Calibrating photometric redshifts of luminous red galaxies

We discuss the construction of a photometric redshift catalogue of luminous red galaxies (LRGs) from the Sloan Digital Sky Survey (SDSS), emphasizing the principal steps necessary for constructing such a catalogue: (i) photometrically selecting the sample, (ii) measuring photometric redshifts and their error distributions, and (iii) estimating the true redshift distribution. We compare two photometric redshift algorithms for these data and find that they give comparable results. Calibrating against the SDSS and SDSS-2dF (Two Degree Field) spectroscopic surveys, we find that the photometric redshift accuracy is sigma similar to 0.03 for redshifts less than 0.55 and worsens at higher redshift (similar to 0.06 for z < 0.7). These errors are caused by photometric scatter, as well as systematic errors in the templates, filter curves and photometric zero-points. We also parametrize the photometric redshift error distribution with a sum of Gaussians and use this model to deconvolve the errors from the measured photometric redshift distribution to estimate the true redshift distribution. We pay special attention to the stability of this deconvolution, regularizing the method with a prior on the smoothness of the true redshift distribution. The methods that we develop are applicable to general photometric redshift surveys.

Mechanical properties of interfacial films formed by lysozyme self-assembly at the air-water interface

We present the first characterization of the mechanical properties of lysozyme films formed by self-assembly at the air-water interface using the Cambridge interfacial tensiometer (CIT), an apparatus capable of subjecting protein films to a much higher level of extensional strain than traditional dilatational techniques. CIT analysis, which is insensitive to surface pressure, provides a direct measure of the extensional stress-strain behavior of an interfacial film without the need to assume a mechanical model (e.g., viscoelastic), and without requiring difficult-to-test assumptions regarding low-strain material linearity. This testing method has revealed that the bulk solution pH from which assembly of an interfacial lysozyme film occurs influences the mechanical properties of the film more significantly than is suggested by the observed differences in elastic moduli or surface pressure. We have also identified a previously undescribed pH dependency in the effect of solution ionic strength on the mechanical strength of the lysozyme films formed at the air-water interface. Increasing solution ionic strength was found to increase lysozyme film strength when assembly occurred at pH 7, but it caused a decrease in film strength at pH 11, close to the pI of lysozyme. This result is discussed in terms of the significant contribution made to protein film strength by both electrostatic interactions and the hydrophobic effect. Washout experiments to remove protein from the bulk phase have shown that a small percentage of the interfacially adsorbed lysozyme molecules are reversibly adsorbed. Finally, the washout tests have probed the role played by additional adsorption to the fresh interface formed by the application of a large strain to the lysozyme film and have suggested the movement of reversibly bound lysozyme molecules from a subinterfacial layer to the interface.

Drug combination: pharmaceutical technologies applied to the manufacturing of combined dosage forms for oral administration

Lo scopo di questa ricerca di dottorato è stato lo studio di una forma di dosaggio flessibile e personalizzabile, indirizzata alle necessità individuali di ogni paziente, per il trattamento dell’iperplasia prostatica benigna. La terapia proposta prevede l’utilizzo di due farmaci, un alfa bloccante (farmaco A) e un inibitore delle 5- fosfodiesterasi (farmaco B) e, somministrati in una singola forma di dosaggio contenenti differenti dosi e combinazioni dei due farmaci. Lo sviluppo di un sistema di rilascio per la somministrazione orale di farmaco A e farmaco B è stato realizzato grazie alla tecnologia Dome Matrix. La tecnologia si basa sull’assemblaggio di moduli utilizzati come elementi di controllo del rilascio. L’assemblaggio dei moduli può essere ottenuto attraverso diverse configurazioni. Sono stati quindi realizzati sistemi assemblati in grado di galleggiare sul contenuto gastrico; la prolungata permanenza della forma farmaceutica nello stomaco favorisce la solubilizzazione dei due principi attivi che quindi potrebbero raggiungere il sito di assorbimento nel primo tratto intestinale già in dispersione molecolare, condizione ideale per essere assorbiti. La prima parte della ricerca è stata focalizzata sulla realizzazione di un sistema assemblato a rilascio modificato di farmaco A. Moduli contenenti diversi dosaggi di farmaco sono stati assemblati in varie configurazioni e dosi differenti per ottenere una forma di dosaggio flessibile, adattabile alle esigenze terapeutiche del paziente. La seconda parte del lavoro di tesi ha riguardato la realizzazione di un sistema assemblato, contenente entrambi i farmaci in associazione. L’ultima parte della ricerca è stata svolta presso la “University of Texas at Austin” sotto la supervisione del Professor Nicholas Peppas. Il lavoro svolto è stato focalizzato sullo studio delle caratteristiche di rigonfiamento dei singoli moduli di farmaco e dei loro sistemi assemblati; il comportamento di tali sistemi è stato investigato anche grazie all’utilizzo della tecnica di tomografia computerizzata a raggi X.

The vibrational spectra of rectangular plates

The wire drive pulse-echo system has been extensively used to excite and measure modes of vibration of thin rectangular plates. The frequency spectra of different modes have been investigated as a function of the material elastic moduli and the plate geometry. Most of the work was carried out on isotropic materials. For square plates a wide selection of materials were used. These were made isotropic in their in-plane dimensions where the displacements are taking place. The range of rnaterials enabled the dependence on Poisson's ratio to be investigated. A method of determining the value of Poisson's ratio resulted from this investigation. Certain modes are controlled principally by the shear modulus. Of these the fundamental has two nodal lines across the plate surface. One of them, which has nodes at the corners, (the Lame mode) is uniquely a pure shear mode where the diagonal is a full wave length. One controlled by the Young's modulus has been found. The precise harmonic relationship of the Lame mode series in square and rectangular plates was established. Use of the Rayleigh-Lamb equation has extended the theoretical support. The low order modes were followed over a wide range of sides ratios. Two fundamental types of modes have been recognised; These are the longitudinal modes where the frequency is controlled by the length of the plate only and the 2~f product has an asymptotic value approaching the rod velocity. The other type is the in-plane flexural modes (in effect a flexurally vibrating bar where the -2/w is the geometrical parameter). Where possible the experimental work was related to theory. Other modes controlled by the width dimension of the plate were followed. Anisotropic materials having rolled sheet elastic symmetry were investigated in terms of the appropriate theory. The work has been extended to examine materials from welds in steel plates.

Studies on the generalisation of Gaussian processes and Bayesian neural networks

The assessment of the reliability of systems which learn from data is a key issue to investigate thoroughly before the actual application of information processing techniques to real-world problems. Over the recent years Gaussian processes and Bayesian neural networks have come to the fore and in this thesis their generalisation capabilities are analysed from theoretical and empirical perspectives. Upper and lower bounds on the learning curve of Gaussian processes are investigated in order to estimate the amount of data required to guarantee a certain level of generalisation performance. In this thesis we analyse the effects on the bounds and the learning curve induced by the smoothness of stochastic processes described by four different covariance functions. We also explain the early, linearly-decreasing behaviour of the curves and we investigate the asymptotic behaviour of the upper bounds. The effect of the noise and the characteristic lengthscale of the stochastic process on the tightness of the bounds are also discussed. The analysis is supported by several numerical simulations. The generalisation error of a Gaussian process is affected by the dimension of the input vector and may be decreased by input-variable reduction techniques. In conventional approaches to Gaussian process regression, the positive definite matrix estimating the distance between input points is often taken diagonal. In this thesis we show that a general distance matrix is able to estimate the effective dimensionality of the regression problem as well as to discover the linear transformation from the manifest variables to the hidden-feature space, with a significant reduction of the input dimension. Numerical simulations confirm the significant superiority of the general distance matrix with respect to the diagonal one.In the thesis we also present an empirical investigation of the generalisation errors of neural networks trained by two Bayesian algorithms, the Markov Chain Monte Carlo method and the evidence framework; the neural networks have been trained on the task of labelling segmented outdoor images.

A peak-clustering method for MEG group analysis to minimise artefacts due to smoothness

Magnetoencephalography (MEG), a non-invasive technique for characterizing brain electrical activity, is gaining popularity as a tool for assessing group-level differences between experimental conditions. One method for assessing task-condition effects involves beamforming, where a weighted sum of field measurements is used to tune activity on a voxel-by-voxel basis. However, this method has been shown to produce inhomogeneous smoothness differences as a function of signal-to-noise across a volumetric image, which can then produce false positives at the group level. Here we describe a novel method for group-level analysis with MEG beamformer images that utilizes the peak locations within each participant's volumetric image to assess group-level effects. We compared our peak-clustering algorithm with SnPM using simulated data. We found that our method was immune to artefactual group effects that can arise as a result of inhomogeneous smoothness differences across a volumetric image. We also used our peak-clustering algorithm on experimental data and found that regions were identified that corresponded with task-related regions identified in the literature. These findings suggest that our technique is a robust method for group-level analysis with MEG beamformer images.

A decade of silicone hydrogel development:surface properties, mechanical properties, and ocular compatibility

Since the initial launch of silicone hydrogel lenses, there has been a considerable broadening in the range of available commercial material properties. The very mobile silicon–oxygen bonds convey distinctive surface and mechanical properties on silicone hydrogels, in which advantages of enhanced oxygen permeability, reduced protein deposition, and modest frictional interaction are balanced by increased lipid and elastic response. There are now some 15 silicone hydrogel material variants available to practitioners; arguably, the changes that have taken place have been strongly influenced by feedback based on clinical experience. Water content is one of the most influential properties, and the decade has seen a progressive rise from lotrafilcon-A (24%) to efrofilcon-A (74%). Moduli have decreased over the same period from 1.4 to 0.3 MPa, but not solely as a result of changes in water content. Surface properties do not correlate directly with water content, and ingenious approaches have been used to achieve desirable improvements (e.g., greater lubricity and lower contact angle hysteresis). This is demonstrated by comparing the hysteresis value of the earliest (lotrafilcon-A, >40°) and most recent (delefilcon-A, <10°) coated silicone hydrogels. Although wettability is important, it is not of itself a good predictor of ocular response because this involves a much wider range of physicochemical and biochemical factors. The interference of the lens with ocular dynamics is complex leading separately to tissue–material interactions involving anterior and posterior lens surfaces. The biochemical consequences of these interactions may hold the key to a greater understanding of ocular incompatibility and end of day discomfort.

Fast reconstruction of harmonic functions from Cauchy data using integral equation techniques

We consider the problem of stable determination of a harmonic function from knowledge of the solution and its normal derivative on a part of the boundary of the (bounded) solution domain. The alternating method is a procedure to generate an approximation to the harmonic function from such Cauchy data and we investigate a numerical implementation of this procedure based on Fredholm integral equations and Nyström discretization schemes, which makes it possible to perform a large number of iterations (millions) with minor computational cost (seconds) and high accuracy. Moreover, the original problem is rewritten as a fixed point equation on the boundary, and various other direct regularization techniques are discussed to solve that equation. We also discuss how knowledge of the smoothness of the data can be used to further improve the accuracy. Numerical examples are presented showing that accurate approximations of both the solution and its normal derivative can be obtained with much less computational time than in previous works.

Examining crystallographic orientation dependence of hardness of silica stishovite

We conducted nanoindentation to explore the hardness and elastic properties of silica stishovite, synthesized at high pressure and quenched to ambient conditions. A total of 10 crystallographic orientations were examined on selected grains with a maximum load of 4 or 20 mN. We observed discontinuity in the load-displacement curve (pop-in) for the [2 5 over(1, -)] and [6 2 over(1, -)] grains subjected to a maximum load of 20 mN. The single-crystal hardness at high plastic deformation is quasi-isotropic with an average of 32 ± 1 GPa, similar to the polycrystalline hardness reported earlier; the theoretical hardness determined from the experiments is about 54 ± 3 GPa. These two hardnesses suggest that stishovite is one of the hardest oxides. The measured indentation moduli are close to the predictions at low load (minor plasticity) but are considerably lower at high load (high plasticity). Both indentation hardness and modulus decrease with increasing plasticity. Our results underscore the necessity of considering the degree of plastic deformation when interpreting hardness and elastic moduli from indentation experiments. © 2007 Elsevier B.V. All rights reserved.

Three-dimensional finite element analysis of the effects of anisotropy on bone mechanical properties measured by nanoindentation

A three-dimensional finite element analysis (FEA) model with elastic-plastic anisotropy was built to investigate the effects of anisotropy on nanoindentation measurements for cortical bone. The FEA model has demonstrated a capability to capture the cortical bone material response under the indentation process. By comparison with the contact area obtained from monitoring the contact profile in FEA simulations, the Oliver-Pharr method was found to underpredict or overpredict the contact area due to the effects of anisotropy. The amount of error (less than 10% for cortical bone) depended on the indentation orientation. The indentation modulus results obtained from FEA simulations at different surface orientations showed a trend similar to experimental results and were also similar to moduli calculated from a mathematical model. The Oliver-Pharr method has been shown to be useful for providing first-order approximations in the analysis of anisotropic mechanical properties of cortical bone, although the indentation modulus is influenced by anisotropy.

Effect of thermal and mechanical processing on tensile properties of powder formed 2124 aluminium and 2124 Al-SiC p metal matrix composite

The aging responses of 2124 Al-SiC p metal matrix composite (MMC) and unreinforced matrix alloy are studied and related to variations in tensile properties. The MMC is aged from Wo starting conditions: (i) stretched and naturally aged and (ii) re-solution treated. Accelerated aging occurs in both MMC conditions compared with unreinforced alloy. Tensile strengths and elastic moduli are improved in the MMC compared with the alloy, but ductility is reduced. Stretched MMC exhibits higher strength but lower ductility and modulus than re-solutioned MMC. The re-solutioned MMC fails by microvoid coalescence in low aging conditions, and by void nucleation and shear in high aging conditions. Failure of the stretched MMC initiates at the surface at specimen shoulders, illustrating the increased notch sensitivity of this condition, and propagates via a zigzag shear fracture mode. Zigzag facet size increases on gross aging. Particle fracture occurs during tensile failure, but also before testing as a result of the manufacturing process. © 1995 The Institute of Materials.

On The Brill-noether Theory of Spanned Vector Bundles on Smooth Curves

Here we study the integers (d, g, r) such that on a smooth projective curve of genus g there exists a rank r stable vector bundle with degree d and spanned by its global sections.

Symplectic Representation of a Braid Group on 3-Sheeted Covers of the Riemann Sphere

We define Picard cycles on each smooth three-sheeted Galois cover C of the Riemann sphere. The moduli space of all these algebraic curves is a nice Shimura surface, namely a symmetric quotient of the projective plane uniformized by the complex two-dimensional unit ball. We show that all Picard cycles on C form a simple orbit of the Picard modular group of Eisenstein numbers. The proof uses a special surface classification in connection with the uniformization of a classical Picard-Fuchs system. It yields an explicit symplectic representation of the braid groups (coloured or not) of four strings.

A Note on Preserved Smoothness

* Supported by NSERC (Canada)

A Note on Coercivity of Lower Semicontinuous Functions and Nonsmooth Critical Point Theory

The first motivation for this note is to obtain a general version of the following result: let E be a Banach space and f : E → R be a differentiable function, bounded below and satisfying the Palais-Smale condition; then, f is coercive, i.e., f(x) goes to infinity as ||x|| goes to infinity. In recent years, many variants and extensions of this result appeared, see [3], [5], [6], [9], [14], [18], [19] and the references therein. A general result of this type was given in [3, Theorem 5.1] for a lower semicontinuous function defined on a Banach space, through an approach based on an abstract notion of subdifferential operator, and taking into account the “smoothness” of the Banach space. Here, we give (Theorem 1) an extension in a metric setting, based on the notion of slope from [11] and coercivity is considered in a generalized sense, inspired by [9]; our result allows to recover, for example, the coercivity result of [19], where a weakened version of the Palais-Smale condition is used. Our main tool (Proposition 1) is a consequence of Ekeland’s variational principle extending [12, Corollary 3.4], and deals with a function f which is, in some sense, the “uniform” Γ-limit of a sequence of functions.