The VITEWRITE Model of Handwriting Production

This article describes the VITEWRITE model for generating handwriting movements. The model consists of a sequential controller, or motor program, that interacts with a trajectory generator to move a hand with redundant degrees of freedom. The neural trajectory generator is the Vector Integration to Endpoint (VITE) model for synchronous variable-speed control of multijoint movements. VITE properties enable a simple control strategy to generate complex handwritten script if the hand model contains redundant degrees of freedom. The controller launches transient directional commands to independent hand synergies at times when the hand begins to move, or when a velocity peak in the outflow command to a given synergy occurs. The VITE model translates these temporally disjoint synergy commands into smooth curvilinear trajectories among temporally overlapping synergetic movements. Each synergy exhibits a unimodal velocity profile during any stroke, generates letters that are invariant under speed and size rescaling, and enables effortless connection of letter shapes into words. Speed and size rescaling are achieved by scalar GO and GRO signals that express computationally simple volitional commands. Psychophysical data such as the isochrony principle, asymmetric velocity profiles, and the two-thirds power law relating movement curvature and velocity arise as emergent properties of model interactions.

A Neural Model of 3D Shape-From-Texture: Multiple-Scale Filtering, Boundary Grouping, and Surface Filling-In

A neural model is presented of how cortical areas V1, V2, and V4 interact to convert a textured 2D image into a representation of curved 3D shape. Two basic problems are solved to achieve this: (1) Patterns of spatially discrete 2D texture elements are transformed into a spatially smooth surface representation of 3D shape. (2) Changes in the statistical properties of texture elements across space induce the perceived 3D shape of this surface representation. This is achieved in the model through multiple-scale filtering of a 2D image, followed by a cooperative-competitive grouping network that coherently binds texture elements into boundary webs at the appropriate depths using a scale-to-depth map and a subsequent depth competition stage. These boundary webs then gate filling-in of surface lightness signals in order to form a smooth 3D surface percept. The model quantitatively simulates challenging psychophysical data about perception of prolate ellipsoids (Todd and Akerstrom, 1987, J. Exp. Psych., 13, 242). In particular, the model represents a high degree of 3D curvature for a certain class of images, all of whose texture elements have the same degree of optical compression, in accordance with percepts of human observers. Simulations of 3D percepts of an elliptical cylinder, a slanted plane, and a photo of a golf ball are also presented.

Texture Segregation By Visual Cortex: Perceptual Grouping, Attention, and Learning

A neural model is proposed of how laminar interactions in the visual cortex may learn and recognize object texture and form boundaries. The model brings together five interacting processes: region-based texture classification, contour-based boundary grouping, surface filling-in, spatial attention, and object attention. The model shows how form boundaries can determine regions in which surface filling-in occurs; how surface filling-in interacts with spatial attention to generate a form-fitting distribution of spatial attention, or attentional shroud; how the strongest shroud can inhibit weaker shrouds; and how the winning shroud regulates learning of texture categories, and thus the allocation of object attention. The model can discriminate abutted textures with blurred boundaries and is sensitive to texture boundary attributes like discontinuities in orientation and texture flow curvature as well as to relative orientations of texture elements. The model quantitatively fits a large set of human psychophysical data on orientation-based textures. Object boundar output of the model is compared to computer vision algorithms using a set of human segmented photographic images. The model classifies textures and suppresses noise using a multiple scale oriented filterbank and a distributed Adaptive Resonance Theory (dART) classifier. The matched signal between the bottom-up texture inputs and top-down learned texture categories is utilized by oriented competitive and cooperative grouping processes to generate texture boundaries that control surface filling-in and spatial attention. Topdown modulatory attentional feedback from boundary and surface representations to early filtering stages results in enhanced texture boundaries and more efficient learning of texture within attended surface regions. Surface-based attention also provides a self-supervising training signal for learning new textures. Importance of the surface-based attentional feedback in texture learning and classification is tested using a set of textured images from the Brodatz micro-texture album. Benchmark studies vary from 95.1% to 98.6% with attention, and from 90.6% to 93.2% without attention.

A Neural Network Model for Cursive Script Production

This article describes a neural network model, called the VITEWRITE model, for generating handwriting movements. The model consists of a sequential controller, or motor program, that interacts with a trajectory generator to move a. hand with redundant degrees of freedom. The neural trajectory generator is the Vector Integration to Endpoint (VITE) model for synchronous variable-speed control of multijoint movements. VITE properties enable a simple control strategy to generate complex handwritten script if the hand model contains redundant degrees of freedom. The proposed controller launches transient directional commands to independent hand synergies at times when the hand begins to move, or when a velocity peak in a given synergy is achieved. The VITE model translates these temporally disjoint synergy commands into smooth curvilinear trajectories among temporally overlapping synergetic movements. The separate "score" of onset times used in most prior models is hereby replaced by a self-scaling activity-released "motor program" that uses few memory resources, enables each synergy to exhibit a unimodal velocity profile during any stroke, generates letters that are invariant under speed and size rescaling, and enables effortless. connection of letter shapes into words. Speed and size rescaling are achieved by scalar GO and GRO signals that express computationally simple volitional commands. Psychophysical data concerning band movements, such as the isochrony principle, asymmetric velocity profiles, and the two-thirds power law relating movement curvature and velocity arise as emergent properties of model interactions.

Flat surfaces of finite type in the 3-sphere

We introduce the notion of flat surfaces of finite type in the 3- sphere, give the algebro-geometric description in terms of spectral curves and polynomial Killing fields, and show that finite type flat surfaces generated by curves on S2 with periodic curvature functions are dense in the space of all flat surfaces generated by curves on S2 with periodic curvature functions.

The influence of thermal plasma profiles on low-frequency Alfvén eigenmode dynamics in a tokamak

The confinement of fast particles, present in a tokamak plasma as nuclear fusion products and through external heating, will be essential for any future fusion reactor. Fast particles can be expelled from the plasma through their interaction with Alfvén eigenmode (AE) instabilities. AEs can exist in gaps in the Alfvén continuum created by plasma equilibrium non-uniformities. In the ASDEX Upgrade tokamak, low-frequency modes in the frequency range from f ≈ 10 − 90kHz, including beta-induced Alfvén eigenmodes (BAEs) and lower frequency modes with mixed Alfvén and acoustic polarisations, have been observed. These exist in gaps in the Alfvén continuum opened up by geodesic curvature and finite plasma compressibility. In this thesis, a kinetic dispersion relation is solved numerically to investigate the influence of thermal plasma profiles on the evolution of these low-frequency modes during the sawtooth cycle. Using information gained from various experimental sources to constrain the equilibrium reconstructions, realistic safety factor profiles are obtained for the analysis using the CLISTE code. The results for the continuum accumulation point evolution are then compared with experimental results from ASDEX Upgrade during periods of ICRH only as well as for periods with both ICRH and ECRH applied simultaneously. It is found that the diamagnetic frequency plays an important role in influencing the dynamics of BAEs and low-frequency acoustic Alfvén eigenmodes, primarily through the presence of gradients in the thermal plasma profiles. Different types of modes that are observed during discharges heated almost exclusively by ECRH were also investigated. These include electron internal transport barrier (eITB) driven modes, which are observed to coincide with the occurrence of an eITB in the plasma during the low-density phase of the discharge. Also observed are BAE-like modes and edge-TAEs, both of which occur during the H-mode phase of the discharge.

Lovelock terms and BRST cohomology

Lovelock terms are polynomial scalar densities in the Riemann curvature tensor that have the remarkable property that their Euler-Lagrange derivatives contain derivatives of the metric of an order not higher than 2 (while generic polynomial scalar densities lead to Euler-Lagrange derivatives with derivatives of the metric of order 4). A characteristic feature of Lovelock terms is that their first nonvanishing term in the expansion g λμ = η λμ + h λμ of the metric around flat space is a total derivative. In this paper, we investigate generalized Lovelock terms defined as polynomial scalar densities in the Riemann curvature tensor and its covariant derivatives (of arbitrarily high but finite order) such that their first nonvanishing term in the expansion of the metric around flat space is a total derivative. This is done by reformulating the problem as a BRST cohomological one and by using cohomological tools. We determine all the generalized Lovelock terms. We find, in fact, that the class of nontrivial generalized Lovelock terms contains only the usual ones. Allowing covariant derivatives of the Riemann tensor does not lead to a new structure. Our work provides a novel algebraic understanding of the Lovelock terms in the context of BRST cohomology. © 2005 IOP Publishing Ltd.

3D refraction correction and extraction of clinical parameters from spectral domain optical coherence tomography of the cornea.

Capable of three-dimensional imaging of the cornea with micrometer-scale resolution, spectral domain-optical coherence tomography (SDOCT) offers potential advantages over Placido ring and Scheimpflug photography based systems for accurate extraction of quantitative keratometric parameters. In this work, an SDOCT scanning protocol and motion correction algorithm were implemented to minimize the effects of patient motion during data acquisition. Procedures are described for correction of image data artifacts resulting from 3D refraction of SDOCT light in the cornea and from non-idealities of the scanning system geometry performed as a pre-requisite for accurate parameter extraction. Zernike polynomial 3D reconstruction and a recursive half searching algorithm (RHSA) were implemented to extract clinical keratometric parameters including anterior and posterior radii of curvature, central cornea optical power, central corneal thickness, and thickness maps of the cornea. Accuracy and repeatability of the extracted parameters obtained using a commercial 859nm SDOCT retinal imaging system with a corneal adapter were assessed using a rigid gas permeable (RGP) contact lens as a phantom target. Extraction of these parameters was performed in vivo in 3 patients and compared to commercial Placido topography and Scheimpflug photography systems. The repeatability of SDOCT central corneal power measured in vivo was 0.18 Diopters, and the difference observed between the systems averaged 0.1 Diopters between SDOCT and Scheimpflug photography, and 0.6 Diopters between SDOCT and Placido topography.

Refractive changes after descemet stripping endothelial keratoplasty: a simplified mathematical model.

PURPOSE: To develop a mathematical model that can predict refractive changes after Descemet stripping endothelial keratoplasty (DSEK). METHODS: A mathematical formula based on the Gullstrand eye model was generated to estimate the change in refractive power of the eye after DSEK. This model was applied to four DSEK cases retrospectively, to compare measured and predicted refractive changes after DSEK. RESULTS: The refractive change after DSEK is determined by calculating the difference in the power of the eye before and after DSEK surgery. The power of the eye post-DSEK surgery can be calculated with modified Gullstrand eye model equations that incorporate the change in the posterior radius of curvature and change in the distance between the principal planes of the cornea and lens after DSEK. Analysis of this model suggests that the ratio of central to peripheral graft thickness (CP ratio) and central thickness can have significant effect on refractive change where smaller CP ratios and larger graft thicknesses result in larger hyperopic shifts. This model was applied to four patients, and the average predicted hyperopic shift in the overall power of the eye was calculated to be 0.83 D. This change reflected in a mean of 93% (range, 75%-110%) of patients' measured refractive shifts. CONCLUSIONS: This simplified DSEK mathematical model can be used as a first step for estimating the hyperopic shift after DSEK. Further studies are necessary to refine the validity of this model.

Sticky central limit theorems on open books

Given a probability distribution on an open book (a metric space obtained by gluing a disjoint union of copies of a half-space along their boundary hyperplanes), we define a precise concept of when the Fréchet mean (barycenter) is sticky. This nonclassical phenomenon is quantified by a law of large numbers (LLN) stating that the empirical mean eventually almost surely lies on the (codimension 1 and hence measure 0) spine that is the glued hyperplane, and a central limit theorem (CLT) stating that the limiting distribution is Gaussian and supported on the spine.We also state versions of the LLN and CLT for the cases where the mean is nonsticky (i.e., not lying on the spine) and partly sticky (i.e., is, on the spine but not sticky). © Institute of Mathematical Statistics, 2013.

Locomotor head movements and semicircular canal morphology in primates.

Animal locomotion causes head rotations, which are detected by the semicircular canals of the inner ear. Morphologic features of the canals influence rotational sensitivity, and so it is hypothesized that locomotion and canal morphology are functionally related. Most prior research has compared subjective assessments of animal "agility" with a single determinant of rotational sensitivity: the mean canal radius of curvature (R). In fact, the paired variables of R and body mass are correlated with agility and have been used to infer locomotion in extinct species. To refine models of canal functional morphology and to improve locomotor inferences for extinct species, we compare 3D vector measurements of head rotation during locomotion with 3D vector measures of canal sensitivity. Contrary to the predictions of conventional models that are based upon R, we find that axes of rapid head rotation are not aligned with axes of either high or low sensitivity. Instead, animals with fast head rotations have similar sensitivities in all directions, which they achieve by orienting the three canals of each ear orthogonally (i.e., along planes at 90° angles to one another). The extent to which the canal configuration approaches orthogonality is correlated with rotational head speed independent of body mass and phylogeny, whereas R is not.

Hopf hypersurfaces in pseudo-Riemannian complex and para-complex space forms

The study of real hypersurfaces in pseudo-Riemannian complex space forms and para-complex space forms, which are the pseudo-Riemannian generalizations of the complex space forms, is addressed. It is proved that there are no umbilic hypersurfaces, nor real hypersurfaces with parallel shape operator in such spaces. Denoting by J be the complex or para-complex structure of a pseudo-complex or para-complex space form respectively, a non-degenerate hypersurface of such space with unit normal vector field N is said to be Hopf if the tangent vector field JN is a principal direction. It is proved that if a hypersurface is Hopf, then the corresponding principal curvature (the Hopf curvature) is constant. It is also observed that in some cases a Hopf hypersurface must be, locally, a tube over a complex (or para-complex) submanifold, thus generalizing previous results of Cecil, Ryan and Montiel.

Modelling technology to predict flip-chip assembly

This paper describes modelling technology and its use in providing data governing the assembly of flip-chip components. Details are given on the reflow and curing stages as well as the prediction of solder joint shapes. The reflow process involves the attachment of a die to a board via solder joints. After a reflow process, underfill material is placed between the die and the substrate where it is heated and cured. Upon cooling the thermal mismatch between the die, underfill, solder bumps, and substrate will result in a nonuniform deformation profile across the assembly and hence stress. Shape predictions then thermal solidification and stress prediction are undertaken on solder joints during the reflow process. Both thermal and stress calculations are undertaken to predict phenomena occurring during the curing of the underfill material. These stresses may result in delamination between the underfill and its surrounding materials leading to a subsequent reduction in component performance and lifetime. Comparisons between simulations and experiments for die curvature will be given for the reflow and curing process

Modeling of ingot development during the start-up phase of direct chill casting

Direct chill (DC) casting is a core primary process in the production of aluminum ingots. However, its operational optimization is still under investigation with regard to a number of features, one of which is the issue of curvature at the base of the ingot. Analysis of these features requires a computational model of the process that accounts for the fluid flow, heat transfer, solidification phase change, and thermomechanical analysis. This article describes an integrated approach to the modeling of all the preceding phenomena and their interactions.

Integration of shading and texture cues: testing the linear model

One of the first attempts to develop a formal model of depth cue integration is to be found in Maloney and Landy's (1989) "human depth combination rule". They advocate that the combination of depth cues by the visual sysetem is best described by a weighted linear model. The present experiments tested whether the linear combination rule applies to the integration of texture and shading. As would be predicted by a linear combination rule, the weight assigned to the shading cue did vary as a function of its curvature value. However, the weight assigned to the texture cue varied systematically as a function of the curvature value of both cues. Here we descrive a non-linear model which provides a better fit to the data. Redescribing the stimuli in terms of depth rather than curvature reduced the goodness of fit for all models tested. These results support the hypothesis that the locus of cue integration is a curvature map, rather than a depth map. We conclude that the linear comination rule does not generalize to the integration of shading and texture, and that for these cues it is likely that integration occurs after the recovery of surface curvature.