The distribution of species range size: a stochastic process

The major role played by environmental factors in determining the geographical range sizes of species raises the possibility of describing their long-term dynamics in relatively simple terms, a goal which has hitherto proved elusive. Here we develop a stochastic differential equation to describe the dynamics of the range size of an individual species based on the relationship between abundance and range size, derive a limiting stationary probability model to quantify the stochastic nature of the range size for that species at steady state, and then generalize this model to the species-range size distribution for an assemblage. The model fits well to several empirical datasets of the geographical range sizes of species in taxonomic assemblages, and provides the simplest explanation of species-range size distributions to date

The inexorable resistance of inertia determines the initial regime of drop coalescence

Drop coalescence is central to diverse processes involving dispersions of drops in industrial, engineering and scientific realms. During coalescence, two drops first touch and then merge as the liquid neck connecting them grows from initially microscopic scales to a size comparable to the drop diameters. The curvature of the interface is infinite at the point where the drops first make contact, and the flows that ensue as the two drops coalesce are intimately coupled to this singularity in the dynamics. Conventionally, this process has been thought to have just two dynamical regimes: a viscous and an inertial regime with a crossover region between them. We use experiments and simulations to reveal that a third regime, one that describes the initial dynamics of coalescence for all drop viscosities, has been missed. An argument based on force balance allows the construction of a new coalescence phase diagram

Statistical modelling of transcript profiles of differentially regulated genes

Background: The vast quantities of gene expression profiling data produced in microarray studies, and the more precise quantitative PCR, are often not statistically analysed to their full potential. Previous studies have summarised gene expression profiles using simple descriptive statistics, basic analysis of variance (ANOVA) and the clustering of genes based on simple models fitted to their expression profiles over time. We report the novel application of statistical non-linear regression modelling techniques to describe the shapes of expression profiles for the fungus Agaricus bisporus, quantified by PCR, and for E. coli and Rattus norvegicus, using microarray technology. The use of parametric non-linear regression models provides a more precise description of expression profiles, reducing the "noise" of the raw data to produce a clear "signal" given by the fitted curve, and describing each profile with a small number of biologically interpretable parameters. This approach then allows the direct comparison and clustering of the shapes of response patterns between genes and potentially enables a greater exploration and interpretation of the biological processes driving gene expression. Results: Quantitative reverse transcriptase PCR-derived time-course data of genes were modelled. "Splitline" or "broken-stick" regression identified the initial time of gene up-regulation, enabling the classification of genes into those with primary and secondary responses. Five-day profiles were modelled using the biologically-oriented, critical exponential curve, y(t) = A + (B + Ct)Rt + ε. This non-linear regression approach allowed the expression patterns for different genes to be compared in terms of curve shape, time of maximal transcript level and the decline and asymptotic response levels. Three distinct regulatory patterns were identified for the five genes studied. Applying the regression modelling approach to microarray-derived time course data allowed 11% of the Escherichia coli features to be fitted by an exponential function, and 25% of the Rattus norvegicus features could be described by the critical exponential model, all with statistical significance of p < 0.05. Conclusion: The statistical non-linear regression approaches presented in this study provide detailed biologically oriented descriptions of individual gene expression profiles, using biologically variable data to generate a set of defining parameters. These approaches have application to the modelling and greater interpretation of profiles obtained across a wide range of platforms, such as microarrays. Through careful choice of appropriate model forms, such statistical regression approaches allow an improved comparison of gene expression profiles, and may provide an approach for the greater understanding of common regulatory mechanisms between genes

Nonlinear stabilitty for steady vortex pairs

In this article, we prove nonlinear orbital stability for steadily translating vortex pairs, a family of nonlinear waves that are exact solutions of the incompressible, two-dimensional Euler equations. We use an adaptation of Kelvin's variational principle, maximizing kinetic energy penalised by a multiple of momentum among mirror-symmetric isovortical rearrangements. This formulation has the advantage that the functional to be maximized and the constraint set are both invariant under the flow of the time-dependent Euler equations, and this observation is used strongly in the analysis. Previous work on existence yields a wide class of examples to which our result applies.Comment: 25 page

Borromean rays and hyperplanes

Three disjoint rays in euclidean 3-space form Borromean rays provided their union is knotted, but the union of any two components is unknotted. We construct infinitely many Borromean rays, uncountably many of which are pairwise inequivalent. We obtain uncountably many Borromean hyperplanes.Comment: 41 pages, 30 figures (19 with captions, 11 inline

Screening for mood disorders after stroke: a systematic review of psychometric properties and clinical utility

BackgroundRoutine mood screening is recommended after stroke. However, clinicians report difficulty selecting appropriate tools from the wide range available. We aimed to systematically review the psychometric properties and clinical utility of mood screening tools for stroke survivors.MethodElectronic databases (AMED, EMBASE, CINAHL, Medline and PsycINFO) were searched to identify studies assessing the sensitivity and specificity of mood screening tools. Tools that demonstrated at least 80% sensitivity and 60% specificity with stroke survivors with identifiable cut-off scores indicating major and/or any mood disorder in at least one study were selected and clinical utility was assessed. Those with high clinical utility (against predefined criteria) were selected for recommendation.ResultsThirty papers examining 27 screening tools were identified and 16 tools met the psychometric and clinical utility criteria: 10 were verbal self-report tools, four were observational and two incorporated visual prompts for those with communication problems. Only the Stroke Aphasic Depression Questionnaire –Hospital version (SADQ-H) met all the psychometric and utility criteria. The nine-item Patient Health Questionnaire (PHQ-9) can detect major depression and the 15-item Geriatric Depression Scale (GDS-15) can identify milder symptoms; both are feasible to use in clinical practice. The Hospital Anxiety and Depression Scale (HADS) was the only tool able to identify anxiety accurately, but clinical utility was mixed.ConclusionsValid and clinically feasible mood screening tools for stroke have been identified but methodological inconsistency prevented recommendations about the optimal cut-off scores.</jats:sec

The molecular environment of massive star forming cores associated with Class II methanol maser emission

Methanol maser emission has proven to be an excellent signpost of regions undergoing massive star formation (MSF). To investigate their role as an evolutionary tracer, we have recently completed a large observing program with the ATCA to derive the dynamical and physical properties of molecular/ionised gas towards a sample of MSF regions traced by 6.7 GHz methanol maser emission. We find that the molecular gas in many of these regions breaks up into multiple sub-clumps which we separate into groups based on their association with/without methanol maser and cm continuum emission. The temperature and dynamic state of the molecular gas is markedly different between the groups. Based on these differences, we attempt to assess the evolutionary state of the cores in the groups and thus investigate the role of class II methanol masers as a tracer of MSF.Comment: 5 pages, 1 figure, IAU Symposium 242 Conference Proceeding

Weak containment of measure-preserving group actions

This paper concerns the study of the global structure of measure-preserving actions of countable groups on standard probability spaces. Weak containment is a hierarchical notion of complexity of such actions, motivated by an analogous concept in the theory of unitary representations. This concept gives rise to an associated notion of equivalence of actions, called weak equivalence, which is much coarser than the notion of isomorphism (conjugacy). It is well understood now that, in general, isomorphism is a very complex notion, a fact which manifests itself, for example, in the lack of any reasonable structure in the space of actions modulo isomorphism. On the other hand, the space of weak equivalence classes is quite well behaved. Another interesting fact that relates to the study of weak containment is that many important parameters associated with actions, such as the type, cost, and combinatorial parameters, turn out to be invariants of weak equivalence and in fact exhibit desirable monotonicity properties with respect to the pre-order of weak containment, a fact that can be useful in certain applications. There has been quite a lot of activity in this area in the last few years, and our goal in this paper is to provide a survey of this work

Invariant random subgroups and action versus representation maximality

We show that weak containment of free ergodic measure-preserving actions of F∞ is not equivalent to weak containment of the corresponding Koopman representations. This result is based on the construction of an invariant random subgroup of F∞ which is supported on the maximal actions