Functional equations from generating functions: a novel approach to deriving identities for the Bernstein basis functions

The main aim of this paper is to provide a novel approach to deriving identities for the Bernstein polynomials using functional equations. We derive various functional equations and differential equations using generating functions. Applying these equations, we give new proofs for some standard identities for the Bernstein basis functions, including formulas for sums, alternating sums, recursion, subdivision, degree raising, differentiation and a formula for the monomials in terms of the Bernstein basis functions. We also derive many new identities for the Bernstein basis functions based on this approach. Moreover, by applying the Laplace transform to the generating functions for the Bernstein basis functions, we obtain some interesting series representations for the Bernstein basis functions.Comment: 1

Impact of Vitamin D Supplementation on Arterial Vasomotion, Stiffness and Endothelial Biomarkers in Chronic Kidney Disease Patients

Background: Cardiovascular events are frequent and vascular endothelial function is abnormal in patients with chronic kidney disease (CKD). We demonstrated endothelial dysfunction with vitamin D deficiency in CKD patients; however the impact of cholecalciferol supplementation on vascular stiffness and vasomotor function, endothelial and bone biomarkers in CKD patients with low 25-hydroxy vitamin D [25(OH)D] is unknown, which this study investigated. Methods: We assessed non-diabetic patients with CKD stage 3/4, age 17–80 years and serum 25(OH)D ,75 nmol/L. Brachial artery Flow Mediated Dilation (FMD), Pulse Wave Velocity (PWV), Augmentation Index (AI) and circulating blood biomarkers were evaluated at baseline and at 16 weeks. Oral 300,000 units cholecalciferol was administered at baseline and 8-weeks. Results: Clinical characteristics of 26 patients were: age 50614 (mean61SD) years, eGFR 41611 ml/min/1.73 m2, males 73%, dyslipidaemia 36%, smokers 23% and hypertensives 87%. At 16-week serum 25(OH)D and calcium increased (43616 to 84629 nmol/L, p,0.001 and 2.3760.09 to 2.4260.09 mmol/L; p = 0.004, respectively) and parathyroid hormone decreased (10.868.6 to 7.464.4; p = 0.001). FMD improved from 3.163.3% to 6.163.7%, p = 0.001. Endothelial biomarker concentrations decreased: E-Selectin from 566662123 to 525662058 pg/mL; p = 0.032, ICAM-1, 3.4560.01 to 3.1061.04 ng/mL; p = 0.038 and VCAM-1, 54633 to 42633 ng/mL; p = 0.006. eGFR, BP, PWV, AI, hsCRP, von Willebrand factor and Fibroblast Growth Factor-23, remained unchanged. Conclusion: This study demonstrates for the first time improvement of endothelial vasomotor and secretory functions with vitamin D in CKD patients without significant adverse effects on arterial stiffness, serum calcium or FGF-23. Trial Registration: ClinicalTrials.gov NCT0200571

Intercalated theophylline-smectite hybrid for pH-mediated delivery

On the basis of their large specific surface areas, high adsorption and cation exchange capacities, swelling potential and low toxicity, natural smectite clays are attractive substrates for the gastric protection of neutral and cationic drugs. Theophylline is an amphoteric xanthine derivative that is widely used as a bronchodilator in the treatment of asthma and chronic obstructive pulmonary disease. This study considers the in vitro uptake and release characteristics of the binary theophylline-smectite system. The cationic form of theophylline was readily ion exchanged into smectite clay at pH 1.2 with a maximum uptake of 67±2 mg g−1. Characterisation of the drug-clay hybrid system by powder X-ray diffraction analysis, Fourier transform infrared spectroscopy, differential scanning calorimetry and scanning electron microscopy confirmed that the theophylline had been exclusively intercalated into the clay system in an amorphous form. The drug remained bound within the clay under simulated gastric conditions at pH 1.2; and the prolonged release of approximately 40% of the drug was observed in simulated intestinal fluid at pH 6.8 and 7.4 within a 2-h timeframe. The incomplete reversibility of the intercalation process was attributed to chemisorption of the drug within the clay lattice. These findings indicate that smectite clay is a potentially suitable vehicle for the safe passage of theophylline into the duodenum. Protection from absorption in the stomach and subsequent prolonged release in the small intestine are advantageous in reducing fluctuations in serum concentration which may impact therapeutic effect and toxicit

Pten dependence distinguishes haematopoietic stem cells from leukaemia-initiating cells

Recent advances have highlighted extensive phenotypic and functional similarities between normal stem cells and cancer stem cells. This raises the question of whether disease therapies can be developed that eliminate cancer stem cells without eliminating normal stem cells. Here we address this issue by conditionally deleting the Pten tumour suppressor gene in adult haematopoietic cells. This led to myeloproliferative disease within days and transplantable leukaemias within weeks. Pten deletion also promoted haematopoietic stem cell (HSC) proliferation. However, this led to HSC depletion via a cell-autonomous mechanism, preventing these cells from stably reconstituting irradiated mice. In contrast to leukaemia-initiating cells, HSCs were therefore unable to maintain themselves without Pten. These effects were mostly mediated by mTOR as they were inhibited by rapamycin. Rapamycin not only depleted leukaemia-initiating cells but also restored normal HSC function. Mechanistic differences between normal stem cells and cancer stem cells can thus be targeted to deplete cancer stem cells without damaging normal stem cells.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/62514/1/nature04703.pd

Studying the Underlying Event in Drell-Yan and High Transverse Momentum Jet Production at the Tevatron

We study the underlying event in proton-antiproton collisions by examining the behavior of charged particles (transverse momentum pT > 0.5 GeV/c, pseudorapidity |\eta| < 1) produced in association with large transverse momentum jets (~2.2 fb-1) or with Drell-Yan lepton-pairs (~2.7 fb-1) in the Z-boson mass region (70 < M(pair) < 110 GeV/c2) as measured by CDF at 1.96 TeV center-of-mass energy. We use the direction of the lepton-pair (in Drell-Yan production) or the leading jet (in high-pT jet production) in each event to define three regions of \eta-\phi space; toward, away, and transverse, where \phi is the azimuthal scattering angle. For Drell-Yan production (excluding the leptons) both the toward and transverse regions are very sensitive to the underlying event. In high-pT jet production the transverse region is very sensitive to the underlying event and is separated into a MAX and MIN transverse region, which helps separate the hard component (initial and final-state radiation) from the beam-beam remnant and multiple parton interaction components of the scattering. The data are corrected to the particle level to remove detector effects and are then compared with several QCD Monte-Carlo models. The goal of this analysis is to provide data that can be used to test and improve the QCD Monte-Carlo models of the underlying event that are used to simulate hadron-hadron collisions.Comment: Submitted to Phys.Rev.

Measurement of the W+W−W^+W^- Production Cross Section and Search for Anomalous WWγWW\gamma and WWZWWZ Couplings in ppˉp \bar p Collisions at s=1.96\sqrt{s} = 1.96 TeV

This Letter describes the current most precise measurement of the $W$ boson pair production cross section and most sensitive test of anomalous $WW\gamma$ and $WWZ$ couplings in $p \bar p$ collisions at a center-of-mass energy of 1.96 TeV. The $WW$ candidates are reconstructed from decays containing two charged leptons and two neutrinos, where the charged leptons are either electrons or muons. Using data collected by the CDF II detector from 3.6 fb$^{-1}$ of integrated luminosity, a total of 654 candidate events are observed with an expected background contribution of $320 \pm 47$ events. The measured total cross section is $\sigma (p \bar p \to W^+ W^- + X) = 12.1 \pm 0.9 \textrm{(stat)} ^{+1.6}_{-1.4} \textrm{(syst)}$ pb, which is in good agreement with the standard model prediction. The same data sample is used to place constraints on anomalous $WW\gamma$ and $WWZ$ couplings.Comment: submitted to Phys. Rev. Let

Jet energy measurement with the ATLAS detector in proton-proton collisions at root s=7 TeV

The jet energy scale and its systematic uncertainty are determined for jets measured with the ATLAS detector at the LHC in proton-proton collision data at a centre-of-mass energy of √s = 7TeV corresponding to an integrated luminosity of 38 pb-1. Jets are reconstructed with the anti-kt algorithm with distance parameters R=0. 4 or R=0. 6. Jet energy and angle corrections are determined from Monte Carlo simulations to calibrate jets with transverse momenta pT≥20 GeV and pseudorapidities {pipe}η{pipe}<4. 5. The jet energy systematic uncertainty is estimated using the single isolated hadron response measured in situ and in test-beams, exploiting the transverse momentum balance between central and forward jets in events with dijet topologies and studying systematic variations in Monte Carlo simulations. The jet energy uncertainty is less than 2. 5 % in the central calorimeter region ({pipe}η{pipe}<0. 8) for jets with 60≤pT<800 GeV, and is maximally 14 % for pT<30 GeV in the most forward region 3. 2≤{pipe}η{pipe}<4. 5. The jet energy is validated for jet transverse momenta up to 1 TeV to the level of a few percent using several in situ techniques by comparing a well-known reference such as the recoiling photon pT, the sum of the transverse momenta of tracks associated to the jet, or a system of low-pT jets recoiling against a high-pT jet. More sophisticated jet calibration schemes are presented based on calorimeter cell energy density weighting or hadronic properties of jets, aiming for an improved jet energy resolution and a reduced flavour dependence of the jet response. The systematic uncertainty of the jet energy determined from a combination of in situ techniques is consistent with the one derived from single hadron response measurements over a wide kinematic range. The nominal corrections and uncertainties are derived for isolated jets in an inclusive sample of high-pT jets. Special cases such as event topologies with close-by jets, or selections of samples with an enhanced content of jets originating from light quarks, heavy quarks or gluons are also discussed and the corresponding uncertainties are determined. © 2013 CERN for the benefit of the ATLAS collaboration

Measurement of the inclusive and dijet cross-sections of b-jets in pp collisions at sqrt(s) = 7 TeV with the ATLAS detector

The inclusive and dijet production cross-sections have been measured for jets containing b-hadrons (b-jets) in proton-proton collisions at a centre-of-mass energy of sqrt(s) = 7 TeV, using the ATLAS detector at the LHC. The measurements use data corresponding to an integrated luminosity of 34 pb^-1. The b-jets are identified using either a lifetime-based method, where secondary decay vertices of b-hadrons in jets are reconstructed using information from the tracking detectors, or a muon-based method where the presence of a muon is used to identify semileptonic decays of b-hadrons inside jets. The inclusive b-jet cross-section is measured as a function of transverse momentum in the range 20 < pT < 400 GeV and rapidity in the range |y| < 2.1. The bbbar-dijet cross-section is measured as a function of the dijet invariant mass in the range 110 < m_jj < 760 GeV, the azimuthal angle difference between the two jets and the angular variable chi in two dijet mass regions. The results are compared with next-to-leading-order QCD predictions. Good agreement is observed between the measured cross-sections and the predictions obtained using POWHEG + Pythia. MC@NLO + Herwig shows good agreement with the measured bbbar-dijet cross-section. However, it does not reproduce the measured inclusive cross-section well, particularly for central b-jets with large transverse momenta.Comment: 10 pages plus author list (21 pages total), 8 figures, 1 table, final version published in European Physical Journal

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

Measurement of the Forward-Backward Asymmetry in the B -> K(*) mu+ mu- Decay and First Observation of the Bs -> phi mu+ mu- Decay

We reconstruct the rare decays $B^+ \to K^+\mu^+\mu^-$, $B^0 \to K^{*}(892)^0\mu^+\mu^-$, and $B^0_s \to \phi(1020)\mu^+\mu^-$ in a data sample corresponding to $4.4 {\rm fb^{-1}}$ collected in $p\bar{p}$ collisions at $\sqrt{s}=1.96 {\rm TeV}$ by the CDF II detector at the Fermilab Tevatron Collider. Using $121 \pm 16$ $B^+ \to K^+\mu^+\mu^-$ and $101 \pm 12$ $B^0 \to K^{*0}\mu^+\mu^-$ decays we report the branching ratios. In addition, we report the measurement of the differential branching ratio and the muon forward-backward asymmetry in the $B^+$ and $B^0$ decay modes, and the $K^{*0}$ longitudinal polarization in the $B^0$ decay mode with respect to the squared dimuon mass. These are consistent with the theoretical prediction from the standard model, and most recent determinations from other experiments and of comparable accuracy. We also report the first observation of the $B^0_s \to \phi\mu^+\mu^- decay and measure its branching ratio${\mathcal{B}}(B^0_s \to \phi\mu^+\mu^-) = [1.44 \pm 0.33 \pm 0.46] \times 10^{-6}$using$27 \pm 6$signal events. This is currently the most rare$B^0_s$ decay observed.Comment: 7 pages, 2 figures, 3 tables. Submitted to Phys. Rev. Let