DISTRIBUTION FUNCTIONS, MEAN SQUARED ERRORS, AND CONFIDENCE LIMITS FOR RIDGE REGRESSION ESTIMATORS

A large number of ridge regression estimators have been proposed and used with little knowledge of their true distributions. Because of this lack of knowledge, these estimators cannot be used to test hypotheses or to form confidence intervals.^ This paper presents a basic technique for deriving the exact distribution functions for a class of generalized ridge estimators. The technique is applied to five prominent generalized ridge estimators. Graphs of the resulting distribution functions are presented. The actual behavior of these estimators is found to be considerably different than the behavior which is generally assumed for ridge estimators.^ This paper also uses the derived distributions to examine the mean squared error properties of the estimators. A technique for developing confidence intervals based on the generalized ridge estimators is also presented. ^

An adaptive algorithm for clustering cumulative probability distribution functions using the Kolmogorov–Smirnov two-sample test

This paper proposes an adaptive algorithm for clustering cumulative probability distribution functions (c.p.d.f.) of a continuous random variable, observed in different populations, into the minimum homogeneous clusters, making no parametric assumptions about the c.p.d.f.’s. The distance function for clustering c.p.d.f.’s that is proposed is based on the Kolmogorov–Smirnov two sample statistic. This test is able to detect differences in position, dispersion or shape of the c.p.d.f.’s. In our context, this statistic allows us to cluster the recorded data with a homogeneity criterion based on the whole distribution of each data set, and to decide whether it is necessary to add more clusters or not. In this sense, the proposed algorithm is adaptive as it automatically increases the number of clusters only as necessary; therefore, there is no need to fix in advance the number of clusters. The output of the algorithm are the common c.p.d.f. of all observed data in the cluster (the centroid) and, for each cluster, the Kolmogorov–Smirnov statistic between the centroid and the most distant c.p.d.f. The proposed algorithm has been used for a large data set of solar global irradiation spectra distributions. The results obtained enable to reduce all the information of more than 270,000 c.p.d.f.’s in only 6 different clusters that correspond to 6 different c.p.d.f.’s.

Characterization of time-resolved laser differential phase using 3D complementary cumulative distribution functions

An experimental method for characterizing the time-resolved phase noise of a fast switching tunable laser is discussed. The method experimentally determines a complementary cumulative distribution function of the laser's differential phase as a function of time after a switching event. A time resolved bit error rate of differential quadrature phase shift keying formatted data, calculated using the phase noise measurements, was fitted to an experimental time-resolved bit error rate measurement using a field programmable gate array, finding a good agreement between the time-resolved bit error rates.

Cross section and double helicity asymmetry for eta mesons and their comparison to pi(0) production in p plus p collisions at root s=200 GeV

Measurements of double-helicity asymmetries in inclusive hadron production in polarized p + p collisions are sensitive to helicity-dependent parton distribution functions, in particular, to the gluon helicity distribution, Delta g. This study focuses on the extraction of the double-helicity asymmetry in eta production ((p) over right arrow + (p) over right arrow -> eta + X), the eta cross section, and the eta/pi(0) cross section ratio. The cross section and ratio measurements provide essential input for the extraction of fragmentation functions that are needed to access the helicity-dependent parton distribution functions.

Simultaneous measurements of the tt¯, W+W−, and Z/γ∗→ττ production cross-sections in pp collisions at s√=7 TeV with the ATLAS detector

Simultaneous measurements of the tt¯, W+W−, and Z/γ∗→ττ production cross-sections using an integrated luminosity of 4.6 fb−1 of pp collisions at s√=7 TeV collected by the ATLAS detector at the LHC are presented. Events are selected with two high transverse momentum leptons consisting of an oppositely charged electron and muon pair. The three processes are separated using the distributions of the missing transverse momentum of events with zero and greater than zero jet multiplicities. Measurements of the fiducial cross-section are presented along with results that quantify for the first time the underlying correlations in the predicted and measured cross-sections due to proton parton distribution functions. These results indicate that the correlated NLO predictions for tt¯ and Z/γ∗→ττ significantly underestimate the data, while those at NNLO generally describe the data well. The full cross-sections are measured to be σ(tt¯)=181.2±2.8+9.7−9.5±3.3±3.3 pb, σ(W+W−)=53.3±2.7+7.3−8.0±1.0±0.5 pb, and σ(Z/γ∗→ττ)=1174±24+72−87±21±9 pb, where the cited uncertainties are due to statistics, systematic effects, luminosity and the LHC beam energy measurement, respectively.

Measurement of the inclusive jet cross-section in proton--proton collisions at s√=7 TeV using 4.5 fb−1 of data with the ATLAS detector

The inclusive jet cross-section is measured in proton--proton collisions at a centre-of-mass energy of 7 TeV using a data set corresponding to an integrated luminosity of 4.5 fb−1 collected with the ATLAS detector at the Large Hadron Collider in 2011. Jets are identified using the anti-kt algorithm with radius parameter values of 0.4 and 0.6. The double-differential cross-sections are presented as a function of the jet transverse momentum and the jet rapidity, covering jet transverse momenta from 100 GeV to 2 TeV. Next-to-leading-order QCD calculations corrected for non-perturbative effects and electroweak effects, as well as Monte Carlo simulations with next-to-leading-order matrix elements interfaced to parton showering, are compared to the measured cross-sections. A quantitative comparison of the measured cross-sections to the QCD calculations using several sets of parton distribution functions is performed.

Measurement of the production and lepton charge asymmetry of W bosons in Pb plus Pb collisions at root s(NN)=2.76 TeV with the ATLAS detec

A measurement of W boson production in lead-lead collisions at sNN−−−√=2.76 TeV is presented. It is based on the analysis of data collected with the ATLAS detector at the LHC in 2011 corresponding to an integrated luminosity of 0.14 nb−1 and 0.15 nb−1 in the muon and electron decay channels, respectively. The differential production cross-sections and lepton charge asymmetry are each measured as a function of the average number of participating nucleons ⟨Npart⟩ and absolute pseudorapidity of the charged lepton. The results are compared to predictions based on next-to-leading-order QCD calculations. These measurements are, in principle, sensitive to possible nuclear modifications to the parton distribution functions and also provide information on scaling of W boson production in multi-nucleon systems.

Measurement of three-jet production cross-sections in pp collisions at 7 TeV centre-of-mass energy using the ATLAS detector

Double-differential three-jet production cross-sections are measured in proton--proton collisions at a centre-of-mass energy of s√=7TeV using the ATLAS detector at the Large Hadron Collider. The measurements are presented as a function of the three-jet mass (mjjj), in bins of the sum of the absolute rapidity separations between the three leading jets (|Y∗|). Invariant masses extending up to 5 TeV are reached for 8<|Y∗|<10. These measurements use a sample of data recorded using the ATLAS detector in 2011, which corresponds to an integrated luminosity of 4.51fb−1. Jets are identified using the anti-kt algorithm with two different jet radius parameters, R=0.4 and R=0.6. The dominant uncertainty in these measurements comes from the jet energy scale. Next-to-leading-order QCD calculations corrected to account for non-perturbative effects are compared to the measurements. Good agreement is found between the data and the theoretical predictions based on most of the available sets of parton distribution functions, over the full kinematic range, covering almost seven orders of magnitude in the measured cross-section values.

Could saturation effects be visible in a future electron-ion collider?

We expect to observe parton saturation in a future electron-ion collider. In this Letter we discuss this expectation in more detail considering two different models which are in good agreement with the existing experimental data on nuclear structure functions. In particular, we study the predictions of saturation effects in electron-ion collisions at high energies, using a generalization for nuclear targets of the b-CGC model, which describes the ep HERA quite well. We estimate the total. longitudinal and charm structure functions in the dipole picture and compare them with the predictions obtained using collinear factorization and modern sets of nuclear parton distributions. Our results show that inclusive observables are not very useful in the search for saturation effects. In the small x region they are very difficult to disentangle from the predictions of the collinear approaches. This happens mainly because of the large uncertainties in the determination of the nuclear parton distribution functions. On the other hand, our results indicate that the contribution of diffractive processes to the total cross section is about 20% at large A and small Q(2), allowing for a detailed study of diffractive observables. The study of diffractive processes becomes essential to observe parton Saturation. (C) 2008 Elsevier B.V. All rights reserved.

Quark distributions in a medium

We derive the formal expressions needed to discuss the change of the twist-two parton distribution functions when a hadron is placed in a medium with relativistic scalar and vector mean fields. (C) 2004 Elsevier B.V. All rights reserved.

Measurement of the differential cross section for the production of an isolated photon with associated jet in p(p)over-bar collisions at root s=1.96 TeV

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Collective Perspective on Advances in Dyson-Schwinger Equation QCD

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Measurement of three-jet differential cross sections d sigma(3jet)/dM(3jet) in p(p)over-bar collisions at root s=1.96 TeV

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Measurement of the muon charge asymmetry from W boson decays

We present a measurement of the muon charge asymmetry from W boson decays using 0.3 fb(-1) of data collected at root s =1.96 GeV between 2002 and 2004 with the D0 detector at the Fermilab Tevatron (p) over bar Collider. We compare our findings with expectations from next-to-leading-order calculations performed using the CTEQ6.1M and MRST04 NLO parton distribution functions. Our findings can be used to constrain future parton distribution function fits.

Measurement of the top quark mass in final states with two leptons

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)