Gauss hypergeometric function and quadratic RR-matrix algebras

We consider representations of quadratic $R$-matrix algebras by means of certain first order ordinary differential operators. These operators turn out to act as parameter shifting operators on the Gauss hypergeometric function and its limit cases and on classical orthogonal polynomials. The relationship with W. Miller's treatment of Lie algebras of first order differential operators will be discussed.Comment: 26 page

The Geometry Of Modified Newtonian Dynamics

Modified Newtonian Dynamics is an empirical modification to Poisson's equation which has had success in accounting for the `gravitational field' $\Phi$ in a variety of astrophysical systems. The field $\Phi$ may be interpreted in terms of the weak field limit of a variety of spacetime geometries. Here we consider three of these geometries in a more comprehensive manner and look at the effect on timelike and null geodesics. In particular we consider the Aquadratic Lagrangian (AQUAL) theory, Tensor-Vector-Scalar (TeVeS) theory and Generalized Einstein-{\AE}ther (GEA) theory. We uncover a number of novel features, some of which are specific to the theory considered while others are generic. In the case of AQUAL and TeVeS theories, the spacetime exhibits an excess (AQUAL) or deficit (TeVeS) solid angle akin to the case of a Barriola-Vilenkin global monopole. In the case of GEA, a disformal symmetry of the action emerges in the limit of \grad\Phi\rightarrow 0. Finally, in all theories studied, massive particles can never reach spatial infinity while photons can do so only after experiencing infinite redshift.Comment: 18 page

Hydrodynamic mean field solutions of 1D exclusion processes with spatially varying hopping rates

We analyze the open boundary partially asymmetric exclusion process with smoothly varying internal hopping rates in the infinite-size, mean field limit. The mean field equations for particle densities are written in terms of Ricatti equations with the steady-state current $J$ as a parameter. These equations are solved both analytically and numerically. Upon imposing the boundary conditions set by the injection and extraction rates, the currents $J$ are found self-consistently. We find a number of cases where analytic solutions can be found exactly or approximated. Results for $J$ from asymptotic analyses for slowly varying hopping rates agree extremely well with those from extensive Monte Carlo simulations, suggesting that mean field currents asymptotically approach the exact currents in the hydrodynamic limit, as the hopping rates vary slowly over the lattice. If the forward hopping rate is greater than or less than the backward hopping rate throughout the entire chain, the three standard steady-state phases are preserved. Our analysis reveals the sensitivity of the current to the relative phase between the forward and backward hopping rate functions.Comment: 12 pages, 4 figure

Silicon Waveguides and Ring Resonators at 5.5 {\mu}m

We demonstrate low loss ridge waveguides and the first ring resonators for the mid-infrared, for wavelengths ranging from 5.4 to 5.6 {\mu}m. Structures were fabricated using electron-beam lithography on the silicon-on-sapphire material system. Waveguide losses of 4.0 +/- 0.7 dB/cm are achieved, as well as Q-values of 3.0 k.Comment: 4 pages, 4 figures, includes supplemental material

The pitfalls of ecological forecasting

Ecological forecasting is difficult but essential, because reactive management results in corrective actions that are often too late to avert significant environmental damage. Here, we appraise different forecasting methods with a particular focus on the modelling of species populations. We show how simple extrapolation of current trends in state is often inadequate because environmental drivers change in intensity over time and new drivers emerge. However, statistical models, incorporating relationships with drivers, simply offset the prediction problem, requiring us to forecast how the drivers will themselves change over time. Some authors approach this problem by focusing in detail on a single driver, whilst others use ‘storyline’ scenarios, which consider projected changes in a wide range of different drivers. We explain why both approaches are problematic and identify a compromise to model key drivers and interactions along with possible response options to help inform environmental management. We also highlight the crucial role of validation of forecasts using independent data. Although these issues are relevant for all types of ecological forecasting, we provide examples based on forecasts for populations of UK butterflies. We show how a high goodness-of-fit for models used to calibrate data is not sufficient for good forecasting. Long-term biological recording schemes rather than experiments will often provide data for ecological forecasting and validation because these schemes allow capture of landscape-scale land-use effects and their interactions with other drivers

Predicting resilience of ecosystem functioning from co‐varying species' responses to environmental change

Understanding how environmental change affects ecosystem function delivery is of primary importance for fundamental and applied ecology. Current approaches focus on single environmental driver effects on communities, mediated by individual response traits. Data limitations present constraints in scaling up this approach to predict the impacts of multivariate environmental change on ecosystem functioning. We present a more holistic approach to determine ecosystem function resilience, using long‐term monitoring data to analyze the aggregate impact of multiple historic environmental drivers on species' population dynamics. By assessing covariation in population dynamics between pairs of species, we identify which species respond most synchronously to environmental change and allocate species into “response guilds.” We then use “production functions” combining trait data to estimate the relative roles of species to ecosystem functions. We quantify the correlation between response guilds and production functions, assessing the resilience of ecosystem functioning to environmental change, with asynchronous dynamics of species in the same functional guild expected to lead to more stable ecosystem functioning. Testing this method using data for butterflies collected over four decades in the United Kingdom, we find three ecosystem functions (resource provisioning, wildflower pollination, and aesthetic cultural value) appear relatively robust, with functionally important species dispersed across response guilds, suggesting more stable ecosystem functioning. Additionally, by relating genetic distances to response guilds we assess the heritability of responses to environmental change. Our results suggest it may be feasible to infer population responses of butterflies to environmental change based on phylogeny—a useful insight for conservation management of rare species with limited population monitoring data. Our approach holds promise for overcoming the impasse in predicting the responses of ecosystem functions to environmental change. Quantifying co‐varying species' responses to multivariate environmental change should enable us to significantly advance our predictions of ecosystem function resilience and enable proactive ecosystem management

Strength is negatively associated with depression and accounts for some of the sex difference A replication and extension

Background Depression occurs about twice as often in women as in men, a disparity that remains poorly understood. In a previous publication, Hagen and Rosenstrom predicted and found that grip strength, a highly sexually dimorphic index of physical formidability, mediated much of the effect of sex on depression. Striking results like this are more likely to be published than null results, potentially biasing the scientific record. It is therefore critical to replicate and extend them. Methodology Using new data from the 2013-14 cycle of the National Health and Nutrition Examination Survey, a nationally representative sample of US households (n = 3650), we replicated models of the effect of sex and grip strength on depression reported in Hagen and Rosenstrom, along with additional potential confounds and a new detailed symptom-level exploration. Results Overall, the effects from the original paper were reproduced although with smaller effect sizes. Grip strength mediated 38% of the effect of sex on depression, compared to 63% in Hagen and Rosenstrom. These results were extended with findings that grip strength had a stronger association with some depression symptoms, like suicidality, low interest and low mood than with other symptoms, like appetite changes. Conclusions Grip strength is negatively associated with depression, especially its cognitive-affective symptoms, controlling for numerous possible confounds. Although many factors influence depression, few of these reliably occur cross-culturally in a sex-stratified manner and so are unlikely to explain the well-established, cross-cultural sex difference in depression. The sex difference in upper body strength occurs in all populations and is therefore a candidate evolutionary explanation for some of the sex difference in depression. Lay summary: Why are women at twice the risk of developing depression as men? Depression typically occurs during social conflicts, such as physical or sexual abuse. Physically strong individuals can often single-handedly resolve conflicts in their favor, whereas physically weaker individuals often need help from others. We argue that depression is a credible cry for help. Because men generally have greater strength than women, we argue that men may be more likely to resolve conflicts using physical formidability and women to signal others for help. We find that higher grip strength is associated with lower depression, particularly symptoms like feeling down or thoughts of suicide and that strength accounts for part of the sex difference in rates of depression.Peer reviewe