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THEME 1 = COMPETITION, COOPERATION AND COMPLEXITY - NETWORK MODELS OF INTERACTIVE PROCESSESAs a basis for cooperation or competition, the evolution of networks is illustrated in an interactive demo written for SIENA, a program for the analysis of data on entire social networks, collected at two time points. The name stands for Simulation Investigation for Empirical Network Analysis. The purpose is the statistical modeling of the evolution of the first to the second observed network. The statistical analysis is done on the basis of computer simulation of a probabilistic model for this evolution.
Lots of physicists have gotten into the act of modeling network evolution following the publication of Duncan Watts' book Small Worlds: The Dynamics of Networks between Order and Randomness - Sample Reviews:       and extensions Newman, M.E.J., Strogatz, S. H. and Watts, D. J. Random graphs with arbitrary degree distributions and their applications. (2000) and on Network robustness and fragility. Hence we can start from some of the models for competition, and work our way towards cooperation and other aspects of complexity.
Reading: Watts D. J. and Strogatz S. H. Collective dynamics of 'small-world' networks. Nature 393, 440-442 (1998).
Bose-Einstein condensation in complex networks G. Bianconi, A.-L. BarabĚsi
Econophysics Forum -
Abstract: "The evolution of many complex systems, including the world wide web, business and citation networks is encoded in the dynamic web describing the interactions between the system's constituents. Despite their irreversible and non-equilibrium nature these networks follow Bose statistics and can undergo Bose-Einstein condensation. Addressing the dynamical properties of these non-equilibrium systems within the framework of equilibrium quantum gases predicts that the 'first-mover-advantage', 'fit-get-rich' and 'winner-takes-all' phenomena observed in competitive systems are thermodynamically distinct phases of the underlying evolving networks." from Abstracts
Limitations of Barabasi's 'Emergence of scaling in random networks' as applied to the WWW, Science 286, 509-512 (1999).
see also: Zipf, Power-laws, and Pareto - a ranking tutorial Lada A. Adamic
Technical comment to ŰEmergence of Scaling in Random NetworksÝ Lada A. Adamic Bernardo A. Huberman
Evolutionary Dynamics of the World Wide Web Lada A. Adamic Bernardo A. Huberman
Degree Distributions of Growing Random Networks, P. L. Krapivsky, G. J. Rodgers, and S. Redner, preprint (cond-mat/0012181)
Organization of Growing Random Networks, P. L. Krapivsky and S. Redner. Phys. Rev. E xx, xxxx (2001); (cond-mat/0011094)
Connectivity of Growing Random Networks, P. L. Krapivsky, S. Redner, F. Leyvraz. Phys. Rev. Lett. 85, 4629-4632 (2000).
Wealth Distributions in Models of Capital Exchange, S. Ispolatov, P. L. Krapivsky, S. Redner. Eur. Phys. J. B 2, 267-76 (1998)
Aggregation Kinetics in Gelation, Traffic, Wealth, and other Everyday Phenomena Sid Redner
More is Different Phil Anderson
A Guide to First-Passage Processes Table of Contents. S. Redner, Cambridge University Press, (in press, to appear June 2001).
For an extended example by an economist on complex dynamics in the movie industry, see Art Devany
and David Walls on Bose-Einstein distributions ... one of three ways energy is distributed in nature (check out the statistical distributions!). And speaking of
statistics for complex systems, here are two SFI authors on
that change our thinking about statistics. What are the Bose statistics all about? Let's look at how physicists look at this stuff -
see image 2/3 way thru
this file from Physics 2000 for the phenomenon of growing and potentially unlimited variance in motion at higher energies.
Just how BIG will the next blockbuster movie be? Just how many links will the premier node
have in the evolution of one of BarabĚsi's power-distribution networks below?
Topology of evolving networks: local events and universality. Reka Albert and Albert-Laszlo BarabĚsi. 13 pages, 3 figures. Abstract from: Phys. Rev. Lett. 85, 5234-5237 (2000). "Networks grow and evolve by local events, such as the addition of new nodes and links, or rewiring of links from one node to another. We show that depending on the frequency of these processes two topologically different networks can emerge, the connectivity distribution following either a generalized power-law or an exponential. We propose a continuum theory that predicts these two regimes as well as the scaling function and the exponents, in good agreement with the numerical results. Finally, we use the obtained predictions to fit the connectivity distribution of the network describing the professional links between movie actors."
For a full bibliography of network publications from BarabĚsi's group, see: Self-Organized Networks
BarabĚsi's extended model of network evolution is implemented as a network evolution simulation by Pajek: Package for Large Network Analysis, using options /Net/Random Network/Extended Model, and then /Net/Transform/Generate in time. The Pajek package is worth learning for analysis of empirical network datasets as well as for studying network simulations.
See Coding and analyzing simulated and actual network evolution - Douglas R White
See A dynamic model of social network formation. Brian Skyrms and Robin Pemantle. Proc. Natl. Acad. Sci. USA, Vol. 97, Issue 16, 9340-9346, August 1, 2000. Inaugural Article.
A controversial but fascinating general introduction by the physicist Per Bak, who first described self-organized criticality as an explanation of power law phenomena, is How Nature Works: The Science of Self-Organized Criticality. 1996 (Reprint edition 1999). Amazon Price $18.00: "The critical state, with [events] of all sizes [1/f 'fractality'], is the most efficient state. The system has self-organized to the critical state with the highest throughput... [it] is the the most efficient state that can actually be reached dynamically." (p. 198)
On the cooperative side, let's take another physical model as alternative: "a peculiar small-scale, spatial heterogeneity generated by chaotic advection can lead to coexistence. In open flows this imperfect mixing lets the populations accumulate along fractal filaments, where competition is governed by an 'advantage of rarity' principle" : Chaotic flow: The physics of species coexistence Gyľrgy KĚrolyi, íron P╚ntek, IstvĚn Scheuring, TamĚs T╚l, and ZoltĚn Toroczkai - PNAS Nov 21 2000. There is a wide variety of physical modeling of cooperation/competition.
And before we get to Axelrod's work on cooperation, let's look at a physicist's model of Beyond game theory: Theory of Moves, by Steven J Brams
THEME 2 = AGENT BASED SIMULATIONS, COOPERATION AND COMPLEXITY
Reading: Last chapter, pp. 137-155, Micro Motives and Macro Behavior - Thomas C. Schelling; 1978. Paperback Usually ships in 24 hours - Amazon Price: $17.50. Good introduction to multi-agent modeling.
Eight "Social Science" Simulation Models, discussed in Robert Axelrod, "Advancing the Art of Simulation in the Social Sciences,"
in Rosario Conte, Rainer Hegselmann and Pietro Terna (eds.), Simulating Social Phenomena
(A pdf version, generated from the postscript above, so use the ps if you can.) (Berlin: Springer, 1997), pp. 21-40. See: CAR Project: Axelrod, Cohen, Riolo on the Prisoner's Dilemma, Cooperation and Complexity
What is the Study of Complex Systems?, Center for the Study of Complex Systems (U Michigan)
See also: In an Iterated Prisoner's Dilemma Game, a simple dynamics on graphs, motivated by co-learning, yeilds the proof that: On cycles cooperation emerges in O(n log(n)) steps
Bill Harms has a simulator for the dynamics of some of the games in Evolution of the Social Contract: see also Harm's et al. Evolving Artificial Moral Ecologies and its contents page, at the E.A.M.E. site
Mathematical Complexity of Simple Economics
(Notices of AMS, Vol 42 (Feb. 1995), pages 222-230)
Abstract: The purpose of this article (which is directed toward mathematicians without a previous background in economics) is to show that even simple models coming from mathematical economics can generate dynamics far more complex than anything found coming from the physical or biological sciences. As such, this assertion places in serious doubt the validity of the commonly told Adam Smith ``Invisible Hand" story about how market pressures drive prices to a price equilibrium where supply equals demand. The reason this weird dynamical behavior occurs is explained. It is shown how this argument extends to cast doubt on other basic conclusions and assumptions from economics.
For network modeling in economics and economic sociology, see
Granovetter, Mark. A Theoretical Agenda for Economic Sociology. To appear in Economic Sociology at the Millenium, edited by Mauro F. Guillen, Randall Collins, Paula England, and Marshall Meyer (New York: Russell Sage Foundation, 2001). [postscript]
Formation of Social and Economic Networks, a relevant listing of sites, the
Agent-Based Computational Economics (ACE) web site, and Rauch's
Research on incomplete information and networks in international trade (his forthcoming book is on
Networks and Markets. New York: Russell Sage Foundation).
THEME 3 = SELF-ORGANIZING SYSTEMSReview: by Gert Korthof on Kauffman - At Home in the Universe. "The secret of life is auto-catalysis"
Autocatalytic Sets and the Growth of Complexity in an Evolutionary Model
Sanjay Jain, Sandeep Krishna
Emergence and growth of complex networks in adaptive systems, Jain, S. and S. Krishna, Computer Phys. Comm. 121-122 (1999) 116-121.
A model for the emergence of cooperation, interdependence and structure in evolving networks, Jain, S. and S. Krishna, SFI preprint (2000).
Biology is going through its network revolution (see Eisenberg et al. 2000 on the network view of gene function),
and network context is studied for what Kauffman would call auto-catalytic sets. See also
Seminar in Ecological Complexity (Fall 1996 Department of Biology UNM) for topics on complexity, percolation, scaling, legacy, self-organization
and Percolation Theory Tim Frey and Ethan Decker Ecological Complexity Seminar: Fall 1996
Norman Johnson's Collective Problem Solving:
Functionality beyond the Individual provides results on the effects of network contexts
on the evolutionary self-organization of problem-solving among individuals given to independent
exploration of a common world.
THEME 4 = CHALLENGES AND RESOURCES IN APPLIED COMPLEXITY and DECENTRALIZED SYSTEMS
Reading: first chapter, pp. 3-19 (on decentralization): Turtles, Termites, and Traffic Jams: Explorations in Massively Parallel Microworlds (Complex Adaptive Systems) - Mitchel Resnick, Mitchell Resnick; 1997. Paperback Usually ships in 2-3 days - Amazon Price: $12.50.
21 Grand Challenges, starting with networks Applied Complexity: 35 min conf keynote video
See Doug's papers on distributed cohesion, downloadable from the bibliography listings at SFI below:
Structure and Dynamics of Complex Interactive Networks, SFI Workshop Video Notes and powerpoint (John Doyle's talk). See: SFI network dynamics workshop, with login, bibliography, abstracts, and links. Cosma Shalizi writes a workshop summary on Networks: Growth, Form, Function, Crashes, and the theme of robustness to crashes is taken up in Our Nation's Critical Infrastructures
Browse the Complexity Digest, index of articles
Browse the SFI Complexity journal
That's where Phil's suggested course components fit:
1. Gary Flake, The Computational Beauty of Nature. An excellent intro to chaos and mathematical complexity. It also comes with a floppy of computer programs to illustrate and simulate the processes. (DW: if you install the zipped file for the Windows version most of these programs run beautifully)
2. Edward Lorenz, The Essence of Chaos. A non-mathematical but intelligent intro
3. Per Bak, How Nature Works
4. John Holland, Hidden Order
5. John Holland, Emergence
6. Stuart Kauffman, At Home in the Universe
1. L. Douglas Kiel and Euel Elliott, Chaos Theory in the Social Sciences
2. Raymond A. Eve, Sara Horsfall, and Mary E. Lee, Chaos, Complexity, and Sociology.
Phil has also accumulated some computer programs to compute chaos indices - lyopanov coefficients, and so forth.
Doug has reviewed as well:
Simulation for the Social Scientist - Nigel Gilbert, Klaus G. Troitzsch; 1999. Paperback Usually ships in 24 hours - Amazon Price: $28.95. Overview of methods. Has a useful web site for Computer Simulation of Societies. Outline:
Growing Artificial Societies: Social Science from the Bottom Up (Complex Adaptive Systems) - Joshua M. Epstein and Robert Axtell; 1996. Paperback Usually ships in 1-2 weeks - Amazon Price: $22.00. Outstanding but harder to get and somewhat superceded in its usefulness as a text by Axelrod 1997.
Harnessing Complexity: Organizational Implications of a Scientific Frontier - Robert Axelrod, Michael D. Cohen; 2000. Hardcover Usually ships in 2-3 days - List Price: $26.00 - Amazon Price: $20.80
see also the INSNA, the International Network for Social Network Analysis home page, and the Santa Fe Institute focus page on network dynamics
Another possible theme: COMPLEXITY THEORY AND ORGANIZATIONS
Readings in Complexity Theory and Organizations, see also Organizations as Self-Adaptive Complex Systems
Internet Industry Strategic Alliances, Joint Ventures, and Other Partnerships: Infrastructure, Commerce, Content (graphic)
Walter Powell's papers on biotech and organizational theory
Individual Strategy and Social Structure : An Evolutionary Theory of Institutions, by H. Peyton Young (Brookings Institute), Peyton H. Young Amazon Price: $37.50
Networks in Action: Communication, Economics and Human Knowledge, by David Batten, John Casti, Roland Thord (Editor)
Cooperation and Conflict in General Evolutionary Processes, by John L. Casti (Editor), Anders Karlqvist (Editor)
Complex Systems pages
Complexity: applications some web links
Complexification: Explaining a Paradoxical World Through the Science of Surprise, by John L. Casti
Emergence and Explanation
Would-Be Worlds: How Simulation Is Changing the Frontiers of Science,
by John L. Casti
Brief Overview of Swarm Agent Simulation
Agent-Based Computational Economics
Adaptive Agent Simulation SANTA FE INSTITUTE
Yahoo's Artificial Life pages
ALife home page
Croatian Society for Computer Simulation Modelling
---- Simulations ----
Computer Simulation: The Art and Science of Digital
World Construction, by Paul A. Fishwick
Roger A. McCain Strategy and Conflict:
An Introductory Sketch of Game Theory
The Logics of Social Structure by Kyriakos M. Kontopolous $52.95+