Computing Fresnel integrals via modified trapezium rules

In this paper we propose methods for computing Fresnel integrals based on truncated trapezium rule approximations to integrals on the real line, these trapezium rules modified to take into account poles of the integrand near the real axis. Our starting point is a method for computation of the error function of complex argument due to Matta and Reichel (J Math Phys 34:298–307, 1956) and Hunter and Regan (Math Comp 26:539–541, 1972). We construct approximations which we prove are exponentially convergent as a function of N , the number of quadrature points, obtaining explicit error bounds which show that accuracies of 10−15 uniformly on the real line are achieved with N=12 , this confirmed by computations. The approximations we obtain are attractive, additionally, in that they maintain small relative errors for small and large argument, are analytic on the real axis (echoing the analyticity of the Fresnel integrals), and are straightforward to implement.

Production and on-line comprehension of definite articles and clitic pronouns by Greek sequential bilingual children and monolingual children with specific language impairment

The present study compared production and on-line comprehension of definite articles and third person direct object clitic pronouns in Greek-speaking typically developing, sequential bilingual (L2-TD) children and monolingual children with specific language impairment (L1-SLI). Twenty Turkish Greek L2-TD children, 16 Greek L1-SLI children, and 31 L1-TD Greek children participated in a production task examining definite articles and clitic pronouns and, in an on-line comprehension task, involving grammatical sentences with definite articles and clitics and sentences with grammatical violations induced by omitted articles and clitics. The results showed that the L2-TD children were sensitive to the grammatical violations despite low production. In contrast, the children with SLI were not sensitive to clitic omission in the on-line task, despite high production. These results support a dissociation between production and on-line comprehension in L2 children and for impaired grammatical representations and lack of automaticity in children with SLI. They also suggest that on-line comprehension tasks may complement production tasks by differentiating between the language profiles of L2-TD children and children with SLI.

Production of definite and indefinite articles in typically developing English-speaking children and children with SLI

The present paper examines the production of definite and indefinite articles in English-speaking typically developing (TD) children and children with Specific Language Impairment (SLI). Twenty four English-speaking children with SLI (mean age: 7;5), twenty nine TD age-matched (TD-AM) children (mean age: 7;5) and eleven younger (mean age: 5;5) TD vocabulary-matched (TD-VM) children participated in a production task involving short stories without picture props based on Schafer and de Villiers (2000). Article production was examined in two different semantic contexts for the definite article, namely in the anaphoric and the bridging context. In the anaphoric condition, definiteness is established via linguistic means, whereas in the bridging condition via shared world knowledge. Indefinite article production was examined in the referential specific, non-referential predicational, and non-referential instrumental contexts. The referential specific context involves [+speaker, −hearer] knowledge and the non-referential predicational and instrumental [−speaker, −hearer] knowledge. Results showed that in the definite article contexts, all three groups performed better on the bridging compared with the anaphoric condition; in the indefinite article contexts, they had better performance on the non-referential predicational vs. the referential specific and the non-referential instrumental conditions. In terms of errors, the TD-VM children and the children with SLI produced significantly more substitutions than the TD-AM children in the definite article contexts. In the indefinite article contexts, the three groups did not differ in terms of accuracy or error patterns. The present results point towards problems in the discourse integration of entities that are part of the speaker's and hearer's knowledge in children with SLI and TD-VM controls, especially in definite articles. These problems are accentuated in the children with SLI due to their grammatical impairment and suggest that children with SLI exhibit a delayed acquisition profile.

Low rank representation on Riemannian manifold of symmetric positive definite matrices

Sparse coding aims to find a more compact representation based on a set of dictionary atoms. A well-known technique looking at 2D sparsity is the low rank representation (LRR). However, in many computer vision applications, data often originate from a manifold, which is equipped with some Riemannian geometry. In this case, the existing LRR becomes inappropriate for modeling and incorporating the intrinsic geometry of the manifold that is potentially important and critical to applications. In this paper, we generalize the LRR over the Euclidean space to the LRR model over a specific Rimannian manifold—the manifold of symmetric positive matrices (SPD). Experiments on several computer vision datasets showcase its noise robustness and superior performance on classification and segmentation compared with state-of-the-art approaches.

A new perspective on Southern hemisphere storm-tracks.

A detailed view of Southern Hemisphere storm tracks is obtained based on the application of filtered variance and modern feature-tracking techniques to a wide range of 45-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40) data. It has been checked that the conclusions drawn in this study are valid even if data from only the satellite era are used. The emphasis of the paper is on the winter season, but results for the four seasons are also discussed. Both upper- and lower-tropospheric fields are used. The tracking analysis focuses on systems that last longer than 2 days and are mobile (move more than 1000 km). Many of the results support previous ideas about the storm tracks, but some new insights are also obtained. In the summer there is a rather circular, strong, deep high-latitude storm track. In winter the high-latitude storm track is more asymmetric with a spiral from the Atlantic and Indian Oceans in toward Antarctica and a subtropical jet–related lower-latitude storm track over the Pacific, again tending to spiral poleward. At all times of the year, maximum storm activity in the higher-latitude storm track is in the Atlantic and Indian Ocean regions. In the winter upper troposphere, the relative importance of, and interplay between, the subtropical and subpolar storm tracks is discussed. The genesis, lysis, and growth rate of lower-tropospheric winter cyclones together lead to a vivid picture of their behavior that is summarized as a set of overlapping plates, each composed of cyclone life cycles. Systems in each plate appear to feed the genesis in the next plate through downstream development in the upper-troposphere spiral storm track. In the lee of the Andes in South America, there is cyclogenesis associated with the subtropical jet and also, poleward of this, cyclogenesis largely associated with system decay on the upslope and regeneration on the downslope. The genesis and lysis of cyclones and anticyclones have a definite spatial relationship with each other and with the Andes. At 500 hPa, their relative longitudinal positions are consistent with vortex-stretching ideas for simple flow over a large-scale mountain. Cyclonic systems near Antarctica have generally spiraled in from lower latitudes. However, cyclogenesis associated with mobile cyclones occurs around the Antarctic coast with an interesting genesis maximum over the sea ice near 150°E. The South Pacific storm track emerges clearly from the tracking as a coherent deep feature spiraling from Australia to southern South America. A feature of the summer season is the genesis of eastward-moving cyclonic systems near the tropic of Capricorn off Brazil, in the central Pacific and, to a lesser extent, off Madagascar, followed by movement along the southwest flanks of the subtropical anticyclones and contribution to the “convergence zone” cloud bands seen in these regions.

The counter-propagating Rossby-wave perspective on baroclinic instability. I: Mathematical basis

It is shown that Bretherton's view of baroclinic instability as the interaction of two counter-propagating Rossby waves (CRWs) can be extended to a general zonal flow and to a general dynamical system based on material conservation of potential vorticity (PV). The two CRWs have zero tilt with both altitude and latitude and are constructed from a pair of growing and decaying normal modes. One CRW has generally large amplitude in regions of positive meridional PV gradient and propagates westwards relative to the flow in such regions. Conversely, the other CRW has large amplitude in regions of negative PV gradient and propagates eastward relative to the zonal flow there. Two methods of construction are described. In the first, more heuristic, method a ‘home-base’ is chosen for each CRW and the other CRW is defined to have zero PV there. Consideration of the PV equation at the two home-bases gives ‘CRW equations’ quantifying the evolution of the amplitudes and phases of both CRWs. They involve only three coefficients describing the mutual interaction of the waves and their self-propagation speeds. These coefficients relate to PV anomalies formed by meridional fluid displacements and the wind induced by these anomalies at the home-bases. In the second method, the CRWs are defined by orthogonality constraints with respect to wave activity and energy growth, avoiding the subjective choice of home-bases. Using these constraints, the same form of CRW equations are obtained from global integrals of the PV equation, but the three coefficients are global integrals that are not so readily described by ‘PV-thinking’ arguments. Each CRW could not continue to exist alone, but together they can describe the time development of any flow whose initial conditions can be described by the pair of growing and decaying normal modes, including the possibility of a super-modal growth rate for a short period. A phase-locking configuration (and normal-mode growth) is possible only if the PV gradient takes opposite signs and the mean zonal wind and the PV gradient are positively correlated in the two distinct regions where the wave activity of each CRW is concentrated. These are easily interpreted local versions of the integral conditions for instability given by Charney and Stern and by Fjørtoft.

Autocyclic erosion in tidal marshes

A common mode whereby destruction of coastal lowlands occurs is frontal erosion. The edge cliffing, nonetheless, is also an inherent aspect of salt marsh development in many northwest European tidal marshes. Quite a few geomorphologists in the earlier half of the past century recognized such edge erosion as a definite repetitive stage within an autocyclic mode of marsh growth. A shift in research priorities during the past decades (primarily because of coastal management concerns, however) has resulted in an enhanced focus on sediment-flux measurement campaigns on salt marshes. This, somewhat "object-oriented" strategy hindered any further development of the once-established autocyclic growth concept, which virtually has gone into oblivion in recent times. This work makes an attempt to resurrect the notion of autocyclicity by employing its premises to address edge erosion in tidal marshes. Through a review of intertidal morphosedimentology the underlying framework for autocyclicity is envisaged. The phenomenon is demonstrated in the Holocene salt marsh plain of Moricambe basin in NW England that displays several distinct phases of marsh retreat in the form of abandoned clifflets. The suite of abandoned shorelines and terraces has been identified in detailed field mapping that followed analysis of topographic maps and aerial photographs. Vertical trends in marsh plain sediments are recorded in trenches for signs of past marsh front movements. The characteristic sea level history of the area offers an opportunity to differentiate the morphodynamic variability induced in the autocyclic growth of the marsh plain in scenarios of rising and falling sea level and the accompanied change in sediment budget. The ideas gathered are incorporated to construct a conceptual model that links temporal extent of marsh erosion to inner tidal flat sediment budget and sea level tendency. The review leads to recognition of the necessity of adopting an holistic approach in the morphodynamic investigations where marshes should be treated as a component within the "marsh-mudflat system" as each element apparently modulates evolution of the other, with an eventual linkage to subtidal channels. (C) 2009 Elsevier B.V. All rights reserved.

Separating hoarding from OCD

There is confusion about the status of excessive hoarding. In particular, there is an unresolved question about whether or not it is a manifestation of obsessive-compulsive disorder (OCD). There are some definite similarities between 'compulsive' hoarding and OCD, but they are outweighed by the differences between them. It is proposed that the matter can be clarified by separating hoarding from OCD, and that this would advance clinical work and research. (c) 2009 Elsevier Ltd. All rights reserved.

Impairment in movement skills of children with autistic spectrum disorders

We undertook this study to explore the degree of impairment in movement skills in children with autistic spectrum disorders (ASD) and a wide IQ range. Movement skills were measured using the Movement Assessment Battery for Children (M-ABC) in a large, well defined, population-derived group of children (n=101: 89 males,12 females; mean age 11y 4mo, SD 10mo; range 10y-14y 3mo) with childhood autism and broader ASD and a wide range of IQ scores. Additionally, we tested whether a parent-completed questionnaire, the Developmental Coordination Disorder Questionnaire (DCDQ), was useful in identifying children who met criteria for movement impairments after assessment (n=97 with complete M-ABCs and DCDQs). Of the children with ASD, 79% had definite movement impairments on the M-ABC; a further 10% had borderline problems. Children with childhood autism were more impaired than children with broader ASD, and children with an IQ less than 70 were more impaired than those with IQ more than 70. This is consistent with the view that movement impairments may arise from a more severe neurological impairment that also contributes to intellectual disability and more severe autism. Movement impairment was not associated with everyday adaptive behaviour once the effect of IQ was controlled for. The DCDQ performed moderately well as a screen for possible motor difficulties. Movement impairments are common in children with ASD. Systematic assessment of movement abilities should be considered a routine investigation.

Exact error estimates and optimal randomized algorithms for integration

Exact error estimates for evaluating multi-dimensional integrals are considered. An estimate is called exact if the rates of convergence for the low- and upper-bound estimate coincide. The algorithm with such an exact rate is called optimal. Such an algorithm has an unimprovable rate of convergence. The problem of existing exact estimates and optimal algorithms is discussed for some functional spaces that define the regularity of the integrand. Important for practical computations data classes are considered: classes of functions with bounded derivatives and Holder type conditions. The aim of the paper is to analyze the performance of two optimal classes of algorithms: deterministic and randomized for computing multidimensional integrals. It is also shown how the smoothness of the integrand can be exploited to construct better randomized algorithms.

Parallel Monte Carlo approach for integration of the rendering equation

This paper is addressed to the numerical solving of the rendering equation in realistic image creation. The rendering equation is integral equation describing the light propagation in a scene accordingly to a given illumination model. The used illumination model determines the kernel of the equation under consideration. Nowadays, widely used are the Monte Carlo methods for solving the rendering equation in order to create photorealistic images. In this work we consider the Monte Carlo solving of the rendering equation in the context of the parallel sampling scheme for hemisphere. Our aim is to apply this sampling scheme to stratified Monte Carlo integration method for parallel solving of the rendering equation. The domain for integration of the rendering equation is a hemisphere. We divide the hemispherical domain into a number of equal sub-domains of orthogonal spherical triangles. This domain partitioning allows to solve the rendering equation in parallel. It is known that the Neumann series represent the solution of the integral equation as a infinity sum of integrals. We approximate this sum with a desired truncation error (systematic error) receiving the fixed number of iteration. Then the rendering equation is solved iteratively using Monte Carlo approach. At each iteration we solve multi-dimensional integrals using uniform hemisphere partitioning scheme. An estimate of the rate of convergence is obtained using the stratified Monte Carlo method. This domain partitioning allows easy parallel realization and leads to convergence improvement of the Monte Carlo method. The high performance and Grid computing of the corresponding Monte Carlo scheme are discussed.

'Flat phase' PID controllers

Flat Phase PID Controllers have the property that the phase of the transfer function round the associated feedback loop is constant or flat around the design frequency, with the aim that the phase margin and overshoot to a step response is unaffected when the gain of the device under control changes. Such designs have been achieved using Bode Integrals and by ensuring the phase is the same at two frequencies. This paper extends the ‘two frequency’ controller and describes a novel three frequency controller. The different design strategies arc compared.

Sparse kernel density estimation technique based on zero-norm constraint

A sparse kernel density estimator is derived based on the zero-norm constraint, in which the zero-norm of the kernel weights is incorporated to enhance model sparsity. The classical Parzen window estimate is adopted as the desired response for density estimation, and an approximate function of the zero-norm is used for achieving mathemtical tractability and algorithmic efficiency. Under the mild condition of the positive definite design matrix, the kernel weights of the proposed density estimator based on the zero-norm approximation can be obtained using the multiplicative nonnegative quadratic programming algorithm. Using the -optimality based selection algorithm as the preprocessing to select a small significant subset design matrix, the proposed zero-norm based approach offers an effective means for constructing very sparse kernel density estimates with excellent generalisation performance.

Determiner spreading as DP-predication

Determiner Spreading (DS) occurs in adjectivally modified nominal phrases comprising more than one definite article, a phenomenon that has received considerable attention and has been extensively described in Greek. This paper discusses the syntactic properties of DS in detail and argues that DS structures are both arguments and predication configurations involving two DPs. This account successfully captures the word-order facts and the distinctive interpretation of DS, while also laying the groundwork towards unifying it with other structures linking two DPs in a predicative relation.