Online Makespan Minimization with Parallel Schedules

In online makespan minimization a sequence of jobs $\sigma = J_1,..., J_n$ has to be scheduled on $m$ identical parallel machines so as to minimize the maximum completion time of any job. We investigate the problem with an essentially new model of resource augmentation. Here, an online algorithm is allowed to build several schedules in parallel while processing $\sigma$. At the end of the scheduling process the best schedule is selected. This model can be viewed as providing an online algorithm with extra space, which is invested to maintain multiple solutions. The setting is of particular interest in parallel processing environments where each processor can maintain a single or a small set of solutions. We develop a (4/3+\eps)-competitive algorithm, for any 0<\eps\leq 1, that uses a number of 1/\eps^{O(\log (1/\eps))} schedules. We also give a (1+\eps)-competitive algorithm, for any 0<\eps\leq 1, that builds a polynomial number of (m/\eps)^{O(\log (1/\eps) / \eps)} schedules. This value depends on $m$ but is independent of the input $\sigma$. The performance guarantees are nearly best possible. We show that any algorithm that achieves a competitiveness smaller than 4/3 must construct $\Omega(m)$ schedules. Our algorithms make use of novel guessing schemes that (1) predict the optimum makespan of a job sequence $\sigma$ to within a factor of 1+\eps and (2) guess the job processing times and their frequencies in $\sigma$. In (2) we have to sparsify the universe of all guesses so as to reduce the number of schedules to a constant. The competitive ratios achieved using parallel schedules are considerably smaller than those in the standard problem without resource augmentation

Deterministic Priority Mean-payoff Games as Limits of Discounted Games

International audienceInspired by the paper of de Alfaro, Henzinger and Majumdar about discounted $\mu$-calculus we show new surprising links between parity games and different classes of discounted games

Dissipative Dynamics of a Josephson Junction In the Bose-Gases

The dissipative dynamics of a Josephson junction in the Bose-gases is considered within the framework of the model of a tunneling Hamiltonian. The effective action which describes the dynamics of the phase difference across the junction is derived using functional integration method. The dynamic equation obtained for the phase difference across the junction is analyzed for the finite temperatures in the low frequency limit involving the radiation terms. The asymmetric case of the Bose-gases with the different order parameters is calculated as well

Evolution of the macroscopically entangled states in optical lattices

We consider dynamics of boson condensates in finite optical lattices under a slow external perturbation which brings the system to the unstable equilibrium. It is shown that quantum fluctuations drive the condensate into the maximally entangled state. We argue that the truncated Wigner approximation being a natural generalization of the Gross-Pitaevskii classical equations of motion is adequate to correctly describe the time evolution including both collapse and revival of the condensate.Comment: 14 pages, 10 figures, Discussion of reversibility of entanglement is adde

A quantum beam splitter for atoms

An interferometric method is proposed to controllably split an atomic condensate in two spatial components with strongly reduced population fluctuations. All steps in our proposal are in current use in cold atom laboratories, and we show with a theoretical calculation that our proposal is very robust against imperfections of the interferometer.Comment: 6 pages, 3 figures, revtex

Prototype scintillator cell for an In-based solar neutrino detector

We describe the work carried out at MPIK to design, model, build and characterize a prototype cell filled with a novel indium-loaded scintillator of interest for real-time low energy solar neutrino spectroscopy. First, light propagation in optical modules was studied with experiments and Monte Carlo simulations. Subsequently a 5 cm x 5 cm x 100 cm prototype detector was set up and the optical performances of several samples were measured. We first tested a benchmark PXE-based scintillator, which performed an attenuation length of ~ 4.2 m and a photo-electron yield of ~ 730 pe/MeV. Then we measured three In-loaded samples. At an In-loading of 44 g/l, an energy resolution of ~ 11.6 % and a spatial resolution of ~ 7 cm were attained for 477 keV recoil electrons. The long-range attenuation length in the cell was ~1.3 m and the estimated photo-electron yield ~ 200 pe/MeV. Light attenuation and relative light output of all tested samples could be reproduced reasonably well by MC. All optical properties of this system have remained stable over a period of > 1 y.Comment: 57 pages, 19 figures, 10 tables elsevier template for manuscript submission submitted to NIMA 10 February 200

Bogoliubov theory of entanglement in a Bose-Einstein condensate

We consider a Bose-Einstein condensate which is illuminated by a short resonant light pulse that coherently couples two internal states of the atoms. We show that the subsequent time evolution prepares the atoms in an interesting entangled state called a spin squeezed state. This evolution is analysed in detail by developing a Bogoliubov theory which describes the entanglement of the atoms. Our calculation is a consistent expansion in $1/\sqrt{N}$, where $N$ is the number of particles in the condensate, and our theory predict that it is possible to produce spin squeezing by at least a factor of $1/\sqrt{N}$. Within the Bogoliubov approximation this result is independent of temperature.Comment: 14 pages, including 5 figures, minor changes in the presentatio