Numerical conformal mapping and mesh generation for polygonal and multiply-connected regions

Details are given of a boundary-fitted mesh generation method for use in modelling free surface flow and water quality. A numerical method has been developed for generating conformal meshes for curvilinear polygonal and multiply-connected regions. The method is based on the Cauchy-Riemann conditions for the analytic function and is able to map a curvilinear polygonal region directly onto a regular polygonal region, with horizontal and vertical sides. A set of equations have been derived for determining the lengths of these sides and the least-squares method has been used in solving the equations. Several numerical examples are presented to illustrate the method.

Evaluation of a boundary integral representation for the conformal mapping of the unit disk onto a simply-connected domain

A representation of the conformal mapping g of the interior or exterior of the unit circle onto a simply-connected domain Ω as a boundary integral in terms ofƒ|∂Ω is obtained, whereƒ :=g -l. A product integration scheme for the approximation of the boundary integral is described and analysed. An ill-conditioning problem related to the domain geometry is discussed. Numerical examples confirm the conclusions of this discussion and support the analysis of the quadrature scheme.

Approximations to the scattering of water waves by steep topography

A new method is developed for approximating the scattering of linear surface gravity waves on water of varying quiescent depth in two dimensions. A conformal mapping of the fluid domain onto a uniform rectangular strip transforms steep and discontinuous bed profiles into relatively slowly varying, smooth functions in the transformed free-surface condition. By analogy with the mild-slope approach used extensively in unmapped domains, an approximate solution of the transformed problem is sought in the form of a modulated propagating wave which is determined by solving a second-order ordinary differential equation. This can be achieved numerically, but an analytic solution in the form of a rapidly convergent infinite series is also derived and provides simple explicit formulae for the scattered wave amplitudes. Small-amplitude and slow variations in the bedform that are excluded from the mapping procedure are incorporated in the approximation by a straightforward extension of the theory. The error incurred in using the method is established by means of a rigorous numerical investigation and it is found that remarkably accurate estimates of the scattered wave amplitudes are given for a wide range of bedforms and frequencies.

Taxonomic free sorting: a successful method with older consumers and a novel approach to preference mapping

Taxonomic free sorting (TFS) is a fast, reliable and new technique in sensory science. The method extends the typical free sorting task where stimuli are grouped according to similarities, by asking respondents to combine their groups two at a time to produce a hierarchy. Previously, TFS has been used for the visual assessment of packaging whereas this study extends the range of potential uses of the technique to incorporate full sensory analysis by the target consumer, which, when combined with hedonic liking scores, was used to generate a novel preference map. Furthermore, to fully evaluate the efficacy of using the sorting method, the technique was evaluated with a healthy older adult consumer group. Participants sorted eight products into groups and described their reason at each stage as they combined those groups, producing a consumer-specific vocabulary. This vocabulary was combined with hedonic data from a separate group of older adults, to give the external preference map. Taxonomic sorting is a simple, fast and effective method for use with older adults, and its combination with liking data can yield a preference map constructed entirely from target consumer data.

Modelling habitat selection and distribution of the critically endangered Jerdon's courser Rhinoptilus bitorquatus in scrub jungle: an application of a new tracking method

1. Jerdon's courser Rhinoptilus bitorquatus is a nocturnally active cursorial bird that is only known to occur in a small area of scrub jungle in Andhra Pradesh, India, and is listed as critically endangered by the IUCN. Information on its habitat requirements is needed urgently to underpin conservation measures. We quantified the habitat features that correlated with the use of different areas of scrub jungle by Jerdon's coursers, and developed a model to map potentially suitable habitat over large areas from satellite imagery and facilitate the design of surveys of Jerdon's courser distribution. 2. We used 11 arrays of 5-m long tracking strips consisting of smoothed fine soil to detect the footprints of Jerdon's coursers, and measured tracking rates (tracking events per strip night). We counted the number of bushes and trees, and described other attributes of vegetation and substrate in a 10-m square plot centred on each strip. We obtained reflectance data from Landsat 7 satellite imagery for the pixel within which each strip lay. 3. We used logistic regression models to describe the relationship between tracking rate by Jerdon's coursers and characteristics of the habitat around the strips, using ground-based survey data and satellite imagery. 4. Jerdon's coursers were most likely to occur where the density of large (>2 m tall) bushes was in the range 300-700 ha(-1) and where the density of smaller bushes was less than 1000 ha(-1). This habitat was detectable using satellite imagery. 5. Synthesis and applications. The occurrence of Jerdon's courser is strongly correlated with the density of bushes and trees, and is in turn affected by grazing with domestic livestock, woodcutting and mechanical clearance of bushes to create pasture, orchards and farmland. It is likely that there is an optimal level of grazing and woodcutting that would maintain or create suitable conditions for the species. Knowledge of the species' distribution is incomplete and there is considerable pressure from human use of apparently suitable habitats. Hence, distribution mapping is a high conservation priority. A two-step procedure is proposed, involving the use of ground surveys of bush density to calibrate satellite image-based mapping of potential habitat. These maps could then be used to select priority areas for Jerdon's courser surveys. The use of tracking strips to study habitat selection and distribution has potential in studies of other scarce and secretive species.

Modelling habitat selection and distribution of the critically endangered Jerdon's courser Rhinoptilus bitorquatus in scrub jungle: an application of a new tracking method

1. Jerdon's courser Rhinoptilus bitorquatus is a nocturnally active cursorial bird that is only known to occur in a small area of scrub jungle in Andhra Pradesh, India, and is listed as critically endangered by the IUCN. Information on its habitat requirements is needed urgently to underpin conservation measures. We quantified the habitat features that correlated with the use of different areas of scrub jungle by Jerdon's coursers, and developed a model to map potentially suitable habitat over large areas from satellite imagery and facilitate the design of surveys of Jerdon's courser distribution. 2. We used 11 arrays of 5-m long tracking strips consisting of smoothed fine soil to detect the footprints of Jerdon's coursers, and measured tracking rates (tracking events per strip night). We counted the number of bushes and trees, and described other attributes of vegetation and substrate in a 10-m square plot centred on each strip. We obtained reflectance data from Landsat 7 satellite imagery for the pixel within which each strip lay. 3. We used logistic regression models to describe the relationship between tracking rate by Jerdon's coursers and characteristics of the habitat around the strips, using ground-based survey data and satellite imagery. 4. Jerdon's coursers were most likely to occur where the density of large (>2 m tall) bushes was in the range 300-700 ha(-1) and where the density of smaller bushes was less than 1000 ha(-1). This habitat was detectable using satellite imagery. 5. Synthesis and applications. The occurrence of Jerdon's courser is strongly correlated with the density of bushes and trees, and is in turn affected by grazing with domestic livestock, woodcutting and mechanical clearance of bushes to create pasture, orchards and farmland. It is likely that there is an optimal level of grazing and woodcutting that would maintain or create suitable conditions for the species. Knowledge of the species' distribution is incomplete and there is considerable pressure from human use of apparently suitable habitats. Hence, distribution mapping is a high conservation priority. A two-step procedure is proposed, involving the use of ground surveys of bush density to calibrate satellite image-based mapping of potential habitat. These maps could then be used to select priority areas for Jerdon's courser surveys. The use of tracking strips to study habitat selection and distribution has potential in studies of other scarce and secretive species.

Mapping fibre orientation in complex-shaped biological systems with micrometre resolution by scanning X-ray microdiffraction

A fully automated procedure to extract and to image local fibre orientation in biological tissues from scanning X-ray diffraction is presented. The preferred chitin fibre orientation in the flow sensing system of crickets is determined with high spatial resolution by applying synchrotron radiation based X-ray microbeam diffraction in conjunction with advanced sample sectioning using a UV micro-laser. The data analysis is based on an automated detection of azimuthal diffraction maxima after 2D convolution filtering (smoothing) of the 2D diffraction patterns. Under the assumption of crystallographic fibre symmetry around the morphological fibre axis, the evaluation method allows mapping the three-dimensional orientation of the fibre axes in space. The resulting two-dimensional maps of the local fibre orientations - together with the complex shape of the flow sensing system - may be useful for a better understanding of the mechanical optimization of such tissues.

Determining feature relevance for the grouping of motor unit action potentials through generative topographic mapping

The study of motor unit action potential (MUAP) activity from electrornyographic signals is an important stage on neurological investigations that aim to understand the state of the neuromuscular system. In this context, the identification and clustering of MUAPs that exhibit common characteristics, and the assessment of which data features are most relevant for the definition of such cluster structure are central issues. In this paper, we propose the application of an unsupervised Feature Relevance Determination (FRD) method to the analysis of experimental MUAPs obtained from healthy human subjects. In contrast to approaches that require the knowledge of a priori information from the data, this FRD method is embedded on a constrained mixture model, known as Generative Topographic Mapping, which simultaneously performs clustering and visualization of MUAPs. The experimental results of the analysis of a data set consisting of MUAPs measured from the surface of the First Dorsal Interosseous, a hand muscle, indicate that the MUAP features corresponding to the hyperpolarization period in the physisiological process of generation of muscle fibre action potentials are consistently estimated as the most relevant and, therefore, as those that should be paid preferential attention for the interpretation of the MUAP groupings.

Force shading and bump mapping using the friction cone algorithm

Previous work has presented the friction cone algorithm, a generalised method to resolve forces on a simulated haptic object when two or more fingers are in contact. Two extensions to the friction cone algorithm are presented: force shading and bump mapping. Force shading removes the discontinuities that are present when transitioning from one face to the next, whilst bump mapping provides a mechanism for rendering haptic textures on polygonal surfaces. Both these extensions can be combined whilst still maintaining the friction cone algorithm's intrinsic ability to simulate arbitrarily complex friction models.

Landscape state machines: Tools for evolutionary algorithm performance analyses and landscape/algorithm mapping

Many evolutionary algorithm applications involve either fitness functions with high time complexity or large dimensionality (hence very many fitness evaluations will typically be needed) or both. In such circumstances, there is a dire need to tune various features of the algorithm well so that performance and time savings are optimized. However, these are precisely the circumstances in which prior tuning is very costly in time and resources. There is hence a need for methods which enable fast prior tuning in such cases. We describe a candidate technique for this purpose, in which we model a landscape as a finite state machine, inferred from preliminary sampling runs. In prior algorithm-tuning trials, we can replace the 'real' landscape with the model, enabling extremely fast tuning, saving far more time than was required to infer the model. Preliminary results indicate much promise, though much work needs to be done to establish various aspects of the conditions under which it can be most beneficially used. A main limitation of the method as described here is a restriction to mutation-only algorithms, but there are various ways to address this and other limitations.

Modelling complex systems for project planning - A semiotics motivated method

A large and complex IT project may involve multiple organizations and be constrained within a temporal period. An organization is a system comprising of people, activities, processes, information, resources and goals. Understanding and modelling such a project and its interrelationship with relevant organizations are essential for organizational project planning. This paper introduces the problem articulation method (PAM) as a semiotic method for organizational infrastructure modelling. PAM offers a suite of techniques, which enables the articulation of the business, technical and organizational requirements, delivering an infrastructural framework to support the organization. It works by eliciting and formalizing (e. g. processes, activities, relationships, responsibilities, communications, resources, agents, dependencies and constraints) and mapping these abstractions to represent the manifestation of the "actual" organization. Many analysts forgo organizational modelling methods and use localized ad hoc and point solutions, but this is not amenable for organizational infrastructures modelling. A case study of the infrared atmospheric sounding interferometer (IASI) will be used to demonstrate the applicability of PAM, and to examine its relevancy and significance in dealing with the innovation and changes in the organizations.

A change detection approach to flood mapping in urban areas using TerraSAR-X

Very high-resolution Synthetic Aperture Radar sensors represent an alternative to aerial photography for delineating floods in built-up environments where flood risk is highest. However, even with currently available SAR image resolutions of 3 m and higher, signal returns from man-made structures hamper the accurate mapping of flooded areas. Enhanced image processing algorithms and a better exploitation of image archives are required to facilitate the use of microwave remote sensing data for monitoring flood dynamics in urban areas. In this study a hybrid methodology combining radiometric thresholding, region growing and change detection is introduced as an approach enabling the automated, objective and reliable flood extent extraction from very high-resolution urban SAR images. The method is based on the calibration of a statistical distribution of “open water” backscatter values inferred from SAR images of floods. SAR images acquired during dry conditions enable the identification of areas i) that are not “visible” to the sensor (i.e. regions affected by ‘layover’ and ‘shadow’) and ii) that systematically behave as specular reflectors (e.g. smooth tarmac, permanent water bodies). Change detection with respect to a pre- or post flood reference image thereby reduces over-detection of inundated areas. A case study of the July 2007 Severn River flood (UK) observed by the very high-resolution SAR sensor on board TerraSAR-X as well as airborne photography highlights advantages and limitations of the proposed method. We conclude that even though the fully automated SAR-based flood mapping technique overcomes some limitations of previous methods, further technological and methodological improvements are necessary for SAR-based flood detection in urban areas to match the flood mapping capability of high quality aerial photography.

Association mapping of partitioning loci in barley

Background: Association mapping, initially developed in human disease genetics, is now being applied to plant species. The model species Arabidopsis provided some of the first examples of association mapping in plants, identifying previously cloned flowering time genes, despite high population sub-structure. More recently, association genetics has been applied to barley, where breeding activity has resulted in a high degree of population sub-structure. A major genotypic division within barley is that between winter- and spring-sown varieties, which differ in their requirement for vernalization to promote subsequent flowering. To date, all attempts to validate association genetics in barley by identifying major flowering time loci that control vernalization requirement (VRN-H1 and VRN-H2) have failed. Here, we validate the use of association genetics in barley by identifying VRN-H1 and VRN-H2, despite their prominent role in determining population sub-structure. Results: By taking barley as a typical inbreeding crop, and seasonal growth habit as a major partitioning phenotype, we develop an association mapping approach which successfully identifies VRN-H1 and VRN-H2, the underlying loci largely responsible for this agronomic division. We find a combination of Structured Association followed by Genomic Control to correct for population structure and inflation of the test statistic, resolved significant associations only with VRN-H1 and the VRN-H2 candidate genes, as well as two genes closely linked to VRN-H1 (HvCSFs1 and HvPHYC). Conclusion: We show that, after employing appropriate statistical methods to correct for population sub-structure, the genome-wide partitioning effect of allelic status at VRN-H1 and VRN-H2 does not result in the high levels of spurious association expected to occur in highly structured samples. Furthermore, we demonstrate that both VRN-H1 and the candidate VRN-H2 genes can be identified using association mapping. Discrimination between intragenic VRN-H1 markers was achieved, indicating that candidate causative polymorphisms may be discerned and prioritised within a larger set of positive associations. This proof of concept study demonstrates the feasibility of association mapping in barley, even within highly structured populations. A major advantage of this method is that it does not require large numbers of genome-wide markers, and is therefore suitable for fine mapping and candidate gene evaluation, especially in species for which large numbers of genetic markers are either unavailable or too costly.

A depth-integrated 2D coastal and estuarine model with conformal boundary-fitted mesh generation

Details are given of the development and application of a 2D depth-integrated, conformal boundary-fitted, curvilinear model for predicting the depth-mean velocity field and the spatial concentration distribution in estuarine and coastal waters. A numerical method for conformal mesh generation, based on a boundary integral equation formulation, has been developed. By this method a general polygonal region with curved edges can be mapped onto a regular polygonal region with the same number of horizontal and vertical straight edges and a multiply connected region can be mapped onto a regular region with the same connectivity. A stretching transformation on the conformally generated mesh has also been used to provide greater detail where it is needed close to the coast, with larger mesh sizes further offshore, thereby minimizing the computing effort whilst maximizing accuracy. The curvilinear hydrodynamic and solute model has been developed based on a robust rectilinear model. The hydrodynamic equations are approximated using the ADI finite difference scheme with a staggered grid and the solute transport equation is approximated using a modified QUICK scheme. Three numerical examples have been chosen to test the curvilinear model, with an emphasis placed on complex practical applications

Brief communication: a proposed method for the assessment of pubertal stage in human skeletal remains using cervical vertebrae maturation.

The assessment of age-at-death in non-adult skeletal remains is under constant review. However, in many past societies an individual's physical maturation may have been more important in social terms than their exact age, particularly during the period of adolescence. In a recent article (Shapland and Lewis: Am J Phys Anthropol 151 (2013) 302–310) highlighted a set of dental and skeletal indicators that may be useful in mapping the progress of the pubertal growth spurt. This article presents a further skeletal indicator of adolescent development commonly used by modern clinicians: cervical vertebrae maturation (CVM). This method is applied to a collection of 594 adolescents from the medieval cemetery of St. Mary Spital, London. Analysis reveals a potential delay in ages of attainment of the later CVM stages compared with modern adolescents, presumably reflecting negative environmental conditions for growth and development. The data gathered on CVM is compared to other skeletal indicators of pubertal maturity and long bone growth from this site to ascertain the usefulness of this method on archaeological collections.