Search results for " Gradient"
showing 10 items of 575 documents
A method to transform a nonlocal model into a gradient one within elasticity and plasticity
2014
Abstract A method based on the principle of the virtual power (PVP) is presented, by which a mechanical problem of nonlocal elasticity, or plasticity, is transformed into one of gradient nature. Different Taylor series expansion techniques are applied to the driving local strain fields of the nonlocal problem, either full spatial expansion within the bulk volume, or uni-directional expansion along the normal to the thin boundary layer. This, at the limit when the boundary layer thickness tends to zero, makes the PVP of the nonlocal model transform itself into one featuring a counterpart gradient model. Also, for a class of “associated” nonlocal and gradient elasticity models (i.e. the kerne…
Experimental Realization of a Dirac Monopole through the Decay of an Isolated Monopole
2017
We experimentally observe the decay dynamics of deterministically created isolated monopoles in spin-1 Bose-Einstein condensates. As the condensate undergoes a change between magnetic phases, the isolated monopole gradually evolves into a spin configuration hosting a Dirac monopole in its synthetic magnetic field. We characterize in detail the Dirac monopole by measuring the particle densities of the spin states projected along different quantization axes. Importantly, we observe the spontaneous emergence of nodal lines in the condensate density that accompany the Dirac monopole. We also demonstrate that the monopole decay accelerates in weaker magnetic field gradients.
Hunting active Brownian particles: Learning optimal behavior
2021
We numerically study active Brownian particles that can respond to environmental cues through a small set of actions (switching their motility and turning left or right with respect to some direction) which are motivated by recent experiments with colloidal self-propelled Janus particles. We employ reinforcement learning to find optimal mappings between the state of particles and these actions. Specifically, we first consider a predator-prey situation in which prey particles try to avoid a predator. Using as reward the squared distance from the predator, we discuss the merits of three state-action sets and show that turning away from the predator is the most successful strategy. We then rem…
A fast and recursive algorithm for clustering large datasets with k-medians
2012
Clustering with fast algorithms large samples of high dimensional data is an important challenge in computational statistics. Borrowing ideas from MacQueen (1967) who introduced a sequential version of the $k$-means algorithm, a new class of recursive stochastic gradient algorithms designed for the $k$-medians loss criterion is proposed. By their recursive nature, these algorithms are very fast and are well adapted to deal with large samples of data that are allowed to arrive sequentially. It is proved that the stochastic gradient algorithm converges almost surely to the set of stationary points of the underlying loss criterion. A particular attention is paid to the averaged versions, which…
Fast Estimation of the Median Covariation Matrix with Application to Online Robust Principal Components Analysis
2017
International audience; The geometric median covariation matrix is a robust multivariate indicator of dispersion which can be extended without any difficulty to functional data. We define estimators, based on recursive algorithms, that can be simply updated at each new observation and are able to deal rapidly with large samples of high dimensional data without being obliged to store all the data in memory. Asymptotic convergence properties of the recursive algorithms are studied under weak conditions. The computation of the principal components can also be performed online and this approach can be useful for online outlier detection. A simulation study clearly shows that this robust indicat…
Recursive estimation of the conditional geometric median in Hilbert spaces
2012
International audience; A recursive estimator of the conditional geometric median in Hilbert spaces is studied. It is based on a stochastic gradient algorithm whose aim is to minimize a weighted L1 criterion and is consequently well adapted for robust online estimation. The weights are controlled by a kernel function and an associated bandwidth. Almost sure convergence and L2 rates of convergence are proved under general conditions on the conditional distribution as well as the sequence of descent steps of the algorithm and the sequence of bandwidths. Asymptotic normality is also proved for the averaged version of the algorithm with an optimal rate of convergence. A simulation study confirm…
Quantitative analysis of numerical estimates for the permeability of porous media from lattice-Boltzmann simulations
2010
During the last decade, lattice-Boltzmann (LB) simulations have been improved to become an efficient tool for determining the permeability of porous media samples. However, well known improvements of the original algorithm are often not implemented. These include for example multirelaxation time schemes or improved boundary conditions, as well as different possibilities to impose a pressure gradient. This paper shows that a significant difference of the calculated permeabilities can be found unless one uses a carefully selected setup. We present a detailed discussion of possible simulation setups and quantitative studies of the influence of simulation parameters. We illustrate our results b…
A gradient-based deletion diagnostic measure for generalized linear mixed models
2016
ABSTRACTA gradient-statistic-based diagnostic measure is developed in the context of the generalized linear mixed models. Its performance is assessed by some real examples and simulation studies, in terms of ability in detecting influential data structures and of concordance with the most used influence measures.
The “ThreePlusOne” Likelihood-Based Test Statistics: Unified Geometrical and Graphical Interpretations
2014
The presentation of the well known Likelihood Ratio, Wald and Score test statistics in textbooks appears to lack a unified graphical and geometrical interpretation. We present two simple graphical representations on a common scale for these three test statistics, and also the recently proposed Gradient test statistic. These unified graphical displays may favour better understanding of the geometrical meaning of the likelihood based statistics and provide useful insights into their connections.
Inferential tools in penalized logistic regression for small and sparse data: A comparative study.
2016
This paper focuses on inferential tools in the logistic regression model fitted by the Firth penalized likelihood. In this context, the Likelihood Ratio statistic is often reported to be the preferred choice as compared to the ‘traditional’ Wald statistic. In this work, we consider and discuss a wider range of test statistics, including the robust Wald, the Score, and the recently proposed Gradient statistic. We compare all these asymptotically equivalent statistics in terms of interval estimation and hypothesis testing via simulation experiments and analyses of two real datasets. We find out that the Likelihood Ratio statistic does not appear the best inferential device in the Firth penal…