Application of block Cayley-Hamilton theorem to generalized inversion

In this paper we propose two algorithms for computation of the outer inverse with prescribed range and null space and the Drazin inverse of block matrix. The proposed algorithms are based on the extension of the Leverrier-Faddeev algorithm and the block Cayley-Hamilton theorem. These algorithms are implemented using symbolic and functional possibilities of the packages {\it Mathematica} and using numerical possibilities of {\it Matlab}

Complex-valued Adaptive Digital Signal Enhancement For Applications In Wireless Communication Systems

In recent decades, the wireless communication industry has attracted a great deal of research efforts to satisfy rigorous performance requirements and preserve high spectral efficiency. Along with this trend, I/Q modulation is frequently applied in modern wireless communications to develop high performance and high data rate systems. This has necessitated the need for applying efficient complex-valued signal processing techniques to highly-integrated, multi-standard receiver devices. In this dissertation, novel techniques for complex-valued digital signal enhancement are presented and analyzed for various applications in wireless communications. The first technique is a unified block processing approach to generate the complex-valued conjugate gradient Least Mean Square (LMS) techniques with optimal adaptations. The proposed algorithms exploit the concept of the complex conjugate gradients to find the orthogonal directions for updating the adaptive filter coefficients at each iteration. Along each orthogonal direction, the presented algorithms employ the complex Taylor series expansion to calculate time-varying convergence factors tailored for the adaptive filter coefficients. The performance of the developed technique is tested in the applications of channel estimation, channel equalization, and adaptive array beamforming. Comparing with the state of the art methods, the proposed techniques demonstrate improved performance and exhibit desirable characteristics for practical use. The second complex-valued signal processing technique is a novel Optimal Block Adaptive algorithm based on Circularity, OBA-C. The proposed OBA-C method compensates for a complex imbalanced signal by restoring its circularity. In addition, by utilizing the complex iv Taylor series expansion, the OBA-C method optimally updates the adaptive filter coefficients at each iteration. This algorithm can be applied to mitigate the frequency-dependent I/Q mismatch effects in analog front-end. Simulation results indicate that comparing with the existing methods, OBA-C exhibits superior convergence speed while maintaining excellent accuracy. The third technique is regarding interference rejection in communication systems. The research on both LMS and Independent Component Analysis (ICA) based techniques continues to receive significant attention in the area of interference cancellation. The performance of the LMS and ICA based approaches is studied for signals with different probabilistic distributions. Our research indicates that the ICA-based approach works better for super-Gaussian signals, while the LMS-based method is preferable for sub-Gaussian signals. Therefore, an appropriate choice of interference suppression algorithms can be made to satisfy the ever-increasing demand for better performance in modern receiver design

Multiple System Modelling and Analysis of Physiological and Brain Activity and Performance at Rest and During Exercise

One of the current interests of exercise physiologists is to understand the nature and control of fatigue related to physical activity to optimise athletic performance. Therefore, this research focuses on the mathematical modelling and analysis of the energy system pathways and the system control mechanisms to investigate the various human metabolic processes involved both at rest and during exercise. The first case study showed that the PCr utilisation was the highest energy contributor during sprint running, and the rate of ATP production for each anaerobic subsystem was similar for each athlete. The second study showed that the energy expenditure derived from the aerobic and anaerobic processes for different types of pacing were significantly different. The third study demonstrated the presence of the control mechanisms, and their characteristics as well as complexity differed significantly for any physiological organ system. The fourth study showed that the control mechanisms manifest themselves in specific ranges of frequency bands, and these influence athletic performance. The final study demonstrated a significant difference in both reaction time and accuracy of the responses to visual cues between the control and exercise-involved cognitive trials. Moreover, the difference in the EEG power ratio at specific regions of the brain; the difference in the ERP components’ amplitudes and latencies; and the difference in entropy of the EEG signals represented the physiological factors in explaining the poor cognitive performance of the participants following an exhaustive exercise bout. Therefore, by using mathematical modelling and analysis of the energy system pathways and the system control mechanisms responsible for homeostasis, this research has expanded the knowledge how performance is regulated during physical activity and together with the support of the existing biological control theories to explain the development of fatigue during physical activity

Near real-time monitoring of buried oil pipeline right-of-way for third-party incursion

Many security systems employing different methods have been proposed to protect buried oil pipelines transporting petroleum products from the well head via the refinery to: depots and other receiving stations. Currently there is a security gap in the monitoring of these buried pipelines in real time and in keeping them protected from third party interference. This thesis addresses the problem of monitoring these systems by developing an automated image analysis system with the aid of a low-cost multisensory Unmanned Aerial Vehicle (UAV) for monitoring of buried pipeline right-of-way (ROW). The method used in this research is based on the identification of threat objects of interest from the video frame sequences of the pipeline right-of-way acquired by the UAV. This is achieved by training the system to recognise objects of interest using trained correlation filters. To determine the geographical location of detected objects, the Video frame sequences captured by the UAV platform were ortho-rectified to form ortho-images which were then mosaicked to form a seamless Digital Surface Model (DSM) covering the test area using a photogrammetry model. The DSM formed from the mosaicking of ortho-images is then emerged with a digital globe for geo-referencing of detected objects. Experiments were carried out on a test field located in United Kingdom and Nigeria, where video and telemetry data were collected, then processed using the techniques created in this research. The results demonstrated that the developed correlation filter was able to detect objects of interest despite the distortions that come with the object image, due to the fact that the expected distortion was compensated for using the training images. When compared with the 6 control points in the digital globe the accuracy of the two-dimension DSM gave a misalignment error of between 2 and 3 metres

Multiple system modelling and analysis of physiological and brain activity and performance at rest and during exercise

One of the current interests of exercise physiologists is to understand the nature and control of fatigue related to physical activity to optimise athletic performance. Therefore, this research focuses on the mathematical modelling and analysis of the energy system pathways and the system control mechanisms to investigate the various human metabolic processes involved both at rest and during exercise. The first case study showed that the PCr utilisation was the highest energy contributor during sprint running, and the rate of ATP production for each anaerobic subsystem was similar for each athlete. The second study showed that the energy expenditure derived from the aerobic and anaerobic processes for different types of pacing were significantly different. The third study demonstrated the presence of the control mechanisms, and their characteristics as well as complexity differed significantly for any physiological organ system. The fourth study showed that the control mechanisms manifest themselves in specific ranges of frequency bands, and these influence athletic performance. The final study demonstrated a significant difference in both reaction time and accuracy of the responses to visual cues between the control and exercise-involved cognitive trials. Moreover, the difference in the EEG power ratio at specific regions of the brain; the difference in the ERP components’ amplitudes and latencies; and the difference in entropy of the EEG signals represented the physiological factors in explaining the poor cognitive performance of the participants following an exhaustive exercise bout. Therefore, by using mathematical modelling and analysis of the energy system pathways and the system control mechanisms responsible for homeostasis, this research has expanded the knowledge how performance is regulated during physical activity and together with the support of the existing biological control theories to explain the development of fatigue during physical activity.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Recurrent neural networks for solving matrix algebra problems

The aim of this dissertation is the application of recurrent neural networks (RNNs) to solving some problems from a matrix algebra with particular reference to the computations of the generalized inverses as well as solving the matrix equations of constant (timeinvariant) matrices. We examine the ability to exploit the correlation between the dynamic state equations of recurrent neural networks for computing generalized inverses and integral representations of these generalized inverses. Recurrent neural networks are composed of independent parts (sub-networks). These sub-networks can work simultaneously, so parallel and distributed processing can be accomplished. In this way, the computational advantages over the existing sequential algorithms can be attained in real-time applications. We investigate and exploit an analogy between the scaled hyperpower family (SHPI family) of iterative methods for computing the matrix inverse and the discretization of Zhang Neural Network (ZNN) models. A class of ZNN models corresponding to the family of hyperpower iterative methods for computing the generalized inverses on the basis of the discovered analogy is defined. The Matlab Simulink implementation of the introduced ZNN models is described in the case of scaled hyperpower methods of the order 2 and 3. We present the Matlab Simulink model of a hybrid recursive neural implicit dynamics and give a simulation and comparison to the existing Zhang dynamics for real-time matrix inversion. Simulation results confirm a superior convergence of the hybrid model compared to Zhang model

Distance measures and whitening procedures for high dimensional data

The need to effectively analyse high dimensional data is increasingly crucial to many fields as data collection and storage capabilities continue to grow. Working with high dimensional data is fraught with difficulties, making many data analysis methods inadvisable, unstable or entirely unavailable. The Mahalanobis distance and data whitening are two methods that are integral to multivariate data analysis. These methods are reliant on the inverse of the covariance matrix, which is often non-existent or unstable in high dimensions. The methods that are currently used to circumvent singularity in the covariance matrix often impose structural assumptions on the data, which are not always appropriate or known. In this thesis, three novel methods are proposed. Two of these methods are distance measures which measure the proximity of a point x to a set of points X. The simplicial distances find the average volume of all k-dimensional simplices between x and vertices of X. The minimal-variance distances aim to minimize the variance of the distances produced, while adhering to a constraint ensuring similar behaviour to the Mahalanobis distance. Finally, the minimal-variance whitening method is detailed. This is a method of data whitening, and is constructed by minimizing the total variation of the transformed data subject to a constraint. All of these novel methods are shown to behave similarly to the Mahalanobis distances and data whitening methods that are used for full-rank data. Furthermore, unlike the methods that rely on the inverse covariance matrix, these new methods are well-defined for degenerate data and do not impose structural assumptions. This thesis explores the aims, constructions and limitations of these new methods, and offers many empirical examples and comparisons of their performances when used with high dimensional data