On the theory of equivalent operators and application to the numerical solution of uniformly elliptic partial differential equations

AbstractThis work is motivated by the preconditioned iterative solution of linear systems that arise from the discretization of uniformly elliptic partial differential equations. Iterative methods with bounds independent of the discretization are possible only if the preconditioning strategy is based upon equivalent operators. The operators A, B: W → V are said to be V norm equivalent if ∥Au∥v∥Bu∥v is bounded above and below by positive constants for u ϵ D, where D is “sufficiently dense.” If A is V norm equivalent to B, then for certain discretization strategies one can use B to construct a preconditioned iterative scheme for the approximate solution of the problem Au = F. The iteration will require an amount of work that is at most a constant times the work required to approximately solve the problem Bû = \̂tf to reduce the V norm of the error by a fixed factor. This paper develops the theory of equivalent operators on Hubert spaces. Then, the theory is applied to uniformly elliptic operators. Both the strong and weak forms are considered. Finally, finite element and finite difference discretizations are examined

On the Monadic Second-Order Transduction Hierarchy

We compare classes of finite relational structures via monadic second-order transductions. More precisely, we study the preorder where we set C \subseteq K if, and only if, there exists a transduction {\tau} such that C\subseteq{\tau}(K). If we only consider classes of incidence structures we can completely describe the resulting hierarchy. It is linear of order type {\omega}+3. Each level can be characterised in terms of a suitable variant of tree-width. Canonical representatives of the various levels are: the class of all trees of height n, for each n \in N, of all paths, of all trees, and of all grids

Prehospital Systolic Blood Pressure Thresholds: A Community‐based Outcomes Study

Objectives Emergency medical services (EMS) personnel commonly use systolic blood pressure ( sBP ) to triage and treat acutely ill patients. The definition of prehospital hypotension and its associated outcomes are poorly defined. The authors sought to determine the discrimination of prehospital sBP thresholds for 30‐day mortality and to compare patient classification by best‐performing thresholds to traditional cutoffs. Methods In a community‐based cohort of adult, nontrauma, noncardiac arrest patients transported by EMS between 2002 and 2006, entries to state hospital discharge data and death certificates were linked. Prehospital sBP thresholds between 40 and 140 mm Hg in derivation ( n =  132,624) and validation ( n =  22,020) cohorts and their discrimination for 30‐day mortality, were examined. Cutoffs were evaluated using the 0/1 distance, Youden index, and adjusted Z‐statistics from multivariable logistic regression models. Results In the derivation cohort, 1,594 (1.2%) died within 24 hours, 7,404 (6%) were critically ill during hospitalization, and 6,888 (5%) died within 30 days. The area under the receiver operating characteristic (ROC) curve for sBP was 0.60 (95% confidence interval [CI] = 0.59, 0.61) for 30‐day mortality and 0.64 (95% CI = 0.62 0.66) for 24‐hour mortality. The 0/1 distance, Youden index, and adjusted Z‐statistics found best‐performing sBP thresholds between 110 and 120 mm Hg. When compared to an sBP ≤ 90 mm Hg, a cutoff of 110 mm Hg would identify 17% ( n =  137) more deaths at 30 days, while overtriaging four times as many survivors. Conclusions Prehospital sBP is a modest discriminator of clinical outcomes, yet no threshold avoids substantial misclassification of 30‐day mortality among noninjured patients. Resumen Los Umbrales de la Presión Arterial Sistólica Prehospitalaria: Un Estudio de Base Comunitaria Acerca de la Evolución de los Pacientes Objetivos El personal de los sistemas de emergencias médicas ( SEM ) usa frecuentemente la presión arterial sistólica ( PAS ) para clasificar y tratar a los pacientes agudos. Las definiciones de hipotensión prehospitalaria y sus resultados asociados están pobremente definidos. Se determinó la discriminación de los umbrales de PAS prehospitalaria para la mortalidad a los 30 días, y se comparó la clasificación del paciente por los mejores umbrales con los puntos de corte tradicionales. Metodología Estudio de cohorte de base comunitaria de pacientes adultos no traumatológicos ni con paradas cardiorrespiratorias transportados por los SEM entre 2002 y 2006, cuyas historias estaban vinculadas con los datos de alta hospitalaria y los certificados de mortalidad. Se examinaron los umbrales de PAS prehospitalaria entre 40 mm Hg y 140 mm Hg en las cohortes de derivación ( n =  132.624), y validación ( n =  22,020), y su discriminación para la mortalidad a los 30 días. Los puntos de corte se evaluaron usando la distancia 0/1, el índice de Youden y los estadísticos Z ajustados de los modelos de regresión logística multivariable. Resultados: En la cohorte de derivación, 1.594 (1,2%) fallecieron en las primeras 24 horas, 7.404 (6%) estuvieron críticamente enfermos durante el ingreso y 6.888 (5%) fallecieron en los 30 primeros días. El área bajo la curva de la ROC para PAS fue 0,60 ( IC 95% = 0,59–0,61) para la mortalidad a los 30 días y 0,64 ( IC 95% = 0,62–0,66) para la mortalidad a las 24 horas. La distancia 0/1, el índice de Youden y las estadísticas Z ajustadas hallaronque los mejores umbrales de PAS estaban entre 110 y 120 mm Hg. Cuando se comparó con una PAS ≤ 90 mm Hg, un punto de corte de 110 mm Hg identificaría un 17% ( n =  137) más de muertes a los 30 días, mientras que sobreclasificaría cuatro veces más a los supervivientes. Conclusiones La presión arterial sistólica es un discriminador modesto de resultados clínicos. No obstante, ningún umbral evita una mala clasificación de la mortalidad a los 30 días entre los pacientes no traumatológicos.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/98303/1/acem12142-sup-0002-DataSupplementS2_FigS1.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/98303/2/acem12142-sup-0007-DataSupplementS7_FigS4.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/98303/3/acem12142-sup-0006-DataSupplementS6_FigS3.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/98303/4/acem12142-sup-0009-DataSupplementS9_TableS3.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/98303/5/acem12142-sup-0003-DataSupplementS3.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/98303/6/acem12142-sup-0008-DataSupplementS8_TableS2.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/98303/7/acem12142-sup-0004-DataSupplementS4_TableS1.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/98303/8/acem12142-sup-0001-DataSupplementS1.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/98303/9/acem12142.pd

Chemical Plants Remain Vulnerable to Terrorists: A Call to Action

U.S. chemical plants currently have potentially catastrophic vulnerabilities as terrorist targets. The possible consequences of these vulnerabilities echo from the tragedies of the Bhopal incident in 1984 to the terrorist attacks on 11 September 2001 and, most recently, Hurricanes Katrina and Rita. Findings from a 2004 nationwide participatory research study of 125 local union leaders at sites with very large volumes of highly hazardous chemicals suggest that voluntary efforts to achieve chemical plant security are not succeeding. Study respondents reported that companies had only infrequently taken actions that are most effective in preventing or in preparing to respond to a terrorist threat. In addition, companies reportedly often failed to involve key stakeholders, including workers, local unions, and the surrounding communities, in these efforts. The environmental health community thus has an opportunity to play a key role in advocating for and supporting improvements in prevention of and preparation for terrorist attacks. Policy-level recommendations to redress chemical site vulnerabilities and the related ongoing threats to the nation’s security are as follows: a) specify detailed requirements for chemical site assessment and security; b) mandate audit inspections supported by significant penalties for cases of noncompliance; c) require progress toward achieving inherently safer processes, including the minimizing of storage of highly hazardous chemicals; d) examine and require additional effective actions in prevention, emergency preparedness, and response and remediation; e) mandate and fund the upgrading of emergency communication systems; and f) involve workers and community members in plan creation and equip and prepare them to prevent and respond effectively to an incident

Pressure tuning of strain in CdTe/InSb epilayer: A photoluminescence and photomodulated reflectivity study

doi:10.1063/1.354415The heavy‐hole and light‐hole excitons of a CdTe epilayer, pseudomorphically grown on an InSb epilayer by molecular beam epitaxy, are studied with a diamond anvil cell as a function of applied hydrostatic pressure via photoluminescence (PL) and photomodulated reflectivity (PR) spectroscopies. They are compared with the excitonic features in the simultaneously measured PL spectra of a sample of bulk CdTe. Under applied pressure, the lattice mismatch‐induced splitting between the light‐hole and heavy‐hole related transitions increases in a continuous and reversible manner because of the additional pressure‐induced compression due to the difference in the compressibilities of CdTe and InSb. The unusually large strain sustained by the CdTe epilayer under pressure is discussed in the light of various models. The PR signal vanishes after the InSb epilayer goes through a structural phase transition at approximately 20 kbar, while the PL signal persists until it is irreversibly quenched by the CdTe epilayer undergoing a structural phase transition at approximately 30 kbar. For pressures between 20 and 30 kbar, the behavior of the CdTe epilayer is similar to that of the bulk sample; the strain appears to have been relaxed due to the structural phase transition which has taken place in InSb. Values of the first‐ and second‐order pressure coefficients for bulk CdTe and for the CdTe epilayer as well as values of the hydrostatic and shear deformation potentials are obtained at 14 and 80 K and compared with previously quoted values.The work by H.R.C. was supported in part by the U.S. Department of Energy under Contract No. DE-FG02-89ER45402. M.C. acknowledges partial support from the Research Corporation and the U.S. Army Grant No. DAAL-03-92-G-038 1. M.S.B. acknowledges partial support by the G. Ellsworth Huggins Fellowship. A.K.R. and R.L.G. acknowledge support from the National Science Foundation (Materials Research Group No. DMR89-13706)

Substrate Type Determines Metagenomic Profiles from Diverse Chemical Habitats

Environmental parameters drive phenotypic and genotypic frequency variations in microbial communities and thus control the extent and structure of microbial diversity. We tested the extent to which microbial community composition changes are controlled by shifting physiochemical properties within a hypersaline lagoon. We sequenced four sediment metagenomes from the Coorong, South Australia from samples which varied in salinity by 99 Practical Salinity Units (PSU), an order of magnitude in ammonia concentration and two orders of magnitude in microbial abundance. Despite the marked divergence in environmental parameters observed between samples, hierarchical clustering of taxonomic and metabolic profiles of these metagenomes showed striking similarity between the samples (>89%). Comparison of these profiles to those derived from a wide variety of publically available datasets demonstrated that the Coorong sediment metagenomes were similar to other sediment, soil, biofilm and microbial mat samples regardless of salinity (>85% similarity). Overall, clustering of solid substrate and water metagenomes into discrete similarity groups based on functional potential indicated that the dichotomy between water and solid matrices is a fundamental determinant of community microbial metabolism that is not masked by salinity, nutrient concentration or microbial abundance.</p

Testing nonperturbative techniques in the scalar sector of the standard model

We discuss the current picture of the standard model's scalar sector at strong coupling. We compare the pattern observed in the scalar sector in perturbation theory up to two-loop with the nonperturbative solution obtained by a next-to-leading order 1/N expansion. In particular, we analyze two resonant Higgs scattering processes, ff -> H -> f'f' and ff -> H -> ZZ, WW. We describe the ingredients of the nonperturbative calculation, such as the tachyonic regularization, the higher order 1/N intermediate renormalization, and the numerical methods for evaluating the graphs. We discuss briefly the perspectives and usefulness of extending these nonperturbative methods to other theories

The behaviour of political parties and MPs in the parliaments of the Weimar Republic

Copyright @ 2012 The Authors. This is the author's accepted manuscript. The final published article is available from the link below.Analysing the roll-call votes of the MPs of the Weimar Republic we find: (1) that party competition in the Weimar parliaments can be structured along two dimensions: an economic left–right and a pro-/anti-democratic. Remarkably, this is stable throughout the entire lifespan of the Republic and not just in the later years and despite the varying content of votes across the lifespan of the Republic, and (2) that nearly all parties were troubled by intra-party divisions, though, in particular, the national socialists and communists became homogeneous in the final years of the Republic.Zukunftskolleg, University of Konstan

Nonlinear time-series analysis of Hyperion's lightcurves

Hyperion is a satellite of Saturn that was predicted to remain in a chaotic rotational state. This was confirmed to some extent by Voyager 2 and Cassini series of images and some ground-based photometric observations. The aim of this aticle is to explore conditions for potential observations to meet in order to estimate a maximal Lyapunov Exponent (mLE), which being positive is an indicator of chaos and allows to characterise it quantitatively. Lightcurves existing in literature as well as numerical simulations are examined using standard tools of theory of chaos. It is found that existing datasets are too short and undersampled to detect a positive mLE, although its presence is not rejected. Analysis of simulated lightcurves leads to an assertion that observations from one site should be performed over a year-long period to detect a positive mLE, if present, in a reliable way. Another approach would be to use 2---3 telescopes spread over the world to have observations distributed more uniformly. This may be achieved without disrupting other observational projects being conducted. The necessity of time-series to be stationary is highly stressed.Comment: 34 pages, 12 figures, 4 tables; v2 after referee report; matches the version accepted in Astrophysics and Space Scienc

Highly selective and solvent-dependent reduction of Nitrobenzene to N-phenylhydroxylamine, azoxybenzene, and aniline catalyzed by phosphino-modified polymer immobilized ionic liquid-stabilized AuNPs

Gold nanoparticles stabilized by phosphine-decorated polymer immobilized ionic liquids (AuNP@PPh2-PIILP) is an extremely efficient multiproduct selective catalyst for the sodium borohydride-mediated reduction of nitrobenzene giving N-phenylhydroxylamine, azoxybenzene, or aniline as the sole product under mild conditions and a very low catalyst loading. The use of a single nanoparticle-based catalyst for the partial and complete reduction of nitroarenes to afford three different products with exceptionally high selectivities is unprecedented. Under optimum conditions, thermodynamically unfavorable N-phenylhydroxylamine can be obtained as the sole product in near quantitative yield in water, whereas a change in reaction solvent to ethanol results in a dramatic switch in selectivity to afford azoxybenzene. The key to obtaining such a high selectivity for N-phenylhydroxylamine is the use of a nitrogen atmosphere at room temperature as reactions conducted under an inert atmosphere occur via the direct pathway and are essentially irreversible, while reactions in air afford significant amounts of azoxy-based products by virtue of competing condensation due to reversible formation of N-phenylhydroxylamine. Ultimately, aniline can also be obtained quantitatively and selectively by adjusting the reaction temperature and time accordingly. Introduction of PEG onto the polyionic liquid resulted in a dramatic improvement in catalyst efficiency such that N-phenylhydroxylamine could be obtained with a turnover number (TON) of 100 000 (turnover frequency (TOF) of 73 000 h–1, with >99% selectivity), azoxybenzene with a TON of 55 000 (TOF of 37 000 h–1 with 100% selectivity), and aniline with a TON of 500 000 (TOF of 62 500 h–1, with 100% selectivity). As the combination of ionic liquid and phosphine is required to achieve high activity and selectivity, further studies are currently underway to explore whether interfacial electronic effects influence adsorption and thereby selectivity and whether channeling of the substrate by the electrostatic potential around the AuNPs is responsible for the high activity. This is the first report of a AuNP-based system that can selectively reduce nitroarenes to either of two synthetically important intermediates as well as aniline and, in this regard, is an exciting discovery that will form the basis to develop a continuous flow process enabling facile scale-up