History Matching with Subset Simulation

Computational cost often hinders the calibration of complex computer models. In this context, history matching (HM) is becoming a widespread calibration strategy, with applications in many disciplines. HM uses a statistical approximation, also known as an emulator, to the model output, in order to mitigate computational cost. The process starts with an observation of a physical system. It then produces progressively more accurate emulators to determine a non-implausible domain: a subset of the input space that provides a good agreement between the model output and the data, conditional on the model structure, the sources of uncertainty, and an implausibility measure. In HM, it is essential to generate samples from the nonimplausible domain, in order to run the model and train the emulator until a stopping condition is met. However, this sampling can be very challenging, since the nonimplausible domain can become orders of magnitude smaller than the original input space very quickly. This paper proposes a solution to this problem using subset simulation, a rare event sampling technique that works efficiently in high dimensions. The proposed approach is demonstrated via calibration and robust design examples from the field of aerospace engineering

3D Modelling of Twist Wall at the Electrode Edge of Liquid Crystal Cells

Q-tensor simulation of the liquid crystal structure at the edge of electrodes has been carried out. The modeling shows a twist wall, which reverses direction to form a zig-zag structure. The results are compared with experiment. Also a defect loop is found in micro-lenses formed using a hole electrode structure

Improving Detection of Events at Water Treatment Works: A UK Case Study

This is the author accepted manuscriptThis study presents improvements to the event detection capabilities of the existing, thresholdbased detection system used by United Utilities in one of their Water Treatment Works. These improvements were achieved by using new threshold and persistence values identified by performing a sensitivity type analysis. The findings from this study show that, although an overall increase in the true detection rate and decrease in the number of false alarms were achieved, the high number of false alarms remains an issue

Emerging pollutants in developing countries: Optimising sustainable treatment solutions

This is the author accepted manuscriptOver the past decade the research surrounding the occurrence, source, fate and removal of emerging pollutants has been increasing. The aim of this study was to create an add-on program which analyses the removal of emerging pollutants, to an existing decision support tool (WiSDOM). The tool was also used to evaluate the performance of each optimal solution in terms of removal of conventional pollutants using Multi Objective Genetic Algorithms and Multi Criteria Decision Analysis. Information was collated regarding minimum and maximum concentrations of emerging pollutants for surface water, groundwater, untreated wastewater, drinking water and treated wastewater. This information was used to populate an Excel Spreadsheet Program (ESP) which analysed the removal efficiencies of 13 different emerging pollutants for 42 wastewater treatment unit processes. The ESP is incorporated into the WiSDOM tool to allow the tool to calculate the removal of emerging pollutants. Three main scenarios were created to test the application of the tool and ESP. Scenario 1 focussed on the removal of emerging pollutants from from areas effected by tourism at different scales. Scenario 2 looked at the treatment suited for the removal of emerging pollutants from different socio-economic regions. Lastly, Scenario 3 looked at removing emerging pollutants from hospital and industrial wastewater. The scenarios were focused on wastewater treatment in India and investigated the removal of 13 emerging pollutants commonly found in India.Engineering and Physical Sciences Research Council (EPSRC)European CommissionNatural Environment Research Council (NERC

Effectiveness of an automatic tracking software in underwater motion analysis

Tracking of markers placed on anatomical landmarks is a common practice in sports science to perform the kinematic analysis that interests both athletes and coaches. Although different software programs have been developed to automatically track markers and/or features, none of them was specifically designed to analyze underwater motion. Hence, this study aimed to evaluate the effectiveness of a software developed for automatic tracking of underwater movements (DVP), based on the Kanade-Lucas-Tomasi feature tracker. Twenty-one video recordings of different aquatic exercises (n = 2940 markers' positions) were manually tracked to determine the markers' center coordinates. Then, the videos were automatically tracked using DVP and a commercially available software (COM). Since tracking techniques may produce false targets, an operator was instructed to stop the automatic procedure and to correct the position of the cursor when the distance between the calculated marker's coordinate and the reference one was higher than 4 pixels. The proportion of manual interventions required by the software was used as a measure of the degree of automation. Overall, manual interventions were 10.4% lower for DVP (7.4%) than for COM (17.8%). Moreover, when examining the different exercise modes separately, the percentage of manual interventions was 5.6% to 29.3% lower for DVP than for COM. Similar results were observed when analyzing the type of marker rather than the type of exercise, with 9.9% less manual interventions for DVP than for COM. In conclusion, based on these results, the developed automatic tracking software presented can be used as a valid and useful tool for underwater motion analysis. Key PointsThe availability of effective software for automatic tracking would represent a significant advance for the practical use of kinematic analysis in swimming and other aquatic sports.An important feature of automatic tracking software is to require limited human interventions and supervision, thus allowing short processing time.When tracking underwater movements, the degree of automation of the tracking procedure is influenced by the capability of the algorithm to overcome difficulties linked to the small target size, the low image quality and the presence of background clutters.The newly developed feature-tracking algorithm has shown a good automatic tracking effectiveness in underwater motion analysis with significantly smaller percentage of required manual interventions when compared to a commercial software

One-point functions in massive integrable QFT with boundaries

We consider the expectation value of a local operator on a strip with non-trivial boundaries in 1+1 dimensional massive integrable QFT. Using finite volume regularisation in the crossed channel and extending the boundary state formalism to the finite volume case we give a series expansion for the one-point function in terms of the exact form factors of the theory. The truncated series is compared with the numerical results of the truncated conformal space approach in the scaling Lee-Yang model. We discuss the relevance of our results to quantum quench problems.Comment: 43 pages, 20 figures, v2: typos correcte

Distributed Testing of Excluded Subgraphs

We study property testing in the context of distributed computing, under the classical CONGEST model. It is known that testing whether a graph is triangle-free can be done in a constant number of rounds, where the constant depends on how far the input graph is from being triangle-free. We show that, for every connected 4-node graph H, testing whether a graph is H-free can be done in a constant number of rounds too. The constant also depends on how far the input graph is from being H-free, and the dependence is identical to the one in the case of testing triangles. Hence, in particular, testing whether a graph is K_4-free, and testing whether a graph is C_4-free can be done in a constant number of rounds (where K_k denotes the k-node clique, and C_k denotes the k-node cycle). On the other hand, we show that testing K_k-freeness and C_k-freeness for k>4 appear to be much harder. Specifically, we investigate two natural types of generic algorithms for testing H-freeness, called DFS tester and BFS tester. The latter captures the previously known algorithm to test the presence of triangles, while the former captures our generic algorithm to test the presence of a 4-node graph pattern H. We prove that both DFS and BFS testers fail to test K_k-freeness and C_k-freeness in a constant number of rounds for k>4

Note on Bonus Relations for N=8 Supergravity Tree Amplitudes

We study the application of non-trivial relations between gravity tree amplitudes, the bonus relations, to all tree-level amplitudes in N=8 supergravity. We show that the relations can be used to simplify explicit formulae of supergravity tree amplitudes, by reducing the known form as a sum of (n-2)! permutations obtained by solving on-shell recursion relations, to a new form as a (n-3)!-permutation sum. We demonstrate the simplification by explicit calculations of the next-to-maximally helicity violating (NMHV) and next-to-next-to-maximally helicity violating (N^2MHV) amplitudes, and provide a general pattern of bonus coefficients for all tree-level amplitudes.Comment: 21 pages, 9 figures; v2, minor changes, references adde

Lessons from crossing symmetry at large N

20 pages, v2: Assumptions stated more clearly, version published in JHEPWe consider the four-point correlator of the stress tensor multiplet in N=4 SYM. We construct all solutions consistent with crossing symmetry in the limit of large central charge c ~ N^2 and large g^2 N. While we find an infinite tower of solutions, we argue most of them are suppressed by an extra scale \Delta_{gap} and are consistent with the upper bounds for the scaling dimension of unprotected operators observed in the numerical superconformal bootstrap at large central charge. These solutions organize as a double expansion in 1/c and 1/\Delta_{gap}. Our solutions are valid to leading order in 1/c and to all orders in 1/\Delta_{gap} and reproduce, in particular, instanton corrections previously found. Furthermore, we find a connection between such upper bounds and positivity constraints arising from causality in flat space. Finally, we show that certain relations derived from causality constraints for scattering in AdS follow from crossing symmetry.Peer reviewe