Artificial Examples Research Articles

Damage and molecular changes under a laser beam in SEM‐EDX/MRS interface: a case study on iron‐rich particles

AbstractThe control of damage to individual environmental particles by a laser beam during Raman spectroscopy carried out in ambient air is generally well understood. The nature and control of damage under vacuum conditions (e.g. in the scanning electron microscopy with energy X‐ray detection combined with micro‐Raman spectroscopy—interfaced SEM‐EDX/MRS) are more complex and less well comprehended. The physical and chemical processes that affect the damage caused to small particles by lasers still remain somewhat unclear, but certainly the atmosphere (vacuum/air) and the beam intensity have very significant influences. Furthermore, it has been determined that some particles (e.g. haematite), although stable under an electron beam, are damaged by the laser beam, hampering their analysis. Additionally, when simultaneous analyses by SEM/EDX and MRS are considered, the correct choice of the collection surface plays a crucial role. As a result, the following collection substrates were tested to determine their influence on the laser beam damage process to the particle: silver and aluminium foils and silicon wafers. A test study was performed using artificial examples of haematite (Fe2O3) particles. Exposure of Fe2O3 particles in vacuum to 514‐ and 785‐nm laser radiation often leads to their melting, transformation and evaporation. The dependence of the damage caused by the laser beam on the particle structure is reported here. Molecular and crystallographic changes have also been revealed. Formation of magnetite (as an effect of re‐crystallisation) and Raman inactive structures was detected. Copyright © 2010 John Wiley & Sons, Ltd.

Self-Organizing MultiLayer Perceptron

In this paper, we propose an extension of a self-organizing map called self-organizing multilayer perceptron (SOMLP) whose purpose is to achieve quantization of spaces of functions. Based on the use of multilayer perceptron networks, SOMLP comprises the unsupervised as well as supervised learning algorithms. We demonstrate that it is possible to use the commonly used vector quantization algorithms (LVQ algorithms) to build new algorithms called functional quantization algorithms (LFQ algorithms). The SOMLP can be used to model nonlinear and/or nonstationary complex dynamic processes, such as speech signals. While most of the functional data analysis (FDA) research is based on B-spline or similar univariate functions, the SOMLP algorithm allows quantization of function with high dimensional input space. As a consequence, classical FDA methods can be outperformed by increasing the dimensionality of the input space of the functions under analysis. Experiments on artificial and real world examples are presented which illustrate the potential of this approach.

A centrality measure based on spectral optimization of modularity density

Centrality analysis has been shown to be a valuable method for the structural analysis of complex networks. It is used to identify key elements within networks and to rank network elements such that experiments can be tailored to interesting candidates. In this paper, we show that the optimization process of modularity density can be written in terms of the eigenspectrum of kernel matrix. Based on the eigenvectors belonging to the largest eigenvalue of kernel matrix, we present a new centrality measure that characterizes the contribution of each node to its assigned community in a network, called modularity density centrality. The measure is illustrated and compared with the standard centrality measures by using respectively an artificial example and a classic network data set. The statistical distribution of modularity density centrality is investigated by considering large computer generated graphs and two large networks from the real world. Experimental results show the significance of the proposed approach.

Combining VAR Forecast Densities Using Fast Fourier Transform

In this paper, I propose the use of fast Fourier transform (FFT) as a convenient tool for combining forecast densities of vector autoregressive models in a hybrid Bayesian manner. While a vast amount of papers comprises combinations based on normal approximations, Monte Carlo methods were fully utilized here, which made the analysis computationally demanding. For the sake of minimization of computational time, the FFT algorithm was used to combine the densities of poorly simulated partial models. As a result, a minor loss of quality in the final combined model was allowed, in contrast with the reduction in the necessary simulation time. However, it turns out in the end that the FFT-based approach exceeds ´brute-force´ simulation in all aspects. The suggested method is demonstrated on an ex ante prediction of the Czech GDP and on a pair of artificial examples.

Reconstruction of the orientation distribution function in single‐ and multiple‐shell q‐ball imaging within constant solid angle

q-Ball imaging is a high-angular-resolution diffusion imaging technique that has been proven very successful in resolving multiple intravoxel fiber orientations in MR images. The standard computation of the orientation distribution function (the probability of diffusion in a given direction) from q-ball data uses linear radial projection, neglecting the change in the volume element along each direction. This results in spherical distributions that are different from the true orientation distribution functions. For instance, they are neither normalized nor as sharp as expected and generally require postprocessing, such as artificial sharpening. In this paper, a new technique is proposed that, by considering the solid angle factor, uses the mathematically correct definition of the orientation distribution function and results in a dimensionless and normalized orientation distribution function expression. Our model is flexible enough so that orientation distribution functions can be estimated either from single q-shell datasets or by exploiting the greater information available from multiple q-shell acquisitions. We show that the latter can be achieved by using a more accurate multiexponential model for the diffusion signal. The improved performance of the proposed method is demonstrated on artificial examples and high-angular-resolution diffusion imaging data acquired on a 7-T magnet.

Multivariate Pareto Distributions: Inference and Financial Applications

Univariate Pareto distributions are extensively studied. In this article, we propose a Bayesian inference methodology in the context of multivariate Pareto distributions of the second kind (Mardia's type). Computational techniques organized around Gibbs sampling with data augmentation are proposed to implement Bayesian inference in practice. The new methods are shown to work well in artificial examples involving a trivariate distribution, and to an empirical application involving daily exchange rate data for four major currencies.

Ensembles of Artificial Example based Neural Networks

Ensembles with several neural networks are widely used to improve the generalization performance over a single network. A proper diversity among component networks is considered as an important parameter for ensemble construction so that the failure of one may be compensated by others. Data sampling, i.e., different training sets for different networks, is the most investigated technique for diversity than other approaches. This paper presents a data sampling based neural network ensemble method where the individual networks are trained on the union of original training set and a set of some artificially generated examples. Generated examples are different for different networks and are the element to produce diversity among the networks. After each network is trained, the method checks whether the trained network is suitable to ensemble or not, and absorbs the network based on the ensemble performance with it. The effectiveness of the method is evaluated on a suite of 20 benchmark classification problems. The experimental results show that the performance of this ensemble method is better or competitive with respect to the existing popular methods.

Impulsive Control of Satellite Formation Flying using Orbital Period Difference

AbstractThis paper is mainly concerned with impulsive control of satellite formation flying using orbital period difference. Gauss's Variational Equation is used as a main equation and corresponding six orbital elements represent satellite status. Schaub and Alfriend's three-impulse algorithm constitutes a basic algorithm of this paper. In three-impulse algorithm, required impulses are determined by orbit element difference between current and desired orbit. Among orbit element difference, mean anomaly difference is an only time-varying term, and it comes from orbital period difference. In this paper, we analytically derive an impulse time which minimizes required impulse magnitude using orbital period difference, based on three-impulse algorithm. In addition, considering a case when proposed delayed impulse maneuver is not useful, alternative impulse maneuver is suggested. Finally, simulation studies are presented with artificial mission examples.

On Convergence of Stratification Algorithms for Skewed Populations

For stratifying skewed populations, the Lavallee-Hidiroglou(LH) algorithm is often considered to have a take-all stratum with the largest units and some take-some strata with the middle-size and small units. Related to its iterative nature have been reported some numerical difficulties such as the dependency of the ultimate stratum boundaries to a choice of initial boundaries and the slow convergence to locally-optimum boundaries. The geometric stratification has been recently proposed to provide initial boundaries that can avoid such numerical difficulties in implementing the LH algorithm. Since the geometric stratification does not pursuit the optimization but the equalization of the stratum CVs, the corresponding stratum boundaries may not be (near) optimal. This paper revisits these issues concerning convergence and near-optimality of optimal stratification algorithms using artificial numerical examples. We also discuss the formation of the strata and the sample allocation under the optimization process and some aspects related to discontinuity arisen from the finiteness of both population and sample as well.

A case study in selecting optimal number of trials in Bayesian decision making

This educational paper presents an illustration of choosing the optimal sample size within the framework of Bayesian Decision Theory. Using a somewhat artificial but entertaining example (electing an optimal number of dates for a marriage decision), it provides a tutorial for the challenging problem of decision making and walks the reader through various steps needed to be accomplished: formalizing the loss function, choosing priors for the parameters of interest, and computing the posterior expected loss for either of the two possible actions (to marry or not). Finally the optimal sample size (number of dates) is selected as a minimizer for the Bayes risk, evaluated (via simulations) under the assumption that the action with smallest posterior expected loss would be taken.

On the modelling and estimation of attribute rankings with ties in the Thurstonian framework

A Thurstonian type approach is applied to modelling ranking data with ties. It uses a non-totally differentiable discriminational process instead of the conventional totally differential one to relate the observed rankings and the underlying subjective values. A Monte Carlo expectation-maximization algorithm is proposed to find the maximum likelihood estimates together with the standard errors of the parameters. The approach is examined numerically by means of an artificial example and a simulation study and is applied to a study of attribute assessment.

Deblurring Poissonian images by split Bregman techniques

The restoration of blurred images corrupted by Poisson noise is an important task in various applications such as astronomical imaging, electronic microscopy, single particle emission computed tomography (SPECT) and positron emission tomography (PET). In this paper, we focus on solving this task by minimizing an energy functional consisting of the I-divergence as similarity term and the TV regularization term. Our minimizing algorithm uses alternating split Bregman techniques (alternating direction method of multipliers) which can be reinterpreted as Douglas-Rachford splitting applied to the dual problem. In contrast to recently developed iterative algorithms, our algorithm contains no inner iterations and produces nonnegative images. The high efficiency of our algorithm in comparison to other recently developed algorithms to minimize the same functional is demonstrated by artificial and real-world numerical examples.

Semi-supervised clustering algorithm for community structure detection in complex networks

Discovering a community structure is fundamental for uncovering the links between structure and function in complex networks. In this paper, we discuss an equivalence of the objective functions of the symmetric nonnegative matrix factorization (SNMF) and the maximum optimization of modularity density. Based on this equivalence, we develop a new algorithm, named the so-called SNMF-SS, by combining SNMF and a semi-supervised clustering approach. Previous NMF-based algorithms often suffer from the restriction of measuring network topology from only one perspective, but our algorithm uses a semi-supervised mechanism to get rid of the restriction. The algorithm is illustrated and compared with spectral clustering and NMF by using artificial examples and other classic real world networks. Experimental results show the significance of the proposed approach, particularly, in the cases when community structure is obscure.

The Effect of Spectral Pre-Treatments on Interpretation

different horizontal baselines have been added to the three spectra, and a different multiplicative scaling has been applied to each one. Now both peaks vary in height, because of the effect of the different scaling, and the interpretation is much less clear. this, unfortunately, is the typical situation with NIR spectra. the usual remedy for this problem is to apply a pre-treatment designed to correct for scatter effects. Since the transformation that converted the spectra of Figure 1 into those of Figure 2 was a baseline shift and a multiplicative scaling, one might hope that either the SNV or MSC pretreatments, both of which shift and scale the spectra, might undo these idealised scatter effects. Figures 3 and 4 show the results of applying SNV and MSC, respectively. the effects of the two treatments are, as is often but not always the case, very similar. this common effect, though, is not the desired one. After pre-treatment it is the first peak, which was constant in the original spectra, that shows variation, and the second peak, which originally varied, that is now almost constant. the obvious interpretation from either of Figures 3 or 4 would be incorrect, assigning the wrong peak to the analyte. I t is common practice in NIR calibration to apply pre-treatments designed to correct for the scatter effects usually seen in absorbance data. these pretreatments can interfere with interpretation of the spectra. this is illustrated here with the aid of a rather extreme artificial example.

Determination Of Spatial Grain Size Distribution Of A Sintered Metal

The determination of the spatial grain size distribution of a sintered metal from the size distribution estimated from a sample obtained in the section plane is a stereological problem. This problem is discussed with reference to homothetic particles (cubes of two different sizes) and to a system of three types of grains (fine and coarse cubes and coarse triangular prism). Two models are developed to solve the problem, one taking into account the size of the grains and section profiles only and one that includes shape considerations. The models are tested with simple and artificial examples, as well as with simulated data.

An adaptive algorithm for estimating inclusion probabilities and performing the Horvitz–Thompson criterion in complex designs

An algorithm for estimating inclusion probabilities and applying the Horvitz–Thompson criterion is considered for complex sampling designs, when the computation of the actual inclusion probabilities is prohibitive. The inclusion probabilities are estimated by means of independent replications of the sampling scheme. In turn, the number of replications is determined on the basis of the stability of the resulting estimates as well as on the basis of their precision, checked by means of the Bennet inequality. The number of replications is adaptively increased until a suitable level of precision is reached in a sustainable computational time. Details on the FORTRAN routines adopted for implementing the algorithm are given. The procedure is checked using three artificial examples.

Perturbation Selection and Local Influence Analysis for Nonlinear Structural Equation Model

Local influence analysis is an important statistical method for studying the sensitivity of a proposed model to model inputs. One of its important issues is related to the appropriate choice of a perturbation vector. In this paper, we develop a general method to select an appropriate perturbation vector and a second-order local influence measure to address this issue in the context of latent variable models. An application to nonlinear structural equation models is considered. Six perturbation schemes are investigated, including three schemes under which simultaneous perturbations are made on components of latent vectors to assess the influence of these components and pinpoint the influential ones. The proposed procedure is illustrated by artificial examples and a simulation study as well as a real example.

Density-Weighted Fuzzy c-Means Clustering

In this short paper, a unified framework for performing density-weighted fuzzy c-means (FCM) clustering of feature and relational datasets is presented. The proposed approach consists of reducing the original dataset to a smaller one, assigning each selected datum a weight reflecting the number of nearby data, clustering the weighted reduced dataset using a weighted version of the feature or relational data FCM algorithm, and if desired, extending the reduced data results back to the original dataset. Several methods are given for each of the tasks of data subset selection, weight assignment, and extension of the weighted clustering results. The newly proposed weighted version of the non-Euclidean relational FCM algorithm is proved to produce the identical results as its feature data analog for a certain type of relational data. Artificial and real data examples are used to demonstrate and contrast various instances of this general approach.

Diagnosing Multivariate Outliers Detected by Robust Estimators

We propose a number of diagnostic methods that can be used whenever multiple outliers are identified by robust estimates for multivariate location and scatter. Their main purpose is visualization of the multivariate data to help determine whether the detected outliers (a) form separate clusters or (b) are isolated or randomly scattered (such as heavy tails compared with Gaussian). We make use of Mahalanobis distances and linear projections, to check for separation and to reveal additional aspects of the data structure. Several real data examples are analyzed, and artificial examples are used to illustrate the diagnostic power of the proposed plots.Code to perform the diagnostics, datasets used as examples in the article and documention are available in the online supplements.

Optimal Solutions for Sparse Principal Component Analysis

Given a sample covariance matrix, we examine the problem of maximizing the variance explained by a linear combination of the input variables while constraining the number of nonzero coefficients in this combination. This is known as sparse principal component analysis and has a wide array of applications in machine learning and engineering. We formulate a new semidefinite relaxation to this problem and derive a greedy algorithm that computes a full set of good solutions for all target numbers of non zero coefficients, with total complexity O(n3), where n is the number of variables. We then use the same relaxation to derive sufficient conditions for global optimality of a solution, which can be tested in O(n3), per pattern. We discuss applications in subset selection and sparse recovery and show on artificial examples and biological data that our algorithm does provide globally optimal solutions in many cases.