Data compression in the presence of observational error correlations

Numerical weather prediction (NWP) models are moving towards km-scale (and smaller) resolutions in order to forecast high-impact weather. As the resolution of NWP models increase the need for high-resolution observations to constrain these models also increases. A major hurdle to the assimilation of dense observations in NWP is the presence of non-negligible observation error correlations (OECs). Despite the difficulty in estimating these error correlations, progress is being made, with centres around the world now explicitly accounting for OECs in a variety of observation types. This paper explores how to make efficient use of this potentially dramatic increase in the amount of data available for assimilation. In an idealised framework it is illustrated that as the length-scales of the OECs increase the scales that the analysis is most sensitive to the observations become smaller. This implies that a denser network of observations is more beneficial with increasing OEC length-scales. However, the computational and storage burden associated with such a dense network may not be feasible. To reduce the amount of data, a compression technique based on retaining the maximum information content of the observations can be used. When the OEC length-scales are large (in comparison to the prior error correlations), the data compression will select observations of the smaller scales for assimilation whilst throwing out the larger scale information. In this case it is shown that there is a discrepancy between the observations with the maximum information and those that minimise the analysis error variances. Experiments are performed using the Ensemble Kalman Filter and the Lorenz-1996 model, comparing different forms of data reduction. It is found that as the OEC length-scales increase the assimilation becomes more sensitive to the choice of data reduction technique

Quantum Error Correction via Convex Optimization

We show that the problem of designing a quantum information error correcting procedure can be cast as a bi-convex optimization problem, iterating between encoding and recovery, each being a semidefinite program. For a given encoding operator the problem is convex in the recovery operator. For a given method of recovery, the problem is convex in the encoding scheme. This allows us to derive new codes that are locally optimal. We present examples of such codes that can handle errors which are too strong for codes derived by analogy to classical error correction techniques.Comment: 16 page

Large-scale Bright Fronts in the Solar Corona: A Review of "EIT waves"

``EIT waves" are large-scale coronal bright fronts (CBFs) that were first observed in 195 \AA\ images obtained using the Extreme-ultraviolet Imaging Telescope (EIT) onboard the \emph{Solar and Heliospheric Observatory (SOHO)}. Commonly called ``EIT waves", CBFs typically appear as diffuse fronts that propagate pseudo-radially across the solar disk at velocities of 100--700 km s$^{-1}$ with front widths of 50-100 Mm. As their speed is greater than the quiet coronal sound speed ($c_s\leq$200 km s$^{-1}$) and comparable to the local Alfv\'{e}n speed ($v_A\leq$1000 km s$^{-1}$), they were initially interpreted as fast-mode magnetoacoustic waves ($v_{f}=(c_s^2 + v_A^2)^{1/2}$). Their propagation is now known to be modified by regions where the magnetosonic sound speed varies, such as active regions and coronal holes, but there is also evidence for stationary CBFs at coronal hole boundaries. The latter has led to the suggestion that they may be a manifestation of a processes such as Joule heating or magnetic reconnection, rather than a wave-related phenomena. While the general morphological and kinematic properties of CBFs and their association with coronal mass ejections have now been well described, there are many questions regarding their excitation and propagation. In particular, the theoretical interpretation of these enigmatic events as magnetohydrodynamic waves or due to changes in magnetic topology remains the topic of much debate.Comment: 34 pages, 19 figure

On the Nature and Genesis of EUV Waves: A Synthesis of Observations from SOHO, STEREO, SDO, and Hinode

A major, albeit serendipitous, discovery of the SOlar and Heliospheric Observatory mission was the observation by the Extreme Ultraviolet Telescope (EIT) of large-scale Extreme Ultraviolet (EUV) intensity fronts propagating over a significant fraction of the Sun's surface. These so-called EIT or EUV waves are associated with eruptive phenomena and have been studied intensely. However, their wave nature has been challenged by non-wave (or pseudo-wave) interpretations and the subject remains under debate. A string of recent solar missions has provided a wealth of detailed EUV observations of these waves bringing us closer to resolving their nature. With this review, we gather the current state-of-art knowledge in the field and synthesize it into a picture of an EUV wave driven by the lateral expansion of the CME. This picture can account for both wave and pseudo-wave interpretations of the observations, thus resolving the controversy over the nature of EUV waves to a large degree but not completely. We close with a discussion of several remaining open questions in the field of EUV waves research.Comment: Solar Physics, Special Issue "The Sun in 360",2012, accepted for publicatio

Comparison of some Reduced Representation Approximations

In the field of numerical approximation, specialists considering highly complex problems have recently proposed various ways to simplify their underlying problems. In this field, depending on the problem they were tackling and the community that are at work, different approaches have been developed with some success and have even gained some maturity, the applications can now be applied to information analysis or for numerical simulation of PDE's. At this point, a crossed analysis and effort for understanding the similarities and the differences between these approaches that found their starting points in different backgrounds is of interest. It is the purpose of this paper to contribute to this effort by comparing some constructive reduced representations of complex functions. We present here in full details the Adaptive Cross Approximation (ACA) and the Empirical Interpolation Method (EIM) together with other approaches that enter in the same category

Signatures of the slow solar wind streams from active regions in the inner corona

Some of local sources of the slow solar wind can be associated with spectroscopically detected plasma outflows at edges of active regions accompanied with specific signatures in the inner corona. The EUV telescopes (e.g. SPIRIT/CORONAS-F, TESIS/CORONAS-Photon and SWAP/PROBA2) sometimes observed extended ray-like structures seen at the limb above active regions in 1MK iron emission lines and described as "coronal rays". To verify the relationship between coronal rays and plasma outflows, we analyze an isolated active region (AR) adjacent to small coronal hole (CH) observed by different EUV instruments in the end of July - beginning of August 2009. On August 1 EIS revealed in the AR two compact outflows with the Doppler velocities V =10-30 km/s accompanied with fan loops diverging from their regions. At the limb the ARCH interface region produced coronal rays observed by EUVI/STEREO-A on July 31 as well as by TESIS on August 7. The rays were co-aligned with open magnetic field lines expanded to the streamer stalks. Using the DEM analysis, it was found that the fan loops diverged from the outflow regions had the dominant temperature of ~1 MK, which is similar to that of the outgoing plasma streams. Parameters of the solar wind measured by STEREO-B, ACE, WIND, STEREO-A were conformed with identification of the ARCH as a source region at the Wang-Sheeley-Arge map of derived coronal holes for CR 2086. The results of the study support the suggestion that coronal rays can represent signatures of outflows from ARs propagating in the inner corona along open field lines into the heliosphere.Comment: Accepted for publication in Solar Physics; 31 Pages; 13 Figure

Coherent electron-phonon coupling and polaron-like transport in molecular wires

We present a technique to calculate the transport properties through one-dimensional models of molecular wires. The calculations include inelastic electron scattering due to electron-lattice interaction. The coupling between the electron and the lattice is crucial to determine the transport properties in one-dimensional systems subject to Peierls transition since it drives the transition itself. The electron-phonon coupling is treated as a quantum coherent process, in the sense that no random dephasing due to electron-phonon interactions is introduced in the scattering wave functions. We show that charge carrier injection, even in the tunneling regime, induces lattice distortions localized around the tunneling electron. The transport in the molecular wire is due to polaron-like propagation. We show typical examples of the lattice distortions induced by charge injection into the wire. In the tunneling regime, the electron transmission is strongly enhanced in comparison with the case of elastic scattering through the undistorted molecular wire. We also show that although lattice fluctuations modify the electron transmission through the wire, the modifications are qualitatively different from those obtained by the quantum electron-phonon inelastic scattering technique. Our results should hold in principle for other one-dimensional atomic-scale wires subject to Peierls transitions.Comment: 21 pages, 8 figures, accepted for publication in Phys. Rev. B (to appear march 2001

Two-sided Grassmann-Rayleigh quotient iteration

The two-sided Rayleigh quotient iteration proposed by Ostrowski computes a pair of corresponding left-right eigenvectors of a matrix $C$. We propose a Grassmannian version of this iteration, i.e., its iterates are pairs of $p$-dimensional subspaces instead of one-dimensional subspaces in the classical case. The new iteration generically converges locally cubically to the pairs of left-right $p$-dimensional invariant subspaces of $C$. Moreover, Grassmannian versions of the Rayleigh quotient iteration are given for the generalized Hermitian eigenproblem, the Hamiltonian eigenproblem and the skew-Hamiltonian eigenproblem.Comment: The text is identical to a manuscript that was submitted for publication on 19 April 200

Norms, Networks, Power, and Control: Understanding Informal Payments and Brokerage in Cross-Border Trade in Sierra Leone

Recent research has cast light on the variety of informal payments and practices that govern the day-to-day interactions between traders and customs agents at border posts in low-income countries. Building on this literature, this paper draws on survey and qualitative evidence in an effort to explore which groups are most advantaged and disadvantaged by the largely informal processes and norms governing cross-border trade. We find that understanding variation in strategies and outcomes across traders can only be effectively understood with reference to the importance of norms, networks, power, and the logic of control.Department for International DevelopmentBill and Melinda Gates Foundatio

Cumulative burden of depression and all-cause mortality in women living with human immunodeficiency virus

Background Research linking depression to mortality among people living with human immunodeficiency virus (PLWH) has largely focused on binary "always vs never" characterizations of depression. However, depression is chronic and is likely to have cumulative effects on mortality over time. Quantifying depression as a cumulative exposure may provide a better indication of the clinical benefit of enhanced depression treatment protocols delivered in HIV care settings. Methods Women living with HIV (WLWH), naive to antiretroviral therapy, from the Women's Interagency HIV Study were followed from their first visit in or after 1998 for up to 10 semiannual visits (5 years). Depressive symptoms were assessed using the Center for Epidemiologic Studies Depression (CES-D) scale. An area-under-the-curve approach was used to translate CES-D scores into a time-updated measure of cumulative days with depression (CDWD). We estimated the effect of CDWD on all-cause mortality using marginal structural Cox proportional hazards models. Results Overall, 818 women contributed 3292 woman-years over a median of 4.8 years of follow-up, during which the median (interquartile range) CDWD was 366 (97-853). Ninety-four women died during follow-up (2.9 deaths/100 woman-years). A dose-response relationship was observed between CDWD and mortality. Each additional 365 days spent with depression increased mortality risk by 72% (hazard ratio, 1.72; 95% confidence interval, 1.34-2.20). Conclusions In this sample of WLWH, increased CDWD elevated mortality rates in a dose-response fashion. More frequent monitoring and enhanced depression treatment protocols designed to reduce CDWD may interrupt the accumulation of mortality risk among WLWH