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 $\overrightarrow{v}\times \overrightarrow{E}$ 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&lt;.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&gt;.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