CSSS 2008 Argentina-Readings
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CSSS Argentina 2008 |
Forming project group teams
An important part of the school has to do with interacting with Faculty and your class mates. To foster this interaction interdisciplinary working groups will be formed. Each group will work on a project that will be presented by the end of the school. Projects are expected to elaborate on questions emerging from the working group internal brainstorming. Use the help and advise of the faculty around. They are open to interact and provide advise for the development of working group projects. And remember, the best way of tackling complexity is to aim for simplicity!
Week 1 (tentative)
- Elizabeth Bradley (Nonlinear dynamics)
Definition of chaos; examples in various fields
An extended example: the logistic map. Introduce: bifurcations; bifurcation diagram and its structure, incl. Feigenbaum number; fractals and their connection to chaos
Continuous-time dynamics: definition
Introduce concepts: state variables, state space, trajectory, initial condition, transient, attractor, basin of attraction, fixed point, stability, bifurcation, parameter
An extended example: the Lorenz system: history, physical meaning, trajectories, attractors, bifurcations (examples & definitions), types of attractors, stability: definition & mathematics, eigen. , un/stable manifolds, Lyapunov exponent and the connection to chaos
Numerical solvers: roles and issues
Shadowing
Projection vs section
Poincare sections in space & time
Delay-coordinate embedding
Examples: roulette, the SFI competition
Applications: filtering, control of chaos, synchronization & communication, spacecraft orbits, chaos in the solar system, harnessing the butterfly effect in fluids
Supporting Material:
Time Series Analysis - E. Bradley
Error in Numerical Methods - E. Bradley
Numerical Solution for Differential Equations - E. Bradley
Supporting Material:
- Is Anything Ever New? Considering Emergence
- Regularities Unseen, Randomness Observed: Levels of Entropy Convergence
- The Calculi of Emergence: Computation, Dynamics, and Induction
- Computational Mechanics: Pattern and Prediction, Structure and Simplicity
- The Organization of Intrinsic Computation: Complexity-Entropy Diagrams and the Diversity of Natural Information Processing
- Structure or Noise?
- Kunihiko Kaneko (Complex Systems Biology)
References: (Book)
K. Kaneko, Life: An Introduction to Complex Systems Biology, Springer, 2006
K. Kaneko and I.Tsuda, Complex Systems: Chaos and Beyond, Springer 2000
(Papers) available at: [1] (including some other related materials)
C. Furusawa and K. Kaneko, ``A generic mechanism for adaptive gowth
rate regulation", PLoS Computationa Biology, 4(2008) e3
K. Kaneko, Evolution of Robustness to Noise and Mutation in Gene
Expression Dynamics, PLoS One(2007) 2 e434
K. Kaneko and C. Furusawa, "An Evolutionary Relationship between
Genetic Variation and Phenotypic Fluctuation", J. Theo. Biol. 240
(2006) 78-86
K. Kaneko" On Recursive Production and Evolvabilty of Cells: Catalytic
Reaction Network Approach " Adv. Chem. Phys. , 130 (2005) 543-598
K. Sato, Y. Ito, T. Yomo, and K. Kaneko " On the Relation between
Fluctuation and Response in Biological Systems " Proc. Nat. Acad. Sci.
USA 100 (2003) 14086-14090
C. Furusawa and K. Kaneko " Zipf's law in Gene Expression " Phys. Rev.
Lett., 90 (2003) 088102
C. Furusawa and K. Kaneko"Theory of Robustness of Irreversible
Differentiation in a Stem Cell System: Chaos Hypothesis" J. Theor.
Biol. (2001) 209 (2001) 395-416
K. Kaneko and T. Yomo," ``Isologous Diversification for Robust
Development of Cell Society", J.theor.Biol. 199 (1999) 243-256
Supporting Material:
Nonequilibrium Potential in Reaction-Diffusion Systems - Horacio S. Wio
Supporting Material:
Programs as models: Kappa language basics - J. Kirvine, V. Danos, J. Feret, R. Harmer, W. Fontana
Programs as models: Execution - J. Kirvine, V. Danos, J. Feret, R. Harmer, W. Fontana
Internal coarse-graining of molecular systems - J. Feret, V. Danos, J. Krivine, R. Harmer, W. Fontana
Supporting Material:
Chaos in learning a simple two-person game
Coupled replicator equations for the dynamics of learning in multiagent systems
Stability and diversity in collective adaption
Adaptive Dynamics for Interacting Markovian Processes
Week 2
References:
-G. Nicolis and C. Nicolis, Foundations of Complex Systems, World Scientific, Singapore (2007).
-W. Ebeling and G. Nicolis, Word frequency and entropy of symbolic sequences: a dynamical perspective, Chaos Solitons and Fractals 2, 635 (1992).
-G. Nicolis and P. Gaspard, Toward a probabilistic approach to complex systems, Chaos Solitons and Fractals 4, 41 (1994).
-G. Nicolis, Thermodynamics today, Physica A213, 1 (1995).
-G. Nicolis and D. Daems, Probabilistic and thermodynamic aspects of dynamical systems, Chaos 8, 311 (1998).
-G. Nicolis, Nonequilibrium Statistical Mechanics, in Encyclopedia of Nonlinear Science, A. Scott ed., Routledge, New York (2005).
-P. Gaspard, Chaos, Scattering and Statistical Mechanics, Cambridge University Press, Cambridge (1998).
-P. Gaspard, Time-reversed dynamical entropy and irreversibility in Markovian random processes, J. Stat. Phys. 117, 599 (2004).
Supporting Material:
Complex Systems - Scholarpedia
Interdisciplinary Center for Nonlinear Phenomena and Complex Systems - G. Nicolis
Foundations of Complex Systems - G. Nicolis, C. Nicolis
Figure 1
Figure 2
Figure 3
Frontiers of Complex Systems Research: A View From the Foundations
Supporting Material:
Simple rules yield complex food webs - R. Williams & N. Martinez
Network Structure and biodiversity loss in food webs: robustness increases with connectance - J. Dunne, R. Williams & N. Martinez
Supporting Material:
Classical thermodynamics and economic general equilibrium theory - E. Smith & D. Foley
Thermodynamics of natural selection I: Energy flow and the limits of organization - E. Smith
Thermodynamics of natural selection II: Chemical Carnot cycles - E. Smith
Thermodynamics of natural selection III: Landauer's principle in computation and chemistry - E. Smith
Supporting Material:
Calcium - a life and death signal
Calcium stores regulate the polarity and input specificity of synaptic modification
Noise Propagation in Gene Networks
The organization and functions of local Ca2+ signals
Phasic characteristic of elementary Ca2 release sites underlies quantal responses to IP3
Role of elementary Ca2 puffs in generating repetitive Ca2+ oscillations