Search results for "Probability"
showing 10 items of 3417 documents
Solving chance constrained optimal control problems in aerospace via Kernel Density Estimation
2017
International audience; The goal of this paper is to show how non-parametric statistics can be used to solve some chance constrained optimization and optimal control problems. We use the Kernel Density Estimation method to approximate the probability density function of a random variable with unknown distribution , from a relatively small sample. We then show how this technique can be applied and implemented for a class of problems including the God-dard problem and the trajectory optimization of an Ariane 5-like launcher.
Fractal Weyl law for open quantum chaotic maps
2014
We study the semiclassical quantization of Poincar\'e maps arising in scattering problems with fractal hyperbolic trapped sets. The main application is the proof of a fractal Weyl upper bound for the number of resonances/scattering poles in small domains near the real axis. This result encompasses the case of several convex (hard) obstacles satisfying a no-eclipse condition.
Event-Based Trajectory Prediction Using Spiking Neural Networks
2021
International audience; In recent years, event-based sensors have been combined with spiking neural networks (SNNs) to create a new generation of bio-inspired artificial vision systems. These systems can process spatio-temporal data in real time, and are highly energy efficient. In this study, we used a new hybrid event-based camera in conjunction with a multi-layer spiking neural network trained with a spike-timing-dependent plasticity learning rule. We showed that neurons learn from repeated and correlated spatio-temporal patterns in an unsupervised way and become selective to motion features, such as direction and speed. This motion selectivity can then be used to predict ball trajectory…
Automated uncertainty quantification analysis using a system model and data
2015
International audience; Understanding the sources of, and quantifying the magnitude of, uncertainty can improve decision-making and, thereby, make manufacturing systems more efficient. Achieving this goal requires knowledge in two separate domains: data science and manufacturing. In this paper, we focus on quantifying uncertainty, usually called uncertainty quantification (UQ). More specifically, we propose a methodology to perform UQ automatically using Bayesian networks (BN) constructed from three types of sources: a descriptive system model, physics-based mathematical models, and data. The system model is a high-level model describing the system and its parameters; we develop this model …
Scheduling independent stochastic tasks on heterogeneous cloud platforms
2019
International audience; This work introduces scheduling strategies to maximize the expected number of independent tasks that can be executed on a cloud platform within a given budget and under a deadline constraint. The cloud platform is composed of several types of virtual machines (VMs), where each type has a unitexecution cost that depends upon its characteristics. The amount of budget spent during the execution of a task on a given VM is the product of its execution length by the unit execution cost of that VM. The execution lengths of tasks follow a variety of standard probability distributions (exponential, uniform, halfnormal, etc.), which is known beforehand and whose mean and stand…
Scheduling independent stochastic tasks under deadline and budget constraints
2018
This article discusses scheduling strategies for the problem of maximizing the expected number of tasks that can be executed on a cloud platform within a given budget and under a deadline constraint. The execution times of tasks follow independent and identically distributed probability laws. The main questions are how many processors to enroll and whether and when to interrupt tasks that have been executing for some time. We provide complexity results and an asymptotically optimal strategy for the problem instance with discrete probability distributions and without deadline. We extend the latter strategy for the general case with continuous distributions and a deadline and we design an ef…
Probability and algorithmics: a focus on some recent developments
2017
Jean-François Coeurjolly, Adeline Leclercq-Samson Eds.; International audience; This article presents different recent theoretical results illustrating the interactions between probability and algorithmics. These contributions deal with various topics: cellular automata and calculability, variable length Markov chains and persistent random walks, perfect sampling via coupling from the past. All of them involve discrete dynamics on complex random structures.; Cet article présente différents résultats récents de nature théorique illustrant les interactions entre probabilités et algorithmique. Ces contributions traitent de sujets variés : automates cellulaires et calculabilité, chaînes de Mark…
Study and Comparison of Surface Roughness Measurements
2014
Journées du Groupe de Travail en Modélisation Géométrique (GTMG'14), Lyon; This survey paper focus on recent researches whose goal is to optimize treatments on 3D meshes, thanks to a study of their surface features, and more precisely their roughness and saliency. Applications like watermarking or lossy compression can benefit from a precise roughness detection, to better hide the watermarks or quantize coarsely these areas, without altering visually the shape. Despite investigations on scale dependence leading to multi-scale approaches, an accurate roughness or pattern characterization is still lacking, but challenging for those treatments. We think there is still room for investigations t…
Synchronization and fluctuations for interacting stochastic systems with individual and collective reinforcement
2020
The Pólya urn is the paradigmatic example of a reinforced stochastic process. It leads to a random (non degenerated) time-limit. The Friedman urn is a natural generalization whose a.s. time-limit is not random anymore. In this work, in the stream of previous recent works, we introduce a new family of (finite) systems of reinforced stochastic processes, interacting through an additional collective reinforcement of mean field type. The two reinforcement rules strengths (one componentwise, one collective) are tuned through (possibly) different rates n −γ. In the case the reinforcement rates are like n −1 , these reinforcements are of Pólya or Friedman type as in urn contexts and may thus lead …
Statistics of transitions for Markov chains with periodic forcing
2013
The influence of a time-periodic forcing on stochastic processes can essentially be emphasized in the large time behaviour of their paths. The statistics of transition in a simple Markov chain model permits to quantify this influence. In particular the first Floquet multiplier of the associated generating function can be explicitly computed and related to the equilibrium probability measure of an associated process in higher dimension. An application to the stochastic resonance is presented.