718 research outputs found
Wavelet treatment of the intra-chain correlation functions of homopolymers in dilute solutions
Discrete wavelets are applied to parametrization of the intra-chain two-point
correlation functions of homopolymers in dilute solutions obtained from Monte
Carlo simulation. Several orthogonal and biorthogonal basis sets have been
investigated for use in the truncated wavelet approximation. Quality of the
approximation has been assessed by calculation of the scaling exponents
obtained from des Cloizeaux ansatz for the correlation functions of
homopolymers with different connectivities in a good solvent. The resulting
exponents are in a better agreement with those from the recent renormalisation
group calculations as compared to the data without the wavelet denoising. We
also discuss how the wavelet treatment improves the quality of data for
correlation functions from simulations of homopolymers at varied solvent
conditions and of heteropolymers.Comment: RevTeX, 19 pages, 7 PS figures. Accepted for publication in PR
Non-equispaced B-spline wavelets
This paper has three main contributions. The first is the construction of
wavelet transforms from B-spline scaling functions defined on a grid of
non-equispaced knots. The new construction extends the equispaced,
biorthogonal, compactly supported Cohen-Daubechies-Feauveau wavelets. The new
construction is based on the factorisation of wavelet transforms into lifting
steps. The second and third contributions are new insights on how to use these
and other wavelets in statistical applications. The second contribution is
related to the bias of a wavelet representation. It is investigated how the
fine scaling coefficients should be derived from the observations. In the
context of equispaced data, it is common practice to simply take the
observations as fine scale coefficients. It is argued in this paper that this
is not acceptable for non-interpolating wavelets on non-equidistant data.
Finally, the third contribution is the study of the variance in a
non-orthogonal wavelet transform in a new framework, replacing the numerical
condition as a measure for non-orthogonality. By controlling the variances of
the reconstruction from the wavelet coefficients, the new framework allows us
to design wavelet transforms on irregular point sets with a focus on their use
for smoothing or other applications in statistics.Comment: 42 pages, 2 figure
Ordinal Probit Functional Regression Models with Application to Computer-Use Behavior in Rhesus Monkeys
Research in functional regression has made great strides in expanding to
non-Gaussian functional outcomes, however the exploration of ordinal functional
outcomes remains limited. Motivated by a study of computer-use behavior in
rhesus macaques (\emph{Macaca mulatta}), we introduce the Ordinal Probit
Functional Regression Model or OPFRM to perform ordinal function-on-scalar
regression. The OPFRM is flexibly formulated to allow for the choice of
different basis functions including penalized B-splines, wavelets, and
O'Sullivan splines. We demonstrate the operating characteristics of the model
in simulation using a variety of underlying covariance patterns showing the
model performs reasonably well in estimation under multiple basis functions. We
also present and compare two approaches for conducting posterior inference
showing that joint credible intervals tend to out perform point-wise credible.
Finally, in application, we determine demographic factors associated with the
monkeys' computer use over the course of a year and provide a brief analysis of
the findings
Damage detection in beams from modal and wavelet analysis using a stationary roving mass and noise estimation
This paper uses the Continuous Wavelet Transform Analysis on mode shapes for damage identification. The wavelet analysis is applied to the difference in the mode shapes between a healthy and a damaged state. The paper also includes a novel methodology for estimating the level of noise of the experimental mode shapes based on a standard Signal to Noise Ratio (SNR). The estimated SNRs are used for identifying and making emphasis on the less noisy data. Moreover, a mass attached to the structure is considered to enhance the sensitivity of the structure to damage. Modal analysis is performed for different positions of the mass along the beam. The results obtained for all the positions of the mass are combined so an averaging process is implicitly applied. The paper presents the results from an experimental test of a cantilever steel beam with different severity levels of damage at the same location. The results show that the use of the attached mass reduces the effect of noise and increases the sensitivity to damage. Little damage can be identified with the proposed methodology even using a small number of sensors and only the first five bending modesConsejerĂa de EconomĂa, InnovaciĂłn, Ciencia y Empleo, Junta de AndalucĂa. Grant Number: P12-TEP-2546Ministerio de EconomĂa y Competitividad. Grant Numbers: BIA2013-43085-P, BIA2016-75042-C2-1-
The Multilevel Structures of NURBs and NURBlets on Intervals
This dissertation is concerned with the problem of constructing biorthogonal wavelets based on non-uniform rational cubic B-Splines on intervals. We call non-uniform rational B-Splines ``NURBs , and such biorthogonal wavelets ``NURBlets . Constructing NURBlets is useful in designing and representing an arbitrary shape of an object in the industry, especially when exactness of the shape is critical such as the shape of an aircraft. As we know presently most popular wavelet models in the industry are approximated at boundaries. In this dissertation a new model is presented that is well suited for generating arbitrary shapes in the industry with mathematical exactness throughout intervals; it fulfills interpolation at boundaries as well
Lack-of-fit tests in semiparametric mixed models.
In this paper we obtain the asymptotic distribution of restricted likelihood ratio tests in mixed linear models with a fixed and finite number of random effects. We explain why for such models the often quoted 50:50 mixture of a chi-s quared random variable with one degree of freedom and a point mass at zero does not hold. Our motivation is a study of the use of wavelets for lack-of-fit testing within a mixed model framework. Even though wavelet shave received a lot of attention in the last say 15 years for the estimation of piecewise smooth functions, much less is known about their ability to check the adequacy of a parametric model when fitting the observed data. In particular we study the testing power of wavelets for testing a hypothesized parametric model within a mixed model framework. Experimental results show that in several situations the wavelet-based test significantly outperforms the com-petitor based on penalized regression splines. The obtained results are also applicable for testing in mixed models in general, and shed some new insight into previous results.Lack-off-fittest; Likelihood ratio test; Mixed models; One-sided test; Penalization; Restricted maximum likelihood; Variance components; Wavel; Asymptotic distribution; Distribution; Likelihood; Tests; Models; Model; Random effects; Effects; Studies; Lack-of-fit; Mixed model; Framework; Functions; Data; Power; Regression;
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