Signal reconstruction from the magnitude of subspace components

We consider signal reconstruction from the norms of subspace components generalizing standard phase retrieval problems. In the deterministic setting, a closed reconstruction formula is derived when the subspaces satisfy certain cubature conditions, that require at least a quadratic number of subspaces. Moreover, we address reconstruction under the erasure of a subset of the norms; using the concepts of $p$-fusion frames and list decoding, we propose an algorithm that outputs a finite list of candidate signals, one of which is the correct one. In the random setting, we show that a set of subspaces chosen at random and of cardinality scaling linearly in the ambient dimension allows for exact reconstruction with high probability by solving the feasibility problem of a semidefinite program

Outlier robust corner-preserving methods for reconstructing noisy images

The ability to remove a large amount of noise and the ability to preserve most structure are desirable properties of an image smoother. Unfortunately, they usually seem to be at odds with each other; one can only improve one property at the cost of the other. By combining M-smoothing and least-squares-trimming, the TM-smoother is introduced as a means to unify corner-preserving properties and outlier robustness. To identify edge- and corner-preserving properties, a new theory based on differential geometry is developed. Further, robustness concepts are transferred to image processing. In two examples, the TM-smoother outperforms other corner-preserving smoothers. A software package containing both the TM- and the M-smoother can be downloaded from the Internet.Comment: Published at http://dx.doi.org/10.1214/009053606000001109 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Bargaining at divorce: The allocation of custody

We model the bargaining process of parents over custody at the time of divorce. First we assume an institutional setting where only sole custody is available. In a second step we reform this institutional setting and introduce the possibility of joint custody. We show that some parents, who would not be able to find an agreement in a sole custody regime, can find an agreement after the joint custody reform. Accordingly, our empirical analysis shows that the introduction of joint custody enables more parents to divorce by mutual consent.(joint) custody; divorce; family law; bargaining

Real Evidence of a Subducting Plate

The objective of this activity is to allow students to manipulate real data and understand how such data are interpreted and used in support of a theory. The concepts studied are maps, earthquakes, and plate tectonics, particularly a subduction zone plate boundary. The student will learn or be refreshed on using latitude and longitude for mapping purposes. The activity should be used in a unit on plate tectonics so that the student has a basic understanding of plate theory, boundaries, and types of crust. It is also useful to guide a class discussion about the different types of evidence used to support the theory of plate tectonics. Educational levels: High school, Undergraduate lower division

Graduating to Success in Employment: How Social Media Can Aid College Students in the Job Search

This issue brief, the second in a series on social media in workforce development, explores how college career service centers can assist college students and recent college graduates in using social media as part of their job search

The complete catalogue of light curves in equal-mass binary microlensing

The light curves observed in microlensing events due to binary lenses span an extremely wide variety of forms, characterised by U-shaped caustic crossings and/or additional smoother peaks. However, all peaks of the binary-lens light curve can be traced back to features of caustics of the lens system. Moreover, all peaks can be categorised as one of only four types (cusp-grazing, cusp-crossing, fold-crossing or fold-grazing). This enables us to present the first complete map of the parameter space of the equal-mass case by identifying regions in which light curves feature the same number and nature of peaks. We find that the total number of morphologies that can be obtained is 73 out of 232 different regions. The partition of the parameter space so-obtained provides a new key to optimise modelling of observed events through a clever choice of initial conditions for fitting algorithms.Comment: 22 pages, 18 figures, accepted for publication in MNRA

Continuity properties of the inf-sup constant for the divergence

The inf-sup constant for the divergence, or LBB constant, is explicitly known for only few domains. For other domains, upper and lower estimates are known. If more precise values are required, one can try to compute a numerical approximation. This involves, in general, approximation of the domain and then the computation of a discrete LBB constant that can be obtained from the numerical solution of an eigenvalue problem for the Stokes system. This eigenvalue problem does not fall into a class for which standard results about numerical approximations can be applied. Indeed, many reasonable finite element methods do not yield a convergent approximation. In this article, we show that under fairly weak conditions on the approximation of the domain, the LBB constant is an upper semi-continuous shape functional, and we give more restrictive sufficient conditions for its continuity with respect to the domain. For numerical approximations based on variational formulations of the Stokes eigenvalue problem, we also show upper semi-continuity under weak approximation properties, and we give stronger conditions that are sufficient for convergence of the discrete LBB constant towards the continuous LBB constant. Numerical examples show that our conditions are, while not quite optimal, not very far from necessary

A case report: retigabine induced oral mucosal dyspigmentation of the hard palate

Background Dyspigmentation of the oral mucosa has a multitude of aetiological causes. Retigabine, a new antiepileptic drug, has the potential side effect of inducing a blue/purple pigmentation of the oral mucosa in addition to the skin, lips, nails and retina of the eyes. This article presents a unique case of dyspigmentation present in the oral mucosa of the hard palate which has previously been unreported in the dental literature. Case presentation A 70 year old white male presented to a secondary care oral surgery department with an unusual asymptomatic pigmented lesion present in the hard palate of the oral cavity. The pigmentation was remarkable for its distinct blue/purple colouration which was associated with a similar discolouration of the nail beds of the hands. This is believed to be a side effect of the anti-epileptic medication retigabine. Conclusion The dental profession and wider healthcare community should be made fully aware of the potential side effect of oral dyspigmentation associated with the novel anti-epileptic medication retigabine. Enhanced knowledge of the causative role of retigabine in dyspigementation of the oral mucosa will allow the practitioner to make an appropriate diagnosis. As far the authors are aware this is reaction is unreported in the dental literature and should be disseminated to the wider oral health professional’s community

The lived experience of the aged care nurse

The purpose of this phenomenological study was to describe and interpret the common, shared meanings of the experience of aged care nursing from the perspective of the registered nurse working in a nursing home. There are insufficient registered nurses being attracted into aged care, with resulting difficulties in maintaining regular staffing levels in nursing homes. Previous studies conducted in Australia have predominantly used quantitative research methods to investigate various influences QD the recruitment and retention of aged care nurses. These studies do not take into account the practitioners\u27 perceptions of their experience of aged care nursing. A purposive sample of 15 registered nurses was interviewed and the resulting data were analysed using phenomenology to identify thematic structures of the experience of aged care nursing. The NUD.IST qualitative data analysis software package was used as an analysis tool. Significant statements were coded, patterns and relations between categories were identified and the categories were clustered into conceptual, hierarchical themes. Four major themes emerged as being central to the experience of aged care nursing-Gratification, Rapport, Non-productivity and Conflict. While constraints and obstacles to productivity and personal and political conflict may be seen as the negative aspects of aged care, these experiences were relieved by uplifting events described within the framework of resident care and rapport, and collegial support. The nature of aged care nursing is both complex and ambiguous but nurses have readily identified the interwoven threads of the experience. Findings from this study will increase the depth of understanding of aged care nursing and hence contribute to the development of a nursing home environment which enriches the experience of both nurse and resident