Fast divide-and-conquer algorithms for preemptive scheduling problems with controllable processing times – A polymatroid optimization approach

We consider a variety of preemptive scheduling problems with controllable processing times on a single machine and on identical/uniform parallel machines, where the objective is to minimize the total compression cost. In this paper, we propose fast divide-and-conquer algorithms for these scheduling problems. Our approach is based on the observation that each scheduling problem we discuss can be formulated as a polymatroid optimization problem. We develop a novel divide-and-conquer technique for the polymatroid optimization problem and then apply it to each scheduling problem. We show that each scheduling problem can be solved in O(Tfeas(n) log n) time by using our divide-and-conquer technique, where n is the number of jobs and Tfeas(n) denotes the time complexity of the corresponding feasible scheduling problem with n jobs. This approach yields faster algorithms for most of the scheduling problems discussed in this paper

Effective interaction between helical bio-molecules

The effective interaction between two parallel strands of helical bio-molecules, such as deoxyribose nucleic acids (DNA), is calculated using computer simulations of the "primitive" model of electrolytes. In particular we study a simple model for B-DNA incorporating explicitly its charge pattern as a double-helix structure. The effective force and the effective torque exerted onto the molecules depend on the central distance and on the relative orientation. The contributions of nonlinear screening by monovalent counterions to these forces and torques are analyzed and calculated for different salt concentrations. As a result, we find that the sign of the force depends sensitively on the relative orientation. For intermolecular distances smaller than $6\AA$ it can be both attractive and repulsive. Furthermore we report a nonmonotonic behaviour of the effective force for increasing salt concentration. Both features cannot be described within linear screening theories. For large distances, on the other hand, the results agree with linear screening theories provided the charge of the bio-molecules is suitably renormalized.Comment: 18 pages, 18 figures included in text, 100 bibliog

Heavy baryon properties with NLO accuracy in perturbative QCD

We present an analysis of the static properties of heavy baryons at next-to-leading order in the perurbative expansion of QCD. We obtain analytical next-to-leading order three-loop results for the two-point correlators of baryonic currents with one finite mass quark field for a variety of quantum numbers of the baryonic currents. We consider both the massless limit and the HQET limit of the correlator as special cases of the general finite mass formula and find agreement with previous results. We present closed form expressions for the moments of the spectral density. We determine the residues of physical baryon states using sum rule techniques.Comment: 43 pages in LaTeX, including 3 figure

Solutions of the Two-Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms

Numerical results for ground-state and excited-state properties (energies, double occupancies, and Matsubara-axis self-energies) of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an assessment of our ability to compute accurate results in the thermodynamic limit. Many methods are employed, including auxiliary-field quantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method of dual fermions, density matrix embedding theory, density matrix renormalization group, dynamical cluster approximation, diffusion Monte Carlo within a fixed-node approximation, unrestricted coupled cluster theory, and multireference projected Hartree-Fock methods. Comparison of results obtained by different methods allows for the identification of uncertainties and systematic errors. The importance of extrapolation to converged thermodynamic-limit values is emphasized. Cases where agreement between different methods is obtained establish benchmark results that may be useful in the validation of new approaches and the improvement of existing methods

Transverse spin effects in hadron-pair production from semi-inclusive deep inelastic scattering

First measurements of azimuthal asymmetries in hadron-pair production in deep-inelastic scattering of muons on transversely polarised ^6LiD (deuteron) and NH_3 (proton) targets are presented. The data were taken in the years 2002-2004 and 2007 with the COMPASS spectrometer using a muon beam of 160 GeV/c at the CERN SPS. The asymmetries provide access to the transversity distribution functions, without involving the Collins effect as in single hadron production. The sizeable asymmetries measured on the NH_ target indicate non-vanishing u-quark transversity and two-hadron interference fragmentation functions. The small asymmetries measured on the ^6LiD target can be interpreted as indication for a cancellation of u- and d-quark transversities.Comment: 13 pages, 4 figures, updated to the published versio

The Spin-dependent Structure Function of the Proton g_1^p and a Test of the Bjorken Sum Rule

The inclusive double-spin asymmetry, A_1^p, has been measured at COMPASS in deepinelastic polarised muon scattering off a large polarised NH3 target. The data, collected in the year 2007, cover the range Q2 > 1 (GeV/c)^2, 0.004 < x < 0.7 and improve the statistical precision of g_1^p(x) by a factor of two in the region x < 0.02. The new proton asymmetries are combined with those previously published for the deuteron to extract the non-singlet spin-dependent structure function g_1^NS(x,Q2). The isovector quark density, Delta_q_3(x,Q2), is evaluated from a NLO QCD fit of g_1^NS. The first moment of Delta_q3 is in good agreement with the value predicted by the Bjorken sum rule and corresponds to a ratio of the axial and vector coupling constants g_A/g_V = 1.28+-0.07(stat)+-0.10(syst).Comment: 12 pages, 5 figure

Leading order determination of the gluon polarisation from DIS events with high-p_T hadron pairs

We present a determination of the gluon polarisation Delta g/g in the nucleon, based on the longitudinal double-spin asymmetry of DIS events with a pair of large transverse-momentum hadrons in the final state. The data were obtained by the COMPASS experiment at CERN using a 160 GeV/c polarised muon beam scattering off a polarised ^6LiD target. The gluon polarisation is evaluated by a Neural Network approach for three intervals of the gluon momentum fraction x_g covering the range 0.04 < x_g < 0.27. The values obtained at leading order in QCD do not show any significant dependence on x_g. Their average is Delta g/g = 0.125 +/- 0.060 (stat.) +/- 0.063 (syst.) at x_g=0.09 and a scale of mu^2 = 3 (GeV/c)^2.Comment: 13 pages, 6 figures and 3 table

Experimental investigation of transverse spin asymmetries in muon-p SIDIS processes: Collins asymmetries

The COMPASS Collaboration at CERN has measured the transverse spin azimuthal asymmetry of charged hadrons produced in semi-inclusive deep inelastic scattering using a 160 GeV positive muon beam and a transversely polarised NH_3 target. The Collins asymmetry of the proton was extracted in the Bjorken x range 0.003<x<0.7. These new measurements confirm with higher accuracy previous measurements from the COMPASS and HERMES collaborations, which exhibit a definite effect in the valence quark region. The asymmetries for negative and positive hadrons are similar in magnitude and opposite in sign. They are compatible with model calculations in which the u-quark transversity is opposite in sign and somewhat larger than the d-quark transversity distribution function. The asymmetry is extracted as a function of Bjorken $x$, the relative hadron energy $z$ and the hadron transverse momentum p_T^h. The high statistics and quality of the data also allow for more detailed investigations of the dependence on the kinematic variables. These studies confirm the leading-twist nature of the Collins asymmetry.Comment: 11 pages, 5 figure

Measurement of the Collins and Sivers asymmetries on transversely polarised protons

The Collins and Sivers asymmetries for charged hadrons produced in deeply inelastic scattering on transversely polarised protons have been extracted from the data collected in 2007 with the CERN SPS muon beam tuned at 160 GeV/c. At large values of the Bjorken x variable non-zero Collins asymmetries are observed both for positive and negative hadrons while the Sivers asymmetry for positive hadrons is slightly positive over almost all the measured x range. These results nicely support the present theoretical interpretation of these asymmetries, in terms of leading-twist quark distribution and fragmentation functions.Comment: 9 Pages, 5 figure

Quark helicity distributions from longitudinal spin asymmetries in muon-proton and muon-deuteron scattering

Double-spin asymmetries for production of charged pions and kaons in semi-inclusive deep-inelastic muon scattering have been measured by the COMPASS experiment at CERN. The data, obtained by scattering a 160 GeV muon beam off a longitudinally polarised NH_3 target, cover a range of the Bjorken variable x between 0.004 and 0.7. A leading order evaluation of the helicity distributions for the three lightest quarks and antiquark flavours derived from these asymmetries and from our previous deuteron data is presented. The resulting values of the sea quark distributions are small and do not show any sizable dependence on x in the range of the measurements. No significant difference is observed between the strange and antistrange helicity distributions, both compatible with zero. The integrated value of the flavour asymmetry of the helicity distribution of the light-quark sea, \Delta u-bar - \Delta d-bar, is found to be slightly positive, about 1.5 standard deviations away from zero.Comment: 13 pages, 5 figure