Search results for "Linear"
showing 10 items of 7165 documents
Heteroclinic contours and self-replicated solitary waves in a reaction–diffusion lattice with complex threshold excitation
2008
Abstract The space–time dynamics of the network system modeling collective behavior of electrically coupled nonlinear cells is investigated. The dynamics of a local cell is described by the FitzHugh–Nagumo system with complex threshold excitation. Heteroclinic orbits defining traveling wave front solutions are investigated in a moving frame system. A heteroclinic contour formed by separatrix manifolds of two saddle-foci is found in the phase space. The existence of such structure indicates the appearance of complex wave patterns in the network. Such solutions have been confirmed and analyzed numerically. Complex homoclinic orbits found in the neighborhood of the heteroclinic contour define …
Polynomials generated by linear operators
2004
We study the class of Banach algebra-valued n n -homogeneous polynomials generated by the n t h n^{th} powers of linear operators. We compare it with the finite type polynomials. We introduce a topology w E F w_{EF} on E , E, similar to the weak topology, to clarify the features of these polynomials.
Rough Search of Vague Knowledge
2017
This chapter presents the theoretical basis of the vague knowledge search algorithmization of a rough method. It introduces some data granulation method which aggregates this data as rough sets of data or ways to search this data in the semantic networks. As a result of this method is the possibility of the rough sets description, analogically to sets in the classical theory of sets. We try to answer the question how the agent searching some knowledge can conceive the search of vague knowledge in the semantic networks: (1) if it can, accordingly to the semantic and the conceiving rules, describe the relationships between nodes in this semantic network which are identified as ways of searchi…
Impulsive control of the bilinear Schrödinger equation: propagators and attainable sets
2019
International audience; We consider a linear Schrödinger equation with an unbounded bilinear control term. The control term is the derivative of function with bounded variations (impulsive control). Well-posedness results and regularity of the associated propagators follow from classical theory from Kato. As a byproduct, one obtains a topological obstruction to exact controllability of the system in the spirit of the results of Ball, Marsden and Slemrod.
Evaluation of enantioselective binding of fluoxetine to human serum albumin by ultrafiltration and CE - Experimental design and quality considerations
2012
Several pharmacokinetic processes are affected by enantioselectivity (ES). At the level of distribution, protein binding (PB) is one of the most important. The enantioselective binding of fluoxetine (FLX) to HSA has been evaluated in this work by ultrafiltration of FLX–HSA mixtures and chiral analysis of unbound fractions by EKC-CD. PB, affinity constants (K) and ES were obtained for both enantiomers of FLX. In order to improve the consistency of the estimations, the evaluation of affinity constants of each enantiomer was performed using two designs, one keeping constant the total concentration of protein and varying the total concentration of the enantiomers, and the other in the opposite …
Evaluation of enantioselective binding of propanocaine to human serum albumin by ultrafiltration and electrokinetic chromatography under intermediate…
2011
Abstract Stereoselectivity in protein binding can have a significant effect on the pharmacokinetic and pharmacodynamic properties of chiral drugs. In this paper, the enantioselective binding of propanocaine (PRO) enantiomers to human serum albumin (HSA), the most relevant plasmatic protein in view of stereoselectivity, has been evaluated by incubation and ultrafiltration of racemic PRO–HSA mixtures and chiral analysis of the bound and unbound fractions by electrokinetic chromatography using HSA as chiral selector. Experimental conditions for the separation of PRO enantiomers using HSA as chiral selector and electrokinetic chromatography have been optimised. Affinity constants and protein bi…
Efficient unsupervised clustering for spatial bird population analysis along the Loire river
2015
International audience; This paper focuses on application and comparison of Non Linear Dimensionality Reduction (NLDR) methods on natural high dimensional bird communities dataset along the Loire River (France). In this context, biologists usually use the well-known PCA in order to explain the upstream-downstream gradient.Unfortunately this method was unsuccessful on this kind of nonlinear dataset.The goal of this paper is to compare recent NLDR methods coupled with different data transformations in order to find out the best approach. Results show that Multiscale Jensen-Shannon Embedding (Ms JSE) outperform all over methods in this context.
The on-line curvilinear component analysis (onCCA) for real-time data reduction
2015
Real time pattern recognition applications often deal with high dimensional data, which require a data reduction step which is only performed offline. However, this loses the possibility of adaption to a changing environment. This is also true for other applications different from pattern recognition, like data visualization for input inspection. Only linear projections, like the principal component analysis, can work in real time by using iterative algorithms while all known nonlinear techniques cannot be implemented in such a way and actually always work on the whole database at each epoch. Among these nonlinear tools, the Curvilinear Component Analysis (CCA), which is a non-convex techni…
Making nonlinear manifold learning models interpretable: The manifold grand tour
2015
Smooth nonlinear topographic maps of the data distribution to guide a Grand Tour visualisation.Prioritisation of data linear views that are most consistent with data structure in the maps.Useful visualisations that cannot be obtained by other more classical approaches. Dimensionality reduction is required to produce visualisations of high dimensional data. In this framework, one of the most straightforward approaches to visualising high dimensional data is based on reducing complexity and applying linear projections while tumbling the projection axes in a defined sequence which generates a Grand Tour of the data. We propose using smooth nonlinear topographic maps of the data distribution to…
Dimensionality reduction via regression on hyperspectral infrared sounding data
2014
This paper introduces a new method for dimensionality reduction via regression (DRR). The method generalizes Principal Component Analysis (PCA) in such a way that reduces the variance of the PCA scores. In order to do so, DRR relies on a deflationary process in which a non-linear regression reduces the redundancy between the PC scores. Unlike other nonlinear dimensionality reduction methods, DRR is easy to apply, it has out-of-sample extension, it is invertible, and the learned transformation is volume-preserving. These properties make the method useful for a wide range of applications, especially in very high dimensional data in general, and for hyperspectral image processing in particular…