20,744 research outputs found
Fourier Series Formalization in ACL2(r)
We formalize some basic properties of Fourier series in the logic of ACL2(r),
which is a variant of ACL2 that supports reasoning about the real and complex
numbers by way of non-standard analysis. More specifically, we extend a
framework for formally evaluating definite integrals of real-valued, continuous
functions using the Second Fundamental Theorem of Calculus. Our extended
framework is also applied to functions containing free arguments. Using this
framework, we are able to prove the orthogonality relationships between
trigonometric functions, which are the essential properties in Fourier series
analysis. The sum rule for definite integrals of indexed sums is also
formalized by applying the extended framework along with the First Fundamental
Theorem of Calculus and the sum rule for differentiation. The Fourier
coefficient formulas of periodic functions are then formalized from the
orthogonality relations and the sum rule for integration. Consequently, the
uniqueness of Fourier sums is a straightforward corollary.
We also present our formalization of the sum rule for definite integrals of
infinite series in ACL2(r). Part of this task is to prove the Dini Uniform
Convergence Theorem and the continuity of a limit function under certain
conditions. A key technique in our proofs of these theorems is to apply the
overspill principle from non-standard analysis.Comment: In Proceedings ACL2 2015, arXiv:1509.0552
Impact of NHS Direct on other services: the characteristics and origins of its nurses
OBJECTIVE:: To characterise the NHS Direct nurse workforce and estimate the impact of NHS Direct on the staffing of other NHS nursing specialties.
METHOD: A postal survey of NHS Direct nurses in all 17 NHS Direct call centres operating in June 2000.
RESULTS: The response rate was 74% (682 of 920). In the three months immediately before joining NHS Direct, 20% (134 of 682, 95% confidence intervals 17% to 23%) of respondents had not been working in the NHS. Of the 540 who came from NHS nursing posts, one fifth had come from an accident and emergency department or minor injury unit (110 of 540), and one in seven from practice nursing (75 of 540). One in ten (65 of 681) nurses said that previous illness, injury, or disability had been an important reason for deciding to join NHS Direct. Sixty two per cent (404 of 649) of nurses felt their job satisfaction and work environment had improved since joining NHS Direct.
CONCLUSION: The NHS Direct nurse workforce currently constitutes a small proportion (about 0.5%) of all qualified nurses in the NHS, although it recruits relatively experienced and well qualified nurses more heavily from some specialties, such as accident and emergency nursing, than others. However, its overall impact on staffing in any one specialty is likely to be small. NHS Direct has succeeded in providing employment for some nurses who might otherwise be unable to continue in nursing because of disability
A simulation model for wind energy storage systems. Volume 1: Technical report
A comprehensive computer program for the modeling of wind energy and storage systems utilizing any combination of five types of storage (pumped hydro, battery, thermal, flywheel and pneumatic) was developed. The level of detail of Simulation Model for Wind Energy Storage (SIMWEST) is consistent with a role of evaluating the economic feasibility as well as the general performance of wind energy systems. The software package consists of two basic programs and a library of system, environmental, and load components. The first program is a precompiler which generates computer models (in FORTRAN) of complex wind source storage application systems, from user specifications using the respective library components. The second program provides the techno-economic system analysis with the respective I/O, the integration of systems dynamics, and the iteration for conveyance of variables. SIMWEST program, as described, runs on the UNIVAC 1100 series computers
An assessment of inductive coupling roadway powered vehicles
The technical concept underlying the roadway powered vehicle system is the combination of an electrical power source embedded in the roadway and a vehicle-mounted power pickup that is inductively coupled to the roadway power source. The feasibility of such a system, implemented on a large scale was investigated. Factors considered included current and potential transportation modes and requirements, economics, energy, technology, social and institutional issues. These factors interrelate in highly complex ways, and a firm understanding of each of them does not yet exist. The study therefore was structured to manipulate known data in equally complex ways to produce a schema of options and useful questions that can form a basis for further, harder research. A dialectical inquiry technique was used in which two adversary teams, mediated by a third-party team, debated each factor and its interrelationship with the whole of the known information on the topic
Distribution of the second virial coefficients of globular proteins
George and Wilson [Acta. Cryst. D 50, 361 (1994)] looked at the distribution
of values of the second virial coefficient of globular proteins, under the
conditions at which they crystallise. They found the values to lie within a
fairly narrow range. We have defined a simple model of a generic globular
protein. We then generate a set of proteins by picking values for the
parameters of the model from a probability distribution. At fixed solubility,
this set of proteins is found to have values of the second virial coefficient
that fall within a fairly narrow range. The shape of the probability
distribution of the second virial coefficient is Gaussian because the second
virial coefficient is a sum of contributions from different patches on the
protein surface.Comment: 5 pages, including 3 figure
Elastic Deformation of Polycrystals
We propose a framework to model elastic properties of polycrystals by
coupling crystal orientational degrees of freedom with elastic strains. Our
model encodes crystal symmetries and takes into account explicitly the strain
compatibility induced long-range interaction between grains. The coupling of
crystal orientation and elastic interactions allows for the rotation of
individual grains by an external load. We apply the model to simulate uniaxial
tensile loading of a 2D polycrystal within linear elasticity and a system with
elastic anharmonicities that describe structural phase transformations. We
investigate the constitutive response of the polycrystal and compare it to that
of single crystals with crystallographic orientations that form the
polycrystal.Comment: 4 pages, 4 ps figure
A Tuned and Scalable Fast Multipole Method as a Preeminent Algorithm for Exascale Systems
Among the algorithms that are likely to play a major role in future exascale
computing, the fast multipole method (FMM) appears as a rising star. Our
previous recent work showed scaling of an FMM on GPU clusters, with problem
sizes in the order of billions of unknowns. That work led to an extremely
parallel FMM, scaling to thousands of GPUs or tens of thousands of CPUs. This
paper reports on a a campaign of performance tuning and scalability studies
using multi-core CPUs, on the Kraken supercomputer. All kernels in the FMM were
parallelized using OpenMP, and a test using 10^7 particles randomly distributed
in a cube showed 78% efficiency on 8 threads. Tuning of the
particle-to-particle kernel using SIMD instructions resulted in 4x speed-up of
the overall algorithm on single-core tests with 10^3 - 10^7 particles. Parallel
scalability was studied in both strong and weak scaling. The strong scaling
test used 10^8 particles and resulted in 93% parallel efficiency on 2048
processes for the non-SIMD code and 54% for the SIMD-optimized code (which was
still 2x faster). The weak scaling test used 10^6 particles per process, and
resulted in 72% efficiency on 32,768 processes, with the largest calculation
taking about 40 seconds to evaluate more than 32 billion unknowns. This work
builds up evidence for our view that FMM is poised to play a leading role in
exascale computing, and we end the paper with a discussion of the features that
make it a particularly favorable algorithm for the emerging heterogeneous and
massively parallel architectural landscape
Linear electric field frequency shift (important for next generation electric dipole moment searches) induced in confined gases by a magnetic field gradient
The search for particle electric dipole moments (edm) represents a most
promising way to search for physics beyond the standard model. A number of
groups are planning a new generation of experiments using stored gases of
various kinds. In order to achieve the target sensitivities it will be
necessary to deal with the systematic error resulting from the interaction of
the well-known field with
magnetic field gradients (often referred to as the geometric phase effect
(Commins, ED; Am. J. Phys. \QTR{bf}{59}, 1077 (1991), Pendlebury, JM
\QTR{em}{et al;} Phys. Rev. \QTR{bf}{A70}, 032102 (2004)). This interaction
produces a frequency shift linear in the electric field, mimicking an edm. In
this work we introduce an analytic form for the velocity auto-correlation
function which determines the velocity-position correlation function which in
turn determines the behavior of the frequency shift (Lamoreaux, SK and Golub,
R; Phys. Rev \QTR{bf}{A71}, 032104 (2005)) and show how it depends on the
operating conditions of the experiment. We also discuss some additional issues.Comment: 21 pages, 5 figure
Prevalence and predictors of postdischarge antibiotic use following mastectomy
OBJECTIVESurvey results suggest that prolonged administration of prophylactic antibiotics is common after mastectomy with reconstruction. We determined utilization, predictors, and outcomes of postdischarge prophylactic antibiotics after mastectomy with or without immediate breast reconstruction.DESIGNRetrospective cohort.PATIENTSCommercially insured women aged 18–64 years coded for mastectomy from January 2004 to December 2011 were included in the study. Women with a preexisting wound complication or septicemia were excluded.METHODSPredictors of prophylactic antibiotics within 5 days after discharge were identified in women with 1 year of prior insurance enrollment; relative risks (RR) were calculated using generalized estimating equations.RESULTSOverall, 12,501 mastectomy procedures were identified; immediate reconstruction was performed in 7,912 of these procedures (63.3%). Postdischarge prophylactic antibiotics were used in 4,439 procedures (56.1%) with immediate reconstruction and 1,053 procedures (22.9%) without immediate reconstruction (P<.001). The antibiotics most commonly prescribed were cephalosporins (75.1%) and fluoroquinolones (11.1%). Independent predictors of postdischarge antibiotics were implant reconstruction (RR, 2.41; 95% confidence interval [CI], 2.23–2.60), autologous reconstruction (RR, 2.17; 95% CI, 1.93–2.45), autologous reconstruction plus implant (RR, 2.11; 95% CI, 1.92–2.31), hypertension (RR, 1.05; 95% CI, 1.00–1.10), tobacco use (RR, 1.07; 95% CI, 1.01–1.14), surgery at an academic hospital (RR, 1.14; 95% CI, 1.07–1.21), and receipt of home health care (RR, 1.11; 95% CI, 1.04–1.18). Postdischarge prophylactic antibiotics were not associated with SSI after mastectomy with or without immediate reconstruction (bothP>.05).CONCLUSIONSProphylactic postdischarge antibiotics are commonly prescribed after mastectomy; immediate reconstruction is the strongest predictor. Stewardship efforts in this population to limit continuation of prophylactic antibiotics after discharge are needed to limit antimicrobial resistance.Infect Control Hosp Epidemiol2017;38:1048–1054</jats:sec
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