Methods of studying the planar distribution of objects in histological sections of brain tissue

This article reviews the statistical methods that have been used to study the planar distribution, and especially clustering, of objects in histological sections of brain tissue. The objective of these studies is usually quantitative description, comparison between patients or correlation between histological features. Objects of interest such as neurones, glial cells, blood vessels or pathological features such as protein deposits appear as sectional profiles in a two-dimensional section. These objects may not be randomly distributed within the section but exhibit a spatial pattern, a departure from randomness either towards regularity or clustering. The methods described include simple tests of whether the planar distribution of a histological feature departs significantly from randomness using randomized points, lines or sample fields and more complex methods that employ grids or transects of contiguous fields, and which can detect the intensity of aggregation and the sizes, distribution and spacing of clusters. The usefulness of these methods in understanding the pathogenesis of neurodegenerative diseases such as Alzheimer's disease and Creutzfeldt-Jakob disease is discussed. © 2006 The Royal Microscopical Society.

Hairpin vortex solution in planar Couette flow: a tapestry of knotted vortices

A numerical continuation method has been carried out seeking solutions for two distinct flow configurations, planar Couette flow (PCF) and laterally heated flow in a vertical slot (LHF). We found that the spanwise vortex solution in LHF identifies a new solution in PCF. The vortical structure of our new solution has the shape of a hairpin observed ubiquitously in high-Reynolds-number turbulent flow, and we believe this discovery may provide the paradigm for a hierarchical organization of coherent structures in turbulent shear layers.

Professionalisation and ophthalmic optics

This thesis is a sociological study of the ophthalmic optical profession in Britain. It includes a survey of the development of ophthalmic optics as an occupation and three questionnaire, surveys, one each of first and final year ophthalmic optics students, and one of practising opticians. The developmental survey showed that four themes have been important in the occupation's process of professionalisation - the actions of the opticians' leaders, the gradual unification of the bodies, representing segments of the profession, the struggle with medicine and the involvement of ophthalmic opticians in state-organised optical welfare schemes. The student surveys showed that the profession is now recruiting largely from middle class, state educated groups, and increasingly from women, who hold significantly different attitudes to income, independence and career commitment. In general, both first and final year students considered service to be rather more important than furthering knowledge. Practising opticians have been recruited increasingly, from middle class backgrounds, mostly from state selective secondary schools, but with a large minority from non-state schools. The self-recruitment rate of the profession (18.9%) is very similar to that for British medical students. Significant differences in concepts of professionalism were found among ophthalmic opticians of different ages, sexes and types of practice but few among those in different areas of practice. In general, ophthalmic opticians seemed to stress service more·than furthering knowledge. It is suggested that the leaders of the profession have 'negotiated' considerable autonomy for its members and that the possibilities for commercialism within the ophthalmic optician's professional role are intrinsically no greater than those in more 'established' professions.

Dissipative nonlinear structures in fiber optics

Optical fiber materials exhibit a nonlinear response to strong electric fields, such as those of optical signals confined within the small fiber core. Fiber nonlinearity is an essential component in the design of the next generation of advanced optical communication systems, but its use is often avoided by engineers because of its intractability. The application of nonlinear technologies in fiber optics offers new opportunities for the design of photonic systems and devices. In this chapter, we make an overview of recent progress in mathematical theory and practical applications of temporal dissipative solitons and self-similar nonlinear structures in optical fiber systems. The design of all-optical high-speed signal processing devices, based on nonlinear dissipative structures, is discussed.

Single process femtosecond microfabrication of key components for integrated optics

We present recent results on femtosecond microfabrication of key components for integrated optics such as highly curved low-loss waveguides in glasses, depressed cladding waveguides in crystals. Details of microfabrication and characterisation are discussed.

Fibre optics sensors in tear electrolyte analysis:towards a novel point of care potassium sensor

The diagnosis of ocular disease is increasingly important in optometric practice and there is a need for cost effective point of care assays to assist in that. Although tears are a potentially valuable source of diagnostic information difficulties associated with sample collection and limited sample size together with sample storage and transport have proved major limitations. Progressive developments in electronics and fibre optics together with innovation in sensing technology mean that the construction of inexpensive point of care fibre optic sensing devices is now possible. Tear electrolytes are an obvious family of target analytes, not least to complement the availability of devices that make the routine measurement of tear osmolarity possible in the clinic. In this paper we describe the design, fabrication and calibration of a fibre-optic based electrolyte sensor for the quantification of potassium in tears using the ex vivo contact lens as the sample source. The technology is generic and the same principles can be used in the development of calcium and magnesium sensors. An important objective of this sensor technology development is to provide information at the point of routine optometric examination, which would provide supportive evidence of tear abnormality.

Determining planar multiple sound-soft obstacles from scattered acoustic fields

An inverse problem is considered where the structure of multiple sound-soft planar obstacles is to be determined given the direction of the incoming acoustic field and knowledge of the corresponding total field on a curve located outside the obstacles. A local uniqueness result is given for this inverse problem suggesting that the reconstruction can be achieved by a single incident wave. A numerical procedure based on the concept of the topological derivative of an associated cost functional is used to produce images of the obstacles. No a priori assumption about the number of obstacles present is needed. Numerical results are included showing that accurate reconstructions can be obtained and that the proposed method is capable of finding both the shapes and the number of obstacles with one or a few incident waves.

An alternating potential based approach for a Cauchy problem for the Laplace equation in a planar domain with a cut

We consider a Cauchy problem for the Laplace equation in a bounded region containing a cut, where the region is formed by removing a sufficiently smooth arc (the cut) from a bounded simply connected domain D. The aim is to reconstruct the solution on the cut from the values of the solution and its normal derivative on the boundary of the domain D. We propose an alternating iterative method which involves solving direct mixed problems for the Laplace operator in the same region. These mixed problems have either a Dirichlet or a Neumann boundary condition imposed on the cut and are solved by a potential approach. Each of these mixed problems is reduced to a system of integral equations of the first kind with logarithmic and hypersingular kernels and at most a square root singularity in the densities at the endpoints of the cut. The full discretization of the direct problems is realized by a trigonometric quadrature method which has super-algebraic convergence. The numerical examples presented illustrate the feasibility of the proposed method.