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Electron Ion Collider (EIC) is a particle accelerator facility planned for construction at Brookhaven National Laboratory on Long Island, New York by the United States Department of Energy. EIC will provide capabilities of colliding beams of polarized electrons with polarized beams of proton and light ions. EIC will be one of the largest and most sophisticated new accelerator facilities worldwide, and the only new large-scale accelerator facility planned for construction in the United States in the next few decades. The versatility, resolving power and intensity of EIC will present many new opportunities to address some of the crucial and fundamental open scientific questions in particle physics. This document provides an overview of the science case of EIC from the perspective of the high energy physics community., Submitted to the Proceedings of the US Community Study on the Future of Particle Physics (Snowmass 2021)

The use of Global Navigation Satellite System Radio Occultations (GNSS-RO) for vertical sounding of temperature and moisture in the atmospheric column has become a standard practice of many numerical weather prediction (NWP) centers. The introduction of this observation has seen broad positive impact on analyses and forecasts. On longer timescales the impact of the introduction of this data type in re-analyses can be clearly seen. Further, the observations can be used without bias correction and the consistency between sensors is very good allowing these observation to serve as anchoring observations. This is particularly helpful to constrain the bias-correction applied to satellite radiances. In the following chapter we explore the fundamentals of the measurement, the derivation of the typical observation which is used in NWP, the assimilation methods and error assumptions which are used, and finally some conjecture on the direction to improve the use of the observations and what future measurement systems may look like.

Background Pancreatic cancer has a very poor prognosis. Biomarkers that may help predict or diagnose pancreatic cancer may lead to earlier diagnosis and improved survival. Methods The prospective China Kadoorie Biobank (CKB) recruited 512 891 adults aged 30–79 years during 2004–08, recording 702 incident cases of pancreatic cancer during 9 years of follow-up. We conducted a case-subcohort study measuring 92 proteins in 610 cases and a subcohort of 623 individuals, using the OLINK immuno-oncology panel in stored baseline plasma samples. Cox regression with the Prentice pseudo-partial likelihood was used to estimate adjusted hazard ratios (HRs) for risk of pancreatic cancer by protein levels. Results Among 1233 individuals (including 610 cases), several chemokines, interleukins, growth factors and membrane proteins were associated with risk of pancreatic cancer, with adjusted HRs per 1 standard deviation (SD) of 0.86 to 1.86, including monocyte chemotactic protein 3 (MCP3/CCL7) {1.29 [95% CI (confidence interval) (1.10, 1.51)]}, angiopoietin-2 (ANGPT2) [1.27 (1.10, 1.48)], interleukin-18 (IL18) [1.24 (1.07, 1.43)] and interleukin-6 (IL6) [1.21 (1.06, 1.38)]. Associations between some proteins [e.g. matrix metalloproteinase-7 (MMP7), hepatocyte growth factor (HGF) and tumour necrosis factor receptor superfamily member 9 [TNFRSF9)] and risk of pancreatic cancer were time-varying, with higher levels associated with higher short-term risk. Within the first year, the discriminatory ability of a model with known risk factors (age, age squared, sex, region, smoking, alcohol, education, diabetes and family history of cancer) was increased when several proteins were incorporated (weighted C-statistic changed from 0.85 to 0.99; P for difference = 4.5 × 10–5), although only a small increase in discrimination (0.77 to 0.79, P = 0.04) was achieved for long-term risk. Conclusions Several plasma proteins were associated with subsequent diagnosis of pancreatic cancer. The potential clinical utility of these biomarkers warrants further investigation.

A new method for generating ensemble predictions based on an ensemble of data assimilations has been developed. Using an ensemble of four-dimensional ensemble-variational minimizations provides an approach which is close to the Met Office's operational data assimilation system and less computationally expensive than other alternatives. In developing this system, several inflation schemes have been compared. One form of additive inflation, based on analysis increments, was developed and found to be very effective at increasing the overall ensemble spread and correcting systematic biases in the model. However, the analysis increments are not flow-dependent since they are randomly drawn from a long archive. It was decided to scale back their amplitude to avoid them dominating the overall performance. Of the other inflation schemes considered, it was found that relaxation-to-prior-perturbations was the most effective at maintaining the ensemble spread. However, this scheme also produced perturbations which are too large-scale and too balanced. The relaxation-to-prior-spread scheme performed well in many respects, but required a relaxation factor greater than one to produce an acceptable spread. Therefore these two schemes were combined in order to mitigate the drawbacks of each. This combination proved successful and was used in final testing of the ensemble against the currently operational ensemble transform Kalman filter (ETKF). The ETKF has its perturbations centred around a high-resolution ‘deterministic’ analysis. This was seen to be an important benefit, and the new ensemble system also benefited from being recentred around the high-resolution analysis. This recentred system has slightly lower forecast skill than the ETKF over a variety of variables, due to the fact that the spread of this ensemble is less than the spread of the ETKF ensemble. The deficiency of the spread of the new ensemble system will be addressed in ongoing work.

Outputs from a data assimilation system may be used to diagnose observation and background error statistics, as has been demonstrated by previous researchers. In this study, that technique is extended to diagnose model-error statistics using a weak-constraint data assimilation. It deals with a set of observations over a time window and uses the temporal distribution to separate model errors from errors in the background forecast. In a set of idealised tests this method is shown to be able to successfully distinguish between model and background errors. The success of this method depends on the prior assumptions included in the weak-constraint data assimilation and how well these describe the true nature of the system being modelled. Other authors have demonstrated that it can be challenging to separate observation and background errors in diagnosis schemes. Some separation of these errors is possible within the context of four-dimensional assimilation, provided that observation errors are known to be uncorrelated in time.

Hybrid four-dimensional ensemble-variational (4DEnVar) data assimilation is a method which avoids using a linear and adjoint model by relying on an input ensemble to propagate analysis increments in time. Previous studies have shown that hybrid 4DEnVar performs worse than hybrid four-dimensional variational (4D-Var) assimilation. Given hybrid 4DEnVar's heavy reliance on the ensemble, this comparison may be affected by the quality of the input ensemble. Here we investigate how improvements to the ensemble system affect hybrid 4D-Var and how they affect the comparison with hybrid 4DEnVar. Using the Met Office's operational ensemble generation scheme (the ensemble transform Kalman filter, ETKF) it is found that hybrid 4D-Var gains little benefit from using an enlarged ensemble as input (176 as opposed to 23 members). By contrast, hybrid 4DEnVar benefits more from the increased ensemble size, and it benefits further when the weighting given to the ensemble covariance is increased. Both data assimilation methods benefit when the input ensemble is changed from using the ETKF to using an ensemble of 4DEnVars. Both schemes also show further benefit when a large ensemble (200 members) of 4DEnVars is used, and when a large weight is given to the covariance information from this ensemble. Thus, improving the ensemble covariance used in assimilation (ensemble generation method and ensemble size) and increasing its weight can have substantial benefits. Given that both hybrid 4D-Var and hybrid 4DEnVar benefit from improvements to the input ensemble, the relative performance is largely unaffected by the ensemble changes and hybrid 4D-Var performs better than hybrid 4DEnVar for all input ensembles.

We show how to replace an ensemble of variational data assimilation minimizations by minimizations for the ensemble mean and the perturbations from it. Tests using the Met Office system show that this Mean–Pert method can give practically identical results at much reduced cost. This makes it a good candidate component when designing a cost-effective system for hybrid ensemble-variational data assimilation for numerical weather prediction.

It has long been known that verification of a forecast against the sequence of analyses used to produce those forecasts can under-estimate the magnitude of forecast errors. Here we show that under certain conditions the verification of a short-range forecast against a perturbed analysis coming from an ensemble data assimilation scheme can give the same root-mean-square error as verification against the truth. This means that a perturbed analysis can be used as a reliable proxy for the truth. However, the conditions required for this result to hold are rather restrictive: the analysis must be optimal, the ensemble spread must be equal to the error in the mean, the ensemble size must be large and the forecast being verified must be the background forecast used in the data assimilation. Although these criteria are unlikely to be met exactly it becomes clear that for most cases verification against a perturbed analysis gives better results than verification against an unperturbed analysis. We demonstrate the application of these results in a idealised model framework and a numerical weather prediction context. In deriving this result we recall that an optimal (Kalman) analysis is one for which the analysis increments are uncorrelated with the analysis errors.

The Met Office has developed an ensemble-variational data assimilation method (hybrid-4DEnVar) as a potential replacement for the hybrid four-dimensional variational data assimilation (hybrid-4DVar), which is the current operational method for global NWP. Both are four-dimensional variational methods, using a hybrid combination of a fixed climatological model of background error covariances with localized covariances from an ensemble of current forecasts designed to describe the structure of “errors of the day.” The fundamental difference between the methods is their modeling of the time evolution of errors within each data assimilation window: 4DVar uses a linear model and its adjoint and 4DEnVar uses a localized linear combination of nonlinear forecasts. Both hybrid-4DVar and hybrid-4DEnVar beat their three-dimensional versions, which are equivalent, in NWP trials. With settings based on the current operational system, hybrid-4DVar performs better than hybrid-4DEnVar. Idealized experiments designed to compare the time evolution of covariances in the methods are described: the basic 4DEnVar represents the evolution of ensemble errors as well as 4DVar. However, 4DVar also represents the evolution of errors from the climatological covariances, whereas 4DEnVar does not. This difference is the main cause of the superiority of hybrid-4DVar. Another difference is that the authors’ 4DVar explicitly penalizes rapid variations in the analysis increment trajectory, while the authors’ 4DEnVar contains no dynamical constaints on imbalance. The authors describe a four-dimensional incremental analysis update (4DIAU) method that filters out the high-frequency oscillations introduced by the poorly balanced 4DEnVar increments. Possible methods for improving hybrid-4DEnVar are discussed.

The Met Office Global and Regional Ensemble Prediction System (MOGREPS) uses an on-line inflation factor calculation to calibrate the spread of the ensemble in space and time and counteract the tendency of the Ensemble Transform Kalman Filter (ETKF) to underestimate analysis uncertainty. Sonde measurements are augmented with ATOVS brightness temperature observations to provide sufficient coverage across the globe. This paper describes how the scheme has been extended to improve the vertical distribution of spread. Separate inflation factors are derived for each of three ‘bands’ of model levels, loosely representing the boundary layer, troposphere and stratosphere. A continuous profile is ensured by linearly interpolating between the band centres. The error/spread relationship observed in each ATOVS channel is mapped onto the three bands using a set of weights obtained by integrating the appropriate Jacobians over the range of pressures covered by each band. These weights are found to be approximately constant, thanks to the small number of bands and the fact that near-surface channels are not used over land. The revised initial perturbations lead to increased near-surface spread which persists throughout the 72 h forecast and carries through to improved probabilistic scores. However, the near-surface spread remains too small due to insufficient growth of spread by the forecast model. This suggests perturbation of sea-surface temperatures, soil initial conditions, soil properties and boundary-layer physics as priorities for future work.

The Met Office is currently developing an ensemble-based data-assimilation system for use in numerical weather prediction (NWP). In an effort to inform those developments, a simple model has been used to compare a number of different flavours of ensemble Kalman filter (EnKF). As in many previous studies, deterministic (square-root) filters are seen to perform better than stochastic (perturbed-observations) filters. Two previously proposed methods for mitigating the effects of perturbing the observations were tested. These modified stochastic filters improved performance, but were still worse than the deterministic filters. Very little difference was seen between the performance of the various deterministic filters tested. The typical approach to localization in the Local Ensemble Transform Kalman Filter (LETKF) is based solely on the distance between each observation and the model point being updated. It takes no account of the inter-observation distance and we argue that this is incorrect. However, the difference between covariance localization and observation localization is only relevant when the assimilation is not weak and hence it did not affect performance in these tests. If a hybrid covariance matrix is used to update the ‘deterministic’ forecast around which the ensemble is centred, then using the same covariance matrix when updating the perturbations is seen to be beneficial in a stochastic filter. This is not the case in the square-root filter, due to restrictions imposed by its formulation. Tests with a nonlinear observation operator indicate better behaviour when observations are assimilated simultaneously rather than sequentially. An ensemble of variational minimizations has some advantages in this situation. These results, along with other considerations, have led the Met Office to develop a 4-dimensional ensemble-variational (4D-En-Var) system for data assimilation and ensemble generation.

The Met Office Global and Regional Ensemble Prediction System (MOGREPS) uses an online inflation factor calculation to calibrate the spread of the ensemble in space and time and counteract the tendency of the Ensemble Transform Kalman Filter (ETKF) to underestimate analysis uncertainty. Until 2008, this calibration mechanism relied entirely on sonde and wind profiler data, and was only applied locally in the Extratropics. By producing more appropriate estimates of the error variance of ATOVS brightness temperature observations, it has become possible to include these in the inflation factor calculation. This in turn provides sufficient data to apply localisation uniformly over the globe. The new scheme improves the latitudinal distribution of spread in comparison to forecast error, especially in the Tropics. Issues remain with the vertical distribution of spread, which are addressed by work to be reported in a future paper. © 2011 Crown Copyright, the Met Office. Published by John Wiley & Sons, Ltd.

An important aspect of ensemble forecasting is that the resulting probabilities are reliable (i.e., the forecast probabilities match the observed frequencies). In the medium-range forecasting context, the literature tends to focus on the requirement that, for a reliable ensemble, the ensemble spread should be representative of the uncertainty in the mean, whereas in the seasonal forecasting context, the literature tends to focus on the requirement that, for a reliable ensemble, the ensemble forecasts should have the same climatological variance as the truth. In this note, the authors emphasize that both of these requirements are necessary for reliability and they clarify that a popular calibration method actually achieves both of these requirements.

The Met Office has been routinely running a short-range global and regional ensemble prediction system (EPS) since the summer of 2005. This article describes a major upgrade to the global ensemble, which affected both the initial condition and model uncertainty perturbations applied in that ensemble. The change to the initial condition perturbations is to allow localization within the ensemble transform Kalman filter (ETKF). This enables better specification of the ensemble spread as a function of location around the globe. The change to the model uncertainty perturbations is the addition of a stochastic kinetic energy backscatter scheme (SKEB). This adds vorticity perturbations to the forecast in order to counteract the damping of small-scale features introduced by the semi-Lagrangian advection scheme. Verification of ensemble forecasts is presented for the global ensemble system. It is shown that the localization of the ETKF gives a distribution of the spread as a function of latitude that better matches the forecast error of the ensemble mean. The SKEB scheme has a substantial effect on the power spectrum of the kinetic energy, and with the scheme a shallowing of the spectral slope is seen in the tail. A k−5/3 slope is seen at wavelengths shorter than 1000 km and this better agrees with the observed spectrum. The local ETKF significantly improves forecasts at all lead times over a number of variables. The SKEB scheme increases the rate of growth of ensemble spread in some variables, and improves forecast skill at short lead times. ©Crown Copyright 2009. Reproduced with the permission of HMSO. Published by John Wiley & Sons Ltd.

The Met Office has been routinely running a short-range ensemble prediction system since the summer of 2005. This system consists of two component ensembles, a global ensemble that provides lateral boundary conditions to a regional ensemble. The global ensemble calculates the initial condition perturbations using a local version of the ensemble transform Kalman filter (ETKF). This article details tests of an ETKF run specifically for the regional ensemble. The perturbations using the ETKF for the regional ensemble contain more detail on small scales and less power on large scales. This extra small-scale detail persists for less than 18 h. These perturbations are overall smaller than the ones derived from the global ensemble, since they have been explicitly scaled to match the average error of the ensemble mean forecast at T + 6 h. Aside from the difference in the overall scaling of the perturbations, the skill of the two ensembles is very similar, with slightly higher skill being seen when the perturbations are derived from the global ensemble. The ETKF for the regional ensemble was implemented during May 2007. This change has recently been reversed, following these results. These comparisons may shed some light on whether the regional ensemble is providing a ‘dynamical downscaling’ of the global ensemble, or unique information of its own. In these tests the ensemble run with perturbations from the global ensemble was slightly more skilful than the regional perturbations ensemble, indicating that improving on dynamical downscaling is likely to be difficult. ©Crown Copyright 2009. Reproduced with the permission of HMSO. Published by John Wiley & Sons Ltd.

We have investigated a method to substantially reduce the analysis computations within the Local Ensemble Transform Kalman Filter (LETKF) framework. Instead of computing the LETKF analysis at every model grid point, we compute the analysis on a coarser grid and interpolate onto a high-resolution grid by interpolating the analysis weights of the ensemble forecast members derived from the LETKF. Because the weights vary on larger scales than the analysis increments, there is little degradation in the quality of the weight-interpolated analyses compared to the analyses derived with the high-resolution grid. The weight-interpolated analyses are more accurate than the ones derived by interpolating the analysis increments. Additional benefit from the weight-interpolation method includes improving the analysis accuracy in the data-void regions, where the standard LEKTF with the high-resolution grid gives no analysis corrections due to a lack of available observations. Copyright © Royal Meteorological Society and Crown Copyright, 2008

A new approach to probabilistic forecasting is proposed, based on the generation of an ensemble of equally likely analyses of the current state of the atmosphere. The rationale behind this approach is to mimic a poor man’s ensemble, which combines the deterministic forecasts from national meteorological services around the world. The multianalysis ensemble aims to generate a series of forecasts that are both as skillful as each other and the control forecast. This produces an ensemble mean forecast that is superior not only to the ensemble members, but to the control forecast in the short range even for slowly varying parameters, such as 500-hPa height. This is something that it is not possible with traditional ensemble methods, which perturb a central analysis. The results herein show that the multianalysis ensemble is more skillful than the Met Office’s high-resolution forecast by 4.5% over the first 3 days (on average as measured for RMSE). Similar results are found for different verification scores and various regions of the globe. In contrast, the ensemble mean for the ensemble currently run by the Met Office performs 1.5% worse than the high-resolution forecast (similar results are found for the ECMWF ensemble). It is argued that the multianalysis approach is therefore superior to current ensemble methods. The multianalysis results were achieved with a two-member ensemble: the forecast from a high-resolution model plus a low-resolution perturbed model. It may be possible to achieve greater improvements with a larger ensemble.

The Met Office has recently introduced a short-range ensemble prediction system known as MOGREPS. This system consists of global and regional ensembles, with the global ensemble providing the boundary conditions and initial-condition perturbations for the regional ensemble. Perturbations to the initial conditions are calculated using the ensemble transform Kalman filter, which is a computationally-efficient version of the ensemble Kalman filter. Model uncertainties are represented in the system through a series of schemes designed to tackle the structural and subgrid-scale sources of model error. This paper describes the set-up of the system, and provides justification for the initial-condition and model perturbation schemes chosen. An outline of the structure of the perturbations generated by the system is presented, along with performance results, including verification from case studies and routine running. MOGREPS has been on trial within the operational suite at the Met Office since August 2005. On 20 October 2006 it was decided that this system should be made fully operational, with implementation expected in summer 2008. Results show a good performance. The regional ensemble is more skilful than the global ensemble, and compares favourably to the ECMWF ensemble for the forecast variables examined in this study. © Crown Copyright 2008. Reproduced with the permission of the Controller of HMSO and the Queen's Printer for Scotland. Published by John Wiley & Sons,Ltd

A number of articles have looked at the effect of observation errors on verification statistics. In this article, those methods are brought together in order to assess the importance of observation errors on verification statistics for the Met Office short-range ensemble prediction system (MOGREPS). The results indicate that the effect of observation errors is substantial–reducing the apparent skill of the forecast system by around 1 day in forecast lead time. The effect of observation errors is typically largest at short lead times when forecast errors are smallest. © Crown Copyright 2008. Reproduced with the permission of the Controller of HMSO. Published by John Wiley & Sons, Ltd

An ensemble-based probabilistic precipitation forecasting scheme has been developed that blends an extrapolation nowcast with a downscaled NWP forecast, known as STEPS: Short-Term Ensemble Prediction System. The uncertainties in the motion and evolution of radar-inferred precipitation fields are quantified, and the uncertainty in the evolution of the precipitation pattern is shown to be the more important. The use of ensembles allows the scheme to be used for applications that require forecasts of the probability density function of areal and temporal averages of precipitation, such as fluvial flood forecasting—a capability that has not been provided by previous probabilistic precipitation nowcast schemes. The output from a NWP forecast model is downscaled so that the small scales not represented accurately by the model are injected into the forecast using stochastic noise. This allows the scheme to better represent the distribution of precipitation rate at spatial scales finer than those adequately resolved by operational NWP. The performance of the scheme has been assessed over the month of March 2003. Performance evaluation statistics show that the scheme possesses predictive skill at lead times in excess of six hours. © Crown copyright, 2006.

Given an accurate representation of errors in observations it is possible to remove the effect of those errors from categorical verification scores. The errors in the observations are treated as additive white noise that is statistically independent of the true value of the quantity being observed. This method can be applied to both probabilistic and deterministic verification where the verification method uses a categorical approach. In general this improves the apparent performance of a forecasting system, indicating that forecasting systems are often performing better than they might first appear.

The probabilistic traveling salesman problem concerns the best way to visit a set of customers located in some metric space, where each customer requires a visit only with some known probability. A solution to this problem is an a priori tour which visits all customers, and the objective is to minimize the expected length of the a priori tour over all customer subsets, assuming that customers in any given subset must be visited in the same order as they appear in the a priori tour. This problem belongs to the class of stochastic vehicle routing problems, a class which has received increasing attention in recent years, and which is of major importance in real world applications. Several heuristics have been proposed and tested for the probabilistic traveling salesman problem, many of which are a straightforward adaptation of heuristics for the classical traveling salesman problem. In particular, two local search algorithms (2-p-opt and 1-shift) were introduced by Bertsimas. In a previous report we have shown that the expressions for the cost evaluation of 2-p-opt and 1-shift moves, as proposed by Bertsimas, are not correct. In this paper we derive the correct versions of these expressions, and we show that the local search algorithms based on these expressions perform significantly better than those exploiting the incorrect expressions.

In collaboration with the Bureau of Meteorology (Melbourne, Australia), the Met Office(Joint Centre for Hydro–Meteorological Research, UK) has developed a stochastic precipi-tation nowcast scheme, designed to model and predict the PDF of surface rain rate and rainaccumulation in space and time. Here we demonstrate the range of probabilistic productsgenerated by the scheme, and their potential applications for fluvial flood forecasting andwarning.With the aid of a hydrological model (the PDM), we consider the use of ensemblesof predicted catchment rain accumulation in evaluating the range of possible river flowresponses from a given catchment. When employed in conjunction with a catchment specific,cost-based decision-making model, we highlight the value of PDFs of forecast catchmentrainfall accumulation and river flow as an aid to objective decision making within theflood warning process.  Crown Copyright 2005. Reproduced with the permission ofHer Majesty’s Stationery Office. Published by John Wiley & Sons, Ltd.Keywords: precipitation; nowcasting; probability; stochastic; hydrology; decision-making

A new advection-based nowcasting scheme for precipitation has been developed for the Gandolf system. The method employed removes the need to split the radar analysis into contiguous rain areas (CRA's) and uses a smoothness constraint. Thus, it is similar to the Variational Echo Tracking approach. Optical flow ideas are used to diagnose the advection velocity of blocks within rain analyses, which involve the direct solution of the Lagrangian persistence equation. In block-based approaches, the radar analyses are partitioned a-priori and a CRA may be split over a number of blocks. This scheme is compared with the old Gandolf advection scheme, which is based on CRA's, and the new scheme performs better-both in cases associated with severe flooding and over a continuous verification period of 3 months. The benefit is conjectured to be due mainly to the difficulty in unambiguously identifying CRA's, which is particularly troublesome on small domains, such as the UK. Thus, it is concluded that block-based methods are likely to be superior to object-based methods in the majority of cases.

The promise of smart buildings (SBs) is a safer more productive environment for users and a more operationally efficient building for owners. The automation of building function is highly dependent on sensing devices and Smart Building Applications(SBAs), which are often only evaluated in situ post deployment, making re-development costly. In this paper we explore our experiences developing a Simulated Context (SimCon) Model which currently supports taking information from a Virtual Reality (VR) SB and converting it into three types of location context to conduct early rapid evaluation of location based SBAs. This model is expressed using the Sensor Modelling Language (sensorML). It also explores the integration of this model into the Industry Foundation Classes (IFC) for modelling and simulating SBs. It also details usability evaluations of the SimConfig and SimConViz Tool for improving evaluation during the design phase of smart building development life cycle.

An experiment has been performed, using a simple chaotic model, to compare different ensemble perturbation strategies. The model used is a 300 variable Lorenz 95 model which displays many of the characteristics of atmospheric numerical weather prediction models. Twenty member ensembles were generated using five perturbation strategies, error breeding, singular vectors, random perturbations (RPs), the Ensemble Kalman Filter (EnKF) and the Ensemble Transform Kalman Filter (ETKF). Based on normal verification methods, such as rank histograms and spread of the perturbations, the RPs method performs as well as any other method—this illustrates the limitations of using a simple model. Consideration of the quality of the background error information provided by the ensemble gives a better assessment of the ensemble skill. This measure indicates that the EnKF performs best, with the ETKF combined with RPs being the next most skillful. It was found that neither the ETKF, error breeding nor singular vectors provided useful background information on their own. Central to the success of the EnKF is the localization of the background error covariance which removes spurious long-range correlations within the ensemble. Computationally efficient versions of the EnKF (such as the ETKF) cannot accommodate covariance localization and their performance is seen to suffer. Applying the ETKF to a series of local domains has been tested, which allows covariance localization whilst remaining computational efficient, and this has been found to be nearly as effective as the EnKF with covariance localization.

Using off-lattice noise reduction it is possible to estimate the asymptotic properties of diffusion-limited aggregation clusters grown in three dimensions with greater accuracy than would otherwise be possible. The fractal dimension of these aggregates is found to be 2.50 +/- 0.01, in agreement with earlier studies, and the asymptotic value of the relative penetration depth is 0.122 +/- 0.002. The multipole powers of the growth measure also exhibit universal asymptotes. The fixed point noise reduction is estimated to be \epsilon = 0.0035 meaning that large clusters can be identified with a low noise regime. The slowest correction to scaling exponents are measured for a number of properties of the clusters, and the exponent for the relative penetration depth and quadrupole moment are found to be significantly different from each other. The relative penetration depth exhibits the slowest correction to scaling of all quantities, which is consistent with a theoretical result derived in two dimensions., Comment: Submitted to Phys Rev E April 2004

Diffusion-limited aggregation is consistent with simple scaling. However, strong subdominant terms are present, and these can account for various earlier claims of anomalous scaling. We show this in detail for the case of multiscaling., Comment: 8 pages, 4 figures; proceedings of the conference "Stochastic systems: From randomness to complexity", Erice, 2002. (minor changes)

We demonstrate that is it possible to simulate a system in thermal equilibrium even when the energy cannot be evaluated exactly, provided the error distribution is known. This leads to an effective optimisation strategy for problems where the evaluation of each design can only be sampled statistically., Comment: 4 pages, 2 figures, submitting to PRL

Off-lattice diffusion-limited aggregation (DLA) clusters grown with different levels of noise reduction are found to be consistent with a simple fractal fixed point. Cluster shapes and their ensemble variation exhibit a dominant slowest correction to scaling, and this also accounts for the apparent "multiscaling" in the DLA mass distribution. We interpret the correction to scaling in terms of renormalized noise. The limiting value of this variable is strikingly small and is dominated by fluctuations in cluster shape. Earlier claims of anomalous scaling in DLA were misled by the slow approach to this small fixed point value.

Off-lattice DLA clusters grown with different levels of noise reduction are found to be consistent with a simple fractal fixed point. Cluster shapes and their ensemble variation exhibit a dominant slowest correction to scaling, and this also accounts for the apparent ``multiscaling'' in the DLA mass distribution. We interpret the correction to scaling in terms of renormalized noise. The limiting value of this variable is strikingly small and is dominated by fluctuations in cluster shape. Earlier claims of anomalous scaling in DLA were misled by the slow approach to this small fixed point value., Comment: 7 pages, 11 figures; rewritten and expanded

We show that Stochastic Annealing can be successfully applied to gain new results on the Probabilistic Traveling Salesman Problem (PTSP). The probabilistic "traveling salesman" must decide on an a priori order in which to visit n cities (randomly distributed over a unit square) before learning that some cities can be omitted. We find the optimized average length of the pruned tour follows E(\bar{L}_{pruned}) = \sqrt{np} (0.872-0.105p) f(np) where p is the probability of a city needing to be visited, and f(np) -> 1 as np -> infinity. The average length of the a priori tour (before omitting any cities) is found to follow E(L_{a priori}) =\sqrt{n/p}��(p) where ��(p)=1/(1.25-0.82 ln(p)) is measured for 0.05 < p < 0.6. Scaling arguments and indirect measurements suggest that ��(p) tends towards a constant for p, Updated to: 10 pages, 7 figures, submitted to PRE Updated from: 7 pages, 7 figures

✓ A patient is described who initially presented with subarachnoid hemorrhage and later with acute hypopituitarism. She had an aneurysm situated entirely within the pituitary fossa. The usual clinical features of parasellar aneurysms are described, and the endocrine assessment of the case is discussed.

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A collection of folklore and local history stories from An Pasáiste, Corcaigh (school) (Passage West, Co. Cork), collected as part of the Schools' Folklore Scheme, 1937-1938 under the supervision of teacher William Meiklejohn., Church of Passage West / Lester, Owen -- Holy Well in the Glen, Glenbrook, Passage West, County Cork / Murphy, Michael -- Passage Market / Ahern, Francis -- Mary Russell / Neill, Richard O' -- Rathanker / Connell, C. O' -- Cannon Found in Passage / Connell, C. O' -- Race Between Two Old Jarvey Cars / Leastar, Eoghan de -- Legend of One of the Lanes of Passage / Lester, Eugene -- Caisleán i mBaile na Manach / Leastar, Eoghan de -- Folklore on the Roads / Leastar, Eoghan de -- Ghost Story / Leastar, Eoghan de -- Mary Russell / Murphy, Michael -- Jenning's Well / Stuart, Michael -- Holy Well / Stuart, Michael -- Weather-Signs / Stuart, Michael -- Holy Well / Cocláin, Seán Ó -- Holy Well / Neill, Eamonn O' -- House of Cards / Neill, Richard O' -- Sirius / Neill, Richard O' -- Forgotten Poet of Passage / Neill, Eamonn O' -- Seán Dáth / Neill, Eamonn O' -- Ghost Story / Lester, Owen -- Ghost Story / Neill, Eamonn O' -- Mass Caves / Neill, Eamonn O' -- Delea's Mills / Neill, Richard O' -- Mahon Mac Mahon / Murphy, Michael -- Local Place Names / Ahern, Francis -- Place Names -- Ghost Story / Sullivan, Thomas O' -- Monkstown Castle / Neill, Eamonn O' -- Captive Knight / Neill, Richard O' -- Mount Prospect / Neill, E. O' -- Golden Gap / Neill, Richard O' -- Battles Fought at Passage / Neill, Richard O' -- Old Passage / Neill, Richard O' -- Vessel Found in the River / Neill, R. O' -- White Stone in Red Land / Neill, Richard O' -- Gath na Móna / Connell, John O' -- Holy Well / Neill, Richard O' -- Scaffold in Rochestown / Lester, Owen -- Unploughed Field / Leastar, Eoghan de -- Holy Well / Leastar, Eoghan de -- Sea Captain's Death / Leastar, Eoghan de -- Folklore - A Ghost Story / Leastar, Eoghan de -- Story / Neill, Richard O' -- Hospitals in Passage -- Ghost Story / Neill, Richard O' -- Folklore / Spillane, Victor -- Riddles / Neill, Richard O' -- Shipwreck / Neill, Richard O' -- Frenche's House / Leastar, Eoghan de -- Ship Juno / Leastar, Eoghan de -- Folklore / Neill, Richard O' -- Local Matches / Neill, Richard O' -- Local Cures / Neill, Richard O' -- Suir's Pond / Leastar, E. de -- Minister Drought / Leastar, E. de -- Carrigaloe / Leastar, Eoghan de -- Mass Caves / Neill, D. O' -- Folklore -- Nicknames / Leastar, Eoghan de -- Parish of Passage West / Neill, R. O' -- Monkstown Castle / Neill, Richard O' -- Captain Roberts / Neill, Richard O' -- Martello Tower / Neill, Richard O', Supported by funding from the Department of Arts, Heritage and the Gaeltacht (Ireland), University College Dublin, and the National Folklore Foundation (Fondúireacht Bhéaloideas Éireann), 2014-2016.

This thesis focuses on the role played by fluctuations in both thermal optimisation techniques and diffusion limited aggregation. The key idea is that by tuning the level of input noise asymptotic results may be attained more rapidly. Stochastic optimisation problems are considered, where the function being optimised cannot be known exactly and may only be estimated. The noise in the estimates is used as the analogue of thermal fluctuations in simulated annealing. This analogy is made exact by use of an acceptance function, and stochastic annealing is seen to be the generalisation of simulated annealing to stochastic optimisation problems. The probabilistic travelling salesman problem (PTSP) is used as a test-bed for stochastic annealing, and significant new results are found. A good characterisation is found for the PTSP and scaling arguments are shown to be accurate for determining the expected length of the pruned and a priori tours, specifically E(Lpruned)=βpruned(p)√np. An oil field project, as a complex commercial problem, is considered and stochastic annealing is seen to make a large improvement in the expected return of the project. \ud \ud Noise reduction in diffusion limited aggregation (DLA) is known to be crucial to our understanding. A generalisation of noise reduction off-lattice is introduced, and noise reduction is shown to be a central parameter controlling the growth of DLA. In 2 dimensions, all quantities appear to be influenced by the slowest correction to scaling, with exponent ~ 0.3. In 3 dimensions, some quantities are not affected by the slowest correction to scaling, exponent ~ 0.2. The renormalisation of DLA is considered, and the noise reduction at the fixed point is measured. The noise, given as the relative variability in extremal cluster radius is found to be ε*2D ≃ 0.003 and ε*3D ≃ 0.006 in 2 and 3 dimensions, respectively.