Weighted maximal regularity estimates and solvability of non-smooth elliptic systems II

We continue the development, by reduction to a first order system for the conormal gradient, of $L^2$ \textit{a priori} estimates and solvability for boundary value problems of Dirichlet, regularity, Neumann type for divergence form second order, complex, elliptic systems. We work here on the unit ball and more generally its bi-Lipschitz images, assuming a Carleson condition as introduced by Dahlberg which measures the discrepancy of the coefficients to their boundary trace near the boundary. We sharpen our estimates by proving a general result concerning \textit{a priori} almost everywhere non-tangential convergence at the boundary. Also, compactness of the boundary yields more solvability results using Fredholm theory. Comparison between classes of solutions and uniqueness issues are discussed. As a consequence, we are able to solve a long standing regularity problem for real equations, which may not be true on the upper half-space, justifying \textit{a posteriori} a separate work on bounded domains.Comment: 76 pages, new abstract and few typos corrected. The second author has changed nam

Parallel Unsmoothed Aggregation Algebraic Multigrid Algorithms on GPUs

We design and implement a parallel algebraic multigrid method for isotropic graph Laplacian problems on multicore Graphical Processing Units (GPUs). The proposed AMG method is based on the aggregation framework. The setup phase of the algorithm uses a parallel maximal independent set algorithm in forming aggregates and the resulting coarse level hierarchy is then used in a K-cycle iteration solve phase with a $\ell^1$-Jacobi smoother. Numerical tests of a parallel implementation of the method for graphics processors are presented to demonstrate its effectiveness.Comment: 18 pages, 3 figure

One step multiderivative methods for first order ordinary differential equations

A family of one-step multiderivative methods based on Padé approximants to the exponential function is developed. The methods are extrapolated and analysed for use in PECE mode. Error constants and stability intervals are calculated and the combinations compared with well known linear multi-step combinations and combinations using high accuracy Newton-Cotes quadrature formulas as correctors. w926020

Finite Automata for the Sub- and Superword Closure of CFLs: Descriptional and Computational Complexity

We answer two open questions by (Gruber, Holzer, Kutrib, 2009) on the state-complexity of representing sub- or superword closures of context-free grammars (CFGs): (1) We prove a (tight) upper bound of $2^{\mathcal{O}(n)}$ on the size of nondeterministic finite automata (NFAs) representing the subword closure of a CFG of size $n$. (2) We present a family of CFGs for which the minimal deterministic finite automata representing their subword closure matches the upper-bound of $2^{2^{\mathcal{O}(n)}}$ following from (1). Furthermore, we prove that the inequivalence problem for NFAs representing sub- or superword-closed languages is only NP-complete as opposed to PSPACE-complete for general NFAs. Finally, we extend our results into an approximation method to attack inequivalence problems for CFGs

Disseminating evidence from health technology assessment : the case of tobacco prevention

OBJECTIVES: The aims of the present study were to investigate the awareness among dentists and dental hygienists of evidence-based reports and guidelines on tobacco cessation activities and the impact these publications had on clinical practice. METHODS: A questionnaire was mailed to dental hygienists and dentists in Stockholm County, Sweden, and the results were compared with a previous investigation. RESULTS: Among the respondents, awareness of a popular science version of a systematic review on smoking and its effect on oral health was reported by 90 percent of the hygienists and 66 percent of the dentists. The information was used in clinical work by 34 percent of the dentists and 54 percent of the hygienists. Reported changes in patterns of practice were more frequent recommendations to use nicotine replacement therapy and a more widespread use of setting quit dates. Approximately one quarter of the dental professionals reported that they had increased tobacco cessation consultation because of the results from the reports. CONCLUSIONS: Changes in patterns of practice were observed after dissemination of evidence-based information on tobacco cessation. Methods that were proven to be effective in the evidence-based report such as discussing quit dates and recommending nicotine replacement therapy were more commonly used after the publication of the report. Short, popular versions of extensive systematic reviews seem to be useful for implementing evidence-based knowledge and changing clinical practice.NonePublishe

Improving the condition number of estimated covariance matrices

High dimensional error covariance matrices and their inverses are used to weight the contribution of observation and background information in data assimilation procedures. As observation error covariance matrices are often obtained by sampling methods, estimates are often degenerate or ill-conditioned, making it impossible to invert an observation error covariance matrix without the use of techniques to reduce its condition number. In this paper we present new theory for two existing methods that can be used to ‘recondition’ any covariance matrix: ridge regression, and the minimum eigenvalue method. We compare these methods with multiplicative variance inflation, which cannot alter the condition number of a matrix, but is often used to account for neglected correlation information. We investigate the impact of reconditioning on variances and correlations of a general covariance matrix in both a theoretical and practical setting. Improved theoretical understanding provides guidance to users regarding method selection, and choice of target condition number. The new theory shows that, for the same target condition number, both methods increase variances compared to the original matrix, with larger increases for ridge regression than the minimum eigenvalue method. We prove that the ridge regression method strictly decreases the absolute value of off-diagonal correlations. Theoretical comparison of the impact of reconditioning and multiplicative variance inflation on the data assimilation objective function shows that variance inflation alters information across all scales uniformly, whereas reconditioning has a larger effect on scales corresponding to smaller eigenvalues. We then consider two examples: a general correlation function, and an observation error covariance matrix arising from interchannel correlations. The minimum eigenvalue method results in smaller overall changes to the correlation matrix than ridge regression, but can increase off-diagonal correlations. Data assimilation experiments reveal that reconditioning corrects spurious noise in the analysis but underestimates the true signal compared to multiplicative variance inflation

Peptide microarray-based characterization of antibody responses to host proteins after bacille Calmette-Guerin vaccination

BACKGROUND: Bacille Calmette–Guérin (BCG) is the world’s most widely distributed vaccine, used against tuberculosis (TB), in cancer immunotherapy, and in autoimmune diseases due to its immunomodulatory properties. To date, the effect of BCG vaccination on antibody responses to host proteins has not been reported. High-content peptide microarrays (HCPM) offer a unique opportunity to gauge specific humoral immune responses. METHODS: The sera of BCG-vaccinated healthy adults were tested on a human HCPM platform (4953 randomly selected epitopes of human proteins) to detect specific immunoglobulin gamma (IgG) responses. Samples were obtained at 56, 112, and 252 days after vaccination. Immunohistology was performed on lymph node tissue from patients with TB lymphadenitis. Results were analysed with a combination of existing and novel statistical methods. RESULTS: IgG recognition of host peptides exhibited a peak at day 56 post BCG vaccination in all study subjects tested, which diminished over time. Primarily, IgG responses exhibited increased reactivity to ion transporters (sodium, calcium channels), cytokine receptors (interleukin 2 receptor β (IL2Rβ), fibroblast growth factor receptor 1 (FGFR1)), other cell surface receptors (inositol, somatostatin, angiopoeitin), ribonucleoprotein, and enzymes (tyrosine kinases, phospholipase) on day 56. There was decreased IgG reactivity to transforming growth factor-beta type 1 receptor (TGFβR1) and, in agreement with the peptide microarray findings, immunohistochemical analysis of TB-infected lymph node samples revealed an overexpression of TGFβR in granulomatous lesions. Moreover, the vesicular monoamine transporter (VMAT2) showed increased reactivity on days 112 and 252, but not on day 56 post-vaccination. IgG to interleukin 4 receptor (IL4R) showed increased reactivity at 112 days post-vaccination, while IgG to IL2Rβ and FGFR1 showed decreased reactivity on days 112 and 252 as compared to day 56 post BCG vaccination. CONCLUSIONS: BCG vaccination modifies the host’s immune landscape after 56 days, but this imprint changes over time. This may influence the establishment of immunological memory in BCG-vaccinated individuals

Searching for hidden mirror symmetries in CMB fluctuations from WMAP 7 year maps

We search for hidden mirror symmetries at large angular scales in the WMAP 7 year Internal Linear Combination map of CMB temperature anisotropies using global pixel based estimators introduced for this aim. Two different axes are found for which the CMB intensity pattern is anomalously symmetric (or anti-symmetric) under reflection with respect to orthogonal planes at the 99.84(99.96)% CL (confidence level), if compared to a result for an arbitrary axis in simulations without the symmetry. We have verified that our results are robust to the introduction of the galactic mask. The direction of such axes is close to the CMB kinematic dipole and nearly orthogonal to the ecliptic plane, respectively. If instead the real data are compared to those in simulations taken with respect to planes for which the maximal mirror symmetry is generated by chance, the confidence level decreases to 92.39 (76.65)%. But when the effect in question translates into the anomalous alignment between normals to planes of maximal mirror (anti)-symmetry and these natural axes mentioned. We also introduce the representation of the above estimators in the harmonic domain, confirming the results obtained in the pixel one. The symmetry anomaly is shown to be almost entirely due to low multipoles, so it may have a cosmological and even primordial origin. Contrary, the anti-symmetry one is mainly due to intermediate multipoles that probably suggests its non-fundamental nature. We have demonstrated that these anomalies are not connected to the known issue of the low variance in WMAP observations and we have checked that axially symmetric parts of these anomalies are small, so that the axes are not the symmetry ones.Comment: 18 pages, 10 figures, 2 tables. Consideration and discussion expanded, 5 figures and 1 table added, main conclusions unchange

Conical square function estimates in UMD Banach spaces and applications to H-infinity functional calculi

We study conical square function estimates for Banach-valued functions, and introduce a vector-valued analogue of the Coifman-Meyer-Stein tent spaces. Following recent work of Auscher-McIntosh-Russ, the tent spaces in turn are used to construct a scale of vector-valued Hardy spaces associated with a given bisectorial operator (A) with certain off-diagonal bounds, such that (A) always has a bounded (H^{\infty})-functional calculus on these spaces. This provides a new way of proving functional calculus of (A) on the Bochner spaces (L^p(\R^n;X)) by checking appropriate conical square function estimates, and also a conical analogue of Bourgain's extension of the Littlewood-Paley theory to the UMD-valued context. Even when (X=\C), our approach gives refined (p)-dependent versions of known results.Comment: 28 pages; submitted for publicatio