The third moment of quadratic Dirichlet L-functions

We study the third moment of quadratic Dirichlet L-functions, obtaining an error term of size $O(X^{3/4 + \varepsilon})$.Comment: 27 pages. v2: modified a remark on p.

A generalization of the Bombieri-Pila determinant method

The so-called determinant method was developed by Bombieri and Pila in 1989 for counting integral points of bounded height on affine plane curves. In this paper we give a generalization of that method to varieties of higher dimension, yielding a proof of Heath-Brown's 'Theorem 14' by real-analytic considerations alone.Comment: 13 page

Mixed sums of primes and other terms

In this paper we study mixed sums of primes and linear recurrences. We show that if m=2(mod 4) and m+1 is a prime then $(m^{2^n-1}-1)/(m-1)\not=m^n+p^a$ for any n=3,4,... and prime power p^a. We also prove that if a>1 is an integer, u_0=0, u_1=1 and u_{i+1}=au_i+u_{i-1} for i=1,2,3,..., then all the sums u_m+au_n (m,n=1,2,3,...) are distinct. One of our conjectures states that any integer n>4 can be written as the sum of an odd prime, an odd Fibonacci number and a positive Fibonacci number.Comment: 11 page

Evidence for the classical integrability of the complete AdS(4) x CP(3) superstring

We construct a zero-curvature Lax connection in a sub-sector of the superstring theory on AdS(4) x CP(3) which is not described by the OSp(6|4)/U(3) x SO(1,3) supercoset sigma-model. In this sub-sector worldsheet fermions associated to eight broken supersymmetries of the type IIA background are physical fields. As such, the prescription for the construction of the Lax connection based on the Z_4-automorphism of the isometry superalgebra OSp(6|4) does not do the job. So, to construct the Lax connection we have used an alternative method which nevertheless relies on the isometry of the target superspace and kappa-symmetry of the Green-Schwarz superstring.Comment: 1+26 pages; v2: minor typos corrected, acknowledgements adde

Utilisation of an operative difficulty grading scale for laparoscopic cholecystectomy

Background A reliable system for grading operative difficulty of laparoscopic cholecystectomy would standardise description of findings and reporting of outcomes. The aim of this study was to validate a difficulty grading system (Nassar scale), testing its applicability and consistency in two large prospective datasets. Methods Patient and disease-related variables and 30-day outcomes were identified in two prospective cholecystectomy databases: the multi-centre prospective cohort of 8820 patients from the recent CholeS Study and the single-surgeon series containing 4089 patients. Operative data and patient outcomes were correlated with Nassar operative difficultly scale, using Kendall’s tau for dichotomous variables, or Jonckheere–Terpstra tests for continuous variables. A ROC curve analysis was performed, to quantify the predictive accuracy of the scale for each outcome, with continuous outcomes dichotomised, prior to analysis. Results A higher operative difficulty grade was consistently associated with worse outcomes for the patients in both the reference and CholeS cohorts. The median length of stay increased from 0 to 4 days, and the 30-day complication rate from 7.6 to 24.4% as the difficulty grade increased from 1 to 4/5 (both p < 0.001). In the CholeS cohort, a higher difficulty grade was found to be most strongly associated with conversion to open and 30-day mortality (AUROC = 0.903, 0.822, respectively). On multivariable analysis, the Nassar operative difficultly scale was found to be a significant independent predictor of operative duration, conversion to open surgery, 30-day complications and 30-day reintervention (all p < 0.001). Conclusion We have shown that an operative difficulty scale can standardise the description of operative findings by multiple grades of surgeons to facilitate audit, training assessment and research. It provides a tool for reporting operative findings, disease severity and technical difficulty and can be utilised in future research to reliably compare outcomes according to case mix and intra-operative difficulty

Tobacco and the risk of acute leukaemia in adults

Self-reported smoking histories were collected during face-to-face interviews with 807 patients with acute leukaemia and 1593 age- and sex-matched controls. Individuals who had smoked regularly at some time during their lives were more likely to develop acute leukaemia than those who had never smoked (odds ratio (OR) = 1.2, 95% confidence interval (CI) 1.0–1.4). The association was strongest for current smokers, defined here as smoking 2 years before diagnosis (OR = 1.4, 95% CI 1.1–1.7). With respect to the numbers of years smoked, risk estimates were raised in all groups except those who had smoked for fewer than 10 years. Similarly, the odds ratio decreased as the number of years ‘stopped smoking’ increased, falling to one amongst those who had given up smoking for more than 10 years. No significant linear trends were found, however, with either the numbers of years smoked or the numbers of years stopped smoking, and no significant differences were found between AML and ALL. © 1999 Cancer Research Campaig

Performance of CMS muon reconstruction in pp collision events at sqrt(s) = 7 TeV

The performance of muon reconstruction, identification, and triggering in CMS has been studied using 40 inverse picobarns of data collected in pp collisions at sqrt(s) = 7 TeV at the LHC in 2010. A few benchmark sets of selection criteria covering a wide range of physics analysis needs have been examined. For all considered selections, the efficiency to reconstruct and identify a muon with a transverse momentum pT larger than a few GeV is above 95% over the whole region of pseudorapidity covered by the CMS muon system, abs(eta) < 2.4, while the probability to misidentify a hadron as a muon is well below 1%. The efficiency to trigger on single muons with pT above a few GeV is higher than 90% over the full eta range, and typically substantially better. The overall momentum scale is measured to a precision of 0.2% with muons from Z decays. The transverse momentum resolution varies from 1% to 6% depending on pseudorapidity for muons with pT below 100 GeV and, using cosmic rays, it is shown to be better than 10% in the central region up to pT = 1 TeV. Observed distributions of all quantities are well reproduced by the Monte Carlo simulation.Comment: Replaced with published version. Added journal reference and DO

Performance of CMS muon reconstruction in pp collision events at sqrt(s) = 7 TeV

The performance of muon reconstruction, identification, and triggering in CMS has been studied using 40 inverse picobarns of data collected in pp collisions at sqrt(s) = 7 TeV at the LHC in 2010. A few benchmark sets of selection criteria covering a wide range of physics analysis needs have been examined. For all considered selections, the efficiency to reconstruct and identify a muon with a transverse momentum pT larger than a few GeV is above 95% over the whole region of pseudorapidity covered by the CMS muon system, abs(eta) < 2.4, while the probability to misidentify a hadron as a muon is well below 1%. The efficiency to trigger on single muons with pT above a few GeV is higher than 90% over the full eta range, and typically substantially better. The overall momentum scale is measured to a precision of 0.2% with muons from Z decays. The transverse momentum resolution varies from 1% to 6% depending on pseudorapidity for muons with pT below 100 GeV and, using cosmic rays, it is shown to be better than 10% in the central region up to pT = 1 TeV. Observed distributions of all quantities are well reproduced by the Monte Carlo simulation.Comment: Replaced with published version. Added journal reference and DO

X-ray emission from the Sombrero galaxy: discrete sources

We present a study of discrete X-ray sources in and around the bulge-dominated, massive Sa galaxy, Sombrero (M104), based on new and archival Chandra observations with a total exposure of ~200 ks. With a detection limit of L_X = 1E37 erg/s and a field of view covering a galactocentric radius of ~30 kpc (11.5 arcminute), 383 sources are detected. Cross-correlation with Spitler et al.'s catalogue of Sombrero globular clusters (GCs) identified from HST/ACS observations reveals 41 X-rays sources in GCs, presumably low-mass X-ray binaries (LMXBs). We quantify the differential luminosity functions (LFs) for both the detected GC and field LMXBs, whose power-low indices (~1.1 for the GC-LF and ~1.6 for field-LF) are consistent with previous studies for elliptical galaxies. With precise sky positions of the GCs without a detected X-ray source, we further quantify, through a fluctuation analysis, the GC LF at fainter luminosities down to 1E35 erg/s. The derived index rules out a faint-end slope flatter than 1.1 at a 2 sigma significance, contrary to recent findings in several elliptical galaxies and the bulge of M31. On the other hand, the 2-6 keV unresolved emission places a tight constraint on the field LF, implying a flattened index of ~1.0 below 1E37 erg/s. We also detect 101 sources in the halo of Sombrero. The presence of these sources cannot be interpreted as galactic LMXBs whose spatial distribution empirically follows the starlight. Their number is also higher than the expected number of cosmic AGNs (52+/-11 [1 sigma]) whose surface density is constrained by deep X-ray surveys. We suggest that either the cosmic X-ray background is unusually high in the direction of Sombrero, or a distinct population of X-ray sources is present in the halo of Sombrero.Comment: 11 figures, 5 tables, ApJ in pres

Azimuthal anisotropy of charged particles at high transverse momenta in PbPb collisions at sqrt(s[NN]) = 2.76 TeV

The azimuthal anisotropy of charged particles in PbPb collisions at nucleon-nucleon center-of-mass energy of 2.76 TeV is measured with the CMS detector at the LHC over an extended transverse momentum (pt) range up to approximately 60 GeV. The data cover both the low-pt region associated with hydrodynamic flow phenomena and the high-pt region where the anisotropies may reflect the path-length dependence of parton energy loss in the created medium. The anisotropy parameter (v2) of the particles is extracted by correlating charged tracks with respect to the event-plane reconstructed by using the energy deposited in forward-angle calorimeters. For the six bins of collision centrality studied, spanning the range of 0-60% most-central events, the observed v2 values are found to first increase with pt, reaching a maximum around pt = 3 GeV, and then to gradually decrease to almost zero, with the decline persisting up to at least pt = 40 GeV over the full centrality range measured.Comment: Replaced with published version. Added journal reference and DO