On a moment problem associated with Chebyshev polynomials

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Random regression models using Legendre polynomials or linear splines for test-day milk yield of dairy Gyr (Bos indicus) cattle

Studies investigating the use of random regression models for genetic evaluation of milk production in Zebu cattle are scarce. In this study, 59,744 test-day milk yield records from 7,810 first lactations of purebred dairy Gyr (Bos indicus) and crossbred (dairy Gyr × Holstein) cows were used to compare random regression models in which additive genetic and permanent environmental effects were modeled using orthogonal Legendre polynomials or linear spline functions. Residual variances were modeled considering 1, 5, or 10 classes of days in milk. Five classes fitted the changes in residual variances over the lactation adequately and were used for model comparison. The model that fitted linear spline functions with 6 knots provided the lowest sum of residual variances across lactation. On the other hand, according to the deviance information criterion (DIC) and Bayesian information criterion (BIC), a model using third-order and fourth-order Legendre polynomials for additive genetic and permanent environmental effects, respectively, provided the best fit. However, the high rank correlation (0.998) between this model and that applying third-order Legendre polynomials for additive genetic and permanent environmental effects, indicates that, in practice, the same bulls would be selected by both models. The last model, which is less parameterized, is a parsimonious option for fitting dairy Gyr breed test-day milk yield records. © 2013 American Dairy Science Association.

Role of the range of the dipole function in the classical dynamics of molecular dissociation

The dissociation dynamics of heteronuclear diatomic molecules induced by infrared laser pulses is investigated within the framework of the classical driven Morse oscillator. The interaction between the molecule and the laser field described in the dipole formulation is given by the product of a time-dependent external field with a position-dependent permanent dipole function. The effects of changing the spatial range of the dipole function in the classical dissociation dynamics of large ensembles of trajectories are studied. Numerical calculations have been performed for distinct amplitudes and carrier frequencies of the external pulses and also for ensembles with different initial energies. It is found that there exist a set of values of the dipole range for which the dissociation probability can be completely suppressed. The dependence of the dissociation on the dipole range is explained through the examination of the Fourier series coefficients of the dipole function in the angle variable of the free system. In particular, the suppression of dissociation corresponds to dipole ranges for which the Fourier coefficients associated with nonlinear resonances are null and the chaotic region in the phase space is reduced to thin layers. In this context, it is shown that the suppression of dissociation of heteronuclear molecules for certain frequencies of the external field is a consequence of the finite range of the corresponding permanent dipole. © 2013 American Physical Society.

Quantum-classical correspondence and the role of the dipole function in molecular dissociation

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On the optical properties of copper nanocubes as a function of the edge length as modeled by the discrete dipole approximation

This Letter reports an investigation on the optical properties of copper nanocubes as a function of size as modeled by the discrete dipole approximation. In the far-field, our results showed that the extinction resonances shifted from 595 to 670 nm as the size increased from 20 to 100 nm. Also, the highest optical efficiencies for absorption and scattering were obtained for nanocubes that were 60 and 100 nm in size, respectively. In the near-field, the electric-field amplitudes were investigated considering 514, 633 and 785 nm as the excitation wavelengths. The E-fields increased with size, being the highest at 633 nm. (c) 2012 Elsevier B.V. All rights reserved.

Polynomial function intervals for floating-point software verification

The focus of our work is the verification of tight functional properties of numerical programs, such as showing that a floating-point implementation of Riemann integration computes a close approximation of the exact integral. Programmers and engineers writing such programs will benefit from verification tools that support an expressive specification language and that are highly automated. Our work provides a new method for verification of numerical software, supporting a substantially more expressive language for specifications than other publicly available automated tools. The additional expressivity in the specification language is provided by two constructs. First, the specification can feature inclusions between interval arithmetic expressions. Second, the integral operator from classical analysis can be used in the specifications, where the integration bounds can be arbitrary expressions over real variables. To support our claim of expressivity, we outline the verification of four example programs, including the integration example mentioned earlier. A key component of our method is an algorithm for proving numerical theorems. This algorithm is based on automatic polynomial approximation of non-linear real and real-interval functions defined by expressions. The PolyPaver tool is our implementation of the algorithm and its source code is publicly available. In this paper we report on experiments using PolyPaver that indicate that the additional expressivity does not come at a performance cost when comparing with other publicly available state-of-the-art provers. We also include a scalability study that explores the limits of PolyPaver in proving tight functional specifications of progressively larger randomly generated programs. © 2014 Springer International Publishing Switzerland.

Combining Legendre's Polynomials and Genetic Algorithm in the Solution of Nonlinear Initial-Value Problems

This work develops a method for solving ordinary differential equations, that is, initial-value problems, with solutions approximated by using Legendre's polynomials. An iterative procedure for the adjustment of the polynomial coefficients is developed, based on the genetic algorithm. This procedure is applied to several examples providing comparisons between its results and the best polynomial fitting when numerical solutions by the traditional Runge-Kutta or Adams methods are available. The resulting algorithm provides reliable solutions even if the numerical solutions are not available, that is, when the mass matrix is singular or the equation produces unstable running processes.

Direct Computation of Operational Matrices for Polynomial Bases

Several numerical methods for boundary value problems use integral and differential operational matrices, expressed in polynomial bases in a Hilbert space of functions. This work presents a sequence of matrix operations allowing a direct computation of operational matrices for polynomial bases, orthogonal or not, starting with any previously known reference matrix. Furthermore, it shows how to obtain the reference matrix for a chosen polynomial base. The results presented here can be applied not only for integration and differentiation, but also for any linear operation.

Modelling of species in hood fires by conditional moment closure

Carbon monoxide, the chief killer in fires, and other species are modelled for a series of enclosure fires. The conditions emulate building fires where CO is formed in the rich, turbulent, nonpremixed flame and is transported frozen to lean mixtures by the ceiling jet which is cooled by radiation and dilution. Conditional moment closure modelling is used and computational domain minimisation criteria are developed which reduce the computational cost of this method. The predictions give good agreement for CO and other species in the lean, quenched-gas stream, holding promise that this method may provide a practical means of modelling real, three-dimensional fire situations. (c) 2005 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

A comparison of low-storage strategies for spectral analysis in dissipative systems: filter diagonalisation in the Lanczos representation and harmonic inversion of the Chebychev-order-domain autocorrelation function

We compare the performance of two different low-storage filter diagonalisation (LSFD) strategies in the calculation of complex resonance energies of the HO2, radical. The first is carried out within a complex-symmetric Lanczos subspace representation [H. Zhang, S.C. Smith, Phys. Chem. Chem. Phys. 3 (2001) 2281]. The second involves harmonic inversion of a real autocorrelation function obtained via a damped Chebychev recursion [V.A. Mandelshtam, H.S. Taylor, J. Chem. Phys. 107 (1997) 6756]. We find that while the Chebychev approach has the advantage of utilizing real algebra in the time-consuming process of generating the vector recursion, the Lanczos, method (using complex vectors) requires fewer iterations, especially for low-energy part of the spectrum. The overall efficiency in calculating resonances for these two methods is comparable for this challenging system. (C) 2001 Elsevier Science B.V. All rights reserved.

A monolithic smoothing-gap algorithm for contact-impact based on the signed distance function

A new algorithm has been developed for smoothing the surfaces in finite element formulations of contact-impact. A key feature of this method is that the smoothing is done implicitly by constructing smooth signed distance functions for the bodies. These functions are then employed for the computation of the gap and other variables needed for implementation of contact-impact. The smoothed signed distance functions are constructed by a moving least-squares approximation with a polynomial basis. Results show that when nodes are placed on a surface, the surface can be reproduced with an error of about one per cent or less with either a quadratic or a linear basis. With a quadratic basis, the method exactly reproduces a circle or a sphere even for coarse meshes. Results are presented for contact problems involving the contact of circular bodies. Copyright (C) 2002 John Wiley Sons, Ltd.

Logarithmically proportional objective function for planar surfaces recognition in 3D point cloud

3D laser scanning is becoming a standard technology to generate building models of a facility's as-is condition. Since most constructions are constructed upon planar surfaces, recognition of them paves the way for automation of generating building models. This paper introduces a new logarithmically proportional objective function that can be used in both heuristic and metaheuristic (MH) algorithms to discover planar surfaces in a point cloud without exploiting any prior knowledge about those surfaces. It can also adopt itself to the structural density of a scanned construction. In this paper, a metaheuristic method, genetic algorithm (GA), is used to test this introduced objective function on a synthetic point cloud. The results obtained show the proposed method is capable to find all plane configurations of planar surfaces (with a wide variety of sizes) in the point cloud with a minor distance to the actual configurations. © 2014 IEEE.

Chebyshev polynomial approximation to approximate partial differential equations

This paper suggests a simple method based on Chebyshev approximation at Chebyshev nodes to approximate partial differential equations. The methodology simply consists in determining the value function by using a set of nodes and basis functions. We provide two examples. Pricing an European option and determining the best policy for chatting down a machinery. The suggested method is flexible, easy to program and efficient. It is also applicable in other fields, providing efficient solutions to complex systems of partial differential equations.

Generating controlled image sets in cognitive neuroscience research.

The investigation of perceptual and cognitive functions with non-invasive brain imaging methods critically depends on the careful selection of stimuli for use in experiments. For example, it must be verified that any observed effects follow from the parameter of interest (e.g. semantic category) rather than other low-level physical features (e.g. luminance, or spectral properties). Otherwise, interpretation of results is confounded. Often, researchers circumvent this issue by including additional control conditions or tasks, both of which are flawed and also prolong experiments. Here, we present some new approaches for controlling classes of stimuli intended for use in cognitive neuroscience, however these methods can be readily extrapolated to other applications and stimulus modalities. Our approach is comprised of two levels. The first level aims at equalizing individual stimuli in terms of their mean luminance. Each data point in the stimulus is adjusted to a standardized value based on a standard value across the stimulus battery. The second level analyzes two populations of stimuli along their spectral properties (i.e. spatial frequency) using a dissimilarity metric that equals the root mean square of the distance between two populations of objects as a function of spatial frequency along x- and y-dimensions of the image. Randomized permutations are used to obtain a minimal value between the populations to minimize, in a completely data-driven manner, the spectral differences between image sets. While another paper in this issue applies these methods in the case of acoustic stimuli (Aeschlimann et al., Brain Topogr 2008), we illustrate this approach here in detail for complex visual stimuli.

Early antibiotic administration affects the gut barrier function and the immune response to oral antigen in suckling rats

Abstract: The increasingly high hygienic standards characterizing westernized societies correlate with an increasingly high prevalence of allergic disease. Initially based on these observations, the hygiene hypothesis postulates that reduced microbial stimulation during infancy impairs the immune system development and increases the risk of allergy. Moreover, there is increasing evidence that the crosstalk existing between the intestine and the resident microbiota is crucial for gut homeostasis. In particular, bacterial colonization of the gut affects the integrity of the gut barrier and stimulates the development of the gut associated immune tissue, both phenomena being essential for the immune system to mount a controlled response to food antigens. Therefore, alterations in the microbial colonization process, by compromising the barrier homeostasis, may increase the risk of food allergy. In this context, antibiotic treatment, frequently prescribed during infancy, affects gut colonization by bacteria. However, little is known about the impact of alterations in the colonization process on the maturation of the gut barrier and on the immunological response to oral antigens. The objective of this work was to determine the impact of a commercial antibiotic preparation employed in pediatric settings on the gut barrier status at the critical period of the suckling/weaning transition and to evaluate the physiological consequences of this treatment in terms of immune response to food antigens. We established an antibiotic-treated suckling rat model relevant to the pediatric population in terms of type, dose and route of administration of the antibiotic and of changes in the patterns of microbial colonization. Oral tolerance to a novel luminal antigen (ovalbumin) was impaired when the antigen was introduced during antibiotic treatment. These results paralleled to alterations in the intestinal permeability to macromolecules and reduced intestinal expression of genes coding for the major histocomptatibility complex II molecules, which suggest a reduced capacity of antigen handling and presentation in the intestine of the antibiotic-treated animals. In addition, low luminal IgA levels and reduced intestinal expression of genes coding for antimicrobial proteins suggest that protection against pathogens was reduced under antibiotic treatment. In conclusion, we observed in suckling rats that treatment with abroad-spectrum antibiotic commonly used in pediatric practices reduced the capacity of the immune system to develop tolerance. The impact of the antibiotic treatment on the immune response to the antigen-was likely mediated by the alterations of the gut microbiota, through impairment in the mechanisms of antigen handling and presentation. This work reinforces the body of data supporting a key role of the intestinal microbiota modulating the risk of allergy development and leads us to propose that the introduction of new food antigens should be avoided during antibiotic treatment in infants. Résumé: L'augmentation du niveau d'hygiène caractérisant les sociétés occidentales semble être fortement corrélée avec l'augmentation des cas d'allergie dans ces pays. De cette observation est née l'hypothèse qu'une diminution des stimuli microbiens pendant l'enfance modifie le développement du système immunitaire augmentant ainsi le risque d'allergie. En ce sens, un nombre croissant de données indiquent que les interactions existant entre l'intestin et les bactéries résidantes sont cruciales pour l'équilibre du système. En effet, la présence de bactéries dans l'intestin affecte l'intégrité de sa fonction de barrière et stimule le développement du système immunitaire intestinal. Ces deux paramètres étant essentiels à la mise en place d'une réponse contrôlée vis à vis d'un antigène reçu oralement, toute modification du processus naturel de colonisation compromettant l'équilibre intestinal pourrait augmenter le risque d'allergie. Les traitements aux antibiotiques, fréquemment prescrits en pédiatrie, modifient de façon conséquente le processus de colonisation bactérienne. Cependant peu de données existent concernant l'impact d'une altération du processus de colonisation sur la maturation de la barrière intestinale et de la réponse immunitaire dirigée contre un antigène. L'objectif de ce travail était de déterminer l'impact d'un antibiotique commercial et employé en pédiatrie sur l'état de la barrière intestinale au moment critique du sevrage et d'évaluer les conséquences physiologiques d'un tel traitement sur la réponse immune à un antigène alimentaire. Nous avons mis en place un modèle de rats allaités, traités à l'antibiotique, le plus proche possible des pratiques pédiatriques, en terme de nature, dose et voie d'administration de l'antibiotique. Nous avons constaté que l'établissement de la tolérance orale à un nouvel antigène (l'ovalbumine) est altéré quand celui-ci est donné pour la première fois au cours du traitement antibiotique. Ces résultats coïncident avec une diminution de la perméabilité intestinale aux macromolécules, ainsi qu'avec une diminution de l'expression des gènes codant pour les molécules du complexe majeur d'histocomptatibilité de classe II, suggérant une modification de l'apprêtement et de la présentation de l'antigène au niveau intestinal chez les rats traités à l'antibiotique. De plus, un faible taux d'IgA et une diminution de l'expression des gènes codant pour des protéines antimicrobiennes, observés après l'administration d'antibiotique, laissent à penser que la protection contre un pathogène est diminuée lors d'un traitement antibiotique. En conclusion, nous avons observé qu'un traitement antibiotique à large spectre d'activité, couramment utilisé en pédiatrie, réduit la capacité d'induction de la tolérance orale chez le rat allaité. L'impact du traitement antibiotique sur la réponse immune semble induite par l'altération de la flore intestinale via son effet sur les mécanismes d'apprêtement et de présentation de l'antigène. Ce travail renforce l'ensemble des données existantes qui accorde à la flore intestinale un rôle clef dans la modulation du risque de développement d'allergie et nous amène à recommander d'éviter l'introduction d'un nouvel aliment lorsqu'un enfant est traité aux antibiotiques.