Uncertainties of predictions from parton distribution functions II: the Hessian method

We develop a general method to quantify the uncertainties of parton distribution functions and their physical predictions, with emphasis on incorporating all relevant experimental constraints. The method uses the Hessian formalism to study an effective chi-squared function that quantifies the fit between theory and experiment. Key ingredients are a recently developed iterative procedure to calculate the Hessian matrix in the difficult global analysis environment, and the use of parameters defined as components along appropriately normalized eigenvectors. The result is a set of 2d Eigenvector Basis parton distributions (where d=16 is the number of parton parameters) from which the uncertainty on any physical quantity due to the uncertainty in parton distributions can be calculated. We illustrate the method by applying it to calculate uncertainties of gluon and quark distribution functions, W boson rapidity distributions, and the correlation between W and Z production cross sections.Comment: 30 pages, Latex. Reference added. Normalization of Hessian matrix changed to HEP standar

Neutrino Dimuon Production and the Strangeness Asymmetry of the Nucleon

We have performed the first global QCD analysis to include the CCFR and NuTeV dimuon data, which provide direct constraints on the strange and anti-strange parton distributions, $s(x)$ and $\bar{s}(x)$. To explore the strangeness sector, we adopt a general parametrization of the non-perturbative $s(x), \bar{s}(x)$ functions satisfying basic QCD requirements. We find that the strangeness asymmetry, as represented by the momentum integral $[S^{-}]\equiv \int_0^1 x [s(x)-\bar{s}(x)] dx$, is sensitive to the dimuon data provided the theoretical QCD constraints are enforced. We use the Lagrange Multiplier method to probe the quality of the global fit as a function of $[S^-]$ and find $-0.001 < [S^-] < 0.004$. Representative parton distribution sets spanning this range are given. Comparisons with previous work are made.Comment: 23 pages, 4 figures; expanded version for publicatio

Association of Meniscal Status, Lower Extremity Alignment, and Body Mass Index With Chondrosis at Revision Anterior Cruciate Ligament Reconstruction

BACKGROUND: Knees undergoing revision anterior cruciate ligament reconstruction (rACLR) have a high prevalence of articular cartilage lesions. HYPOTHESIS: The prevalence of chondrosis at the time of rACLR is associated with meniscal status and lower extremity alignment. STUDY DESIGN: Cross-sectional study; Level of evidence, 3. METHODS: Data from the prospective Multicenter ACL Revision Study (MARS) cohort were reviewed to identify patients with preoperative lower extremity alignment films. Lower extremity alignment was defined by the weightbearing line (WBL) as a percentage of the tibial plateau width, while the chondral and meniscal status of each weightbearing compartment was recorded at the time of surgery. Multivariable proportional odds models were constructed and adjusted for relevant factors to examine which risk factors were independently associated with the degree of medial and lateral compartment chondrosis. RESULTS: The cohort included 246 patients with lower extremity alignment films at the time of rACLR. Mean (+/-SD) patient age was 26.9 +/- 9.5 years and body mass index (BMI) was 26.4 +/- 4.6. The medial compartment had more chondrosis (grade 2/3, 42%; grade 4, 6.5%) than did the lateral compartment (grade 2/3, 26%; grade 4, 6.5%). Disruption of the meniscus was noted in 35% of patients on the medial side and 16% in the lateral side. The mean WBL was 0.43 +/- 0.13. Medial compartment chondrosis was associated with BMI (P = .025), alignment (P = .002), and medial meniscal status (P = .001). None of the knees with the WBL lateral to 0.625 had grade 4 chondrosis in the medial compartment. Lateral compartment chondrosis was significantly associated with age (P = .013) and lateral meniscal status (P \u3c .001). Subjects with intact menisci were found to decrease their odds of having chondrosis by 64% to 84%. CONCLUSION: The status of articular cartilage in the tibiofemoral compartments at the time of rACLR is related to meniscal status. Lower extremity alignment and BMI are associated with medial compartment chondrosis

A simplified structure for the second order cosmological perturbation equations

Increasingly accurate observations of the cosmic microwave background and the large scale distribution of galaxies necessitate the study of nonlinear perturbations of Friedmann-Lemaitre cosmologies, whose equations are notoriously complicated. In this paper we present a new derivation of the governing equations for second order perturbations within the framework of the metric-based approach that is minimal, as regards amount of calculation and length of expressions, and flexible, as regards choice of gauge and stress-energy tensor. Because of their generality and the simplicity of their structure our equations provide a convenient starting point for determining the behaviour of nonlinear perturbations of FL cosmologies with any given stress-energy content, using either the Poisson gauge or the uniform curvature gauge.Comment: 30 pages, no figures. Changed title to the one in published version and some minor changes and addition