An Evaluation of Nutrient Trading Options in Virginia: A Role for Agriculture?

Water Quality Trading, offsets, nutrients, agriculture, BMPs, Environmental Economics and Policy,

Agreement Between the Stages Cycling and SRM Powermeter Systems during Field-Based Off-Road Climbing.

The aim of this study was to determine the agreement between two portable cycling powermeters for use doing field based mountain biking. A single participant performed 15 timed ascents of an off-road climbs. The participants bicycle was instrumented with Stages Cycling and SRM powermeters. Mean and peak power output and cadence were recorded at 1 s intervals by both systems. Significant differences were determined using paired t-tests, whilst agreement was determined using 95% ratio limits of agreement (LoA). Significant differences were found between the two systems for mean power output (p<.001), with the Stages powermeter under reporting power by 8 % compared to the SRM. LoA for mean power output were 0.92 ×÷ 1.02 (95% LoA = 0.90 – 0.93). Peak power output was also significantly lower with the Stages powermeter (p=.02) by 5 % when compared to the SRM powermeter. LoA for peak power output were 0.94 ×÷ 1.09 (95% limits of agreement = 0.87 – 1.03). Significant differences were found for mean cadence between the two powermeters (p=.009), with LoA being 0.99 ×÷ 1.01 (95% limits of agreement = 0.99 – 1.00). This study found that though the Stages Cycling powermeter provided a reliable means of recording power output and cadence, the system significantly underestimated mean and peak power output when compared with the SRM system. This may in part be due to differences in strain gauge configuration and the subsequent algorithms used in the calculation of power output and the potential influence of bilateral imbalances within the muscles may have on these calculations

A novel, structure-preserving, second-order-in-time relaxation scheme for Schrödinger-Poisson systems

The authors acknowledge the support from The Carnegie Trust Research Incentive Grant RIG008215 . I.K. would also like to acknowledge the support from London Mathematical Society through an Emmy Noether Fellowship . In addition, Th. K. and I.K. thank the Edinburgh Mathematical Society for the Covid Recovery Fund that allowed for the completion and the submission of this paper.We introduce a new structure preserving, second order in time relaxation-type scheme for approximating solutions of the Schrödinger-Poisson system. More specifically, we use the Crank-Nicolson scheme as a time stepping mechanism, whilst the nonlinearity is handled by means of a relaxation approach in the spirit of [10,11,34] for the nonlinear Schrödinger equation. For the spatial discretisation we use the standard conforming finite element scheme. The resulting scheme is explicit with respect to the nonlinearity, i.e. it requires the solution of a linear system for each time-step, and satisfies discrete versions of the system's mass conservation and energy balance laws for constant meshes. The scheme is seen to be second order in time. We conclude by presenting some numerical experiments, including an example from cosmology and an example with variable time-steps which demonstrate the effectiveness and robustness of the new scheme.Peer reviewe

A novel, structure-preserving, second-order-in-time relaxation scheme for Schrödinger-Poisson systems

We introduce a new second order in time relaxation-type scheme for approximating solutions of the Schr\"odinger-Poisson system. More specifically, we use the Crank-Nicolson scheme as a time stepping mechanism, whilst the nonlinearity is handled by means of a relaxation approach in the spirit of \cite{Besse, KK} for the nonlinear Schr\"odinger equation. For the spatial discretisation we use the standard conforming finite element scheme. The resulting scheme is explicit with respect to the nonlinearity, satisfies discrete versions of the system's conservation laws, and is seen to be second order in time. We conclude by presenting some numerical experiments, including an example from cosmology, that demonstrate the effectiveness and robustness of the new scheme.Comment: 17pages, 10 figure

An empirical investigation of sector correlation forecasting techniques and the potential benefits to investors

Financial modelling is of considerable value to portfolio management. The effectiveness of different methods of forecasting correlation between sub-sectors, as part of the sector-allocation stage of the portfolio-construction process, has not yet been investigated. This focus is useful since it is relatively practical to collect data pertaining to sector and sub-sector indices, and hence the calculation of figures necessary to determine their investment performance is simpler. The aim of this research paper was to examine the performance of various correlation estimation techniques under two assessment criteria and to identify, if possible, the most suitable methods to employ in the sub-sector allocation stage of the ‘top-down’ approach to portfolio construction. Monthly total returns were calculated for each of the market indices, the sectors and their sub-sectors from the relevant total return indices as part of the analysis. The first assessment criterion was the statistical performance of the methods, which measured their ability to estimate future correlation coefficients between different sub-sectors by analysing the distributions of their absolute forecast errors. The second assessment criterion was the economic performance of the forecast methods. MPT was used to select the optimal portfolios for certain levels of expected return and the economic performance of the efficient sub-sector allocations, selected using the different correlation estimation techniques, was then evaluated. The two models used to estimate correlation that stood out from the rest in terms of their overall performance were the full HCM model and the industry mean model. From the perspective of the statistical performance criterion, the industry mean model consistently performed the best and the full HCM model also performed well. The economic performance of all the models tested, with the exception of the overall mean model, outperformed the passive investment strategy of holding the market portfolio. The economic performance of the full HCM model was best overall and that of the industry mean model was also strong. Prior research has found that the industry mean model is useful in forecasting future correlation between individual shares. This research found that the industry mean model also has value in forecasting future correlation between sub-sectors. Furthermore, despite demonstration in prior research of the full HCM model’s poor ability to estimate future correlation between individual shares, it was one of the most effective models at forecasting correlation between sub-sectors. Both of these models therefore hold value to investors for the purposes of sub-sector allocation as part of a top-down approach to financial portfolio construction