Search results for "Polynomial"
showing 10 items of 566 documents
Learning non-linear time-scales with kernel -filters
2009
A family of kernel methods, based on the @c-filter structure, is presented for non-linear system identification and time series prediction. The kernel trick allows us to develop the natural non-linear extension of the (linear) support vector machine (SVM) @c-filter [G. Camps-Valls, M. Martinez-Ramon, J.L. Rojo-Alvarez, E. Soria-Olivas, Robust @c-filter using support vector machines, Neurocomput. J. 62(12) (2004) 493-499.], but this approach yields a rigid system model without non-linear cross relation between time-scales. Several functional analysis properties allow us to develop a full, principled family of kernel @c-filters. The improved performance in several application examples suggest…
Global extrapolation with a parallel splitting method
1992
Extrapolation with a parallel splitting method is discussed. The parallel splitting method reduces a multidimensional problem into independent one-dimensional problems and can improve the convergence order of space variables to an order as high as the regularity of the solution permits. Therefore, in order to match the convergence order of the space variables, a high order method should also be used for the time integration. Second and third order extrapolation methods are used to improve the time convergence and it was found that the higher order extrapolation method can produce a more accurate solution than the lower order extrapolation method, but the convergence order of high order extr…
The Relationship Between Tooth Size Discrepancy and Archform Classification in Orthodontic Patients
2015
Background: To determine the relationship between clinically significant tooth size discrepancies (TSD) and archform classification in orthodontic patients. Material and Methods: Two hundred and forty consecutive sets of pre-treatment orthodontic study models were scanned and landmarked. All models had permanent teeth erupted from first molar to first molar in both arches. Sixty sets of images were classified into two groups of 30 according to the presence (group 1) or absence (group 2) of a clinically significant overall or anterior TSD (>2 SD from Bolton’s original means). Mean upper and lower archforms were created for each group using a fourth degree polynomial curve. Upper and lower ar…
Fractional viscoelastic beam under torsion
2017
Abstract This paper introduces a study on twisted viscoelastic beams, having considered fractional calculus to capture the viscoelastic behaviour. Further another novelty of this paper is extending a recent numerical approach, labelled line elementless method (LEM), to viscoelastic beams. The latter does not require any discretization neither in the domain nor in the boundary. Some numerical applications have been reported to demonstrate the efficiency and accuracy of the method.
On Pietsch measures for summing operators and dominated polynomials
2012
We relate the injectivity of the canonical map from $C(B_{E'})$ to $L_p(\mu)$, where $\mu$ is a regular Borel probability measure on the closed unit ball $B_{E'}$ of the dual $E'$ of a Banach space $E$ endowed with the weak* topology, to the existence of injective $p$-summing linear operators/$p$-dominated homogeneous polynomials defined on $E$ having $\mu$ as a Pietsch measure. As an application we fill the gap in the proofs of some results of concerning Pietsch-type factorization of dominated polynomials.
On holomorphic functions attaining their norms
2004
Abstract We show that on a complex Banach space X , the functions uniformly continuous on the closed unit ball and holomorphic on the open unit ball that attain their norms are dense provided that X has the Radon–Nikodym property. We also show that the same result holds for Banach spaces having a strengthened version of the approximation property but considering just functions which are also weakly uniformly continuous on the unit ball. We prove that there exists a polynomial such that for any fixed positive integer k , it cannot be approximated by norm attaining polynomials with degree less than k . For X=d ∗ (ω,1) , a predual of a Lorentz sequence space, we prove that the product of two p…
ean-Square Filtering for Polynomial System States Confused with Poisson Noises over Polynomial Observations
2011
Published version of an article in the journal: Modeling, Identification and Control. Also available from the publisher at: http://dx.doi.org/10.4173/mic.2011.2.1 In this paper, the mean-square filtering problem for polynomial system states confused with white Poisson noises over polynomial observations is studied proceeding from the general expression for the stochastic Ito differentials of the mean-square estimate and the error variance. In contrast to the previously obtained results, the paper deals with the general case of nonlinear polynomial states and observations with white Poisson noises. As a result, the Ito differentials for the mean-square estimate and error variance corre- spon…
Visual acuity with computer simulated and lens-induced astigmatism
2014
[EN] The relationship between spherical and astigmatic refractive errors and their associated visual acuity is investigated in this work by means of two different approaches. In the first one, different refractive errors were induced in normal subjects by trial lenses. In the second one, defocused images were simulated numerically by the optical transfer function of a model eye and then judged by the same subjects. The amount of defocus (measured in terms of the modulus of the dioptric power vector) necessary to reduce the visual acuity to 0.1 logMAR and to 0.4 logMAR was computed with each method and then compared. We found that the visual system is clearly more tolerant to lens-induced de…
Optical quality comparison between 2 collagen copolymer posterior chamber phakic intraocular lens designs
2014
Purpose To compare the optical quality in vitro of 2 designs of the Visian Implantable Collamer Lens phakic intraocular lens (pIOL) for different powers and optical apertures. Setting University of Valencia, Valencia, Spain. Design Experimental study. Methods The Nimo TR1504 deflectometry device was used to measure the V4c pIOL, which has a smaller optic diameter, and the V5 pIOL, which has a larger optic diameter. The pIOLs were measured for −3.00 diopters (D), −6.00 D, −9.50 D, and −10.50 D at different optical apertures from 3.00 to 6.00 mm depending on the IOL power and model. The root mean square of higher-order aberrations (RMS HOAs) was analyzed. The Strehl ratio, point-spread functi…
Optical phase retrieval using four rotated versions of a single binary amplitude modulating mask
2019
In recent years, phase retrieval methods recovering the phase of an object from coded diffraction patterns have gained popularity. A numerical phase retrieval method called PhaseLift that recovers the phase of an object from a very limited number of coded diffraction patterns was recently proposed. Performance of PhaseLift has been analyzed for different types and the number of masks modulating an object. We present a unique application of PhaseLift that uses four rotations of a single mask, modulating only the amplitude of an object. In simulations, a phase screen with the root-mean-square (RMS) value 0.294 μm was used as the test object. The RMS value of the retrieved phase screen after …