New Algorithms for Position Heaps

We present several results about position heaps, a relatively new alternative to suffix trees and suffix arrays. First, we show that, if we limit the maximum length of patterns to be sought, then we can also limit the height of the heap and reduce the worst-case cost of insertions and deletions. Second, we show how to build a position heap in linear time independent of the size of the alphabet. Third, we show how to augment a position heap such that it supports access to the corresponding suffix array, and vice versa. Fourth, we introduce a variant of a position heap that can be simulated efficiently by a compressed suffix array with a linear number of extra bits

Solution of Orthopositronium lifetime Puzzle

The intrinsic decay rate of orthopositronium formed in ${\rm SiO_2}$ powder is measured using the direct $2\gamma$ correction method such that the time dependence of the pick-off annihilation rate is precisely determined. The decay rate of orthopositronium is found to be $7.0396\pm0.0012 (stat.)\pm0.0011 (sys.)\mu s^{-1}$, which is consistent with our previous measurements with about twice the accuracy. Results agree well with the $O(\alpha^2)$ QED prediction, and also with a result reported very recently using nanoporous film

Fractal geometry of aggregate snowflakes revealed by triple wavelength radar measurements

Radar reflectivity measurements from three different wavelengths are used to retrieve information about the shape of aggregate snowflakes in deep stratiform ice clouds. Dual-wavelength ratios are calculated for different shape models and compared to observations at 3, 35 and 94 GHz. It is demonstrated that many scattering models, including spherical and spheroidal models, do not adequately describe the aggregate snowflakes that are observed. The observations are consistent with fractal aggregate geometries generated by a physically-based aggregation model. It is demonstrated that the fractal dimension of large aggregates can be inferred directly from the radar data. Fractal dimensions close to 2 are retrieved, consistent with previous theoretical models and in-situ observations

Vacuum Polarization and the Electric Charge of the Positron

We show that higher-order vacuum polarization would contribute a measureable net charge to atoms, if the charges of electrons and positrons do not balance precisely. We obtain the limit $|Q_e+Q_{\bar e}| < 10^{-18} e$ for the sum of the charges of electron and positron. This also constitutes a new bound on certain violations of PCT invariance.Comment: 9 pages, 1 figure attached as PostScript file, DUKE-TH-92-38. Revised versio

Dynamic Windows Scheduling with Reallocation

We consider the Windows Scheduling problem. The problem is a restricted version of Unit-Fractions Bin Packing, and it is also called Inventory Replenishment in the context of Supply Chain. In brief, the problem is to schedule the use of communication channels to clients. Each client ci is characterized by an active cycle and a window wi. During the period of time that any given client ci is active, there must be at least one transmission from ci scheduled in any wi consecutive time slots, but at most one transmission can be carried out in each channel per time slot. The goal is to minimize the number of channels used. We extend previous online models, where decisions are permanent, assuming that clients may be reallocated at some cost. We assume that such cost is a constant amount paid per reallocation. That is, we aim to minimize also the number of reallocations. We present three online reallocation algorithms for Windows Scheduling. We evaluate experimentally these protocols showing that, in practice, all three achieve constant amortized reallocations with close to optimal channel usage. Our simulations also expose interesting trade-offs between reallocations and channel usage. We introduce a new objective function for WS with reallocations, that can be also applied to models where reallocations are not possible. We analyze this metric for one of the algorithms which, to the best of our knowledge, is the first online WS protocol with theoretical guarantees that applies to scenarios where clients may leave and the analysis is against current load rather than peak load. Using previous results, we also observe bounds on channel usage for one of the algorithms.Comment: 6 figure

Not Just Efficiency: Insolvency Law in the EU and Its Political Dimension

Certain insolvency law rules, like creditors’ priorities and set-off rights, have a distributive impact on creditors. Distributional rules reflect the hierarchies of values and interests in each jurisdiction and, as a result, have high political relevance and pose an obstacle to reforming the EU Insolvency Regulation. This paper will show the difficulty of reform by addressing two alternative options to regulate cross-border insolvencies in the European Union. The first one is the ‘choice model’, under which companies can select the insolvency law they prefer. Although such a model would allow distressed firms to select the most efficient insolvency law, it would also displace Member States’ power to protect local constituencies. The choice model therefore produces negative externalities and raises legitimacy concerns. The opposite solution is full harmonisation of insolvency law at EU level, including distributional rules. Full harmonisation would have the advantage of internalising all externalities produced by cross-border insolvencies. However, the EU legislative process, which is still based on negotiations between states, is not apt to decide on distributive insolvency rules; additionally, if harmonisation includes such rules, it will indirectly modify national social security strategies and equilibria. This debate shows that the choice regarding power allocation over bankruptcies in the EU depends on the progress of European integration and is mainly a matter of political legitimacy, not only of efficiency

Producing and Detecting Correlated atoms

We discuss experiments to produce and detect atom correlations in a degenerate or nearly degenerate gas of neutral atoms. First we treat the atomic analog of the celebrated Hanbury Brown Twiss experiment, in which atom correlations result simply from interference effects without any atom interactions.We have performed this experiment for both bosons and fermions. Next we show how atom interactions produce correlated atoms using the atomic analog of spontaneous four-wavemixing. Finally, we briefly mention experiments on a one dimensional gas on an atom chip in which correlation effects due to both interference and interactions have been observed.Comment: to appear in conference proceedings "Atomic Physics 20

Trapped-ion probing of light-induced charging effects on dielectrics

We use a string of confined $^{40}$Ca$^+$ ions to measure perturbations to a trapping potential which are caused by light-induced charging of an anti-reflection coated window and of insulating patches on the ion-trap electrodes. The electric fields induced at the ions' position are characterised as a function of distance to the dielectric, and as a function of the incident optical power and wavelength. The measurement of the ion-string position is sensitive to as few as $40$ elementary charges per $\sqrt{\mathrm{Hz}}$ on the dielectric at distances of order millimetres, and perturbations are observed for illumination with light of wavelengths as long as 729\,nm. This has important implications for the future of miniaturised ion-trap experiments, notably with regards to the choice of electrode material, and the optics that must be integrated in the vicinity of the ion. The method presented can be readily applied to the investigation of charging effects beyond the context of ion trap experiments.Comment: 11 pages, 5 figure

PREDICTING THE DATE OF FIRST CATCH OF THE CORN EARWORM, HELICOVERPA ZEA, IN CENTRAL U.S.

This paper develops predictive (or correlative) models for the date of first catch of the com earworm, Helicoverpa zea, as a basis for identifying biotic and abiotic factors that influence dispersal and migration. Data described in Goodenough et al. (1988, J. Econ. Entomol.) on the catch of H. zea gathered at over 150 sites predominantly in the central U.S. from 1983 to 1986 are analyzed. The dependent variables, Y1 and Y2, are date of first meaningful catch and date when cumulative catch exceeds 5, respectively; the independent variables are latitude, longitude and elevation of the site. Outstanding among the findings are the following : 1) There is no statistical evidence based on all the data that the slopes of the simple linear regression models of Y2 on latitude differ among the four years. The common slope estimate is 8.11 days/degree, the intercepts differ by as many as 16 days, and the combined model has r2 = 0.69. 2) There is no statistical evidence based on the data in the central U.S. that the partial slopes of the multiple regression models of Y2 on latitude and longitude differ among the four years. The common partial slope estimates are 7.36 and -1.27 days/degree, the intercepts differ by as many as 17 days, and the combined model has R 2= 0.69. Second order terms are not significant . 3) An exploratory analysis using GIS mapping software suggests that elevation is also a significant predictor variable. The suggestion is confirmed in multiple regression models for both Y1 and Y22= 0.71 and 0.72 respectively. The intercepts differ by as many as 20 and 17 days, respectively, over the four years . These results imply that the time of fi!\u27st appearance at any location in the central U.S. could be predicted once the date of first appearance in South Texas is ascertained. They also demonstrate the utility of analyzing residuals using GIS mapping software. Research is in progress to investigate other possible predictor variables including soil moisture, soil temperature and precipitation

Real time approach to tunneling in open quantum systems: decoherence and anomalous diffusion

Macroscopic quantum tunneling is described using the master equation for the reduced Wigner function of an open quantum system at zero temperature. Our model consists of a particle trapped in a cubic potential interacting with an environment characterized by dissipative and normal and anomalous diffusion coefficients. A representation based on the energy eigenfunctions of the isolated system, i.e. the system uncoupled to the environment, is used to write the reduced Wigner function, and the master equation becomes simpler in that representation. The energy eigenfunctions computed in a WKB approximation incorporate the tunneling effect of the isolated system and the effect of the environment is described by an equation that it is in many ways similar to a Fokker-Planck equation. Decoherence is easily identified from the master equation and we find that when the decoherence time is much shorter than the tunneling time the master equation can be approximated by a Kramers like equation describing thermal activation due to the zero point fluctuations of the quantum environment. The effect of anomalous diffusion can be dealt with perturbatively and its overall effect is to inhibit tunneling.Comment: 25 pages, 1 figur