7,564 research outputs found
A particle system in interaction with a rapidly varying environment: Mean field limits and applications
We study an interacting particle system whose dynamics depends on an
interacting random environment. As the number of particles grows large, the
transition rate of the particles slows down (perhaps because they share a
common resource of fixed capacity). The transition rate of a particle is
determined by its state, by the empirical distribution of all the particles and
by a rapidly varying environment. The transitions of the environment are
determined by the empirical distribution of the particles. We prove the
propagation of chaos on the path space of the particles and establish that the
limiting trajectory of the empirical measure of the states of the particles
satisfies a deterministic differential equation. This deterministic
differential equation involves the time averages of the environment process.
We apply our results to analyze the performance of communication networks
where users access some resources using random distributed multi-access
algorithms. For these networks, we show that the environment process
corresponds to a process describing the number of clients in a certain loss
network, which allows us provide simple and explicit expressions of the network
performance.Comment: 31 pages, 2 figure
Exact Dimensionality Selection for Bayesian PCA
We present a Bayesian model selection approach to estimate the intrinsic
dimensionality of a high-dimensional dataset. To this end, we introduce a novel
formulation of the probabilisitic principal component analysis model based on a
normal-gamma prior distribution. In this context, we exhibit a closed-form
expression of the marginal likelihood which allows to infer an optimal number
of components. We also propose a heuristic based on the expected shape of the
marginal likelihood curve in order to choose the hyperparameters. In
non-asymptotic frameworks, we show on simulated data that this exact
dimensionality selection approach is competitive with both Bayesian and
frequentist state-of-the-art methods
Nonintrusive approximation of parametrized limits of matrix power algorithms -- application to matrix inverses and log-determinants
We consider in this work quantities that can be obtained as limits of powers
of parametrized matrices, for instance the inverse matrix or the logarithm of
the determinant. Under the assumption of affine dependence in the parameters,
we use the Empirical Interpolation Method (EIM) to derive an approximation for
powers of these matrices, from which we derive a nonintrusive approximation for
the aforementioned limits. We derive upper bounds of the error made by the
obtained formula. Finally, numerical comparisons with classical intrusive and
nonintrusive approximation techniques are provided: in the considered
test-cases, our algorithm performs well compared to the nonintrusive ones
Online Mutual Foreground Segmentation for Multispectral Stereo Videos
The segmentation of video sequences into foreground and background regions is
a low-level process commonly used in video content analysis and smart
surveillance applications. Using a multispectral camera setup can improve this
process by providing more diverse data to help identify objects despite adverse
imaging conditions. The registration of several data sources is however not
trivial if the appearance of objects produced by each sensor differs
substantially. This problem is further complicated when parallax effects cannot
be ignored when using close-range stereo pairs. In this work, we present a new
method to simultaneously tackle multispectral segmentation and stereo
registration. Using an iterative procedure, we estimate the labeling result for
one problem using the provisional result of the other. Our approach is based on
the alternating minimization of two energy functions that are linked through
the use of dynamic priors. We rely on the integration of shape and appearance
cues to find proper multispectral correspondences, and to properly segment
objects in low contrast regions. We also formulate our model as a frame
processing pipeline using higher order terms to improve the temporal coherence
of our results. Our method is evaluated under different configurations on
multiple multispectral datasets, and our implementation is available online.Comment: Preprint accepted for publication in IJCV (December 2018
Le concept d'égalité : définition et expérience
The right to equality is one of the most fundamental of human concepts. The author draws attention to the fact that this right is often depicted in negative terms, usually stating that any form of discrimination is forbidden. The concrete application of equality can sometimes lead to inequalitarian measures. An even policy for equality that is applied to unequal parties can result in a form of inequality. This is the reason why the author endorses equality in fact and not just as a formality in law. According to him, it is indispensable to take positive and specific measures in order to place minorities in a situation of equality and development. These measures, far from being contrary to the principle of non-discrimination, are in conformity with provisions in international treaties pertaining to the right to equality
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