On the number of critical periods for planar polynomial systems

In this paper we get some lower bounds for the number of critical periods of families of centers which are perturbations of the linear one. We give a method which lets us prove that there are planar polynomial centers of degree l with at least 2[(l - 2)/2] critical periods as well as study concrete families of potential, reversible and Lienard centers. This last case is studied in more detail and we prove that the number of critical periods obtained with our approach does not. increases with the order of the perturbation. (C) 2007 Elsevier Ltd. All rights reserved.

An extremal nonnegative sine polynomial

For any positive integer n, the sine polynomials that are nonnegative in [0, π] and which have the maximal derivative at the origin are determined in an explicit form. Associated cosine polynomials Kn (θ) are constructed in such a way that {Kn(θ)} is a summability kernel. Thus, for each Pi 1 ≤ P ≤ ∞ and for any 27π-periodic function f ∈ Lp [-π, π], the sequence of convolutions Kn * f is proved to converge to f in Lp[-ππ]. The pointwise and almost everywhere convergences are also consequences of our construction.

Landau and Kolmogoroff type polynomial inequalities II

Let 0 < j < m ≤ n. Kolmogoroff type inequalities of the form ∥f(j)∥2 ≤ A∥f(m)∥ 2 + B∥f∥2 which hold for algebraic polynomials of degree n are established. Here the norm is defined by ∫ f2(x)dμ(x), where dμ(x) is any distribution associated with the Jacobi, Laguerre or Bessel orthogonal polynomials. In particular we characterize completely the positive constants A and B, for which the Landau weighted polynomial inequalities ∥f′∥ 2 ≤ A∥f″∥2 + B∥f∥ 2 hold. © Dynamic Publishers, Inc.

Fractional polynomial response surface models

Second-order polynomial models have been used extensively to approximate the relationship between a response variable and several continuous factors. However, sometimes polynomial models do not adequately describe the important features of the response surface. This article describes the use of fractional polynomial models. It is shown how the models can be fitted, an appropriate model selected, and inference conducted. Polynomial and fractional polynomial models are fitted to two published datasets, illustrating that sometimes the fractional polynomial can give as good a fit to the data and much more plausible behavior between the design points than the polynomial model. © 2005 American Statistical Association and the International Biometric Society.

Improving the accuracy of the optimum-path forest supervised classifier for large datasets

In this work, a new approach for supervised pattern recognition is presented which improves the learning algorithm of the Optimum-Path Forest classifier (OPF), centered on detection and elimination of outliers in the training set. Identification of outliers is based on a penalty computed for each sample in the training set from the corresponding number of imputable false positive and false negative classification of samples. This approach enhances the accuracy of OPF while still gaining in classification time, at the expense of a slight increase in training time. © 2010 Springer-Verlag.

Encoding through generalized polynomial codes

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

Improving accuracy and speed of optimum-path forest classifier using combination of disjoint training subsets

The Optimum-Path Forest (OPF) classifier is a recent and promising method for pattern recognition, with a fast training algorithm and good accuracy results. Therefore, the investigation of a combining method for this kind of classifier can be important for many applications. In this paper we report a fast method to combine OPF-based classifiers trained with disjoint training subsets. Given a fixed number of subsets, the algorithm chooses random samples, without replacement, from the original training set. Each subset accuracy is improved by a learning procedure. The final decision is given by majority vote. Experiments with simulated and real data sets showed that the proposed combining method is more efficient and effective than naive approach provided some conditions. It was also showed that OPF training step runs faster for a series of small subsets than for the whole training set. The combining scheme was also designed to support parallel or distributed processing, speeding up the procedure even more. © 2011 Springer-Verlag.

A snoring classifier based on heart rate variability analysis

The effect of snoring on the cardiovascular system is not well-known. In this study we analyzed the Heart Rate Variability (HRV) differences between light and heavy snorers. The experiments are done on the full-whole-night polysomnography (PSG) with ECG and audio channels from patient group (heavy snorer) and control group (light snorer), which are gender- and age-paired, totally 30 subjects. A feature Snoring Density (SND) of audio signal as classification criterion and HRV features are computed. Mann-Whitney statistical test and Support Vector Machine (SVM) classification are done to see the correlation. The result of this study shows that snoring has close impact on the HRV features. This result can provide a deeper insight into the physiological understand of snoring. © 2011 CCAL.

Limit Cycles for a Class of Continuous and Discontinuous Cubic Polynomial Differential Systems

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Rank Aggregation for Pattern Classifier Selection in Remote Sensing Images

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A path- and label-cost propagation approach to speedup the training of the optimum-path forest classifier

In general, pattern recognition techniques require a high computational burden for learning the discriminating functions that are responsible to separate samples from distinct classes. As such, there are several studies that make effort to employ machine learning algorithms in the context of big data classification problems. The research on this area ranges from Graphics Processing Units-based implementations to mathematical optimizations, being the main drawback of the former approaches to be dependent on the graphic video card. Here, we propose an architecture-independent optimization approach for the optimum-path forest (OPF) classifier, that is designed using a theoretical formulation that relates the minimum spanning tree with the minimum spanning forest generated by the OPF over the training dataset. The experiments have shown that the approach proposed can be faster than the traditional one in five public datasets, being also as accurate as the original OPF. (C) 2014 Elsevier B. V. All rights reserved.

Darboux invariants for planar polynomial differential systems having an invariant conic

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Limit cycles of cubic polynomial differential systems with rational first integrals of degree 2

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A brief look at the least-squares approach as a classifier applied to restricted-vocabulary speech recognition

In this letter, a speech recognition algorithm based on the least-squares method is presented. Particularly, the intention is to exemplify how such a traditional numerical technique can be applied to solve a signal processing problem that is usually treated by using more elaborated formulations.

A new transmission model in cognitive radio based on cyclic generalized polynomial codes for bandwidth reduction

The frequency spectrums are inefficiently utilized and cognitive radio has been proposed for full utilization of these spectrums. The central idea of cognitive radio is to allow the secondary user to use the spectrum concurrently with the primary user with the compulsion of minimum interference. However, designing a model with minimum interference is a challenging task. In this paper, a transmission model based on cyclic generalized polynomial codes discussed in [2] and [15], is proposed for the improvement in utilization of spectrum. The proposed model assures a non interference data transmission of the primary and secondary users. Furthermore, analytical results are presented to show that the proposed model utilizes spectrum more efficiently as compared to traditional models.