The Ginibre Ensemble and Gaussian Analytic Functions

We show that as n changes, the characteristic polynomial of the n x n random matrix with i.i.d. complex Gaussian entries can be described recursively through a process analogous to Polya's urn scheme. As a result, we get a random analytic function in the limit, which is given by a mixture of Gaussian analytic functions. This suggests another reason why the zeros of Gaussian analytic functions and the Ginibre ensemble exhibit similar local repulsion, but different global behavior. Our approach gives new explicit formulas for the limiting analytic function.

The generator coordinate method in the unrestricted Hartree-Fock formalism

The generator coordinate method was implemented in the unrestricted Hartree-Fock formalism. Weight functions were built from Gaussian generator functions for 1s, 2s, and 2p orbitals of carbon and oxygen atoms. These weight functions show a similar behavior to those found in the generator coordinate restricted Hartree-Fock method, i.e., they are smooth, continuous, and tend to zero in the limits of integration. Moreover, the weight functions obtained are different for spin-up and spin-down electrons what is a result from spin polarization. (C) 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012

Guiding of 150 keV O6+ ions through nanocapillaries in an uncoated Al2O3 membrane: special time dependence of the transmission profile width

This paper reports that the transmission of O6+ ions with energy of 150keV through capillaries in an uncoated Al2O3 membrane was measured, and agreements with previously reported results in general angular distribution of the transmitted ions and the transmission fractions as a function of the tilt angle well fitted to Gaussian-like functions were observed. Due to using an uncoated capillary membrane, our c is larger than that using a gold-coated one with a smaller value of E-p/q, which suggests a larger equilibrium charge Q(infinity) in our experiment. The observed special width variation with time and a larger width than that using a smaller E-p/q were qualitatively explained by using mean-field classical transport theory based on a classical-trajectory Monte Carlo simulation.

A Connection Between GRBF and MLP

Both multilayer perceptrons (MLP) and Generalized Radial Basis Functions (GRBF) have good approximation properties, theoretically and experimentally. Are they related? The main point of this paper is to show that for normalized inputs, multilayer perceptron networks are radial function networks (albeit with a non-standard radial function). This provides an interpretation of the weights w as centers t of the radial function network, and therefore as equivalent to templates. This insight may be useful for practical applications, including better initialization procedures for MLP. In the remainder of the paper, we discuss the relation between the radial functions that correspond to the sigmoid for normalized inputs and well-behaved radial basis functions, such as the Gaussian. In particular, we observe that the radial function associated with the sigmoid is an activation function that is good approximation to Gaussian basis functions for a range of values of the bias parameter. The implication is that a MLP network can always simulate a Gaussian GRBF network (with the same number of units but less parameters); the converse is true only for certain values of the bias parameter. Numerical experiments indicate that this constraint is not always satisfied in practice by MLP networks trained with backpropagation. Multiscale GRBF networks, on the other hand, can approximate MLP networks with a similar number of parameters.

On velocity-based local model networks for nonlinear identification

This paper exposes the strengths and weaknesses of the recently proposed velocity-based local model (LM) network. The global dynamics of the velocity-based blended representation are directly related to the dynamics of the underlying local models, an important property in the design of local controller networks. Furthermore, the sub-models are continuous-time and linear providing continuity with established linear theory and methods. This is not true for the conventional LM framework, where the global dynamics are only weakly related to the affine sub-models. In this paper, a velocity-based multiple model network is identified for a highly nonlinear dynamical system. The results show excellent dynamical modelling performances, highlighting the value of the velocity-based approach for the design and analysis of LM based control. Three important practical issues are also addressed. These relate to the blending of the velocity-based local models, the use of normalised Gaussian basis functions and the requirement of an input derivative.

Classification of incomplete feature vectors by radial basis function networks

The paper describes the use of radial basis function neural networks with Gaussian basis functions to classify incomplete feature vectors. The method uses the fact that any marginal distribution of a Gaussian distribution can be determined from the mean vector and covariance matrix of the joint distribution.

Spectroscopic Investigation of Tooth Caries and Demineralization

Dental caries persists to be the most predominant oral disease in spite of remarkable progress made during the past half- century to reduce its prevalence. Early diagnosis of carious lesions is an important factor in the prevention and management of dental caries. Conventional procedures for caries detection involve visual-tactile and radiographic examination, which is considered as “gold standard”. These techniques are subjective and are unable to detect the lesions until they are well advanced and involve about one-third of the thickness of enamel. Therefore, all these factors necessitate the need for the development of new techniques for early diagnosis of carious lesions. Researchers have been trying to develop various instruments based on optical spectroscopic techniques for detection of dental caries during the last two decades. These optical spectroscopic techniques facilitate noninvasive and real-time tissue characterization with reduced radiation exposure to patient, thereby improving the management of dental caries. Nonetheless, a costeffective optical system with adequate sensitivity and specificity for clinical use is still not realized and development of such a system is a challenging task.Two key techniques based on the optical properties of dental hard tissues are discussed in this current thesis, namely laser-induced fluorescence (LIF) and diffuse reflectance (DR) spectroscopy for detection of tooth caries and demineralization. The work described in this thesis is mainly of applied nature, focusing on the analysis of data from in vitro tooth samples and extending these results to diagnose dental caries in a clinical environment. The work mainly aims to improve and contribute to the contemporary research on fluorescence and diffuse reflectance for discriminating different stages of carious lesions. Towards this, a portable and compact laser-induced fluorescence and reflectance spectroscopic system (LIFRS) was developed for point monitoring of fluorescence and diffuse reflectance spectra from tooth samples. The LIFRS system uses either a 337 nm nitrogen laser or a 404 nm diode laser for the excitation of tooth autofluorescence and a white light source (tungsten halogen lamp) for measuring diffuse reflectance.Extensive in vitro studies were carried out on extracted tooth samples to test the applicability of LIFRS system for detecting dental caries, before being tested in a clinical environment. Both LIF and DR studies were performed for diagnosis of dental caries, but special emphasis was given for early detection and also to discriminate between different stages of carious lesions. Further the potential of LIFRS system in detecting demineralization and remineralization were also assessed.In the clinical trial on 105 patients, fluorescence reference standard (FRS) criteria was developed based on LIF spectral ratios (F500/F635 and F500/F680) to discriminate different stages of caries and for early detection of dental caries. The FRS ratio scatter plots developed showed better sensitivity and specificity as compared to clinical and radiographic examination, and the results were validated with the blindtests. Moreover, the LIF spectra were analyzed by curve-fitting using Gaussian spectral functions and the derived curve-fitted parameters such as peak position, Gaussian curve area, amplitude and width were found to be useful for distinguishing different stages of caries. In DR studies, a novel method was established based on DR ratios (R500/R700, R600/R700 and R650/R700) to detect dental caries with improved accuracy. Further the diagnostic accuracy of LIFRS system was evaluated in terms of sensitivity, specificity and area under the ROC curve. On the basis of these results, the LIFRS system was found useful as a valuable adjunct to the clinicians for detecting carious lesions.

A comparative study of multilayered and single layered neural network based predictive controllers

The authors compare the performance of two types of controllers one based on the multilayered network and the other based on the single layered CMAC network (cerebellar model articulator controller). The neurons (information processing units) in the multi-layered network use Gaussian activation functions. The control scheme which is considered is a predictive control algorithm, along the lines used by Willis et al. (1991), Kambhampati and Warwick (1991). The process selected as a test bed is a continuous stirred tank reactor. The reaction taking place is an irreversible exothermic reaction in a constant volume reactor cooled by a single coolant stream. This reactor is a simplified version of the first tank in the two tank system given by Henson and Seborg (1989).

A unified neurofuzzy model for classification

This work proposes a unified neurofuzzy modelling scheme. To begin with, the initial fuzzy base construction method is based on fuzzy clustering utilising a Gaussian mixture model (GMM) combined with the analysis of covariance (ANOVA) decomposition in order to obtain more compact univariate and bivariate membership functions over the subspaces of the input features. The mean and covariance of the Gaussian membership functions are found by the expectation maximisation (EM) algorithm with the merit of revealing the underlying density distribution of system inputs. The resultant set of membership functions forms the basis of the generalised fuzzy model (GFM) inference engine. The model structure and parameters of this neurofuzzy model are identified via the supervised subspace orthogonal least square (OLS) learning. Finally, instead of providing deterministic class label as model output by convention, a logistic regression model is applied to present the classifier’s output, in which the sigmoid type of logistic transfer function scales the outputs of the neurofuzzy model to the class probability. Experimental validation results are presented to demonstrate the effectiveness of the proposed neurofuzzy modelling scheme.

RBF circuits based on folded cascode differential pairs

We propose new circuits for the implementation of Radial Basis Functions such as Gaussian and Gaussian-like functions. These RBFs are obtained by the subtraction of two differential pair output currents in a folded cascode configuration. We also propose a multidimensional version based on the unidimensional circuits. SPICE simulation results indicate good functionality. These circuits are intended to be applied in the implementation of radial basis function networks. One possible application of these networks is transducer signal conditioning in aircraft and spacecraft vehicles onboard telemetry systems. Copyright 2008 ACM.

Quebra da simetria de sabor na interação de mésons charmosos com o núcleon

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Desenvolvimento de metodologias automáticas para obtenção do parâmetro de forma ótimo para o método RPIM

Neste trabalho, são propostas metodologias para otimização do parâmetro de forma local c do método RPIM (Radial Point Interpolation Method). Com as técnicas apresentadas, é possível reduzir problemas com inversão de matrizes comuns em métodos sem malha e, também, garantir um maior grau de liberdade e precisão para a utilização da técnica, já que se torna possível uma definição semi-automática dos fatores de forma mais adequados para cada domínio de suporte. Além disso, é apresentado um algoritmo baseado no Line Sweep para a geração eficiente dos domínios de suporte.

An automatic methodology for obtaining optimum shape factors for the radial point interpolation method

In this letter, a methodology is proposed for automatically (and locally) obtaining the shape factor c for the Gaussian basis functions, for each support domain, in order to increase numerical precision and mainly to avoid matrix inversion impossibilities. The concept of calibration function is introduced, which is used for obtaining c. The methodology developed was applied for a 2-D numerical experiment, which results are compared to analytical solution. This comparison revels that the results associated to the developed methodology are very close to the analytical solution for the entire bandwidth of the excitation pulse. The proposed methodology is called in this work Local Shape Factor Calibration Method (LSFCM).

Genetic algorithm optimization of adaptive multi-scale GLCM features

We introduce a new second-order method of texture analysis called Adaptive Multi-Scale Grey Level Co-occurrence Matrix (AMSGLCM), based on the well-known Grey Level Co-occurrence Matrix (GLCM) method. The method deviates significantly from GLCM in that features are extracted, not via a fixed 2D weighting function of co-occurrence matrix elements, but by a variable summation of matrix elements in 3D localized neighborhoods. We subsequently present a new methodology for extracting optimized, highly discriminant features from these localized areas using adaptive Gaussian weighting functions. Genetic Algorithm (GA) optimization is used to produce a set of features whose classification worth is evaluated by discriminatory power and feature correlation considerations. We critically appraised the performance of our method and GLCM in pairwise classification of images from visually similar texture classes, captured from Markov Random Field (MRF) synthesized, natural, and biological origins. In these cross-validated classification trials, our method demonstrated significant benefits over GLCM, including increased feature discriminatory power, automatic feature adaptability, and significantly improved classification performance.