Analysis of generalized interictal discharges using quantitative EEG

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

Variational and perturbative schemes for a spiked harmonic oscillator

A variational analysis of the spiked harmonic oscillator Hamiltonian operator - d2/dx2 + x2 + l(l + 1)/x2 + λ|x| -α, where α is a real positive parameter, is reported in this work. The formalism makes use of the functional space spanned by the solutions of the Schrödinger equation for the linear harmonic oscillator Hamiltonian supplemented by a Dirichlet boundary condition, and a standard procedure for diagonalizing symmetric matrices. The eigenvalues obtained by increasing the dimension of the basis set provide accurate approximations for the ground state energy of the model system, valid for positive and relatively large values of the coupling parameter λ. Additionally, a large coupling perturbative expansion is carried out and the contributions up to fourth-order to the ground state energy are explicitly evaluated. Numerical results are compared for the special case α = 5/2. © 1989 American Institute of Physics.

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.

Estudo sobre a teoria de vínculos de Hamilton-Jacobi

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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.

Práticas algébricas no contexto da modelagem compreendida como proposta pedagógica

Pós-graduação em Educação Matemática - IGCE

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.

Poverty Reduction and the Income Inequality in China

In 2000, the United Nations adopted the Millennium Development Goals which set targets for raising living standards in low-income countries. The first goal was to “eradicate extreme poverty and hunger” (United Nations). The World Bank defines extreme poverty as income of less than $1.25 per day (World Bank, 2010a). Based on this definition, the World Bank estimates that the percentage of the population in China living in extreme poverty has fallen from 84 percent in 1981 to about 16 percent in 2005, a period during which China’s population grew by more than 300 million people (see Table 1 on last page). Because China is a very large country with a current population approaching 1.4 billion (more than four times the United States population), its dramatic reduction in poverty over the past 30 years has had a profound effect on global poverty measures. In fact, poverty reduction in China is the main reason that the incidence of extreme poverty in developing countries has fallen from about 52 percent in 1981 to 25 percent in 2005 (Table 1). While the absolute number of poor in China fell by some 627 million, the number of poor in other developing countries actually grew slightly (from 1,065 million to 1,166 million). These figures represent a decline in the percentage of the total population in poverty in other developing countries because of general population growth over that 25-year period (World Bank, 2010b).

SOCIAL POLICY AS REGIONAL POLICY: MARKET AND NONMARKET FACTORS DETERMINING REGIONAL INEQUALITY

We decompose the recent changes in regional inequality in Brazil into its components, highlighting the role of spatially blind social programs. We aggregate personal income micro data to the state level, differentiating nine income sources, and assess the role of these components in the observed changes in regional inequality indicators. The main results indicate that the largest part of the recent reduction in regional inequality is related to the dynamics of the market-related labor income, with manufacturing and services favoring deconcentration. Labor income in agriculture, retirement and pensions, and property rents and other sources favored concentration. The social programs Bolsa Familia and Beneficios de Prestacao Continuada are responsible for more than 24 percent of the reduction in inequality, although they account for less than 1.7 percent of the disposable household income. Such positive impact on regional concentration is impressive, since the goals of the programs are clearly nonspatial.

Linear matrix inequality-based robust model predictive control for time-delayed systems

This work addresses the solution to the problem of robust model predictive control (MPC) of systems with model uncertainty. The case of zone control of multi-variable stable systems with multiple time delays is considered. The usual approach of dealing with this kind of problem is through the inclusion of non-linear cost constraint in the control problem. The control action is then obtained at each sampling time as the solution to a non-linear programming (NLP) problem that for high-order systems can be computationally expensive. Here, the robust MPC problem is formulated as a linear matrix inequality problem that can be solved in real time with a fraction of the computer effort. The proposed approach is compared with the conventional robust MPC and tested through the simulation of a reactor system of the process industry.

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.