Caustics of plane curves, their birationality and matrix projections

After recalling the notion of caustics of plane curves and basic equations, we first show the birationality of the caustic map for a general source point S in the plane. Then we prove more generally a theorem for curves D in the projective space of 3x3 symmetric matrices B. For a general 3x1 vector S the projection to the plane given by B --- BS is birational on D, unless D is not a line and D is contained in a plane of the form Delta_v = {B | Bv = 0}.Comment: 10 pages, to appear in a Springer Verlag volume dedicated to Klaus Hulek on the occasion of his 60-th birthday. Final version, added some remarks by the refere

Geometry of isophote curves

In this paper, we consider the intensity surface of a 2D image, we study the evolution of the symmetry sets (and medial axes) of 1-parameter families of iso-intensity curves. This extends the investigation done on 1-parameter families of smooth plane curves (Bruce and Giblin, Giblin and Kimia, etc.) to the general case when the family of curves includes a singular member, as will happen if the curves are obtained by taking plane sections of a smooth surface, at the moment when the plane becomes tangent to the surface. Looking at those surface sections as isophote curves, of the pixel values of an image embedded in the real plane, this allows us to propose to combine object representation using a skeleton or symmetry set representation and the appearance modelling by representing image information as a collection of medial representations for the level-sets of an image.Comment: 15 pages, 7 figure

Ophthalmic factors in dyslexia

Although the role of ophthalmic factors in dyslexia remains the subject of controversy, recent research has indicated that the correlates of dyslexia may include binocular dysfunction, unstable motor ocular dominance, a deficit of the transient visual subsystem, and an anomaly that can be treated with tinted lenses. These features, typically, have been studied in isolation and their inter-relationship has received little attention. The aim of the present research was to investigate ophthalmic factors in dyslexia, with a particular emphasis on the interaction between optometric variables. Further aims were to establish the most appropriate investigative techniques for optometric practice and to explore the relationship between optometric and psychometric variables. A pilot study was used to refine the experimental design for a subsequent detailed study of 39 children with a specific reading disability and 43 good readers, who were selected from 240 children. The groups were matched for age, sex, and performance IQ. The following factors emerged as correlates of dyslexia: slight impaired visual acuity; reduced vergence amplitudes; increased vergence instability; decreased accommodative amplitude; poor peformance at tests that were designed to assess the function of the transient visual system; and slightly slower performance at a non-verbal simulated reading visual search task. The `transient system deficit', as measured by reduced flicker sensitivity, was significantly associated with decreased accommodative and vergence amplitudes. This links the motor and sensory visual correlates of dyslexia. Although the binocular dysfunction was correlated with increased symptoms, the difference in the groups' simulated reading visual search task performance was largely attributable to psychometric variables. The results suggest tht optometric problems may be a contributory factor in dyslexia, but are unlikely to play a key causative role. Several optometric variables were confounded by psychometric parameters, and this interaction should be a priority for future investigation

Pre-Symmetry Sets of 3D shapes

The investigation of 3D euclidean symmetry sets (SS) and medial axis is an important area, due in particular to their various important applications. The pre-symmetry set of a surface M in 3-space (resp. smooth closed curve in 2D) is the set of pairs of points which contribute to the symmetry set, that is, the closure of the set of pairs of distinct points p and q in M, for which there exists a sphere (resp. a circle) tangent to M at p and at q. The aim of this paper is to address problems related to the smoothness and the singularities of the pre-symmetry sets of 3D shapes. We show that the pre-symmetry set of a smooth surface in 3-space has locally the structure of the graph of a function from R^2 to R^2, in many cases of interest.Comment: ACM-class: I.2; I.5; I.4; J.2. Latex, 3 grouped figures. The final version will appear in the proceedings of the First International Workshop on Deep Structure, Singularities and Computer Vision, Maastricht June 200

SIFT: Sonification integrable flexible toolkit

Presented at the 11th International Conference on Auditory Display (ICAD2005)This paper describes work-in-progress on a platformindependent toolkit for sonification of scientific data. The data being displayed and the sonification control information can be provided in real-time and distributed over a wide area via Ethernet. The toolkit allows the designer to process, scale, and map data to a wide variety of sonification parameters and methods. Sonification processing and control commands are stored in standard XML syntax files and can be applied or modified in real-time. The toolkit described here is easily added to existing visualization applications and can be quickly expanded to use new data formats and sonification modalities. Early results of interactive auditory and visual analysis of an example domain are described, and extensive user tests are being planned

Existence and uniqueness for Legendre curves

We give a moving frame of a Legendre curve (or, a frontal) in the unite tangent bundle and define a pair of smooth functions of a Legendre curve like as the curvature of a regular plane curve. The existence and uniqueness for Legendre curves are holded like as regular plane curves. It is quite useful to analyse the Legendre curves. As applications, we consider contact between Legendre curves and the arc-length parameter of Legendre immersions in the unite tangent bundle.

A rock-magnetic and geomagnetic secular variation record from late-Pleistocene Lake Estancia, New Mexico [abstract]

EXTRACT (SEE PDF FOR FULL ABSTRACT): Exposed sediments of Late Pleistocene Lake Estancia contain a high resolution record of regional climate variability for the period about 12,000 to 32,000 years. A detailed rock-magnetic study is being performed on this well-dated, well-preserved sedimentary sequence to determine how the magnetic signature of sediments responded to regional climate change

Weakly--exceptional quotient singularities

A singularity is said to be weakly--exceptional if it has a unique purely log terminal blow up. In dimension $2$, V. Shokurov proved that weakly--exceptional quotient singularities are exactly those of types $D_{n}$, $E_{6}$, $E_{7}$, $E_{8}$. This paper classifies the weakly--exceptional quotient singularities in dimensions $3$ and $4$

Size and frequency of natural forest disturbances and Amazon carbon balance

Forest inventory studies in the Amazon indicate a large terrestrial carbon sink. However, field plots may fail to represent forest mortality processes at landscape-scales of tropical forests. Here we characterize the frequency distribution of disturbance events in natural forests from 0.01 ha to 2,651 ha size throughout Amazonia using a novel combination of forest inventory, airborne lidar and satellite remote sensing data. We find that small-scale mortality events are responsible for aboveground biomass losses of B1.28 Pg C y 1 over the entire Amazon region. We also find that intermediate-scale disturbances account for losses of B0.01 Pg C y 1 , and that the largest-scale disturbances as a result of blow-downs only account for losses of B0.003 Pg C y 1 . Simulation of growth and mortality indicates that even when all carbon losses from intermediate and large-scale disturbances are considered, these are outweighed by the net biomass accumulation by tree growth, supporting the inference of an Amazon carbon sink