Self-organizing search lists using probabilistic back-pointers

A class of algorithms is given for maintaining self-organizing sequential search lists, where the only permutation applied is to move the accessed record of each search some distance towards the front of the list. During searches, these algorithms retain a back-pointer to a previously probed record in order to determine the destination of the accessed record's eventual move. The back-pointer does not traverse the list, but rather it is advanced occationally to point to the record just probed by the search algorithm. This avoids the cost of a second traversal through a significant portion of the list, which may be a significant savings when each record access may require a new page to be brought into primary memory. Probabilistic functions for deciding when to advance the pointer are presented and analyzed. These functions demonstrate average case complexities of measures such as asymptotic cost and convergence similar to some of the more common list update algorithms in the literature. In cases where the accessed record is moved forward a distance proportional to the distance to the front of the list, the use of these functions may save up to 50% of the time required for permuting the list

Generation of optimal binary split trees

A binary split tree is a search structure combining features of heaps and binary search trees. Building an optimal binary split tree was originally conjectured to be intractable due to difficulties in applying dynamic programming techniques to the problem. However, two algorithms have recently been published which purportedly generate optimal trees in O(n^5) time, for records with distinct access probabilities. An extension allowing non-distinct access probabilities required exponential time. These algorithms consider a range of values when only a single value is possible, and may select an infeasible value which leads to an incorrect result. A dynamic programming method for determining the correct value is given, resulting in an algorithm which builds an optimal binary split tree in O(n^5) time for non-distinct access probabilities and Θ(n^4) time for distinct access probabilities

Constitutional Law—Right to Counsel—Alleged Parole Violator Has Right to Counsel at a Parole Revocation Hearing

People ex rel. Combs v. La Vallee, 29 A.D. 2d 128, 286 N.Y.S.2d 600 (4th Dept. 1968), appeal dismissed, 22 N.Y.2d 857, 293 N.Y.S.2d 117 (1968)

Optimal Pebbling in Products of Graphs

We prove a generalization of Graham's Conjecture for optimal pebbling with arbitrary sets of target distributions. We provide bounds on optimal pebbling numbers of products of complete graphs and explicitly find optimal $t$-pebbling numbers for specific such products. We obtain bounds on optimal pebbling numbers of powers of the cycle $C_5$. Finally, we present explicit distributions which provide asymptotic bounds on optimal pebbling numbers of hypercubes.Comment: 28 pages, 1 figur

Break up of returning plasma after the 7 June 2011 filament eruption by Rayleigh-Taylor instabilities

A prominence eruption on 7 June 2011 produced spectacular curtains of plasma falling through the lower corona. At the solar surface they created an incredible display of extreme ultraviolet brightenings. The aim is to identify and analyze some of the local instabilities which produce structure in the falling plasma. The structures were investigated using SDO/AIA 171A and 193A images in which the falling plasma appeared dark against the bright coronal emission. Several instances of the Rayleigh-Taylor instability were investigated. In two cases the Alfven velocity associated with the dense plasma could be estimated from the separation of the Rayleigh-Taylor fingers. A second type of feature, which has the appearance of self-similar branching horns, is also discussed.Comment: 6 pages, 7 figures, submitted A&A. Movies are at http://www.mps.mpg.de/data/outgoing/innes/arcs_movie.avi and http://www.mps.mpg.de/data/outgoing/innes/horns_movie.av

Time Synchronisation for Wireless Sensors using Low-cost GPS module and Arduino (article)

This is the final version. Available on open access from Frontiers Media via the DOI in this recordThe dataset associated with this article is located in ORE at: https://doi.org/10.24378/exe.1063Time synchronisation for wireless sensors is important for a proper interpretation of measurements, particularly for acceleration measurements to estimate mode-shapes correctly. This paper presents a new time synchronisation method working independently on each node without exchanging time-sync packets among nodes. This stand-along operation can make field measurement campaigns very time-efficient without a need of constructing and validating the wireless sensor network. The proposed method firstly time-stamps measurements using the accurate time-source from a GPS module on each node, and secondly re-samples the time-stamped data to get time-synchronised data. The time-stamping method proposed in the study utilises Pulse-Per-Second (PPS) signals and NMEA (National Marine Electronics Association) sentences generated by a low-cost GPS module, and the internal timer/counter unit of Arduino. Error analysis on the proposed time-stamping method was carried out and derived an analytical expression for the maximum variance of time-stamping error of the proposed method. Four experiments have been carried out to observe 1) the long-term operational stability of the GPS module, 2) the accuracy of the PPS signals, 3) the accuracy of the proposed time-stamping method, and 4) the validity of the proposed time-synchronisation method for output-only modal analysis on a laboratory floor structure. The GPS module was found to operate or to resume operating stably for the entire test period of seven days even with the limited field of view to the sky. The relative time errors of two PPS signals from four GPS modules were found to be within +/-400 nsec. The time-stamping error measured by two identical time-stamping Arduinos for common trigger signals was found to have a standard deviation of 40.8 nsec, which agreed well with the maximum value of 42.0 nsec predicted by the error analysis. From the output-only modal analysis, the estimated modal parameters were found to agree well with that from the wired acceleration sensors. The phase angle of the cross spectral density of the two wireless accelerations showed that there was no apparent time-synchronisation error observable. These observations indicated a successful operation of the proposed time-synchronisation method

Time-dependence in Relativistic Collisionless Shocks: Theory of the Variable "Wisps" in the Crab Nebula

We describe results from time-dependent numerical modeling of the collisionless reverse shock terminating the pulsar wind in the Crab Nebula. We treat the upstream relativistic wind as composed of ions and electron-positron plasma embedded in a toroidal magnetic field, flowing radially outward from the pulsar in a sector around the rotational equator. The relativistic cyclotron instability of the ion gyrational orbit downstream of the leading shock in the electron-positron pairs launches outward propagating magnetosonic waves. Because of the fresh supply of ions crossing the shock, this time-dependent process achieves a limit-cycle, in which the waves are launched with periodicity on the order of the ion Larmor time. Compressions in the magnetic field and pair density associated with these waves, as well as their propagation speed, semi-quantitatively reproduce the behavior of the wisp and ring features described in recent observations obtained using the Hubble Space Telescope and the Chandra X-Ray Observatory. By selecting the parameters of the ion orbits to fit the spatial separation of the wisps, we predict the period of time variability of the wisps that is consistent with the data. When coupled with a mechanism for non-thermal acceleration of the pairs, the compressions in the magnetic field and plasma density associated with the optical wisp structure naturally account for the location of X-ray features in the Crab. We also discuss the origin of the high energy ions and their acceleration in the equatorial current sheet of the pulsar wind.Comment: 13 pages, 4 figures, accepted to ApJ. High-resolution figures and mpeg movies available at http://astron.berkeley.edu/~anatoly/wisp

Molecular excitation in the Eagle nebula's fingers

Context: The M16 nebula is a relatively nearby Hii region, powered by O stars from the open cluster NGC 6611, which borders to a Giant Molecular Cloud. Radiation from these hot stars has sculpted columns of dense obscuring material on a few arcmin scales. The interface between these pillars and the hot ionised medium provides a textbook example of a Photodissociation Region (PDR). Aims: To constrain the physical conditions of the atomic and molecular material with submillimeter spectroscopic observations. Methods: We used the APEX submillimeter telescope to map a ~3'x3' region in the CO J=3-2, 4-3 and 7-6 rotational lines, and a subregion in atomic carbon lines. We also observed C18O(3-2) and CO(7-6) with longer integrations on five peaks found in the CO(3-2) map. The large scale structure of the pillars is derived from the molecular lines' emission distribution. We estimate the magnitude of the velocity gradient at the tips of the pillars and use LVG modelling to constrain their densities and temperatures. Excitation temperatures and carbon column densities are derived from the atomic carbon lines. Results: The atomic carbon lines are optically thin and excitation temperatures are of order 60 K to 100 K, well consistent with observations of other Hii region-molecular cloud interfaces. We derive somewhat lower temperatures from the CO line ratios, of order 40 K. The Ci/CO ratio is around 0.1 at the fingers tips.Comment: 4 pages, APEX A&A special issue, accepte