Human societies use complexity -- within their institutions and technologies -- to address their various problems, and they need high-quality energy to create and sustain this complexity. But now greater complexity is producing diminishing returns in wellbeing, while the energetic cost of key sources of energy is rising fast. Simultaneously, humankind's problems are becoming vastly harder, which requires societies to deliver yet more complexity and thus consume yet more energy. Resolving this paradox is the central challenge of the 21st century. Thomas Homer-Dixon holds the CIGI Chair of Global Systems at the Balsillie School of International Affairs in Waterloo, Canada, and is a Professor at the University of Waterloo.
Three forms of creativity are exemplified in biology and studied in ALife. Combinational creativity exists as the first step in genetic algorithms. Exploratory creativity is seen in models using cellular automata or evolutionary programs. Transformational creativity can result from evolutionary programming. Even radically novel forms can do so, given input from outside the program itself. Transformational creativity appears also in reaction-diffusion models of morphogenesis. That there are limits to biological creativity is suggested by ALife work bearing on instances of biological impossibility.
We intend to show that transient chaos is a very appealing, but still not widely appreciated, subfield of nonlinear dynamics. Besides flashing its basic properties and giving a brief overview of the many applications, a few recent transient-chaos-related subjects are introduced in some detail. These include the dynamics of decision making, dispersion, and sedimentation of volcanic ash, doubly transient chaos of undriven autonomous mechanical systems, and a dynamical systems approach to energy absorption or explosion.
The financial crisis illustrated the need for a functional understanding of systemic risk in strongly interconnected financial structures. Dynamic processes on complex networks being intrinsically difficult to model analytically, most recent studies of this problem have relied on numerical simulations. Here we report analytical results in a network model of interbank lending based on directly relevant financial parameters, such as interest rates and leverage ratios. We obtain a closed-form formula for the “critical degree” (the number of creditors per bank below which an individual shock can propagate throughout the network), and relate failures distributions to network topologies, in particular scalefree ones. Our criterion for the onset of contagion turns out to be isomorphic to the condition for cooperation to evolve on graphs and social networks, as recently formulated in evolutionary game theory. This remarkable connection supports recent calls for a methodological rapprochement between finance and ecology.
It has been suggested that major transitions in evolution require the emergence of novelties, often associated to the cooperative behaviour of previously existing objects or agents. A key innovation involves the first cooperative interactions among molecules in a prebiotic biosphere. One of the simplest scenarios includes two molecular species capable of helping each other forming a catalytic loop or hypercycle. The second order kinetics of the hypercycle implies a hyperbolic growth dynamics, capable of overcoming some selection barriers associated to non-cooperative molecular systems. Moreover, it has been suggested that molecular replicators might have benefited from a limited diffusion associated to their attachment to surfaces: evolution and escape from extinction might have been tied to living on a surface. In this paper we propose a field theoretical model of the hypercycle involving reaction and diffusion through the use of a many-body Hamiltonian. This treatment allows a characterisation of the spatially correlated dynamics of the system, where the critical dimension is found to be d_c=2. We discuss the role of surface dynamics as a selective advantage for the system's survival.
Field theory of molecular cooperators Jordi Piñero, Ricard Solé
In spiking neural networks an action potential could in principle trigger subsequent spikes in the neighbourhood of the initial neuron. A successful spike is that which trigger subsequent spikes giving rise to cascading behaviour within the system. In this study we introduce a metric to assess the success of spikes emitted by integrate-and-fire neurons arranged in complex topologies and whose collective behaviour is undergoing a phase transition that is identified by neuronal avalanches that become clusters of activation whose distribution of sizes can be approximated by a power-law. In numerical simulations we report that scale-free networks with the small-world property is the structure in which neurons possess more successful spikes. As well, we conclude both analytically and in numerical simulations that fully-connected networks are structures in which neurons perform worse. Additionally, we study how the small-world property affects spiking behaviour and its success in scale-free networks.
The success of complex networks at criticality Victor Hernandez-Urbina, Tom L. Underwood, J. Michael Herrmann
Temporal networks come with a wide variety of heterogeneities, from burstiness of event sequences to correlations between timingsof node and link activations. In this paper, we set to explore the latter by using greedy walks as probes of temporal network structure. Given a temporal network (a sequence of contacts), greedy walks proceed from node to node by always following the first available contact. Because of this, their structure is particularly sensitive to temporal-topological patterns involving repeated contacts between sets of nodes. This becomes evident in their small coverage per step as compared to a temporal reference model -- in empirical temporal networks, greedy walks often get stuck within small sets of nodes because of correlated contact patterns. While this may also happen in static networks that have pronounced community structure, the use of the temporal reference model takes the underlying static network structure out of the equation and indicates that there is a purely temporal reason for the observations. Further analysis of the structure of greedy walks indicates that burst trains, sequences of repeated contacts between node pairs, are the dominant factor. However, there are larger patterns too, as shown with non-backtracking greedy walks. We proceed further to study the entropy rates of greedy walks, and show that the sequences of visited nodes are more structured and predictable in original data as compared to temporally uncorrelated references. Taken together, these results indicate a richness of correlated temporal-topological patterns in temporal networks.
Exploring Temporal Networks with Greedy Walks Jari Saramaki, Petter Holme
Pinpointing the nodes whose removal most effectively disrupts a network has become a lot easier with the development of an efficient algorithm. Potential applications might include cybersecurity and disease control.
Network science: Destruction perfected • István A. Kovács & Albert-László Barabási
Data from social media are providing unprecedented opportunities to investigate the processes that rule the dynamics of collective social phenomena. Here, we consider an information theoretical approach to define and measure the temporal and structural signatures typical of collective social events as they arise and gain prominence. We use the symbolic transfer entropy analysis of micro-blogging time series to extract directed networks of influence among geolocalized sub-units in social systems. This methodology captures the emergence of system-level dynamics close to the onset of socially relevant collective phenomena. The framework is validated against a detailed empirical analysis of five case studies. In particular, we identify a change in the characteristic time-scale of the information transfer that flags the onset of information-driven collective phenomena. Furthermore, our approach identifies an order-disorder transition in the directed network of influence between social sub-units. In the absence of a clear exogenous driving, social collective phenomena can be represented as endogenously-driven structural transitions of the information transfer network. This study provides results that can help define models and predictive algorithms for the analysis of societal events based on open source data.
The dynamic of information-driven coordination phenomena: a transfer entropy analysis Javier Borge-Holthoefer, Nicola Perra, Bruno Gonçalves, Sandra González-Bailón, Alex Arenas, Yamir Moreno, Alessandro Vespignani
In studying fundamental physical limits and properties of computational processes, one is faced with the challenges of interpreting primitive information-processing functions through well-defined information-theoretic as well as thermodynamic quantities. In particular, transfer entropy, characterizing the function of computational transmission and its predictability, is known to peak near critical regimes. We focus on a thermodynamic interpretation of transfer entropy aiming to explain the underlying critical behavior by associating information flows intrinsic to computational transmission with particular physical fluxes. Specifically, in isothermal systems near thermodynamic equilibrium, the gradient of the average transfer entropy is shown to be dynamically related to Fisher information and the curvature of system's entropy. This relationship explicitly connects the predictability, sensitivity, and uncertainty of computational processes intrinsic to complex systems and allows us to consider thermodynamic interpretations of several important extreme cases and trade-offs.
Information thermodynamics of near-equilibrium computation Mikhail Prokopenko and Itai Einav Phys. Rev. E 91, 062143
Classic life history models are often based on optimization algorithms, focusing on the adaptation of survival and reproduction to the environment, while neglecting frequency dependent interactions in the population. Evolutionary game theory, on the other hand, studies frequency dependent strategy interactions, but usually omits life history and the demographic structure of the population. Here we show how an integration of both aspects can substantially alter the underlying evolutionary dynamics.
The PhD student will work within the larger LAB-M project "Live agent based models and the theory of adaptive multi-type and multilayer networks to study economic complexity and financial instability", funded by Ghent University and by the Flemish Fund for Scientific Research (FWO-Vlaanderen). The LAB-M project aims to model interactions of real persons with real incentives in massive multiplayer online games (MMOG) with realistic economic environments to test a wide plethora of economic and political theories and develop new theories rooted in network theory and methodology. The LAB-M world provides natural experiments and collects multi-faceted data on the interaction of people in adaptive multilayer networks. We will develop a new methodological language for social physics, rooted in adaptive multi-type multilayer networks. The PhD students will be based at the Economics and Physics Department of Ghent University (Belgium), and will be part of a research team, coordinated by Prof. Jan Ryckebusch and Prof. Koen Schoors. The PhD student will also be guided by international external advisors.
Network reconstruction helps us understand, diagnose and control complex networked systems by inferring properties of their interaction matrices, which characterize how nodes in the systems directly interact with each other. Despite a decade of extensive studies, network reconstruction remains an outstanding challenge. The fundamental limitations on which properties of the interaction matrix can be inferred from accessing the dynamics of individual nodes remain unknown. Here we characterize these fundamental limitations by deriving the necessary and sufficient condition to reconstruct any property of the interaction matrix. Counterintuitively, we prove that inferring less information ---such as the sign/connectivity pattern or the degree sequence--- does not make the network reconstruction problem easier than recovering the interaction matrix itself (i.e. the traditional parameter identification problem). Our analysis also reveals that using prior information of the interaction matrix ---such as bound on the edge-weights--- is the only way to circumvent these fundamental limitations of network reconstruction. This sheds light on designing new algorithms with practical improvements over parameter identification methods.
Fundamental limitations of network reconstruction Marco Tulio Angulo, Jaime A. Moreno, Albert-László Barabási, Yang-Yu Liu
Introduction to the Modeling and Analysis of Complex Systems introduces students to mathematical/computational modeling and analysis developed in the emerging interdisciplinary field of Complex Systems Science. Complex systems are systems made of a large number of microscopic components interacting with each other in nontrivial ways. Many real-world systems can be understood as complex systems, where critically important information resides in the relationships between the parts and not necessarily within the parts themselves. This textbook offers an accessible yet technically-oriented introduction to the modeling and analysis of complex systems. The topics covered include: fundamentals of modeling, basics of dynamical systems, discrete-time models, continuous-time models, bifurcations, chaos, cellular automata, continuous field models, static networks, dynamic networks, and agent-based models. Most of these topics are discussed in two chapters, one focusing on computational modeling and the other on mathematical analysis. This unique approach provides a comprehensive view of related concepts and techniques, and allows readers and instructors to flexibly choose relevant materials based on their objectives and needs. Python sample codes are provided for each modeling example.
Many biological systems execute tasks by dividing them into finer sub-tasks first. This is seen for example in the advanced division of labor of social insects like ants, bees or termites. One of the unsolved mysteries in biology is how a blind process of Darwinian selection could have led to such highly complex forms of sociality. To answer this question, we used simulated teams of robots and artificially evolved them to achieve maximum performance in a foraging task. We find that, as in social insects, this favored controllers that caused the robots to display a self-organized division of labor in which the different robots automatically specialized into carrying out different subtasks in the group. Remarkably, such a division of labor could be achieved even if the robots were not told beforehand how the global task of retrieving items back to their base could best be divided into smaller subtasks. This is the first time that a self-organized division of labor mechanism could be evolved entirely de-novo. In addition, these findings shed significant new light on the question of how natural systems managed to evolve complex sociality and division of labor.
Which topics spark the most heated debates in social media? Identifying these topics is a first step towards creating systems which pierce echo chambers. In this paper, we perform the first systematic methodological study of controversy detection using social-media network structure and content. Unlike previous work, rather than identifying controversy in a single hand-picked topic and use domain-specific knowledge, we focus on comparing topics in any domain. Our approach to quantifying controversy is a graph-based three-stage pipeline, which involves (i) building a conversation graph about a topic, which represents alignment of opinion among users; (ii) partitioning the conversation graph to identify potential sides of controversy; and (iii) measuring the amount of controversy from characteristics of the graph. We perform an extensive comparison of controversy measures, as well as graph building approaches and data sources. We use both controversial and non-controversial topics on Twitter, as well as other external datasets. We find that our new random-walk-based measure outperforms existing ones in capturing the intuitive notion of controversy, and show that content features are vastly less helpful in this task.
Quantifying Controversy in Social Media Kiran Garimella, Gianmarco De Francisci Morales, Aristides Gionis, Michael Mathioudakis
In this article, we analyze the interrelationships among such notions as entropy, information, complexity, order and chaos and show using the theory of categories how to generalize the second law of thermodynamics as a law of increasing generalized entropy or a general law of complification. This law could be applied to any system with morphisms, including all of our universe and its subsystems. We discuss how such a general law and other laws of nature drive the evolution of the universe, including physicochemical and biological evolutions. In addition, we determine eliminating selection in physicochemical evolution as an extremely simplified prototype of natural selection. Laws of nature do not allow complexity and entropy to reach maximal values by generating structures. One could consider them as a kind of “breeder” of such selection.
Entropy, Information and Complexity or Which Aims the Arrow of Time? George E. Mikhailovsky and Alexander P. Levich
The Diverse Applications of GenomicsCracking Open NatureFunctional Genome Annotation and In Silico BiologyGenetics, Bioethics, and Equivalency of RiskComplex Genetics: Anticipating a Billion Human Genome SequencesMiniaturized Genomic MonitoringPersonalized Genomics: Towards a Proactive ModelPopulation Genetics: More Traits, More Populations, and More Species
Tyler-Smith C, Yang H, Landweber LF, Dunham I, Knoppers BM, Donnelly P, et al. (2015) Where Next for Genetics and Genomics? PLoS Biol 13(7): e1002216. doi:10.1371/journal.pbio.1002216
Here, it is proposed that thinking on a different level is required to understand, what really triggers or removes this barrier. Just counting “dimensions” or “variables” is insufficient. The true intrinsic curse we are facing is the curse of instability. In fact, we argue below that instabilities (a) cause an increase in dimensionality, (b) substantially raise the analytical difficulty, and (c) are a strong indicator for multiscale dynamical complexity. Of course, it turns out that (a)–(c) are intimately related. Although we shall primarily illustrate the concepts with examples arising in mathematics and closely related disciplines, it will be shown that the abstract concept occurs, independently, across disciplines. In fact, we shall see that the curse of instability has already implicitly triggered the emergence of entirely new scientific disciplines. Furthermore, it may lead to formulate more concrete guiding principles to address the complexity challenges of the 21st century.
After growing up together, and mostly growing apart in the second half of the 20th century, the fields of artificial intelligence (AI), cognitive science, and neuroscience are reconverging on a shared view of the computational foundations of intelligence that promotes valuable cross-disciplinary exchanges on questions, methods, and results. We chart advances over the past several decades that address challenges of perception and action under uncertainty through the lens of computation. Advances include the development of representations and inferential procedures for large-scale probabilistic inference and machinery for enabling reflection and decisions about tradeoffs in effort, precision, and timeliness of computations. These tools are deployed toward the goal of computational rationality: identifying decisions with highest expected utility, while taking into consideration the costs of computation in complex real-world problems in which most relevant calculations can only be approximated. We highlight key concepts with examples that show the potential for interchange between computer science, cognitive science, and neuroscience.
Computational rationality: A converging paradigm for intelligence in brains, minds, and machines Samuel J. Gershman, Eric J. Horvitz, Joshua B. Tenenbaum
Social and biological contagions are influenced by the spatial embeddedness of networks. Historically, many epidemics spread as a wave across part of the Earth’s surface; however, in modern contagions long-range edges—for example, due to airline transportation or communication media—allow clusters of a contagion to appear in distant locations. Here we study the spread of contagions on networks through a methodology grounded in topological data analysis and nonlinear dimension reduction. We construct ‘contagion maps’ that use multiple contagions on a network to map the nodes as a point cloud. By analysing the topology, geometry and dimensionality of manifold structure in such point clouds, we reveal insights to aid in the modelling, forecast and control of spreading processes. Our approach highlights contagion maps also as a viable tool for inferring low-dimensional structure in networks.
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