Complexity Theory: an Overview with Potential Applications for the Social Sciences
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What Is a Complex Adaptive System?
PROJECT GUTS What is a Complex Adaptive System? Introduction During the last three decades a leap has been made from the application of computing to help scientists ‘do’ science to the integration of computer science concepts, tools and theorems into the very fabric of science. The modeling of complex adaptive systems (CAS) is an example of such an integration of computer science into the very fabric of science; models of complex systems are used to understand, predict and prevent the most daunting problems we face today; issues such as climate change, loss of biodiversity, energy consumption and virulent disease affect us all. The study of complex adaptive systems, has come to be seen as a scientific frontier, and an increasing ability to interact systematically with highly complex systems that transcend separate disciplines will have a profound affect on future science, engineering and industry as well as in the management of our planet’s resources (Emmott et al., 2006). The name itself, “complex adaptive systems” conjures up images of complicated ideas that might be too difficult for a novice to understand. Instead, the study of CAS does exactly the opposite; it creates a unified method of studying disparate systems that elucidates the processes by which they operate. A complex system is simply a system in which many independent elements or agents interact, leading to emergent outcomes that are often difficult (or impossible) to predict simply by looking at the individual interactions. The “complex” part of CAS refers in fact to the vast interconnectedness of these systems. Using the principles of CAS to study these topics as related disciplines that can be better understood through the application of models, rather than a disparate collection of facts can strengthen learners’ understanding of these topics and prepare them to understand other systems by applying similar methods of analysis (Emmott et al., 2006). -
Dimensions of Ecosystem Complexity: Heterogeneity, Connectivity, and History
ecological complexity 3 (2006) 1–12 available at www.sciencedirect.com journal homepage: http://www.elsevier.com/locate/ecocom Viewpoint Dimensions of ecosystem complexity: Heterogeneity, connectivity, and history M.L. Cadenasso a,*, S.T.A. Pickett b, J.M. Grove c a Hixon Center for Urban Ecology, School of Forestry and Environmental Studies, Yale University, 205 Prospect Street, New Haven, CT 06511, United States b Institute of Ecosystem Studies, Box AB, Millbrook, NY 12545, United States c USDA Forest Service, Northeastern Research Station, 705 Spear Street, P.O. Box 968, Burlington, VT 05401, United States article info abstract Article history: Biocomplexity was introduced to most ecologists through the National Science Foundation’s Received 2 June 2005 grant program, and the literature intended to introduce that program. The generalities of that Received in revised form literature contrast with the abstract and mathematical sophistication of literature from 30 June 2005 physics, systems theory, and indeed even of pioneering ecologists who have translated the Accepted 2 July 2005 conceptintoecology. Thissituation leaves a middle ground, that isboth accessibletoecologists Published on line 23 January 2006 in general, and cognizant of the fundamentals of complexity, to be more completely explored. To help scope this middle ground, and to promote empirical explorations that may be located Keywords: there, we propose a non-exclusive framework for the conceptual territory. While recognizing Biocomplexity the deep foundations in the studies of complex behavior, we take ecological structure as the Framework entry point for framework development. This framework is based on a definition of biocom- Coupled systems plexity as the degree to which ecological systems comprising biological, social and physical Spatial heterogeneity components incorporate spatially explicit heterogeneity, organizational connectivity, and Legacies historical contingency through time. -
Complexity Theory Lecture 9 Co-NP Co-NP-Complete
Complexity Theory 1 Complexity Theory 2 co-NP Complexity Theory Lecture 9 As co-NP is the collection of complements of languages in NP, and P is closed under complementation, co-NP can also be characterised as the collection of languages of the form: ′ L = x y y <p( x ) R (x, y) { |∀ | | | | → } Anuj Dawar University of Cambridge Computer Laboratory NP – the collection of languages with succinct certificates of Easter Term 2010 membership. co-NP – the collection of languages with succinct certificates of http://www.cl.cam.ac.uk/teaching/0910/Complexity/ disqualification. Anuj Dawar May 14, 2010 Anuj Dawar May 14, 2010 Complexity Theory 3 Complexity Theory 4 NP co-NP co-NP-complete P VAL – the collection of Boolean expressions that are valid is co-NP-complete. Any language L that is the complement of an NP-complete language is co-NP-complete. Any of the situations is consistent with our present state of ¯ knowledge: Any reduction of a language L1 to L2 is also a reduction of L1–the complement of L1–to L¯2–the complement of L2. P = NP = co-NP • There is an easy reduction from the complement of SAT to VAL, P = NP co-NP = NP = co-NP • ∩ namely the map that takes an expression to its negation. P = NP co-NP = NP = co-NP • ∩ VAL P P = NP = co-NP ∈ ⇒ P = NP co-NP = NP = co-NP • ∩ VAL NP NP = co-NP ∈ ⇒ Anuj Dawar May 14, 2010 Anuj Dawar May 14, 2010 Complexity Theory 5 Complexity Theory 6 Prime Numbers Primality Consider the decision problem PRIME: Another way of putting this is that Composite is in NP. -
Complexity” Makes a Difference: Lessons from Critical Systems Thinking and the Covid-19 Pandemic in the UK
systems Article How We Understand “Complexity” Makes a Difference: Lessons from Critical Systems Thinking and the Covid-19 Pandemic in the UK Michael C. Jackson Centre for Systems Studies, University of Hull, Hull HU6 7TS, UK; [email protected]; Tel.: +44-7527-196400 Received: 11 November 2020; Accepted: 4 December 2020; Published: 7 December 2020 Abstract: Many authors have sought to summarize what they regard as the key features of “complexity”. Some concentrate on the complexity they see as existing in the world—on “ontological complexity”. Others highlight “cognitive complexity”—the complexity they see arising from the different interpretations of the world held by observers. Others recognize the added difficulties flowing from the interactions between “ontological” and “cognitive” complexity. Using the example of the Covid-19 pandemic in the UK, and the responses to it, the purpose of this paper is to show that the way we understand complexity makes a huge difference to how we respond to crises of this type. Inadequate conceptualizations of complexity lead to poor responses that can make matters worse. Different understandings of complexity are discussed and related to strategies proposed for combatting the pandemic. It is argued that a “critical systems thinking” approach to complexity provides the most appropriate understanding of the phenomenon and, at the same time, suggests which systems methodologies are best employed by decision makers in preparing for, and responding to, such crises. Keywords: complexity; Covid-19; critical systems thinking; systems methodologies 1. Introduction No one doubts that we are, in today’s world, entangled in complexity. At the global level, economic, social, technological, health and ecological factors have become interconnected in unprecedented ways, and the consequences are immense. -
Database-Centric Programming for Wide-Area Sensor Systems
Database-Centric Programming for Wide-Area Sensor Systems 1 2 1 2 Shimin Chen , Phillip B. Gibbons , and Suman Nath ; 1 Carnegie Mellon University fchensm,[email protected] 2 Intel Research Pittsburgh [email protected] Abstract. A wide-area sensor system is a complex, dynamic, resource-rich col- lection of Internet-connected sensing devices. In this paper, we propose X-Tree Programming, a novel database-centric programming model for wide-area sen- sor systems designed to achieve the seemingly conflicting goals of expressive- ness, ease of programming, and efficient distributed execution. To demonstrate the effectiveness of X-Tree Programming in achieving these goals, we have in- corporated the model into IrisNet, a shared infrastructure for wide-area sensing, and developed several widely different applications, including a distributed in- frastructure monitor running on 473 machines worldwide. 1 Introduction A wide-area sensor system [2, 12, 15, 16] is a complex, dynamic, resource-rich collec- tion of Internet-connected sensing devices. These devices are capable of collecting high bit-rate data from powerful sensors such as cameras, microphones, infrared detectors, RFID readers, and vibration sensors, and performing collaborative computation on the data. A sensor system can be programmed to provide useful sensing services that com- bine traditional data sources with tens to millions of live sensor feeds. An example of such a service is a Person Finder, which uses cameras or smart badges to track people and supports queries for a person's current location. A desirable approach for develop- ing such a service is to program the collection of sensors as a whole, rather than writing software to drive individual devices. -
A General Representation of Dynamical Systems for Reservoir Computing
A general representation of dynamical systems for reservoir computing Sidney Pontes-Filho∗,y,x, Anis Yazidi∗, Jianhua Zhang∗, Hugo Hammer∗, Gustavo B. M. Mello∗, Ioanna Sandvigz, Gunnar Tuftey and Stefano Nichele∗ ∗Department of Computer Science, Oslo Metropolitan University, Oslo, Norway yDepartment of Computer Science, Norwegian University of Science and Technology, Trondheim, Norway zDepartment of Neuromedicine and Movement Science, Norwegian University of Science and Technology, Trondheim, Norway Email: [email protected] Abstract—Dynamical systems are capable of performing com- TABLE I putation in a reservoir computing paradigm. This paper presents EXAMPLES OF DYNAMICAL SYSTEMS. a general representation of these systems as an artificial neural network (ANN). Initially, we implement the simplest dynamical Dynamical system State Time Connectivity system, a cellular automaton. The mathematical fundamentals be- Cellular automata Discrete Discrete Regular hind an ANN are maintained, but the weights of the connections Coupled map lattice Continuous Discrete Regular and the activation function are adjusted to work as an update Random Boolean network Discrete Discrete Random rule in the context of cellular automata. The advantages of such Echo state network Continuous Discrete Random implementation are its usage on specialized and optimized deep Liquid state machine Discrete Continuous Random learning libraries, the capabilities to generalize it to other types of networks and the possibility to evolve cellular automata and other dynamical systems in terms of connectivity, update and learning rules. Our implementation of cellular automata constitutes an reservoirs [6], [7]. Other systems can also exhibit the same initial step towards a general framework for dynamical systems. dynamics. The coupled map lattice [8] is very similar to It aims to evolve such systems to optimize their usage in reservoir CA, the only exception is that the coupled map lattice has computing and to model physical computing substrates. -
EMERGENT COMPUTATION in CELLULAR NEURRL NETWORKS Radu Dogaru
IENTIFIC SERIES ON Series A Vol. 43 EAR SCIENC Editor: Leon 0. Chua HI EMERGENT COMPUTATION IN CELLULAR NEURRL NETWORKS Radu Dogaru World Scientific EMERGENT COMPUTATION IN CELLULAR NEURAL NETWORKS WORLD SCIENTIFIC SERIES ON NONLINEAR SCIENCE Editor: Leon O. Chua University of California, Berkeley Series A. MONOGRAPHS AND TREATISES Volume 27: The Thermomechanics of Nonlinear Irreversible Behaviors — An Introduction G. A. Maugin Volume 28: Applied Nonlinear Dynamics & Chaos of Mechanical Systems with Discontinuities Edited by M. Wiercigroch & B. de Kraker Volume 29: Nonlinear & Parametric Phenomena* V. Damgov Volume 30: Quasi-Conservative Systems: Cycles, Resonances and Chaos A. D. Morozov Volume 31: CNN: A Paradigm for Complexity L O. Chua Volume 32: From Order to Chaos II L. P. Kadanoff Volume 33: Lectures in Synergetics V. I. Sugakov Volume 34: Introduction to Nonlinear Dynamics* L Kocarev & M. P. Kennedy Volume 35: Introduction to Control of Oscillations and Chaos A. L. Fradkov & A. Yu. Pogromsky Volume 36: Chaotic Mechanics in Systems with Impacts & Friction B. Blazejczyk-Okolewska, K. Czolczynski, T. Kapitaniak & J. Wojewoda Volume 37: Invariant Sets for Windows — Resonance Structures, Attractors, Fractals and Patterns A. D. Morozov, T. N. Dragunov, S. A. Boykova & O. V. Malysheva Volume 38: Nonlinear Noninteger Order Circuits & Systems — An Introduction P. Arena, R. Caponetto, L Fortuna & D. Porto Volume 39: The Chaos Avant-Garde: Memories of the Early Days of Chaos Theory Edited by Ralph Abraham & Yoshisuke Ueda Volume 40: Advanced Topics in Nonlinear Control Systems Edited by T. P. Leung & H. S. Qin Volume 41: Synchronization in Coupled Chaotic Circuits and Systems C. W. Wu Volume 42: Chaotic Synchronization: Applications to Living Systems £. -
Organization, Self-Organization, Autonomy and Emergence: Status and Challenges
Organization, Self-Organization, Autonomy and Emergence: Status and Challenges Sven Brueckner 1 Hans Czap 2 1 New Vectors LLC 3520 Green Court, Suite 250, Ann Arbor, MI 48105-1579, USA Email: [email protected] http://www.altarum.net/~sbrueckner 2 University of Trier, FB IV Business Information Systems I D-54286 Trier, Germany Email: [email protected] http://www.wi.uni-trier.de/ Abstract: Development of IT-systems in application react and adapt autonomously to changing requirements. domains is facing an ever-growing complexity resulting from Therefore, approaches that rely on the fundamental principles a continuous increase in dynamics of processes, applications- of self-organization and autonomy are growing in acceptance. and run-time environments and scaling. The impact of this Following such approaches, software system functionality trend is amplified by the lack of central control structures. As is no longer explicitly designed into its component processes a consequence, controlling this complexity and dynamics is but emerges from lower-level interactions that are one of the most challenging requirements of today’s system purposefully unaware of the system-wide behavior. engineers. Furthermore, organization, the meaningful progression of The lack of a central control instance immediately raises local sensing, processing and action, is achieved by the the need for software systems which can react autonomously system components themselves at runtime and in response to to changing environmental requirements and conditions. the current state of the environment and the problem that is to Therefore, a new paradigm is necessary how to build be solved, rather than being enforced from the “outside” software systems changing radically the way one is used to through design or external control. -
Week 1: an Overview of Circuit Complexity 1 Welcome 2
Topics in Circuit Complexity (CS354, Fall’11) Week 1: An Overview of Circuit Complexity Lecture Notes for 9/27 and 9/29 Ryan Williams 1 Welcome The area of circuit complexity has a long history, starting in the 1940’s. It is full of open problems and frontiers that seem insurmountable, yet the literature on circuit complexity is fairly large. There is much that we do know, although it is scattered across several textbooks and academic papers. I think now is a good time to look again at circuit complexity with fresh eyes, and try to see what can be done. 2 Preliminaries An n-bit Boolean function has domain f0; 1gn and co-domain f0; 1g. At a high level, the basic question asked in circuit complexity is: given a collection of “simple functions” and a target Boolean function f, how efficiently can f be computed (on all inputs) using the simple functions? Of course, efficiency can be measured in many ways. The most natural measure is that of the “size” of computation: how many copies of these simple functions are necessary to compute f? Let B be a set of Boolean functions, which we call a basis set. The fan-in of a function g 2 B is the number of inputs that g takes. (Typical choices are fan-in 2, or unbounded fan-in, meaning that g can take any number of inputs.) We define a circuit C with n inputs and size s over a basis B, as follows. C consists of a directed acyclic graph (DAG) of s + n + 2 nodes, with n sources and one sink (the sth node in some fixed topological order on the nodes). -
Dissipative Structures, Complexity and Strange Attractors: Keynotes for a New Eco-Aesthetics
Dissipative structures, complexity and strange attractors: keynotes for a new eco-aesthetics 1 2 3 3 R. M. Pulselli , G. C. Magnoli , N. Marchettini & E. Tiezzi 1Department of Urban Studies and Planning, M.I.T, Cambridge, U.S.A. 2Faculty of Engineering, University of Bergamo, Italy and Research Affiliate, M.I.T, Cambridge, U.S.A. 3Department of Chemical and Biosystems Sciences, University of Siena, Italy Abstract There is a new branch of science strikingly at variance with the idea of knowledge just ended and deterministic. The complexity we observe in nature makes us aware of the limits of traditional reductive investigative tools and requires new comprehensive approaches to reality. Looking at the non-equilibrium thermodynamics reported by Ilya Prigogine as the key point to understanding the behaviour of living systems, the research on design practices takes into account the lot of dynamics occurring in nature and seeks to imagine living shapes suiting living contexts. When Edgar Morin speaks about the necessity of a method of complexity, considering the evolutive features of living systems, he probably means that a comprehensive method should be based on deep observations and flexible ordering laws. Actually designers and planners are engaged in a research field concerning fascinating theories coming from science and whose playground is made of cities, landscapes and human settlements. So, the concept of a dissipative structure and the theory of space organized by networks provide a new point of view to observe the dynamic behaviours of systems, finally bringing their flowing patterns into the practices of design and architecture. However, while science discovers the fashion of living systems, the question asked is how to develop methods to configure open shapes according to the theory of evolutionary physics. -
Environmental Influences: Family Systems Theory
Environmental Influences: Family Systems Theory Family Systems Theory provides a broad and comprehensive mechanism for understanding the core aspects of the Performance Competence Lifespan Framework — quality of life, member- ship, and a personal sense of competence. It also focuses on the most important component of environmental influences—home and family. From birth, a child’s Quality of Life is directly influ- enced by the kind of care, support, stimulation and education he or she receives from family mem- bers in the home. As infants begin to develop secure attachments with significant others, particu- larly family members, they begin to establish themselves as members of the first and most basic unit of society—the family, which forms the foundation for secure Membership in other groups throughout life. The infant begins to develop a Personal Sense of Competence when his mother responds consistently to his distress, when he takes his first step or says his first word, or when his father praises him for using the toilet. These early beginnings, then, are at the core of what each individual child will come to know and be able to do. As the PC Framework indicates, there are multiple environmental influences on performance and competence, but the family is the first and most important. The influence of family members on one another is not simple, but complex; it is not one-way, but reciprocal. The family, like a mechanical system, is made up of multiple parts that are interdependent. When one part does not function well, all other parts are impacted. Further, the family interacts with other systems, includ- ing those that provide direct services to the child—child care/preschools, schools and community agencies—and each system affects the other. -
Chapter 24 Conp, Self-Reductions
Chapter 24 coNP, Self-Reductions CS 473: Fundamental Algorithms, Spring 2013 April 24, 2013 24.1 Complementation and Self-Reduction 24.2 Complementation 24.2.1 Recap 24.2.1.1 The class P (A) A language L (equivalently decision problem) is in the class P if there is a polynomial time algorithm A for deciding L; that is given a string x, A correctly decides if x 2 L and running time of A on x is polynomial in jxj, the length of x. 24.2.1.2 The class NP Two equivalent definitions: (A) Language L is in NP if there is a non-deterministic polynomial time algorithm A (Turing Machine) that decides L. (A) For x 2 L, A has some non-deterministic choice of moves that will make A accept x (B) For x 62 L, no choice of moves will make A accept x (B) L has an efficient certifier C(·; ·). (A) C is a polynomial time deterministic algorithm (B) For x 2 L there is a string y (proof) of length polynomial in jxj such that C(x; y) accepts (C) For x 62 L, no string y will make C(x; y) accept 1 24.2.1.3 Complementation Definition 24.2.1. Given a decision problem X, its complement X is the collection of all instances s such that s 62 L(X) Equivalently, in terms of languages: Definition 24.2.2. Given a language L over alphabet Σ, its complement L is the language Σ∗ n L. 24.2.1.4 Examples (A) PRIME = nfn j n is an integer and n is primeg o PRIME = n n is an integer and n is not a prime n o PRIME = COMPOSITE .