On the ratio of consecutive gaps between primes

In the present work we prove a common generalization of Maynard-Tao's recent result about consecutive bounded gaps between primes and on the Erd\H{o}s-Rankin bound about large gaps between consecutive primes. The work answers in a strong form a 60 years old problem of Erd\"os, which asked whether the ratio of two consecutive primegaps can be infinitely often arbitrarily small, and arbitrarily large, respectively

Collaborative dynamic decision making: a case study from B2B supplier selection

The problem of supplier selection can be easily modeled as a multiple-criteria decision making (MCDM) problem: businesses express their preferences with respect to suppliers, which can then be ranked and selected. This approach has two major pitfalls: first, it does not consider a dynamic scenario, in which suppliers and their ratings are constantly changing; second, it only addressed the problem from the point of view of a single business, and cannot be easily applied when considering more than one business. To overcome these problems, we introduce a method for supplier selection that builds upon the dynamic MCDM framework of Campanella and Ribeiro [1] and, by means of a linear programming model, can be used in the case of multiple collaborating businesses plan- ning their next batch of orders together.Fundação para a Ciência e a Tecnologia, Portugal, under contract CONT DOUT/49/UNINOVA/0/5902/1/200

Emergency hospital care for adults with suspected seizures in the NHS in England 2007-2013: a cross-sectional study

Aims To quantify the frequency, characteristics, geographical variation and costs of emergency hospital care for suspected seizures. Design Cross-sectional study using routinely collected data (Hospital Episode Statistics). Setting The National Health Service in England 2007–2013. Participants Adults who attended an emergency department (ED) or were admitted to hospital. Results In England (population 2011: 53.11 million, 41.77 million adults), suspected seizures gave rise to 50 111 unscheduled admissions per year among adults (≥18 years). This is 47.1% of unscheduled admissions for neurological conditions and 0.71% of all unscheduled admissions. Only a small proportion of admissions for suspected seizures were coded as status epilepticus (3.5%) and there were a very small number of dissociative (non-epileptic) seizures. The median length of stay for each admission was 1 day, the median cost for each admission was £1651 ($2175) and the total cost of all admissions for suspected seizures in England was £88.2 million ($116.2 million) per year. 16.8% of patients had more than one admission per year. There was significant geographical variability in the rate of admissions corrected for population age and gender differences and some areas had rates of admission which were consistently higher than the average. Conclusions Our data show that suspected seizures are the most common neurological cause of admissions to hospital in England, that readmissions are common and that there is significant geographical variability in admission rates. This variability has not previously been reported in the published literature. The cause of the geographical variation is unknown; important factors are likely to include prevalence, deprivation and clinical practice and these require further investigation. Dissociative seizures are not adequately diagnosed during ED attendances and hospital admissions

Quantification of Myocardial Blood Flow in Absolute Terms Using (82)Rb PET Imaging: The RUBY-10 Study.

OBJECTIVES: The purpose of this study was to compare myocardial blood flow (MBF) and myocardial flow reserve (MFR) estimates from rubidium-82 positron emission tomography ((82)Rb PET) data using 10 software packages (SPs) based on 8 tracer kinetic models. BACKGROUND: It is unknown how MBF and MFR values from existing SPs agree for (82)Rb PET. METHODS: Rest and stress (82)Rb PET scans of 48 patients with suspected or known coronary artery disease were analyzed in 10 centers. Each center used 1 of 10 SPs to analyze global and regional MBF using the different kinetic models implemented. Values were considered to agree if they simultaneously had an intraclass correlation coefficient >0.75 and a difference <20% of the median across all programs. RESULTS: The most common model evaluated was the Ottawa Heart Institute 1-tissue compartment model (OHI-1-TCM). MBF values from 7 of 8 SPs implementing this model agreed best. Values from 2 other models (alternative 1-TCM and Axially distributed) also agreed well, with occasional differences. The MBF results from other models (e.g., 2-TCM and retention) were less in agreement with values from OHI-1-TCM. CONCLUSIONS: SPs using the most common kinetic model-OHI-1-TCM-provided consistent results in measuring global and regional MBF values, suggesting that they may be used interchangeably to process data acquired with a common imaging protocol

Low-energy cutoffs in electron spectra of solar flares: statistical survey

The Ramaty High Energy Solar Spectroscopic Imager (RHESSI) X-ray data base (February 2002 -- May 2006) has been searched to find solar flares with weak thermal components and flat photon spectra. Using a regularised inversion technique, we determine the mean electron flux distribution from count spectra of a selection of events with flat photon spectra in the 15--20 keV energy range. Such spectral behaviour is expected for photon spectra either affected by photospheric albedo or produced by electron spectra with an absence of electrons in a given energy range, e.g. a low-energy cutoff in the mean electron spectra of non-themal particles. We have found 18 cases which exhibit a statistically significant local minimum (a dip) in the range of 10--20 keV. The positions and spectral indices of events with low-energy cutoff indicate that such features are likely to be the result of photospheric albedo. It is shown that if the isotropic albedo correction was applied, all low-energy cutoffs in the mean electron spectrum were removed and hence the low energy cutoffs in the mean electron spectrum of solar flares above $\sim$12 keV cannot be viewed as real features in the electron spectrum. If low-energy cutoffs exist in the mean electron spectra, the energy of low energy cutoffs should be less than $\sim$12 keV.Comment: 9 pages, 5 figures, submitted to Solar Physic

Differential cross section and recoil polarization measurements for the gamma p to K+ Lambda reaction using CLAS at Jefferson Lab

We present measurements of the differential cross section and Lambda recoil polarization for the gamma p to K+ Lambda reaction made using the CLAS detector at Jefferson Lab. These measurements cover the center-of-mass energy range from 1.62 to 2.84 GeV and a wide range of center-of-mass K+ production angles. Independent analyses were performed using the K+ p pi- and K+ p (missing pi -) final-state topologies; results from these analyses were found to exhibit good agreement. These differential cross section measurements show excellent agreement with previous CLAS and LEPS results and offer increased precision and a 300 MeV increase in energy coverage. The recoil polarization data agree well with previous results and offer a large increase in precision and a 500 MeV extension in energy range. The increased center-of-mass energy range that these data represent will allow for independent study of non-resonant K+ Lambda photoproduction mechanisms at all production angles.Comment: 22 pages, 16 figure

A Bayesian analysis of pentaquark signals from CLAS data

We examine the results of two measurements by the CLAS collaboration, one of which claimed evidence for a $\Theta^{+}$ pentaquark, whilst the other found no such evidence. The unique feature of these two experiments was that they were performed with the same experimental setup. Using a Bayesian analysis we find that the results of the two experiments are in fact compatible with each other, but that the first measurement did not contain sufficient information to determine unambiguously the existence of a $\Theta^{+}$. Further, we suggest a means by which the existence of a new candidate particle can be tested in a rigorous manner.Comment: 5 pages, 3 figure

Measurement of the nuclear multiplicity ratio for Ks0K^0_s hadronization at CLAS

The influence of cold nuclear matter on lepto-production of hadrons in semi-inclusive deep inelastic scattering is measured using the CLAS detector in Hall B at Jefferson Lab and a 5.014 GeV electron beam. We report the $K_s^0$ multiplicity ratios for targets of C, Fe, and Pb relative to deuterium as a function of the fractional virtual photon energy $z$ transferred to the $K_s^0$ and the transverse momentum squared $p_{T}^2$ of the $K_s^0$. We find that the multiplicity ratios for $K^0_s$ are reduced in the nuclear medium at high $z$ and low $p_{T}^2$, with a trend for the $K^0_s$ transverse momentum to be broadened in the nucleus for large $p_{T}^2$.Comment: Submitted to Phys. Lett.

Coherent Photoproduction of pi^+ from 3^He

We have measured the differential cross section for the $\gamma$$^3$He$\rightarrow \pi^+ t$ reaction. This reaction was studied using the CEBAF Large Acceptance Spectrometer (CLAS) at Jefferson Lab. Real photons produced with the Hall-B bremsstrahlung tagging system in the energy range from 0.50 to 1.55 GeV were incident on a cryogenic liquid $^3$He target. The differential cross sections for the $\gamma$$^3$He$\rightarrow \pi^+ t$ reaction were measured as a function of photon-beam energy and pion-scattering angle. Theoretical predictions to date cannot explain the large cross sections except at backward angles, showing that additional components must be added to the model.Comment: 11 pages, 16 figure