Single Machine Scheduling with Release Dates

We consider the scheduling problem of minimizing the average weighted completion time of n jobs with release dates on a single machine. We first study two linear programming relaxations of the problem, one based on a time-indexed formulation, the other on a completiontime formulation. We show their equivalence by proving that a O(n log n) greedy algorithm leads to optimal solutions to both relaxations. The proof relies on the notion of mean busy times of jobs, a concept which enhances our understanding of these LP relaxations. Based on the greedy solution, we describe two simple randomized approximation algorithms, which are guaranteed to deliver feasible schedules with expected objective value within factors of 1.7451 and 1.6853, respectively, of the optimum. They are based on the concept of common and independent a-points, respectively. The analysis implies in particular that the worst-case relative error of the LP relaxations is at most 1.6853, and we provide instances showing that it is at least e/(e - 1) 1.5819. Both algorithms may be derandomized, their deterministic versions running in O(n2 ) time. The randomized algorithms also apply to the on-line setting, in which jobs arrive dynamically over time and one must decide which job to process without knowledge of jobs that will be released afterwards

Random-Based Scheduling: New Approximations and LP Lower Bounds

Three characteristics encountered frequently in real-world machine scheduling are jobs released over time, precedence constraints between jobs, and average performance optimization. The general constrained one-machine scheduling problem to minimize the average weighted completion time not only captures these features, but also is an important building block for more complex problems involving multiple machines

The Power of α-Points in Preemptive Single Machine Scheduling

We consider the NP-hard preemptive single machine scheduling problem to minimize the total weighted completion time subject to release dates. A natural extension of Smith's ratio rule is to preempt the currently active job whenever a new job arrives that has higher ratio of weight to processing time. We prove that the competitive ratio of this simple on-line algorithm is precisely~2. We also show that list scheduling in order of random α-points drawn from the same schedule results in an on-line algorithm with competitive ratio~4/3. Since its analysis relies on a well-known integer programming relaxation of the scheduling problem, the relaxation has performance guarantee~4/3 as well. On the other hand, we show that it is at best an~8/7-relaxation

Simulations of Baryon Oscillations

The coupling of photons and baryons by Thomson scattering in the early universe imprints features in both the Cosmic Microwave Background (CMB) and matter power spectra. The former have been used to constrain a host of cosmological parameters, the latter have the potential to strongly constrain the expansion history of the universe and dark energy. Key to this program is the means to localize the primordial features in observations of galaxy spectra which necessarily involve galaxy bias, non-linear evolution and redshift space distortions. We present calculations, based on mock catalogs produced from high-resolution N-body simulations, which show the range of behaviors we might expect of galaxies in the real universe. We investigate physically motivated fitting forms which include the effects of non-linearity, galaxy bias and redshift space distortions and discuss methods for analysis of upcoming data. In agreement with earlier work, we find that a survey of several Gpc^3 would constrain the sound horizon at z~1 to about 1%.Comment: 33 pages, to appear in Astroparticle Physics. Discussion of Blake & Glazebrook procedure changed, minor edits to match version accepted by the journa

Mixed-Spin Ladders and Plaquette Spin Chains

We investigate low-energy properties of a generalized spin ladder model with both of the spin alternation and the bond alternation, which allows us to systematically study not only ladder systems but also alternating spin chains. By exploiting non-linear $\sigma$ model techniques we study the model with particular emphasis on the competition between gapful and gapless states. Our approach turns out to provide a more consistent semi-classical description of alternating spin chains than that in the previous work. We also study a closely related model, i.e., a spin chain with plaquette structure, and show that frustration causes little effect on its low-energy properties so far as the strength of frustration is weaker than a certain critical value.Comment: 7 pages, REVTeX, 3 figures, submitted to JPS

Spin- and charge-density waves in the Hartree-Fock ground state of the two-dimensional Hubbard model

The ground states of the two-dimensional repulsive Hubbard model are studied within the unrestricted Hartree-Fock (UHF) theory. Magnetic and charge properties are determined by systematic, large-scale, exact numerical calculations, and quantified as a function of electron doping $h$. In the solution of the self-consistent UHF equations, multiple initial configurations and simulated annealing are used to facilitate convergence to the global minimum. New approaches are employed to minimize finite-size effects in order to reach the thermodynamic limit. At low to moderate interacting strengths and low doping, the UHF ground state is a linear spin-density wave (l-SDW), with antiferromagnetic order and a modulating wave. The wavelength of the modulating wave is $2/h$. Corresponding charge order exists but is substantially weaker than the spin order, hence holes are mobile. As the interaction is increased, the l-SDW states evolves into several different phases, with the holes eventually becoming localized. A simple pairing model is presented with analytic calculations for low interaction strength and small doping, to help understand the numerical results and provide a physical picture for the properties of the SDW ground state. By comparison with recent many-body calculations, it is shown that, for intermediate interactions, the UHF solution provides a good description of the magnetic correlations in the true ground state of the Hubbard model.Comment: 13 pages, 17 figure, 0 table

Comparison of absolute gain photometric calibration between Planck/HFI and Herschel/SPIRE at 545 and 857 GHz

We compare the absolute gain photometric calibration of the Planck/HFI and Herschel/SPIRE instruments on diffuse emission. The absolute calibration of HFI and SPIRE each relies on planet flux measurements and comparison with theoretical far-infrared emission models of planetary atmospheres. We measure the photometric cross calibration between the instruments at two overlapping bands, 545 GHz / 500 $\mu$m and 857 GHz / 350 $\mu$m. The SPIRE maps used have been processed in the Herschel Interactive Processing Environment (Version 12) and the HFI data are from the 2015 Public Data Release 2. For our study we used 15 large fields observed with SPIRE, which cover a total of about 120 deg^2. We have selected these fields carefully to provide high signal-to-noise ratio, avoid residual systematics in the SPIRE maps, and span a wide range of surface brightness. The HFI maps are bandpass-corrected to match the emission observed by the SPIRE bandpasses. The SPIRE maps are convolved to match the HFI beam and put on a common pixel grid. We measure the cross-calibration relative gain between the instruments using two methods in each field, pixel-to-pixel correlation and angular power spectrum measurements. The SPIRE / HFI relative gains are 1.047 ($\pm$ 0.0069) and 1.003 ($\pm$ 0.0080) at 545 and 857 GHz, respectively, indicating very good agreement between the instruments. These relative gains deviate from unity by much less than the uncertainty of the absolute extended emission calibration, which is about 6.4% and 9.5% for HFI and SPIRE, respectively, but the deviations are comparable to the values 1.4% and 5.5% for HFI and SPIRE if the uncertainty from models of the common calibrator can be discounted. Of the 5.5% uncertainty for SPIRE, 4% arises from the uncertainty of the effective beam solid angle, which impacts the adopted SPIRE point source to extended source unit conversion factor (Abridged)Comment: 13 pages, 10 figures; Incorporates revisions in response to referee comments; cross calibration factors unchange

Magnetic excitation spectrum of dimerized antiferromagnetic chains

Motivated by recent measurements on CuGeO$_3$ the spectrum of magnetic excitations of an antiferromagnetic $S=\frac{1}{2}$ chain with alternating coupling strength is investigated. Wave vector dependent magnons and a continuum with square root behavior at the band edges are found. The spectral density of the continua is calculated. Spin rotation symmetry fixes the gap of the continuum to be twice the elementary magnon gap. This is in excellent agreement with experimental results. In addition, the existence of bound states of two magnons is predicted: below the continuum a singlet and a triplet, above the continuum an ``anti-bound'' quintuplet. The results are based on field theoretic arguments, RPA calculations, and consideration of the limit of strong alternation.Comment: 4 pages, 4 figures included, Revte

The effects of ram-pressure stripping on the internal kinematics of simulated spiral galaxies

We investigate the influence of ram-pressure stripping on the internal gas kinematics of simulated spiral galaxies. Additional emphasis is put on the question of how the resulting distortions of the gaseous disc are visible in the rotation curve and/or the full 2D velocity field of galaxies at different redshifts. A Milky-Way type disc galaxy is modelled in combined N-body/hydrodynamic simulations with prescriptions for cooling, star formation, stellar feedback, and galactic winds. This model galaxy moves through a constant density and temperature gas, which has parameters similar to the intra-cluster medium (ICM). Rotation curves (RCs) and 2D velocity fields of the gas are extracted from these simulations in a way that follows the procedure applied to observations of distant, small, and faint galaxies as closely as possible. We find that the appearance of distortions of the gaseous disc due to ram-pressure stripping depends on the direction of the acting ram pressure. In the case of face-on ram pressure, the distortions mainly appear in the outer parts of the galaxy in a very symmetric way. In contrast, in the case of edge-on ram pressure we find stronger distortions. The 2D velocity field also shows signatures of the interaction in the inner part of the disc. At angles smaller than 45 degrees between the ICM wind direction and the disc, the velocity field asymmetry increases significantly compared to larger angles. Compared to distortions caused by tidal interactions, the effects of ram-pressure stripping on the velocity field are relatively low in all cases and difficult to observe at intermediate redshift in seeing-limited observations. (abridged)Comment: 9 pages, 11 figures, accepted for publication in A&