Well-Posedness And Accuracy Of The Ensemble Kalman Filter In Discrete And Continuous Time

The ensemble Kalman filter (EnKF) is a method for combining a dynamical model with data in a sequential fashion. Despite its widespread use, there has been little analysis of its theoretical properties. Many of the algorithmic innovations associated with the filter, which are required to make a useable algorithm in practice, are derived in an ad hoc fashion. The aim of this paper is to initiate the development of a systematic analysis of the EnKF, in particular to do so in the small ensemble size limit. The perspective is to view the method as a state estimator, and not as an algorithm which approximates the true filtering distribution. The perturbed observation version of the algorithm is studied, without and with variance inflation. Without variance inflation well-posedness of the filter is established; with variance inflation accuracy of the filter, with resepct to the true signal underlying the data, is established. The algorithm is considered in discrete time, and also for a continuous time limit arising when observations are frequent and subject to large noise. The underlying dynamical model, and assumptions about it, is sufficiently general to include the Lorenz '63 and '96 models, together with the incompressible Navier-Stokes equation on a two-dimensional torus. The analysis is limited to the case of complete observation of the signal with additive white noise. Numerical results are presented for the Navier-Stokes equation on a two-dimensional torus for both complete and partial observations of the signal with additive white noise

The golden circle: A way of arguing and acting about technology in the London ambulance service

This paper analyses the way in which the London Ambulance Service recovered from the events of October 1992, when it implemented a computer-aided despatch system (LASCAD) that remained in service for less than two weeks. It examines the enactment of a programme of long-term organizational change, focusing on the implementation of an alternative computer system in 1996. The analysis in this paper is informed by actor-network theory, both by an early statement of this approach developed by Callon in the sociology of translation, and also by concepts and ideas from Latour’s more recent restatement of his own position. The paper examines how alternative interests emerged and were stabilized over time, in a way of arguing and acting among key players in the change programme, christened the Golden Circle. The story traces four years in the history of the London Ambulance Service, from the aftermath of October 1992 through the birth of the Golden Circle to the achievement of National Health Service (NHS) trust status. LASCAD was the beginning of the story, this is the middle, an end lies in the future, when the remaining elements of the change programme are enacted beyond the Golden Circle

Wave attenuation and dispersion due to floating ice covers

Experiments investigating the attenuation and dispersion of surface waves in a variety of ice covers are performed using a refrigerated wave flume. The ice conditions tested in the experiments cover naturally occurring combinations of continuous, fragmented, pancake and grease ice. Attenuation rates are shown to be a function of ice thickness, wave frequency, and the general rigidity of the ice cover. Dispersion changes were minor except for large wavelength increases when continuous covers were tested. Results are verified and compared with existing literature to show the extended range of investigation in terms of incident wave frequency and ice conditions

Measuring what matters to patients: Using goal content to inform measure choice and development

Introduction: Personalised care requires personalised outcomes and ways of feeding back clinically useful information to clinicians and practitioners, but it is not clear how to best personalise outcome measurement and feedback using existing standardised outcome measures. / Method: The constant comparison method of grounded theory was used to compare goal themes derived from goals set at the outset of therapy for 180 children aged between 4 and 17 years, visiting eight child and adolescent mental health services, to existing standardised outcome measures used as part of common national datasets. / Results: In all, 20 out of 27 goal themes corresponded to items on at least one commonly used outcome measure. Discussion: Consideration of goal themes helped to identify potential relevant outcome measures. However, there were several goal themes that were not captured by items on standardised outcome measures. These seemed to be related to existential factors such as understanding, thinking about oneself and future planning. / Conclusion: This presents a powerful framework for how clinicians can use goals to help select a standardised outcome measure (where this is helpful) in addition to the use of a goal-based outcome measure and personalise choices. There may be areas not captured by standardised outcome measures that may be important for children and young people and which may only be currently captured in goal measurement. There is an indication that we may not be measuring what is important to children and young people. We may need to develop or look for new measures that capture these areas

Generating entangled photon pairs from a cavity-QED system

We propose a scheme for the controlled generation of Einstein-Podosky-Rosen (EPR) entangled photon pairs from an atom coupled to a high Q optical cavity, extending the prototype system as a source for deterministic single photons. A thorough theoretical analysis confirms the promising operating conditions of our scheme as afforded by currently available experimental setups. Our result demonstrates the cavity QED system as an efficient and effective source for entangled photon pairs, and shines new light on its important role in quantum information science.Comment: It has recently come to our attention that the experiment by T. Wilk, S. C. Webster, A. Kuhn and G. Rempe, published in Science 317, 488 (2007), exactly realizes what we proposed in this article, which is published in Phy. Rev. A 040302(R) (2005

Kinematic and tectonic significance of microstructures and crystallographic fabrics within quartz mylonites from the Assynt and Eriboll regions of the Moine thrust zone, NW Scotland

Using a combination of optical microscopy and X-ray texture goniometry, an integrated microstructural and crystallographic fabric study has been made of quartz mylonites from thrust sheets located beneath, but immediately adjacent to, the Moine thrust in the Assynt and Eriboll regions of NW Scotland. A correlation is established between shape fabric symmetry and pattern of crystallographic preferred orientation, a particularly clear relationship being observed between shape fabric variation and quartz a-axis fabrics. Coaxial strain paths dominate the internal parts of the thrust sheets and are indicated by quartz c- and a-axis fabrics which are symmetrical with respect to foliation and lineation. Non-coaxial strain paths are indicated within the more intensely deformed quartzites located near the boundaries of the sheets by asymmetrical c- and a-axis fabrics. These kinematic interpretations are supported by microstructural studies. At the Stack of Glencoul in the northern part of the Assynt region, the transition zone between these kinematic (strain path) domains is located at approximately 20 cm beneath the Moine thrust and is marked by a progression from symmetrical cross-girdle c-axis fabrics (30cm beneath the thrust), through asymmetrical cross-girdle c-axis fabrics to asymmetrical single girdle c-axis fabrics (0·5 cm beneath the thrust). Tectonic models (incorporating processes such as extensional flow, gravity spreading and tectonic loading) which may account for the presence of strain path domains within the thrust sheets are considered, and their compatibility with local thrust sheet geometries assesse

Towards practice-based studies of HRM: an actor-network and communities of practice informed approach

HRM may have become co-terminus with the new managerialism in the rhetorical orthodoxies of the HRM textbooks and other platforms for its professional claims. However, we have detailed case-study data showing that HR practices can be much more complicated, nuanced and indeed resistive toward management within organizational settings. Our study is based on ethnographic research, informed by actor-network theory and community of practice theory conducted by one of the authors over an 18-month period. Using actor-network theory in a descriptive and critical way, we analyse practices of managerial resistance, enrolment and counter-enrolment through which an unofficial network of managers used a formal HRM practice to successfully counteract the official strategy of the firm, which was to close parts of a production site. As a consequence, this network of middle managers effectively changed top management strategy and did so through official HRM practices, coupled with other actor-network building processes, arguably for the ultimate benefit of the organization, though against the initial views of the top management. The research reported here, may be characterized as a situated study of HRM-in-practice and we draw conclusions which problematize the concept of HRM in contemporary management literature

Stability of Filters for the Navier-Stokes Equation

Data assimilation methodologies are designed to incorporate noisy observations of a physical system into an underlying model in order to infer the properties of the state of the system. Filters refer to a class of data assimilation algorithms designed to update the estimation of the state in a on-line fashion, as data is acquired sequentially. For linear problems subject to Gaussian noise filtering can be performed exactly using the Kalman filter. For nonlinear systems it can be approximated in a systematic way by particle filters. However in high dimensions these particle filtering methods can break down. Hence, for the large nonlinear systems arising in applications such as weather forecasting, various ad hoc filters are used, mostly based on making Gaussian approximations. The purpose of this work is to study the properties of these ad hoc filters, working in the context of the 2D incompressible Navier-Stokes equation. By working in this infinite dimensional setting we provide an analysis which is useful for understanding high dimensional filtering, and is robust to mesh-refinement. We describe theoretical results showing that, in the small observational noise limit, the filters can be tuned to accurately track the signal itself (filter stability), provided the system is observed in a sufficiently large low dimensional space; roughly speaking this space should be large enough to contain the unstable modes of the linearized dynamics. Numerical results are given which illustrate the theory. In a simplified scenario we also derive, and study numerically, a stochastic PDE which determines filter stability in the limit of frequent observations, subject to large observational noise. The positive results herein concerning filter stability complement recent numerical studies which demonstrate that the ad hoc filters perform poorly in reproducing statistical variation about the true signal