Complex systems present problems both in mathematical modelling and philosophical foundations. The study of complex systems represents a new approach to science that investigates how relationships between parts give rise to the collective behaviors of a system and how the system interacts and forms relationships with its environment. The equations from which models of complex systems are developed generally derive from statistical physics, information theory and non-linear dynamics, and represent organized but unpredictable behaviors of natural systems that are considered fundamentally complex.
We introduce a non-partisan probability distribution on congressional redistricting of North Carolina which emphasizes the equal partition of the population and the compactness of districts. When random districts are drawn and the results of the 2012 election were re-tabulated under the drawn districtings, we find that an average of 7.6 democratic representatives are elected. 95% of the randomly sampled redistrictings produced between 6 and 9 Democrats. Both of these facts are in stark contrast with the 4 Democrats elected in the 2012 elections with the same vote counts. This brings into serious question the idea that such elections represent the "will of the people." It underlines the ability of redistricting to undermine the democratic process, while on the face allowing democracy to proceed.
Network infrastructures, such as roads, pipelines or the power grid face a multitude of challenges, from organizational and use changes, to climate change and resource scarcity. These challenges require the adaptation of existing infrastructures or their complete new development. Traditionally, infrastructure planning and routing issues are solved through top-down optimization strategies such as mixed integer non linear programming or graph approaches, or through bottom up approaches such as particle swarm optimizations or ant colony optimizations. While some integrated approaches have been proposed int he literature, no direct comparison of the two approaches as applied to the same problem have been reported. Therefore, we implement two routing algorithms to connect a single source node to multiple consuming nodes in a topology with hard boundaries and no-go areas. We compare a geometric graph algorithm finding an (sub)optimum edge-weighted Steiner minimal tree with a Ant Colony Optimization algorithm implemented as an Agent Based Model. Experimenting with 100 randomly generated routing problems, we find that both algorithms perform surprisingly similar in terms of topology, cost and computational performance. We also discovered that by approaching the problem from both top-down and bottom-up perspective, we were able to enrich both algorithms in a co-evolutionary fashion. Our main findings are that the two algorithms, as currently implemented in our test environment hardly differ in the quality of solution and computational performance. There are however significant differences in ease of problem encoding and future extensibility.
This paper presents an idealized design for a legislative system. The concept of idealized design is explained. The paper critiques two critical (and often taken for granted) features of the legislative branches of most contemporary democratic governments: legislators are chosen by election, and the same bodies perform all legislative and meta-legislative functions, for all laws. Seven problems with these two features are described. A new model of lawmaking is proposed, based on three concepts from ancient Athenian democracy — random selection, dividing legislative functions among multiple bodies, and the use of temporary bodies (like contemporary juries) for final decision making. The benefits of the model are laid out, and likely objections are addressed.
Forecasting epidemic outbreaks has long been the goal of health researchers. By modeling the interactions of two diseases occurring simultaneously, scientists show that specific parameters control the thresholds of epidemics.
Dynamics of Interacting Diseases Joaquín Sanz, Cheng-Yi Xia, Sandro Meloni, and Yamir Moreno Phys. Rev. X 4, 041005 (2014)
Understanding, modeling, and predicting the impact of global change on ecosystem functioning across biogeographical gradients can benefit from enhanced capacity to represent biota as a continuous distribution of traits. However, this is a challenge for the field of biogeography historically grounded on the species concept. Here we focus on the newly emergent field of functional biogeography: the study of the geographic distribution of trait diversity across organizational levels. We show how functional biogeography bridges species-based biogeography and earth science to provide ideas and tools to help explain gradients in multifaceted diversity (including species, functional, and phylogenetic diversities), predict ecosystem functioning and services worldwide, and infuse regional and global conservation programs with a functional basis. Although much recent progress has been made possible because of the rising of multiple data streams, new developments in ecoinformatics, and new methodological advances, future directions should provide a theoretical and comprehensive framework for the scaling of biotic interactions across trophic levels and its ecological implications.
Teotihuacan was the first urban civilization of Mesoamerica and one of the largest of the ancient world. Following a tradition in archaeology to equate social complexity with centralized hierarchy, it is widely believed that the city’s origin and growth was controlled by a lineage of powerful individuals. However, much data is indicative of a government of co-rulers, and artistic traditions expressed an egalitarian ideology. Yet this alternative keeps being marginalized because the problems of collective action make it difficult to conceive how such a coalition could have functioned in principle. We therefore devised a mathematical model of the city’s hypothetical network of representatives as a formal proof of concept that widespread cooperation was realizable in a fully distributed manner. In the model, decisions become self-organized into globally optimal configurations even though local representatives behave and modify their relations in a rational and selfish manner. This self-optimization crucially depends on occasional communal interruptions of normal activity, and it is impeded when sections of the network are too independent. We relate these insights to theories about community-wide rituals at Teotihuacan and the city’s eventual disintegration.
Proceedings from the 2014 Complex Systems Summer School are now posted, complete with a network map of the students’ collaborations. The students welcome comments and feedback.
Included in the proceedings are an exemplary set of more than two dozen papers -- more than half of which are being considered for publication.
Some of the topics: Can simple models reproduce complex transportation networks? What are the non-linear effects of pesticides on food dynamics? What role do fractals and scaling play in finance models?
Modelled as finite homogeneous Markov chains, probabilistic cellular automata with local transition probabilities in (0, 1) always posses a stationary distribution. This result alone is not very helpful when it comes to predicting the final configuration; one needs also a formula connecting the probabilities in the stationary distribution to some intrinsic feature of the lattice configuration. Previous results on the asynchronous cellular automata have showed that such feature really exists. It is the number of zero-one borders within the automaton's binary configuration. An exponential formula in the number of zero-one borders has been proved for the 1-D, 2-D and 3-D asynchronous automata with neighborhood three, five and seven, respectively. We perform computer experiments on a synchronous cellular automaton to check whether the empirical distribution obeys also that theoretical formula. The numerical results indicate a perfect fit for neighbourhood three and five, which opens the way for a rigorous proof of the formula in this new, synchronous case.
"In this review I show that four major kinds of theoretical approaches have been used to explain the scaling of metabolic rate in cells, organisms and groups of organisms in relation to system size. They include models focusing on surface-area related fluxes of resources and wastes (including heat), internal resource transport, system composition, and various processes affecting resource demand, all of which have been discussed extensively for nearly a century or more. I argue that, although each of these theoretical approaches has been applied to multiple levels of biological organization, none of them alone can fully explain the rich diversity of metabolic scaling relationships, including scaling exponents (log-log slopes) that vary from ~0 to >1. Furthermore, I demonstrate how a synthetic theory of metabolic scaling can be constructed by including the context-dependent action of each of the above modal effects. This “contextual multimodal theory” (CMT) posits that various modulating factors (including metabolic level, surface permeability, body shape, modes of thermoregulation and resource-transport, and other internal and external influences) affect the mechanistic expression of each theoretical module. By involving the contingent operation of several mechanisms, the “meta-mechanistic” CMT differs from most metabolic scaling theories that are deterministically mechanistic. The CMT embraces a systems view of life, and as such recognizes the open, dynamic nature and complex hierarchical and interactive organization of biological systems, and the importance of multiple (upward, downward and reciprocal) causation, biological regulation of resource supply and demand and their interaction, and contingent internal (system) and external (environmental) influences on metabolic scaling, all of which are discussed. I hope that my heuristic attempt at building a unifying theory of metabolic scaling will not only stimulate further testing of all of the various subtheories composing it, but also foster an appreciation that many current models are, at least in part, complementary or even synergistic, rather than antagonistic. Further exploration about how the scaling of the rates of metabolism and other biological processes are interrelated should also provide the groundwork for formulating a general metabolic theory of biology. "
The Santa Fe Institute (SFI) has launched a web-based educational platform, Complexity Explorer. SFI is a private research institute well known for its cross-disciplinary approach to complex systems such as ant colonies, biological cells, economies, and social systems. The stated mission of the institute is to “discover, comprehend, and communicate the common fundamental principles in complex physical, computational, biological, and social systems that underlie many of the most profound problems facing science and society today.”
As part of the institute’s outreach mission, SFI’s Complexity Explorer offers free open online courses (“MOOCs”) as well as searchable repositories of education-related resources. Past SFI MOOCs have attracted over 20,000 enrollees from nearly 100 countries.
This Fall SFI is offering three free MOOCS for people at different levels of expertise to learn about complex systems
We evaluated the education system of the United States from 1870 to 2011 using emergy methods. The system was partitioned into three subsystems (elementary, secondary and college/university education) and the emergy inputs required to support each subsystem were determined for every year over the period of analysis. We calculated the emergy required to produce an individual with a given number of years of education by summing over the years of support needed to attain that level of education. In 1983, the emergy per individual ranged from 8.63E+16 semj/ind. for a pre-school student to 165.9E+16 semj/ind. for a Ph.D. with 2 years of postdoctoral experience. The emergy of teaching and learning per hour spent in this process was calculated as the sum of the emergy delivered by the education and experience of the teachers and the emergy brought to the process of learning by the students. The emergy of teaching and learning was about an order of magnitude larger than the annual emergy supporting the U.S. education system (i.e., the emergy inflows provided by the environment, energy and materials, teachers, entering students, goods and services). The implication is that teaching and learning is a higher order social process related to the development and maintenance of the national information cycle. Also, the results imply that there is a 10-fold return on the emergy invested in operating the education system of the United States.
In this paper, the authors continue to build on their proposed model for incorporating randomly selected citizens into the decision-making processes of government. The first article presented a case for the benefits of random selection; proposed a lawmaking process that replaces elected, all-purpose legislatures with multiple, limited-function bodies composed of randomly selected citizens; and identified possible objections to the model (see An Idealized Design for the Legislative Branch of Government, http://stwj.systemswiki.org/?p=140). In the current article, the authors extend the model to the executive branch, discussing how redesigning the executive branch could improve accountability to the legislature and to the people.The potentialfor current executive branch designs to negatively affect performance and accountability is used to propose a new model that reduces the power of the executive branch, increases accountability, and has the potential to reduce corruption. The benefits of the model are outlined, and possible objections are addressed.
We develop a general formalism for representing and understanding structure in complex systems. In our view, structure is the totality of relationships among a system's components, and these relationships can be quantified using information theory. In the interest of flexibility we allow information to be quantified using any function, including Shannon entropy and Kolmogorov complexity, that satisfies certain fundamental axioms. Using these axioms, we formalize the notion of a dependency among components, and show how a system's structure is revealed in the amount of information assigned to each dependency. We explore quantitative indices that summarize system structure, providing a new formal basis for the complexity profile and introducing a new index, the "marginal utility of information". Using simple examples, we show how these indices capture intuitive ideas about structure in a quantitative way. Our formalism also sheds light on a longstanding mystery: that the mutual information of three or more variables can be negative. We discuss applications to complex networks, gene regulation, the kinetic theory of fluids and multiscale cybernetic thermodynamics.
An Information-Theoretic Formalism for Multiscale Structure in Complex Systems Benjamin Allen, Blake C. Stacey, Yaneer Bar-Yam
This paper is concerned with the limits of narrative understanding, and how they are thrown into relief by the challenge of emergent behaviour in complex systems. Such behaviour is a feature of much more of life than we tend to appreciate, but to recognize emergence is intrinsically to encounter the limits of narrative explanation. If we are not to be led astray by our cognitive dependence upon narrative, we need talk about emergent behaviour in a way that reaches beyond the limits of narrative sense; in discussions of emergence, sometimes even in definitions of emergence, this has tended to involve a vocabulary of surprise and wonder. I will examine the sources and implications of this vocabulary, and draw out its relation to the specific affordances of narrative sense-making in general, and the functions of narrative perspective and inference in particular. The discussion takes off from attempts to define emergence in complexity science, but goes on to elaborate the argument by appeal to analogous cultural contexts including Christian iconography and belief, Hitchcock on the suspense thriller, and Don DeLillo’s White Noise; it engages with narratological discussions of omniscience and inference, as well as a larger philosophical perspective upon the nature of knowledge.
Malignant cancers that lead to fatal outcomes for patients may remain dormant for very long periods of time. Although individual mechanisms such as cellular dormancy, angiogenic dormancy and immunosurveillance have been proposed, a comprehensive understanding of cancer dormancy and the “switch” from a dormant to a proliferative state still needs to be strengthened from both a basic and clinical point of view. Computational modeling enables one to explore a variety of scenarios for possible but realistic microscopic dormancy mechanisms and their predicted outcomes. The aim of this paper is to devise such a predictive computational model of dormancy with an emergent “switch” behavior. Specifically, we generalize a previous cellular automaton (CA) model for proliferative growth of solid tumor that now incorporates a variety of cell-level tumor-host interactions and different mechanisms for tumor dormancy, for example the effects of the immune system. Our new CA rules induce a natural “competition” between the tumor and tumor suppression factors in the microenvironment. This competition either results in a “stalemate” for a period of time in which the tumor either eventually wins (spontaneously emerges) or is eradicated; or it leads to a situation in which the tumor is eradicated before such a “stalemate” could ever develop. We also predict that if the number of actively dividing cells within the proliferative rim of the tumor reaches a critical, yet low level, the dormant tumor has a high probability to resume rapid
Electrical communication between cardiomyocytes can be perturbed during arrhythmia, but these perturbations are not captured by conventional electrocardiographic metrics. In contrast, information theory metrics can quantify how arrhythmia impacts the sharing of information between individual cells. We developed a theoretical framework to quantify communication during normal and abnormal heart rhythms in two commonly used models of action potential propagation: a reaction diffusion model and a cellular automata model with realistic restitution properties. For both models, the tissue was simulated as a 2-D cell lattice. The time series generated by each cell was coarse-grained to 1 when excited or 0 when resting. The Shannon entropy for each cell and the mutual information between each pair of cells were calculated from the time series during normal heartbeats, spiral wave, anatomical reentry, and multiple wavelets. We found that information sharing between cells was spatially heterogeneous on the simple lattice structure. In addition, arrhythmia significantly impacted information sharing within the heart. Mutual information could distinguish the spiral wave from multiple wavelets, which may help identify the mechanism of cardiac fibrillation in individual patients. Furthermore, entropy localized the path of the drifting core of the spiral wave, which could be an optimal target of therapeutic ablation. We conclude that information theory metrics can quantitatively assess electrical communication among cardiomyocytes. The traditional concept of the heart as a functional syncytium sharing electrical information via gap junctions cannot predict altered entropy and information sharing during complex arrhythmia. Information theory metrics may find clinical application in the identification of rhythm-specific treatments which are currently unmet by traditional electrocardiographic techniques.
We argue that a critical difference distinguishing machines from organisms and computers from brains is not complexity in a structural sense, but a difference in dynamical organization that is not well accounted for by current complexity measures. We propose a measure of the complexity of a system that is largely orthogonal to computational, information theoretic, or thermodynamic conceptions of structural complexity. What we call a system’s dynamical depth is a separate dimension of system complexity that measures the degree to which it exhibits discrete levels of nonlinear dynamical organization in which successive levels are distinguished by local entropy reduction and constraint generation. A system with greater dynamical depth than another consists of a greater number of such nested dynamical levels. Thus, a mechanical or linear thermodynamic system has less dynamical depth than an inorganic self-organized system, which has less dynamical depth than a living system. Including an assessment of dynamical depth can provide a more precise and systematic account of the fundamental difference between inorganic systems (low dynamical depth) and living systems (high dynamical depth), irrespective of the number of their parts and the causal relations between them.