ultimatum game open the gate to fascinatingly rich dynamical behavior. The highly webbed phase diagram, featuring both continuous and discontinuous phase transitions as well as tri-critical points, reveals the hidden complexity behind the pursuit of human fair play.


• Alexander Povolotsky, Interacting particle systems: Integrability vs. universality
Stochastic models of interacting particles attracted a lot of attention as exactly solvable models sharing the universal behaviour of the Kardar-Parisi-Zhang (KPZ) and Edwards-Wilkinson (EW) universality classes. Special mathematical structure of integrable systems makes plenty analytic results available. Among them are universal distributions and correlation functions. The first simplest models having been solved are the asymmetric and symmetric simple exclusion processes, which were used as a paradigmatic examples for KPZ and EW universality classes respectively. Both these models were solved by the Bethe ansatz technique, which is the the basic method of solving the integrable models. Though the simple exclusion processes allow probing into main features of the KPZ and EW universal behaviour it is desirable to include various types of interactions into the dynamics to see whether the universality is stable against the modification of the dynamics. However not all interactions are consistent with exact solvability. Integrability imposes strict limitations on the dynamical rules. Therefore it is of primary interest to find as general as possible model, which would preserve the integrability property. Another important property that has long been recognized to be shared by many exactly solvable stochastic particle models is the simple structure of traslationally invariant stationary measure having a form of product of one-site factors. This allows for complete characterization of the stationary correlations by the use of the toolbox of equilibrium statistical mechanics, developed for systems with non-interacting degrees of freedom. In the talk we show how to obtain the most general three-parametric interacting particle model, which possesses both the product stationary measure and the Bethe anstaz solvability. This model includes the asymmetric simple exclusion process as well as many other models as a limiting cases. We give a brief review of the particular models that can be obtained from the general model, some of which were studied before and some are new, and discuss different types of universal and non-universal behaviour exhibited by the model at different values of parameters.


• Andrea Rapisarda, Micro and Macro Benefits of Random Investments in Financial Markets
In this paper, making use of statistical physics tools, we address the specific role of randomness in financial markets, both at micro and macro level. In particular, we will review some recent results obtained about the effectiveness of random strategies of investment, compared with some of the most used trading strategies for forecasting the behavior of real financial indexes. We also push forward our analysis by means of a Self-Organized Criticality model, able to simulate financial avalanches in trading communities with different network topologies, where a Pareto-like power law behavior of wealth spontaneously emerges. In this context we present new findings and suggestions for policies based on the effects that random strategies can have in terms of reduction of dangerous financial extreme events, i.e. bubbles and crashes. References: [1] A.E. Biondo, A. Pluchino, A. Rapisarda, Journal of Statistical Physics 151 (2013) 607. [2] A.E. Biondo, A. Pluchino, A. Rapisarda, D. Helbing, (2013) PLOS ONE 8(7): e68344. doi:10.1371/journal.pone.0068344. [3] A.E. Biondo, A. Pluchino, A. Rapisarda, D. Helbing, Phys. Rev. E 88, 062814 (2013)


• Raul Rechtman, Topological bifurcations in a model of a society of reasonable contrarians
People are often divided into conformists and contrarians, the former tending to align to the majority opinion in their neighborhood and the latter tending to disagree with that majority. In practice, however, the contrarian tendency is rarely followed when there is an overwhelming majority with a given opinion, which denotes a social norm. Such reasonable contrarian behavior is often considered a mark of independent thought, and can be a useful strategy in financial markets. We present the opinion dynamics of a society of reasonable contrarian agents. The model is a cellular automaton of Ising type, with antiferromagnetic pair interactions modeling contrarianism and plaquette terms modeling social norms. We introduce the entropy of the collective variable as a way of comparing deterministic (mean-field) and probabilistic (simulations) bifurcation diagrams. In the mean field approximation the model exhibits bifurcations and a chaotic phase, interpreted as coherent oscillations of the whole society. However, in a one-dimensional spatial arrangement one observes incoherent oscillations and a constant average. In simulations on Watts-Strogatz networks with a small-world effect the mean field behavior is recovered, with a bifurcation diagram that resembles the mean-field one, but using the rewiring probability as the control parameter. Similar bifurcation diagrams are found for scale free networks, and we are able to compute an effective connectivity for such networks.


• Geoff Rodgers, Network growth model with intrinsic vertex fitness
A class of network growth models with attachment rules governed by intrinsic node fitness is investigated. Both the individual node degree distribution and the degree correlation properties of the network are obtained as functions of the network growth rules. We find analytical solutions to the inverse, design, problems of matching the growth rules to the required (e.g., power-law) node degree distribution and more generally to the required degree correlation function. We find that the design problems do not always have solutions. Among the specific conditions on the existence of solutions to the design problems is the requirement that the node degree distribution has to be broader than a certain threshold and the fact that factorizability of the correlation functions requires singular distributions of the node fitnesses. More generally, the restrictions on the input distributions and correlations that ensure solvability of the design problems are expressed in terms of the analytical properties of their generating functions.


• Milovan Suvakov, New Numerical Solutions of Newtonian Three-body Problem: Scaling and Regularities
For two centuries, attempts were made at a general solution to the Newtonian three-body problem, until H. Bruns showed that only specific particular solutions were possible. Yet only three families of collisionless periodic orbits were known until recently. Presently, systematic numerical searching for periodic solutions has become possible. In [1], we showed 13 new periodic orbits, and in [2] we found 11 more. We used topological method based on the shape-sphere projection to classify and identify orbits [3]. Furthermore, we use all presently known planar collisionless periodic three-body orbits with vanishing angular momentum to study the three-body version of Kepler's third law: we found that the scaling regularities are related to orbit's topological property on the shape sphere. This fact can be used to predict properties of several classes of as yet undiscovered orbits. [1] M. Suvakov and V. Dmitrasinovic , Three classes of Newtonian three-body periodic orbits, Phys. Rev. Lett. 110 (2013) 114301; [2] M. Suvakov, Numerical Search for Periodic Solutions in the Vicinity of the Figure-Eight Orbit: Slaloming around Singularities on the Shape Sphere, submitted to Celestial Mechanics and Dynamical Astronomy, arXiv:1312.7002; [3] M. Suvakov and V. Dmitrasinovic, A guide to hunting periodic three-body orbits, American J. Physics, in press;


• Stefan Thurner, Entropies for Complex Systems
Shannon and Khinchin built their foundational information theoretic work on four axioms that completely determine the information-theoretic entropy to be of Boltzmann-Gibbs type, SBG = - Σ_i p_i log p_i. For non-ergodic systems the separation axiom (Shannon-Khinchin axiom 4) is not valid. We show that whenever this axiom is violated -as is the case in most complex systems - entropy takes the more general form, Sc,d ~ Σ_i=1^W Γ(d +1, 1 - c log p_i), where c and d are characteristic scaling exponents, and Γ is the incomplete Gamma function. The exponents (c,d) parametrize equivalence classes which precisely characterise all (!) interacting and non-interacting statistical systems in the thermodynamic limit, including those that typically exhibit power laws or stretched exponential distributions. This allows us for example to derive Tsallis entropy (as a special case) from solid first principles. Further we show how the knowledge of the phase space volume of a system and the requirement of extensivity allows to uniquely determine (c, d). We ask how the these entropies are related to the 'Maximum entropy principle' (MEP). In particular we show how the first Shannon-Khinchin axiom allows us to separate the value for observing the most likely distribution function of a statistical system, into a 'maximum entropy' (log of multiplicity) and constraint terms. Remarkably, the generalized extensive entropy is not necessarily identical with the generalized maximum entropy functional. In general for non-ergodic systems both concepts are tightly related but distinct. We demonstrate the practical relevance of our results on path-dependent random walks (non-Markovian systems with long-term memory) where the random walker's choices (left or right) depending on the history of the trajectory. We are able to compute the time dependent distribution functions from the knowledge of the maximum entropy, which is analytically derived from the microscopic update rules. Self-organized critical systems such as sand piles or particular types of spin systems with densifying interactions are other examples that can be understood within the presented framework.