Search results for "Invariant"
showing 10 items of 783 documents
Self-stabilizing processes: uniqueness problem for stationary measures and convergence rate in the small-noise limit
2011
In the context of self-stabilizing processes, that is processes attracted by their own law, living in a potential landscape, we investigate different properties of the invariant measures. The interaction between the process and its law leads to nonlinear stochastic differential equations. In [S. Herrmann and J. Tugaut. Electron. J. Probab. 15 (2010) 2087–2116], the authors proved that, for linear interaction and under suitable conditions, there exists a unique symmetric limit measure associated to the set of invariant measures in the small-noise limit. The aim of this study is essentially to point out that this statement leads to the existence, as the noise intensity is small, of one unique…
Uniform convergence and asymptotic confidence bands for model-assisted estimators of the mean of sampled functional data
2013
When the study variable is functional and storage capacities are limited or transmission costs are high, selecting with survey sampling techniques a small fraction of the observations is an interesting alternative to signal compression techniques, particularly when the goal is the estimation of simple quantities such as means or totals. We extend, in this functional framework, model-assisted estimators with linear regression models that can take account of auxiliary variables whose totals over the population are known. We first show, under weak hypotheses on the sampling design and the regularity of the trajectories, that the estimator of the mean function as well as its variance estimator …
Unacceptable implications of the left haar measure in a standard normal theory inference problem
1978
For a very common statistical problem, inference about the mean of a normal random variable, some inadmissible consequences of the left Haar invariant prior measure, which is that recommended as a suitable prior by Jeffreys’ multivariate rule and by the methods of Villegas and Kashyap, are uncovered and investigated.
Explicit near-symplectic mappings of Hamiltonian systems with Lie-generating functions
2008
The construction of explicit near-symplectic mappings for generic Hamiltonian systems with the utilization of Lie transforms is presented. The method is mathematically rigorous and systematically extended to high order with respect to a perturbation parameter. The explicit mappings are compared to their implicit counterparts, which use mixed-variable generating functions, in terms of conservation of invariant quantities, calculation speed and accurate construction of Poincare surfaces of sections. The comparative study considers a wide range of parameters and initial conditions for which different time scales are involved due to large differences between internal and external frequencies of…
Remarks on ergodicity and invariant occupation measure in branching diffusions with immigration☆
2005
Abstract We give a necessary and sufficient condition for ergodicity with finite invariant occupation measure for branching diffusions with immigration. We do not assume uniformly subcritial reproduction means. We discuss the structure of the invariant occupation measure and of its density.
Spin-1/2 sub-dynamics nested in the quantum dynamics of two coupled qutrits
2017
In this paper we investigate the quantum dynamics of two spin-1 systems, $\vec{\textbf{S}}_1$ and $\vec{\textbf{S}}_2$, adopting a generalized $(\vec{\textbf{S}}_1+\vec{\textbf{S}}_2)^2$-nonconserving Heisenberg model. We show that, due to its symmetry property, the nine-dimensional dynamics of the two qutrits exactly decouples into the direct sum of two sub-dynamics living in two orthogonal four- and five-dimensional subspaces. Such a reduction is further strengthened by our central result consisting in the fact that in the four-dimensional dynamically invariant subspace, the two qutrits quantum dynamics, with no approximations, is equivalent to that of two non interacting spin 1/2's. The …
On the usage of joint diagonalization in multivariate statistics
2022
Scatter matrices generalize the covariance matrix and are useful in many multivariate data analysis methods, including well-known principal component analysis (PCA), which is based on the diagonalization of the covariance matrix. The simultaneous diagonalization of two or more scatter matrices goes beyond PCA and is used more and more often. In this paper, we offer an overview of many methods that are based on a joint diagonalization. These methods range from the unsupervised context with invariant coordinate selection and blind source separation, which includes independent component analysis, to the supervised context with discriminant analysis and sliced inverse regression. They also enco…
Standard forms and entanglement engineering of multimode Gaussian states under local operations
2007
We investigate the action of local unitary operations on multimode (pure or mixed) Gaussian states and single out the minimal number of locally invariant parametres which completely characterise the covariance matrix of such states. For pure Gaussian states, central resources for continuous-variable quantum information, we investigate separately the parametre reduction due to the additional constraint of global purity, and the one following by the local-unitary freedom. Counting arguments and insights from the phase-space Schmidt decomposition and in general from the framework of symplectic analysis, accompany our description of the standard form of pure n-mode Gaussian states. In particula…
Mohr-cyclides, a 3D representation of geological tensors: The examples of stress and flow
2008
Mohr-circles are commonly used to represent second-rank tensors in two dimensions. In geology, this mainly applies to stress, flow, strain and deformation. Three-dimensional second rank tensors have been represented by sets of three Mohr-circles, mainly in the application of stress. This paper demonstrates that three-dimensional second rank tensors can in fact be represented in a three-dimensional reference frame by Mohr surfaces, which are members of the cyclide family. Such Mohr-cyclides can be used to represent any second rank tensor and are exemplified with the stress and flow tensors.
Solving the Problems of Inspection Planning under Parametric Uncertainty of Underlying Models
2013
Certain fatigued structures must be inspected in order to detect fatigue damages that would otherwise not be apparent. A technique for obtaining optimal inspection strategies is proposed for situations where it is difficult to quantify the costs associated with inspections and undetected failure. For fatigued structures for which failures (fatigue damages) are only detected at the time of inspection, it is important to be able to determine the optimal times of inspection. Fewer inspections will lead to lower fatigue reliability of the structure upon demand, and frequent inspection will lead to higher cost. When there is a fatigue reliability requirement, the problem is usually to develop an…