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X-WR-CALNAME:[MTV] Sara Riva (U. Côte d'Azur) - Hypotheses and Equations on
  Discrete Dynamical Systems
X-WR-TIMEZONE:Europe/Paris
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TZUNTIL:20240331T010000Z
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DTSTART:20211031T030000
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TZOFFSETTO:+0100
RDATE:20221030T030000
RDATE:20231029T030000
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DTSTAMP:20260522T191441Z
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DESCRIPTION:A Finite Discrete-time Dynamical System (DDS) consists of a fin
 ite set X\, called state space\, and a function f\, called next-state map 
 (which associates to a state v the state f(v)). DDS are a formal tool for 
 modelling phenomena that appear in Physics\, Mathematics\, Biology\, and\,
  of course\, in Computer Science. While the mathematical formalisation and
  the results that found up to nowadays are elegant and meaningful\, often 
 they are not very suitable in practice because of their high computational
  cost. In the literature\, it is known that DDS equipped with appropriate 
 sum and product operations form a commutative semiring. This algebraic str
 ucture allows us to write polynomial equations in which the coefficients a
 nd unknowns are DDS. In particular\, if we are interested in some dynamics
  derived from experimental data\, we can write an equation with this as a 
 constant right-hand term and model assumptions about the function f (or it
 s properties) in a polynomial left-hand term. Finding solutions to this eq
 uation allow us to better understand the phenomenon and its properties. Th
 is approach is interesting but it has important limitations from a computa
 tional point of view. Solving a polynomial equation (with several variable
 s) is\, in general\, undecidable\, and even if we focus on the case of hyp
 othesis validation\, the computational cost remains high. The idea is then
  to look for approximations that give relevant information about the solut
 ions of the original equation. It is possible to introduce three abstracti
 ons (simpler equations) to identify: the number of states of the variables
 \, the asymptotic behaviour\, or the transient behaviour (what happens bef
 ore the system stabilises). Each one is built from a theoretical and algor
 ithmic point of view to introduce a method to perform hypothesis validatio
 n on DDS. Through algebraic transformations\, it is possible to enumerate 
 the solutions of a polynomial equation with a constant term by enumerating
  a finite number of simpler equations. Finally\, the connection between th
 e solution of these simple equations and the cancellation problem\, known 
 in graph theory\, is explored to find a linear upper bound on the number o
 f solutions.
DTSTART;TZID=Europe/Paris:20220922T130000
DTEND;TZID=Europe/Paris:20220922T140000
LOCATION:salle 178\, zoom: https://bordeaux-inp-fr.zoom.us/j/89508306159
SEQUENCE:0
SUMMARY:[MTV] Sara Riva (U. Côte d'Azur) - Hypotheses and Equations on Disc
 rete Dynamical Systems
TRANSP:OPAQUE
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