8,222 research outputs found
Equivariant Poincar\'e series of filtrations and topology
Earlier, for an action of a finite group on a germ of an analytic
variety, an equivariant -Poincar\'e series of a multi-index filtration in
the ring of germs of functions on the variety was defined as an element of the
Grothendieck ring of -sets with an additional structure. We discuss to which
extend the -Poincar\'e series of a filtration defined by a set of curve or
divisorial valuations on the ring of germs of analytic functions in two
variables determines the (equivariant) topology of the curve or of the set of
divisors
A spatially explicit Markovian individual-based model for terrestrial plant dynamics
An individual-based model (IBM) of a spatiotemporal terrestrial ecological
population is proposed. This model is spatially explicit and features the
position of each individual together with another characteristic, such as the
size of the individual, which evolves according to a given stochastic model.
The population is locally regulated through an explicit competition kernel. The
IBM is represented as a measure-valued branching/diffusing stochastic process.
The approach allows (i) to describe the associated Monte Carlo simulation and
(ii) to analyze the limit process under large initial population size
asymptotic. The limit macroscopic model is a deterministic integro-differential
equation.Comment: 31 pages, 1 figur
Parallel and interacting Markov chains Monte Carlo method
In many situations it is important to be able to propose independent
realizations of a given distribution law. We propose a strategy for making
parallel Monte Carlo Markov Chains (MCMC) interact in order to get an
approximation of an independent -sample of a given target law. In this
method each individual chain proposes candidates for all other chains. We prove
that the set of interacting chains is itself a MCMC method for the product of
target measures. Compared to independent parallel chains this method is
more time consuming, but we show through concrete examples that it possesses
many advantages: it can speed up convergence toward the target law as well as
handle the multi-modal case
A mass-structured individual-based model of the chemostat: convergence and simulation
We propose a model of chemostat where the bacterial population is
individually-based, each bacterium is explicitly represented and has a mass
evolving continuously over time. The substrate concentration is represented as
a conventional ordinary differential equation. These two components are coupled
with the bacterial consumption. Mechanisms acting on the bacteria are
explicitly described (growth, division and up-take). Bacteria interact via
consumption. We set the exact Monte Carlo simulation algorithm of this model
and its mathematical representation as a stochastic process. We prove the
convergence of this process to the solution of an integro-differential equation
when the population size tends to infinity. Finally, we propose several
numerical simulations
On the topological type of a set of plane valuations with symmetries
On the topological type of a set of plane valuations with symmetriesMTM2015-65764-C3-1-P (MINECO/FEDER
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