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SUMMERSOLSTICE2014: Discrete Models of Complex Systems
Short Abstracts of Invited Talks
 Anna Carbone, Detrending Moving Average Algorithm: a NonRandom 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 highdimensional random structures.
A short review of the Detrending Moving Average (DMA) algorithm is presented. The DMA has the ability to quantify temporal and spatial longrange 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 longmemory 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, selforganized criticality and entropy of longrange 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 codewords 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. FontClos, 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 LargeScale 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 microscopiclevel discrete models to describe the individual mobility behavior precisely, and macroscopiclevel discrete models to characterize the gross quantities or metrics, by treating the traffic according to fluid dynamics and, therefore, can reveal the largescale 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 multiagent setting. In the presented work we
develop cognitive agents, which we call naïve creatures, able to operate in a multiagent and multispecies
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
 Joaquin Marro, Nonequilibrium Phase Transitions in the Brain
 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 manmade 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 biomolecules, 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 coarsegrained methodologies.
 Jose Fernando Mendes, Structural properties of complex networks
 Marija Mitrovic, AgentBased Modeling and Social Structure in Bloggers' Dynamics
 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 tricritical points, reveals the hidden complexity behind the pursuit of human fair play.
 Alexander Povolotsky, Interacting particle systems: Integrability vs. universality
 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 SelfOrganized Criticality model, able to simulate financial avalanches in trading communities with different network topologies, where a Paretolike 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 (meanfield) 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 onedimensional spatial arrangement one observes incoherent oscillations
and a constant average.
In simulations on WattsStrogatz networks with a smallworld effect the mean field behavior is recovered, with
a bifurcation diagram that resembles the meanfield 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
 Milovan Suvakov, New Numerical Solutions of Newtonian Threebody Problem: Scaling and Regularities
For two centuries, attempts were made at a general solution to the Newtonian threebody 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
shapesphere projection to classify and identify orbits [3].
Furthermore, we use all presently known planar collisionless periodic threebody orbits with vanishing angular
momentum to study the threebody 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 threebody periodic orbits, Phys. Rev. Lett. 110 (2013) 114301; [2] M. Suvakov, Numerical Search for Periodic Solutions in the Vicinity of the FigureEight 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 threebody 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
informationtheoretic entropy to be of BoltzmannGibbs type, SBG =  Σ_{i} p_{i} log p_{i}. For nonergodic systems the separation axiom
(ShannonKhinchin 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 noninteracting 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 ShannonKhinchin 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 nonergodic
systems both concepts are tightly related but distinct. We demonstrate the practical relevance of our results on pathdependent random walks
(nonMarkovian systems with longterm 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. Selforganized 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.
