Multidimensional polynomial powers of sigmoid (PPS) Wavelet neural networks

Wavelet functions have been used as the activation function in feedforward neural networks. An abundance of R&D has been produced on wavelet neural network area. Some successful algorithms and applications in wavelet neural network have been developed and reported in the literature. However, most of the aforementioned reports impose many restrictions in the classical backpropagation algorithm, such as low dimensionality, tensor product of wavelets, parameters initialization, and, in general, the output is one dimensional, etc. In order to remove some of these restrictions, a family of polynomial wavelets generated from powers of sigmoid functions is presented. We described how a multidimensional wavelet neural networks based on these functions can be constructed, trained and applied in pattern recognition tasks. As an example of application for the method proposed, it is studied the exclusive-or (XOR) problem.

Human face verification based on multidimensional Polynomial Powers of Sigmoid (PPS)

In this paper, we described how a multidimensional wavelet neural networks based on Polynomial Powers of Sigmoid (PPS) can be constructed, trained and applied in image processing tasks. In this sense, a novel and uniform framework for face verification is presented. The framework is based on a family of PPS wavelets,generated from linear combination of the sigmoid functions, and can be considered appearance based in that features are extracted from the face image. The feature vectors are then subjected to subspace projection of PPS-wavelet. The design of PPS-wavelet neural networks is also discussed, which is seldom reported in the literature. The Stirling Universitys face database were used to generate the results. Our method has achieved 92 % of correct detection and 5 % of false detection rate on the database.

Synthesis and thermal characterization of luminescent powers of terbium(III) with mixed ligands

This work deals with the synthesis and thermal decomposition of complexes of general formula: Ln(beta-dik)(3)L (where Ln=Tb(+3), beta-dik=4,4,4-trifluoro-1-phenyl-1,3butanedione(btfa) and L=1,10-fenantroline(phen) or 2,2-bipiridine(bipy). The powders were characterized by melting point, FTIR spectroscopy, LTV-visible, elemental analysis, scanning differential calorimeter(DSC) and thermogravimetry(TG). The TG/DSC curves were obtained simultaneously in a system DSC-TGA, under nitrogen atmosphere. The experimental conditions were: 0.83 ml.s(-1) carrier gas flow, 2.0 +/- 0.5 mg samples and 10 degrees C.min(-1) heating rate. The CHN elemental analysis of the Tb(btfa)(3)bipy and Tb(btfa)(3)phen complexes, are in good agreement with the expected values. The IR spectra evinced that the metal ion is coordinated to the ligands via C=O and C-N groups. The TG/DTG/DSC curves of the complexes show that they decompose before melting. The profiles of the thermal decomposition of the Tb(btfa)3phen and Tb(btfa)3bipy showed six and five decomposition stages, respectively. Our data suggests that the thermal stability of the complexes under investigation followed the order: Tb(btfa)(3)phen < Tb(btfa)(3)bipy.

Learning kernels for support vector machines with polynomial powers of sigmoid

In the pattern recognition research field, Support Vector Machines (SVM) have been an effectiveness tool for classification purposes, being successively employed in many applications. The SVM input data is transformed into a high dimensional space using some kernel functions where linear separation is more likely. However, there are some computational drawbacks associated to SVM. One of them is the computational burden required to find out the more adequate parameters for the kernel mapping considering each non-linearly separable input data space, which reflects the performance of SVM. This paper introduces the Polynomial Powers of Sigmoid for SVM kernel mapping, and it shows their advantages over well-known kernel functions using real and synthetic datasets.

Comparative study between powers of sigmoid functions, MLP-backpropagation and polynomials in function approximation problems

Function approximation is a very important task in environments where the computation has to be based on extracting information from data samples in real world processes. So, the development of new mathematical model is a very important activity to guarantee the evolution of the function approximation area. In this sense, we will present the Polynomials Powers of Sigmoid (PPS) as a linear neural network. In this paper, we will introduce one series of practical results for the Polynomials Powers of Sigmoid, where we will show some advantages of the use of the powers of sigmiod functions in relationship the traditional MLP-Backpropagation and Polynomials in functions approximation problems.

Some orbital characteristics of lunar artificial satellites

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Consistent modified gravity: dark energy, acceleration and the absence of cosmic doomsday

We discuss modified gravity which includes negative and positive powers of curvature and provides gravitational dark energy. It is shown that in GR plus a term containing a negative power of curvature, cosmic speed-up may be achieved while the effective phantom phase (with w less than -1) follows when such a term contains a fractional positive power of curvature. Minimal coupling with matter makes the situation more interesting: even 1/R theory coupled with the usual ideal fluid may describe the (effective phantom) dark energy. The account of the R(2) term (consistent modified gravity) may help to escape cosmic doomsday.

Renormalization of the ladder light-front Bethe-Salpeter equation in the Yukawa model

The reduction of the two-fermion Bethe-Salpeter equation in the framework of light-front dynamics is studied for the Yukawa model. It yields auxiliary three-dimensional quantities for the transition matrix and the bound state. The arising effective interaction can be perturbatively expanded in powers of the coupling constant gs allowing a defined number of boson exchanges; it is divergent and needs renormalization; it also includes the instantaneous term of the Dirac propagator. One possible solution of the renormalization problem of the boson exchanges is shown to be provided by expanding the effective interaction beyond single boson exchange. The effective interaction in ladder approximation up to order g4 s is discussed in detail. It is shown that the effective interaction naturally yields the box counterterm required to be introduced ad hoc previously. The covariant results of the Bethe-Salpeter equation can be recovered from the corresponding auxiliary three-dimensional quantities.

Population genetic data of five X-chromosomal loci in Bauru (São Paulo, Brazil)

Genetic population data for five X-STR (DXS6854, DXS7424, DXS101, DXS6808 and DXS7132) were obtained from Bauru population (São Paulo, Brazil). No deviations from the Hardy-Weinberg equilibrium were observed, with the exception of DXS101. The combined powers of discrimination in males and females were 0.99897253 and 0.99999120, respectively. These high values show the potential of this system in human identification and paternity testing. © 2008 Elsevier B.V. All rights reserved.

Genetic data of 10 X-chromosomal loci in Vitória population (Espírito Santo State, Brazil)

Genetic population data for 10 X-STR (DXS8378, DXS9898, DXS7133, GATA31E08, GATA172D05, DXS7423, DXS6809, DXS7132, DXS9902 and DXS6789) were obtained from Vitória population (Espírito Santo State, Brazil). No deviations from the Hardy-Weinberg equilibrium and linkage disequilibrium were observed. The combined powers of discrimination in males and females were 0.9999995 and 0.99999999996, respectively. These high values show the potential of this system in human identification in Vitória population, Brazil. © 2009 Elsevier B.V. All rights reserved.

Análise da reprodutibilidade de parâmetros no domínio da frequência do sinal EMG utilizados na caracterização da fadiga muscular localizada

The aim of this study was to analyze the reproducibility of the electromyography signal's parameters (EMG) in the frequency domain used in the characterization of localized muscle fatigue. Fifteen male subjects underwent a fatigue test based on isometric knee extension, being held at three different times at intervals of seven days. To assess the reproducibility of data between the tests we calculated the correlation coefficient (ICC) for the median frequency (MF) in total exercise time (MFT), MF obtained for every 10% of exercise time (MF10%) and the powers of the frequency bands obtained by dividing the power spectrum at windows of 20 Hz. The results showed: (1) excellent reproducibility for MFT, (2) good reproducibility for MF10%, and (3) greater variation in the signal EMG bands from 20 to 120 Hz, especially at the bands of 20-40 Hz and 40-60 Hz, which showed greater sensitivity to the process of muscle fatigue. We conclude that the MF is a variable that shows good reproducibility and that the fragmented analysis of the power spectrum, by means of frequency bands, showed that significant variations occur in the EMG signal during the installation of the fatigue process, having potential to become a new method for the characterization of localized muscle fatigue.

Comparative study between RBF and radial-PPS neural networks

The study of function approximation is motivated by the human limitation and inability to register and manipulate with exact precision the behavior variations of the physical nature of a phenomenon. These variations are referred to as signals or signal functions. Many real world problem can be formulated as function approximation problems and from the viewpoint of artificial neural networks these can be seen as the problem of searching for a mapping that establishes a relationship from an input space to an output space through a process of network learning. Several paradigms of artificial neural networks (ANN) exist. Here we will be investigated a comparative of the ANN study of RBF with radial Polynomial Power of Sigmoids (PPS) in function approximation problems. Radial PPS are functions generated by linear combination of powers of sigmoids functions. The main objective of this paper is to show the advantages of the use of the radial PPS functions in relationship traditional RBF, through adaptive training and ridge regression techniques.

Efeitos do ultra-som terapêutico sobre o crescimento longitudinal do fêmur e da tíbia em ratos

Objectives: To determine the effects of ultrasound therapy on the femur and tibia growth in young rats. Method: Four-week-old male Ratus Norvegicus totaling 115 animals, divided into four groups, were submitted to ultrasound therapy (0.8 MHz, fixed tube head, continuous pulse, for 10 minutes, once a day, ten times) on the medial face of the right knee, with powers of 0.0 W/cm2 (group 31), 0.5 W/cm2 (group G2), 1.0 W/cm2 (group G3), and 1.5 W/cm2 (group G4). Histological slides of the epiphysis, growth plate and metaphysis and the femoral and tibial length measurements were studied in the sixth, thirteenth and twenty-sixth weeks of life. The data were submitted to factorial analysis of variance according to a one-way layout. Results: No statistically significant bone growth alteration was established between any of the three treated groups and the control group. However, alterations in femoral and tibial growth suggesting a decrease in G4 in relation to 02 and G3 were noted. In G4, histopathological alterations, such as cellular necrosis and post-necrosis bone neoformation were found. Conclusion: According to this study, no statistical evidence of bone growth stimulus or inhibition resulting from the application of ultrasound therapy was found when comparing the treated groups with the control group. Histological alterations regarded as pathological were only observed in G4. Also, smaller significant bone growth was found in G4 compared to G2 and G3. Level of Evidence: Level II, cross-sectional study.

Cooper pair dispersion relation for weak to strong coupling

Cooper pairing in two dimensions is analyzed with a set of renormalized equations to determine its binding energy for any fermion number density and all coupling assuming a,generic pairwise residual interfermion interaction. Also considered are Cooper pairs (CP's) with nonzero center-of-mass momentum (CMM) and their binding energy is expanded analytically in powers of the CMM up to quadratic terms. A Fermi-sea-dependent linear term in the CMM dominates the pair excitation energy in weak coupling (also called the BCS regime) while the more familiar quadratic term prevails in strong coupling (the Bose regime). The crossover, though strictly unrelated to BCS theory per se, is studied numerically as it is expected to play a central role in a model of superconductivity as a Bose-Einstein condensation of CPs where the transition temperature vanishes for all dimensionality d less than or equal to 2 for quadratic dispersion, but is nonzero for all d greater than or equal to 1 for linear dispersion.