Some solutions to the multivariate Behrens-Fisher problem for dissimilarity-based analyses

The essence of the generalised multivariate Behrens–Fisher problem (BFP) is how to test the null hypothesis of equality of mean vectors for two or more populations when their dispersion matrices differ. Solutions to the BFP usually assume variables are multivariate normal and do not handle high‐dimensional data. In ecology, species' count data are often high‐dimensional, non‐normal and heterogeneous. Also, interest lies in analysing compositional dissimilarities among whole communities in non‐Euclidean (semi‐metric or non‐metric) multivariate space. Hence, dissimilarity‐based tests by permutation (e.g., PERMANOVA, ANOSIM) are used to detect differences among groups of multivariate samples. Such tests are not robust, however, to heterogeneity of dispersions in the space of the chosen dissimilarity measure, most conspicuously for unbalanced designs. Here, we propose a modification to the PERMANOVA test statistic, coupled with either permutation or bootstrap resampling methods, as a solution to the BFP for dissimilarity‐based tests. Empirical simulations demonstrate that the type I error remains close to nominal significance levels under classical scenarios known to cause problems for the un‐modified test. Furthermore, the permutation approach is found to be more powerful than the (more conservative) bootstrap for detecting changes in community structure for real ecological datasets. The utility of the approach is shown through analysis of 809 species of benthic soft‐sediment invertebrates from 101 sites in five areas spanning 1960 km along the Norwegian continental shelf, based on the Jaccard dissimilarity measure

Use of approximations of Hamilton-Jacobi-Bellman inequality for solving periodic optimization problems

We show that necessary and sufficient conditions of optimality in periodic optimization problems can be stated in terms of a solution of the corresponding HJB inequality, the latter being equivalent to a max-min type variational problem considered on the space of continuously differentiable functions. We approximate the latter with a maximin problem on a finite dimensional subspace of the space of continuously differentiable functions and show that a solution of this problem (existing under natural controllability conditions) can be used for construction of near optimal controls. We illustrate the construction with a numerical example.Comment: 29 pages, 2 figure

Progression of sleep disturbances in Parkinson’s Disease. A 5-year longitudinal study.

BACKGROUND: Sleep disorders can occur in early Parkinson’s disease (PD). However, the relationship between different sleep disturbances and their longitudinal evolution has not been fully explored. OBJECTIVE: To describe the frequency, coexistence and longitudinal change in excessive daytime sleepiness (EDS), insomnia and probable REM sleep behaviour disorder (pRBD) in early PD. METHODS: Data were obtained from the Parkinson’s Progression Markers Initiative (PPMI). EDS, insomnia, and pRBD were defined using the Epworth Sleepiness Scale, MDS-UPDRS Part I sub-item 1.7, and RBD screening questionnaire. RESULTS: 218 PD subjects and 102 controls completed five years of follow up. At baseline, 69 (31.7%) PD subjects reported one type of sleep disturbance, 25 (11.5%) reported two types of sleep disturbances, and three (1.4%) reported all three types of sleep disturbances. At five years, the number of PD subjects reporting one, two and three types of sleep disturbances was 85 (39.0%), 51 (23.4%), and 16 (7.3%), respectively. Only 41(18.8%) patients were taking sleep medications. The largest increase in frequency was seen in insomnia (44.5%), followed by EDS (32.1%) and pRBD (31.2%). Insomnia was the most common sleep problem at any time over the 5-year follow-up. The frequency of sleep disturbances in HCs remained stable. CONCLUSIONS: There is a progressive increase in the frequency of sleep disturbances in PD, with the number of subjects reporting multiple sleep disturbances increasing over time. Relatively few patients reported multiple sleep disturbances, suggesting that they can have different pathogenesis. A large number of patients were not treated for their sleep disturbances

Non-supersymmetric heterotic model building

We investigate orbifold and smooth Calabi-Yau compactifications of the non-supersymmetric heterotic SO(16)xSO(16) string. We focus on such Calabi-Yau backgrounds in order to recycle commonly employed techniques, like index theorems and cohomology theory, to determine both the fermionic and bosonic 4D spectra. We argue that the N=0 theory never leads to tachyons on smooth Calabi-Yaus in the large volume approximation. As twisted tachyons may arise on certain singular orbifolds, we conjecture that such tachyonic states are lifted in the full blow-up. We perform model searches on selected orbifold geometries. In particular, we construct an explicit example of a Standard Model-like theory with three generations and a single Higgs field.Comment: 1+30 pages latex, 11 tables; v2: references and minor revisions added, matches version published in JHE

Why do Particle Clouds Generate Electric Charges?

Grains in desert sandstorms spontaneously generate strong electrical charges; likewise volcanic dust plumes produce spectacular lightning displays. Charged particle clouds also cause devastating explosions in food, drug and coal processing industries. Despite the wide-ranging importance of granular charging in both nature and industry, even the simplest aspects of its causes remain elusive, because it is difficult to understand how inert grains in contact with little more than other inert grains can generate the large charges observed. Here, we present a simple yet predictive explanation for the charging of granular materials in collisional flows. We argue from very basic considerations that charge transfer can be expected in collisions of identical dielectric grains in the presence of an electric field, and we confirm the model's predictions using discrete-element simulations and a tabletop granular experiment

What can managers learn online? Investigating possibilities for active understanding in the online MBA classroom

Online MBAs have become integral to business schools’ portfolios and the number of MBA students opting for an online version looks set to grow. In the wake of well documented critiques of traditional MBA formats, this expansion prompted us to examine the potential for critically reflexive learning ideals in asynchronous MBA learning environments. Building the Community of Inquiry (CoI) model we elaborate elements of Bakhtin and Shotter’s dialogism to develop the notion of ‘active understanding’ as a means to study an online MBA classroom. We present two illustrative episodes to show how aspects of active understanding may unfold and we point to the role of infrastructure, curriculum and instructor interventions in developing more genuine dialogical exchanges. Our findings suggest that online MBA course designers can learn from CoI approaches to which we add that critically reflexive learning is situationally sensitive; requiring the capacity to create and recognize nuance and difference in the written communication; making the other the focus of learning. We conclude with implications for pedagogy and technology infrastructure