Para-orthogonal polynomials from constant Verblunsky coefficients

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Bounds for the zeros of symmetric kravchuk polynomials

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

Analysis of generalized interictal discharges using quantitative EEG

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

Szegö polynomials: quadrature rules on the unit circle and on [-1, 1]

We consider some of the relations that exist between real Szegö polynomials and certain para-orthogonal polynomials defined on the unit circle, which are again related to certain orthogonal polynomials on [-1, 1] through the transformation x = (z1/2+z1/2)/2. Using these relations we study the interpolatory quadrature rule based on the zeros of polynomials which are linear combinations of the orthogonal polynomials on [-1, 1]. In the case of any symmetric quadrature rule on [-1, 1], its associated quadrature rule on the unit circle is also given.

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.

Investigation of the cingulate cortex in idiopathic generalized epilepsy

Studies using quantitative neuroimaging have shown subtle abnormalities in patients with idiopathic generalized epilepsy (IGE). These findings have several locations, but the midline parasagittal structures are most commonly implicated. The cingulate cortex is related and may be involved. The objective of the current investigation was to perform a comprehensive analysis of the cingulate cortex using multiple quantitative structural neuroimaging techniques. Thirty-two patients (18 women, 30 ± 10 years) and 36 controls (18 women, 32 ± 11 years) were imaged by 3 Tesla magnetic resonance imaging (MRI). A volumetric three-dimensional (3D) sequence was acquired and used for this investigation. Regions-of-interest were selected and voxel-based morphometry (VBM) analyses compared the cingulate cortex of the two groups using Statistical Parametric Mapping (SPM8) and VBM8 software. Cortical analyses of the cingulate gyrus was performed using Freesurfer. Images were submitted to automatic processing using built-in routines and recommendations. Structural parameters were extracted for individual analyses, and comparisons between groups were restricted to the cingulate gyrus. Finally, shape analyses was performed on the anterior rostral, anterior caudal, posterior, and isthmus cingulate using spherical harmonic description (SPHARM). VBM analyses of cingulate gyrus showed areas of gray matter atrophy, mainly in the anterior cingulate gyrus (972 mm(3) ) and the isthmus (168 mm(3) ). Individual analyses of the cingulate cortex were similar between patients with IGE and controls. Surface-based comparisons revealed abnormalities located mainly in the posterior cingulate cortex (718.12 mm(2) ). Shape analyses demonstrated a predominance of anterior and posterior cingulate abnormalities. This study suggests that patients with IGE have structural abnormalities in the cingulate gyrus mainly localized at the anterior and posterior portions. This finding is subtle and variable among patients.

On partial derivative-Neumann's problem in generalized functions framework

In this paper, we show that the equation delta u/delta (z) over bar + Gu = f, where the elements involved are in generalized functions context, has a local solution in the generalized functions context.

Regra de Sinais de Descartes para polinômios ortogonais

Pós-graduação em Matematica Aplicada e Computacional - FCT

An Extended Kernel for Generalized Multiple-Instance Learning

The multiple-instance learning (MIL) model has been successful in areas such as drug discovery and content-based image-retrieval. Recently, this model was generalized and a corresponding kernel was introduced to learn generalized MIL concepts with a support vector machine. While this kernel enjoyed empirical success, it has limitations in its representation. We extend this kernel by enriching its representation and empirically evaluate our new kernel on data from content-based image retrieval, biological sequence analysis, and drug discovery. We found that our new kernel generalized noticeably better than the old one in content-based image retrieval and biological sequence analysis and was slightly better or even with the old kernel in the other applications, showing that an SVM using this kernel does not overfit despite its richer representation.

Continuity of Lyapunov functions and of energy level for generalized gradient semigroup

The global attractor of a gradient-like semigroup has a Morse decomposition. Associated to this Morse decomposition there is a Lyapunov function (differentiable along solutions)-defined on the whole phase space- which proves relevant information on the structure of the attractor. In this paper we prove the continuity of these Lyapunov functions under perturbation. On the other hand, the attractor of a gradient-like semigroup also has an energy level decomposition which is again a Morse decomposition but with a total order between any two components. We claim that, from a dynamical point of view, this is the optimal decomposition of a global attractor; that is, if we start from the finest Morse decomposition, the energy level decomposition is the coarsest Morse decomposition that still produces a Lyapunov function which gives the same information about the structure of the attractor. We also establish sufficient conditions which ensure the stability of this kind of decomposition under perturbation. In particular, if connections between different isolated invariant sets inside the attractor remain under perturbation, we show the continuity of the energy level Morse decomposition. The class of Morse-Smale systems illustrates our results.

Generalized correlation functions for conductance fluctuations and the mesoscopic spin Hall effect

We study the spin Hall conductance fluctuations in ballistic mesoscopic systems. We obtain universal expressions for the spin and charge current fluctuations, cast in terms of current-current autocorrelation functions. We show that the latter are conveniently parametrized as deformed Lorentzian shape lines, functions of an external applied magnetic field and the Fermi energy. We find that the charge current fluctuations show quite unique statistical features at the symplectic-unitary crossover regime. Our findings are based on an evaluation of the generalized transmission coefficients correlation functions within the stub model and are amenable to experimental test. DOI: 10.1103/PhysRevB.86.235112

Differential calculus and integration of generalized functions over membranes

In this paper we continue the development of the differential calculus started in Aragona et al. (Monatsh. Math. 144: 13-29, 2005). Guided by the so-called sharp topology and the interpretation of Colombeau generalized functions as point functions on generalized point sets, we introduce the notion of membranes and extend the definition of integrals, given in Aragona et al. (Monatsh. Math. 144: 13-29, 2005), to integrals defined on membranes. We use this to prove a generalized version of the Cauchy formula and to obtain the Goursat Theorem for generalized holomorphic functions. A number of results from classical differential and integral calculus, like the inverse and implicit function theorems and Green's theorem, are transferred to the generalized setting. Further, we indicate that solution formulas for transport and wave equations with generalized initial data can be obtained as well.

Boundedness of solutions of retarded functional differential equations with variable impulses via generalized ordinary differential equations

In this paper, we give sufficient conditions for the uniform boundedness and uniform ultimate boundedness of solutions of a class of retarded functional differential equations with impulse effects acting on variable times. We employ the theory of generalized ordinary differential equations to obtain our results. As an example, we investigate the boundedness of the solution of a circulating fuel nuclear reactor model.

Robust modeling using the generalized epsilon-skew-t distribution

In this paper, an alternative skew Student-t family of distributions is studied. It is obtained as an extension of the generalized Student-t (GS-t) family introduced by McDonald and Newey [10]. The extension that is obtained can be seen as a reparametrization of the skewed GS-t distribution considered by Theodossiou [14]. A key element in the construction of such an extension is that it can be stochastically represented as a mixture of an epsilon-skew-power-exponential distribution [1] and a generalized-gamma distribution. From this representation, we can readily derive theoretical properties and easy-to-implement simulation schemes. Furthermore, we study some of its main properties including stochastic representation, moments and asymmetry and kurtosis coefficients. We also derive the Fisher information matrix, which is shown to be nonsingular for some special cases such as when the asymmetry parameter is null, that is, at the vicinity of symmetry, and discuss maximum-likelihood estimation. Simulation studies for some particular cases and real data analysis are also reported, illustrating the usefulness of the extension considered.

The new class of Kummer beta generalized distributions

Ng and Kotz (1995) introduced a distribution that provides greater flexibility to extremes. We define and study a new class of distributions called the Kummer beta generalized family to extend the normal, Weibull, gamma and Gumbel distributions, among several other well-known distributions. Some special models are discussed. The ordinary moments of any distribution in the new family can be expressed as linear functions of probability weighted moments of the baseline distribution. We examine the asymptotic distributions of the extreme values. We derive the density function of the order statistics, mean absolute deviations and entropies. We use maximum likelihood estimation to fit the distributions in the new class and illustrate its potentiality with an application to a real data set.