Coincidence points of fiber maps on S-n-bundles

In this note we study coincidence of pairs of fiber-preserving maps f, g : E-1 -> E-2 where E-1, E-2 are S-n-bundles over a space B. We will show that for each homotopy class vertical bar f vertical bar of fiber-preserving maps over B, there is only one homotopy class vertical bar g vertical bar such that the pair (f, g), where vertical bar g vertical bar = vertical bar tau circle f vertical bar can be deformed to a coincidence free pair. Here tau : E-2 -> E-2 is a fiber-preserving map which is fixed point free. In the case where the base is S-1 we classify the bundles, the homotopy classes of maps over S-1 and the pairs which can be deformed to coincidence free. At the end we discuss the self-coincidence problem. (C) 2010 Elsevier B.V. All rights reserved.

Oriented vehicles travelling in spherical space

This paper tackles the path planning problem for oriented vehicles travelling in the non-Euclidean 3-Dimensional space; spherical space S3. For such problem, the orientation of the vehicle is naturally represented by orthonormal frame bundle; the rotation group SO(4). Orthonormal frame bundles of space forms coincide with their isometry groups and therefore the focus shifts to control systems defined on Lie groups. The oriented vehicles, in this case, are constrained to travel at constant speed in a forward direction and their angular velocities directly controlled. In this paper we identify controls that induce steady motions of these oriented vehicles and yield closed form parametric expressions for these motions. The paths these vehicles trace are defined explicitly in terms of the controls and therefore invariant with respect to the coordinate system used to describe the motion.

The Dirac-Hestenes equation for spherical symmetric potentials in the spherical and Cartesian gauges

In this paper, using the apparatus of the Clifford bundle formalism, we show how straightforwardly solve in Minkowski space-time the Dirac-Hestenes equation - which is an appropriate representative in the Clifford bundle of differential forms of the usual Dirac equation - by separation of variables for the case of a potential having spherical symmetry in the Cartesian and spherical gauges. We show that, contrary to what is expected at a first sight, the solution of the Dirac-Hestenes equation in both gauges has exactly the same mathematical difficulty. © World Scientific Publishing Company.

Limits of spherical blur determined with an adaptive optics mirror

We extended an earlier study (Vision Research, 45, 1967–1974, 2005) in which we investigated limits at which induced blur of letter targets becomes noticeable, troublesome and objectionable. Here we used a deformable adaptive optics mirror to vary spherical defocus for conditions of a white background with correction of astigmatism; a white background with reduction of all aberrations other than defocus; and a monochromatic background with reduction of all aberrations other than defocus. We used seven cyclopleged subjects, lines of three high-contrast letters as targets, 3–6 mm artificial pupils, and 0.1–0.6 logMAR letter sizes. Subjects used a method of adjustment to control the defocus component of the mirror to set the 'just noticeable', 'just troublesome' and 'just objectionable' defocus levels. For the white-no adaptive optics condition combined with 0.1 logMAR letter size, mean 'noticeable' blur limits were ±0.30, ±0.24 and ±0.23 D at 3, 4 and 6 mm pupils, respectively. White-adaptive optics and monochromatic-adaptive optics conditions reduced blur limits by 8% and 20%, respectively. Increasing pupil size from 3–6 mm decreased blur limits by 29%, and increasing letter size increased blur limits by 79%. Ratios of troublesome to noticeable, and of objectionable to noticeable, blur limits were 1.9 and 2.7 times, respectively. The study shows that the deformable mirror can be used to vary defocus in vision experiments. Overall, the results of noticeable, troublesome and objectionable blur agreed well with those of the previous study. Attempting to reduce higher-order aberrations or chromatic aberrations, reduced blur limits to only a small extent.

Modeling videokeratoscopic height data with spherical harmonics

Purpose: All currently considered parametric models used for decomposing videokeratoscopy height data are viewercentered and hence describe what the operator sees rather than what the surface is. The purpose of this study was to ascertain the applicability of an object-centered representation to modeling of corneal surfaces. Methods: A three-dimensional surface decomposition into a series of spherical harmonics is considered and compared with the traditional Zernike polynomial expansion for a range of videokeratoscopic height data. Results: Spherical harmonic decomposition led to significantly better fits to corneal surfaces (in terms of the root mean square error values) than the corresponding Zernike polynomial expansions with the same number of coefficients, for all considered corneal surfaces, corneal diameters, and model orders. Conclusions: Spherical harmonic decomposition is a viable alternative to Zernike polynomial decomposition. It achieves better fits to videokeratoscopic height data and has the advantage of an object-centered representation that could be particularly suited to the analysis of multiple corneal measurements.

Influence of spherical intraocular lens implantation and conventional laser in situ keratomileusis on peripheral ocular aberrations

Aim: To measure the influence of spherical intraocular lens implantation and conventional myopic laser in situ keratomileusis on peripheral ocular aberrations. Setting: Visual & Ophthalmic Optics Laboratory, School of Optometry & Institute of Health and Biomedical Innovation, Queensland University of Technology, Brisbane, Australia. Methods: Peripheral aberrations were measured using a modified commercial Hartmann-Shack aberrometer across 42° x 32° of the central visual field in 6 subjects after spherical intraocular lens (IOL) implantation and in 6 subjects after conventional laser in situ keratomileusis (LASIK) for myopia. The results were compared with those of age matched emmetropic and myopic control groups. Results: The IOL group showed a greater rate of quadratic change of spherical equivalent refraction across the visual field, higher spherical aberration, and greater rates of change of higher-order root-mean-square aberrations and total root-mean-square aberrations across the visual field than its emmetropic control group. However, coma trends were similar for the two groups. The LASIK group had a greater rate of quadratic change of spherical equivalent refraction across the visual field, higher spherical aberration, the opposite trend in coma across the field, and greater higher-order root-mean-square aberrations and total root-mean-square aberrations than its myopic control group. Conclusion: Spherical IOL implantation and conventional myopia LASIK increase ocular peripheral aberrations. They cause considerable increase in spherical aberration across the visual field. LASIK reverses the sign of the rate of change in coma across the field relative to that of the other groups. Keywords: refractive surgery, LASIK, IOL implantation, aberrations, peripheral aberrations

Spherical image-based visual servo and structure estimation

This paper presents a formulation of image-based visual servoing (IBVS) for a spherical camera where coordinates are parameterized in terms of colatitude and longitude: IBVSSph. The image Jacobian is derived and simulation results are presented for canonical rotational, translational as well as general motion. Problems with large rotations that affect the planar perspective form of IBVS are not present on the sphere, whereas the desirable robustness properties of IBVS are shown to be retained. We also describe a structure from motion (SfM) system based on camera-centric spherical coordinates and show how a recursive estimator can be used to recover structure. The spherical formulations for IBVS and SfM are particularly suitable for platforms, such as aerial and underwater robots, that move in SE(3).

A practical implementation of a continuous isotropic spherical omnidirectional drive

This paper presents a continuous isotropic spherical omnidirectional drive mechanism that is efficient in its mechanical simplicity and use of volume. Spherical omnidirectional mechanisms allow isotropic motion, although many are limited from achieving true isotropic motion by practical mechanical design considerations. The mechanism presented in this paper uses a single motor to drive a point on the great circle of the sphere parallel to the ground plane, and does not require a gearbox. Three mechanisms located 120 degrees apart provide a stable drive platform for a mobile robot. Results show the omnidirectional ability of the robot and demonstrate the performance of the spherical mechanism compared to a popular commercial omnidirectional wheel over edges of varying heights and gaps of varying widths.

Cost-effectiveness of a central venous catheter care bundle

Background: A bundled approach to central venous catheter care is currently being promoted as an effective way of preventing catheter-related bloodstream infection (CR-BSI). Consumables used in the bundled approach are relatively inexpensive which may lead to the conclusion that the bundle is cost-effective. However, this fails to consider the nontrivial costs of the monitoring and education activities required to implement the bundle, or that alternative strategies are available to prevent CR-BSI. We evaluated the cost-effectiveness of a bundle to prevent CR-BSI in Australian intensive care patients. ---------- Methods and Findings: A Markov decision model was used to evaluate the cost-effectiveness of the bundle relative to remaining with current practice (a non-bundled approach to catheter care and uncoated catheters), or use of antimicrobial catheters. We assumed the bundle reduced relative risk of CR-BSI to 0.34. Given uncertainty about the cost of the bundle, threshold analyses were used to determine the maximum cost at which the bundle remained cost-effective relative to the other approaches to infection control. Sensitivity analyses explored how this threshold alters under different assumptions about the economic value placed on bed-days and health benefits gained by preventing infection. If clinicians are prepared to use antimicrobial catheters, the bundle is cost-effective if national 18-month implementation costs are below $1.1 million. If antimicrobial catheters are not an option the bundle must cost less than $4.3 million. If decision makers are only interested in obtaining cash-savings for the unit, and place no economic value on either the bed-days or the health benefits gained through preventing infection, these cost thresholds are reduced by two-thirds.---------- Conclusions: A catheter care bundle has the potential to be cost-effective in the Australian intensive care setting. Rather than anticipating cash-savings from this intervention, decision makers must be prepared to invest resources in infection control to see efficiency improvements.

Mechanism of Resistance to Rice Tungro Spherical Virus (RTSV)

RTSV is one of two viruses that cause tungro disease. RTSV is independently transmitted, whereas the other virus, rice tungro bacilliform virus (RTBV), is dependent on RTSV for its transmission by the green leafhopper (GLH), Nephotettix virescens. The occurrence and spread of tungro disease therefore depend on the presence of RTSV in the field. Resistance to RTSV infection would slow down the spread of the disease.

Differentiation of Rice Tungro Spherical Virus Variants by RTPCR and RFLP

Differentiation of rice tungro spherical virus variants by RTPCR and RFLP tungro bacilliform virus (RTBV), the other causal agent, which causes the symptoms. RTSV is a single-stranded RNA virus of 12,180 nucleotides (Hull 1996).

Complete Nucleotide Sequence of Rice Tungro Spherical Virus Genome of a Highly Virulent Strain Vt6

The complete nucleotide sequence of rice tungro spherical virus (RTSV) strain Vt6, originally from Mindanao, the Philippines, with higher virulence to resistant rice cultivars, was determined and compared with the published sequence for the Philippine-type strain A (RTSV-A-Shen). It was reported that RTSV-A was not able to infect a rice resistant cultivar TKM 6 (10). RTSV-Vt6 and RTSV-A-Shen share 90% and 95% homology at nucleotide and amino-acid levels, respectively. The N-terminal leader sequence of RTSV-Vt6 contained a 39-amino acids-region (positions 65 to 103) which was totally different from that of RTSV-A-Shen; the difference resulted from frame shifting by nucleotide insertions and deletions. To confirm the amino-acid sequence differences of the leader polypeptide, the same region was cloned and sequenced using a newly obtained variant of RTSV-type 6, which had been collected in the field of IRRI, and seven field isolates from Mindanao, the Philippines. Since all the sequences of the target region are identical to that of the Vt6 leader polypeptide, the sequence difference in the leader region seems not to correlate with the virulence of Vt6.

Genetic Diversity of Rice Tungro Spherical Virus in Tungro-Endemic Provinces of the Philippines and Indonesia

The two adjacent genes of coat protein 1 and 2 of rice tungro spherical virus (RTSV) were amplified from total RNA extracts of serologically indistinguishable field isolates from the Philippines and Indonesia, using reverse transcriptase polymerase chain reaction (RT-PCR). Digestion with HindIII and BstYI restriction endonucleases differentiated the amplified DNA products into eight distinct coat protein genotypes. These genotypes were then used as indicators of virus diversity in the field. Inter- and intra-site diversities were determined over three cropping seasons. At each of the sites surveyed, one or two main genotypes prevailed together with other related minor or mixed genotypes that did not replace the main genotype over the sampling time. The cluster of genotypes found at the Philippines sites was significantly different from the one at the Indonesia sites, suggesting geographic isolation for virus populations. Phylogenetic studies based on the nucleotide sequences of 38 selected isolates confirm the spatial distribution of RTSV virus populations but show that gene flow may occur between populations. Under the present conditions, rice varieties do not seem to exert selective pressure on the virus populations. Based on the selective constraints in the coat protein amino acid sequences and the virus genetic composition per site, a negative selection model followed by random-sampling events due to vector transmissions is proposed to explain the inter-site diversity observed

Inheritance of Resistance to Rice Tungro Spherical Virus in a Near-Isogenic Line Derived from Utri Merah and in Rice Cultivar TKM6

Resistance to rice virus diseases is an important requirement in many Southeast Asian rice breeding programs. Inheritance of resistance to rice tungro spherical virus (RTSV) in TW5, a near-isogenic line derived from Indonesian rice cultivar Utri Merah, was compared to that in TKM6, an Indian rice cultivar. Both TKM6 and Utri Merah are cultivars resistant to RTSV infections. Crosses were made between TKM6 and TN1, a susceptible cultivar, and between TW5 and TN1, and F3 lines were evaluated for their resistance to RTSV using two RTSV inoculum sources and a serological assay (ELISA). In TKM6, the resistance to the mixture of RTSV-V + RTBV inoculum source was controlled by a single recessive gene, whereas in TW5, the resistance was controlled by two recessive genes. A single recessive gene, however, controlled the resistance in TW5 when another RTSV variant, RTSV-VI, was used, suggesting that the resistance in TW5 depends on the nature of the RTSV inoculum used. RT-PCR, sequence, and phylogenetic analyses confirmed that RTSV-VI inoculum differs from RTSV-V inoculum and accurate phenotyping of the resistance to RTSV requires the use of a genetic marker.