CSSS 2008 Argentina-Readings

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

James P. Crutchfield

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

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

Week 2

Grégoire Nicolis

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
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