Search results for "Linear Algebra."
showing 10 items of 552 documents
Asymptotics of accessibility sets along an abnormal trajectory
2001
We describe precisely, under generic conditions, the contact of the accessibility set at time $T$ with an abnormal direction, first for a single-input affine control system with constraint on the control, and then as an application for a sub-Riemannian system of rank 2. As a consequence we obtain in sub-Riemannian geometry a new splitting-up of the sphere near an abnormal minimizer $\gamma$ into two sectors, bordered by the first Pontryagin's cone along $\gamma$, called the $\xLinfty$-sector and the $\xLtwo$-sector. Moreover we find again necessary and sufficient conditions of optimality of an abnormal trajectory for such systems, for any optimization problem.
Enhancement and assessment of WKS variance parameter for intelligent 3D shape recognition and matching based on MPSO
2016
This paper presents an improved wave kernel signature (WKS) using the modified particle swarm optimization (MPSO)-based intelligent recognition and matching on 3D shapes. We select the first feature vector from WKS, which represents the 3D shape over the first energy scale. The choice of this vector is to reinforce robustness against non-rigid 3D shapes. Furthermore, an optimized WKS-based method for extracting key-points from objects is introduced. Due to its discriminative power, the associated optimized WKS values with each point remain extremely stable, which allows for efficient salient features extraction. To assert our method regarding its robustness against topological deformations,…
Feature extraction from remote sensing data using Kernel Orthonormalized PLS
2007
This paper presents the study of a sparse kernel-based method for non-linear feature extraction in the context of remote sensing classification and regression problems. The so-called kernel orthonormalized PLS algorithm with reduced complexity (rKOPLS) has two core parts: (i) a kernel version of OPLS (called KOPLS), and (ii) a sparse (reduced) approximation for large scale data sets, which ultimately leads to rKOPLS. The method demonstrates good capabilities in terms of expressive power of the extracted features and scalability.
On the calculation of derived variables in the analysis of multivariate responses
1992
AbstractThe multivariate regression of a p × 1 vector Y of random variables on a q × 1 vector X of explanatory variables is considered. It is assumed that linear transformations of the components of Y can be the basis for useful interpretation whereas the components of X have strong individual identity. When p ≥ q a transformation is found to a new q × 1 vector of responses Y∗ such that in the multiple regression of, say, Y1∗ on X, only the coefficient of X1 is nonzero, i.e. such that Y1∗ is conditionally independent of X2, …, Xq, given X1. Some associated inferential procedures are sketched. An illustrative example is described in which the resulting transformation has aided interpretation.
$MC$-hypercentral groups
2007
This paper is devoted to the imposition of some chain conditions on groups having a generalized central series. It is also given a characterization of MC-groups with finite abelian section rank: such class of groups is a suitable enlargement of the class of FC-groups. Mathematics Subject Classification: 20F24; 20F14
Restricted and complete-active-space multiconfiguration linear response calculations of the polarizability of formamide and urea
1991
Abstract Using the polarized basis sets of Sadlej, we have carried out multiconfiguration linear response (MCLR) calculations of static and dynamic polarizabilities of water, carbon dioxide, formamide and urea. It is found that the polarized basis sets give a good description of the polarizabilities. The uncorrelates (self-consistent field) polarizabilities are in general 10% or more lower than the experimental values. The correlation as introduced in the complete-active-space (CAS) and restricted-active-space (RAS) MCLR calculations recovers the major part of this deviation.
Basic kinetic model for the reaction yielding linear polyurethanes. II
1995
On the basis of the gradual polyaddition kinetic model developed earlier, an attempt was made to provide a generalized mathematical model for the set of reactions yielding linear polyurethanes. The model is a system of first-order ordinary differential equations. It was assumed at the present stage of this model that the rate constants for the reaction considered do not change. The model developed was then solved numerically. Average molecular weight of the polymer and composition data for oligomers were calculated for a constant volume batch reactor and varied process parameters. The GPC method, which was tested for model urethane oligomers, was employed to verify the model developed. The …
Calculation of vapor pressures not requiring the derivatives of the energy of mixing
1997
A method is presented for the calculation of vapor pressures exclusively on the basis of the energy of mixing, the knowledge of chemical potentials is not required. The only condition used for the calculation is the minimum of the energy of mixing of the overall system in equilibrium. The gas phase is treated as an ideal gas, for the liquid phase no specific thermodynamic description is assumed. The method is demonstrated for a mixture of two solvents and one polymer. The system water/poly(ethylene oxide), the thermodynamics of which are described by an equation that can only be solved numerically thus impeding the calculation of chemical potentials, serves as an example. Interaction parame…
On Variational Measures Related to Some Bases
2000
Abstract We extend, to a certain class of differentiation bases, some results on the variational measure and the δ-variation obtained earlier for the full interval basis. In particular the theorem stating that the variational measure generated by an interval function is σ-finite whenever it is absolutely continuous with respect to the Lebesgue measure is extended to any Busemann–Feller basis.
Discrete cortical representations and their stability in the presence of synaptic turnover
2015
Population imaging in mouse auditory cortex revealed clustering of neural responses to brief complex sounds: the activity of a local population typically falls close to one out of a small number of observed states [1]. These clusters appear to group sets of auditory stimuli into a discrete set of activity patterns and could thereby form the basis for representations of sound categories. However, to be useful for the brain, such representations should be robust against fluctuations in the underlying circuitry, which are significant even in the absences of any explicit learning paradigm [2]. Here we introduce a novel firing rate based circuit model of mouse auditory cortex to study the emerge…