A simple application of implicit function theorem

In this note we show that the roots of a polynomial are C∞ depend of the coefficients. The main tool to show this is the Implicit Function Theorem.

Algorithms for automatic segmentation of bovine embryos produced

In vitro production has been employed in bovine embryos and quantification of lipids is fundamental to understand the metabolism of these embryos. This paper presents a unsupervised segmentation method for histological images of bovine embryos. In this method, the anisotropic filter was used in the differents RGB components. After pre-processing step, the thresholding technique based on maximum entropy was applied to separate lipid droplets in the histological slides in different stages: early cleavage, morula and blastocyst. In the postprocessing step, false positives are removed using the connected components technique that identify regions with excess of dye near pellucid zone. The proposed segmentation method was applied in 30 histological images of bovine embryos. Experiments were performed with the images and statistical measures of sensitivity, specificity and accuracy were calculated based on reference images (gold standard). The value of accuracy of the proposed method was 96% with standard deviation of 3%.

Automatic classification of prostate stromal tissue in histological images using Haralick descriptors and Local Binary Patterns

In this paper we presente a classification system that uses a combination of texture features from stromal regions: Haralick features and Local Binary Patterns (LBP) in wavelet domain. The system has five steps for classification of the tissues. First, the stromal regions were detected and extracted using segmentation techniques based on thresholding and RGB colour space. Second, the Wavelet decomposition was applied in the extracted regions to obtain the Wavelet coefficients. Third, the Haralick and LBP features were extracted from the coefficients. Fourth, relevant features were selected using the ANOVA statistical method. The classication (fifth step) was performed with Radial Basis Function (RBF) networks. The system was tested in 105 prostate images, which were divided into three groups of 35 images: normal, hyperplastic and cancerous. The system performance was evaluated using the area under the ROC curve and resulted in 0.98 for normal versus cancer, 0.95 for hyperplasia versus cancer and 0.96 for normal versus hyperplasia. Our results suggest that texture features can be used as discriminators for stromal tissues prostate images. Furthermore, the system was effective to classify prostate images, specially the hyperplastic class which is the most difficult type in diagnosis and prognosis.

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.

Fourier series for quaternions and the square of the error theorem

In this paper we introduce a type of Hypercomplex Fourier Series based on Quaternions, and discuss on a Hypercomplex version of the Square of the Error Theorem. Since their discovery by Hamilton (Sinegre [1]), quaternions have provided beautifully insights either on the structure of different areas of Mathematics or in the connections of Mathematics with other fields. For instance: I) Pauli spin matrices used in Physics can be easily explained through quaternions analysis (Lan [2]); II) Fundamental theorem of Algebra (Eilenberg [3]), which asserts that the polynomial analysis in quaternions maps into itself the four dimensional sphere of all real quaternions, with the point infinity added, and the degree of this map is n. Motivated on earlier works by two of us on Power Series (Pendeza et al. [4]), and in a recent paper on Liouville’s Theorem (Borges and Mar˜o [5]), we obtain an Hypercomplex version of the Fourier Series, which hopefully can be used for the treatment of hypergeometric partial differential equations such as the dumped harmonic oscillation.

Square of the Error Octonionic Theorem and Hypercomplex Fourier Series

The focus of this paper is to address some classical results for a class of hypercomplex numbers. More specifically we present an extension of the Square of the Error Theorem and a Bessel inequality for octonions.

Automatic method to classify images based on multiscale fractal descriptors and paraconsistent logic

In this study is presented an automatic method to classify images from fractal descriptors as decision rules, such as multiscale fractal dimension and lacunarity. The proposed methodology was divided in three steps: quantification of the regions of interest with fractal dimension and lacunarity, techniques under a multiscale approach; definition of reference patterns, which are the limits of each studied group; and, classification of each group, considering the combination of the reference patterns with signals maximization (an approach commonly considered in paraconsistent logic). The proposed method was used to classify histological prostatic images, aiming the diagnostic of prostate cancer. The accuracy levels were important, overcoming those obtained with Support Vector Machine (SVM) and Bestfirst Decicion Tree (BFTree) classifiers. The proposed approach allows recognize and classify patterns, offering the advantage of giving comprehensive results to the specialists.

Thick braneworlds and the Gibbons-Kallosh-Linde no-go theorem in the Gauss-Bonnet framework

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Theorem for series in three-parameter mittag-leffler function

The new result presented here is a theorem involving series in the three-parameter Mittag-Le er function. As a by-product, we recover some known results and discuss corollaries. As an application, we obtain the solution of a fractional di erential equation associated with a RLC electrical circuit in a closed form, in terms of the two-parameter Mittag-Le er function.

Bourgin-Yang version of the Borsuk-Ulam theorem for Z(pk)-equivariant maps

Let G = Z(pk) be a cyclic group of prime power order and let V and W be orthogonal representations of G with V-G = W-G = W-G = {0}. Let S(V) be the sphere of V and suppose f: S(V) -> W is a G-equivariant mapping. We give an estimate for the dimension of the set f(-1){0} in terms of V and W. This extends the Bourgin-Yang version of the Borsuk-Ulam theorem to this class of groups. Using this estimate, we also estimate the size of the G-coincidences set of a continuous map from S(V) into a real vector space W'.

Automatic design of decision-tree induction algorithms tailored to flexible-receptor docking data

Background: This paper addresses the prediction of the free energy of binding of a drug candidate with enzyme InhA associated with Mycobacterium tuberculosis. This problem is found within rational drug design, where interactions between drug candidates and target proteins are verified through molecular docking simulations. In this application, it is important not only to correctly predict the free energy of binding, but also to provide a comprehensible model that could be validated by a domain specialist. Decision-tree induction algorithms have been successfully used in drug-design related applications, specially considering that decision trees are simple to understand, interpret, and validate. There are several decision-tree induction algorithms available for general-use, but each one has a bias that makes it more suitable for a particular data distribution. In this article, we propose and investigate the automatic design of decision-tree induction algorithms tailored to particular drug-enzyme binding data sets. We investigate the performance of our new method for evaluating binding conformations of different drug candidates to InhA, and we analyze our findings with respect to decision tree accuracy, comprehensibility, and biological relevance. Results: The empirical analysis indicates that our method is capable of automatically generating decision-tree induction algorithms that significantly outperform the traditional C4.5 algorithm with respect to both accuracy and comprehensibility. In addition, we provide the biological interpretation of the rules generated by our approach, reinforcing the importance of comprehensible predictive models in this particular bioinformatics application. Conclusions: We conclude that automatically designing a decision-tree algorithm tailored to molecular docking data is a promising alternative for the prediction of the free energy from the binding of a drug candidate with a flexible-receptor.

Automatic aspect discrimination in data clustering

The attributes describing a data set may often be arranged in meaningful subsets, each of which corresponds to a different aspect of the data. An unsupervised algorithm (SCAD) that simultaneously performs fuzzy clustering and aspects weighting was proposed in the literature. However, SCAD may fail and halt given certain conditions. To fix this problem, its steps are modified and then reordered to reduce the number of parameters required to be set by the user. In this paper we prove that each step of the resulting algorithm, named ASCAD, globally minimizes its cost-function with respect to the argument being optimized. The asymptotic analysis of ASCAD leads to a time complexity which is the same as that of fuzzy c-means. A hard version of the algorithm and a novel validity criterion that considers aspect weights in order to estimate the number of clusters are also described. The proposed method is assessed over several artificial and real data sets.

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.

Kleiner's theorem for unitary representations of posets

A subspace representation of a poset S = {s(1), ..., S-t} is given by a system (V; V-1, ..., V-t) consisting of a vector space V and its sub-spaces V-i such that V-i subset of V-j if s(i) (sic) S-j. For each real-valued vector chi = (chi(1), ..., chi(t)) with positive components, we define a unitary chi-representation of S as a system (U: U-1, ..., U-t) that consists of a unitary space U and its subspaces U-i such that U-i subset of U-j if S-i (sic) S-j and satisfies chi 1 P-1 + ... + chi P-t(t) = 1, in which P-i is the orthogonal projection onto U-i. We prove that S has a finite number of unitarily nonequivalent indecomposable chi-representations for each weight chi if and only if S has a finite number of nonequivalent indecomposable subspace representations; that is, if and only if S contains any of Kleiner's critical posets. (c) 2012 Elsevier Inc. 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.