Efficient Kernel Computation for Volterra Filter Structure Evaluation

Despite their generality, conventional Volterra filters are inadequate for some applications, due to the huge number of parameters that may be needed for accurate modelling. When a state-space model of the target system is known, this can be assessed by computing its kernels, which also provides valuable information for choosing an adequate alternate Volterra filter structure, if necessary, and is useful for validating parameter estimation procedures. In this letter, we derive expressions for the kernels by using the Carleman bilinearization method, for which an efficient algorithm is given. Simulation results are presented, which confirm the usefulness of the proposed approach.

Parameter recovery for a skew-normal IRT model under a Bayesian approach: hierarchical framework, prior and kernel sensitivity and sample size

Item response theory (IRT) comprises a set of statistical models which are useful in many fields, especially when there is an interest in studying latent variables (or latent traits). Usually such latent traits are assumed to be random variables and a convenient distribution is assigned to them. A very common choice for such a distribution has been the standard normal. Recently, Azevedo et al. [Bayesian inference for a skew-normal IRT model under the centred parameterization, Comput. Stat. Data Anal. 55 (2011), pp. 353-365] proposed a skew-normal distribution under the centred parameterization (SNCP) as had been studied in [R. B. Arellano-Valle and A. Azzalini, The centred parametrization for the multivariate skew-normal distribution, J. Multivariate Anal. 99(7) (2008), pp. 1362-1382], to model the latent trait distribution. This approach allows one to represent any asymmetric behaviour concerning the latent trait distribution. Also, they developed a Metropolis-Hastings within the Gibbs sampling (MHWGS) algorithm based on the density of the SNCP. They showed that the algorithm recovers all parameters properly. Their results indicated that, in the presence of asymmetry, the proposed model and the estimation algorithm perform better than the usual model and estimation methods. Our main goal in this paper is to propose another type of MHWGS algorithm based on a stochastic representation (hierarchical structure) of the SNCP studied in [N. Henze, A probabilistic representation of the skew-normal distribution, Scand. J. Statist. 13 (1986), pp. 271-275]. Our algorithm has only one Metropolis-Hastings step, in opposition to the algorithm developed by Azevedo et al., which has two such steps. This not only makes the implementation easier but also reduces the number of proposal densities to be used, which can be a problem in the implementation of MHWGS algorithms, as can be seen in [R.J. Patz and B.W. Junker, A straightforward approach to Markov Chain Monte Carlo methods for item response models, J. Educ. Behav. Stat. 24(2) (1999), pp. 146-178; R. J. Patz and B. W. Junker, The applications and extensions of MCMC in IRT: Multiple item types, missing data, and rated responses, J. Educ. Behav. Stat. 24(4) (1999), pp. 342-366; A. Gelman, G.O. Roberts, and W.R. Gilks, Efficient Metropolis jumping rules, Bayesian Stat. 5 (1996), pp. 599-607]. Moreover, we consider a modified beta prior (which generalizes the one considered in [3]) and a Jeffreys prior for the asymmetry parameter. Furthermore, we study the sensitivity of such priors as well as the use of different kernel densities for this parameter. Finally, we assess the impact of the number of examinees, number of items and the asymmetry level on the parameter recovery. Results of the simulation study indicated that our approach performed equally as well as that in [3], in terms of parameter recovery, mainly using the Jeffreys prior. Also, they indicated that the asymmetry level has the highest impact on parameter recovery, even though it is relatively small. A real data analysis is considered jointly with the development of model fitting assessment tools. The results are compared with the ones obtained by Azevedo et al. The results indicate that using the hierarchical approach allows us to implement MCMC algorithms more easily, it facilitates diagnosis of the convergence and also it can be very useful to fit more complex skew IRT models.

Asymptotic integral kernel for ensembles of random normal matrices with radial potentials

The method of steepest descent is used to study the integral kernel of a family of normal random matrix ensembles with eigenvalue distribution P-N (z(1), ... , z(N)) = Z(N)(-1)e(-N)Sigma(N)(i=1) V-alpha(z(i)) Pi(1 <= i<j <= N) vertical bar z(i) - z(j)vertical bar(2), where V-alpha(z) = vertical bar z vertical bar(alpha), z epsilon C and alpha epsilon inverted left perpendicular0, infinity inverted right perpendicular. Asymptotic formulas with error estimate on sectors are obtained. A corollary of these expansions is a scaling limit for the n-point function in terms of the integral kernel for the classical Segal-Bargmann space. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3688293]

Genetic analysis of kernel oil content in tropical maize with design III and QTL mapping

Oil content and grain yield in maize are negatively correlated, and so far the development of high-oil high-yielding hybrids has not been accomplished. Then a fully understand of the inheritance of the kernel oil content is necessary to implement a breeding program to improve both traits simultaneously. Conventional and molecular marker analyses of the design III were carried out from a reference population developed from two tropical inbred lines divergent for kernel oil content. The results showed that additive variance was quite larger than the dominance variance, and the heritability coefficient was very high. Sixteen QTL were mapped, they were not evenly distributed along the chromosomes, and accounted for 30.91% of the genetic variance. The average level of dominance computed from both conventional and QTL analysis was partial dominance. The overall results indicated that the additive effects were more important than the dominance effects, the latter were not unidirectional and then heterosis could not be exploited in crosses. Most of the favorable alleles of the QTL were in the high-oil parental inbred, which could be transferred to other inbreds via marker-assisted backcross selection. Our results coupled with reported information indicated that the development of high-oil hybrids with acceptable yields could be accomplished by using marker-assisted selection involving oil content, grain yield and its components. Finally, to exploit the xenia effect to increase even more the oil content, these hybrids should be used in the Top Cross((TM)) procedure.

Reproducing kernel Hilbert spaces associated with kernels on topological spaces

We analyze reproducing kernel Hilbert spaces of positive definite kernels on a topological space X being either first countable or locally compact. The results include versions of Mercer's theorem and theorems on the embedding of these spaces into spaces of continuous and square integrable functions.

Weighted Fourier–Laplace transforms in reproducing kernel Hilbert spaces on the sphere

We study the action of a weighted Fourier–Laplace transform on the functions in the reproducing kernel Hilbert space (RKHS) associated with a positive definite kernel on the sphere. After defining a notion of smoothness implied by the transform, we show that smoothness of the kernel implies the same smoothness for the generating elements (spherical harmonics) in the Mercer expansion of the kernel. We prove a reproducing property for the weighted Fourier–Laplace transform of the functions in the RKHS and embed the RKHS into spaces of smooth functions. Some relevant properties of the embedding are considered, including compactness and boundedness. The approach taken in the paper includes two important notions of differentiability characterized by weighted Fourier–Laplace transforms: fractional derivatives and Laplace–Beltrami derivatives.

How wild bearded capuchin monkeys select stones and nuts to minimize the number of strikes per nut cracked

Wild bearded capuchin monkeys, Cebus libidinosus, use stone tools to crack palm nuts to obtain the kernel. In five experiments, we gave 10 monkeys from one wild group of bearded capuchins a choice of two nuts differing in resistance and size and/or two manufactured stones of the same shape, volume and composition but different mass. Monkeys consistently selected the nut that was easier to crack and the heavier stone. When choosing between two stones differing in mass by a ratio of 1.3:1, monkeys frequently touched the stones or tapped them with their fingers or with a nut. They showed these behaviours more frequently before making their first selection of a stone than afterward. These results suggest that capuchins discriminate between nuts and between stones, selecting materials that allow them to crack nuts with fewer strikes, and generate exploratory behaviours to discriminate stones of varying mass. In the final experiment, humans effectively discriminated the mass of stones using the same tapping and handling behaviours as capuchins. Capuchins explore objects in ways that allow them to perceive invariant properties (e.g. mass) of objects, enabling selection of objects for specific uses. We predict that species that use tools will generate behaviours that reveal invariant properties of objects such as mass; species that do not use tools are less likely to explore objects in this way. The precision with which individuals can judge invariant properties may differ considerably, and this also should predict prevalence of tool use across species. (C) 2010 The Association for the Study of Animal Behaviour. Published by Elsevier Ltd. All rights reserved.

Accurate ab initio potential energy surfaces for the (3)A '' and (3)A ' electronic states of the O(P-3) plus HBr system

In this work, we report the construction of potential energy surfaces for the (3)A '' and (3)A' states of the system O(P-3) + HBr. These surfaces are based on extensive ab initio calculations employing the MRCI+Q/CBS+SO level of theory. The complete basis set energies were estimated from extrapolation of MRCI+Q/aug-cc-VnZ(-PP) (n = Q, 5) results and corrections due to spin-orbit effects obtained at the CASSCF/aug-cc-pVTZ(-PP) level of theory. These energies, calculated over a region of the configuration space relevant to the study of the reaction O(P-3) + HBr -> OH + Br, were used to generate functions based on the many-body expansion. The three-body potentials were interpolated using the reproducing kernel Hilbert space method. The resulting surface for the (3)A '' electronic state contains van der Waals minima on the entrance and exit channels and a transition state 6.55 kcal/mol higher than the reactants. This barrier height was then scaled to reproduce the value of 5.01 kcal/mol, which was estimated from coupled cluster benchmark calculations performed to include high-order and core-valence correlation, as well as scalar relativistic effects. The (3)A' surface was also scaled, based on the fact that in the collinear saddle point geometry these two electronic states are degenerate. The vibrationally adiabatic barrier heights are 3.44 kcal/mol for the (3)A '' and 4.16 kcal/mol for the (3)A' state. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4705428]

Availability of processed foods in the perimeter of public schools in urban areas

Objective: To assess the availability of food in relation to their degree of industrial processing and the types of food stores in the perimeters of elementary schools. Method: This is a cross-sectional study. 82 food stores located within a 500 m radius buffer of three public schools located in three distinct regions with different socioeconomic levels in the municipality of Santos, state of Sao Paulo, Brazil, were assessed. All streets within a 500-meter radius of the schools were covered, geographic coordinates were recorded and information about the stores and food items available were collected by direct observation and interview with store managers. Available food items were classified in relation to their degree of industrial processing as ultra-processed foods and minimally processed foods. Kernel's density maps were used to assess the degree of agglomeration of stores near the schools. Results: The stores that offered mostly ultra-processed foods were significantly closer to schools than those who offered mostly minimally processed foods. There was a significant difference between the availability of processed food in different types of stores and between the three regions assessed. Conclusions: The data found by this work evidences that children who attend the three public schools assessed are exposed to an environment that encourages the consumption of ultra-processed foods through easier access of these products in the studied stores.

Home range, movements and diurnal roosts of the endangered thin-spined porcupine, Chaetomys subspinosus (Rodentia: Erethizontidae), in the Brazilian Atlantic Forest

Chaetomys subspinosus is the sole species within the Chaetomyinae subfamily of Caviomorph rodents. This poorly studied porcupine is restricted to the Atlantic Forest in eastern Brazil, where deforestation and habitat fragmentation threaten its survival. Data on the ranging and roosting behavior of C. subspinosus is fairly scarce as it is difficult to observe these behaviors in nature and, consequently, it is very rarely detected during field surveys. We monitored the home ranges of three radio-tagged females over the course of 1 year (2005-2006) and collected data on several aspects of their natural history including movement patterns and the use of diurnal roosts and latrines. The animals were monitored at Parque Estadual Paulo Cesar Vinha, a nature reserve dominated by restinga forests, a subtype of Atlantic Forest occurring on sandy soil. The estimated home range varied little between individuals and was relatively small (mean = 2.14 ha/individual and 1.09 ha/individual using minimum convex polygon and kernel methods, respectively). The animals travelled an average of 147 m/night (range: 21-324 m/night) between two consecutive day roosts. The day roosts were mostly located on vine and liana tangles in the canopy which also aid in connecting the canopy to adjacent trees or the forest floor. Latrines were mostly located near the ground in places heavily protected by spiny bromeliads or by other tangled vegetation. Our data suggests that C. subspinosus has the smallest range among all Neotropical Erethizontids which is likely due to its small size and strictly folivorous diet. Our data also helps explain why C. subspinosus is so difficult to observe in nature: researchers should focus on arboreal masses of tangled vegetation where individuals will normally rest during the day. (C) 2011 Deutsche Gesellschaft fur Saugetierkunde. Published by Elsevier GmbH. All rights reserved.

Admissions due to pneumonia and biomass burning: a spatial approach

Objective: To identify spatial patterns in rates of admission for pneumonia among children and relate them to the number of fires reported in the state of Mato Grosso, Brazil. Methods: We conducted an ecological and exploratory study of data from the state of Mato Grosso for 2008 and 2009 on hospital admissions of children aged 0 to 4 years due to pneumonia and on fires in the same period. Admission rates were calculated and choropleth maps were plotted for rates and for fire outbreaks, Moran's I was calculated and the kernel estimator used to identify "hotspots." Data were analyzed using TerraView 3.3.1. Results: Fifteen thousand six hundred eighty-nine children were hospitalized (range zero to 2,315), and there were 161,785 fires (range 7 to 6,454). The average rate of admissions per 1,000 inhabitants was 2.89 (standard deviation [SD] = 5.18) and the number of fires per 1,000 inhabitants was 152.81 (SD = 199.91). Moran's I for the overall number of admissions was I = 0.02 (p = 0.26), the index for rate of admission was I = 0.02 (p = 0.21) and the index for the number of fires was I = 0.31 (p < 0.01). It proved possible to identify four municipalities with elevated rates of admissions for pneumonia. It was also possible to identify two regions with high admission densities. A clustering of fires was evident along what is known as the "arc of deforestation." Conclusions: This study identified municipalities in the state of Mato Grosso that require interventions to reduce rates of admission due to pneumonia and the number fires.

Integrodifference model for blowfly invasion

We propose a stage-structured integrodifference model for blowflies' growth and dispersion taking into account the density dependence of fertility and survival rates and the non-overlap of generations. We assume a discrete-time, stage-structured, model. The spatial dynamics is introduced by means of a redistribution kernel. We treat one and two dimensional cases, the latter on the semi-plane, with a reflexive boundary. We analytically show that the upper bound for the invasion front speed is the same as in the one-dimensional case. Using laboratory data for fertility and survival parameters and dispersal data of a single generation from a capture-recapture experiment in South Africa, we obtain an estimate for the velocity of invasion of blowflies of the species Chrysomya albiceps. This model predicts a speed of invasion which was compared to actual observational data for the invasion of the focal species in the Neotropics. Good agreement was found between model and observations.

Morphological Homogeneity of Neurons: Searching for Outlier Neuronal Cells

We report a morphology-based approach for the automatic identification of outlier neurons, as well as its application to the NeuroMorpho.org database, with more than 5,000 neurons. Each neuron in a given analysis is represented by a feature vector composed of 20 measurements, which are then projected into a two-dimensional space by applying principal component analysis. Bivariate kernel density estimation is then used to obtain the probability distribution for the group of cells, so that the cells with highest probabilities are understood as archetypes while those with the smallest probabilities are classified as outliers. The potential of the methodology is illustrated in several cases involving uniform cell types as well as cell types for specific animal species. The results provide insights regarding the distribution of cells, yielding single and multi-variate clusters, and they suggest that outlier cells tend to be more planar and tortuous. The proposed methodology can be used in several situations involving one or more categories of cells, as well as for detection of new categories and possible artifacts.

Combining meta-learning and search techniques to select parameters for support vector machines

Support Vector Machines (SVMs) have achieved very good performance on different learning problems. However, the success of SVMs depends on the adequate choice of the values of a number of parameters (e.g., the kernel and regularization parameters). In the current work, we propose the combination of meta-learning and search algorithms to deal with the problem of SVM parameter selection. In this combination, given a new problem to be solved, meta-learning is employed to recommend SVM parameter values based on parameter configurations that have been successfully adopted in previous similar problems. The parameter values returned by meta-learning are then used as initial search points by a search technique, which will further explore the parameter space. In this proposal, we envisioned that the initial solutions provided by meta-learning are located in good regions of the search space (i.e. they are closer to optimum solutions). Hence, the search algorithm would need to evaluate a lower number of candidate solutions when looking for an adequate solution. In this work, we investigate the combination of meta-learning with two search algorithms: Particle Swarm Optimization and Tabu Search. The implemented hybrid algorithms were used to select the values of two SVM parameters in the regression domain. These combinations were compared with the use of the search algorithms without meta-learning. The experimental results on a set of 40 regression problems showed that, on average, the proposed hybrid methods obtained lower error rates when compared to their components applied in isolation.

SINGULARLY PERTURBED DISCOUNTED MARKOV CONTROL PROCESSES IN A GENERAL STATE SPACE

This paper studies the asymptotic optimality of discrete-time Markov decision processes (MDPs) with general state space and action space and having weak and strong interactions. By using a similar approach as developed by Liu, Zhang, and Yin [Appl. Math. Optim., 44 (2001), pp. 105-129], the idea in this paper is to consider an MDP with general state and action spaces and to reduce the dimension of the state space by considering an averaged model. This formulation is often described by introducing a small parameter epsilon > 0 in the definition of the transition kernel, leading to a singularly perturbed Markov model with two time scales. Our objective is twofold. First it is shown that the value function of the control problem for the perturbed system converges to the value function of a limit averaged control problem as epsilon goes to zero. In the second part of the paper, it is proved that a feedback control policy for the original control problem defined by using an optimal feedback policy for the limit problem is asymptotically optimal. Our work extends existing results of the literature in the following two directions: the underlying MDP is defined on general state and action spaces and we do not impose strong conditions on the recurrence structure of the MDP such as Doeblin's condition.