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

A probabilistic model of insolation for the Mojave Desert area

A discussion of mathematical models of insolation characteristics suitable for use in analysis of solar energy systems is presented and shows why such models are essential for solar energy system design. A model of solar radiation for the Mojave Desert area is presented with probabilistic and deterministic components which reflect the occurrence and density of clouds and haze, and mimic their effects on both direct and indirect radiation. Multiple comparisons were made between measured total energy received per day and the corresponding simulated totals. The simulated totals were all within 11 percent of the measured total. The conclusion is that a useful probabilistic model of solar radiation for the Goldstone, California, area of the Mojave Desert has been constructed

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

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

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

Criminal History Enhancements Sourcebook

Criminal history scores make up one of the two most significant determinants of the punishment an offender receives in a sentencing guidelines jurisdiction. While prior convictions are taken into account by all U.S. sentencing systems, sentencing guidelines make the role of prior crimes more explicit by specifying the counting rules and by indicating the effect of prior convictions on sentence severity. Yet, once established, criminal history scoring formulas go largely unexamined. Moreover, there is great diversity across state and federal jurisdictions in the ways that an offender's criminal record is considered by courts at sentencing. This Sourcebook brings together for the first time information on criminal history enhancements in all existing U.S. sentencing guidelines systems. Building on this base, the Sourcebook examines major variations in the approaches taken by these systems, and identifies the underlying sentencing policy issues raised by such enhancements.The Sourcebook contains the following elements:A summary of criminal history enhancements in all guidelines jurisdictions;An analysis of the critical dimensions of an offender's previous convictions;A discussion of the policy options available to commissions considering amendments to their criminal history enhancements;A bibliography of key readings on the role of prior convictions at sentencing

Proper Motions of PSRs B1757-24 and B1951+32: Implications for Ages and Associations

Over the last decade, considerable effort has been made to measure the proper motions of the pulsars B1757-24 and B1951+32 in order to establish or refute associations with nearby supernova remnants and to understand better the complicated geometries of their surrounding nebulae. We present proper motion measurements of both pulsars with the Very Large Array, increasing the time baselines of the measurements from 3.9 yr to 6.5 yr and from 12.0 yr to 14.5 yr, respectively, compared to previous observations. We confirm the non-detection of proper motion of PSR B1757-24, and our measurement of (mu_a, mu_d) = (-11 +/- 9, -1 +/- 15) mas yr^{-1} confirms that the association of PSR B1757-24 with SNR G5.4-1.2 is unlikely for the pulsar characteristic age of 15.5 kyr, although an association can not be excluded for a significantly larger age. For PSR B1951+32, we measure a proper motion of (mu_a, mu_d) = (-28.8 +/- 0.9, -14.7 +/- 0.9) mas yr^{-1}, reducing the uncertainty in the proper motion by a factor of two compared to previous results. After correcting to the local standard of rest, the proper motion indicates a kinetic age of ~51 kyr for the pulsar, assuming it was born near the geometric center of the supernova remnant. The radio-bright arc of emission along the pulsar proper motion vector shows time-variable structure, but moves with the pulsar at an approximately constant separation ~2.5", lending weight to its interpretation as a shock structure driven by the pulsar.Comment: LaTeX file uses emulateapj.cls; 7 pages, 4 figures, to be published ApJ February 10, 2008, v674 p271-278. Revision reflects journal formatting; there are no substantial revision

Interaction of Supernova Ejecta with Nearby Protoplanetary Disks

The early Solar System contained short-lived radionuclides such as 60Fe (t1/2 = 1.5 Myr) whose most likely source was a nearby supernova. Previous models of Solar System formation considered a supernova shock that triggered the collapse of the Sun's nascent molecular cloud. We advocate an alternative hypothesis, that the Solar System's protoplanetary disk had already formed when a very close (< 1 pc) supernova injected radioactive material directly into the disk. We conduct the first numerical simulations designed to answer two questions related to this hypothesis: will the disk be destroyed by such a close supernova; and will any of the ejecta be mixed into the disk? Our simulations demonstrate that the disk does not absorb enough momentum from the shock to escape the protostar to which it is bound. Only low amounts (< 1%) of mass loss occur, due to stripping by Kelvin-Helmholtz instabilities across the top of the disk, which also mix into the disk about 1% of the intercepted ejecta. These low efficiencies of destruction and injectation are due to the fact that the high disk pressures prevent the ejecta from penetrating far into the disk before stalling. Injection of gas-phase ejecta is too inefficient to be consistent with the abundances of radionuclides inferred from meteorites. On the other hand, the radionuclides found in meteorites would have condensed into dust grains in the supernova ejecta, and we argue that such grains will be injected directly into the disk with nearly 100% efficiency. The meteoritic abundances of the short-lived radionuclides such as 60Fe therefore are consistent with injection of grains condensed from the ejecta of a nearby (< 1 pc) supernova, into an already-formed protoplanetary disk.Comment: 57 pages, 16 figure