6,495 research outputs found
On the variations of the principal eigenvalue with respect to a parameter in growth-fragmentation models
We study the variations of the principal eigenvalue associated to a
growth-fragmentation-death equation with respect to a parameter acting on
growth and fragmentation. To this aim, we use the probabilistic
individual-based interpretation of the model. We study the variations of the
survival probability of the stochastic model, using a generation by generation
approach. Then, making use of the link between the survival probability and the
principal eigenvalue established in a previous work, we deduce the variations
of the eigenvalue with respect to the parameter of the model
Time-Staging Enhancement of Hybrid System Falsification
Optimization-based falsification employs stochastic optimization algorithms
to search for error input of hybrid systems. In this paper we introduce a
simple idea to enhance falsification, namely time staging, that allows the
time-causal structure of time-dependent signals to be exploited by the
optimizers. Time staging consists of running a falsification solver multiple
times, from one interval to another, incrementally constructing an input signal
candidate. Our experiments show that time staging can dramatically increase
performance in some realistic examples. We also present theoretical results
that suggest the kinds of models and specifications for which time staging is
likely to be effective
Stochastic homogenization of subdifferential inclusions via scale integration
We study the stochastic homogenization of the system -div \sigma^\epsilon =
f^\epsilon \sigma^\epsilon \in \partial \phi^\epsilon (\nabla u^\epsilon),
where (\phi^\epsilon) is a sequence of convex stationary random fields, with
p-growth. We prove that sequences of solutions (\sigma^\epsilon,u^\epsilon)
converge to the solutions of a deterministic system having the same
subdifferential structure. The proof relies on Birkhoff's ergodic theorem, on
the maximal monotonicity of the subdifferential of a convex function, and on a
new idea of scale integration, recently introduced by A. Visintin.Comment: 23 page
The Evolution of a Spatial Stochastic Network
The asymptotic behavior of a stochastic network represented by a birth and
death processes of particles on a compact state space is analyzed. Births:
Particles are created at rate and their location is independent of
the current configuration. Deaths are due to negative particles arriving at
rate . The death of a particle occurs when a negative particle
arrives in its neighborhood and kills it. Several killing schemes are
considered. The arriving locations of positive and negative particles are
assumed to have the same distribution. By using a combination of monotonicity
properties and invariance relations it is shown that the configurations of
particles converge in distribution for several models. The problems of
uniqueness of invariant measures and of the existence of accumulation points
for the limiting configurations are also investigated. It is shown for several
natural models that if then the asymptotic configuration
has a finite number of points with probability 1. Examples with
and an infinite number of particles in the limit are also
presented
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