Polarization singularities in the clear sky

Ideas from singularity theory provide a simple account of the pattern of polarization directions in daylight. The singularities (two near the Sun and two near the anti-Sun) are points in the sky where the polarization line pattern has index +1/2 and the intensity of polarization is zero. The singularities are caused by multiple scattering that splits into two each of the unstable index +1 singularities at the Sun and anti-Sun, which occur in the single-dipole scattering (Rayleigh) theory. The polarization lines are contours of an elliptic integral. For the intensity of polarization (unnormalized degree), it is necessary to incorporate the strong depolarizing effect of multiple scattering near the horizon. Singularity theory is compared with new digital images of sky polarization, and gives an excellent description of the pattern of polarization directions. For the intensity of polarization, the theory can reproduce not only the zeros but also subtle variations in the polarization maxima

"It's been a helluva year": the experience of vestibular disorders on the significant other's quality of life

A dissertation on a study presented to the Discipline of Speech Pathology and Audiology , School of Human and Community Development , Faculty of Humanities , University of the Witwatersrand , In fulfilment of the requirements for the degree M.A. Audiology , March 2017In health care, there appears to be greater consideration for the biopsychosocial model of disability and viewing disability in terms of functional health. Recently, the effect of impairment on the significant other’s (SO’s) quality of life (QOL) has been explored. In audiology, there appear to be very few published studies in this area, particularly related to vestibular disorders. The purpose of this study was to investigate the experiences of vestibular disorders on the SO’s QOL. A qualitative research design was employed, including 11 interviews and two focus groups. Participants were SO’s of individuals with chronic vestibular disorders, and were recruited from a private audiology practice in Gauteng through purposive sampling strategies. Data were analysed using thematic analysis. Eight primary themes emerged in the data analysis: social implications, financial implications, searching for a diagnosis, emotional effects, changes in family dynamics, support systems, comparison-oriented coping mechanisms, and referrals for psychological services. Findings suggested that SO’s experienced third-party vestibular disability; however, having the appropriate support systems, including family and friends, was pertinent. It was also indicated that the relationship with the audiologist was essential in providing better understanding of the condition and prognosis thereof, resulting in less frustration and improved adaptation to the reported changes. A key finding was the lack of referral for psychological or counselling services. These findings suggest the need to account for third-party vestibular disability in clinical, theoretical, and academic settings, and they call for the inclusion of third-party disability in policy-making.MT 201

Optical Mobius Strips in Three Dimensional Ellipse Fields: Lines of Circular Polarization

The major and minor axes of the polarization ellipses that surround singular lines of circular polarization in three dimensional optical ellipse fields are shown to be organized into Mobius strips. These strips can have either one or three half-twists, and can be either right- or left-handed. The normals to the surrounding ellipses generate cone-like structures. Two special projections, one new geometrical, and seven new topological indices are developed to characterize the rather complex structures of the Mobius strips and cones. These eight indices, together with the two well-known indices used until now to characterize singular lines of circular polarization, could, if independent, generate 16,384 geometrically and topologically distinct lines. Geometric constraints and 13 selection rules are discussed that reduce the number of lines to 2,104, some 1,150 of which have been observed in practice; this number of different C lines is ~ 350 times greater than the three types of lines recognized previously. Statistical probabilities are presented for the most important index combinations in random fields. It is argued that it is presently feasible to perform experimental measurements of the Mobius strips and cones described here theoretically

Optical M0bius Strips in Three Dimensional Ellipse Fields: Lines of Linear Polarization

The minor axes of, and the normals to, the polarization ellipses that surround singular lines of linear polarization in three dimensional optical ellipse fields are shown to be organized into Mobius strips and into structures we call rippled rings (r-rings). The Mobius strips have two full twists, and can be either right- or left-handed. The major axes of the surrounding ellipses generate cone-like structures. Three orthogonal projections that give rise to 15 indices are used to characterize the different structures. These indices, if independent, could generate 839,808 geometrically and topologically distinct lines; selection rules are presented that reduce the number of lines to 8,248, some 5,562 of which have been observed in a computer simulation. Statistical probabilities are presented for the most important index combinations in random fields. It is argued that it is presently feasible to perform experimental measurements of the Mobius strips, r-rings, and cones described here theoretically

Theory of charcteristics of second order partial differential equations

In the following material we shall be concerned with the secon-order partial differential equation

Loxosceles Rufescens Found in Columbus, Ohio

Author Institution: Faculty of Entomology, Ohio State University, Columbus, Ohio 4321

Using Underapproximations for Sparse Nonnegative Matrix Factorization

Nonnegative Matrix Factorization consists in (approximately) factorizing a nonnegative data matrix by the product of two low-rank nonnegative matrices. It has been successfully applied as a data analysis technique in numerous domains, e.g., text mining, image processing, microarray data analysis, collaborative filtering, etc. We introduce a novel approach to solve NMF problems, based on the use of an underapproximation technique, and show its effectiveness to obtain sparse solutions. This approach, based on Lagrangian relaxation, allows the resolution of NMF problems in a recursive fashion. We also prove that the underapproximation problem is NP-hard for any fixed factorization rank, using a reduction of the maximum edge biclique problem in bipartite graphs. We test two variants of our underapproximation approach on several standard image datasets and show that they provide sparse part-based representations with low reconstruction error. Our results are comparable and sometimes superior to those obtained by two standard Sparse Nonnegative Matrix Factorization techniques.Comment: Version 2 removed the section about convex reformulations, which was not central to the development of our main results; added material to the introduction; added a review of previous related work (section 2.3); completely rewritten the last part (section 4) to provide extensive numerical results supporting our claims. Accepted in J. of Pattern Recognitio