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.
Social systems have recently attracted much attention, with attempts to understand social behavior with the aid of statistical mechanics applied to complex systems. Collective properties of such systems emerge from couplings between components, for example, individual persons, transportation nodes such as airports or subway stations, and administrative districts. Among various collective properties, criticality is known as a characteristic property of a complex system, which helps the systems to respond flexibly to external perturbations. This work considers the criticality of the urban transportation system entailed in the massive smart card data on the Seoul transportation network. Analyzing the passenger flow on the Seoul bus system during one week, we find explicit power-law correlations in the system, that is, power-law behavior of the strength correlation function of bus stops and verify scale invariance of the strength fluctuations. Such criticality is probed by means of the scaling and renormalization analysis of the modified gravity model applied to the system. Here a group of nearby (bare) bus stops are transformed into a (renormalized) “block stop” and the scaling relations of the network density turn out to be closely related to the fractal dimensions of the system, revealing the underlying structure. Specifically, the resulting renormalized values of the gravity exponent and of the Hill coefficient give a good description of the Seoul bus system: The former measures the characteristic dimensionality of the network whereas the latter reflects the coupling between distinct transportation modes. It is thus demonstrated that such ideas of physics as scaling and renormalization can be applied successfully to social phenomena exemplified by the passenger flow.
The Resources section contains annotated links to a wide variety of web-based resources related to complex systems. These include journals, conferences, tutorials, software, videos, among other types of resources that will be useful for all levels of interest.
KONECT is the Koblenz Network Collection. KONECT is a project to collect large network datasets of all types in order to perform research in the area of network mining, collected by the Institute of Web Science and Technologies of the University of Koblenz–Landau. KONECT contains over a hundred network datasets of various types.
A network as provided by KONECT is a set of nodes connected by links. An example of a network is a social network: a set of users connected by links which represent friendship relations. A network is represented mathematically by a graph, in which nodes are called vertices and links are called edges.
Most networks are asymmetric: The fact that user A follows user B on the microblogging site Twitter does not imply that user B follows user A. The Twitter graph is thus directed. In the DBLP authorship network, scientific publications are connected to their authors. The DBLP publication network thus has two classes of nodes; it is bipartite.
Code to generate all network datasets from the Web Statistics and plots viewable online Download of selected datasets (where legally possible)
To be added in the future:
Analysis code to generate all statistics and plots
We've all heard the buzzwords - chaos, fractals, networks, power laws. What do these terms mean in a rigorous, mathematical sense? This 1-2 credit seminar will explore formalisms associated with the study of complex systems. These include non-linear dynamics (and their associated phase space mappings, as well as chaos), graph theory (networks), and fractals (and their associated power laws). Through readings, in-class problem sets, and hands-on computer-based simulations, we will pursue a concrete understanding of these concepts as well as the ability to implement them as mathematical tools. A basic course in calculus and differential equations and some coding experience would be helpful but is not required.
Due to recent advances in synthetic biology and artificial life, the origin of life is currently a hot topic of research. We review the literature and argue that the two traditionally competing replicator-first and metabolism-first approaches are merging into one integrated theory of individuation and evolution. We contribute to the maturation of this more inclusive approach by highlighting some problematic assumptions that still lead to an ximpoverished conception of the phenomenon of life. In particular, we argue that the new consensus has so far failed to consider the relevance of intermediate time scales. We propose that an adequate theory of life must account for the fact that all living beings are situated in at least four distinct time scales, which are typically associated with metabolism, motility, development, and evolution. In this view, self-movement, adaptive behavior, and morphological changes could have already been present at the origin of life. In order to illustrate this possibility, we analyze a minimal model of lifelike phenomena, namely, of precarious, individuated, dissipative structures that can be found in simple reaction-diffusion systems. Based on our analysis, we suggest that processes on intermediate time scales could have already been operative in prebiotic systems. They may have facilitated and constrained changes occurring in the faster- and slower-paced time scales of chemical self-individuation and evolution by natural selection, respectively.
Main concern: Are there two types of gray swans? 1) Conceivable, Unpredictable but forecast-able and 2) Conceivable, Unpredictable in the long-run but predictable in the (very) short term. Earthquakes are in the first category. Terrorist attacks are in the second category. 9.0 Earthquakes and 9/11 are both conceivable (and NOT unknown unknowns) but intelligence analysts had enough info to predict 9/11. Earthquakes are inherently unpredictable.
As scientific advances in perturbing biological systems and technological advances in data acquisition allow the large-scale quantitative analysis of biological function, the robustness of organisms to both transient environmental stresses and inter-generational genetic changes is a fundamental impediment to the identifiability of mathematical models of these functions. An approach to overcoming this impediment is to reduce the space of possible models to take into account both types of robustness. However, the relationship between the two is still controversial. This work uncovers a network characteristic, transient responsiveness, for a specific function that correlates environmental imperturbability and genetic robustness. We test this characteristic extensively for dynamic networks of ordinary differential equations ranging up to 30 interacting nodes and find that there is a power-law relating environmental imperturbability and genetic robustness that tends to linearity as the number of nodes increases. Using our methods, we refine the classification of known 3-node motifs in terms of their environmental and genetic robustness. We demonstrate our approach by applying it to the chemotaxis signaling network. In particular, we investigate plausible models for the role of CheV protein in biochemical adaptation via a phosphorylation pathway, testing modifications that could improve the robustness of the system to environmental and/or genetic perturbation.
Urban Emergencies : Emergent Urbanism (UE:EU) is an independent research group exploring international and interdisciplinary perspectives on the implications of emergent risks on the built environment and its inhabitants.
We discuss models and data of crowd disasters, crime, terrorism, war and disease spreading to show that conventional recipes, such as deterrence strategies, are not effective and sufficient to contain them. The failure of many conventional approaches results from their neglection of feedback loops, instabilities and/or cascade effects, due to which equilibrium models do often not provide a good picture of the actual system behavior. However, the complex and often counter-intuitive behavior of social systems and their macro-level collective dynamics can be understood by means of complexity science, which enables one to address the aforementioned problems more successfully. We highlight that a suitable system design and management can help to stop undesirable cascade effects and to enable favorable kinds of self-organization in the system. In such a way, complexity science can help to save human lives.
The Course Syllabi database contains a collection of annotated links to course syllabi related to complex systems. These syllabi can be searched according to class topics, institution, instructor, education level, and several other attributes. These syllabi will be useful for instructors developing their own courses on various topics, as well as serving as guides to people who want to learn on their own.
In 1987, George Soros introduced his concepts of reflexivity and fallibility and has further developed and applied these concepts over subsequent decades. This paper attempts to build on Soros's framework, provide his concepts with a more precise definition, and put them in the context of recent thinking on complex adaptive systems. The paper proposes that systems can be classified along a ‘spectrum of complexity’ and that under specific conditions not only social systems but also natural and artificial systems can be considered ‘complex reflexive.’ The epistemological challenges associated with scientifically understanding a phenomenon stem not from whether its domain is social, natural, or artificial, but where it falls along this spectrum. Reflexive systems present particular challenges; however, evolutionary model-dependent realism provides a bridge between Soros and Popper and a potential path forward for economics.
"I find the ideas in the fractals, both as a body of knowledge and as a metaphor, an incredibly important way of looking at the world." Vice President and Nobel Laureate Al Gore, New York Times, Wednesday, June 21, 2000, discussing some of the "big think" questions that intrigue him.
This is a collection of pages meant to support a first course in fractal geometry for students without especially strong mathematical preparation, or any particular interest in science. Each of the topics contains examples of fractals in the arts, humanities, or social sciences; these and other examples are collected in the panorama. Fractal geometry is a new way of looking at the world; we have been surrounded by natural patterns, unsuspected but easily recognized after only an hour's training.
Mark D. Longo introduces the field of Complexity and puts it into context as a collection of shifts in our ways of understanding our world. <This is the introductory lecture for the fall, 2012, class - The Mathematics of Complexity (BIO 131) at Stanford University.
Human language defines the most complex outcomes of evolution. The emergence of such an elaborated form of communication allowed humans to create extremely structured societies and manage symbols at different levels including, among others, semantics. All linguistic levels have to deal with an astronomic combinatorial potential that stems from the recursive nature of languages. This recursiveness is indeed a key defining trait. However, not all words are equally combined nor frequent. In breaking the symmetry between less and more often used and between less and more meaning-bearing units, universal scaling laws arise. Such laws, common to all human languages, appear on different stages from word inventories to networks of interacting words. Among these seemingly universal traits exhibited by language networks, ambiguity appears to be a specially relevant component. Ambiguity is avoided in most computational approaches to language processing, and yet it seems to be a crucial element of language architecture. Here we review the evidence both from language network architecture and from theoretical reasonings based on a least effort argument.Ambiguity is shown to play an essential role in providing a source of language efficiency, and is likely to be an inevitable byproduct of network growth.
Chances are if you’ve on the internet over the last few years you’ve run into a few amazing bird murmuration videos, like this one from Islands and Rivers or the one we featured on Colossal from Neels Castillion, where countless numbers of starlings flock together and move almost impossibly in concert. Artist Dennis Hlynsky, a professor at the Rhode Island School of Design, wondered what would happen if he could better trace the flight paths of individual birds, what kinds of patterns would emerge from these flying social networks?
Understanding how humans control unstable systems is central to many research problems, with applications ranging from quiet standing to aircraft landing. Much evidence appears in favor of event-driven control hypothesis: human operators are passive by default and only start actively controling the system when the discrepancy between the current and desired system states becomes in some sense large. The present paper argues that the control triggering mechanism in humans is intrinsically stochastic. We propose a model which captures the stochastic threshold mechanism and show that it matches the experimental data on human balancing of virtual overdamped stick. Our results suggest that the stochasticity of the threshold mechanism is a fundamental property and may play an important role in the dynamics of human-controlled systems.