The dynamics of a genetic algorithm for a simple learning problem

A formalism for describing the dynamics of Genetic Algorithms (GAs) using method s from statistical mechanics is applied to the problem of generalization in a perceptron with binary weights. The dynamics are solved for the case where a new batch of training patterns is presented to each population member each generation, which considerably simplifies the calculation. The theory is shown to agree closely to simulations of a real GA averaged over many runs, accurately predicting the mean best solution found. For weak selection and large problem size the difference equations describing the dynamics can be expressed analytically and we find that the effects of noise due to the finite size of each training batch can be removed by increasing the population size appropriately. If this population resizing is used, one can deduce the most computationally efficient size of training batch each generation. For independent patterns this choice also gives the minimum total number of training patterns used. Although using independent patterns is a very inefficient use of training patterns in general, this work may also prove useful for determining the optimum batch size in the case where patterns are recycled.

The dynamics of a genetic algorithm under stabilizing selection

A formalism recently introduced by Prugel-Bennett and Shapiro uses the methods of statistical mechanics to model the dynamics of genetic algorithms. To be of more general interest than the test cases they consider. In this paper, the technique is applied to the subset sum problem, which is a combinatorial optimization problem with a strongly non-linear energy (fitness) function and many local minima under single spin flip dynamics. It is a problem which exhibits an interesting dynamics, reminiscent of stabilizing selection in population biology. The dynamics are solved under certain simplifying assumptions and are reduced to a set of difference equations for a small number of relevant quantities. The quantities used are the population's cumulants, which describe its shape, and the mean correlation within the population, which measures the microscopic similarity of population members. Including the mean correlation allows a better description of the population than the cumulants alone would provide and represents a new and important extension of the technique. The formalism includes finite population effects and describes problems of realistic size. The theory is shown to agree closely to simulations of a real genetic algorithm and the mean best energy is accurately predicted.

Kineto-elastodynamic analysis of high-speed four-bar mechanism

This thesis addresses the kineto-elastodynamic analysis of a four-bar mechanism running at high-speed where all links are assumed to be flexible. First, the mechanism, at static configurations, is considered as structure. Two methods are used to model the system, namely the finite element method (FEM) and the dynamic stiffness method. The natural frequencies and mode shapes at different positions from both methods are calculated and compared. The FEM is used to model the mechanism running at high-speed. The governing equations of motion are derived using Hamilton's principle. The equations obtained are a set of stiff ordinary differential equations with periodic coefficients. A model is developed whereby the FEM and the dynamic stiffness method are used conjointly to provide high-precision results with only one element per link. The principal concern of the mechanism designer is the behaviour of the mechanism at steady-state. Few algorithms have been developed to deliver the steady-state solution without resorting to costly time marching simulation. In this study two algorithms are developed to overcome the limitations of the existing algorithms. The superiority of the new algorithms is demonstrated. The notion of critical speeds is clarified and a distinction is drawn between "critical speeds", where stresses are at a local maximum, and "unstable bands" where the mechanism deflections will grow boundlessly. Floquet theory is used to assess the stability of the system. A simple method to locate the critical speeds is derived. It is shown that the critical speeds of the mechanism coincide with the local maxima of the eigenvalues of the transition matrix with respect to the rotational speed of the mechanism.

Computer simulation of liquid flow patterns on distillation trays

This thesis describes work carried out to improve the fundamental modelling of liquid flows on distillation trays. A mathematical model is presented based on the principles of computerised fluid dynamics. It models the liquid flow in the horizontal directions allowing for the effects of the vapour through the use of an increased liquid turbulence, modelled by an eddy viscosity, and a resistance to liquid flow caused by the vapour being accelerated horizontally by the liquid. The resultant equations are similar to the Navier-Stokes equations with the addition of a resistance term.A mass-transfer model is used to calculate liquid concentration profiles and tray efficiencies. A heat and mass transfer analogy is used to compare theoretical concentration profiles to experimental water-cooling data obtained from a 2.44 metre diameter air-water distillation simulation rig. The ratios of air to water flow rates are varied in order to simulate three pressures: vacuum, atmospheric pressure and moderate pressure.For simulated atmospheric and moderate pressure distillation, the fluid mechanical model constantly over-predicts tray efficiencies with an accuracy of between +1.7% and +11.3%. This compares to -1.8% to -10.9% for the stagnant regions model (Porter et al. 1972) and +12.8% to +34.7% for the plug flow plus back-mixing model (Gerster et al. 1958). The model fails to predict the flow patterns and tray efficiencies for vacuum simulation due to the change in the mechanism of liquid transport, from a liquid continuous layer to a spray as the liquid flow-rate is reduced. This spray is not taken into account in the development of the fluid mechanical model. A sensitivity analysis carried out has shown that the fluid mechanical model is relatively insensitive to the prediction of the average height of clear liquid, and a reduction in the resistance term results in a slight loss of tray efficiency. But these effects are not great. The model is quite sensitive to the prediction of the eddy viscosity term. Variations can produce up to a 15% decrease in tray efficiency. The fluid mechanical model has been incorporated into a column model so that statistical optimisation techniques can be employed to fit a theoretical column concentration profile to experimental data. Through the use of this work mass-transfer data can be obtained.

Early visual detection of oriented line targets: spatial characteristics,and reference frames of early visual orientation-processing

The orientations of lines and edges are important in defining the structure of the visual environment, and observers can detect differences in line orientation within the first few hundred milliseconds of scene viewing. The present work is a psychophysical investigation of the mechanisms of early visual orientation-processing. In experiments with briefly presented displays of line elements, observers indicated whether all the elements were uniformly oriented or whether a uniquely oriented target was present among uniformly oriented nontargets. The minimum difference between nontarget and target orientations that was required for effective target-detection (the orientation increment threshold) varied little with the number of elements and their spatial density, but the percentage of correct responses in detection of a large orientation-difference increased with increasing element density. The differing variations with element density of thresholds and percent-correct scores may indicate the operation of more than one mechanism in early visual orientation-processIng. Reducing element length caused threshold to increase with increasing number of elements, showing that the effectiveness of rapid, spatially parallel orientation-processing depends on element length. Orientational anisotropy in line-target detection has been reported previously: a coarse periodic variation and some finer variations in orientation increment threshold with nontarget orientation have been found. In the present work, the prominence of the coarse variation in relation to finer variations decreased with increasing effective viewing duration, as if the operation of coarse orientation-processing mechanisms precedes the operation of finer ones. Orientational anisotropy was prominent even when observers lay horizontally and viewed displays by looking upwards through a black cylinder that excluded all possible visual references for orientation. So, gravitational and visual cues are not essential to the definition of an orientational reference frame for early vision, and such a reference can be well defined by retinocentric neural coding, awareness of body-axis orientation, or both.

Statnote 31:analysis of covariance

Analysis of covariance (ANCOVA) is a useful method of ‘error control’, i.e., it can reduce the size of the error variance in an experimental or observational study. An initial measure obtained before the experiment, which is closely related to the final measurement, is used to adjust the final measurements, thus reducing the error variance. When this method is used to reduce the error term, the X variable must not itself be affected by the experimental treatments, because part of the treatment effect would then also be removed. Hence, the method can only be safely used when X is measured before an experiment. A further limitation of the analysis is that only the linear effect of Y on X is being removed and it is possible that Y could be a curvilinear function of X. A question often raised is whether ANCOVA should be used routinely in experiments rather than a randomized blocks or split-plot design, which may also reduce the error variance. The answer to this question depends on the relative precision of the difference methods with reference to each scenario. Considerable judgment is often required to select the best experimental design and statistical help should be sought at an early stage of an investigation.

An integral equation method for a mixed initial boundary value problem for unsteady Stokes system in a doubly-connected domain

We present a novel numerical method for a mixed initial boundary value problem for the unsteady Stokes system in a planar doubly-connected domain. Using a Laguerre transformation the unsteady problem is reduced to a system of boundary value problems for the Stokes resolvent equations. Employing a modied potential approach we obtain a system of boundary integral equations with various singularities and we use a trigonometric quadrature method for their numerical solution. Numerical examples are presented showing that accurate approximations can be obtained with low computational cost.

Population lensing vs thermal lensing in Yb:YAG rods and disks

The induced lenses in the Yb:YAG rods and disks end-pumped by a Gaussian beam were analyzed both analytically and numerically. The thermally assisted mechanisms of the lens formation were considered to include: the conventional volume thermal index changes ("dn/dT"), the bulging of end faces, the photoelastic effect, and the bending (for a disk). The heat conduction equations (with an axial heat flux for a disk and a radial heat flux for a rod), and quasi-static thermoelastic equations (in the plane-stress approximation with free boundary conditions) were solved to find the thermal lens power. The population rate equation with saturation (by amplified spontaneous emission or an external wave) was examined to find the electronic lens power in the active elements.

The use of computational QSAR analysis in the toxicological evaluation of a series of 2-pyridylcarboxamidrazone candidate anti-tuberculosis compounds

A series of N1-benzylidene pyridine-2-carboxamidrazone anti-tuberculosis compounds has been evaluated for their cytotoxicity using human mononuclear leucocytes (MNL) as target cells. All eight compounds were significantly more toxic than dimethyl sulphoxide control and isoniazid (INH) with the exception of a 4-methoxy-3-(2-phenylethyloxy) derivative, which was not significantly different in toxicity compared with INH. The most toxic agent was an ethoxy derivative, followed by 3-nitro, 4-methoxy, dimethylpropyl, 4-methylbenzyloxy, 3-methoxy-4-(-2-phenylethyloxy) and 4-benzyloxy in rank order. In comparison with the effect of selected carboxamidrazone agents on cells alone, the presence of either N-acetyl cysteine (NAC) or glutathione caused a significant reduction in the toxicity of INH, as well as on the 4-benzyloxy derivative, although both increased the toxicity of a 4-N,N-dimethylamino-1-naphthylidene and a 2-t-butylthio derivative. The derivatives from this and three previous studies were subjected to computational analysis in order to derive equations designed to establish quantitative structure activity relationships for these agents. Twenty-five compounds were thus resolved into two groups (1 and 2), which on analysis yielded equations with r2 values in the range 0.65-0.92. Group 1 shares a common mode of toxicity related to hydrophobicity, where cytotoxicity peaked at logP of 3.2, while Group 2 toxicity was strongly related to ionisation potential. The presence of thiols such as NAC and GSH both promoted and attenuated toxicity in selected compounds from Group 1, suggesting that secondary mechanisms of toxicity were operating. These studies will facilitate the design of future low toxicity high activity anti-tubercular carboxamidrazone agents. © 2003 Elsevier Science B.V. All rights reserved.

Predicting changes in measured introcular pressure with non-contact tonometry after LASIK

Purpose: Optometrists are becoming more integrally involved in the diagnosis of and care for glaucoma patients in the UK. The correlation of apparent change in non contact tonometry (NCT) IOP measurement and change in other ocular parameters such as refractive error, corneal curvature, corneal thickness and treatment zone size (data available to optometrists after LASIK) would facilitate care of these patients. Setting: A UK Laser Eye Clinic. Methods: This is a retrospective study study of 200 sequential eyes with myopia with or without astigmatism which underwent LASIK using a Hansatome and an Alcon LADARvision 4000 excimer laser. Refraction keratometry, pachymetry and NCT IOP mesurements were taken before treatmebnt and agian 3 months after treatment. The relationship between these variables anfd teh treatment zones were studied using stepwise multiple regression analysis. Results: There was a mean difference of 5.54mmHg comnparing pre and postoperative NCT IOP. IOP change correlates with refractive error change (P < 0.001), preoperative corneal thickness (P < 0.001) and treatment zone size (P = 0.047). Preoperative corneal thickness correlates with preoperative IOP (P < 0.001) and postoperative IOP (P < 0.001). Using these correlations, the measured difference in NCT IIOP can be predicted preoperatively or postoperatively using derived equations.Conclusion: There is a significant reduction in measured NCT IOP after LASIK. The amount of reduction can be calculated using data acquired by optometrists. This is helpful for opthalmologists and optometrists who co-manage glaucoma patients who have had LASIK or with glaucoma pateints who are consideraing having LASIK.

Premature cardiovascular events and mortality in south Asians with type 2 diabetes in the United Kingdom Asian Diabetes Study - effect of ethnicity on risk

Background/Aim - People of south Asian origin have an excessive risk of morbidity and mortality from cardiovascular disease. We examined the effect of ethnicity on known risk factors and analysed the risk of cardiovascular events and mortality in UK south Asian and white Europeans patients with type 2 diabetes over a 2 year period. Methods - A total of 1486 south Asian (SA) and 492 white European (WE) subjects with type 2 diabetes were recruited from 25 general practices in Coventry and Birmingham, UK. Baseline data included clinical history, anthropometry and measurements of traditional risk factors – blood pressure, total cholesterol, HbA1c. Multiple linear regression models were used to examine ethnicity differences in individual risk factors. Ten-year cardiovascular risk was estimated using the Framingham and UKPDS equations. All subjects were followed up for 2 years. Cardiovascular events (CVD) and mortality between the two groups were compared. Findings - Significant differences were noted in risk profiles between both groups. After adjustment for clustering and confounding a significant ethnicity effect remained only for higher HbA1c (0.50 [0.22 to 0.77]; P?=?0.0004) and lower HDL (-0.09 [-0.17 to -0.01]; P?=?0.0266). Baseline CVD history was predictive of CVD events during follow-up for SA (P?difference of 7.4 years (95% CI 1.0 to 13.7 years), P?=?0.023. The adjusted odds ratio of CVD event or death from CVD was greater but not significantly so in SA than in WE (OR 1.4 [0.9 to 2.2]). Limitations - Fewer events in both groups and short period of follow-up are key limitations. Longer follow-up is required to see if the observed differences between the ethnic groups persist. Conclusion - South Asian patients with type 2 diabetes in the UK have a higher cardiovascular risk and present with cardiovascular events at a significantly younger age than white Europeans. Enhanced and ethnicity specific targets and effective treatments are needed if these inequalities are to be reduced.