Response plateau models fitting via isotonic regression

Within the nutritional context, the supplementation of microminerals in bird food is often made in quantities exceeding those required in the attempt to ensure the proper performance of the animals. The experiments of type dosage x response are very common in the determination of levels of nutrients in optimal food balance and include the use of regression models to achieve this objective. Nevertheless, the regression analysis routine, generally, uses a priori information about a possible relationship between the response variable. The isotonic regression is a method of estimation by least squares that generates estimates which preserves data ordering. In the theory of isotonic regression this information is essential and it is expected to increase fitting efficiency. The objective of this work was to use an isotonic regression methodology, as an alternative way of analyzing data of Zn deposition in tibia of male birds of Hubbard lineage. We considered the models of plateau response of polynomial quadratic and linear exponential forms. In addition to these models, we also proposed the fitting of a logarithmic model to the data and the efficiency of the methodology was evaluated by Monte Carlo simulations, considering different scenarios for the parametric values. The isotonization of the data yielded an improvement in all the fitting quality parameters evaluated. Among the models used, the logarithmic presented estimates of the parameters more consistent with the values reported in literature.

On the zeros of polynomials: an extension of the Enestrom-Kakeya theorem

This paper presents an extension of the Enestrom-Kakeya theorem concerning the roots of a polynomial that arises from the analysis of the stability of Brown (K, L) methods. The generalization relates to relaxing one of the inequalities on the coefficients of the polynomial. Two results concerning the zeros of polynomials will be proved, one of them providing a partial answer to a conjecture by Meneguette (1994)[6]. (C) 2011 Elsevier Inc. All rights reserved.

The influence of the degree of back-mixing on hydrogen production in an anaerobic fixed-bed reactor

This paper reports on results obtained from experiments carried out in an acidogenic anaerobic reactor aiming at the optimization of hydrogen production by altering the degree of back-mixing. It was hypothesized that there is an optimum operating point that maximizes the hydrogen yield. Experiments were performed in a packed-bed bioreactor by covering a broad range of recycle ratios (R) and the optimum point was obtained for an R value of 0.6. In this operating condition the reactor behaved as 8 continuous stirred-tank reactors in series and the maximum yield was 4.22 mol H-2 mol sucrose(-1). Such optimum point was estimated by deriving a polynomial function fitted to experimental data and it was obtained as the conjugation of three factors related to the various degrees of back-mixing applied to the reactor: mass transfer from the bulk liquid to the biocatalyst, liquid-to-gas mass transfer and the kinetic behavior of irreversible reactions in series. Copyright (C) 2012, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.

Regularity at infinity of real mappings and a Morse-Sard theorem

We prove a new Morse-Sard-type theorem for the asymptotic critical values of semi-algebraic mappings and a new fibration theorem at infinity for C-2 mappings. We show the equivalence of three different types of regularity conditions which have been used in the literature in order to control the asymptotic behaviour of mappings. The central role of our picture is played by the p-regularity and its bridge toward the rho-regularity which implies topological triviality at infinity.

Modeling and identification of freeplay nonlinearity

A nonlinear analysis is performed for the purpose of identification of the pitch freeplay nonlinearity and its effect on the type of bifurcation of a two degree-of-freedom aeroelastic system. The databases for the identification are generated from experimental investigations of a pitch-plunge rigid airfoil supported by a nonlinear torsional spring. Experimental data and linear analysis are performed to validate the parameters of the linearized equations. Based on the periodic responses of the experimental data which included the flutter frequency and its third harmonics, the freeplay nonlinearity is approximated by a polynomial expansion up to the third order. This representation allows us to use the normal form of the Hopf bifurcation to characterize the type of instability. Based on numerical integrations, the coefficients of the polynomial expansion representing the freeplay nonlinearity are identified. Published by Elsevier Ltd.

MATHEMATICAL MODELS AND POLYHEDRAL STUDIES FOR INTEGRAL SHEET METAL DESIGN

We deal with the optimization of the production of branched sheet metal products. New forming techniques for sheet metal give rise to a wide variety of possible profiles and possible ways of production. In particular, we show how the problem of producing a given profile geometry can be modeled as a discrete optimization problem. We provide a theoretical analysis of the model in order to improve its solution time. In this context we give the complete convex hull description of some substructures of the underlying polyhedron. Moreover, we introduce a new class of facet-defining inequalities that represent connectivity constraints for the profile and show how these inequalities can be separated in polynomial time. Finally, we present numerical results for various test instances, both real-world and academic examples.

Probabilistic crack growth analyses using a boundary element model: Applications in linear elastic fracture and fatigue problems

This paper addresses the numerical solution of random crack propagation problems using the coupling boundary element method (BEM) and reliability algorithms. Crack propagation phenomenon is efficiently modelled using BEM, due to its mesh reduction features. The BEM model is based on the dual BEM formulation, in which singular and hyper-singular integral equations are adopted to construct the system of algebraic equations. Two reliability algorithms are coupled with BEM model. The first is the well known response surface method, in which local, adaptive polynomial approximations of the mechanical response are constructed in search of the design point. Different experiment designs and adaptive schemes are considered. The alternative approach direct coupling, in which the limit state function remains implicit and its gradients are calculated directly from the numerical mechanical response, is also considered. The performance of both coupling methods is compared in application to some crack propagation problems. The investigation shows that direct coupling scheme converged for all problems studied, irrespective of the problem nonlinearity. The computational cost of direct coupling has shown to be a fraction of the cost of response surface solutions, regardless of experiment design or adaptive scheme considered. (C) 2012 Elsevier Ltd. All rights reserved.

Use of a Single L1 GPS Receiver for Monitoring Structures: First Results of the Detection of Millimetric Dynamic Oscillations

This paper presents preliminary results to determine small displacements of a global positioning system (GPS) antenna fastened to a structure using only one L1 GPS receiver. Vibrations, periodic or not, are common in large structures, such as bridges, footbridges, tall buildings, and towers under dynamic loads. The behavior in time and frequency leads to structural analysis studies. The hypothesis of this article is that any large structure that presents vibrations in the centimeter-to-millimeter range can be monitored by phase measurements of a single L1 receiver with a high data rate, as long as the direction of the displacement is pointing to a particular satellite. Within this scenario, the carrier phase will be modulated by antenna displacement. During a period of a few dozen seconds, the relative displacement to the satellite, the satellite clock, and the atmospheric phase delays can be assumed as a polynomial time function. The residuals from a polynomial adjustment contain the phase modulation owing to small displacements, random noise, receiver clock short time instabilities, and multipath. The results showed that it is possible to detect displacements of centimeters in the phase data of a single satellite and millimeters in the difference between the phases of two satellites. After applying a periodic nonsinusoidal displacement of 10 m to the antenna, it is clearly recovered in the difference of the residuals. The time domain spectrum obtained by the fast Fourier transform (FFT) exhibited a defined peak of the third harmonic much more than the random noise using the proposed third-degree polynomial model. DOI: 10.1061/(ASCE)SU.1943-5428.0000070. (C) 2012 American Society of Civil Engineers.

Bayesian analysis of random regression models using B-splines to model test-day milk yield of Holstein cattle in Brazil

The objective of this paper is to model variations in test-day milk yields of first lactations of Holstein cows by RR using B-spline functions and Bayesian inference in order to fit adequate and parsimonious models for the estimation of genetic parameters. They used 152,145 test day milk yield records from 7317 first lactations of Holstein cows. The model established in this study was additive, permanent environmental and residual random effects. In addition, contemporary group and linear and quadratic effects of the age of cow at calving were included as fixed effects. Authors modeled the average lactation curve of the population with a fourth-order orthogonal Legendre polynomial. They concluded that a cubic B-spline with seven random regression coefficients for both the additive genetic and permanent environment effects was to be the best according to residual mean square and residual variance estimates. Moreover they urged a lower order model (quadratic B-spline with seven random regression coefficients for both random effects) could be adopted because it yielded practically the same genetic parameter estimates with parsimony. (C) 2012 Elsevier B.V. All rights reserved.

Generators of supersymmetric polynomials in positive characteristic

In Kantor and Trishin (1997) [3], Kantor and Trishin described the algebra of polynomial invariants of the adjoint representation of the Lie superalgebra gl(m vertical bar n) and a related algebra A, of what they called pseudosymmetric polynomials over an algebraically closed field K of characteristic zero. The algebra A(s) was investigated earlier by Stembridge (1985) who in [9] called the elements of A(s) supersymmetric polynomials and determined generators of A(s). The case of positive characteristic p of the ground field K has been recently investigated by La Scala and Zubkov (in press) in [6]. We extend their work and give a complete description of generators of polynomial invariants of the adjoint action of the general linear supergroup GL(m vertical bar n) and generators of A(s).

Performance of juveniles of Pseudoplatystoma fasciatum fed graded levels of corn gluten meal

The objective of this work was to evaluate corn gluten meal (CGM) as a substitute for fish meal in diets for striped catfish (Pseudoplatystoma fasciatum) juveniles. Eight isonitrogenous (46% crude protein) and isoenergetic (3,450 kcal kg(-1) digestible energy) diets, with increasing levels of CGM - 0, 6, 12, 18, 24, 30, 36, and 42%-, were fed to juvenile striped catfish (113.56 +/- 5.10 g) for seven weeks. Maximum values for weight gain, specific growth rate, protein efficiency ratio and feed conversion ratio, evaluated by polynomial quadratic regression, were observed with 10.4, 11.4, 15.4 and 15% of CGM inclusion, respectively. Feed intake decreased significantly from 0.8% CGM. Mesenteric fat index and body gross energy decreased linearly with increasing levels of CGM; minimum body protein contents were observed with 34.1% CGM. Yellow pigmentation of fillets significantly increased until 26.5% CGM, and decreased from this point forth. Both plasma glucose and protein concentrations decreased with increased CGM levels. The inclusion of 10-15% CGM promotes optimum of striped catfish juveniles depending on the parameter evaluated. Yellow coloration in fillets produced by CGM diets can have marketing implications.

A comparative study on multiscale fractal dimension descriptors

Fractal theory presents a large number of applications to image and signal analysis. Although the fractal dimension can be used as an image object descriptor, a multiscale approach, such as multiscale fractal dimension (MFD), increases the amount of information extracted from an object. MFD provides a curve which describes object complexity along the scale. However, this curve presents much redundant information, which could be discarded without loss in performance. Thus, it is necessary the use of a descriptor technique to analyze this curve and also to reduce the dimensionality of these data by selecting its meaningful descriptors. This paper shows a comparative study among different techniques for MFD descriptors generation. It compares the use of well-known and state-of-the-art descriptors, such as Fourier, Wavelet, Polynomial Approximation (PA), Functional Data Analysis (FDA), Principal Component Analysis (PCA), Symbolic Aggregate Approximation (SAX), kernel PCA, Independent Component Analysis (ICA), geometrical and statistical features. The descriptors are evaluated in a classification experiment using Linear Discriminant Analysis over the descriptors computed from MFD curves from two data sets: generic shapes and rotated fish contours. Results indicate that PCA, FDA, PA and Wavelet Approximation provide the best MFD descriptors for recognition and classification tasks. (C) 2012 Elsevier B.V. All rights reserved.

Estimation of transpiration of the 'Valencia' orange young plant using thermal dissipation probe method

Most studies on measures of transpiration of plants, especially woody fruit, relies on methods of heat supply in the trunk. This study aimed to calibrate the Thermal Dissipation Probe Method (TDP) to estimate the transpiration, study the effects of natural thermal gradients and determine the relation between outside diameter and area of xylem in 'Valencia' orange young plants. TDP were installed in 40 orange plants of 15 months old, planted in boxes of 500 L, in a greenhouse. It was tested the correction of the natural thermal differences (DTN) for the estimation based on two unheated probes. The area of the conductive section was related to the outside diameter of the stem by means of polynomial regression. The equation for estimation of sap flow was calibrated having as standard lysimeter measures of a representative plant. The angular coefficient of the equation for estimating sap flow was adjusted by minimizing the absolute deviation between the sap flow and daily transpiration measured by lysimeter. Based on these results, it was concluded that the method of TDP, adjusting the original calibration and correction of the DTN, was effective in transpiration assessment.

Usable work of macro-scale cavities in liquids

It is shown that the generation of cavities in a liquid can produce usable work, which is illustrated by the stretching of a string. This work is done during the expansion of the cavity, and not with its collapse. Basic equations are presented for the movement of a device moved by the so called cavity events. A theoretical solution is also proposed, which uses polynomial functions relating the so called "excess of pressure" in the cavity and time. Evaluations of the force generated during the expansion of the cavity showed a mean peak value of about 58 N for the moving container, while measurements with the container fixed to a support showed a peak value of 476 N, considered somewhat overestimated, because high frequency oscillations seem to superpose the mean behavior. Simultaneous phenomena occurring during the cavity events are also described. Series of pictures of the experiments are presented.

Dissociative electron attachment to chloromethane.

A low energy electron may attach to a molecule, forming a metastable resonance, which may dissociate into a stable anion and a neutral radical. Chloromethane has been a good target for dissociative electron attachment studies, since it is a small molecule with a clear dissociative ‘sigma*’ shape resonance. We present potential energy curves for CH3Cl and its anion, as a function of the C-Cl distance. Due to the resonant nature of the anion, a correct description requires a treatment based on scattering calculations. In order to compute elastic cross sections and phase shifts we employed the Schwinger multichannel method, implemented with pseudopotentials of Bachelet, Hamann and Schlüter, at the static-exchange plus polarization approximation. At the equilibrium geometry, the resonance was found arround 3.3 eV, in accordance to experience. The incoming electron is captured by a ‘sigma*’ orbital located at the C-Cl bond, which will relax in the presence of this extra electron. We took this bond as the reaction coordinate, and performed several scattering calculations for a series of nuclear conformations. The phase shift obtained in each calculation was fitted by a two component function, consisting in the usual Breit-Wigner profile, which captures the resonant character, and a second order polynomial in the wave number, which accounts for the background contribution. That way, we obtained position and width of the resonance, which allowed us to build the potential energy curve. For larger distances, the anion becomes stable and usual electronic structure calculations suffice. Furthermore, the existence of a dipole-bound anion state is revealed when we employed a set of very diffuse functions. The knowledge on the behaviour of the neutral and anionic electronic states helps us in elucidating how the dissociation takes place.