Foundations & Socio-Ecology  (FS) Session 1

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Time and Date: 14:15 - 15:45 on 19th Sep 2016

Room: I - Roland Holst kamer

Chair: Debraj Roy

18 Symmetric and Asymmetric Tendencies in Stable Complex Systems [abstract]
Abstract: Stable complex systems must subscribe to certain structures in order to be stable. By obtaining eigenvalue bounds of the Jacobian matrix at an equilibrium point, we show that stable complex systems will favor mutualistic and competitive interactions that are asymmetric (non-reciprocative) and antagonistic interactions that are symmetric (reciprocative). This prediction is in line with real-world ecological observations. Furthermore, we show that increasing dispersion in the interaction strengths has a destabilizing effect, and that this effect is more pronounced for mutualistic and competitive interactions than antagonistic interactions. This prediction is also consistent with real-world ecological observations. Finally, we demonstrate that these results can be used to make stabilization algorithms of an equilibrium point more efficient. The generality of the analysis presented suggests that our findings should not be limited to ecological systems.
James Tan
378 Coherent and incoherent strategists: Evolutionary dynamics on multiplex networks [abstract]
Abstract: Cooperation is a very common, yet not fully-understood phenomenon in natural and human systems. The introduction of a network structure within the population is known to affect the outcome of cooperative dynamics, as described by the Game Theory paradigm, allowing for the survival of cooperation in adverse scenarios. Recently, the introduction of multiplex networks, where individuals can adopt different strategies in different layers, has yet again modified the expectations for the outcome of the Prisoner’s Dilemma game, compared to the single-layer case: for example, it is known that the average level of cooperation is slightly lower in the multiplex scenario for very low values of temptation, but also, cooperation is able to resist until higher values of the temptation. These phenomena, however, are not well understood at a microscopic level, and much remains to be studied regarding the rest of the social dilemmas in the TS plane on multiplex. We have explored the microscopic organization of the strategies across layers, and have found some remarkable and previously unknown phenomena, that are at the root of the differences between monoplex and multiplex. Specifically, we have found that in the stationary state and for any given time step, there are individuals that play the same strategy in all layers (“coherent”), and others that don’t (“incoherent”). We have found that this group of incoherent players is responsible for the surprising fact of a non full-cooperation in the Harmony Game on multiplex, which has never been observed before, as well as a higher-than-expected survival of cooperation in some regions of the other three social dilemmas. Moreover, we are able to prove mathematically the existence of defectors in the case of the harmony game on multiplex networks, calculating the probability of the necessary topological configuration happening for uncorrelated ER layers.
Joan T. Matamalas, Julia Poncela-Casasnovas, Sergio Gómez and Alex Arenas
484 Equivalence Classes in Complex System Dynamics [abstract]
Abstract: We present an unsupervised learning technique to identify coherent behavior patterns in heterogeneous multi-dimensional time-series data and apply it to the results of select agent-based models as well as empirical datasets from economics and neuroscience. Many systems of interest in complexity science are non-equilibrium in nature, and for others it is the out-of-equilibrium dynamics which reveal complexity. By mapping the phase space of such systems as multi-dimensional time-series data and capturing the revealed dynamics in an empirically-derived Markov model we can identify recurring patterns in the behavior through structural network properties. Specifically, applying a weighted and directional diffusion-based community detection algorithm identifies sustainable behavioral regimes; i.e., collections of states for which there is a greater likelihood to stay within than to leave. In combination with other likelihood measures and structural features we develop a partial categorization of behavioral equivalence classes that can be compared across a variety of systems from different domains. First we explain the technique through stylized two-dimensional motion data. After laying that groundwork we present the analyses of data from three sources: polarization measures from an agent-based simulation of reason-based argument, multiple characteristics of players in an online social game, and neural activation patterns in the motor cortex. Each dataset embodies its own modeling challenges, but our data-driven approach is parsimonious in its application across these systems. As a result one can compare the qualitative and quantitative behavioral characteristics of these disparate systems in a common language. The ability to capture, identify, and describe quasi-attractors and punctuated equilibria, as well as the transient behaviors in between, with an unsupervised and minimally-parameterized technique fosters deeper understanding of a broad class of complex behaviors including a refined categorization of equivalence classes within that broad class.
Aaron Bramson and Atsushi Iriki
204 Beyond Communities: Dynamical Markov Modules [abstract]
Abstract: Mesoscopic structures have attracted researchers attention in the network science community since its very first stages triggering the production of a wide range of community detection algorithms. Scientific research have since covered other type of mesoscopic structures such as Core-Periphery, bi/multi-partite to the more general Stochastic Block Model. We propose a new module detection algorithm based on the system dynamics which avoid an "a priori" mesoscopic structure choice. The dynamics of a Markov process on a network are determined by the topology of the latter but, when aggregated to the underlying communities or modules, the resulting kinetics can exhibit unwanted memory effects. We provide a methodology to consistently check if the detailed Markov chain is lumpable to a mesoscopic modular structure, a partition of the original network. Focusing on the aggregated dynamics, the flow of information from its past toward its future as means of mutual information provides a proxy for the lumpability of such process. The deeper in the past the process provides information about its future, the more the memory effects contaminate its aggregated dynamics. We propose a partition detection algorithm which minimize these memory effects. In both synthetic and real-world networks it successfully detects usual community structures but also extends to any kind of mesoscopic structures such as core-periphery and stochastic block models providing a unified and general approach to network modularity. This methodology open the doors to a new mesoscopic structure definition which focus on the dynamical properties of the process and the role played by each node. Acknowledgments: This work was supported by the Belgian Programme of Interuniversity Attraction Poles, initiated by the Belgian Federal Science Policy Office and an Action de Recherche Concertée (ARC) of the French Community of Belgium.
Mauro Faccin and Jean-Charles Delvenne
104 Towards understanding the interactions between antimicrobial usage and pig health using an agent-based model [abstract]
Abstract: The aim of this paper is to demonstrate the application of complex systems to support policy making. Reduction in antimicrobial usage in livestock is needed to decrease antimicrobial resistance threatening human and animal health. Antimicrobial usage results from an interaction of biological processes and farmers’ decisions. These decisions are driven by economic considerations, disease status of the herd, motivations, cognitions and social networks. Antimicrobial usage effect the transmission dynamics of infectious diseases. Little is known about integrated influence of these economic, social and epidemiologic aspects. We constructed an agent-based model capturing the essentials of antimicrobial usage in Dutch fattening pig farming. The farmers make decisions based on their observations of health problems on the farm and their beliefs and motivations influenced by information on public health effects of antimicrobial usage, pressure from peers and incentives arising from policies. Each farm consisted of a number of pens with pigs, which were healthy, diseased by an endemic or emerging disease. The agent-based model was calibrated to data on antimicrobial usage and endemic disease prevalence. Data on measures to reduce antibiotic usage, costs and effects were taken from literature and expert information. Without additional measures, farmers might adopt a less favourable strategy of waiting to treat individual animals until group treatment is required and in that case antimicrobial usage does not decrease. Changes in farm management or investments can compensate for this effect and lead to reduction in antimicrobial usage. These effects emerge from individual processes. Policy interventions such as subsidies for investments in housing systems, promotion of particular management practices, and taxing antibiotic use can potentially change the usage of antimicrobials. Complex interactions between system components and actors need to be included in order to satisfactorily model the effect of policy interventions.
Egil A.J. Fischer, Thomas J. Hagenaars, Natalia I. Valeeva and Tim Verwaart

Foundations & Socio-Ecology  (FS) Session 2

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Time and Date: 16:15 - 18:00 on 19th Sep 2016

Room: L - Grote Zaal

Chair: Federico Battiston

219 Temporal correlations in social multiplex networks [abstract]
Abstract: Social interactions are composite, involve different communication layers and evolve in time. However, a rigorous analysis of the whole complexity of social networks has been hindered so far by lack of suitable data. Here we consider both the multi-layer and dynamic nature of social relations by analysing a diverse set of empirical tem- poral multiplex networks. We focus on the measurement and charac- terization of inter-layer correlations to investigate how activity in one layer affects social acts in another layer. We define observables able to detect when genuine correlations are present in empirical data, and single out spurious correlation induced by the bursty nature of human dynamics. We show that such temporal correlations do exist in social interactions, where they act to depress the tendency to con- centrate long stretches of activity on the same layer. They also imply some amount of potential predictability in the connection patterns between layers, and may affect the dynamics of spreading processes unfolding on different layers. Our work sets up a general framework to measure temporal correlations in multiplex networks, and we an- ticipate that it will be of interest to researchers in a broad array of fields.
Michele Starnini, Andrea Baronchelli and Romualdo Pastor-Satorras
110 The Law of Complementary Variety: when does it pay off for evolution to coarse- or fine-grain in space and time? [abstract]
Abstract: Biological and socio-economic populations can sometimes increase their fitness by identifying and adjusting to more details of the fitness landscape in which they evolve. When does it pay off for the population to use a more detailed classification system? This depends on the particular shape of the fitness matrix in both space and time. Sometimes the population does not need to bother looking closer. It is at least as beneficial to simply let natural selection act as a blind watchmaker. Other times, proactive resource redistribution among fine-grained distinctions pays off, such as done by a portfolio manager or genetic phenotype switches. In order to understand the difference we decompose population fitness and represent the strength of evolutionary selection with the information theoretic metric of relative entropy (Kullback-Leibler divergence). It is a multivariate metric that allows us to analyze selection pressure over multiple taxonomic levels in one single equation. It turns out that difference in relative entropy between different strategies is proportional to the potential to increase population fitness through intervention. As such, differences in relative entropy allow to quantify the potential to increase fitness. An intuitive interpretation is that it quantifies the amount of complementary variety between different population types and corresponding environmental states. The more type fitness is skewed to opposing directions in different environmental states, the proportionally larger the potential benefit of strategic intervention over natural selection. In reference to the literature of bet-hedging and portfolio theory, it is shown that the higher the degree of specialization of different population types to different environmental states, the larger the complementary variety among them, and therefore the larger the potential payoff. Complementary variety is the necessary condition to increase overall fitness through resource redistribution. This suggests developing classification systems of population types and environmental states that contain complementary variety.
Martin Hilbert
140 Effect of environmental colored noise in population dynamics [abstract]
Abstract: Variability on the external conditions, such as the temperature, humidity, available nutrients, etc., have important consequences for the dynamics and organization of communities of living systems. Furthermore, the interplay between the timescales of the environment and the intrinsic dynamics plays a fundamental role in many situations. However, most of the mathematical models neglect temporal correlations of the environment. We propose a unifying framework of some precedent available analytical and numerical tools to deal with colored noise, and provide a general scheme to answer some relevant questions concerning population dynamics: quantification of the population growth rate and population density, under which internal and internal conditions the population may become extinct, and in such a case, how much time does it take to disappear. These questions are of fundamental relevance, for instance, in the context of epidemiology, as they provide valuable information for the control and eradication of disease spreading. We test our results in a SIS model in which the infection rate fluctuates in time with environmental conditions.
Tommaso Spanio, Jorge Hidalgo and Miguel A Muñoz
192 The effect of hierarchical order in directed networks [abstract]
Abstract: Hierarchy is pervasive in both natural and man-made systems. A significant part of complex networks science is concerned with identifying hierarchical features in observed real world networks, explaining their origins via generative models with simple assembly rules and studying the interplay between features on many scales by studying appropriate random network ensembles. Recently it has been shown that a new topological feature of directed networks termed "trophic coherence" is a prominent in many real world networks ranging from ecological food-webs to gene transcription networks. Trophic coherence characterizes how "layered" a directed network is - the tendency of nodes to form well defined, hierarchically organized groups. In networks with high trophic coherence interactions via directed links start from base nodes with no incoming connections and follow up the hierarchy of nodes in a chain-of-command fashion. In networks with less trophic coherence, however, "shortcuts" may be present that distorts the hierarchy and allows interactions between groups of nodes far apart in the network. This has implications on local topological features and information spread. We present results on how trophic coherence affects the local structure of food-webs. Our findings indicate that trophic coherence reveals that the majority of known food-webs fall into one of two groups - those with relatively little omnivory and those with a lot of omnivory as defined by the presence of feed-forward loops. This result complements previous results by Johnson et al. where a network model with trophic coherence was shown to reproduce most food-web features better than the standard Niche and Cascade models. Additionally, work on studying contagion processes on trophically coherent networks has shown that the level of trophic coherence plays a large role in determining the final size of an outbreak. We briefly discuss numerical results and future work.
Janis Klaise
91 Graph partitions and cluster synchronization in networks of oscillators [abstract]
Abstract: Synchronization processes are ubiquitous in nature, from the entrainment of circadian rhythms and the synchronous firing of neurons to the flocking of birds or the shoaling of fish. The emergence of collective consensus in networked systems is thus a current focus in biology, physics, chemistry, as well as in social and technological networks. Previous studies have typically focused on total synchronization, where all agents on the network converge to the same dynamics. Here we use tools from graph theory to study the phenomenon of cluster synchronization, where groups of agents converge to several distinct behaviors. We show that cluster synchronization can emerge in networks with certain regularities, as captured via a graph partition called the external equitable partition. Indeed, when the underlying coupling network presents certain regularities, the dynamics can be coarse-grained into clusters by means of external equitable partitions and their associated quotient graphs. We derive conditions and properties of networks under which such clustered behavior emerges, and show that the ensuing dynamics is the result of a localization of the eigenvectors of the associated graph Laplacians. The framework is applied to both linear (consensus dynamics) and non-linear models (generic oscillator models, including the classic Kuramoto model), first in the standard case of networks with positive edges, before being generalized to the case of signed networks with both positive and negative interactions. Furthermore, we demonstrate how our graph-theoretical approach allows us to extend the analysis to cluster synchronization of signed networks (with positive and negative links), which are used to describe social interactions and inhibitory-excitatory interactions in biology.
Michael Schaub, Neave O'Clery, Yazan N. Billeh, Jean-Charles Delvenne, Renaud Lambiotte and Mauricio Barahona
470 Percolation-based precursors of transitions in extended systems [abstract]
Abstract: Complex systems may display strong changes in their dynamics: bifurcations, tipping points, phase transitions, etc. Some examples of special relevance are phase transitions in condensed matter systems (magnetism, superconductivity), sudden physiological alterations (strokes, epileptic seizures), economic crisis or climatic changes associated to the global warming such as potential modifications of weather and oceanic circulation patterns. The origin of these sudden changes can be traced down to the interactions between the system components. In most cases, the correlation of the components' dynamics enhances before the transition due to the cooperative phenomena that give raise to the emergence of a new global dynamical state. While understanding the ultimate causes of the change is of great importance, from a practical point of view it is absolutely crucial to count with metrics able to act as early warning signals or precursors of the dynamic transition. This may mean the difference between being able to react preemptively to the change or arriving to it unaware. In this work, we exploit the increase of microscopic correlations when the tipping point gets closer and define a set of early warning metrics using concepts imported from percolation theory on the functional network framework. We show that the functional networks encoding the system dynamics undergo a percolation transition way before the tipping point arrives. Furthermore, the number of clusters of size s peaks way before the percolation transition and, therefore, the sequence of peaks clearly mark the path to the transition. Our warning signals are general, as shown by analyzing three very different types of transitions, they precedes other early warning signals proposed in the literature and are straightforwardly applicable to many real-world complex systems, as proven by the analysis run with them on the South Pacific El Nino Oscillation. Our results have made available online at
Jose J. Ramasco