A Robust AFPTAS for Online Bin Packing with Polynomial Migration

In this paper we develop general LP and ILP techniques to find an approximate solution with improved objective value close to an existing solution. The task of improving an approximate solution is closely related to a classical theorem of Cook et al. in the sensitivity analysis for LPs and ILPs. This result is often applied in designing robust algorithms for online problems. We apply our new techniques to the online bin packing problem, where it is allowed to reassign a certain number of items, measured by the migration factor. The migration factor is defined by the total size of reassigned items divided by the size of the arriving item. We obtain a robust asymptotic fully polynomial time approximation scheme (AFPTAS) for the online bin packing problem with migration factor bounded by a polynomial in $\frac{1}{\epsilon}$. This answers an open question stated by Epstein and Levin in the affirmative. As a byproduct we prove an approximate variant of the sensitivity theorem by Cook at el. for linear programs

Time-Series Photometry of M67: W UMa Systems, Blue Stragglers, and Related Systems

We present an analysis of over 2200 V images taken on 14 nights at the Mt. Laguna 1 m telescope of the open cluster M67. Our observations overlap but extend beyond the field analyzed by Gilliland et al. (1991), and complement data recently published by van den Berg et al. (2002) and Stassun et al. (2002). We show variability in the light curves of all 4 of the known W UMa variables on timescales ranging from a day to decades (for AH Cnc). We have modeled the light curve of AH Cnc, and the total eclipses allow us to determine q = 0.16 +0.03/-0.02 and i = 86 +4/-8 degrees. The position of this system near the turnoff of M67 makes it useful for constraining the turnoff mass for the cluster. We have also detected two unusual features in the light curve of AH Cnc that may be caused by prominences. We have also monitored cluster blue stragglers for variability, and we present evidence hinting at low level variations in the stragglers S752, S968, and S1263, and we place limits on the variability of a number of other cluster blue stragglers. Finally, we provide photometry of the sub-subgiant branch star S1063 showing variability on timescales similar to the orbital period, while the ``red straggler'' S1040 shows evidence of an unexplained drop in brightness at phases corresponding to the passage of the white dwarf in front of the giant.Comment: 44 pages, 16 figures, AASTeX, accepted for A

Spectroscopy of Blue Stragglers and Turnoff Stars in M67 (NGC 2682)

We have analyzed high-resolution spectra of relatively cool blue stragglers and main sequence turnoff stars in the old open cluster M67 (NGC 2682). We attempt to identify blue stragglers whose spectra are least contaminated by binary effects (contamination by a binary companion or absorption by circumstellar material). These ``best'' stragglers have metallicities ([Fe/H] = -0.05) and abundance ratios of the blue stragglers are not significantly different from those of the turnoff stars. Based on arguments from hydrodynamical models of stellar collisions, we assert that the current upper limits for the lithium abundances of all blue stragglers observed in M67 (by us and others) are consistent with no mixing during the formation process, assuming pre-main sequence and main sequence depletion patterns observed for M67 main sequence stars. We discuss composition signatures that could more definitively distinguish between blue straggler formation mechanisms in open cluster stars. We confirm the spectroscopic detection of a binary companion to the straggler S 1082. From our spectra, we measure a projected rotational speed of 90+/-20 km/sec for the secondary, and find that its radial velocity varies with a peak-to-peak amplitude of ~ 25 km/sec. Because the radial velocities do not vary with a period corresponding to the partial eclipses in the system, we believe this system is currently undergoing mass transfer. In addition we present evidence that S 984 is a true blue straggler (and not an unresolved pair). If this can be proven, our detection of lithium may indicate a collisional origin.Comment: 20 pages, 4 figures, to appear in October 2000 A

How to perform the most accurate possible phase measurements

We present the theory of how to achieve phase measurements with the minimum possible variance in ways that are readily implementable with current experimental techniques. Measurements whose statistics have high-frequency fringes, such as those obtained from NOON states, have commensurately high information yield. However this information is also highly ambiguous because it does not distinguish between phases at the same point on different fringes. We provide schemes to eliminate this phase ambiguity in a highly efficient way, providing phase estimates with uncertainty that is within a small constant factor of the Heisenberg limit, the minimum allowed by the laws of quantum mechanics. These techniques apply to NOON state and multi-pass interferometry, as well as phase measurements in quantum computing. We have reported the experimental implementation of some of these schemes with multi-pass interferometry elsewhere. Here we present the theoretical foundation, and also present some new experimental results. There are three key innovations to the theory in this paper. First, we examine the intrinsic phase properties of the sequence of states (in multiple time modes) via the equivalent two-mode state. Second, we identify the key feature of the equivalent state that enables the optimal scaling of the intrinsic phase uncertainty to be obtained. This enables us to identify appropriate combinations of states to use. The remaining difficulty is that the ideal phase measurements to achieve this intrinic phase uncertainty are often not physically realizable. The third innovation is to solve this problem by using realizable measurements that closely approximate the optimal measurements, enabling the optimal scaling to be preserved.Comment: 23 pages, 10 figures; new general definition of resource

Dangling-bond charge qubit on a silicon surface

Two closely spaced dangling bonds positioned on a silicon surface and sharing an excess electron are revealed to be a strong candidate for a charge qubit. Based on our study of the coherent dynamics of this qubit, its extremely high tunneling rate ~ 10^14 1/s greatly exceeds the expected decoherence rates for a silicon-based system, thereby overcoming a critical obstacle of charge qubit quantum computing. We investigate possible configurations of dangling bond qubits for quantum computing devices. A first-order analysis of coherent dynamics of dangling bonds shows promise in this respect.Comment: 17 pages, 3 EPS figures, 1 tabl

GPU Concurrency: Weak Behaviours and Programming Assumptions

Concurrency is pervasive and perplexing, particularly on graphics processing units (GPUs). Current specifications of languages and hardware are inconclusive; thus programmers often rely on folklore assumptions when writing software. To remedy this state of affairs, we conducted a large empirical study of the concurrent behaviour of deployed GPUs. Armed with litmus tests (i.e. short concurrent programs), we questioned the assumptions in programming guides and vendor documentation about the guarantees provided by hardware. We developed a tool to generate thousands of litmus tests and run them under stressful workloads. We observed a litany of previously elusive weak behaviours, and exposed folklore beliefs about GPU programming---often supported by official tutorials---as false. As a way forward, we propose a model of Nvidia GPU hardware, which correctly models every behaviour witnessed in our experiments. The model is a variant of SPARC Relaxed Memory Order (RMO), structured following the GPU concurrency hierarchy

Dark-bright magneto-exciton mixing induced by Coulomb interaction in strained quantum wells

Coupled magneto-exciton states between allowed (`bright') and forbidden (`dark') transitions are found in absorption spectra of strained In$_{0.2}$Ga$_{0.8}$As/GaAs quantum wells with increasing magnetic field up to 30 T. We found large (~ 10 meV) energy splittings in the mixed states. The observed anticrossing behavior is independent of polarization, and sensitive only to the parity of the quantum confined states. Detailed experimental and theoretical investigations indicate that the excitonic Coulomb interaction rather than valence band complexity is responsible for the splittings. In addition, we determine the spin composition of the mixed states.Comment: 4 pages, 4 figure

A deep Chandra observation of the Perseus cluster: shocks and ripples

We present preliminary results from a deep observation lasting almost 200 ks, of the centre of the Perseus cluster of galaxies around NGC 1275. The X-ray surface brightness of the intracluster gas beyond the inner 20 kpc, which contains the inner radio bubbles, is very smooth apart from some low amplitude quasi-periodic ripples. A clear density jump at a radius of 24 kpc to the NE, about 10 kpc out from the bubble rim, appears to be due to a weak shock driven by the northern radio bubble. A similar front may exist round both inner bubbles but is masked elsewhere by rim emission from bright cooler gas. The continuous blowing of bubbles by the central radio source, leading to the propagation of weak shocks and viscously-dissipating sound waves seen as the observed fronts and ripples, gives a rate of working which balances the radiative cooling within the inner 50 kpc of the cluster core.Comment: Accepted for publication in MNRAS (minor changes) Higher picture quality available from http://www-xray.ast.cam.ac.uk/papers/per_200ks.pd

HST Observations of Chromospheres in Metal Deficient Field Giants

HST high resolution spectra of metal-deficient field giants more than double the stars in previous studies, span about 3 magnitudes on the red giant branch, and sample an abundance range [Fe/H]= -1 to -3. These stars, in spite of their age and low metallicity, possess chromospheric fluxes of Mg II (2800 Angstrom) that are within a factor of 4 of Population I stars, and give signs of a dependence on the metal abundance at the lowest metallicities. The Mg II k-line widths depend on luminosity and correlate with metallicity. Line profile asymmetries reveal outflows that occur at lower luminosities (M_V = -0.8) than detected in Ca K and H-alpha lines in metal-poor giants, suggesting mass outflow occurs over a larger span of the red giant branch than previously thought, and confirming that the Mg II lines are good wind diagnostics. These results do not support a magnetically dominated chromosphere, but appear more consistent with some sort of hydrodynamic, or acoustic heating of the outer atmospheres.Comment: 36 pages, 12 figures, 7 tables, and accepted for publication in The Astronomical Journa

Magnon Heat Transport in doped La2CuO4\rm La_2CuO_4

We present results of the thermal conductivity of $\rm La_2CuO_4$ and $\rm La_{1.8}Eu_{0.2}CuO_4$ single-crystals which represent model systems for the two-dimensional spin-1/2 Heisenberg antiferromagnet on a square lattice. We find large anisotropies of the thermal conductivity, which are explained in terms of two-dimensional heat conduction by magnons within the CuO$_2$ planes. Non-magnetic Zn substituted for Cu gradually suppresses this magnon thermal conductivity $\kappa_{\mathrm{mag}}$. A semiclassical analysis of $\kappa_{\mathrm{mag}}$ is shown to yield a magnon mean free path which scales linearly with the reciprocal concentration of Zn-ions.Comment: 4 pages, 3 figure