Pairs Of Rays Research Articles

Linear Inequalities for Flags in Graded Partially Ordered Sets

The closure of the convex cone generated by all flag f-vectors of graded partially ordered sets is shown to be polyhedral. In particular, we give the facet inequalities to the polar cone of all nonnegative chain-enumeration functionals on this class of partially ordered sets. These are in one-to-one correspondence with antichains of intervals on the set of ranks and thus are counted by Catalan numbers. Furthermore, we prove that the convolution operation introduced by Kalai assigns extreme rays to pairs of extreme rays in most cases. We describe the strongest possible inequalities for graded partially ordered sets of rank at most 5.

Patterning of dopaminergic neurotransmitter identity among Caenorhabditis elegans ray sensory neurons by a TGFbeta family signaling pathway and a Hox gene.

We have investigated the mechanism that patterns dopamine expression among Caenorhabditis elegans male ray sensory neurons. Dopamine is expressed by the A-type sensory neurons in three out of the nine pairs of rays. We used expression of a tyrosine hydroxylase reporter transgene as well as direct assays for dopamine to study the genetic requirements for adoption of the dopaminergic cell fate. In loss-of-function mutants affecting a TGFbeta family signaling pathway, the DBL-1 pathway, dopaminergic identity is adopted irregularly by a wider subset of the rays. Ectopic expression of the pathway ligand, DBL-1, from a heat-shock-driven transgene results in adoption of dopaminergic identity by rays 3-9; rays 1 and 2 are refractory. The rays are therefore prepatterned with respect to their competence to be induced by a DBL-1 pathway signal. Temperature-shift experiments with a temperature-sensitive type II receptor mutant, as well as heat-shock induction experiments, show that the DBL-1 pathway acts during an interval that extends from two to one cell generation before ray neurons are born and begin to differentiate. In a mutant of the AbdominalB class Hox gene egl-5, rays that normally express EGL-5 do not adopt dopaminergic fate and cannot be induced to express DA when DBL-1 is provided by a heat-shock-driven dbl-1 transgene. Therefore, egl-5 is required for making a subset of rays capable of adopting dopaminergic identity, while the function of the DBL-1 pathway signal is to pattern the realization of this capability.

3D Camera Has No Lens, Great Depth of Field

IMAGINGOn page [2164][1], a team of electrical engineers describes a lensless digital camera that records three-dimensional views. The system works by bathing an object in ordinary light, rotating it on a stage, and recording the interference of thousands of pairs of light rays reflected from or transmitted through the object. Other researchers say the technique could capture cells and tissues in three dimensions and give depth to machine vision. [1]: http://www.sciencemag.org/cgi/content/short/284/5423/2164

Angular Diameter Distances in Clumpy Friedmann Universes

Solving null-geodesic equations, behavior of angular diameter distances is studied in inhomogeneous cosmological models, which are given by performing N-body simulations with the CDM spectrum. The distances depend on the separation angle of ray pairs, the mass and the radius of particles cosisting of galaxies and dark matter balls, and cosmological model parameters. The calculated distances are compared with the Dyer- Roeder distance, and after many ray-shooting, the average, dispersion and distribution of the clumpiness parameter are derived.

A “rays-as-appendages” model for the origin of pentamerism in echinoderms

AbstractA new hypothesis concerning the evolutionary origin of pentameral symmetry in echinoderms is presented. The BA-A-BA pattern of Lovén's law in echinoids and the 2-1-2 symmetry of the edrioasteroidStromatocystitesappear to be morphogenetically related, and this pattern appears to be locked into development. This pattern may have originated from a unirayed 0-1-0, —A—, ancestor. I propose that a duplication of the uniray occurred and resulted in the addition of a pair of rays that followed Bateson's rules of symmetry to form a three-rayed 0-1-2, —A-BA, construction. This change occurred on the side that corresponds to the left side of the organism. This event made the individual asymmetric with respect to its anterior-posterior axis. Therefore I propose that morphogenetic regulation of bilaterality of the organism then led to homeotic expression of a mirror-image pair of rays on the opposite side. These two morphogenetic steps achieved the 2-1-2, BA-A-BA pattern. “Appendage status” of rays is assumed necessary to invoke the Batesonian mirror-image duplications of the model.Three robust morphological characters emerge from the “rays-as-appendages” model: (1) 2-1-2, BAo-A-BA, organization; (2) “locked-in” pentamerism; and (3) a 2-3 pattern of right and left rays. Results based on ray homology research are presented for echinoids, asteroids, ophiuroids, edrioasteroids, ophiocistioids, and holothurians. I speculate that helicoplacoids may have 0-1-2 triradiate construction, and that solutes may have 0-1-0 uniray construction. The model has limits; it does not explain 1-1, or 2-1, or 2-2 or 1-1-1 organization of ambulacra.

Recursive seismic ray modelling: applications in inversion and VSP

The recursive nature of rays in blocky models can be exploited to solve some difficult problems in seismic modelling. Each segment of a ray travels from an initial point up to a reflecting interface, where it is split into reflected and transmitted ray segments, which each continue in a similar way. The tree structure that thus emanates is conveniently handled by a recursive scheme. Recursion allows an automatic generation of all phases on a seismogram, together with all information necessary to analyse or select them. By operating recursively with a ray cell, bounded by a pair of vicinal rays in 2D, or a triplet of vicinal rays in 3D, and two successive isochrons, the two‐point ray‐tracing problem is reduced to a simple interpolation. Also, the cellular approach allows for a stable and robust evaluation of dynamic ray quantities without any paraxial tracing, which is cumbersome in blocky models of realistic complexity. Geometric shadows are filled by recursively generated diffractions. The recursive ray tracer has found applications in the fast computation of Green's functions in target‐oriented inversion and in phase identification in VSP.

Estimation of multivalued arrivals in 3D models using wavefront construction—Part I1

AbstractA new 3D wavefield modelling approach based on dynamic ray tracing is presented. This approach is called wavefront construction, and it can be used in 3D models with constant or smoothly varying material properties (S‐ and P‐velocity and density) separated by smooth interfaces. Wavefronts consisting of rays arranged in a triangular network are propagated stepwise through the model. At each time step, the differences in a number of parameters are checked between each pair of rays on the wavefront. New rays are interpolated whenever this difference between pairs of rays exceeds some predefined maximum value. A controlled sampling of the wavefront at all time steps is thus obtained. Receivers are given multiple‐event values by interpolation when the wavefronts pass them. The strength of the wavefront construction method is that it is robust and efficient.

Velocity and interface depth determination by tomography of depth migrated gathers

A method for velocity and interface depth determination based on tomography of migrated common reflecting point (CRP) gathers is presented. The method is derived from the tomographic principle that relates traveltime change along a given ray to perturbations in slowness and layer depths. The tomographic principle is used to convert depth errors in migrated CRP gathers to time errors along a CRP ray pair and thus enable use of conventional traveltime tomography. It is also used to affect a very fast prestack migration and set up the tomography matrix. The velocity‐depth determination method uses the available offsets of all CRPs and inverts for the parameters of all layers simultaneously. Hand picking of depth errors on CRP gathers is avoided by a method where the tomography matrix operates directly on the migrated gathers. The velocity‐depth determination method is demonstrated on a synthetic example and on a field example from the North Sea.

An iterative approach to curved ray reconstruction of birefringent fields

The transmission of polarized light through non-homogeneous birefringent fields is examined, and an iterative approach for incorporating ray curvature into the analysis of tomographic data is proposed. The method extends strain-gradient theory and applies iterative algorithms which have been used by other researchers to reconstruct fields which are non-homogeneous but optically Isotropic. Optical anisotropy is incorporated by using a light propagation model which includes both bending and separation of initially coincident light ray pairs. To illustrate the method, data are generated computationally and are analysed to determine the bending moment in a prismatic beam and the forces acting on a diametrically loaded disc.

Quadratic divergence of geodesics in CAT(0) spaces

A finite CAT(0) 2-complexX is produced whose universal cover possesses two geodesic rays which diverge quadratically and such that no pair of rays diverges faster than quadratically. This example shows that an aphorism in Riemannian geometry, that predicts that in nonpositive curvature nonasymptotic geodesic rays either diverge exponentially or diverge linearly, does not hold in the setting of CAT(0) complexes. The fundamental group ofX is that of a compact Riemannian manifold with totally geodesic boundary and nonpositive sectional curvature.

Martin boundaries of sectorial domains

LetD be a domain in R2 whose complement is contained in a pair of rays leaving the origin. That is, D contains two sectors whose base angles sum to 2π. We use balayage to give an integral test that determines if the origin splits into exactly two minimal Martin boundary points, one approached through each sector. This test is related to other integral tests due to Benedicks and Chevallier, the former in the special case of a Denjoy domain. We then generalise our test, replacing the pair of rays by an arbitrary number.

Projection domain compensation of missing angles for fan-beam CT reconstruction

An improved method is proposed for fan-beam computed tomographic (CT) reconstruction from data with limited views. Compensation for the missing projections for fan-beam CT can be partially accomplished by using the coincident ray or by an interpolation technique using circular sample theory. In this article, the authors propose a more accurate compensation method for the missing projections whether the coincident ray pairs exist or not. The fan-beam reprojection algorithm, which is the inverse operator of the convolution filter, was extended from the projection space iteration reconstruction-reprojection (PSIRR) in parallel beam geometry. In addition, this algorithm was validated by applying the Shepp-Logan phantom for a computer simulation in the equi-angular fan-beam CT geometg7.

Relative orientation revisited

Relative orientation is the recovery of the position and orientation of one imaging system relative to another from correspondences among five or more ray pairs. It is one of four core problems in photogrammetry and is of central importance in binocular stereo as well as in long-range motion vision. While five ray correspondences are sufficient to yield a finite number of solutions, more than five correspondences are used in practice to ensure an accurate solution with least-squares methods. Most iterative schemes for minimizing the sum of the squares of weighted errors require a good guess as a starting value. The author has previously published a method that results in the best solution without requiring an initial guess [ J. Opt. Soc. Am. A4, 629 ( 1987)] An even simpler method is presented here that utilizes the representation of rotations by unit quaternions.

Reversible Hopf bifurcation in four-dimensional maps.

Following a recent work [Sevryuk and Lahiri, Phys. Lett. A 154, 104 (1991)], we study the bifurcation of four-dimensional reversible maps in which the eigenvalues of the Jacobian of the map at a symmetric fixed point move off the unit circle along a pair of conjugate rays as some parameter \ensuremath{\epsilon} crosses a threshold value. We construct a perturbation scheme to show that, depending on a control parameter \ensuremath{\gamma}, the bifurcation can be either ``normal'' or ``inverted'' in nature. In the former case, two one-parameter families of elliptic invariant curves passing arbitrarily close to the fixed point (which coexist with Kolmogorov-Arnold-Moser tori) merge together and move away from the fixed point. In the latter case, the families of elliptic invariant curves meet a family of hyperbolic invariant curves. As \ensuremath{\epsilon} is varied, all these invariant curves shrink to the fixed point and are annihilated. The problem of determining whether an invariant curve is elliptic or hyperbolic is related to a tight-binding model on a linear quasiperiodic chain familiar in solid-state theory. Numerical evidence confirming these results is presented. A few areas for further study are indicated.

Common reflecting elements (CRE) ray tracing for the calculation of the global multi-offset time field

SUMMARY We propose a new approach for a fast calculation of the so-called multi-offset time field in a 2-D laterally heterogeneous medium. It comprises the traveltimes of all waves emerging from a set of sources, reflected from a given interface and recorded at the corresponding receivers. A common reflecting elements (CRE) system of observation is used. It is simulated by fans of rays emitted upward by fictitious sources (elements) located on the reflecting interface. The calculated traveltimes for the pairs of rays within the fans are used to construct a global time surface representing the multi-offset time field. They are projected through interpolation (for each branch of arrivals) on an organized table which is used for establishing coefficients for 2-D interpolation. The coeficients determine the desired time surface(s). Some results and formulae from the CRE stacking method are used to show how the distribution of the locations of the shot-offset pairs connected to a CRE and the corresponding traveltimes can be obtained by tracing only the central (normal incidence) rays. The accuracy of these formulae is investigated for two types of models. With the proposed approach, the problem of computing traveltimes for any desired configuration of sources and receivers requires only a minimal number of operations. The method is thus very fast, and its efficiency increases with the total number of shot gathers.

Search for anomalous e+-e- annihilation from 140Pr.

Anomalous ${e}^{+}\ensuremath{-}{e}^{\ensuremath{-}}$ annihilation proceeding through a 1060 keV intermediate state is not observed, demonstrating that the 1062 keV $\ensuremath{\gamma}$-ray pair detected in U + Th collisions is not an artifact of conventional positron annihilation.

Ray solution for finite amplitude two‐dimensional waves in a hard‐walled rectangular waveguide

This paper describes a ray superposition theory for cumulative growth of nonlinear effects in a two‐dimensional acoustic mode, based on decomposition of the mode into a pair of obliquely propagating, nonlinear planar waves. The mathematical foundation of the formulation is an earlier perturbation analysis of the reflection of a distorted planar wave obliquely incident on the boundary of an infinite half‐space [Z. Qian, Sci. Sin. 25, 492–501 (1982)]. Based on the results of the analysis, each of the pair of rays forming the signal at a selected field point is traced back to its origin at the excitation. Each ray is described as a simple planar wave undergoing finite amplitude distortion that depends on the propagation distance along that ray between field and source points. This distance is the same for each ray at a specified field point, but differences in the excitation at the respective source points result in phase differences between the two rays. The overall signal is shown to be the same as a modal...

Systematics of the nematodes that cause ostertagiasis in cattle, sheep and goats in North America

The systematics of the Ostertagiinae is unsettled with no agreement on how many genera and species are present in cattle and sheep. Ten species of Ostertagiinae are commonly parasitic in cattle and sheep. The males can be identified on the basis of differences in morphology of spicules and genital cones but the females of most species cannot be identified. The species-level systematics have been complicated by the proposal that the ten species are polymorphs of only five species. The systematics at genus level has been complicated by the use of numerous genera for the ten species, at present most commonly Ostertagia, Teladorsagia and Marshallagia. This report (1) describes the current knowledge of the systematics and (2) provides diagnoses of the genera recommended for the ten species. The morphology of the ten species was studied to determine whether characteristics could be found to identify females or to further differentiate the males. Characters studied included the system of longitudinal and surface cuticular ridges (synlophe), the internal morphology of the esophagus and the orientation of rays of the copulatory bursa. The study of species morphology resulted in additional support for the polymorphism proposal. All minor species were found to be identical to their major species in characteristics of the synlophe, esophagus and rays of the copulatory bursa. Two recent classifications of the Ostertagiinae both recommended the use of the genus Teladorsagia for the species T. circumcincta and the two minor species that occur with it, T. trifurcata and T. davtiani. Teladorsagia is characterized by a copulatory bursa in which the five lateral rays are arranged 2-2-1 and a ventral swelling of the genital cone (proconus) is absent. One pair of species, Marshallagia marshalli (major species) and Ostertagia occidentalis (minor species) should be included in the genus Marshallagia. This genus has been characterized by an elongated bursa in which the posterior pair of lateral rays are much longer than the ventral pair. The remaining two pairs of species ( O. ostertagi and its minor species O. lyrata, and O. leptospicularis and its minor species O. kolchida) and O. bisonis belong in the genus Ostertagia which is characterized by a 2-1-2 arrangement of the five lateral rays of the copulatory bursa and the presence of a proconus.

Application of two-variable Taylor series to the ray theory of propagation in an unbound medium

The Taylor series method is applied to the ray theory solution for the acoustic field near the initial caustic of the first convergence zone. This field is formed by a pair of rays that are heading downward at the source and upward at the receiver. The ray parameter (namely the phase velocity) of each ray is expressed as a two-variable Taylor series in horizontal range and depth relative to a fixed expansion point. The terms of the series are calculated for derivatives up to fifth order. The method is applied to a typical oceanic example modeled by a bilinear sound-speed profile in which the caustic of the rays passes the expansion point at vertical distances of 15–60 m and at horizontal distances of 200–1200 m, respectively. The Taylor-series phase velocities are inserted into the usual ray theory expressions for relative energy and travel time. It is found in some cases that satisfactory accuracy is obtained over a region of the ocean that is sufficiently large for sonar application. The advantage of this new approach is that, to calculate the sound field at a grid of points within a region, the (relatively expensive) iterative method of determining ray parameters need be applied to only one expansion point.

Dynamic behaviour of the K-corona above a type I radio source

Coronagraph images can be greatly enhanced by subtracting from the brightness of each picture point, the running median brightness over a square surrounding each picture point. The application of this technique to coronal analysis appears to be new. After such enhancement, images recorded by the SMM Coronagraph/Polarimeter reveal a coronal transient with previously undescribed characteristics. The transient began with bright ejecta moving up pre-existing rays and weaker, more diffuse, mass injection in the area between rays. At the sudden onset of this mass ejection the rays began to move apart from one another: during the ensuing 22 hr the separation of one pair of rays increased by 37° of latitude. Towards the end of the event these moving rays looked much like the legs of previously described loop transients. A type I radio source lay close to the centre of symmetry of the transient.