Search results for "Polynomial"
showing 10 items of 566 documents
L\'{e}vy flights in inhomogeneous environments
2009
We study the long time asymptotics of probability density functions (pdfs) of L\'{e}vy flights in different confining potentials. For that we use two models: Langevin - driven and (L\'{e}vy - Schr\"odinger) semigroup - driven dynamics. It turns out that the semigroup modeling provides much stronger confining properties than the standard Langevin one. Since contractive semigroups set a link between L\'{e}vy flights and fractional (pseudo-differential) Hamiltonian systems, we can use the latter to control the long - time asymptotics of the pertinent pdfs. To do so, we need to impose suitable restrictions upon the Hamiltonian and its potential. That provides verifiable criteria for an invarian…
Simulation of BSDEs with jumps by Wiener Chaos Expansion
2016
International audience; We present an algorithm to solve BSDEs with jumps based on Wiener Chaos Expansion and Picard's iterations. This paper extends the results given in Briand-Labart (2014) to the case of BSDEs with jumps. We get a forward scheme where the conditional expectations are easily computed thanks to chaos decomposition formulas. Concerning the error, we derive explicit bounds with respect to the number of chaos, the discretization time step and the number of Monte Carlo simulations. We also present numerical experiments. We obtain very encouraging results in terms of speed and accuracy.
Extremal polynomials in stratified groups
2018
We introduce a family of extremal polynomials associated with the prolongation of a stratified nilpotent Lie algebra. These polynomials are related to a new algebraic characterization of abnormal subriemannian geodesics in stratified nilpotent Lie groups. They satisfy a set of remarkable structure relations that are used to integrate the adjoint equations.
Quantitative Prediction of Concentration Effects in Steric Exclusion Chromatography
1986
Abstract A semiempirical model, based on a previous one quantitatively describing the dependence of the elution volume, V(cA), on the concentration of injected polymer, cA, in exclusion chromatography (SEC) at dilute solutions, has been developed. In the derived equation, concentration effects are mainly governed by the Huggins' coefficient, kA, and by the quadratic coefficient in the polynomial expansion of the reduced specific viscosity, kA. Because of the incertitudes on reliable kA and kA' values, these are respectively removed from the model through she Imai's equation and the empirical correlation kA' + 0.122=kA, here obtained. Thus, A predicted elution volumes besides polymer concent…
Optimization of Complex SVM Kernels Using a Hybrid Algorithm Based on Wasp Behaviour
2010
The aim of this paper is to present a new method for optimization of SVM multiple kernels The kernel substitution can be used to define many other types of learning machines distinct from SVMs We introduced a new hybrid method which uses in the first level an evolutionary algorithm based on wasp behaviour and on the co-mutation operator LR−Mijn and in the second level a SVM algorithm which computes the quality of chromosomes The most important details of our algorithms are presented The testing and validation proves that multiple kernels obtained using our genetic approach are improving the classification accuracy up to 94.12% for the “leukemia” data set.
Applications of Kernel Methods
2009
In this chapter, we give a survey of applications of the kernel methods introduced in the previous chapter. We focus on different application domains that are particularly active in both direct application of well-known kernel methods, and in new algorithmic developments suited to a particular problem. In particular, we consider the following application fields: biomedical engineering (comprising both biological signal processing and bioinformatics), communications, signal, speech and image processing.
HD-RTI: an adaptive multi-light imaging approach for the quality assessment of manufactured surfaces
2021
International audience; Reflectance Transformation Imaging (RTI) is a technique for estimating surface local angular reflectance from a set of stereo-photometric images captured with variable lighting directions. The digitization of this information fully fits into the industry 4.0 approach and makes it possible to characterize the visual properties of a surface. The proposed method, namely HD-RTI, is based on the coupling of RTI and HDR imaging techniques. This coupling is carried out adaptively according to the response at each angle of illumination. The proposed method is applied to five industrial samples which have high local variations of reflectivity because of their heterogeneity of…
A proposed equation of correlation for the study of thermodynamic properties (density, viscosity, surface tension and refractive index) of liquid bin…
2009
Abstract The literature on the physicochemical properties of liquid binary mixtures shows that most such systems exhibit nonlinear behavior. As a result, rigorous data and equations capable of affording a reliable estimate of the behavior of such mixtures are needed. The present study offers an equation of correlation providing a reliable estimation of the properties (density, viscosity, surface tension and refractive index) of binary mixtures of liquids as a function of mole fraction. In order to assess the validity of the proposed equation, the latter has been applied to reference binary mixtures, and comparisons have been made of the experimental values of the studied magnitudes versus t…
MULTIPLICITIES IN THE MIXED TRACE COCHARACTER SEQUENCE OF TWO 3 × 3 MATRICES
2006
We find explicitly the multiplicities in the (mixed) trace cocharacter sequence of two 3 × 3 matrices over a field of characteristic 0 and show that asymptotically they behave as polynomials of seventh degree. As a consequence we obtain also the multiplicities of certain irreducible characters in the cocharacter sequence of the polynomial identities of 3 × 3 matrices.
On a Continuous Sárközy-Type Problem
2022
Abstract We prove that there exists a constant $\epsilon> 0$ with the following property: if $K \subset {\mathbb {R}}^2$ is a compact set that contains no pair of the form $\{x, x + (z, z^{2})\}$ for $z \neq 0$, then $\dim _{\textrm {H}} K \leq 2 - \epsilon $.