An Overview of Schema Theory

The purpose of this paper is to give an introduction to the field of Schema Theory written by a mathematician and for mathematicians. In particular, we endeavor to to highlight areas of the field which might be of interest to a mathematician, to point out some related open problems, and to suggest some large-scale projects. Schema theory seeks to give a theoretical justification for the efficacy of the field of genetic algorithms, so readers who have studied genetic algorithms stand to gain the most from this paper. However, nothing beyond basic probability theory is assumed of the reader, and for this reason we write in a fairly informal style. Because the mathematics behind the theorems in schema theory is relatively elementary, we focus more on the motivation and philosophy. Many of these results have been proven elsewhere, so this paper is designed to serve a primarily expository role. We attempt to cast known results in a new light, which makes the suggested future directions natural. This involves devoting a substantial amount of time to the history of the field. We hope that this exposition will entice some mathematicians to do research in this area, that it will serve as a road map for researchers new to the field, and that it will help explain how schema theory developed. Furthermore, we hope that the results collected in this document will serve as a useful reference. Finally, as far as the author knows, the questions raised in the final section are new.Comment: 27 pages. Originally written in 2009 and hosted on my website, I've decided to put it on the arXiv as a more permanent home. The paper is primarily expository, so I don't really know where to submit it, but perhaps one day I will find an appropriate journa

Inverse Kinematic Analysis of Robot Manipulators

An important part of industrial robot manipulators is to achieve desired position and orientation of end effector or tool so as to complete the pre-specified task. To achieve the above stated goal one should have the sound knowledge of inverse kinematic problem. The problem of getting inverse kinematic solution has been on the outline of various researchers and is deliberated as thorough researched and mature problem. There are many fields of applications of robot manipulators to execute the given tasks such as material handling, pick-n-place, planetary and undersea explorations, space manipulation, and hazardous field etc. Moreover, medical field robotics catches applications in rehabilitation and surgery that involve kinematic, dynamic and control operations. Therefore, industrial robot manipulators are required to have proper knowledge of its joint variables as well as understanding of kinematic parameters. The motion of the end effector or manipulator is controlled by their joint actuator and this produces the required motion in each joints. Therefore, the controller should always supply an accurate value of joint variables analogous to the end effector position. Even though industrial robots are in the advanced stage, some of the basic problems in kinematics are still unsolved and constitute an active focus for research. Among these unsolved problems, the direct kinematics problem for parallel mechanism and inverse kinematics for serial chains constitute a decent share of research domain. The forward kinematics of robot manipulator is simpler problem and it has unique or closed form solution. The forward kinematics can be given by the conversion of joint space to Cartesian space of the manipulator. On the other hand inverse kinematics can be determined by the conversion of Cartesian space to joint space. The inverse kinematic of the robot manipulator does not provide the closed form solution. Hence, industrial manipulator can achieve a desired task or end effector position in more than one configuration. Therefore, to achieve exact solution of the joint variables has been the main concern to the researchers. A brief introduction of industrial robot manipulators, evolution and classification is presented. The basic configurations of robot manipulator are demonstrated and their benefits and drawbacks are deliberated along with the applications. The difficulties to solve forward and inverse kinematics of robot manipulator are discussed and solution of inverse kinematic is introduced through conventional methods. In order to accomplish the desired objective of the work and attain the solution of inverse kinematic problem an efficient study of the existing tools and techniques has been done. A review of literature survey and various tools used to solve inverse kinematic problem on different aspects is discussed. The various approaches of inverse kinematic solution is categorized in four sections namely structural analysis of mechanism, conventional approaches, intelligence or soft computing approaches and optimization based approaches. A portion of important and more significant literatures are thoroughly discussed and brief investigation is made on conclusions and gaps with respect to the inverse kinematic solution of industrial robot manipulators. Based on the survey of tools and techniques used for the kinematic analysis the broad objective of the present research work is presented as; to carry out the kinematic analyses of different configurations of industrial robot manipulators. The mathematical modelling of selected robot manipulator using existing tools and techniques has to be made for the comparative study of proposed method. On the other hand, development of new algorithm and their mathematical modelling for the solution of inverse kinematic problem has to be made for the analysis of quality and efficiency of the obtained solutions. Therefore, the study of appropriate tools and techniques used for the solution of inverse kinematic problems and comparison with proposed method is considered. Moreover, recommendation of the appropriate method for the solution of inverse kinematic problem is presented in the work. Apart from the forward kinematic analysis, the inverse kinematic analysis is quite complex, due to its non-linear formulations and having multiple solutions. There is no unique solution for the inverse kinematics thus necessitating application of appropriate predictive models from the soft computing domain. Artificial neural network (ANN) can be gainfully used to yield the desired results. Therefore, in the present work several models of artificial neural network (ANN) are used for the solution of the inverse kinematic problem. This model of ANN does not rely on higher mathematical formulations and are adept to solve NP-hard, non-linear and higher degree of polynomial equations. Although intelligent approaches are not new in this field but some selected models of ANN and their hybridization has been presented for the comparative evaluation of inverse kinematic. The hybridization scheme of ANN and an investigation has been made on accuracies of adopted algorithms. On the other hand, any Optimization algorithms which are capable of solving various multimodal functions can be implemented to solve the inverse kinematic problem. To overcome the problem of conventional tool and intelligent based method the optimization based approach can be implemented. In general, the optimization based approaches are more stable and often converge to the global solution. The major problem of ANN based approaches are its slow convergence and often stuck in local optimum point. Therefore, in present work different optimization based approaches are considered. The formulation of the objective function and associated constrained are discussed thoroughly. The comparison of all adopted algorithms on the basis of number of solutions, mathematical operations and computational time has been presented. The thesis concludes the summary with contributions and scope of the future research work

A Bio-inspired Distributed Control Architecture: Coupled Artificial Signalling Networks

This thesis studies the applicability of computational models inspired by the structure and dynamics of signalling networks to the control of complex control problems. In particular, this thesis presents two different abstractions that aim to capture the signal processing abilities of biological cells: a stand-alone signalling network and a coupled signalling network. While the former mimics the interacting relationships amongst the components in a signalling pathway, the latter replicates the connectionism amongst signalling pathways. After initially investigating the feasibility of these models for controlling two complex numerical dynamical systems, Chirikov's standard map and the Lorenz system, this thesis explores their applicability to a difficult real world control problem, the generation of adaptive rhythmic locomotion patterns within a legged robotic system. The results highlight that the locomotive movements of a six-legged robot could be controlled in order to adapt the robot's trajectory in a range of challenging environments. In this sense, signalling networks are responsible for the robot adaptability and inter limb coordination as they self-adjust their dynamics according to the terrain's irregularities. More generally, the results of this thesis highlight the capacity of coupled signalling networks to decompose non-linear problems into smaller sub-tasks, which can then be independently solved

Objective Assessment of Neurological Conditions using Machine Learning

Movement disorders are a subset of neurological conditions that are responsible for a significant decline in the health of the world’s population, having multiple negative impacts on the lives of patients, their families, societies and countries’ economy. Parkinson’s disease (PD), the most common of all movement disorders, remains idiopathic (of unknown cause), is incurable, and without any confirmed pathological marker that can be extracted from living patients. As a degenerative condition, early and accurate diagnosis is critical for effective disease management in order to preserve a good quality of life. It also requires an in-depth understanding of clinical symptoms to differentiate the disease from other movement disorders. Unfortunately, clinical diagnosis of PD and other movement disorders is subject to the subjective interpretation of clinicians, resulting in a high rate of misdiagnosis of up to 25%. However, computerised methods can support clinical diagnosis through objective assessment. The major focus of this study is to investigate the use of machine learning approaches, specifically evolutionary algorithms, to diagnose, differentiate and characterise different movement disorders, namely PD, Huntington disease (HD) and Essential Tremor (ET). In the first study, movement features of three standard motor tasks from Unified Parkinson’s Disease Rating Scale (UPDRS), finger tapping, hand opening-closing and hand pronation-supination, were used to evolve the high-performance classifiers. The results obtained for these conditions are encouraging, showing differences between the groups of healthy controls, PD, HD and ET patients. Findings on the most discriminating features of the best classifiers provide insight into different characteristics of the neurological disorders under consideration. The same algorithm has also been applied in the second study on Dystonia patients. A differential classification between Organic Dystonia and Functional Dystonia patients is less convincing, but positive enough to recommend future studies

Development of Atomistic Potentials for Silicate Materials and Coarse-Grained Simulation of Self-Assembly at Surfaces

This thesis is composed of two parts. The first is a study of evolutionary strategies for parametrization of empirical potentials, and their application in development of a charge-transfer potential for silica. An evolutionary strategy was meta-optimized for use in empirical potential parametrization, and a new charge-transfer empirical model was developed for use with isobaric-isothermal ensemble molecular dynamics simulations. The second is a study of thermodynamics and self-assembly in a particular class of athermal two-dimensional lattice models. The effects of shape on self-assembly and thermodynamics for polyominoes and tetrominoes were examined. Many interesting results were observed, including complex clustering, non-ideal mixing, and phase transitions. In both parts, computational efficiency and performance were important goals, and this was reflected in method and program development

Intelligent joint channel parameter estimation techniques for mobile wireless positioning applications

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Mobile wireless positioning has recently received great attention. For mobile wireless communication networks, an inherently suitable approach is to obtain the parameters that are used for positioning estimates from the radio signal measurements between a mobile device and one or more xed base stations. However, obtaining accurate estimates of these location-dependent channel parameters is a challenging task. The focus of this thesis is on the estimation of these channel parameters for mobile wireless positioning applications. In particular, we investigate novel estimators that jointly estimate more than one type of channel parameters. We rst perform a comprehensive critical review on the most recent and popular joint channel parameter estimation techniques. Secondly, we improve a state-of-the-art technique, namely the Space Alternating Generalised Expectation maximisation (SAGE) algorithm by employing adaptive interference cancellation to improve the estimation accuracy of weaker paths. Thirdly, a novel intelligent channel parameter estimation technique using Evolution Strategy (ES) is proposed to overcome the drawbacks of the existing iterative maximum likelihood methods. Furthermore, given that in reality it is di cult to obtain the number of multipath in advance, we propose a two tier Hierarchically Organised ES to jointly estimate the number of multipath as well as the channel parameters. Finally, we extend the proposed ES method to further estimate the Doppler shift in mobile environments. Our proposed intelligent joint channel estimation techniques are shown to exhibit excellent performance even with low Signal to Noise Ratio (SNR) channel conditions as well as robust against uncertainties in initialisations.EPSRC and Cambridge Silicon Radi

Characterization of neurological disorders using evolutionary algorithms

The life expectancy increasing, in the last few decades, leads to a large diffusion of neurodegenerative age-related diseases such as Parkinson’s disease. Neurodegenerative diseases are part of the huge category of neurological disorders, which comprises all the disorders affecting the central nervous system. These conditions have a terrible impact on life quality of both patients and their families, but also on the costs associated to the society for their diagnosis and management. In order to reduce their impact on individuals and society, new better strategies for the diagnosis and monitoring of neurological disorders need to be considered. The main aim of this study is investigating the use of artificial intelligence techniques as a tool to help the doctors in the diagnosis and the monitoring of two specific neurological disorders (Parkinson’s disease and dystonia), for which no objective clinical assessments exist. The evolutionary algorithms are chosen as the artificial intelligence technique to evolve the best classifiers. The classifiers evolved by the chosen technique are then compared with those evolved by two popular well-known techniques: artificial neural network and support vector machine. All the evolved classifiers are not only able to distinguish among patients and healthy subjects but also among different subgroups of patients. For Parkinson’s disease: two different cognitive impairment subgroups of patients are considered, with the aim of an early diagnosis and a better monitoring. For dystonia: two kinds of dystonia patients are considered (organic and functional) to have a better insight in the division of the two groups. The results obtained for Parkinson’s disease are encouraging and evidenced some differences among the cognitive impairment subgroups. Dystonia results are not satisfactory at this stage, but the study presents some limitations that could be overcome in future work

Homologous Pairing Through Dna Driven Harmonics-- A Simulation Investigation

The objective of this research is to determine if a better understanding of the “molecule of life”, deoxyribonucleic acid or DNA can be obtained through Molecular Dynamics (MD) modeling and simulation (M&S) using contemporary MD M&S. It is difficult to overstate the significance of the DNA molecule. The now-completed Human Genome Project stands out as the most significant testimony yet to the importance of understanding DNA. The Human Genome Project (HGP) enumerated many areas of application of genomic research including molecular medicine, energy sources, environmental applications, agriculture and livestock breeding to name just a few. (Science, 2008) In addition to the fact that DNA contains the informational blueprints for all life, it also exhibits other remarkable characteristics most of which are either poorly understood or remain complete mysteries. One of those completely mysterious characteristics is the ability of DNA molecules to spontaneously segregate with other DNA molecules of similar sequence. This ability has been observed for years in living organisms and is known as “homologous pairing.” It is completely reproducible in a laboratory and defies explanation. What is the underlying mechanism that facilitates long-range attraction between 2 double-helix DNA molecules containing similar nucleotide sequences? The fact that we cannot answer this question indicates we are missing a fundamental piece of information concerning the DNA bio-molecule. The research proposed herein investigated using the Nano-scale Molecular Dynamics NAMD (Phillips et al., 2005) simulator the following hypotheses: H(Simulate Observed Closure NULL) : = Current MD force field models when used to model DNA molecule segments, contain sufficient variable terms and parameters to describe and reproduce iv directed segregating movement (closure of the segments) as previously observed by the Imperial College team between two Phi X 174 DNA molecules. H(Resonance NULL) : = Current MD force field models when used to model DNA molecule segments in a condensed phased solvent contain sufficient variable terms and parameters to reproduce theorized molecular resonation in the form of frequency content found in water between the segments. H(Harmonized Resonance NULL) : = Current MD force field models of DNA molecule segments in a condensed phase solvent produce theorized molecular resonation in the form of frequency content above and beyond the expected normal frequency levels found in water between the segments. H(Sequence Relationship NULL): = The specific frequencies and amplitudes of the harmonized resonance postulated in H(Harmonized Resonance NULL) are a direct function of DNA nucleotide sequence. H(Resonance Causes Closure NULL) : = Interacting harmonized resonation produces an aggregate force between the 2 macro-molecule segments resulting in simulation of the same directed motion and segment closure as observed by the Imperial College team between two Phi X 174 DNA molecules. After nearly six months of molecular dynamic simulation for H(Simulate Observed Closure NULL) and H(Resonance Causes Closure NULL) no evidence of closure between two similar sequenced DNA segments was found. There exist several contributing factors that potentially affected this result that are described in detail in the Results section. Simulations investigating H( Resonance NULL), H(Harmonized Resonance NULL) and the emergent hypothesis H(Sequence Relationship NULL) on the other hand, revealed a rich selection of periodic pressure variation occurring in the solvent between simulated DNA molecules. About v 20% of the power in Fourier coefficients returned by Fast Fourier Transforms performed on the pressure data was characterized as statistically significant and was located in less than 2% of the coefficients by count. This unexpected result occurred consistently in 5 different system configurations with considerable system-to-system variation in both frequency and magnitude. After careful analysis given the extent of our experiments the data was found to be in support of H( Resonance NULL), and H(Harmonized Resonance NULL) . Regarding the emergent hypothesis H(Sequence Relationship NULL), further analysis was done on the aggregate data set looking for correlation between nucleotide sequence and frequency/magnitude. Some of the results may be related to sequence but were insufficient to prove it. Overall the conflicting results were inconclusive so the hypothesis was neither accepted nor rejected. Of particular interest to future researchers it was noted that the computational simulations performed herein were NOT able to reproduce what we know actually happens in a laboratory environment. DNA segregation known to occur in-vitro during the Imperial College investigation did not occur in our simulation. Until this discrepancy is resolved MM simulation should not as yet be considered a suitable tool for further investigation of Homologous Chromosome Pairing. In Chapter 5 specific follow on research is described in priority of need addressing several new questions

Classification of Resting-State fMRI using Evolutionary Algorithms: Towards a Brain Imaging Biomarker for Parkinson’s Disease

It is commonly accepted that accurate early diagnosis and monitoring of neurodegenerative conditions is essential for effective disease management and delivery of medication and treatment. This research develops automatic methods for detecting brain imaging preclinical biomarkers for Parkinson’s disease (PD) by considering the novel application of evolutionary algorithms. An additional novel element of this work is the use of evolutionary algorithms to both map and predict the functional connectivity in patients using rs-fMRI data. Specifically, Cartesian Genetic Programming was used to classify dynamic causal modelling data as well as timeseries data. The findings were validated using two other commonly used classification methods (Artificial Neural Networks and Support Vector Machines) and by employing k-fold cross-validation. Across dynamic causal modelling and timeseries analyses, findings revealed maximum accuracies of 75.21% for early stage (prodromal) PD patients in which patients reveal no motor symptoms versus healthy controls, 85.87% for PD patients versus prodromal PD patients, and 92.09% for PD patients versus healthy controls. Prodromal PD patients were classified from healthy controls with high accuracy – this is notable and represents the key finding since current methods of diagnosing prodromal PD have low reliability and low accuracy. Furthermore, Cartesian Genetic Programming provided comparable performance accuracy relative to Artificial Neural Networks and Support Vector Machines. Nevertheless, evolutionary algorithms enable us to decode the classifier in terms of understanding the data inputs that are used, more easily than in Artificial Neural Networks and Support Vector Machines. Hence, these findings underscore the relevance of both dynamic causal modelling analyses for classification and Cartesian Genetic Programming as a novel classification tool for brain imaging data with medical implications for disease diagnosis, particularly in early stages 5-20 years prior to motor symptoms