Introducing Quantified Cuts in Logic with Equality

Cut-introduction is a technique for structuring and compressing formal proofs. In this paper we generalize our cut-introduction method for the introduction of quantified lemmas of the form $\forall x.A$ (for quantifier-free $A$) to a method generating lemmas of the form $\forall x_1\ldots\forall x_n.A$. Moreover, we extend the original method to predicate logic with equality. The new method was implemented and applied to the TSTP proof database. It is shown that the extension of the method to handle equality and quantifier-blocks leads to a substantial improvement of the old algorithm

Influence of anthropogenic and meteorological drivers on temporal patterns of ammonia emissions from agriculture in the UK

Emissions of trace gases originating from anthropogenic activities are vital input data for chemical transport models (CTMs). Other key input datasets such as meteorological drivers, and biogeochemical and physical processes have been subject to detailed investigation and research in the recent past, while the representation of spatio-temporal aspects of emission data in CTMs has been somewhat neglected. Arguably, this has less impact on the regional to hemispheric or global scale, where the grid sizes of currently applied CTMs represent well mixed average concentrations or deposition values. Evaluating model output against ground-based observations or remote sensing results on these spatial levels may not to be overly sensitive to the temporal (and spatial) profiles of emission input data. With increasing level of detail and spatio-temporal resolution, CTMs applied to determine national or local scale air quality are likely prone to be more sensitive to the spatial and temporal patterns of anthropogenic emissions. The location and timing of emission events - for instance peaks of ammonia emissions following the spring and autumn application of manure and mineral fertilisers - may well determine local concentration or deposition episodes, while not necessarily affecting seasonal or even annual mean values. In the case of agriculture, both anthropogenic activities (e.g. manure spreading and fertilizer application) and meteorological factors (e.g. temperature and seasonality) have been investigated regarding their influence on the spatiotemporal distribution of NH3 emissions (see for instance [1], [2], [4], [5] and [6]). The discussion of results in this case will focus on the impact on the deposition of acidifying and eutrophying substances, as well as the contribution to the formation of ammonium nitrates and sulphates and hence ambient concentrations of secondary particulate matter. This paper discusses results of the application of the EMEP4UK CTM on a 5 km x 5 km resolution for the whole of the United Kingdom. To evaluate the effect of changing the temporal profiles, three different model setups, e.g. using rather coarse and potentially outdated temporal profiles of the EMEP unified model, with varying degrees of detail (in this case, a monthly profile (cf. [3]) vs. 3 hourly emission values[6]) are evaluated against the AGANET measurement network stations across the UK. The discussion of results will focus on (a) the effect of temporal emission profiles on modelled vs. measured concentration/deposition values, (b) the influence on deposition of reactive nitrogen on ecosystems near ammonia sources and (c) the magnitude of influence of anthropogenic activity vs. meteorology for the dispersion of ammonia from agriculture. The results presented in this paper will help to determine the appropriate degree of detail with regard to the temporal profiles of anthropogenic emission data, as collecting detailed statistical data on anthropogenic activities for high spatially resolved model applications can be very time consuming and expensive. In addition, the effect on improving the temporal representation of emissions influenced by both anthropogenic activities and meteorological parameters can contribute to reducing uncertainties in model results that are highly relevant for policy development, e.g. covering aspects of critical load exceedance in vulnerable ecosystems or the exceedance of concentrations of PM

The Skorokhod embedding problem for inhomogeneous diffusions

We solve the Skorokhod embedding problem for a class of stochastic processes satisfying an inhomogeneous stochastic differential equation (SDE) of the form $d A_t =\mu (t, A_t) d t + \sigma(t, A_t) d W_t$. We provide sufficient conditions guaranteeing that for a given probability measure $\nu$ on $\mathbb{R}$ there exists a bounded stopping time $\tau$ and a real $a$ such that the solution $(A_t)$ of the SDE with initial value $a$ satisfies $A_\tau \sim \nu$. We hereby distinguish the cases where $(A_t)$ is a solution of the SDE in a weak or strong sense. Our construction of embedding stopping times is based on a solution of a fully coupled forward-backward SDE. We use the so-called method of decoupling fields for verifying that the FBSDE has a unique solution. Finally, we sketch an algorithm for putting our theoretical construction into practice and illustrate it with a numerical experiment.Comment: 39 pages, 2 pictures, To appear in Annales de l'Institut Henri Poincare (B) Probability and Statistic

Noise reduction for DIC measurements

Digital image correlation (DIC) is well known as a contact‐less, full‐field strain and displacement measuring method. The use of the method is widely spread in experimental mechanics. Nevertheless, there are error sources such as light settings, speckle pattern and noisy images, which strongly affect measurement quality, but often stays uninvestigated. Therefore, this work outlines a simple routine to identify errors and enhance the accuracy of DIC measurements. A calibration sample adapted to the specifications of the setup using the beam theory to link machine displacement, DIC measurements and forces. All evaluations are done in the commercial software ISTRA4D. The noise in the measurements is reduced to an error of under two per cent. The routine allows estimating the quality of the images before performing the experiments. Furthermore, the routine is transferable to all experimental setups. The calibration of the setup allows getting reliable experimental results with a known error. With this estimated stochastic error, the advantages of DIC can be used to evaluate mechanical experiments such as three‐point bending tests on single struts of an open cell metal foam

Land-Use Regression Modelling of Intra-Urban Air Pollution Variation in China: Current Status and Future Needs

Rapid urbanization in China is leading to substantial adverse air quality issues, particularly for NO2 and particulate matter (PM). Land-use regression (LUR) models are now being applied to simulate pollutant concentrations with high spatial resolution in Chinese urban areas. However, Chinese urban areas differ from those in Europe and North America, for example in respect of population density, urban morphology and pollutant emissions densities, so it is timely to assess current LUR studies in China to highlight current challenges and identify future needs. Details of twenty-four recent LUR models for NO2 and PM2.5/PM10 (particles with aerodynamic diameters <2.5 µm and <10 µm) are tabulated and reviewed as the basis for discussion in this paper. We highlight that LUR modelling in China is currently constrained by a scarcity of input data, especially air pollution monitoring data. There is an urgent need for accessible archives of quality-assured measurement data and for higher spatial resolution proxy data for urban emissions, particularly in respect of traffic-related variables. The rapidly evolving nature of the Chinese urban landscape makes maintaining up-to-date land-use and urban morphology datasets a challenge. We also highlight the importance for Chinese LUR models to be subject to appropriate validation statistics. Integration of LUR with portable monitor data, remote sensing, and dispersion modelling has the potential to enhance derivation of urban pollution maps

Urban air quality citizen science. Phase 2: suggested programme of research projects

This report contains a short description of the elements of a suggested programme of projects for citizen science in the area of urban air quality. The programme has been put together by the authors of the report based on a review of current work in this area and discussions with the study Advisory Group in August 2013 (for membership see Appendix 1). An overview of the programme is given below, followed by short 2-page summaries of each project. These projects are proposed for a future programme of citizen science urban air quality. We also present in this report a brief description of two small methodological pilot studies. These pilot studies are not intended to cover the full range of the proposed projects, but to test some aspects of the proposed methodology. The findings of the pilot studies will be reported separately

Urban air quality citizen science. Phase 3: findings of the pilot studies

This report provides a summary of the pilot studies conducted in Glasgow, Edinburgh and Prestonpans to test the viability of citizen science air quality monitoring studies within the constraints of existing and available technologies. The pilot studies draw on the experiences with the testing and evaluation of low-cost air quality monitoring devices described in the Scoping report reviewing and evaluating methods for undertaking an air quality Citizen Science programme and by Semple et al. (2012), while the overall study design is based on the framework discussed in Steinle et al. (2013). Furthermore, the pilot studies are based on the detailed elaboration of pilot studies summarised in the report Urban air quality citizen science - suggested programme of research projects. Two different pilot study approaches have been selected to test both a stationary air quality monitoring setup in the context of a secondary school, including the viability of using devices and monitoring methods in regular teaching activities, and using a mobile setup (with small backpacks including the air quality monitor as well as a GPS for geo-referencing). For the latter, the focus was on cyclists and volunteers were approached through existing contacts within the bike charity SPOKES (www.spokes.org.uk) and – through Transport Scotland – the Glasgow Bike Station. The main effort was not on providing air quality measurements, but on testing the approaches, methods, devices and engagement with citizen scientists. Thus, the focus of this deliverable is on the evaluation of these aspects

Urban air quality citizen science. Project overview report

In early 2013, SEPA issued a call for proposals with the overall aim of designing a local air quality programme which would engage the public through the use of Citizen Science. Citizen Science involves the participation of the wider community (particularly non- scientists) in scientific projects. The benefits of Citizen Science include the facility for extensive data collection and the interaction between scientists and the community. In addition citizen scientists get a chance to inform scientists, and in the process, learn more about their environment. Information gained through Citizen Science projects can change public perceptions of the natural world, promote interaction with nature, and engage the community in the management of natural resources. The overall aim of the work was to help build further capabilities in the area of Citizen Science, as a follow-on to existing work in this area, building on existing projects and networks including Scotland’s Environment Web, CAMERAS and Scotland Counts. To carry out the work, SEPA commissioned a consortium of scientific organisations led by the Institute of Occupational Medicine (IOM) in collaboration with the NERC Centre for Ecology & Hydrology (CEH), The Conservation Volunteers (TCV) and the Respiratory Group within the University of Aberdeen (RGA)