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.

Coherent propagation and energy transfer in low-dimension nonlinear arrays

We present a theory of coherent propagation and energy or power transfer in a low-dimension array of coupled nonlinear waveguides. It is demonstrated that in the array with nonequal cores (e.g., with the central core) stable steady-state coherent multicore propagation is possible only in the nonlinear regime, with a power-controlled phase matching. The developed theory of energy or power transfer in nonlinear discrete systems is rather generic and has a range of potential applications including both high-power fiber lasers and ultrahigh-capacity optical communication systems. © 2012 American Physical Society.

Smart structure sensors based on embedded fibre Bragg grating arrays in aluminium alloy matrix by ultrasonic consolidation

Smart structure sensors based on embedded fibre Bragg grating (FBG) arrays in aluminium alloy matrix by ultrasonic consolidation (UC) technique have been proposed and demonstrated successfully. The temperature, loading and bending responses of the embedded FBG arrays have been systematically characterized. The embedded FBGs exhibit an average temperature sensitivity of ~36 pm °C-1, which is three times higher than that of normal FBGs, a bending sensitivity of 0.73 nm/m-1 and a loading responsivity of ~0.1 nm kg-1 within the dynamic range from 0 kg to 3 kg. These initial experimental results clearly demonstrate that the UC produced metal matrix structures can be embedded with FBG sensor arrays to become smart structures with capabilities to monitor the structure operation and health conditions in applications.

Performance data indicate summation for pictorial depth-cues in slanted surfaces

Over recent years much has been learned about the way in which depth cues are combined (e.g. Landy et al., 1995). The majority of this work has used subjective measures, a rating scale or a point of subjective equality, to deduce the relative contributions of different cues to perception. We have adopted a very different approach by using two interval forced-choice (2IFC) performance measures and a signal processing framework. We performed summation experiments for depth cue increment thresholds between pairs of pictorial depth cues in displays depicting slanted planar surfaces made from arrays of circular 'contrast' elements. Summation was found to be ideal when size-gradient was paired with contrast-gradient for a wide range of depth-gradient magnitudes in the null stimulus. For a pairing of size-gradient and linear perspective, substantial summation (> 1.5 dB) was found only when the null stimulus had intermediate depth gradients; when flat or steeply inclined surfaces were depicted, summation was diminished or abolished. Summation was also abolished when one of the target cues was (i) not a depth cue, or (ii) added in conflict. We conclude that vision has a depth mechanism for the constructive combination of pictorial depth cues and suggest two generic models of summation to describe the results. Using similar psychophysical methods, Bradshaw and Rogers (1996) revealed a mechanism for the depth cues of motion parallax and binocular disparity. Whether this is the same or a different mechanism from the one reported here awaits elaboration.

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.

Possibilities and limitations of coded aperture imaging

We have simulated the performance of various apertures used in Coded Aperture Imaging - optically. Coded pictures of extended and continuous-tone planar objects from the Annulus, Twin Annulus, Fresnel Zone Plate and the Uniformly Redundant Array have been decoded using a noncoherent correlation process. We have compared the tomographic capabilities of the Twin Annulus with the Uniformly Redundant Arrays based on quadratic residues and m-sequences. We discuss the ways of reducing the 'd. c.' background of the various apertures used. The non-ideal System-Point-Spread-Function inherent in a noncoherent optical correlation process produces artifacts in the reconstruction. Artifacts are also introduced as a result of unwanted cross-correlation terms from out-of-focus planes. We find that the URN based on m-sequences exhibits good spatial resolution and out-of-focus behaviour when imaging extended objects.

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.

Recovering boundary data in planar heat conduction using boundary integral equation method

We consider a Cauchy problem for the heat equation, where the temperature field is to be reconstructed from the temperature and heat flux given on a part of the boundary of the solution domain. We employ a Landweber type method proposed in [2], where a sequence of mixed well-posed problems are solved at each iteration step to obtain a stable approximation to the original Cauchy problem. We develop an efficient boundary integral equation method for the numerical solution of these mixed problems, based on the method of Rothe. Numerical examples are presented both with exact and noisy data, showing the efficiency and stability of the proposed procedure and approximations.

Transition of planar Couette flow at infinite Reynolds numbers

An outline of the state space of planar Couette flow at high Reynolds numbers (Re<105) is investigated via a variety of efficient numerical techniques. It is verified from nonlinear analysis that the lower branch of the hairpin vortex state (HVS) asymptotically approaches the primary (laminar) state with increasing Re. It is also predicted that the lower branch of the HVS at high Re belongs to the stability boundary that initiates a transition to turbulence, and that one of the unstable manifolds of the lower branch of HVS lies on the boundary. These facts suggest HVS may provide a criterion to estimate a minimum perturbation arising transition to turbulent states at the infinite Re limit. © 2013 American Physical Society.

Emergent behaviour in arrays of coupled nonlinear oscillators

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Planar variations in normal anisotropy in mild steel strip

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Controlled growth of poly(2-(diethylamino)ethyl methacrylate) brushes via atom transfer radical polymerisation on planar silicon surfaces

Progress in making pH-responsive polyelectrolyte brushes with a range of different grafting densities is reported. Polymer brushes of poly(2-(diethylamino)ethyl methacrylate) were synthesised via atom transfer radical polymerisation on silicon wafers using a 'grafted from' approach. The [11-(2-bromo-2-methyl) propionyloxy]undecyl trichlorosilane initiator was covalently attached to the silicon via silylation, from which the brushes were grown using a catalytic system of copper(I) chloride and pentamethyldiethylenetriamine in tetrahydrofuran at 80°C. X-ray reflectivity was used to assess the initiator surfaces and an upper limit on the grafting density of the polymer was determined. The quality of the brushes produced was analysed using ellipsometry and atomic force microscopy, which is also discussed.