Numerically stable methods for quadratic programming

Numerically stable algorithms for quadratic programming are discussed. A new algorithm is described for indefinite quadratic programming which utilizes methods for updating positivedefinite factorizations only. Consequently all the updating procedures required are common to algorithms for linearly-constrained optimization. The new algorithm can be used for the positive-definite case without loss of efficiency.     

The computation of Lagrange-multiplier estimates for constrained minimization

Almost all efficient algorithms for constrained optimization require the repeated computation of Lagrange-multiplier estimates. In this paper we consider the difficulties in providing accurate estimates and what tests can be made in order to check the validity of the estimates obtained. A variety of formulae for the estimation of Lagrange multipliers are derived and their respective merits discussed. Finally the role of Lagrange multipliers within optimization algorithms is discussed and in addition to other results, it is shown that some algorithms are particularly sensitive to errors in the estimates.     

The synthesis and characterisation of some 2,7-diazaphenanthrene derivatives

2,7-Diazaphenanthrene was synthesised in moderate yield by the modified Pomeranz-Fritsch reaction by condensing diethoxyethanal with 1,4-benzenebismethanamine, followed by ring closure with 20% oleum, and its spectral characteristics recorded. A similar reaction with diethyl 1,4-benzenebis(3-aminopropanoate) gave either 2,7-diaza-1,8-dimethylphenanthrene or 2,7-diaza-1,8-phenanthrenebis(methylsulphonic acid), depending on the conditions of the ring closure reaction. The bis methiodides of these compounds were tested for phospholipase A₂ inhibitory action but were found to be inactive.     

Observation of B(+)-->phiphiK(+) and evidence for B(0)-->phiphiK(0) below eta(c) threshold

We report measurements of the decays B(+)-->phiphiK(+) and B(0)-->phiphiK(0) using a sample of 231 x 10(6) BB pairs collected with the BABAR detector at the PEP-II asymmetric-energy B factory at the Stanford Linear Accelerator Center. The branching fractions are measured to be B(B(+)-->phiphiK(+))=(7.5+/-1.0(stat)+/-0.7(syst)) x 10(-6) and B(B(0)-->phiphiK(0))=(4.1(-1.4)(+1.7)(stat)+/-0.4(syst)) x 10(-6) for a phiphi invariant mass below 2.85 GeV/c(2).     

Observation of an excited charm baryon Omega c* decaying to Omega c0gamma

We report the first observation of an excited singly charmed baryon Omega c* (css) in the radiative decay Omega c0gamma, where the Omega c0 baryon is reconstructed in the decays to the final states Omega(-)pi+, Omega(-)pi+pi0, Omega(-)pi+pi(-)pi+, and Xi(-)K(-)pi+pi+. This analysis is performed using a data set of 230.7 fb(-1) collected by the BABAR detector at the PEP-II asymmetric-energy B factory at the Stanford Linear Accelerator Center. The mass difference between the Omega c* and the Omega c0 baryons is measured to be 70.8+/-1.0(stat)+/-1.1(syst) MeV/c2. We also measure the ratio of inclusive production cross sections of Omega c* and Omega c0 in e+e(-) annihilation.     

Measurement of the B-->pi l nu branching fraction and determination of absolute value of V(ub) with tagged B mesons

We report a measurement of the B-->pi l nu branching fraction based on 211 fb(-1) of data collected with the BABAR detector. We use samples of B0 and B+ mesons tagged by a second B meson reconstructed in a semileptonic or hadronic decay and combine the results assuming isospin symmetry to obtain B(B(0)-->pi- l+ nu) = (1.33+/-0.17stat+/-0.11syst) x 10(-4). We determine the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element absolute value V(ub) by combining the partial branching fractions measured in ranges of the momentum transfer squared and theoretical calculations of the form factor. Using a recent lattice QCD calculation, we find absolute value V(ub) = (4.5+/-0.5stat+/-0.3syst(+0.7) -0.5FF x 10(-3), where the last error is due to the normalization of the form factor.     

Measurement of the branching fraction and photon energy moments of B-->Xs gamma and A(CP)(B --> X(s+d gamma))

The photon spectrum in B-->Xs gamma decay, where Xs is any strange hadronic state, is studied using a data sample of 88.5 x 10(6) e+ e- --> Upsilon(4S) --> BB decays collected by the BABAR experiment at the Stanford Linear Accelerator Center. The partial branching fraction, DeltaB(B --> Xs gamma) = (3.67+/-0.29(stat)+/-0.34(syst)+/-0.29(model)) x 10(-4), the first moment = 2.288+/-0.025+/-0.017+/-0.015 GeV, and the second moment E2(gamma) = 0.0328+/-0.0040+/-0.0023+/-0.0036 GeV2 are measured for the photon energy range 1.9 GeV < E gamma < 2.7 GeV. They are also measured for narrower E gamma ranges. The moments are then fit to recent theoretical calculations to extract the heavy quark expansion parameters m(b) and mu2(pi) and to extrapolate the partial branching fraction to E gamma > 1.6 GeV. In addition, the direct CP asymmetry A(CP)(B-->X(s+d gamma) is measured to be -0.110+/-0.115(stat)+/-0.017(syst).     

Peak alignment of urine NMR spectra using fuzzy warping

Proton nuclear magnetic resonance (1H NMR) spectroscopic analysis of mixtures has been used extensively for a variety of applications ranging from the analysis of plant extracts, wine, and food to the evaluation of toxicity in animals. For example, NMR analysis of urine samples has been used extensively for biomarker discovery and, more simply, for the construction of classification models of toxicity, disease, and biochemical phenotype. However, NMR spectra of complex mixtures typically show unwanted local peak shifts caused by matrix and instrument variability, which must be compensated for prior to statistical analysis and interpretation of the data. One approach is to align the spectral peaks across the data set. An efficient and fast warping algorithm is required as the signals typically contain ca. 32,000-64,000 data points and there can be several thousand spectra in a data set. As demonstrated in our study, the iterative fuzzy warping algorithm fulfills these requirements and can be used on-line for an alignment of the NMR spectra. Correlation coefficients between the aligned and target spectra are used as the evaluation function for the algorithm, and its performance is compared with those of other published warping methods.     

Uncovering the Neoproterozoic carbon cycle

Interpretations of major climatic and biological events in Earth history are, in large part, derived from the stable carbon isotope records of carbonate rocks and sedimentary organic matter. Neoproterozoic carbonate records contain unusual and large negative isotopic anomalies within long periods (10-100 million years) characterized by δ(13)C in carbonate (δ(13)C(carb)) enriched to more than +5 per mil. Classically, δ(13)C(carb) is interpreted as a metric of the relative fraction of carbon buried as organic matter in marine sediments, which can be linked to oxygen accumulation through the stoichiometry of primary production. If a change in the isotopic composition of marine dissolved inorganic carbon is responsible for these excursions, it is expected that records of δ(13)C(carb) and δ(13)C in organic carbon (δ(13)C(org)) will covary, offset by the fractionation imparted by primary production. The documentation of several Neoproterozoic δ(13)C(carb) excursions that are decoupled from δ(13)C(org), however, indicates that other mechanisms may account for these excursions. Here we present δ(13)C data from Mongolia, northwest Canada and Namibia that capture multiple large-amplitude (over 10 per mil) negative carbon isotope anomalies, and use these data in a new quantitative mixing model to examine the behaviour of the Neoproterozoic carbon cycle. We find that carbonate and organic carbon isotope data from Mongolia and Canada are tightly coupled through multiple δ(13)C(carb) excursions, quantitatively ruling out previously suggested alternative explanations, such as diagenesis or the presence and terminal oxidation of a large marine dissolved organic carbon reservoir. Our data from Namibia, which do not record isotopic covariance, can be explained by simple mixing with a detrital flux of organic matter. We thus interpret δ(13)C(carb) anomalies as recording a primary perturbation to the surface carbon cycle. This interpretation requires the revisiting of models linking drastic isotope excursions to deep ocean oxygenation and the opening of environments capable of supporting animals.