A study of cluster analysis techniques and their applications

This thesis seeks to describe the development of an inexpensive and efficient clustering technique for multivariate data analysis. The technique starts from a multivariate data matrix and ends with graphical representation of the data and pattern recognition discriminant function. The technique also results in distances frequency distribution that might be useful in detecting clustering in the data or for the estimation of parameters useful in the discrimination between the different populations in the data. The technique can also be used in feature selection. The technique is essentially for the discovery of data structure by revealing the component parts of the data. lhe thesis offers three distinct contributions for cluster analysis and pattern recognition techniques. The first contribution is the introduction of transformation function in the technique of nonlinear mapping. The second contribution is the us~ of distances frequency distribution instead of distances time-sequence in nonlinear mapping, The third contribution is the formulation of a new generalised and normalised error function together with its optimal step size formula for gradient method minimisation. The thesis consists of five chapters. The first chapter is the introduction. The second chapter describes multidimensional scaling as an origin of nonlinear mapping technique. The third chapter describes the first developing step in the technique of nonlinear mapping that is the introduction of "transformation function". The fourth chapter describes the second developing step of the nonlinear mapping technique. This is the use of distances frequency distribution instead of distances time-sequence. The chapter also includes the new generalised and normalised error function formulation. Finally, the fifth chapter, the conclusion, evaluates all developments and proposes a new program. for cluster analysis and pattern recognition by integrating all the new features

A PLL control for self-tuning of parallel wireless power transfer receivers utilizing switch-mode gyrator emulated inductors

In multiple receivers wireless power transfer (WPT) systems, it is preferable to retune the resonant frequency of every receiver to the transmitter operating frequency in front of frequency mismatches. This paper discusses a proposal for electronic tuning for WPT receivers by means of a variable active switch-mode inductance. The proposed method benefits from the gyrator concept to emulate a variable inductance. Instead of the conventional approach of linear amplifier based implementation of a gyrator, a switch-mode gyrator circuit is exploited for more efficient operation. Additionally, a PLL-like control is presented to enable self-tuning for the receiver resonant tank. Furthermore, a design-space characterization for the system dynamic behavior has been discussed to show the control robustness and the instabilities (including slow-scale and fast-scale chaotic instabilities) it may undergo.Peer ReviewedPostprint (published version

Eikonal Approximation to 5D Wave Equations as Geodesic Motion in a Curved 4D Spacetime

We first derive the relation between the eikonal approximation to the Maxwell wave equations in an inhomogeneous anisotropic medium and geodesic motion in a three dimensional Riemannian manifold using a method which identifies the symplectic structure of the corresponding mechanics. We then apply an analogous method to the five dimensional generalization of Maxwell theory required by the gauge invariance of Stueckelberg's covariant classical and quantum dynamics to demonstrate, in the eikonal approximation, the existence of geodesic motion for the flow of mass in a four dimensional pseudo-Riemannian manifold. These results provide a foundation for the geometrical optics of the five dimensional radiation theory and establish a model in which there is mass flow along geodesics. Finally we discuss the case of relativistic quantum theory in an anisotropic medium as well. In this case the eikonal approximation to the relativistic quantum mechanical current coincides with the geodesic flow governed by the pseudo-Riemannian metric obtained from the eikonal approximation to solutions of the Stueckelberg-Schr\"odinger equation. This construction provides a model for an underlying quantum mechanical structure for classical dynamical motion along geodesics on a pseudo-Riemannian manifold. The locally symplectic structure which emerges is that of Stueckelberg's covariant mechanics on this manifold.Comment: TeX file. 17 pages. Rewritten for clarit

Comparison of the spine kinematics by defining lumbar as single and multi-segmental in completing critical daily task

The change of the spinal curvature in completing a variety of daily tasks is essential to independent living. There is still a lack of studies highlighting the lumbar segmental contribution during sit-to-stand (STS) and stand-to-flexion (STF) usingnon-invasive study. The purpose of this study is to compare the spine kinematics by defining lumbar as a single and multi-segmental during continuous daily motion in healthy Asian adults using a non-invasive approach. During STS, most subjects implementedkyphotic lumbar curve during the early stage of motion which revealed poor posture implementation and significant differences in the lumbar kinematics which were only noticeable at specific phases between both approaches. A significant difference in multi-segmental behaviour was observed only at the end of the motion. All three segments displayed different time responses during the transition from kyphotic to lordotic curve. Passive/delayed behavior within the lower lumbar segment was observed between 0-50% of motion completion. During STF, statistically significant differences were found between assuming lumbar as a single and multi-segment in all phases. This in vitro study identified characteristic motion patterns in the lumbar spine during daily motions. The results provided a clear description of the healthy spinal condition of adults and may serve to identify specific multi-segmental contribution

On the equivalence between the Scheduled Relaxation Jacobi method and Richardson's non-stationary method

The Scheduled Relaxation Jacobi (SRJ) method is an extension of the classical Jacobi iterative method to solve linear systems of equations (Au=b) associated with elliptic problems. It inherits its robustness and accelerates its convergence rate computing a set of P relaxation factors that result from a minimization problem. In a typical SRJ scheme, the former set of factors is employed in cycles of M consecutive iterations until a prescribed tolerance is reached. We present the analytic form for the optimal set of relaxation factors for the case in which all of them are strictly different, and find that the resulting algorithm is equivalent to a non-stationary generalized Richardson's method where the matrix of the system of equations is preconditioned multiplying it by D=diag(A). Our method to estimate the weights has the advantage that the explicit computation of the maximum and minimum eigenvalues of the matrix A (or the corresponding iteration matrix of the underlying weighted Jacobi scheme) is replaced by the (much easier) calculation of the maximum and minimum frequencies derived from a von Neumann analysis of the continuous elliptic operator. This set of weights is also the optimal one for the general problem, resulting in the fastest convergence of all possible SRJ schemes for a given grid structure. The amplification factor of the method can be found analytically and allows for the exact estimation of the number of iterations needed to achieve a desired tolerance. We also show that with the set of weights computed for the optimal SRJ scheme for a fixed cycle size it is possible to estimate numerically the optimal value of the parameter ω in the Successive Overrelaxation (SOR) method in some cases. Finally, we demonstrate with practical examples that our method also works very well for Poisson-like problems in which a high-order discretization of the Laplacian operator is employed (e.g., a 9- or 17-points discretization). This is of interest since the former discretizations do not yield consistently ordered A matrices and, hence, the theory of Young cannot be used to predict the optimal value of the SOR parameter. Furthermore, the optimal SRJ schemes deduced here are advantageous over existing SOR implementations for high-order discretizations of the Laplacian operator in as much as they do not need to resort to multi-coloring schemes for their parallel implementation

Infrared thermal imaging as an innovative approach for early detection infestation of stored product insects in certain stored grains

Grains of field crops, such as wheat, maize, faba bean and white bean, are considered strategic food for humanity worldwide and Egypt. Unfortunately, percent losses of grains quantity may reach to 15-30%, as a result of stored product insect damage, and the losses increased dramatically in the last years, as an outcome of quickly productions of these pests. Experiments were conducted on infrared thermal imaging that demonstrate early detection of infestation by stored product insects in wheat, maize, broad bean, white bean and bean grains. The imaging is dependent on subtle significant differences in temperature between infested and healthy grains. Because the thermal imaging data are digital, computer programs can be used to analysis differences in temperature and mining figures explained for that. Results revealed that the use of thermal imaging offers an alternative method to detect an insect infestation. Data concluded that thermal imaging has the potential to identify whether the grains of crops that tested are infested or not, but is less effective in identifying which developmental stage is present. Moreover, it could apply this technique easily on a large scale in silos, storage, mills and granaries without negative impact on quality of stored grains