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Computation of a polytopic invariant
for a polynomial dynamical system (here a
Phytoplankton growth model); the invariant is
computed using linear programing relaxations of
polynomial optimization problems based on the
blossoming principle and properties of
multi-affine maps.
Référence : Antoine
Girard |
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Chains of touching beads form a class of spatially discrete nonlinear systems,
with nonlinearity originating from Hertzian contact between beads.
Such systems can sustain localized propagating waves (solitary waves
or breathers) forming typically after an impact. The picture illustrates
a propagating localized wave in a system of this type: Newton's cradle
(gray levels indicate energy density versus time and space). This wave
corresponds to a ``boomeron'', i.e. a localized wave displaying spontaneous
direction-reversal in a spatially homogeneous nonlinear system.
This origin of this intringuing dynamical behavior and its potential
usefulness for the design of shock reflectors are currently under
investigation.
Référence : Guillaume James |
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Gasip is an algorithm to simulate the gravitational interaction of
point masses.
This problem is known as the n-body problem in physics and astronomy.
The algorithm detects and uses hierarchical structure present in the
momentary distribution of the point masses to speed up the computation.
The structure is represented as a dynamical tree, with the leaves being
the individual point masses.
Référence : Aude Maignan |
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Example of algebraic graph transformation applied to cloud computing:
a transformation is made of a left-hand side L, a right-hand side R,
and an intermediate graph K. In this example we use the algebraic approach
known as "sesqui-pushout" in order to duplicate a virtual machine;
we generalize this approach for dealing with attributes:
for instance the size of a virtual or real machine is a constant attribute,
while the free space on a real machine is a varying attribute.
Référence : Dominique Duval |
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Efficiently and reliably delegating computations.
The idea is to design algorithms that can form a proof of correctness of
a result computed via a probabilistic algorithm or through a potentially
unreliable computing center.
The difficulty is to design proofs that are verifiable at a lower cost
(time, memory, ...) than that of recomputing the result.
Référence : Jean-Guillaume Dumas |
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Illustration de l'utilisation de
modèles symboliques pour le contrôle de systèmes
hybrides
Référence : Antoine
Girard |
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Contrôle hybride de
systèmes dynamiques non linéaires.
Contact : Aude
Rondepierre |
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Attaques laser sur RSA embarqué ;
nombres premiers à distance de perturbation d'un modulo RSA.
Contact : Jean-Guillaume
Dumas |
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Optimisation de la consommation
énergétique lors du transfert orbital.
Contact : Aude
Rondepierre |
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Reconnaissance de motifs dans l'ADN par chaines de Markov puis reconstruction rationnelle bivariée
Contact : Jean-Guillaume Dumas |
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Calcul des états atteignables
d'un système hybride.
Référence : Antoine
Girard |
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Multiplication de matrices rapide en place.
Contact : Brice Boyer |
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DEM-systems are a class of discrete dynamical systems with properties of both cellular automata and L-systems
Référence : Aude Maignan |
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Simulating aggregates of bivalents in 2n=40
mouse meiotic spermatocytes through
inhomogeneous percolation processes
Référence : Aude Maignan |
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GPaR is a parallel graph rewriting software implemented in C++ with a graphical user interface.
Référence : Aude Maignan |
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We examine the planar split thickness of a graph, that is, the smallest k
such that the graph is k-splittable into a planar graph.
A k-split operation substitutes
a vertex v by at most k new vertices such that each neighbor of v
is connected to at least one of the new vertices.
Référence : Aude Maignan |
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