Proceedings of the Rank Forum on Vitamin D

The Rank Forum on Vitamin D was held on 2nd and 3rd July 2009 at the University of Surrey, Guildford, UK. The workshop consisted of a series of scene-setting presentations to address the current issues and challenges concerning vitamin D and health, and included an open discussion focusing on the identification of the concentrations of serum 25-hydroxyvitamin D (25(OH)D) (a marker of vitamin D status) that may be regarded as optimal, and the implications this process may have in the setting of future dietary reference values for vitamin D in the UK. The Forum was in agreement with the fact that it is desirable for all of the population to have a serum 25(OH)D concentration above 25 nmol/l, but it discussed some uncertainty about the strength of evidence for the need to aim for substantially higher concentrations (25(OH)D concentrations . 75 nmol/l). Any discussion of ‘optimal’ concentration of serum 25(OH)D needs to define ‘optimal’ with care since it is important to consider the normal distribution of requirements and the vitamin D needs for a wide range of outcomes. Current UK reference values concentrate on the requirements of particular subgroups of the population; this differs from the approaches used in other European countries where a wider range of age groups tend to be covered. With the re-emergence of rickets and the public health burden of low vitamin D status being already apparent, there is a need for urgent action from policy makers and risk managers. The Forum highlighted concerns regarding the failure of implementation of existing strategies in the UK for achieving current vitamin D recommendations.

On rank, underdetermined systems and consistency

The concepts of rank, underdetermined systems and consistency in linear algebra are discussed in the context of a puzzle. The article begins with a specific example, moving on to a generalization of the example and then to the general n x n case. As well as providing a solution of the puzzle, the article aims to provide students with a greater understanding of these abstract ideas in linear algebra through the study of the puzzle.

Rank histograms of stratified Monte-Carlo ensembles

The application of forecast ensembles to probabilistic weather prediction has spurred considerable interest in their evaluation. Such ensembles are commonly interpreted as Monte Carlo ensembles meaning that the ensemble members are perceived as random draws from a distribution. Under this interpretation, a reasonable property to ask for is statistical consistency, which demands that the ensemble members and the verification behave like draws from the same distribution. A widely used technique to assess statistical consistency of a historical dataset is the rank histogram, which uses as a criterion the number of times that the verification falls between pairs of members of the ordered ensemble. Ensemble evaluation is rendered more specific by stratification, which means that ensembles that satisfy a certain condition (e.g., a certain meteorological regime) are evaluated separately. Fundamental relationships between Monte Carlo ensembles, their rank histograms, and random sampling from the probability simplex according to the Dirichlet distribution are pointed out. Furthermore, the possible benefits and complications of ensemble stratification are discussed. The main conclusion is that a stratified Monte Carlo ensemble might appear inconsistent with the verification even though the original (unstratified) ensemble is consistent. The apparent inconsistency is merely a result of stratification. Stratified rank histograms are thus not necessarily flat. This result is demonstrated by perfect ensemble simulations and supplemented by mathematical arguments. Possible methods to avoid or remove artifacts that stratification induces in the rank histogram are suggested.

Follow the leaders? An analysis of convergence and innovation of faculty recruiting practices in US business schools

The debate associated with the qualifications of business school faculty has raged since the 1959 release of the Gordon–Howell and Pierson reports, which encouraged business schools in the USA to enhance their legitimacy by increasing their faculties’ doctoral qualifications and scholarly rigor. Today, the legitimacy of specific faculty qualifications remains one of the most discussed topics in management education, attracting the interest of administrators, faculty, and accreditation agencies. Based on new institutional theory and the institutional logics perspective, this paper examines convergence and innovation in business schools through an analysis of faculty hiring criteria. The qualifications examined are academic degree, scholarly publications, teaching experience, and professional experience. Three groups of schools are examined based on type of university, position within a media ranking system, and accreditation by the Association to Advance Collegiate Schools of Business. Data are gathered using a content analysis of 441 faculty postings from business schools based in the USA over two time periods. Contrary to claims of global convergence, we find most qualifications still vary by group, even in the mature US market. Moreover, innovative hiring is more likely to be found in non-elite schools.

Low rank representation on Riemannian manifold of symmetric positive definite matrices

Sparse coding aims to find a more compact representation based on a set of dictionary atoms. A well-known technique looking at 2D sparsity is the low rank representation (LRR). However, in many computer vision applications, data often originate from a manifold, which is equipped with some Riemannian geometry. In this case, the existing LRR becomes inappropriate for modeling and incorporating the intrinsic geometry of the manifold that is potentially important and critical to applications. In this paper, we generalize the LRR over the Euclidean space to the LRR model over a specific Rimannian manifold—the manifold of symmetric positive matrices (SPD). Experiments on several computer vision datasets showcase its noise robustness and superior performance on classification and segmentation compared with state-of-the-art approaches.