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.

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.

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.

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.

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.