Conformally Mapped Polynomial Chaos Expansions for Maxwell's Source Problem with Random Input Data

Generalized Polynomial Chaos (gPC) expansions are well established for forward uncertainty propagation in many application areas. Although the associated computational effort may be reduced in comparison to Monte Carlo techniques, for instance, further convergence acceleration may be important to tackle problems with high parametric sensitivities. In this work, we propose the use of conformal maps to construct a transformed gPC basis, in order to enhance the convergence order. The proposed basis still features orthogonality properties and hence, facilitates the computation of many statistical properties such as sensitivities and moments. The corresponding surrogate models are computed by pseudo-spectral projection using mapped quadrature rules, which leads to an improved cost accuracy ratio. We apply the methodology to Maxwell's source problem with random input data. In particular, numerical results for a parametric finite element model of an optical grating coupler are given

The Optimisation of Elementary and Integrative Content-Based Image Retrieval Techniques

Image retrieval plays a major role in many image processing applications. However, a number of factors (e.g. rotation, non-uniform illumination, noise and lack of spatial information) can disrupt the outputs of image retrieval systems such that they cannot produce the desired results. In recent years, many researchers have introduced different approaches to overcome this problem. Colour-based CBIR (content-based image retrieval) and shape-based CBIR were the most commonly used techniques for obtaining image signatures. Although the colour histogram and shape descriptor have produced satisfactory results for certain applications, they still suffer many theoretical and practical problems. A prominent one among them is the well-known “curse of dimensionality “. In this research, a new Fuzzy Fusion-based Colour and Shape Signature (FFCSS) approach for integrating colour-only and shape-only features has been investigated to produce an effective image feature vector for database retrieval. The proposed technique is based on an optimised fuzzy colour scheme and robust shape descriptors. Experimental tests were carried out to check the behaviour of the FFCSS-based system, including sensitivity and robustness of the proposed signature of the sampled images, especially under varied conditions of, rotation, scaling, noise and light intensity. To further improve retrieval efficiency of the devised signature model, the target image repositories were clustered into several groups using the k-means clustering algorithm at system runtime, where the search begins at the centres of each cluster. The FFCSS-based approach has proven superior to other benchmarked classic CBIR methods, hence this research makes a substantial contribution towards corresponding theoretical and practical fronts

Efficient implementation of the nonequilibrium Green function method for electronic transport calculations

An efficient implementation of the nonequilibrium Green function (NEGF) method combined with the density functional theory (DFT) using localized pseudo-atomic orbitals (PAOs) is presented for electronic transport calculations of a system connected with two leads under a finite bias voltage. In the implementation, accurate and efficient methods are developed especially for evaluation of the density matrix and treatment of boundaries between the scattering region and the leads. Equilibrium and nonequilibrium contributions in the density matrix are evaluated with very high precision by a contour integration with a continued fraction representation of the Fermi-Dirac function and by a simple quadratureon the real axis with a small imaginary part, respectively. The Hartree potential is computed efficiently by a combination of the two dimensional fast Fourier transform (FFT) and a finite difference method, and the charge density near the boundaries is constructed with a careful treatment to avoid the spurious scattering at the boundaries. The efficiency of the implementation is demonstrated by rapid convergence properties of the density matrix. In addition, as an illustration, our method is applied for zigzag graphene nanoribbons, a Fe/MgO/Fe tunneling junction, and a LaMnO$_3/$SrMnO$_3$ superlattice, demonstrating its applicability to a wide variety of systems.Comment: 20 pages, 11 figure

Statistical region-based active contours for segmentation: an overview

International audienceIn this paper we propose a brief survey on geometric variational approaches and more precisely on statistical region-based active contours for medical image segmentation. In these approaches, image features are considered as random variables whose distribution may be either parametric, and belongs to the exponential family, or non-parametric estimated with a kernel density method. Statistical region-based terms are listed and reviewed showing that these terms can depict a wide spectrum of segmentation problems. A shape prior can also be incorporated to the previous statistical terms. A discussion of some optimization schemes available to solve the variational problem is also provided. Examples on real medical images are given to illustrate some of the given criteria

WavePacket: A Matlab package for numerical quantum dynamics. I: Closed quantum systems and discrete variable representations

WavePacket is an open-source program package for the numerical simulation of quantum-mechanical dynamics. It can be used to solve time-independent or time-dependent linear Schr\"odinger and Liouville-von Neumann-equations in one or more dimensions. Also coupled equations can be treated, which allows to simulate molecular quantum dynamics beyond the Born-Oppenheimer approximation. Optionally accounting for the interaction with external electric fields within the semiclassical dipole approximation, WavePacket can be used to simulate experiments involving tailored light pulses in photo-induced physics or chemistry.The graphical capabilities allow visualization of quantum dynamics 'on the fly', including Wigner phase space representations. Being easy to use and highly versatile, WavePacket is well suited for the teaching of quantum mechanics as well as for research projects in atomic, molecular and optical physics or in physical or theoretical chemistry.The present Part I deals with the description of closed quantum systems in terms of Schr\"odinger equations. The emphasis is on discrete variable representations for spatial discretization as well as various techniques for temporal discretization.The upcoming Part II will focus on open quantum systems and dimension reduction; it also describes the codes for optimal control of quantum dynamics.The present work introduces the MATLAB version of WavePacket 5.2.1 which is hosted at the Sourceforge platform, where extensive Wiki-documentation as well as worked-out demonstration examples can be found

A neuro-genetic hybrid approach to automatic identification of plant leaves

Plants are essential for the existence of most living things on this planet. Plants are used for providing food, shelter, and medicine. The ability to identify plants is very important for several applications, including conservation of endangered plant species, rehabilitation of lands after mining activities and differentiating crop plants from weeds. In recent times, many researchers have made attempts to develop automated plant species recognition systems. However, the current computer-based plants recognition systems have limitations as some plants are naturally complex, thus it is difficult to extract and represent their features. Further, natural differences of features within the same plant and similarities between plants of different species cause problems in classification. This thesis developed a novel hybrid intelligent system based on a neuro-genetic model for automatic recognition of plants using leaf image analysis based on novel approach of combining several image descriptors with Cellular Neural Networks (CNN), Genetic Algorithm (GA), and Probabilistic Neural Networks (PNN) to address classification challenges in plant computer-based plant species identification using the images of plant leaves. A GA-based feature selection module was developed to select the best of these leaf features. Particle Swam Optimization (PSO) and Principal Component Analysis (PCA) were also used sideways for comparison and to provide rigorous feature selection and analysis. Statistical analysis using ANOVA and correlation techniques confirmed the effectiveness of the GA-based and PSO-based techniques as there were no redundant features, since the subset of features selected by both techniques correlated well. The number of principal components (PC) from the past were selected by conventional method associated with PCA. However, in this study, GA was used to select a minimum number of PC from the original PC space. This reduced computational cost with respect to time and increased the accuracy of the classifier used. The algebraic nature of the GA’s fitness function ensures good performance of the GA. Furthermore, GA was also used to optimize the parameters of a CNN (CNN for image segmentation) and then uniquely combined with PNN to improve and stabilize the performance of the classification system. The CNN (being an ordinary differential equation (ODE)) was solved using Runge-Kutta 4th order algorithm in order to minimize descritisation errors associated with edge detection. This study involved the extraction of 112 features from the images of plant species found in the Flavia dataset (publically available) using MATLAB programming environment. These features include Zernike Moments (20 ZMs), Fourier Descriptors (21 FDs), Legendre Moments (20 LMs), Hu 7 Moments (7 Hu7Ms), Texture Properties (22 TP) , Geometrical Properties (10 GP), and Colour features (12 CF). With the use of GA, only 14 features were finally selected for optimal accuracy. The PNN was genetically optimized to ensure optimal accuracy since it is not the best practise to fix the tunning parameters for the PNN arbitrarily. Two separate GA algorithms were implemented to optimize the PNN, that is, the GA provided by MATLAB Optimization Toolbox (GA1) and a separately implemented GA (GA2). The best chromosome (PNN spread) for GA1 was 0.035 with associated classification accuracy of 91.3740% while a spread value of 0.06 was obtained from GA2 giving rise to improved classification accuracy of 92.62%. The PNN-based classifier used in this study was benchmarked against other classifiers such as Multi-layer perceptron (MLP), K Nearest Neigbhour (kNN), Naive Bayes Classifier (NBC), Radial Basis Function (RBF), Ensemble classifiers (Adaboost). The best candidate among these classifiers was the genetically optimized PNN. Some computational theoretic properties on PNN are also presented