Dynamic non-linear system modelling using wavelet-based soft computing techniques

The enormous number of complex systems results in the necessity of high-level and cost-efficient modelling structures for the operators and system designers. Model-based approaches offer a very challenging way to integrate a priori knowledge into the procedure. Soft computing based models in particular, can successfully be applied in cases of highly nonlinear problems. A further reason for dealing with so called soft computational model based techniques is that in real-world cases, many times only partial, uncertain and/or inaccurate data is available. Wavelet-Based soft computing techniques are considered, as one of the latest trends in system identification/modelling. This thesis provides a comprehensive synopsis of the main wavelet-based approaches to model the non-linear dynamical systems in real world problems in conjunction with possible twists and novelties aiming for more accurate and less complex modelling structure. Initially, an on-line structure and parameter design has been considered in an adaptive Neuro- Fuzzy (NF) scheme. The problem of redundant membership functions and consequently fuzzy rules is circumvented by applying an adaptive structure. The growth of a special type of Fungus (Monascus ruber van Tieghem) is examined against several other approaches for further justification of the proposed methodology. By extending the line of research, two Morlet Wavelet Neural Network (WNN) structures have been introduced. Increasing the accuracy and decreasing the computational cost are both the primary targets of proposed novelties. Modifying the synoptic weights by replacing them with Linear Combination Weights (LCW) and also imposing a Hybrid Learning Algorithm (HLA) comprising of Gradient Descent (GD) and Recursive Least Square (RLS), are the tools utilised for the above challenges. These two models differ from the point of view of structure while they share the same HLA scheme. The second approach contains an additional Multiplication layer, plus its hidden layer contains several sub-WNNs for each input dimension. The practical superiority of these extensions is demonstrated by simulation and experimental results on real non-linear dynamic system; Listeria Monocytogenes survival curves in Ultra-High Temperature (UHT) whole milk, and consolidated with comprehensive comparison with other suggested schemes. At the next stage, the extended clustering-based fuzzy version of the proposed WNN schemes, is presented as the ultimate structure in this thesis. The proposed Fuzzy Wavelet Neural network (FWNN) benefitted from Gaussian Mixture Models (GMMs) clustering feature, updated by a modified Expectation-Maximization (EM) algorithm. One of the main aims of this thesis is to illustrate how the GMM-EM scheme could be used not only for detecting useful knowledge from the data by building accurate regression, but also for the identification of complex systems. The structure of FWNN is based on the basis of fuzzy rules including wavelet functions in the consequent parts of rules. In order to improve the function approximation accuracy and general capability of the FWNN system, an efficient hybrid learning approach is used to adjust the parameters of dilation, translation, weights, and membership. Extended Kalman Filter (EKF) is employed for wavelet parameters adjustment together with Weighted Least Square (WLS) which is dedicated for the Linear Combination Weights fine-tuning. The results of a real-world application of Short Time Load Forecasting (STLF) further re-enforced the plausibility of the above technique

Economic Growth and Income Inequality Relationship: Role of Credit Market Imperfection

This paper examines the empirical relationship between economic growth and income inequality both at aggregate and regional level using more comparable data set for 69 developing countries over the period 1965-2003. The study identifies credit market imperfection in low-income developing countries as the likely reason for a strong negative relationship between income inequality and economic growth. While in short run the relationship between growth and income inequality might be positive but over time more income inequalities reduces economic growth. Moreover, this paper finds evidence that more physical and human capital investment, openness to trade and higher government spending have statistically significant impact on enhancing economic growth and reducing inequality.Economic Growth, Income Inequality, Poverty, Credit Market Imperfection, Trade Openness

On the phase-space structure of the Milky Way dark-matter halo

We analyse a high resolution simulation of the formation of a cluster's dark-matter halo in a $\Lambda$CDM cosmology (Springel et al. 2001). The resolution achieved allows us to map the phase-space structure in detail, and characterize its evolution and degree of lumpiness. Scaling down the cluster halo to a Milky-Way size halo, we probe the substructure expected in the solar neighbourhood. Here we specifically address the relevance of such substructure for direct detection experiments aimed at determining the nature of dark-matter.Comment: 4 pages, 5 figures, uses dunk2001_asp.sty, to appear in "The Dynamics, Structure and History of Galaxies: A Workshop in Honour of Prof. Ken Freeman", (eds) G. S. Da Costa & E. M. Sadler, ASP Conf Serie

Phase Retrieval for Sparse Signals: Uniqueness Conditions

In a variety of fields, in particular those involving imaging and optics, we often measure signals whose phase is missing or has been irremediably distorted. Phase retrieval attempts the recovery of the phase information of a signal from the magnitude of its Fourier transform to enable the reconstruction of the original signal. A fundamental question then is: "Under which conditions can we uniquely recover the signal of interest from its measured magnitudes?" In this paper, we assume the measured signal to be sparse. This is a natural assumption in many applications, such as X-ray crystallography, speckle imaging and blind channel estimation. In this work, we derive a sufficient condition for the uniqueness of the solution of the phase retrieval (PR) problem for both discrete and continuous domains, and for one and multi-dimensional domains. More precisely, we show that there is a strong connection between PR and the turnpike problem, a classic combinatorial problem. We also prove that the existence of collisions in the autocorrelation function of the signal may preclude the uniqueness of the solution of PR. Then, assuming the absence of collisions, we prove that the solution is almost surely unique on 1-dimensional domains. Finally, we extend this result to multi-dimensional signals by solving a set of 1-dimensional problems. We show that the solution of the multi-dimensional problem is unique when the autocorrelation function has no collisions, significantly improving upon a previously known result.Comment: submitted to IEEE TI

Predictive modeling in food mycology using adaptive neuro-fuzzy systems

Fungal growth leads to spoilage of food and animal feeds and to formation of mycotoxins and potentially allergenic spores. There is a growing interest in predictive modeling microbial growth as an alternative to time consuming traditional, microbiological enumeration techniques. Several statistical models have been accounted to describe the growth of different micro-organisms. However neural networks, as highly nonlinear approximator scheme, have the potential of modeling some complex, phenomena better than the others. The application of adaptive neuro-fuzzy systems in predictive microbiology is presented in this paper. This technique is used to build up a model of the joint effect of water-activity, pH level and temperature to predict the maximum specific growth rate of the Ascomycetous Fungus Monascus Ruber. The proposed scheme is compared against standard neural network approaches. Neuro-fuzzy systems offer an alternative and powerful technique to model microbial kinetic parameters and could thus become an efficient tool in predictive mycology

Rates of Heat and Mass Transfers for a Non Darcy Porous Medium Subject to Double Dispersion and Saturated by a Nanofluid

This work aims to quantify the rates of heat and mass transfers occurred between a vertical and nonisothermal plate immersed into a non-Darcy porous medium and saturated with a weak nanofluid. Double dispersion is assumed and natural convection is the exchange mode. The similarity transformations are involved and the governing system of nonlinear partial differential equations is converted into a set of nonlinear ordinary differential equations via similarities. Results are displayed graphically to illustrate the influence of delta and xi on the velocity, the temperature and concentration of the species profiles. For a weak nanofluid, the rate of mass transfer is affected strongly by the double dispersion while the rate of heat transfer coefficient is less sensitive to it

Enhancement of chemotherapy using oncolytic virotherapy: Mathematical and optimal control analysis

Oncolytic virotherapy (OV) has been emerging as a promising novel cancer treatment that may be further combined with the existing therapeutic modalities to enhance their effects. To investigate how OV could enhance chemotherapy, we propose an ODE based model describing the interactions between tumour cells, the immune response, and a treatment combination with chemotherapy and oncolytic viruses. Stability analysis of the model with constant chemotherapy treatment rates shows that without any form of treatment, a tumour would grow to its maximum size. It also demonstrates that chemotherapy alone is capable of clearing tumour cells provided that the drug efficacy is greater than the intrinsic tumour growth rate. Furthermore, OV alone may not be able to clear tumour cells from body tissue but would rather enhance chemotherapy if viruses with high viral potency are used. To assess the combined effect of OV and chemotherapy we use the forward sensitivity index to perform a sensitivity analysis, with respect to chemotherapy key parameters, of the virus basic reproductive number and the tumour endemic equilibrium. The results from this sensitivity analysis indicate the existence of a critical dose of chemotherapy above which no further significant reduction in the tumour population can be observed. Numerical simulations show that a successful combinational therapy of the chemotherapeutic drugs and viruses depends mostly on the virus burst size, infection rate, and the amount of drugs supplied. Optimal control analysis was performed, by means of Pontryagin's principle, to further refine predictions of the model with constant treatment rates by accounting for the treatment costs and sides effects.Comment: This is a preprint of a paper whose final and definite form is with 'Mathematical Biosciences and Engineering', ISSN 1551-0018 (print), ISSN 1547-1063 (online), available at [http://www.aimsciences.org/journal/1551-0018]. Submitted 27-March-2018; revised 04-July-2018; accepted for publication 10-July-201