The VLSI design of a single chip Reed-Solomon encoder

A design for a single chip implementation of a Reed-Solomon encoder is presented. The architecture that leads to this single VLSI chip design makes use of a bit serial finite field multiplication algorithm

Long-Time Dynamics of Variable Coefficient mKdV Solitary Waves

We study the Korteweg-de Vries-type equation dt u=-dx(dx^2 u+f(u)-B(t,x)u), where B is a small and bounded, slowly varying function and f is a nonlinearity. Many variable coefficient KdV-type equations can be rescaled into this equation. We study the long time behaviour of solutions with initial conditions close to a stable, B=0 solitary wave. We prove that for long time intervals, such solutions have the form of the solitary wave, whose centre and scale evolve according to a certain dynamical law involving the function B(t,x), plus an H^1-small fluctuation.Comment: 19 page

Development and application of computer software techniques to human factors task data handling problems Final report, 21 Jun. 1965 - 21 Jun. 1966

Computer software techniques applied to human factors task data handling problem

Effective Hamiltonians for atoms in very strong magnetic fields

We propose three effective Hamiltonians which approximate atoms in very strong homogeneous magnetic fields $B$ modelled by the Pauli Hamiltonian, with fixed total angular momentum with respect to magnetic field axis. All three Hamiltonians describe $N$ electrons and a fixed nucleus where the Coulomb interaction has been replaced by $B$-dependent one-dimensional effective (vector valued) potentials but without magnetic field. Two of them are solvable in at least the one electron case. We briefly sketch how these Hamiltonians can be used to analyse the bottom of the spectrum of such atoms.Comment: 43 page

Evaluating the articulation of programme theory in practice as observed in Quality Improvement initiatives

Background: The Action-Effect Method(AEM) was co-developed by NIHR CLAHRC Northwest London (CLAHRC NWL) researchers and QI practitioners, building on Driver Diagrams(DD). This study aimed to determine AEM effectiveness in terms of technical aspects (how diagrams produced in practice compared with theoretical ideals) and social aspects (how engagement with the method related to social benefits). Methods Diagrams were scored on criteria developed on theoretical ideals of programme theory. 65 programme theory diagrams were reviewed (21 published Driver Diagrams (External DDs), 22 CLAHRC NWL Driver Diagrams (Internal DDs), and 21 CLAHRC NWL Action-Effect Diagrams(AEDs)). Social functions were studied through ethnographic observation of frontline QI teams in AEM sessions facilitated by QI experts. Qualitative analysis used inductive and deductive coding. Results ANOVA indicated the AEM significantly improved the quality of programme theory diagrams over Internal and External DDs on an average of 5 criteria from an 8-point assessment. Articulated aims were more likely to be patient-focused and high-level in AEDs than DDs. The cause/effect relationships from intervention to overall aim also tended to be clearer and were more likely than DDs to contain appropriate measure concepts. Using the AEM also served several social functions such as facilitating dialogue among multidisciplinary teams, and encouraging teams to act scientifically and pragmatically about planning and measuring QI interventions. Implications: The Action-Effect Method developed by CLAHRC NWL resulted in improvements over Driver Diagrams in articulating programme theory, which has wide-ranging benefits to quality improvement, including encouraging broad multi-disciplinary buy-in to clear aims and pre-planning a rigorous evaluation strategy

A new proof of the analyticity of the electronic density of molecules

We give a new, short proof of the regularity away from the nuclei of the electronic density of a molecule obtained in [1,2]. The new argument is based on the regularity properties of the Coulomb interactions underlined in [3,4] and on well-known elliptic technics. [1] S. Fournais, M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, T. Oe stergaard Soerensen: The electron density is smooth away from the nuclei. Comm. Math. Phys. 228, no. 3 (2002), 401-415. [2] S. Fournais, M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, T. Oestergaard Soerensen: Analyticity of the density of electronic wave functions. Ark. Mat. 42, no. 1 (2004), 87-106. [3] W. Hunziker: Distortion analyticity and molecular resonances curves. Ann. Inst. H. Poincar\'e, s. A, t. 45, no 4, 339-358 (1986). [4] M. Klein, A. Martinez, R. Seiler, X.P. Wang: On the Born-Oppenheimer expansion for polyatomic molecules. Comm. Math. Phys. 143, no. 3, 607-639 (1992). The paper is published in Letters in Mathematical Physics 93, number 1, pp. 73-83, 2010. The original publication is available at " www.springerlink.com "

Controllability of spin-boson systems

In this paper we study the so-called spin-boson system, namely {a two-level system} in interaction with a distinguished mode of a quantized bosonic field. We give a brief description of the controlled Rabi and Jaynes--Cummings models and we discuss their appearance in the mathematics and physics literature. We then study the controllability of the Rabi model when the control is an external field acting on the bosonic part. Applying geometric control techniques to the Galerkin approximation and using perturbation theory to guarantee non-resonance of the spectrum of the drift operator, we prove approximate controllability of the system, for almost every value of the interaction parameter

Multiplicity of the Galactic Senior Citizens: A high-resolution search for cool subdwarf companions

Cool subdwarfs are the oldest members of the low mass stellar population. Mostly present in the galactic halo, subdwarfs are characterized by their low metallicity. Measuring their binary fraction and comparing it to solar metallicity stars could give key insights into the star formation process early in the history of the Milky Way. However, because of their low luminosity and relative rarity in the solar neighborhood, binarity surveys of cool subdwarfs have suffered from small sample sizes and incompleteness. Previous surveys have suggested that the binary fraction of red subdwarfs is much lower than for their main sequence cousins. Using the highly efficient RoboAO system, we present the largest yet high-resolution survey of subdwarfs, sensitive to angular separations, down to 0.15 arcsec, and contrast ratios, up to 6 magnitude difference, invisible in past surveys. Of 344 target cool subdwarfs, 40 are in multiple systems, 16 newly discovered, for a binary fraction of 11.6 percent and 1.8 percent error. We also discovered 6 triple star systems for a triplet fraction of 1.7 percent and 0.7 percent error. Comparisons to similar surveys of solar metallicity dwarf stars gives a 3 sigma disparity in luminosity between companion stars, with subdwarfs displaying a shortage of low contrast companions.Comment: 13 pages, 10 figures, submitted to Ap

A VLSI single chip (255,223) Reed-Solomon encoder with interleaver

A single-chip implementation of a Reed-Solomon encoder with interleaving capability is described. The code used was adapted by the CCSDS (Consulative Committee on Space Data Systems). It forms the outer code of the NASA standard concatenated coding system which includes a convolutional inner code of rate 1/2 and constraint length 7. The architecture, leading to this single VLSI chip design, makes use of a bit-serial finite field multiplication algorithm due to E.R. Berlekamp

Longitudinal Monitoring of SARS-CoV-2 IgM and IgG Seropositivity to Detect COVID-19.

BackgroundSevere acute respiratory syndrome coronavirus 2 (SARS-CoV-2), is a novel beta-coronavirus that has recently emerged as the cause of the 2019 coronavirus pandemic (COVID-19). Polymerase chain reaction (PCR) based tests are optimal and recommended for the diagnosis of an acute SARS-CoV-2 infection. Serology tests for viral antibodies provide an important tool to diagnose previous exposure to the virus. Here we evaluate the analytical performance parameters of the Diazyme SARS-CoV-2 IgM/IgG serology assays and describe the kinetics of IgM and IgG seroconversion observed in patients with PCR-confirmed COVID-19 who were admitted to our hospital.MethodsWe validated the performance of the Diazyme assay in 235 presumed SARS-CoV-2 negative subjects to determine specificity. Subsequently, we evaluated the SARS-CoV-2 IgM and IgG seroconversion of 54 PCR-confirmed COVID-19 patients and determined sensitivity of the assay at three different timeframes.ResultSensitivity and specificity for detecting seropositivity at ≥15 days following a positive SARS-CoV-2 PCR result, was 100.0% and 98.7% when assaying for the panel of IgM and IgG. The median time to seropositivity observed for a reactive IgM and IgG result from the date of a positive PCR was 5 days (IQR: 2.75-9 days) and 4 days (IQR: 2.75-6.75 days), respectively.ConclusionsOur data demonstrate that the Diazyme IgM/IgG assays are suited for the purpose of detecting SARS-CoV-2 IgG and IgM in patients with suspected SARS-CoV-2 infections. For the first time, we report longitudinal data showing the evolution of seroconversion for both IgG and IgM in a cohort of acutely ill patients in the United States. We also demonstrate a low false positive rate in patients who were presumed to be disease free