Kernel machines for epilepsy diagnosis via EEG signal classification: A comparative study

Objective: We carry out a systematic assessment on a suite of kernel-based learning machines while coping with the task of epilepsy diagnosis through automatic electroencephalogram (EEG) signal classification. Methods and materials: The kernel machines investigated include the standard support vector machine (SVM), the least squares SVM, the Lagrangian SVM, the smooth SVM, the proximal SVM, and the relevance vector machine. An extensive series of experiments was conducted on publicly available data, whose clinical EEG recordings were obtained from five normal subjects and five epileptic patients. The performance levels delivered by the different kernel machines are contrasted in terms of the criteria of predictive accuracy, sensitivity to the kernel function/parameter value, and sensitivity to the type of features extracted from the signal. For this purpose, 26 values for the kernel parameter (radius) of two well-known kernel functions (namely. Gaussian and exponential radial basis functions) were considered as well as 21 types of features extracted from the EEG signal, including statistical values derived from the discrete wavelet transform, Lyapunov exponents, and combinations thereof. Results: We first quantitatively assess the impact of the choice of the wavelet basis on the quality of the features extracted. Four wavelet basis functions were considered in this study. Then, we provide the average accuracy (i.e., cross-validation error) values delivered by 252 kernel machine configurations; in particular, 40%/35% of the best-calibrated models of the standard and least squares SVMs reached 100% accuracy rate for the two kernel functions considered. Moreover, we show the sensitivity profiles exhibited by a large sample of the configurations whereby one can visually inspect their levels of sensitiveness to the type of feature and to the kernel function/parameter value. Conclusions: Overall, the results evidence that all kernel machines are competitive in terms of accuracy, with the standard and least squares SVMs prevailing more consistently. Moreover, the choice of the kernel function and parameter value as well as the choice of the feature extractor are critical decisions to be taken, albeit the choice of the wavelet family seems not to be so relevant. Also, the statistical values calculated over the Lyapunov exponents were good sources of signal representation, but not as informative as their wavelet counterparts. Finally, a typical sensitivity profile has emerged among all types of machines, involving some regions of stability separated by zones of sharp variation, with some kernel parameter values clearly associated with better accuracy rates (zones of optimality). (C) 2011 Elsevier B.V. All rights reserved.

Extensions of discrete triangular distributions and boundary bias in kernel estimation for discrete functions

Asymmetric discrete triangular distributions are introduced in order to extend the symmetric ones serving for discrete associated kernels in the nonparametric estimation for discrete functions. The extension from one to two orders around the mode provides a large family of discrete distributions having a finite support. Establishing a bridge between Dirac and discrete uniform distributions, some different shapes are also obtained and their properties are investigated. In particular, the mean and variance are pointed out. Applications to discrete kernel estimators are given with a solution to a boundary bias problem. (C) 2010 Elsevier B.V. All rights reserved.

Meat Quality of Lambs Fed on Palm Kernel Meal, a By-product of Biodiesel Production

This study aimed to establish the optimum level of palm kernel meal in the diet of Santa Ines lambs based on the sensorial characteristics and fatty acid profile of the meat. We used 32 lambs with a starting age of 4 to 6 months and mean weight of 22 2.75 kg, kept in individual stalls. The animals were fed with Tifton-85 hay and a concentrate mixed with 0.0, 6.5, 13.0 or 19.5% of palm kernel meal based on the dry mass of the complete diet. These levels formed the treatments. Confinement lasted 80 days and on the last day the animals were fasted and slaughtered. After slaughter, carcasses were weighed and sectioned longitudinally, along the median line, into two antimeres. Half-carcasses were then sliced between the 12th and 13th ribs to collect the loin (longissimus dorsi), which was used to determine the sensorial characteristics and fatty acid profile of the meat. For sensorial evaluation, samples of meat were given to 54 judges who evaluated the tenderness, juiciness, appearance, aroma and flavor of the meat using a hedonic scale. Fatty acids were determined by gas chromatography. The addition of palm kernel meal to the diet had no effect on the sensorial characteristics of meat juiciness, appearance, aroma or flavor. However, tenderness showed a quadratic relationship with the addition of the meal to the diet. The concentration of fatty acids C12:0, C14:0 and C16:0 increased with the addition of palm kernel meal, as did the sum of medium-chain fatty acids and the atherogenicity index. Up to of 19.5% of the diet of Santa Ines lambs can be made up of palm kernel meal without causing significant changes in sensorial characteristics. However, the fatty acid profile of the meat was altered.

The Diffusion Kernel Filter

A particle filter method is presented for the discrete-time filtering problem with nonlinear ItA ` stochastic ordinary differential equations (SODE) with additive noise supposed to be analytically integrable as a function of the underlying vector-Wiener process and time. The Diffusion Kernel Filter is arrived at by a parametrization of small noise-driven state fluctuations within branches of prediction and a local use of this parametrization in the Bootstrap Filter. The method applies for small noise and short prediction steps. With explicit numerical integrators, the operations count in the Diffusion Kernel Filter is shown to be smaller than in the Bootstrap Filter whenever the initial state for the prediction step has sufficiently few moments. The established parametrization is a dual-formula for the analysis of sensitivity to gaussian-initial perturbations and the analysis of sensitivity to noise-perturbations, in deterministic models, showing in particular how the stability of a deterministic dynamics is modeled by noise on short times and how the diffusion matrix of an SODE should be modeled (i.e. defined) for a gaussian-initial deterministic problem to be cast into an SODE problem. From it, a novel definition of prediction may be proposed that coincides with the deterministic path within the branch of prediction whose information entropy at the end of the prediction step is closest to the average information entropy over all branches. Tests are made with the Lorenz-63 equations, showing good results both for the filter and the definition of prediction.

The univalent polynomial of Suffridge as a summability kernel

A positive summability trigonometric kernel {K(n)(theta)}(infinity)(n=1) is generated through a sequence of univalent polynomials constructed by Suffridge. We prove that the convolution {K(n) * f} approximates every continuous 2 pi-periodic function f with the rate omega(f, 1/n), where omega(f, delta) denotes the modulus of continuity, and this provides a new proof of the classical Jackson`s theorem. Despite that it turns out that K(n)(theta) coincide with positive cosine polynomials generated by Fejer, our proof differs from others known in the literature.

O risco espacial e fatores associados ao edentulismo em idosos em município do Sudeste do Brasil

Objetivou-se identificar fatores associados ao edentulismo e o seu risco espacial em idosos. Foi realizado um estudo transversal em uma amostra de 372 indivíduos de 60 anos e mais, no Município de Botucatu, São Paulo, Brasil, em 2005. Razões de prevalência brutas e ajustadas foram estimadas por meio de regressão de Poisson, com estimativa robusta da variância e procedimentos de modelagem hierárquica. A análise espacial foi realizada por estimativas de densidade de Kernel. A prevalência de edentulismo foi de 63,17%. Os fatores sociodemográficos associados ao edentulismo foram a baixa escolaridade, o aumento do número de pessoas por cômodo, não possuir automóvel e idade mais avançada, presença de comorbidades, ausência de um cirurgião-dentista regular e ter realizado a última consulta há três anos ou mais. A análise espacial mostrou maior risco nas áreas periféricas. Obteve-se uma melhor compreensão da perda dentária entre os idosos, subsidiando o planejamento de ações em saúde coletiva.

Evaluation of corn cultivars harvested at two cutting heights for ensilage

The objective of this study was to evaluate the agronomic characteristics, bromatological-chemical composition and digestibility of 11 corn cultivars (Zea mays) harvested at two cutting heights. Cultivars D 766, D 657, D 1000, P 3021, P 3041, C 805, C 333, AG 5011, FO 01, CO 9621 and BR 205 were evaluated when they were harvested 5 cm above ground (low) and 5 cm below the insertion of the first ear (high). The experiment was designed as random blocks, with three replicates, arranged in an 11 x 2 factorial scheme. Cultivars presented similar productions of forage dry matter and grains. Percentages of stalk, leaf, straw, cob and kernel fractions were different among cultivars, as well as dry matter content of the whole plant at harvest. Considering the whole plant, only the contents of gross energy, nitrogen in neutral detergent fiber, and in vitro neutral and acid detergent fiber digestibility did not differ among cultivars. Increase on the cutting height improved forage quality due to the reduction of stalk and leaf fractions and contents of cell wall constituents.

Stability and ergodicity of piecewise deterministic Markov processes

The main goal of this paper is to establish some equivalence results on stability, recurrence, and ergodicity between a piecewise deterministic Markov process ( PDMP) {X( t)} and an embedded discrete-time Markov chain {Theta(n)} generated by a Markov kernel G that can be explicitly characterized in terms of the three local characteristics of the PDMP, leading to tractable criterion results. First we establish some important results characterizing {Theta(n)} as a sampling of the PDMP {X( t)} and deriving a connection between the probability of the first return time to a set for the discrete-time Markov chains generated by G and the resolvent kernel R of the PDMP. From these results we obtain equivalence results regarding irreducibility, existence of sigma-finite invariant measures, and ( positive) recurrence and ( positive) Harris recurrence between {X( t)} and {Theta(n)}, generalizing the results of [ F. Dufour and O. L. V. Costa, SIAM J. Control Optim., 37 ( 1999), pp. 1483-1502] in several directions. Sufficient conditions in terms of a modified Foster-Lyapunov criterion are also presented to ensure positive Harris recurrence and ergodicity of the PDMP. We illustrate the use of these conditions by showing the ergodicity of a capacity expansion model.

Nilpotent noncommutativity and renormalization

We analyze renormalizability properties of noncommutative (NC) theories with a bifermionic NC parameter. We introduce a new four-dimensional scalar field model which is renormalizable at all orders of the loop expansion. We show that this model has an infrared stable fixed point (at the one-loop level). We check that the NC QED (which is one-loop renormalizable with a usual NC parameter) remains renormalizable when the NC parameter is bifermionic, at least to the extent of one-loop diagrams with external photon legs. Our general conclusion is that bifermionic noncommutativity improves renormalizability properties of NC theories.

Support vector machines for detecting age-related changes in running kinematics

Age-related changes in running kinematics have been reported in the literature using classical inferential statistics. However, this approach has been hampered by the increased number of biomechanical gait variables reported and subsequently the lack of differences presented in these studies. Data mining techniques have been applied in recent biomedical studies to solve this problem using a more general approach. In the present work, we re-analyzed lower extremity running kinematic data of 17 young and 17 elderly male runners using the Support Vector Machine (SVM) classification approach. In total, 31 kinematic variables were extracted to train the classification algorithm and test the generalized performance. The results revealed different accuracy rates across three different kernel methods adopted in the classifier, with the linear kernel performing the best. A subsequent forward feature selection algorithm demonstrated that with only six features, the linear kernel SVM achieved 100% classification performance rate, showing that these features provided powerful combined information to distinguish age groups. The results of the present work demonstrate potential in applying this approach to improve knowledge about the age-related differences in running gait biomechanics and encourages the use of the SVM in other clinical contexts. (C) 2010 Elsevier Ltd. All rights reserved.

THE VANISHING DISCOUNT APPROACH FOR THE AVERAGE CONTINUOUS CONTROL OF PIECEWISE DETERMINISTIC MARKOV PROCESSES

This work is concerned with the existence of an optimal control strategy for the long-run average continuous control problem of piecewise-deterministic Markov processes (PDMPs). In Costa and Dufour (2008), sufficient conditions were derived to ensure the existence of an optimal control by using the vanishing discount approach. These conditions were mainly expressed in terms of the relative difference of the alpha-discount value functions. The main goal of this paper is to derive tractable conditions directly related to the primitive data of the PDMP to ensure the existence of an optimal control. The present work can be seen as a continuation of the results derived in Costa and Dufour (2008). Our main assumptions are written in terms of some integro-differential inequalities related to the so-called expected growth condition, and geometric convergence of the post-jump location kernel associated to the PDMP. An example based on the capacity expansion problem is presented, illustrating the possible applications of the results developed in the paper.

Generalized Coupled Algebraic Riccati Equations for Discrete-time Markov Jump with Multiplicative Noise Systems

In this paper we consider the existence of the maximal and mean square stabilizing solutions for a set of generalized coupled algebraic Riccati equations (GCARE for short) associated to the infinite-horizon stochastic optimal control problem of discrete-time Markov jump with multiplicative noise linear systems. The weighting matrices of the state and control for the quadratic part are allowed to be indefinite. We present a sufficient condition, based only on some positive semi-definite and kernel restrictions on some matrices, under which there exists the maximal solution and a necessary and sufficient condition under which there exists the mean square stabilizing solution fir the GCARE. We also present a solution for the discounted and long run average cost problems when the performance criterion is assumed be composed by a linear combination of an indefinite quadratic part and a linear part in the state and control variables. The paper is concluded with a numerical example for pension fund with regime switching.

Structured lipids obtained by chemical interesterification of olive oil and palm stearin

Interesterification of palm stearin (PS) with liquid vegetable oils could yield a good solid fat stock that may impart desirable physical properties, because PS is a useful source of vegetable hard fat, providing beta` stable solid fats Dietary ingestion of olive oil (OO) has been reported to have physiological benefits such as lowering serum cholesterol levels Fat blends, formulated by binary blends of palm stearin and olive oil in different ratios, were subjected to chemical interesterification with sodium methoxide The original and interesterified blends were examined for fatty acid and triacylglycerol composition, melting point, solid fat content (SFC) and consistency. Interestenfication caused rearrangement of triacylglycerol species, reduction of trisaturated and triunsaturated triacylglycerols content and increase in diunsaturated-monosaturated triacylglycerols of all blends, resulting in lowering of melting point and solid fat content The incorporation of OO to PS reduced consistency, producing more plastic blends The mixture and chemical interesterification allowed obtaining fats with various degrees of plasticity, increasing the possibilities for the commercial use of palm stearin and olive oil (C) 2009 Elsevier Ltd All rights reserved

Effects of chemical interesterification on physicochemical properties of blends of palm stearin and palm olein

Chemical interesterification is an important technological option for the production of fats targeting commercial applications. Fat blends, formulated by binary blends of palm stearin and palm olein in different ratios, were subjected to chemical interesterification. The following determinations, before and after the interesterification reactions, were done: fatty acid composition, softening point, melting point, solid fat content and consistency. For the analytical responses a multiple regression statistical model was applied. This study has shown that blending and chemical interesterifications are an effective way to modify the physical and chemical properties of palm stearin, palm olein and their blends. The mixture and chemical interesterification allowed obtaining fats with various degrees of plasticity, increasing the possibilities for the commercial use of palm stearin and palm olein. (C) 2009 Elsevier Ltd. All rights reserved.

Zero trans fats from soybean oil and fully hydrogenated soybean oil: Physico-chemical properties and food applications

Blends of soybean oil (50) and fully hydrogenated soybean oil (FHSBO), with 10%, 20%, 30%, 40% and 50% FHSBO (w/w) content were interesterified under the following conditions: 0.4% sodium methoxide, 500 rpm stirring, 100 degrees C, 20 min. The original and interesterified blends were examined for triacylglycerol composition, melting point, solid fat content (SFC) and consistency. Interesterification caused considerable rearrangement of triacylglycerol species, reduction of trisaturated triacylglycerol content and increase in monounsaturated and diunsaturated triacylglycerols, resulting in lowering of respective melting points. The interesterified blends displayed reduced SFC at all temperatures and more linear melting profiles as compared with the original blends. Yield values showed increased plasticity in the blends after the reaction. Isosolid diagrams before and after the reaction showed no eutectic interactions. The 90:10, 80:20, 70:30 and 60:40 interesterified SO:FHSBO blends displayed characteristics suited to application, respectively, as liquid shortening, table margarine, baking/confectionery fat and all-purpose shortenings/biscuit-filing base. (C) 2009 Elsevier Ltd. All rights reserved.