Sparse shape representation using the Laplace-Beltrami eigenfunctions and its application to modeling subcortical structures

We present a new sparse shape modeling framework on the Laplace-Beltrami (LB) eigenfunctions. Traditionally, the LB-eigenfunctions are used as a basis for intrinsically representing surface shapes by forming a Fourier series expansion. To reduce high frequency noise, only the first few terms are used in the expansion and higher frequency terms are simply thrown away. However, some lower frequency terms may not necessarily contribute significantly in reconstructing the surfaces. Motivated by this idea, we propose to filter out only the significant eigenfunctions by imposing l1-penalty. The new sparse framework can further avoid additional surface-based smoothing often used in the field. The proposed approach is applied in investigating the influence of age (38-79 years) and gender on amygdala and hippocampus shapes in the normal population. In addition, we show how the emotional response is related to the anatomy of the subcortical structures.

Children's representation of family mealtime in the context of maternal eating disorders

Background Recent research provides evidence for specific disturbance in feeding and growth in children of mothers with eating disorders. Aim To investigate the impact of maternal eating disorders during the post-natal year on the internal world of children, as expressed in children's representations of self and their mother in pretend mealtime play at 5 years of age. Methods Children of mothers with eating disorders (n = 33) and a comparison group (n = 24) were videotaped enacting a family mealtime in pretend play. Specific classes of children's play representations were coded blind to group membership. Univariate analyses compared the groups on representations of mother and self. Logistic regression explored factors predicting pretend play representations. Results Positive representations of the mother expressed as feeding, eating or body shape themes were more frequent in the index group. There were no other significant group differences in representations. In a logistic regression analysis, current maternal eating psychopathology was the principal predictor of these positive maternal representations. Marital criticism was associated with negative representations of the mother. Conclusions These findings suggest that maternal eating disorders may influence the development of a child's internal world, such that they are more preoccupied with maternal eating concerns. However, more extensive research on larger samples is required to replicate these preliminary findings.

A novel shape feature for fast region-based pedestrian recognition

A new class of shape features for region classification and high-level recognition is introduced. The novel Randomised Region Ray (RRR) features can be used to train binary decision trees for object category classification using an abstract representation of the scene. In particular we address the problem of human detection using an over segmented input image. We therefore do not rely on pixel values for training, instead we design and train specialised classifiers on the sparse set of semantic regions which compose the image. Thanks to the abstract nature of the input, the trained classifier has the potential to be fast and applicable to extreme imagery conditions. We demonstrate and evaluate its performance in people detection using a pedestrian dataset.

The compositional and configurational heterogeneity of matrix habitats shape woodland carabid communities in wooded-agricultural landscapes

Landscape heterogeneity (the composition and configuration of matrix habitats) plays a major role in shaping species communities in wooded-agricultural landscapes. However, few studies consider the influence of different types of semi-natural and linear habitats in the matrix, despite their known ecological value for biodiversity. Objective To investigate the importance of the composition and configuration of matrix habitats for woodland carabid communities and identify whether specific landscape features can help to maintain long-term populations in wooded-agricultural environments. Methods Carabids were sampled from woodlands in 36 tetrads of 4 km2 across southern Britain. Landscape heterogeneity including an innovative representation of linear habitats was quantified for each tetrad. Carabid community response was analysed using ordination methods combined with variation partitioning and additional response trait analyses. Results Woodland carabid community response was trait-specific and better explained by simultaneously considering the composition and configuration of matrix habitats. Semi-natural and linear features provided significant refuge habitat and functional connectivity. Mature hedgerows were essential for slow-dispersing carabids in fragmented landscapes. Species commonly associated with heathland were correlated with inland water and woodland patches despite widespread heathland conversion to agricultural land, suggesting that species may persist for some decades when elements representative of the original habitat are retained following landscape modification. Conclusions Semi-natural and linear habitats have high biodiversity value. Landowners should identify features that can provide additional resources or functional connectivity for species relative to other habitat types in the landscape matrix. Agri-environment options should consider landscape heterogeneity to identify the most efficacious changes for biodiversity.

Digitisation, representation, and formalisation - Digital libraries of mathematics

One of the main tasks of the mathematical knowledge management community must surely be to enhance access to mathematics on digital systems. In this paper we present a spectrum of approaches to solving the various problems inherent in this task, arguing that a variety of approaches is both necessary and useful. The main ideas presented are about the differences between digitised mathematics, digitally represented mathematics and formalised mathematics. Each has its part to play in managing mathematical information in a connected world. Digitised material is that which is embodied in a computer file, accessible and displayable locally or globally. Represented material is digital material in which there is some structure (usually syntactic in nature) which maps to the mathematics contained in the digitised information. Formalised material is that in which both the syntax and semantics of the represented material, is automatically accessible. Given the range of mathematical information to which access is desired, and the limited resources available for managing that information, we must ensure that these resources are applied to digitise, form representations of or formalise, existing and new mathematical information in such a way as to extract the most benefit from the least expenditure of resources. We also analyse some of the various social and legal issues which surround the practical tasks.

Can wavelets improve the representation of forecast error covariances in variational data assimilation?

Two wavelet-based control variable transform schemes are described and are used to model some important features of forecast error statistics for use in variational data assimilation. The first is a conventional wavelet scheme and the other is an approximation of it. Their ability to capture the position and scale-dependent aspects of covariance structures is tested in a two-dimensional latitude-height context. This is done by comparing the covariance structures implied by the wavelet schemes with those found from the explicit forecast error covariance matrix, and with a non-wavelet- based covariance scheme used currently in an operational assimilation scheme. Qualitatively, the wavelet-based schemes show potential at modeling forecast error statistics well without giving preference to either position or scale-dependent aspects. The degree of spectral representation can be controlled by changing the number of spectral bands in the schemes, and the least number of bands that achieves adequate results is found for the model domain used. Evidence is found of a trade-off between the localization of features in positional and spectral spaces when the number of bands is changed. By examining implied covariance diagnostics, the wavelet-based schemes are found, on the whole, to give results that are closer to diagnostics found from the explicit matrix than from the nonwavelet scheme. Even though the nature of the covariances has the right qualities in spectral space, variances are found to be too low at some wavenumbers and vertical correlation length scales are found to be too long at most scales. The wavelet schemes are found to be good at resolving variations in position and scale-dependent horizontal length scales, although the length scales reproduced are usually too short. The second of the wavelet-based schemes is often found to be better than the first in some important respects, but, unlike the first, it has no exact inverse transform.

The representation of conditional expectations of non-Gaussian noise

For Wiener spaces conditional expectations and $L^{2}$-martingales w.r.t. the natural filtration have a natural representation in terms of chaos expansion. In this note an extension to larger classes of processes is discussed. In particular, it is pointed out that orthogonality of the chaos expansion is not required.

View-based approaches to spatial representation in human vision

In an immersive virtual environment, observers fail to notice the expansion of a room around them and consequently make gross errors when comparing the size of objects. This result is difficult to explain if the visual system continuously generates a 3-D model of the scene based on known baseline information from interocular separation or proprioception as the observer walks. An alternative is that observers use view-based methods to guide their actions and to represent the spatial layout of the scene. In this case, they may have an expectation of the images they will receive but be insensitive to the rate at which images arrive as they walk. We describe the way in which the eye movement strategy of animals simplifies motion processing if their goal is to move towards a desired image and discuss dorsal and ventral stream processing of moving images in that context. Although many questions about view-based approaches to scene representation remain unanswered, the solutions are likely to be highly relevant to understanding biological 3-D vision.

Devolution and the political representation of business interests in the UK

The devolution of political power in Scotland, Wales and Northern Ireland and the developing regional agenda in England are widely read as a significant reconfiguration of the institutions and scales of economic governance. The process is furthest developed in Scotland while Wales and Northern Ireland, in their own distinct ways, provide intermediate cases. Devolution is least developed in England where regional political identities are generally weak and the historical legacy of regional institutions is limited. Within the overall context of devolution government policy has continued to emphasize partnership forms of. governance. Accordingly, the political representation of business interests has a particular salience in the new arrangements. This paper reports on findings from a study designed to examine the relationship between devolution and changes in the political representation of business interests in the territories and regions of the UK. It highlights a number of changes in the nature and extent of business representation. While some of these are significant the evidence suggests that they fail to mark a fundamental shift in the institutional foundation for sub-national business interest representation in the UK. Indeed the political geography of business representation remains dominated by an overarching centralism that is likely to provide a significant check on the further devolution of political power and democratic authority. (c) 2004 Elsevier Ltd. All rights reserved.

Moving towards a more mechanistic approach in the determination of soil heat flux from remote measurements - II. Diurnal shape of soil heat flux

For vegetated surfaces, calculation of soil heat flux, G, with the Exact or Analytical method requires a harmonic analysis of below-canopy soil surface temperature, to obtain the shape of the diurnal course of G. When determining G with remote sensing methods, only composite (vegetation plus soil) radiometric brightness temperature is available. This paper presents a simple equation that relates the sum of the harmonic terms derived for the composite radiometric surface temperature to that of belowcanopy soil surface temperature. The thermal inertia, Gamma(,) for which a simple equation has been presented in a companion paper, paper I, is used to set the magnitude of G. To assess the success of the method proposed in this paper for the estimation of the diurnal shape of G, a comparison was made between 'remote' and in situ calculated values from described field sites. This indicated that the proposed method was suitable for the estimation of the shape of G for a variety of vegetation types and densities. The approach outlined in paper I, to obtain Gamma, was then combined with the estimated harmonic terms to predict estimates of G, which were compared to values predicted by empirical remote methods found in the literature. This indicated that the method proposed in the combination of papers I and II gave reliable estimates of G, which, in comparison to the other methods, resulted in more realistic predictions for vegetated surfaces. This set of equations can also be used for bare and sparsely vegetated soils, making it a universally applicable method. (C) 2007 Elsevier B.V. All rights reserved.

The social relations of business representation and devolved governance in the United Kingdom

The reform of regional governance in the United Kingdom has been, in part, premised on the notion that regions provide new territories of action in which cooperative networks between business communities and state-agencies can be established. Promoting business interests is seen as one mechanism for enhancing the economic competitiveness and performance of 'laggard' regions. Yet, within this context of change, business agendas and capacities are often assumed to exist 'out there, as a resource waiting to be tapped by state institutions. There is little recognition that business organisations' involvement in networks of governance owes much to historical patterns and practices of business representation, to the types of activities that exist within the business sector, and to interpretations of their own role and position within wider policymaking and implementation networks. This paper, drawing on a study of business agendas in post-devolution Scotland, demonstrates that in practice business agendas are highly complex. Their formation in any particular place depends on the actions of reflexive agents, whose perspectives and capacities are shaped by the social, economic, and political contexts within which they are operating. As such, any understanding of business agendas needs to identify the social relations of business as a whole, rather than assuming away such complexities.

Devolution and the political representation of business interests in the UK

The devolution of political power in Scotland, Wales and Northern Ireland and the developing regional agenda in England are widely read as a significant reconfiguration of the institutions and scales of economic governance. The process is furthest developed in Scotland while Wales and Northern Ireland, in their own distinct ways, provide intermediate cases. Devolution is least developed in England where regional political identities are generally weak and the historical legacy of regional institutions is limited. Within the overall context of devolution government policy has continued to emphasize partnership forms of. governance. Accordingly, the political representation of business interests has a particular salience in the new arrangements. This paper reports on findings from a study designed to examine the relationship between devolution and changes in the political representation of business interests in the territories and regions of the UK. It highlights a number of changes in the nature and extent of business representation. While some of these are significant the evidence suggests that they fail to mark a fundamental shift in the institutional foundation for sub-national business interest representation in the UK. Indeed the political geography of business representation remains dominated by an overarching centralism that is likely to provide a significant check on the further devolution of political power and democratic authority. (c) 2004 Elsevier Ltd. All rights reserved.