Feature-point detection using distance transforms: Application to tracking tropical convective complexes

The identification, tracking, and statistical analysis of tropical convective complexes using satellite imagery is explored in the context of identifying feature points suitable for tracking. The feature points are determined based on the shape of complexes using the distance transform technique. This approach has been applied to the determination feature points for tropical convective complexes identified in a time series of global cloud imagery. The feature points are used to track the complexes, and from the tracks statistical diagnostic fields are computed. This approach allows the nature and distribution of organized deep convection in the Tropics to be explored.

Linear and nonlinear generalized Fourier transforms

This article presents an overview of a transform method for solving linear and integrable nonlinear partial differential equations. This new transform method, proposed by Fokas, yields a generalization and unification of various fundamental mathematical techniques and, in particular, it yields an extension of the Fourier transform method.

Geometrical isomers of [TEAH][Co(L-Se)(2)]center dot xH(2)O: synthesis, structural, spectroscopic and computational studies

Trans-1, [HNEt3][Co-III(L-Se)(2)]center dot H2O and cis-1, [HNEt3][Co-III(L-Se)(2)]center dot 3H(2)O have been synthesized and characterized by single-crystal X-ray studies. The counter ion Et3NH+ plays a crucial role in the crystal packing leading to the formation of two distinctly different supramolecular assemblies in the two complexes. In trans-1, Co-bisphenolate units and triethylamine molecules are arranged in a linear fashion leading to a supramolecular columnar assembly along the crystallographic a-axis. In this assembly, triethylammonium ions are sandwiched between successive Co-bisphenolate units and act as gluing agents joining Co-bisphenolate units on either side through C-H center dot center dot center dot pi interactions. In sharp contrast to trans-1, Co-bisphenolate units and triethylammonium ions in cis-1 are arranged in a helical supramolecular assembly through similar C-H center dot center dot center dot pi interactions along the crystallographic b-axis. The Se center dot center dot center dot Se van der Waals interactions may be responsible for the predominant occurrence of the cis-isomer. The cyclic voltammetric studies showed quasi-reversible waves for the cobalt(III) -> cobalt(II) reductions with E-1/2 = 0.635 and 0.628 V vs. Ag/AgCl for cis-1 (at similar to 5 degrees C) and trans-1 (at similar to 25 degrees C), respectively. DFT calculations show that the trans-form is the thermodynamic product with higher stability than the cis-one, which is consistent with the variable temperature H-1 NMR studies

Comparison of extrasystolic ECG signal classifiers using discrete wavelet transforms

This work compares and contrasts results of classifying time-domain ECG signals with pathological conditions taken from the MITBIH arrhythmia database. Linear discriminant analysis and a multi-layer perceptron were used as classifiers. The neural network was trained by two different methods, namely back-propagation and a genetic algorithm. Converting the time-domain signal into the wavelet domain reduced the dimensionality of the problem at least 10-fold. This was achieved using wavelets from the db6 family as well as using adaptive wavelets generated using two different strategies. The wavelet transforms used in this study were limited to two decomposition levels. A neural network with evolved weights proved to be the best classifier with a maximum of 99.6% accuracy when optimised wavelet-transform ECG data wits presented to its input and 95.9% accuracy when the signals presented to its input were decomposed using db6 wavelets. The linear discriminant analysis achieved a maximum classification accuracy of 95.7% when presented with optimised and 95.5% with db6 wavelet coefficients. It is shown that the much simpler signal representation of a few wavelet coefficients obtained through an optimised discrete wavelet transform facilitates the classification of non-stationary time-variant signals task considerably. In addition, the results indicate that wavelet optimisation may improve the classification ability of a neural network. (c) 2005 Elsevier B.V. All rights reserved.

Representing geometrical knowledge

This paper introduces perspex algebra which is being developed as a common representation of geometrical knowledge. A perspex can currently be interpreted in one of four ways. First, the algebraic perspex is a generalization of matrices, it provides the most general representation for all of the interpretations of a perspex. The algebraic perspex can be used to describe arbitrary sets of coordinates. The remaining three interpretations of the perspex are all related to square matrices and operate in a Euclidean model of projective space-time, called perspex space. Perspex space differs from the usual Euclidean model of projective space in that it contains the point at nullity. It is argued that the point at nullity is necessary for a consistent account of perspective in top-down vision. Second, the geometric perspex is a simplex in perspex space. It can be used as a primitive building block for shapes, or as a way of recording landmarks on shapes. Third, the transformational perspex describes linear transformations in perspex space that provide the affine and perspective transformations in space-time. It can be used to match a prototype shape to an image, even in so called 'accidental' views where the depth of an object disappears from view, or an object stays in the same place across time. Fourth, the parametric perspex describes the geometric and transformational perspexes in terms of parameters that are related to everyday English descriptions. The parametric perspex can be used to obtain both continuous and categorical perception of objects. The paper ends with a discussion of issues related to using a perspex to describe logic.

Analysis of spectroscopic measurements of leaf water content at terahertz frequencies using linear transforms

We provide a unified framework for a range of linear transforms that can be used for the analysis of terahertz spectroscopic data, with particular emphasis on their application to the measurement of leaf water content. The use of linear transforms for filtering, regression, and classification is discussed. For illustration, a classification problem involving leaves at three stages of drought and a prediction problem involving simulated spectra are presented. Issues resulting from scaling the data set are discussed. Using Lagrange multipliers, we arrive at the transform that yields the maximum separation between the spectra and show that this optimal transform is equivalent to computing the Euclidean distance between the samples. The optimal linear transform is compared with the average for all the spectra as well as with the Karhunen–Loève transform to discriminate a wet leaf from a dry leaf. We show that taking several principal components into account is equivalent to defining new axes in which data are to be analyzed. The procedure shows that the coefficients of the Karhunen–Loève transform are well suited to the process of classification of spectra. This is in line with expectations, as these coefficients are built from the statistical properties of the data set analyzed.

Hankel and Toeplitz transforms on H 1: continuity, compactness and Fredholm properties

We revisit the boundedness of Hankel and Toeplitz operators acting on the Hardy space H 1 and give a new proof of the old result stating that the Hankel operator H a is bounded if and only if a has bounded logarithmic mean oscillation. We also establish a sufficient and necessary condition for H a to be compact on H 1. The Fredholm properties of Toeplitz operators on H 1 are studied for symbols in a Banach algebra similar to C + H ∞ under mild additional conditions caused by the differences in the boundedness of Toeplitz operators acting on H 1 and H 2.

'Si en i ot de teus qui i conterent plus lor honte que leur honour', Enadain et Gauvain, les chevaliers transformés en nains dans la Suite Vulgate du Merlin

Dans le récit de la transformation de Gauvain en nain, la honte est à la fois la conséquence d'une culpabilité mise en avant par un interlocuteur féminin, et l'instrument de la purgation de la faute commise par le héros. La gestion narrative de cet épisode à la fois dramatique et comique interroge autant les valeurs chrétiennes que les principes de conduite chevaleresques. La nature de la faute et son intériorisation personnelle importent moins que sa dimension sociale et collective.

Formal theory building for the avalanche game: explaining counter-intuitive behaviour of a complex system using geometrical and human behavioural/physiological effects

In 'Avalanche', an object is lowered, players staying in contact throughout. Normally the task is easily accomplished. However, with larger groups counter-intuitive behaviours appear. The paper proposes a formal theory for the underlying causal mechanisms. The aim is to not only provide an explicit, testable hypothesis for the source of the observed modes of behaviour-but also to exemplify the contribution that formal theory building can make to understanding complex social phenomena. Mapping reveals the importance of geometry to the Avalanche game; each player has a pair of balancing loops, one involved in lowering the object, the other ensuring contact. For more players, sets of balancing loops interact and these can allow dominance by reinforcing loops, causing the system to chase upwards towards an ever-increasing goal. However, a series of other effects concerning human physiology and behaviour (HPB) is posited as playing a role. The hypothesis is therefore rigorously tested using simulation. For simplicity a 'One Degree of Freedom' case is examined, allowing all of the effects to be included whilst rendering the analysis more transparent. Formulation and experimentation with the model gives insight into the behaviours. Multi-dimensional rate/level analysis indicates that there is only a narrow region in which the system is able to move downwards. Model runs reproduce the single 'desired' mode of behaviour and all three of the observed 'problematic' ones. Sensitivity analysis gives further insight into the system's modes and their causes. Behaviour is seen to arise only when the geometric effects apply (number of players greater than degrees of freedom of object) in combination with a range of HPB effects. An analogy exists between the co-operative behaviour required here and various examples: conflicting strategic objectives in organizations; Prisoners' Dilemma and integrated bargaining situations. Additionally, the game may be relatable in more direct algebraic terms to situations involving companies in which the resulting behaviours are mediated by market regulations. Finally, comment is offered on the inadequacy of some forms of theory building and the case is made for formal theory building involving the use of models, analysis and plausible explanations to create deep understanding of social phenomena.

Localization of deep water formation: role of atmospheric moisture transport and geometrical constraints on ocean circulation

A series of coupled atmosphere–ocean–ice aquaplanet experiments is described in which topological constraints on ocean circulation are introduced to study the role of ocean circulation on the mean climate of the coupled system. It is imagined that the earth is completely covered by an ocean of uniform depth except for the presence or absence of narrow barriers that extend from the bottom of the ocean to the sea surface. The following four configurations are described: Aqua (no land), Ridge (one barrier extends from pole to pole), Drake (one barrier extends from the North Pole to 35°S), and DDrake (two such barriers are set 90° apart and join at the North Pole, separating the ocean into a large basin and a small basin, connected to the south). On moving from Aqua to Ridge to Drake to DDrake, the energy transports in the equilibrium solutions become increasingly “realistic,” culminating in DDrake, which has an uncanny resemblance to the present climate. Remarkably, the zonal-average climates of Drake and DDrake are strikingly similar, exhibiting almost identical heat and freshwater transports, and meridional overturning circulations. However, Drake and DDrake differ dramatically in their regional climates. The small and large basins of DDrake exhibit distinctive Atlantic-like and Pacific-like characteristics, respectively: the small basin is warmer, saltier, and denser at the surface than the large basin, and is the main site of deep water formation with a deep overturning circulation and strong northward ocean heat transport. A sensitivity experiment with DDrake demonstrates that the salinity contrast between the two basins, and hence the localization of deep convection, results from a deficit of precipitation, rather than an excess of evaporation, over the small basin. It is argued that the width of the small basin relative to the zonal fetch of atmospheric precipitation is the key to understanding this salinity contrast. Finally, it is argued that many gross features of the present climate are consequences of two topological asymmetries that have profound effects on ocean circulation: a meridional asymmetry (circumpolar flow in the Southern Hemisphere; blocked flow in the Northern Hemisphere) and a zonal asymmetry (a small basin and a large basin).