比利时vs摩洛哥足彩
,
university of california san diego
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colloquium sponsored by microsoft research
ami radunskaya
pomona college
random dynamical systems: is noisy growth better?
abstract:
\indent many biological and physiological processes involve self-regulating mechanisms that prevent too much growth while ensuring against extinction: the rate of growth is somewhat random (``noisy"), but the distribution depends on the current state of the system. cancer growth and neurological control mechanisms are just a few examples. in finance, as well, markets self-regulate since people want to "buy low" and "sell high". \indent some questions that we'd like to answer are: does the system have a well-defined average? in more technical terms, we want to know if the system is ergodic. how does this long-term average compare to the long-term behavior of the deterministic (not random) system? what can we say about the distribution of ``survival times", i.e. the distribution of times until the system reaches a particular value? \indent in this talk we will look at (and listen to) a simple example of a noisy, discrete dynamical system with parametric noise and explore ways to answer these questions analytically. we prove ergodicity for a class of growth models, and show that the randomness is harmful to the population in the sense that the long-term average is decreased by the presence of noise. when systems obeying noisy growth laws are connected together as a coupled lattice, the long-term effects of the noise can have damaging effects on the organism as a whole, even though local interactions might favor growth in a particular area. we will present simulations that highlight the effect of both the noise and the local coupling on the survival of the organism.
hosts: microsoft research/ucsd
november 4, 2011
4:00 pm
ap&m 6402
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