Jerusalem Mathematics Colloquium

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Thursday, 17th October 2002, 4:00 pm
Mathematics Building, Lecture Hall 2

Sorin Solomon
(Racah Institute of Physics, Hebrew University)

The emergence of adaptive collective objects from random noise"

Abstract: The discrete microscopic structure of macroscopic objects was postulated since the time of Democritus and came to the forefront of science with the introduction of statistical mechanics by Boltzmann and Maxwell.

It turns out that in systems with auto-catalytic interactions (proliferation, contagion, information spread) as are most biological, social and information systems, the discreteness of the elementary components and interactions (e.g. giving birth to a new individual, informing a neighbor of a new product, adoption of a new idea by an individual, contracting a disease) is even more crucial.

It can be shown rigorously using either physicist's renormalization group and/or mathematician's branching random walks techniques that in such systems there emerge generically macroscopic spatio-temporal localized objects with unexpected collective dynamical properties: adaptability, resilience and sustainability.

This is true even for systems for which a continuum description (ignoring microscopic discreteness) would predict robustly a uniform, static (life-less, trade-less, idea-less) asymptotic state.

I will demonstrate this generic mechanism and some of its applications in various fields.

Branching Random walks with Catalysts, Harry Kesten and Vladas Sidoravicius , preprint 2002

The importance of being discrete: Life always wins on the surface, N. M. Shnerb, Y. Louzoun, E. Bettelheim, and S. Solomon Proc. Natl. Acad. Sci. USA, Vol. 97, No. 19, p 10322 Sept. 2000

New Scientist magazine, 06 May 2000.

Coffee, Cookies at the faculty lounge at 3:30.

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