Stochastic transport in the presence of spatial disorder: fluctuation-induced corrections to homogenization

Motivated by uncertainty quantification in natural transport systems, we investigate an individual-based transport process involving particles undergoing a random walk along a line of point sinks whose strengths are themselves independent random variables. We assume particles are removed from the system via first-order kinetics. We analyse the system using a hierarchy of approaches when the sinks are sparsely distributed, including a stochastic homogenization approximation that yields explicit predictions for the extrinsic disorder in the stationary state due to sink strength fluctuations. The extrinsic noise induces long-range spatial correlations in the particle concentration, unlike fluctuations due to the intrinsic noise alone. Additionally, the mean concentration profile, averaged over both intrinsic and extrinsic noise, is elevated compared with the corresponding profile from a uniform sink distribution, showing that the classical homogenization approximation can be a biased estimator of the true mean.Comment: 16 pages, 8 figure

The Existence and Asymptotic Properties of a Backfitting Projection Algorithm Under Weak Conditions

We derive the asymptotic distribution of a new backfitting procedure for estimating the closest additive approximation to a nonparametric regression function. The procedure employs a recent projection interpretation of popular kernel estimators provided by Mammen et al. (1997), and the asymptotic theory of our estimators is derived using the theory of additive projections reviewed in Bickel et al. (1995). Our procedure achieves the same bias and variance as the oracle estimator based on knowing the other components, and in this sense improves on the method analyzed in Opsomer and Ruppert (1997). We provide 'high level' conditions independent of the sampling scheme. We then verify that these conditions are satisfied in a time series autoregression under weak conditions.Additive models, alternating projections, backfitting, kernel smoothing, local polynomials, nonparametric regression

The existence and asymptotic properties of a backfitting projection algorithm under weak conditions.

We derive the asymptotic distribution of a new backfitting procedure for estimating the closest additive approximation to a nonparametric regression function. The procedure employs a recent projection interpretation of popular kernel estimators provided by Mammen, Marron, Turlach and Wand and the asymptotic theory of our estimators is derived using the theory of additive projections reviewed in Bickel, Klaassen, Ritov and Wellner. Our procedure achieves the same bias and variance as the oracle estimator based on knowing the other components, and in this sense improves on the method analyzed in Opsomer and Ruppert. We provide ‘‘high level’’ conditions independent of the sampling scheme. We then verify that these conditions are satisfied in a regression and a time series autoregression under weak conditions.

Estimating Yield Curves by Kernel Smoothing Methods

We introduce a new method for the estimation of discount functions, yield curves and forward curves for coupon bonds. Our approach is nonparametric and does not assume a particular functional form for the discount function although we do show how to impose various important restrictions in the estimation. Our method is based on kernel smoothing and is defined as the minimum of some localized population moment condition. The solution to the sample problem is not explicit and our estimation procedure is iterative, rather like the backfitting method of estimating additive nonparametric models. We establish the asymptotic normality of our methods using the asymptotic representation of our estimator as an infinite series with declining coefficients. The rate of convergence is standard for one dimensional nonparametric regression.Coupon bonds; forward curve; Hilbert space; local linear; nonparametric regression; yield curve

RascalC: A Jackknife Approach to Estimating Single and Multi-Tracer Galaxy Covariance Matrices

To make use of clustering statistics from large cosmological surveys, accurate and precise covariance matrices are needed. We present a new code to estimate large scale galaxy two-point correlation function (2PCF) covariances in arbitrary survey geometries that, due to new sampling techniques, runs $\sim 10^4$ times faster than previous codes, computing finely-binned covariance matrices with negligible noise in less than 100 CPU-hours. As in previous works, non-Gaussianity is approximated via a small rescaling of shot-noise in the theoretical model, calibrated by comparing jackknife survey covariances to an associated jackknife model. The flexible code, RascalC, has been publicly released, and automatically takes care of all necessary pre- and post-processing, requiring only a single input dataset (without a prior 2PCF model). Deviations between large scale model covariances from a mock survey and those from a large suite of mocks are found to be be indistinguishable from noise. In addition, the choice of input mock are shown to be irrelevant for desired noise levels below $\sim 10^5$ mocks. Coupled with its generalization to multi-tracer data-sets, this shows the algorithm to be an excellent tool for analysis, reducing the need for large numbers of mock simulations to be computed.Comment: 29 pages, 8 figures. Accepted by MNRAS. Code is available at http://github.com/oliverphilcox/RascalC with documentation at http://rascalc.readthedocs.io

Links between soil microbial communities and plant traits in a species-rich grassland under long-term climate change

Climate change can influence soil microorganisms directly by altering their growth and activity but also indirectly via effects on the vegetation, which modifies the availability of resources. Direct impacts of climate change on soil microorganisms can occur rapidly, whereas indirect effects mediated by shifts in plant community composition are not immediately apparent and likely to increase over time. We used molecular fingerprinting of bacterial and fungal communities in the soil to investigate the effects of 17 years of temperature and rainfall manipulations in a species‐rich grassland near Buxton, UK. We compared shifts in microbial community structure to changes in plant species composition and key plant traits across 78 microsites within plots subjected to winter heating, rainfall supplementation, or summer drought. We observed marked shifts in soil fungal and bacterial community structure in response to chronic summer drought. Importantly, although dominant microbial taxa were largely unaffected by drought, there were substantial changes in the abundances of subordinate fungal and bacterial taxa. In contrast to short‐term studies that report high resistance of soil fungi to drought, we observed substantial losses of fungal taxa in the summer drought treatments. There was moderate concordance between soil microbial communities and plant species composition within microsites. Vector fitting of community‐weighted mean plant traits to ordinations of soil bacterial and fungal communities showed that shifts in soil microbial community structure were related to plant traits representing the quality of resources available to soil microorganisms: the construction cost of leaf material, foliar carbon‐to‐nitrogen ratios, and leaf dry matter content. Thus, our study provides evidence that climate change could affect soil microbial communities indirectly via changes in plant inputs and highlights the importance of considering long‐term climate change effects, especially in nutrient‐poor systems with slow‐growing vegetation

'It's a Form of Freedom': The experiences of people with disabilities within equestrian sport

This paper explores the embodied, gendered experiences of disabled horse‐riders. Drawing on data from five in‐depth interviews with paradressage riders, the ways in which their involvement in elite disability sport impacts upon their sense of identity and confidence are explored, as well as the considerable health and social benefits that this involvement brings. Social models of disability are employed and the shortcomings of such models, when applied to disability sport, are highlighted. The data presented here demonstrates the necessity of seeing disability sport as an embodied experience and acknowledging the importance of impairment to the experiences of disabled athletes. Living within an impaired body is also a gendered experience and the implications of this when applied to elite disability sport are considered