Program and Abstracts

Keynote:Critical dynamics in adaptive networks: Neural SOC and universalityStefan BornholdtInstitute for Theoretical Physics, University of Bremen, D-28359 Bremen, GermanyDynamical networks have been studied from the perspective of statistical physics, motivated by questions of information processing in neural networks and genetic networks. In both applications, hypotheses have been discussed that relate optimality of information processing to dynamical criticality in the networks. Consequently, toy models for adaptive networks have been constructed that robustly establish criticality in the network. Here I review a particularly simple model class based on models from physics and discuss its application to the phenomenon of criticality in biological neural networks.

[1] M. Rybarsch and S. Bornholdt, Self-organized criticality in neural network models, in: "Criticality in Neural Systems", Niebur E, Plenz D, Schuster HG (eds.) 2013 (in press); arXiv:1212.3106.

[2] M. Rybarsch and S. Bornholdt, Binary threshold networks as a natural null model for biological networks, Phys. Rev. E 86 (2012) 026114.

[3] M. Rybarsch and S. Bornholdt, Self-organization to criticality in neural networks: A minimal model with binary threshold nodes, arXiv:1206.0166.

Feedback between node and network dynamics can produce real world network propertiesHilla Brot¹, Lev Muchnik², Jacob Goldenberg², and Yoram Louzoun^3,1 1 Gonda Brain Research Center, Bar-Ilan University, Ramat Gan, Israel, 52900 2 School of Business Administration, Hebrew University of Jerusalm ,Jerusalm, Isreal, 3 Department of Mathematics, Bar-Ilan University, Ramat Gan, Israel, 52900 The properties of real world networks are usually explained by the dynamics of edge and node addition and deletion. On the other hand, the dynamics of nodes’ content within a network has been often explained via the interaction between nodes in static networks, ignoring the dynamic aspect of the edge addition and deletion. We here propose to combine the dynamics of the nodes content and of the edges addition and deletion, using a threshold automata framework. Within this framework, we show that the typical properties of real world networks can be reproduced with a Hebbian approach, in which nodes with similar internal dynamics have a high probability of being connected. The proper network properties emerge only if an imbalance exists between excitatory and inhibitory connections, as is indeed observed in real networks. The current work bridges between multiple important domains in network analysis, including: network formation processes, Kaufmann Boolean networks and Hebbian learning. It suggests that the properties of nodes and the network convolve and can be seen as complementary parts of the same process.

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Fishing out collective memory of migratory schoolsGiancarlo De Luca¹, Patrizio Mariani², Brian R. McKenzie³, and Matteo Marsili⁴ 1 SISSA - International School for Advanced Studies, Trieste, Italy 2 Centre for Ocean Life, National Institute for Aquatic Resources, Technical University of Denmark, Charlottenlund, Danmark 3 Centre for Macroecology, Evolution and Climate, National Institute for Aquatic Resources, Technical University of Denmark, Charlottenlund, Danmark 4 The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy Information and individual preference are central aspects of group formation in humans and other social animals. Being in a group is often a big advantage for those individuals performing complex tasks that are usually difficult, or impossible, to be carried alone. Fish schooling is an example of such complex collective dynamics and it is a common feature in species such as tunas, which perform seasonal migrations from spawning to feeding areas. On the one hand, the school retains a collective memory of the destination migratory site over thousands of kilometers. On the other, sudden changes in the migratory patterns have been observed, e. g., in bluefin tuna. We propose a modeling framework, based on stochastic adaptive networks, which can reproduce this collective behavior. We assume that two factors control school formation and migration behavior: the relative number of informed individuals and the preference each individual has for the particular feeding area. Informed individuals are associated with the long term evolutionary process that have selected them, whereas the preference is a short term property of single individuals and is related to the experience and memory of certain places. Intensive fishing targeting the migratory species and also their preferred prey can reduce both terms to a point at which migration to those feeding grounds is suddenly stopped.

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Collective opinion formation in adaptive networksThilo GrossUniversity of Bristol, Department of Engineering Mathematics and Bristol Centre for Complexity Sciences, Bristol, UKMany systems in Science and Engineering need to process information collectively, with examples ranging from neural networks, to biological swarms, and decentralized sensor nets. In this talk I present a series of analytically tractable network models of decision dynamics that are used to identify beneficial and detrimental factors in collective decision making. In particular, I will show that already very simple models make counter-intuitive predictions that can be verified in animal experiments experiments.

Robustness of cooperation on networks under continuous topological changesGenki Ichinose¹, Yuto Tenguishi¹, and Toshihiro Tanizawa² 1 Anan National College of Technology, Japan 2 Kochi National College of Technology, Japan The robustness of cooperation clusters formed on complex networks has been intensively studied. In this paper, we numerically investigate the robustness of cooperation in prisoner’s dilemma played on scale-free networks, where its mixing patterns are continuously changed by removal and addition of nodes. Each of removal and addition can be either random or intentional. We therefore have four different strategies in changing network topology: random removal and random addition (RR), random removal and preferential addition (RP), targeted removal and random addition (TR), and targeted removal and preferential addition (TP). We found that cooperation clusters were most fragile against TR, while they were most robust even in high temptation coefficients for defect against RP. Moreover, the mixing patterns changed along with time due to the removal and addition of nodes and thus the robustness of cooperation was quite different with the result in the static networks. These results imply that the robustness of cooperation clusters increases in accordance with increasing the number of cooperating hubs and that a huge variety of individuals is needed to maintain global cooperation in a real social network where each individual constantly comes and leaves.

Spontaneous centralization of control in a network of company ownershipsSebastian M. Krause, Tiago P. Peixoto, and Stefan Bornholdt Institute for Theoretical Physics, University of Bremen, D-28359 Bremen, Germany In a recent work [S. Vitali et.al., PLoS ONE (2011) e25995] it has been shown that the global network of corporate control is marked by a central, tightly-connected core made of a relatively small number of large companies which control a significant part of the global economy. A central question is what mechanism is responsible for this organization, and whether it arises due to an explicit collusion among the central companies, or simply is a byproduct of a simpler underlying process. Here we show how a simple, adaptive rich-get-richer dynamics can account for this characteristic. The process we propose incorporates the indirect control that companies have on other companies they own, which in turn increases their buying power. The higher buying power can then be used to buy portions of more important companies, or a larger number of less important ones, which further increases their relative control, and progressively marginalizes smaller companies. The system spontaneously organizes into a steady-state comprised of a well-defined core-periphery structure, which reproduces well many qualitative observations in the real data. Our model shows that this kind of centralized structure can emerge without it being an explicit goal of the companies involved.

Adaptive network topology in the control of cluster synchronizationJudith Lehnert¹, Anton Selivanov², Alexander Fradkov^2,3, and Eckehard Schöll¹ 1 Institut fuer Theoretische Physik,TU-Berlin, Hardenbergstr 36, 10623 Berlin, Germany 2 SPb State University, Universitetskii pr.28, St.Petersburg, 198504 Russia 3 Institute for Problems of Mechanical Engineering, Russian Academy of Sciences, Bolshoy Ave, 61, V. O., St. Petersburg, 199178 Russia

Synchronization is a ubiquitous phenomenon in many natural networks and technical applications. For example, in the brain, synchronization is associated with several cognitive capacities but can also become pathological, as for instance in Parkinson or Epilepsy; in laser systems, synchronization can be used for secure communication. Thus, the control of synchronization is of high interest in different fields. Here, we present an algorithm to control different synchronization patterns by adapting the network topology in an appropriate way. In particular, we control zero-lag and cluster synchronization in delay-coupled networks of Stuart-Landau oscillators. Our method is robust towards different initial conditions. Furthermore, it is not necessary to adapt the network as a whole but it is sufficient to apply the method to a subset of the links to control the dynamics of all nodes. Finally, we discuss the topological characteristics of the network after successful control and show that the interplay between excitation and inhibition is crucial for successful control.

Structure of communities and its evolution in mobile social networks Nikolai NefedovISI Lab, ETH Zurich, Switzerland Many biological and social systems show a presence of conflicting processes. To model these phenomena we used Kuramote model with time-dependent coupling, evaluated several scenarios with attractive and inhibitory interactions and compared new links predictions made by modified Kuramoto model with topology-based predictors. At the same time the interplay between topology and local dynamics allows us to find an allocation of attractive and repulsive coupling among nodes such that it keeps the given topology stable. On the other hand, in many cases we may observe only time-evolution of network connectivity, while dynamics of local states remains invisible. In this talk we present a dynamic network as a sequence of spectrally embedded network snapshots and define a time-varying vector field on vertices. It allows us to describe dynamics of nodes and analyze community evolution in networks built from real-world mobile datasets.

Demographic noise in adaptive networks Tim Rogers¹ and Thilo Gross² 1 University of Bath, UK 2 University of Bristol, UKThe discrete nature of an adaptive network is a source of intrinsic demographic noise, which can have profound effects on the system dynamics. In this talk I will introduce an analytical technique to study stochastic effects in these models. The paradigmatic adaptive voter model will be used as a motivating example, where the emergence of consensus is driven by stochastic demographic fluctuations. Our technique allows us to compute the statistics of the time taken to reach consensus for various versions of the model, revealing the relationship between the rules of the system and the resulting noise-driven dynamics.

Introduction to adaptive networks Hiroki Sayama

Collective Dynamics of Complex Systems Research Group, Binghamton University, State University of New York, USA

Adaptive networks are a novel class of dynamical networks whose topologies and states coevolve. Many real-world complex systems can be modeled as adaptive networks, including social networks, transportation networks, neural networks and biological networks. This opening remark will offer a no-more-than-five-minutes introductory overview of adaptive networks, especially in the larger context of Network Science.

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Automatic discovery of adaptive network dynamics from temporal network data Jeffrey Schmidt and Hiroki Sayama Collective Dynamics of Complex Systems Research Group, Binghamton University, State University of New York, USA Traditional social network analysis techniques are powerful tools to analyze real-world complex networks. They have also been extended recently to the analysis of temporal network data. However, to analyze adaptive networks, i.e., networks whose states and topology interact and coevolve over time, such network analysis techniques would do very little to improve our understanding of the underlying dynamics. To provide a new analytical tool, we have applied Generative Network Automata (GNA) to develop algorithms for automatic discovery of the underlying dynamics of adaptive networks from temporal network data. GNA has the ability to represent a wide range of dynamics when the underlying dynamical mechanisms are known. By analyzing the differences between time steps in temporal network data, we uncovered the mechanism responsible selecting subgraphs that will undergo change, called the extraction mechanism. We then compiled and organized all the changes that occurred during the dynamics to construct the replacement mechanism. Once identified, these mechanisms were used to generate simulated temporal network data. The algorithms created are included in a software tool called PyGNA. Our preliminary results showed that PyGNA was able to correctly identify the dynamics of a set of simple adaptive networks. Technical challenges and pathways to further improvements are also identified and being implemented.

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Exploring network dynamics with a mathematical triple jumpHolly Silk¹, Güven Demirel², Martin Homer¹, and Thilo Gross¹ 1 University of Bristol, Department of Engineering Mathematics and Bristol Centre for Complexity Sciences, Bristol, UK 2 Max-Planck-Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, Dresden, Germany In the investigation of network dynamics a prominent role is played by analytical coarse-graining schemes. A powerful class of these schemes are the so-called heterogeneous approximations, which describe the dynamics of an agent-based network model by an infinite-dimensional system of differential equations. Using the example of the adaptive voter model, we perform a mathematical triple jump, combining three different mathematical techniques, to produce the first analytical solution to a heterogeneous moment expansion. The first of the three steps is to approximate the agent-based model by a high-dimensional system of ODEs using the heterogeneous moment expansion. The second step then uses generating functions to convert the high-dimensional ODEs into a low-dimensional system of partial differential equations (PDEs). The final step uses the method of characteristics to convert the PDE into a low-dimensional set of ODEs that can be solved analytically. We expect this triple jump technique to prove valuable in providing analytical solutions for many existing network models that the heterogeneous expansion accurately describes.

Reconsidering the coevolution of cooperative behaviors and network structures from the viewpoint of the evolution of niche construction Reiji Suzuki, Takuro Kojima and Takaya Arita Department of Complex Systems Science, Nagoya University, Japan Niche construction is a process whereby organisms modify their own or others' niches (selection pressures) through their ecological activities. There have been various studies on how dynamically changing networks of interactions can affect the evolution of cooperative behaviors. The behaviors that modify such networks can be interpreted as niche constructions in that they affect the evolutionary dynamics of game strategies, but their coevolution process with game strategies still needs investigation. In this talk, we introduce our recent studies, based on agent-based models, on this issue from the viewpoint of the evolution of physical or social niche-constructing behaviors. First, we discuss how social niche-constructing strategies (e.g., finding a new individual to communicate with or refusing an offer from another to interact with) can coevolve with strategies of the prisoner's dilemma. We show an emergence of coevolutionary cycle of both strategies, and also show that more complex dynamics appear if we further introduce the evolution of game structures into the model. Then, we focus on the evolution of physical niche-constructing behaviors (e.g., constructing a physical obstacle in order to decrease the chance of encounter with another) that limit social interactions and the ecological inheritance of constructed niches (e.g., an inheritance of physical obstacles created by niche-constructing individuals to the succeeding generations). We show that physical niche-constructing behaviors that contribute to the evolution of cooperation can emerge depending on the degree of ecological inheritance.

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Coevolving networks in the 'red queen' regimeStefan Wieland and Ana Nunes Centro de Fisica da Materia Condensada/Departamento de Fisica, Faculdade de Ciencias, Universidade de Lisboa, Portugal We consider a family of two state coevolving network models that interpolates between the Susceptible-Infected-Susceptible model (SIS) and a modification of the voter model (MVM), both with rewiring. The phase diagram of this family is well described in the scope of the standard pair approximation (PA). It features a simple active phase that corresponds to an equilibrium of the PA equations, and, on the actual network, to a steady state where perpetual rewiring and node state change maintain a constant degree distribution, both for the subnetworks of each node type and for the full network.

We present and briefly discuss a semi-analytic method for the determination of the network statistical measures in this regime. As an application, we derive the stady-state subnetwork degree distributions for the SIS and the MVM. The results are compared with simulations and with the predictions of the PA for the two subnetwork mean degrees.

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