Information geometric measurements of generalisation

Neural networks can be regarded as statistical models, and can be analysed in a Bayesian framework. Generalisation is measured by the performance on independent test data drawn from the same distribution as the training data. Such performance can be quantified by the posterior average of the information divergence between the true and the model distributions. Averaging over the Bayesian posterior guarantees internal coherence; Using information divergence guarantees invariance with respect to representation. The theory generalises the least mean squares theory for linear Gaussian models to general problems of statistical estimation. The main results are: (1)~the ideal optimal estimate is always given by average over the posterior; (2)~the optimal estimate within a computational model is given by the projection of the ideal estimate to the model. This incidentally shows some currently popular methods dealing with hyperpriors are in general unnecessary and misleading. The extension of information divergence to positive normalisable measures reveals a remarkable relation between the dlt dual affine geometry of statistical manifolds and the geometry of the dual pair of Banach spaces Ld and Ldd. It therefore offers conceptual simplification to information geometry. The general conclusion on the issue of evaluating neural network learning rules and other statistical inference methods is that such evaluations are only meaningful under three assumptions: The prior P(p), describing the environment of all the problems; the divergence Dd, specifying the requirement of the task; and the model Q, specifying available computing resources.

Nickel(II) complexes of whole set of the simple ethylenediaminetetracarboxylate ligands:DFT study of complexes invoking molecular orbital and configurational analysis

The whole set of the nickel(II) complexes with no derivatized edta-type hexadentate ligands has been investigated from their structural and electronic properties. Two more complexes have been prepared in order to complete the whole set: trans(O5)-[Ni(ED3AP)]2- and trans(O5O6)-[Ni(EDA3P)]2- complexes. trans(O5) geometry has been verified crystallographically and trans(O5O6) geometry of the second complex has been predicted by the DFT theory and spectral analysis. Mutual dependance has been established between: the number of the five-membered carboxylate rings, octahedral/tetrahedral deviation of metal-ligand/nitrogen-neighbour-atom angles and charge-transfer energies (CTE) calculated by the Morokuma’s energetic decomposition analysis; energy of the absorption bands and HOMO–LUMO gap.

Mechanical properties of sheet metal under forming conditions

In the bulge test, a sheet metal specimen is clamped over a circular hole in a die and formed into a bulge by the hydraulic pressure on one side of the specirnen. As the unsupported part of the specimen is deformed in this way, its area is increased, in other words, the material is generally stretched and its thickness generally decreased. The stresses causing this stretching action are the membrane stresses in the shell generated by the hydraulic pressure, in the same way as the rubber in a toy balloon is stretched by the membrane stresses caused by the air inside it. The bulge test is a widely used sheet metal test, to determine the "formability" of sheet materials. Research on this forming process (2)-(15)* has hitherto been almost exclusively confined to predicting the behaviour of the bulged specimen through the constitutive equations (stresses and strains in relation to displacements and shapes) and empirical work hardening characteristics of the material as determined in the tension test. In the present study the approach is reversed; the stresses and strains in the specimen are measured and determined from the geometry of the deformed shell. Thus, the bulge test can be used for determining the stress-strain relationship in the material under actual conditions in sheet metal forming processes. When sheet materials are formed by fluid pressure, the work-piece assumes an approximately spherical shape, The exact nature and magnitude of the deviation from the perfect sphere can be defined and measured by an index called prolateness. The distribution of prolateness throughout the workpiece at any particular stage of the forming process is of fundamental significance, because it determines the variation of the stress ratio on which the mode of deformation depends. It is found. that, before the process becomes unstable in sheet metal, the workpiece is exactly spherical only at the pole and at an annular ring. Between the pole and this annular ring the workpiece is more pointed than a sphere, and outside this ring, it is flatter than a sphere. In the forming of sheet materials, the stresses and hence the incremental strains, are closely related to the curvatures of the workpiece. This relationship between geometry and state of stress can be formulated quantitatively through prolateness. The determination of the magnitudes of prolateness, however, requires special techniques. The success of the experimental work is due to the technique of measuring the profile inclination of the meridional section very accurately. A travelling microscope, workshop protractor and surface plate are used for measurements of circumferential and meridional tangential strains. The curvatures can be calculated from geometry. If, however, the shape of the workpiece is expressed in terms of the current radial (r) and axial ( L) coordinates, it is very difficult to calculate the curvatures within an adequate degree of accuracy, owing to the double differentiation involved. In this project, a first differentiation is, in effect, by-passed by measuring the profile inclination directly and the second differentiation is performed in a round-about way, as explained in later chapters. The variations of the stresses in the workpiece thus observed have not, to the knowledge of the author, been reported experimentally. The static strength of shells to withstand fluid pressure and their buckling strength under concentrated loads, both depend on the distribution of the thickness. Thickness distribution can be controlled to a limited extent by changing the work hardening characteristics of the work material and by imposing constraints. A technique is provided in this thesis for determining accurately the stress distribution, on which the strains associated with thinning depend. Whether a problem of controlled thickness distribution is tackled by theory, or by experiments, or by both combined, the analysis in this thesis supplies the theoretical framework and some useful experimental techniques for the research applied to particular problems. The improvement of formability by allowing draw-in can also be analysed with the same theoretical and experimental techniques. Results on stress-strain relationships are usually represented by single stress-strain curves plotted either between one stress and one strain (as in the tension or compression tests) or between the effective stress and effective strain, as in tests on tubular specimens under combined tension, torsion and internal pressure. In this study, the triaxial stresses and strains are plotted simultaneously in triangular coordinates. Thus, both stress and strain are represented by vectors and the relationship between them by the relationship between two vector functions. From the results so obtained, conclusions are drawn on both the behaviour and the properties of the material in the bulge test. The stress ratios are generally equal to the strain-rate ratios (stress vectors collinear with incremental strain vectors) and the work-hardening characteristics, which apply only to the particular strain paths are deduced. Plastic instability of the material is generally considered to have been reached when the oil pressure has attained its maximum value so that further deformation occurs under a constant or lower pressure. It is found that the instability regime of deformation has already occurred long before the maximum pressure is attained. Thus, a new concept of instability is proposed, and for this criterion, instability can occur for any type of pressure growth curves.

Studies of molecular interactions using physical techniques

The investigations described in this thesis concern the molecular interactions between polar solute molecules and various aromatic compounds in solution. Three different physical methods were employed. Nuclear magnetic resonance (n.m.r.) spectroscopy was used to determine the nature and strength of the interactions and the geometry of the transient complexes formed. Cryoscopic studies were used to provide information on the stoichiometry of the complexes. Dielectric constant studies were conducted in an attempt to confirm and supplement the spectroscopic investigations. The systems studied were those between nitromethane, chloroform, acetonitrile (solutes) and various methyl substituted benzenes. In the n.m.r. work the dependence of the solute chemical shift upon the compositions of the solutions was determined. From this the equilibrium quotients (K) for the formation of each complex and the shift induced in the solute proton by the aromatic in the complex were evaluated. The thermodynamic parameters for the interactions were obtained from the determination of K at several temperatures. The stoichiometries of the complexes obtained from cryoscopic studies were found to agree with those deduced from spectroscopic investigations. For most systems it is suggested that only one type of complex, of 1:1 stiochiometry, predominates except that for the acetonitrile-benzene system a 1:2 complex is formed. Two sets of dielectric studies were conducted, the first to show that the nature of the interaction is dipole-induced dipole and the second to calculate K. The equilibrium quotients obtained from spectroscopic and dielectric studies are compared. Time-averaged geometries of the complexes are proposed. The orientation of solute, with respect to the aromatic for the 1:1 complexes, appears to be the one in which the solute lies symmetrically about the aromatic six-fold axis whereas for the 1:2 complex, a sandwich structure is proposed. It is suggested that the complexes are formed through a dipole-induced dipole interaction and steric factors play some part in the complex formation.

Computer simulation of form-roll design

Changes in modern structural design have created a demand for products which are light but possess high strength. The objective is a reduction in fuel consumption and weight of materials to satisfy both economic and environmental criteria. Cold roll forming has the potential to fulfil this requirement. The bending process is controlled by the shape of the profile machined on the periphery of the rolls. A CNC lathe can machine complicated profiles to a high standard of precision, but the expertise of a numerical control programmer is required. A computer program was developed during this project, using the expert system concept, to calculate tool paths and consequently to expedite the procurement of the machine control tapes whilst removing the need for a skilled programmer. Codifying the expertise of a human and the encapsulation of knowledge within a computer memory, destroys the dependency on highly trained people whose services can be costly, inconsistent and unreliable. A successful cold roll forming operation, where the product is geometrically correct and free from visual defects, is not easy to attain. The geometry of the sheet after travelling through the rolling mill depends on the residual strains generated by the elastic-plastic deformation. Accurate evaluation of the residual strains can provide the basis for predicting the geometry of the section. A study of geometric and material non-linearity, yield criteria, material hardening and stress-strain relationships was undertaken in this research project. The finite element method was chosen to provide a mathematical model of the bending process and, to ensure an efficient manipulation of the large stiffness matrices, the frontal solution was applied. A series of experimental investigations provided data to compare with corresponding values obtained from the theoretical modelling. A computer simulation, capable of predicting that a design will be satisfactory prior to the manufacture of the rolls, would allow effort to be concentrated into devising an optimum design where costs are minimised.

The characterisation of clean metal surfaces

The most perfectly structured metal surface observed in practice is that of a field evaporated field-ion microscope specimen. This surface has been characterised by adopting various optical analogue techniques. Hence a relationship has been determined between the structure of a single plane on the surface of a field-ion emitter and the geometry of a binary zone plate. By relating the known focussing properties of such a zone plate to those obtained from the projected images of such planes in a field-ion micrograph, it is possible to extract new information regarding the local magnification of the image. Further to this, it has been shown that the entire system of planes comprising the field-ion imaging surface may be regarded as a moire pattern formed between over-lapping zone plates. The properties of such moire zone plates are first established in an analysis of the moire pattern formed between zone plates on a flat surface. When these ideas are applied to the field-ion image it becomes possible to deduce further information regarding the precise topography of the emitter. It has also become possible to simulate differently proJected field-ion images by overlapping suitably aberrated zone plates. Low-energy ion bombardment is an essential preliminary to much surface research as a means of producing chemically clean surfaces. Hence it is important to know the nature and distribution of the resultant lattice damage, and the extent to which it may be removed by annealing. The field-ion microscope has been used to investigate such damage because its characterisation lies on the atomic scale. The present study is concerned with the in situ sputtering of tungsten emitters using helium, neon, argon and xenon ions with energies in the range 100eV to 1keV, together with observations of the effect of annealing. The relevance of these results to surface cleaning schedules is discussed.

The stability of pharmaceutical powders: effect of additives and coating

The decomposition of drugs in the solid state has been studied using aspirin and salsalate as models. The feasibility of using suspension systems for predicting the stability of these drugs in the solid state has been investigated.. It has been found that such systems are inappropriate in defining the effect of excipients on 'the decomposition of the active drug due to chqnges in the degradation pathway. Using a high performance liquid chromatographic method, magnesium stearate was shown to induce the formation of potentlally immunogenic products in aspirin powders. These products which included salicylsalicylic acid .and acetylsalicyclsalicylic acid were not detected in aspirin suspensions which had undergone the same extent of decomposition. By studying the effect of pH and of added excipients on the rate of decomposition of aspirin in suspension systems, it has been shown that excipients such as magnesium stearate containing magnesium oxide, most probably enhance the decomposition of both aspirin and salsalate by alkalinising the aqueous phase. In the solid state, pH effects produced by excipients appear to be relatively unimportant. Evidence is presented to suggest that the critical parameter is a depression in melting point induced by: the added excipient. Microscopical examination in fact showed the formation of clear liquid layers in aspirin samples containing added magnesium stearate but not in control samples. Kinetic equations which take into account both the diffusive barrier presented by the liquid films and the. geometry of the aspirin crystals were developed. Fitting of the .experimental data to these equations showed good agreement. with the postulated theory. Monitorjng of weight issues during the decomposition of aspirin revealed that in the solid systems studied where the bulk of the decomposition product sublimes, it is possible to estimate the extent of degradation from the residual weight, provided the initial weight is known. The corollary is that in such open systems, monitoring of decomposition products is inadequate for assessing the extent of decomposition. In addition to the magnesium stearate-aspirin system, mapyramine maleate-aspirin mixtures were used to model interactive systems. Work carried out in an attempt to stabilise such systems included microencapsulation and film coating. The protection obtained was dependent on the interactive species used. Gelatin for example appeared to stabilise aspirin against the adverse effects of magnesium stearate but increased its decomposition in the presence of mapyramine maleate.

The Kinematics of interference mechanisms in certain machining operations

The mechanism of "Helical Interference" in milled slots is examined and a coherent theory for the geometry of such surfaces is presented. An examination of the relevant literature shows a fragmented approach to the problem owing to its normally destructive nature, so a complete analysis is developed for slots of constant lead, thus giving a united and exact theory for many different setting parameters and a range of cutter shapes. For the first time, a theory is developed to explain the "Interference Surface" generated in variable lead slots for cylindrical work and attention is drawn to other practical surfaces, such as cones, where variable leads are encountered. Although generally outside the scope of this work, an introductory analysis of these cases is considered in order to develop the cylindrical theory. Special emphasis is laid upon practical areas where the interference mechanism can be used constructively and its application as the rake face of a cutting tool is discussed. A theory of rake angle for such cutting tools is given for commonly used planes, and relative variations in calculated rake angle between planes is examined. Practical tests are conducted to validate both constant lead and variable lead theories and some design improvements to the conventional dividing head are suggested in order to manufacture variable lead workpieces, by use of a "superposed" rotation. A prototype machine is manufactured and its kinematic principle given for both linear and non-linearly varying superposed rotations. Practical workpieces of the former type are manufactured and compared with analytical predictions,while theoretical curves are generated for non-linear workpieces and then compared with those of linear geometry. Finally suggestions are made for the application of these principles to the manufacture of spiral bevel gears, using the "Interference Surface" along a cone as the tooth form.

Lateral instability of slender reinforced concrete columns in a fire environment

The research concerns the development and application of an analytical computer program, SAFE-ROC, that models material behaviour and structural behaviour of a slender reinforced concrete column that is part of an overall structure and is subjected to elevated temperatures as a result of exposure to fire. The analysis approach used in SAFE-RCC is non-linear. Computer calculations are used that take account of restraint and continuity, and the interaction of the column with the surrounding structure during the fire. Within a given time step an iterative approach is used to find a deformed shape for the column which results in equilibrium between the forces associated with the external loads and internal stresses and degradation. Non-linear geometric effects are taken into account by updating the geometry of the structure during deformation. The structural response program SAFE-ROC includes a total strain model which takes account of the compatibility of strain due to temperature and loading. The total strain model represents a constitutive law that governs the material behaviour for concrete and steel. The material behaviour models employed for concrete and steel take account of the dimensional changes caused by the temperature differentials and changes in the material mechanical properties with changes in temperature. Non-linear stress-strain laws are used that take account of loading to a strain greater than that corresponding to the peak stress of the concrete stress-strain relation, and model the inelastic deformation associated with unloading of the steel stress-strain relation. The cross section temperatures caused by the fire environment are obtained by a preceding non-linear thermal analysis, a computer program FIRES-T.

The pore system and engineering properties of hardened cement paste

The work described in this thesis is an attempt to elucidate the relationships between the pore system and a number of engineering properties of hardened cement paste, particularly tensile strength and resistances to carbonation and ionic penetration. By examining aspects such as the rate of carbonisation, the pore size distribution, the concentration of ions in the pore solution and the phase composition of cement pastes, relationships between the pore system (pores and pore solution) and the resistance to carbonation were investigated. The study was carried out in two parts. First, cement pastes with different pore systems were compared, whilst secondly comparisons were made between the pore systems of cement pastes with different degrees of carbonation. Relationships between the pore structure and ionic penetration were studied by comparing kinetic data relating to the diffusion of various ions in cement pastes with different pore systems. Diffusion coefficients and activation energies for the diffusion process of Cl- and Na+ ions in carbonated and non-carbonated cement pastes were determined by a quasi-steady state technique. The effect of the geometry of pores on ionic diffusion was studied by comparing the mechanisms of ionic diffusion for ions with different radii. In order to investigate the possible relationship between tensile strength and macroporosity, cement paste specimens with cross sectional areas less than 1mm2 were produced so that the chance of a macropore existing within them was low. The tensile strengths of such specimens were then compared with those of larger specimens.

The sedimentology and diagenesis of Lower Permian (Rotliegend) sediments: (onshore U.K. and southern North Sea). Available in 2 volumes.

The thesis provides a comparative study of both sedimentology and diagenesis of Lower Permian (Rotliegend) strata, onshore and offshore U.K. (Southern North Sea). Onshore formations studied include the Bridgnorth, Penrith and Hopeman Sandstone, and are dominated by aeolian facies, with lesser amounts of interbedded fluvial sediments. Aeolian and fluvial strata in onshore basins typically grade laterally into alluvial fan breccias at basin margins. Onshore basins represent proximal examples of Rotliegend desert sediments. The Leman Sandstone Formation of the Ravenspurn area in the Southern North Sea displays a variety of facies indicative of a distal sedimentological setting; Aeolian, fluvial, sabkha, and playa lake sediments all being present. "Sheet-like" geometry of stratigraphical units within the Leman Sandstone, and alternation of fluvial and aeolian deposition was climatically controlled. Major first order bounding surfaces are laterally extensive and were produced by lacustrine transgression and regression from the north-west. Diagenesis within Permian strata was studied using standard petrographic microscopy, scanning electron microscopy, cold cathodo-Iuminescence, X-ray diffraction clay analysis, X-ray fluorescence spectroscopy, fluid inclusion microthermometry, and K-Ar dating of illites. The diagenesis of Permian sediments within onshore basins is remarkably similar, and a paragenetic sequence of early haematite, illitic clays, feldspar, kaolinite, quartz and late calcite is observed. In the Leman Sandstone formation, authigenic mineralogy is complex and includes early quartz, sulphates and dolomite, chlorite, kaolinite, late quartz, illite and siderite. Primary lithological variation, facies type, and the interdigitation and location of facies within a basin are important initial controls upon diagenesis. Subsequently, burial history, structure, the timing of gas emplacement, and the nature of sediments within underlying formations may also exersize significant controls upon diagenesis within Rotliegend strata.

An investigation of the relationship between temperature, forces and tool wear in turning and drilling

Developing a means of predicting tool life has been and continues to be a focus of much research effort. A common experience in attempting to replicate such efforts is an inability to achieve the levels of agreement between theory and practice of the original researcher or to extrapolate the work to different materials or cutting conditions to those originally used. This thesis sets out to examine why most equations or models when replicated do not give good agreements. One reason which was found is that researchers in wear prediction, their predictions are limited because they generally fail to properly identify the nature of wear mechanisms operative in their study. Also they fail to identify or recognise factors having a significant influence on wear such as bar diameter. Also in this research the similarities and differences between the two processes of single point turning and drilling are examined through a series of tests. A literature survey was undertaken in wear and wear prediction. As a result it was found that there was a paucity in information and research in the work of drilling as compared to the turning operation. This was extended to the lack of standards that exist for the drilling operation. One reason for this scarcity in information on drilling is due to the complexity of the drilling and the tool geometry of the drill. In the comparative drilling and turning tests performed in this work, the same tool material; HSS, and similar work material was used in order to eliminate the differences which may occur due to this factor. Results of the tests were evaluated and compared for the two operations and SEM photographs were taken for the chips produced. Specific test results were obtained for the cutting temperatures and forces of the tool. It was found that cutting temperature is influenced by various factors like tool geometry and cutting speed, and the temperature itself influenced the tool wear and wear mechanisms that act on the tool. It was found and proven that bar diameter influences the temperature, a factor not considered previously.

X-ray crystallographic and theoretical studies of an anticonvulsant enaminone:methyl 4-(4'-bromophenyl)amino-6-methyl-2-oxocyclohex-3-en-1-oate

Objective: The aims of this study were to establish the structure of the potent anticonvulsant enaminone methyl 4-(4′-bromophenyl)amino-6-methyl-2- oxocyclohex-3-en-1-oate (E139), and to determine the energetically preferred conformation of the molecule, which is responsible for the biological activity. Materials and Methods: The structure of the molecule was determined by X-ray crystallography. Theoretical ab initio calculations with different basis sets were used to compare the energies of the different enantiomers and to other structurally related compounds. Results: The X-ray crystal structure revealed two independent molecules of E139, both with absolute configuration C11(S), C12(R), and their inverse. Ab initio calculations with the 6-31G, 3-21G and STO-3G basis sets confirmed that the C11(S), C12(R) enantiomer with both substituents equatorial had the lowest energy. Compared to relevant crystal structures, the geometry of the theoretical structures shows a longer C-N and shorter C=O distance with more cyclohexene ring puckering in the isolated molecule. Conclusion: Based on a pharmacophoric model it is suggested that the enaminone system HN-C=C-C=O and the 4-bromophenyl group in E139 are necessary to confer anticonvulsant property that could lead to the design of new and improved anticonvulsant agents. Copyright © 2003 S. Karger AG, Basel.

The role of pinning and instability in a class of non-equilibrium growth models

We study the dynamics of a growing crystalline facet where the growth mechanism is controlled by the geometry of the local curvature. A continuum model, in (2+1) dimensions, is developed in analogy with the Kardar-Parisi-Zhang (KPZ) model is considered for the purpose. Following standard coarse graining procedures, it is shown that in the large time, long distance limit, the continuum model predicts a curvature independent KPZ phase, thereby suppressing all explicit effects of curvature and local pinning in the system, in the "perturbative" limit. A direct numerical integration of this growth equation, in 1+1 dimensions, supports this observation below a critical parametric range, above which generic instabilities, in the form of isolated pillared structures lead to deviations from standard scaling behaviour. Possibilities of controlling this instability by introducing statistically "irrelevant" (in the sense of renormalisation groups) higher ordered nonlinearities have also been discussed.

On the use of the type I and II scheme for classifying ultrafast laser direct-write photonics

The use of the Type I and Type II scheme, first introduced and used by fiber Bragg grating researchers, has recently been adopted by the ultrafast laser direct-write photonics community to classify the physical geometry of waveguides written into glasses and crystals. This has created confusion between the fiber Bragg grating and direct-write photonics community. Here we propose a return to the original basis of the classification based on the characteristics of the material modification rather than the physical geometry of the waveguide.