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.

Encoding through generalized polynomial codes

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

Classification of masses in mammographic image using wavelet domain features and polynomial classifier

Breast cancer is the most common cancer among women. In CAD systems, several studies have investigated the use of wavelet transform as a multiresolution analysis tool for texture analysis and could be interpreted as inputs to a classifier. In classification, polynomial classifier has been used due to the advantages of providing only one model for optimal separation of classes and to consider this as the solution of the problem. In this paper, a system is proposed for texture analysis and classification of lesions in mammographic images. Multiresolution analysis features were extracted from the region of interest of a given image. These features were computed based on three different wavelet functions, Daubechies 8, Symlet 8 and bi-orthogonal 3.7. For classification, we used the polynomial classification algorithm to define the mammogram images as normal or abnormal. We also made a comparison with other artificial intelligence algorithms (Decision Tree, SVM, K-NN). A Receiver Operating Characteristics (ROC) curve is used to evaluate the performance of the proposed system. Our system is evaluated using 360 digitized mammograms from DDSM database and the result shows that the algorithm has an area under the ROC curve Az of 0.98 ± 0.03. The performance of the polynomial classifier has proved to be better in comparison to other classification algorithms. © 2013 Elsevier Ltd. All rights reserved.

Método numérico-analítico generalizado para estimação do campo eletromagnético de linhas de transmissão de energia elétrica utilizando a teoria dos elementos finitos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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)

Multi-scale lacunarity as an alternative to quantify and diagnose the behavior of prostate cancer

Prostate cancer is a serious public health problem accounting for up to 30% of clinical tumors in men. The diagnosis of this disease is made with clinical, laboratorial and radiological exams, which may indicate the need for transrectal biopsy. Prostate biopsies are discerningly evaluated by pathologists in an attempt to determine the most appropriate conduct. This paper presents a set of techniques for identifying and quantifying regions of interest in prostatic images. Analyses were performed using multi-scale lacunarity and distinct classification methods: decision tree, support vector machine and polynomial classifier. The performance evaluation measures were based on area under the receiver operating characteristic curve (AUC). The most appropriate region for distinguishing the different tissues (normal, hyperplastic and neoplasic) was defined: the corresponding lacunarity values and a rule's model were obtained considering combinations commonly explored by specialists in clinical practice. The best discriminative values (AUC) were 0.906, 0.891 and 0.859 between neoplasic versus normal, neoplasic versus hyperplastic and hyperplastic versus normal groups, respectively. The proposed protocol offers the advantage of making the findings comprehensible to pathologists. (C) 2014 Elsevier Ltd. All rights reserved.

Tsukamoto s Theorem in Characteristic two

In this paper it is proved that hermitian forms over quaternion division algebras over local fields of characteristic two are classified by their dimension and discriminant.

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.

Equação de Fokker-Planck e enovelamento de proteínas

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

Normal Forms for Polynomial Differential Systems in R-3 Having an Invariant Quadric and a Darboux Invariant

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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.

Physical and mechanical characteristic of particleboards produced with residues of sugarcane and stem leaves of bamboo bonded with castor oil adhesive

In this research the aim was produce a particleboard with alternative materials and evaluated its physical and mechanical characteristics. The raw materials used are residues from sucarcane bagasse (SC) (Saccharum officinarum) and stem leaves of bamboo (B) (Dendrocalamus giganteus), bonded with a bi component adhesive based on castor oil. It was produced particleboards with five different traces: 100% SC, 75% SC+25% B, 50% SC+50% B, 25% SC +75%B and 100 % B. Their physical and mechanical characteristics were evaluated accordingly to Brazilian standard NBR 14810-3. Regarding the results obtained, it can be detached that for physical and mechanical evaluation it is evident a negative relation among the amount the sugarcane bagasse and their physical and mechanical characteristics, that is particleboards with low concentrations of sugarcane bagasse had better results. However all particleboards could be recommended for use as sealing particleboards in the segment of civil construction.