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UID:www.tcs.tifr.res.in/event/309
DTSTAMP:20230914T125919Z
SUMMARY:Quadratic Dynamical Systems
DESCRIPTION:Speaker: Pritam Bhattacharya\n\nAbstract: \nThe main purpose of
this talk will be to promote the study of computational aspects\, primari
ly the convergence rate\, of non-linear dynamical systems from a combinato
rial perspective.\n\nMany natural phenomenon can be described by dynamical
systems in Euclidean space. In such a description\, there is a fixed set
of types\, and a point in the system (usually referred to as a 'state' or
a 'population') specifies how many elements of each type exist at a given
time instant. The system evolves under a fixed map f\, which attempts to c
apture the underlying phenomenon. A couple of examples follow that help il
lustrate the applicability of these systems.\n\nIn Physics\, the system mi
ght describe the behaviour of gas molecules in a container. In this case\,
the types correspond to velocity values\, and the state $p$ specifies how
many molecules of each type there are at a certain point in time. The map
$f$ should include the Newtonian laws so as to produce from each state $p
$ a new state $f(p)$ in the next time step\, under some assumption about t
he spatial distribution of the molecules.\n\nAgain\, in Biology\, the type
s may correspond to the genotypes of some species. A population $p$ is the
n simply the number of individuals of each type in the current generation.
The map $f$ determines the population in the next generation according to
a fixed set of rules that includes the genetic outcome of mating\, the su
rvival capacity of different types\, random mutations etc. Thus\, such sys
tems also provide an appropriate framework for the study of genetic algori
thms in combinatorial optimization.\n\nIn this talk\, we will first identi
fy the class of symmetric quadratic dynamical systems. Then\, we will go o
n to prove several fundamental general properties of these systems\, inclu
ding a characterization of the set of fixed points to which the system con
verges.\n\nThis talk will be based on the preliminary version of a paper t
itled "Quadratic Dynamical Systems" authored by Yuri Rabinovich\, Alistair
Sinclair and Avi Wigderson.\n
URL:https://www.tcs.tifr.res.in/web/events/309
DTSTART;TZID=Asia/Kolkata:20120928T150000
DTEND;TZID=Asia/Kolkata:20120928T163000
LOCATION:A-212 (STCS Seminar Room)
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