An easy subexponential bound for online chain partitioning

Bosek and Krawczyk exhibited an online algorithm for partitioning an online poset of width $w$ into $w^{14\lg w}$ chains. We improve this to $w^{6.5 \lg w + 7}$ with a simpler and shorter proof by combining the work of Bosek & Krawczyk with work of Kierstead & Smith on First-Fit chain partitioning of ladder-free posets. We also provide examples illustrating the limits of our approach.Comment: 23 pages, 11 figure

Wrapping interactions at strong coupling -- the giant magnon

We derive generalized Luscher formulas for finite size corrections in a theory with a general dispersion relation. For the AdS_5xS^5 superstring these formulas encode leading wrapping interaction effects. We apply the generalized mu-term formula to calculate finite size corrections to the dispersion relation of the giant magnon at strong coupling. The result exactly agrees with the classical string computation of Arutyunov, Frolov and Zamaklar. The agreement involved a Borel resummation of all even loop-orders of the BES/BHL dressing factor thus providing a strong consistency check for the choice of the dressing factor.Comment: 35 pages, 2 figures; v2: comments and references adde

Zitterbewegung of relativistic electrons in a magnetic field and its simulation by trapped ions

One-electron 3+1 and 2+1 Dirac equations are used to calculate the motion of a relativistic electron in a vacuum in the presence of an external magnetic field. First, calculations are carried on an operator level and exact analytical results are obtained for the electron trajectories which contain both intraband frequency components, identified as the cyclotron motion, as well as interband frequency components, identified as the trembling motion (Zitterbewegung, ZB). Next, time-dependent Heisenberg operators are used for the same problem to compute average values of electron position and velocity employing Gaussian wave packets. It is shown that the presence of a magnetic field and the resulting quantization of the energy spectrum has pronounced effects on the electron Zitterbewegung: it introduces intraband frequency components into the motion, influences all the frequencies and makes the motion stationary (not decaying in time) in case of the 2+1 Dirac equation. Finally, simulations of the 2+1 Dirac equation and the resulting electron ZB in the presence of a magnetic field are proposed and described employing trapped ions and laser excitations. Using simulation parameters achieved in recent experiments of Gerritsma and coworkers we show that the effects of the simulated magnetic field on ZB are considerable and can certainly be observed.Comment: 19 pages, 9 figures, published versio

Merger Sites of Double Neutron Stars and their Host Galaxies

Using the StarTrack population synthesis code we analyze the formation channels possibly available to double neutron star binaries and find that they can be richer than previously thought. We identify a group of short lived, tight binaries, which do not live long enough to escape their host galaxies, despite their large center-of-mass velocities. We present our most recent results on all possible evolutionary paths leading to the formation of double neutron stars, calculate their coalescence rates, and also revisit the question of the distribution of merger sites around host galaxies. For a wide variety of binary evolution models and galaxy potentials, we find that most of neutron star mergers take place within galaxies. Our results stem from allowing for radial and common envelope evolution of helium-rich stars (testable in the future with detailed stellar-structure and hydrodynamic calculations) and indicate that double neutron star binaries may not be excluded as Gamma-Ray Burst (GRB) progenitors solely on the basis of their spatial distribution around host galaxies. We also find, in contrast to Bethe & Brown (1998), that in a significant fraction of common envelope (CE) phases neutron stars do not accrete enough material to become black holes, and thus the channels involving CEs are still open for the formation of double neutron stars.Comment: 12 pages, 3 figures, ApJ Letters 2002, accepte

Mechanics of multidimensional isolated horizons

Recently a multidimensional generalization of Isolated Horizon framework has been proposed by Lewandowski and Pawlowski (gr-qc/0410146). Therein the geometric description was easily generalized to higher dimensions and the structure of the constraints induced by the Einstein equations was analyzed. In particular, the geometric version of the zeroth law of the black hole thermodynamics was proved. In this work we show how the IH mechanics can be formulated in a dimension--independent fashion and derive the first law of BH thermodynamics for arbitrary dimensional IH. We also propose a definition of energy for non--rotating horizons.Comment: 25 pages, 4 figures (eps), last sections revised, acknowledgements and a section about the gauge invariance of introduced quantities added; typos corrected, footnote 4 on page 9 adde

Arecibo Timing and Single Pulse Observations of 18 Pulsars

We present new results of timing and single pulse measurements for 18 radio pulsars discovered in 1993 - 1997 by the Penn State/NRL declination-strip survey conducted with the 305-m Arecibo telescope at 430 MHz. Long-term timing measurements have led to significant improvements of the rotational and the astrometric parameters of these sources, including the millisecond pulsar, PSR J1709+2313, and the pulsar located within the supernova remnant S147, PSR J0538+2817. Single pulse studies of the brightest objects in the sample have revealed an unusual "bursting" pulsar, PSR J1752+2359, two new drifting subpulse pulsars, PSR J1649+2533 and PSR J2155+2813, and another example of a pulsar with profile mode changes, PSR J1746+2540. PSR J1752+2359 is characterized by bursts of emission, which appear once every 3-5 min. and decay exponentially on a ~45 sec timescale. PSR J1649+2533 spends ~30% of the time in a null state with no detectable radio emission.Comment: submitted to Ap

Zitterbewegung of Klein-Gordon particles and its simulation by classical systems

The Klein-Gordon equation is used to calculate the Zitterbewegung (ZB, trembling motion) of spin-zero particles in absence of fields and in the presence of an external magnetic field. Both Hamiltonian and wave formalisms are employed to describe ZB and their results are compared. It is demonstrated that, if one uses wave packets to represent particles, the ZB motion has a decaying behavior. It is also shown that the trembling motion is caused by an interference of two sub-packets composed of positive and negative energy states which propagate with different velocities. In the presence of a magnetic field the quantization of energy spectrum results in many interband frequencies contributing to ZB oscillations and the motion follows a collapse-revival pattern. In the limit of non-relativistic velocities the interband ZB components vanish and the motion is reduced to cyclotron oscillations. The exact dynamics of a charged Klein-Gordon particle in the presence of a magnetic field is described on an operator level. The trembling motion of a KG particle in absence of fields is simulated using a classical model proposed by Morse and Feshbach -- it is shown that a variance of a Gaussian wave packet exhibits ZB oscillations.Comment: 16 pages and 7 figure

Differentiating between live and deadﾠMycobacterium smegmatisﾠusing autofluorescence

While there have been research efforts to find faster and more efficient diagnostic techniques for tuberculosis (TB), it is equally important to monitor a patient's response to treatment over time, especially with the increasing prevalence of multi-drug resistant (MDR) and extensively-drug resistant (XDR) TB. Between sputum smear microscopy, culture, and GeneXpert, only culture can verify viability of mycobacteria. However, it may take up to six weeks to grow Mycobacterium tuberculosis (Mtb), during which time the patient may have responded to treatment or the mycobacteria are still viable because the patient has MDR or XDR TB. In both situations, treatment incurs increased patient costs and makes them more susceptible to host-drug effects such as liver damage. Coenzyme Factor 420 (F420) is a fluorescent coenzyme found naturally in mycobacteria, with an excitation peak around 420 nm and an emission peak around 470 nm. Using Mycobacterium smegmatis, we show that live and dead mycobacteria undergo different rates of photobleaching over a period of 2 min. These preliminary experiments suggest that the different photobleaching rates could be used to help monitor a patient's response to TB treatment. In future studies, we propose to describe these experiments with Mtb as both M. smegmatis and Mtb use F420