Complex Systems Summer School 2013

The financial crisis of 2007-2009 demonstrated the need to understand the macrodynamics of interconnected financial systems. A fruitful approach to this problem regards financial infrastructures as weighted directed networks, with banks as nodes and loans as links. Using a simple banking model in which banks are linked through interbank lending, with an exogenous shock applied to a single bank, we find a closedform analytical solution for the degree at which failures begin to propagate in the network. This critical degree is expressed as a function of four financial parameters: banking leverage; interbank exposure; return on the investment opportunity; and interbank lending rate. While the transition to failure propagation is sharpest with regular networks, we observe it numerically for random and scale-free networks as well. We find that, if the expected number of failures is not strongly dependent on the network topology and is well captured by the notion of critical degree, the frequency of catastrophic cascades (with a single shock inducing all or most banks in the network to fail) tends to be much larger on scale-free networks than on classical random networks. We interpret this finding as a manifestation of the “robust-yet-fragile” property of scale-free networks.LINK

The stubborn persistence of poverty is perhaps the central puzzle of development economics. Almost all theories of poverty reduction revolve around the idea of convergence: the proposition that, because the relationship between capital stocks and income (i.e., the production function) is convex and monotonically decreasing in slope, the poor should eventually “catch up” to the rich. A great deal of the development economics literature is devoted to exploring why in fact this does not happen in the real world. Classically, explanations have focused on differences in savings rates, population growth, and technological change [7]; conditioning on these variables, convergence should hold. Later theorists, while acknowledging the importance of these forces, emphasized the role of imperfections in credit, insurance, and information markets as well as the influence of institutions—durable political and social norms that shape economic behavior [6].Together, imperfect markets and institutions can deform the production function away from the assumed characteristics of convexity and decreasing slope. Even more recently, a growing literature argues for the existence of inherent non-convexities in the production function that lead to “poverty traps” [1]. While the empirical data for poverty traps is to date thin [5], researchers have been encouraged by the intuitive appeal and sheer elegance of the theoretical models. In this paper, we explore yet simpler mechanisms for the persistence of poverty, in particular the effects of random chance and variation in rates of return to existing wealth operating over empirically relevant time frames. We run a series of agent-based simulations to investigate these topics, calibrating key agent variables and system parameters to fall within ranges conforming to empirical values from a recently collected dataset of rural Ethiopian householdsLINK

Before writing, chronicles were told by word of mouth. They conveyed information of important historic events that could readily be mixed up with legends – or become them. Chronicles needed to be easily accessible for people to pass them along, and stories lived on in listeners’ short memories. This collective, ever-waning awareness was the technology that kept the tales extant, and this technology required a continuous effort in reminding people never to forget. This way of keeping stories alive also imposed important constrains on the kind and form of the narrative material. Breathtaking epics were perhaps more likely to survive, which could easily tend toward mystification of pre-historic characters. These epics had to be kept in the form of repetitive, easy-to-learn patterns. It comes as a pleasant surprise for us that diverse ancient poems take similar 1 forms in different cultures, that they present similar – if not identical – rhythms, verses, and topics as if to make their transmission easier, and that these similarities can arguably be attributed to the biological reality of human beings [4]. In other words, the available biological technology for the preservation of tales has imposed important constrains on what and how pre-historic events can be produced and preserved. J. Garland from the University of Colorado, Boulder contributed substantially to this project.

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Complex adaptive systems are characterized by a dynamic network of interactions among elements and the capacity to adapt and self-organize when individual or multiple elements are exposed to an event or events that trigger modification of the system's structure (Holland, 2006; Gell-Mann, 1994). The study of such complexity and adaptation is one approach within the field of systems theory, having the goal of identifying principles that can pertain to many types of systems, at many scales and in many fields of research. The ocean is one of the largest entities studied in systems ecology, which concerns interactions between an organism and its surroundings. Systems biology, by contrast, tends to focus on interactions within biological systems such as the human body. However, both the ocean and the human body can be considered as complex adaptive systems. In the context of such a systems-theoretical approach, we question how and to what degree the systems principles and structures pertaining to the ecosystem of the ocean could, at the same time, be relevant to the human body. Could the body be regarded as a microcosm of the ocean and, if so, by studying the sustenance of life in the ocean might we find implications for the maintenance of human health and wellbeing?LINK

Many complex networks are characterized by a community structure, i.e. the presence of groups of nodes that are more densely connected with each other than with the rest of the network. The algorithms developed to detect such communities usually consider the structural properties of the network, i.e. the static links between nodes. In the case of social networks this means considering, for example, “friendship” links on Facebook or “followers” on Twitter. We argue that these kinds of static links are not indicative of the real community structure underlying these networks, since users of social media usually have hundreds of connections even with people they are only acquaintances with. Moreover, users of social media typically only communicate with a subset of these connections, and form real communities only within these subsets. In this paper, we adapt standard community detection algorithms to account for this 1 reality using recent work in information theoretic network analysis. We apply this approach to detect dynamical / functional communities in both synthetic and empirical networks, and determine how the composition of the communities changes over time. We find that by explicitly incorporating the observed dynamics of users in social media, we can identify communities hidden in the structural network. Joshua Garland, from the University of Colorado, Boulder, and Nix Barnett, from the University of California, Davis, contributed substantially to this project.LINK

Real networks are not isolated, but are interlinked with and dependent on other real networks. This paper presents a set of tools for studying multiple interconnected networks. Utilizing simulation, a controlled environment can be created in which to understand multinetwork dynamics at small and large scales. The paper uses simulation to look at interconnected networks of resources and consumers. The paper examines when the removal of any single node in the resource network has the largest impact on the consumer network. The paper finds that it’s import to focus on the network layer that connects the the separate networks of resources and consumers. In a controlled setting, the paper finds that increasing network density of the resource-consumer layer has a positive impact on minimizing negative consumer impact. Increasing Shannon’s diversity index on outgoing degree in the resource-consumer layer minimizes worst case negative impact. Increasing Shannon’s diversity on indegree maximizes negative impact. The paper also finds that separate networks are more ”attuned” to one another under conditions of higher utilization. There is a wide avenue of future opportunities for further research in this new field of burgeoning interest in the social networks literature.LINK

Multilevel societies, containing hierarchically nested social levels, are remarkable social structures whose origins are unclear. The social relationships of sperm whales are organized in a multilevel society with an upper level composed of clans of individuals communicating using similar patterns of clicks (codas). Using agent-based models informed by an 18-year empirical study, we show that clans are unlikely products of stochastic processes (genetic or cultural drift) but likely originate from cultural transmission via biased social learning of codas. Distinct clusters of individuals with similar acoustic repertoires, mirroring the empirical clans, emerge when whales learn preferentially the most common codas (conformism) from behaviourally similar individuals (homophily). Cultural transmission seems key in the partitioning of sperm whales into sympatric clans. These findings suggest that processes similar to those that generate complex human cultures could not only be at play in non-human societies but also create multilevel social structures in the wild. Hal Whitehead, from Dalhousie University (CA), contributed substantially to this project.LINK

We consider the dynamics between population and spatial distribution networks for the 200 largest urban agglomerations. Population dynamics are considered from 1950 to 2010 and distribution networks are analyzed in terms of vehicular transportation infrastructure. We observe that the growth of large urban agglomerations, in terms of population density, has slowed down in the second half of the twentieth century as their transportation infrastructure has become more complex. Computing inequality indices furthermore reveals that the resulting urban system is less concentrated than it used to be, with a larger share of the urban population distributed in more numerous, relatively smaller urban agglomerations. We analyze transportation infrastructure in terms of fractal dimension and found that developed continents have higher fractal dimensions and lower populations than non-developed ones. We speculate this is due to varying road widths existent in some areas and absent in others. More complex networks in effect extend the range of cities and offer increased cost to benet utility. Better understanding of universal principles associated with such networks affords an opportunity to assess our control of urban agglomerations and their relation to the larger ecosystem they inhabit. Further analysis is necessary to combine the above approaches with additional data and to develop a more comprehensive metric for assessing and addressing the long term ecologic, economic and social implications of urban development.LINK

Interactions between individuals or organizations, and the changes and evolutions that result, are a central theme of complexity research. NetAttack aims at modeling a network environment where an attacker and a defender compete to disrupt a network or keep it connected. The choices of how to attack and defend the network are governed by a Genetic Algorithms (GA) which is used to choose among a set of available strategies. Our analysis shows that the choice of strategy is particularly important if the resources available to attacker and defender are similar. In such a situation, the defender and attacker genomes co-evolve and find an equilibrium. The best strategies found through GAs by the attackers and defenders are based on betweenness centrality. Our results agree with previous literature assessing strategies for network attack and defense in a static context. However, our paper is the first to show how a GA approach can be applied in a dynamic game on a network. This research provides a starting-point to further explore strategies and to optimize network disruption and reconstruction. Many applications for our kind of analysis may be found in the field of security and safety dealing with social (criminal networks) and technological (computer networks) contexts.NetAttack: LINK

Nature’s designs inspire technological innovations with research known as biomimicry, which offers promise for “bio inspired energy” to create more efficient energy production, energy storage, and energy delivery with innovations that replicate the designs of natural systems. This brief introduction into this nascent field, where energy networks and natural systems intersect, synthesizes the current state of science. On-going research is encouraged, as opportunity exists for complexity sciences and network models that exist in nature to advance modern technologies, infrastructure, and policy approaches for the energy sector.LINK

Trophic interactions are central to ecosystem functioning, but the link between food web structure and ecosystem functioning remains obscure. Regularities (i.e. consistent patterns) in food web structure suggest the possibility of regularities in ecosystem functioning, which might be used to relate structure to function. We introduce a novel, genetic algorithm approach to simulate food webs with maximized throughput (a proxy for ecosystem functioning) and compare the structure of these simulated food webs to real empirical food webs using common metrics of food web structure. We repeat this analysis using robustness to secondary extinctions (a proxy for ecosystem resilience) instead of throughput to determine the relative contributions of ecosystem functioning and ecosystem resilience to food web structure. Simulated food webs that maximized robustness were similar to real food webs when connectance (i.e. levels of interaction across the food web) was high, but this result did not extend to food webs with low connectance. Simulated food webs that maximized throughput or a combination of throughput and robustness were not similar to any real food webs. Simulated maximum-throughput food webs differed markedly from maximum-robustness food webs, which suggests that maximizing different ecological functions can generate distinct food web structures. Based on our results, food web structure would appear to have a stronger relationship with ecosystem resilience than with ecosystem throughput. Our genetic algorithm approach is general and is well suited to large, realistically complex food webs. Genetic algorithms can incorporate constraints on structure and can generate outputs that can be compared directly to empirical data. Our method can be used to explore a range of maximization or minimization hypotheses, providing new perspectives on the links between structure and function in ecological systems.LINK

In this brief report, we investigate the structure of participant-project network formed during the 2013 Complex Systems Summer School (CSSS) at Santa Fe. The data is based on [1], telling us who works with whom in which project. We have also collected data of participants’ academic background [2]. Each participant’s background is expressed by a 4-component vector (“gene”), representing 4 different categories of subjects in the following order: math & physics, life sciences & ecology, social sciences & economics, and computing & programming. For each category, we ask a participant the following question: “Have you ever taken any graduate level courses or had research experience in that subject?” If the answer is “Yes”, we assign “1” to the component corresponding to that subject; otherwise, “0” is assigned to that component. For example, a participant with “genotype” means that he has graduate level background in both math & physics and social sciences & economics, but none in life sciences & ecology nor computing & programming. In this way, a 4-component genotype vector characterizing academic or research background is associated with each participant. Since the nature of this summer school is transdisciplinary, it is of intrinsic interest to study how various “genotypes” are mixed in the CSSS collaboration network, which may show interesting pattern or complexity.

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