Modelling ocular monochromatic aberrations using schematic eyes with homogeneous optical media

Previous research has indicated that schematic eyes incorporating aspheric surfaces but lacking gradient index are unable to model ocular spherical aberration and peripheral astigmatism simultaneously. This limits their use as wide-angle schematic eyes. This thesis challenges this assumption by investigating the flexibility of schematic eyes comprising aspheric optical surfaces and homogeneous optical media. The full variation of ocular component dimensions found in human eyes was established from the literature. Schematic eye parameter variants were limited to these dimensions. The levels of spherical aberration and peripheral astigmatism modelled by these schematic eyes were compared to the range of measured levels. These were also established from the literature. To simplify comparison of modelled and measured data, single value parameters were introduced; the spherical aberration function (SAF), and peripheral astigmatism function (PAF). Some ocular components variations produced a wide range of aberrations without exceeding the limits of human ocular components. The effect of ocular component variations on coma was also investigated, but no comparison could be made as no empirical data exists. It was demonstrated that by combined manipulation of a number of parameters in the schematic eyes it was possible to model all levels of ocular spherical aberration and peripheral astigmatism. However, the unique parameters of a human eye could not be obtained in this way, as a number of models could be used to produce the same spherical aberration and peripheral astigmatism, while giving very different coma levels. It was concluded that these schematic eyes are flexible enough to model the monochromatic aberrations tested, the absence of gradient index being compensated for by altering the asphericity of one or more surfaces.

Laminar distribution of the pathological changes in sporadic frontotemporal lobar degeneration with transactive response (TAR) DNA-binding protein of 43kDa (TDP-43) proteinopathy:a quantitative study using polynomial curve fitting

Aims: Previous data suggest heterogeneity in laminar distribution of the pathology in the molecular disorder frontotemporal lobar degeneration (FTLD) with transactive response (TAR) DNA-binding protein of 43kDa (TDP-43) proteinopathy (FTLD-TDP). To study this heterogeneity, we quantified the changes in density across the cortical laminae of neuronal cytoplasmic inclusions, glial inclusions, neuronal intranuclear inclusions, dystrophic neurites, surviving neurones, abnormally enlarged neurones, and vacuoles in regions of the frontal and temporal lobe. Methods: Changes in density of histological features across cortical gyri were studied in 10 sporadic cases of FTLD-TDP using quantitative methods and polynomial curve fitting. Results: Our data suggest that laminar neuropathology in sporadic FTLD-TDP is highly variable. Most commonly, neuronal cytoplasmic inclusions, dystrophic neurites and vacuolation were abundant in the upper laminae and glial inclusions, neuronal intranuclear inclusions, abnormally enlarged neurones, and glial cell nuclei in the lower laminae. TDP-43-immunoreactive inclusions affected more of the cortical profile in longer duration cases; their distribution varied with disease subtype, but was unrelated to Braak tangle score. Different TDP-43-immunoreactive inclusions were not spatially correlated. Conclusions: Laminar distribution of pathological features in 10 sporadic cases of FTLD-TDP is heterogeneous and may be accounted for, in part, by disease subtype and disease duration. In addition, the feedforward and feedback cortico-cortical connections may be compromised in FTLD-TDP. © 2012 The Authors. Neuropathology and Applied Neurobiology © 2012 British Neuropathological Society.

An alternating method for Cauchy problems for Helmholtz-type operators in non-homogeneous medium

Kozlov & Maz'ya (1989, Algebra Anal., 1, 144–170) proposed an alternating iterative method for solving Cauchy problems for general strongly elliptic and formally self-adjoint systems. However, in many applied problems, operators appear that do not satisfy these requirements, e.g. Helmholtz-type operators. Therefore, in this study, an alternating procedure for solving Cauchy problems for self-adjoint non-coercive elliptic operators of second order is presented. A convergence proof of this procedure is given.

Precipitation of magnesium ammonium phosphate from homogeneous solution

DUE TO COPYRIGHT RESTRICTIONS ONLY AVAILABLE FOR CONSULTATION AT ASTON UNIVERSITY LIBRARY AND INFORMATION SERVICES WITH PRIOR ARRANGEMENT

Polynomial function intervals for floating-point software verification

The focus of our work is the verification of tight functional properties of numerical programs, such as showing that a floating-point implementation of Riemann integration computes a close approximation of the exact integral. Programmers and engineers writing such programs will benefit from verification tools that support an expressive specification language and that are highly automated. Our work provides a new method for verification of numerical software, supporting a substantially more expressive language for specifications than other publicly available automated tools. The additional expressivity in the specification language is provided by two constructs. First, the specification can feature inclusions between interval arithmetic expressions. Second, the integral operator from classical analysis can be used in the specifications, where the integration bounds can be arbitrary expressions over real variables. To support our claim of expressivity, we outline the verification of four example programs, including the integration example mentioned earlier. A key component of our method is an algorithm for proving numerical theorems. This algorithm is based on automatic polynomial approximation of non-linear real and real-interval functions defined by expressions. The PolyPaver tool is our implementation of the algorithm and its source code is publicly available. In this paper we report on experiments using PolyPaver that indicate that the additional expressivity does not come at a performance cost when comparing with other publicly available state-of-the-art provers. We also include a scalability study that explores the limits of PolyPaver in proving tight functional specifications of progressively larger randomly generated programs. © 2014 Springer International Publishing Switzerland.

Fundamental Pd0/PdII redox steps in cross-coupling reactions:homogeneous, hybrid homogeneous-heterogeneous to heterogeneous mechanistic pathways for C-C couplings

C–C bond-forming, cross-coupling reactions of organohalides with nucleophilic compounds, catalysed by palladium, are amongst the most important chemical reactions available to the synthetic chemist. The intimate mechanisms of these reactions, involving Pd0/PdII redox steps, have been of great historical interest and continue to be so. The myriad of possible mechanisms is reviewed in this chapter. The interplay of mononuclear Pd species with higher order Pd species, e.g. nanoclusters/nanoparticles are considered as being equally important in cross-coupling reaction mechanisms. A focus is placed on trichotomic behaviour of cross-coupling catalytic manifolds, from homogeneous to hybrid homogeneous–heterogeneous to truly heterogeneous behaviour. For the latter, surface chemistry and metal atom leaching (and various experimental techniques) are broadly discussed. It is now clear that mechanism for general cross‐coupling reactions, that is as presented to undergraduate students studying Chemistry degrees across the world, is undoubtedly more complex than first thought. New opportunities for catalyst design have therefore emerged in the area of Pd nanoparticles and nanocatalysis, with some wonderful applications especially in chemical biology, providing a snapshot of what the future might hold.

Selective in vitro glycosylation of recombinant proteins:semi-synthesis of novel homogeneous glycoforms of human erythropoietin

Background: A natural glycoprotein usually exists as a spectrum of glycosylated forms, where each protein molecule may be associated with an array of oligosaccharide structures. The overall range of glycoforms can have a variety of different biophysical and biochemical properties, although details of structure–function relationships are poorly understood, because of the microheterogeneity of biological samples. Hence, there is clearly a need for synthetic methods that give access to natural and unnatural homogeneously glycosylated proteins. The synthesis of novel glycoproteins through the selective reaction of glycosyl iodoacetamides with the thiol groups of cysteine residues, placed by site-directed mutagenesis at desired glycosylation sites has been developed. This provides a general method for the synthesis of homogeneously glycosylated proteins that carry saccharide side chains at natural or unnatural glycosylation sites. Here, we have shown that the approach can be applied to the glycoprotein hormone erythropoietin, an important therapeutic glycoprotein with three sites of N-glycosylation that are essential for in vivo biological activity. Results: Wild-type recombinant erythropoietin and three mutants in which glycosylation site asparagine residues had been changed to cysteines (His10-WThEPO, His10-Asn24Cys, His10-Asn38Cys, His10-Asn83CyshEPO) were overexpressed and purified in yields of 13 mg l−1 from Escherichia coli. Chemical glycosylation with glycosyl-β-N-iodoacetamides could be monitored by electrospray MS. Both in the wild-type and in the mutant proteins, the potential side reaction of the other four cysteine residues (all involved in disulfide bonds) were not observed. Yield of glycosylation was generally about 50% and purification of glycosylated protein from non-glycosylated protein was readily carried out using lectin affinity chromatography. Dynamic light scattering analysis of the purified glycoproteins suggested that the glycoforms produced were monomeric and folded identically to the wild-type protein. Conclusions: Erythropoietin expressed in E. coli bearing specific Asn→Cys mutations at natural glycosylation sites can be glycosylated using β-N-glycosyl iodoacetamides even in the presence of two disulfide bonds. The findings provide the basis for further elaboration of the glycan structures and development of this general methodology for the synthesis of semi-synthetic glycoproteins. Results: Wild-type recombinant erythropoietin and three mutants in which glycosylation site asparagine residues had been changed to cysteines (His10-WThEPO, His10-Asn24Cys, His10-Asn38Cys, His10-Asn83CyshEPO) were overexpressed and purified in yields of 13 mg l−1 from Escherichia coli. Chemical glycosylation with glycosyl-β-N-iodoacetamides could be monitored by electrospray MS. Both in the wild-type and in the mutant proteins, the potential side reaction of the other four cysteine residues (all involved in disulfide bonds) were not observed. Yield of glycosylation was generally about 50% and purification of glycosylated protein from non-glycosylated protein was readily carried out using lectin affinity chromatography. Dynamic light scattering analysis of the purified glycoproteins suggested that the glycoforms produced were monomeric and folded identically to the wild-type protein. Conclusions: Erythropoietin expressed in E. coli bearing specific Asn→Cys mutations at natural glycosylation sites can be glycosylated using β-N-glycosyl iodoacetamides even in the presence of two disulfide bonds. The findings provide the basis for further elaboration of the glycan structures and development of this general methodology for the synthesis of semi-synthetic glycoproteins

On the Hyperbolicity Domain of the Polynomial x^n + a1x^(n-1) + 1/4+ an

∗ Partially supported by INTAS grant 97-1644

Weak Polynomial Identities for M1,1(E)

* Partially supported by Universita` di Bari: progetto “Strutture algebriche, geometriche e descrizione degli invarianti ad esse associate”.

Polynomial Automorphisms Over Finite Fields

It is shown that the invertible polynomial maps over a finite field Fq , if looked at as bijections Fn,q −→ Fn,q , give all possible bijections in the case q = 2, or q = p^r where p > 2. In the case q = 2^r where r > 1 it is shown that the tame subgroup of the invertible polynomial maps gives only the even bijections, i.e. only half the bijections. As a consequence it is shown that a set S ⊂ Fn,q can be a zero set of a coordinate if and only if #S = q^(n−1).

Dubrovin Type Equations for Completely Integrable Systems Associated with a Polynomial Pencil

Dubrovin type equations for the N -gap solution of a completely integrable system associated with a polynomial pencil is constructed and then integrated to a system of functional equations. The approach used to derive those results is a generalization of the familiar process of finding the 1-soliton (1-gap) solution by integrating the ODE obtained from the soliton equation via the substitution u = u(x + λt).

MRI pressure and stress measurement in novel homogeneous soft solids

This paper presents MRI measurements of a novel semi solid MR contrast agent to pressure. The agent is comprised of potassium chloride cross linked carageenan gum at a concentration of 2% w/v, with micron size lipid coated bubbles of air at a concentration of 3% v/v. The choice for an optimum suspending medium, the methods of production and the preliminary MRI results are presented herein. The carageenan gum is shown to be ideally elastic for compressions relating to volume changes less than 15%, in contrast to the inelastic gellan gum also tested. Although slightly lower than that of gellan gum, carageenan has a water diffusion coefficient of 1.72×10-9 m2.s-1 indicating its suitability to this purpose. RARE imaging is performed whilst simultaneously compressing test and control samples and a maximum sensitivity of 1.6% MR signal change per % volume change is found which is shown to be independent of proton density variations due to the presence of microbubbles and compression. This contrast agent could prove useful for numerous applications, and particularly in chemical engineering. More generally the method allows the user to non-invasively image with MRI any process that causes, within the solid, local changes either in bubble size or bubble shape. © 2008 American Institute of Physics.

Quadratic Mean Radius of a Polynomial in C(Z)

* Dedicated to the memory of Prof. N. Obreshkoff

Polynomial Expansions for Solutions of Higher-Order Bessel Heat Equation in Quantum Calculus

Mathematics Subject Class.: 33C10,33D60,26D15,33D05,33D15,33D90

The Eccentric Connectivity Polynomial of some Graph Operations

The eccentric connectivity index of a graph G, ξ^C, was proposed by Sharma, Goswami and Madan. It is defined as ξ^C(G) = ∑ u ∈ V(G) degG(u)εG(u), where degG(u) denotes the degree of the vertex x in G and εG(u) = Max{d(u, x) | x ∈ V (G)}. The eccentric connectivity polynomial is a polynomial version of this topological index. In this paper, exact formulas for the eccentric connectivity polynomial of Cartesian product, symmetric difference, disjunction and join of graphs are presented.