Random template banks and relaxed lattice coverings

Template-based searches for gravitational waves are often limited by the computational cost associated with searching large parameter spaces. The study of efficient template banks, in the sense of using the smallest number of templates, is therefore of great practical interest. The "traditional" approach to template-bank construction requires every point in parameter space to be covered by at least one template, which rapidly becomes inefficient at higher dimensions. Here we study an alternative approach, where any point in parameter space is covered only with a given probability < 1. We find that by giving up complete coverage in this way, large reductions in the number of templates are possible, especially at higher dimensions. The prime examples studied here are "random template banks", in which templates are placed randomly with uniform probability over the parameter space. In addition to its obvious simplicity, this method turns out to be surprisingly efficient. We analyze the statistical properties of such random template banks, and compare their efficiency to traditional lattice coverings. We further study "relaxed" lattice coverings (using Zn and An* lattices), which similarly cover any signal location only with probability < 1. The relaxed An* lattice is found to yield the most efficient template banks at low dimensions (n < 10), while random template banks increasingly outperform any other method at higher dimensions.Comment: 13 pages, 10 figures, submitted to PR

Déjà vu and the entorhinal cortex: dissociating recollective from familiarity disruptions in a single case patient

Past research has demonstrated a relationship between déjà vu and the entorhinal cortex in patients with wider medial temporal lobe damage. The aim of the present research was to investigate this crucial link in a patient (MR) with a selective lesion to the left lateral entorhinal cortex to provide a more direct exploration of this relationship. Two experiments investigated the experiences of déjà vécu (using the IDEA questionnaire) and déjà vu (using an adapted DRM paradigm) in MR and a set of matched controls. The results demonstrated that MR had quantitatively more and qualitatively richer recollective experiences of déjà vécu. In addition, under laboratory-based déjà vu conditions designed to elicit both false recollection (critical lures) and false familiarity (weakly-associated lures), MR only revealed greater memory impairments for the latter. The present results are therefore the first to demonstrate a direct relationship between the entorhinal cortex and the experience of both déjà vu and déjà vécu. They furthermore suggest that the entorhinal cortex is involved in both weakly-associative false memory as well as strongly-associative memory under conditions that promote familiarity-based processing

Pattern Selection in the Complex Ginzburg-Landau Equation with Multi-Resonant Forcing

We study the excitation of spatial patterns by resonant, multi-frequency forcing in systems undergoing a Hopf bifurcation to spatially homogeneous oscillations. Using weakly nonlinear analysis we show that for small amplitudes only stripe or hexagon patterns are linearly stable, whereas square patterns and patterns involving more than three modes are unstable. In the case of hexagon patterns up- and down-hexagons can be simultaneously stable. The third-order, weakly nonlinear analysis predicts stable square patterns and super-hexagons for larger amplitudes. Direct simulations show, however, that in this regime the third-order weakly nonlinear analysis is insufficient, and these patterns are, in fact unstable

Entanglement Distillation Protocols and Number Theory

We show that the analysis of entanglement distillation protocols for qudits of arbitrary dimension $D$ benefits from applying basic concepts from number theory, since the set \zdn associated to Bell diagonal states is a module rather than a vector space. We find that a partition of \zdn into divisor classes characterizes the invariant properties of mixed Bell diagonal states under local permutations. We construct a very general class of recursion protocols by means of unitary operations implementing these local permutations. We study these distillation protocols depending on whether we use twirling operations in the intermediate steps or not, and we study them both analitically and numerically with Monte Carlo methods. In the absence of twirling operations, we construct extensions of the quantum privacy algorithms valid for secure communications with qudits of any dimension $D$. When $D$ is a prime number, we show that distillation protocols are optimal both qualitatively and quantitatively.Comment: REVTEX4 file, 7 color figures, 2 table

Candidate constructional volcanic edifices on Mercury

[Introduction] Studies using MESSENGER data suggest that Mercury’s crust is predominantly a product of effusive volcanism that occurred in the first billion years following the planet’s formation. Despite this planet-wide effusive volcanism, no constructional volcanic edifices, characterized by a topographic rise, have hitherto been robustly identified on Mercury, whereas constructional volcanoes are common on other planetary bodies in the solar system with volcanic histories. Here, we describe two candidate constructional volcanic edifices we have found on Mercury and discuss how these edifices may have formed

Preliminary observations of Rustaveli basin, Mercury

Rustaveli basin on Mercury (82.76° E, 52.39° N) is a 200.5 km diameter peak-ring basin. Since the approval of its name on April 24, 2012, it has not featured prominently in the literature. It is a large and important feature within the Hokusai (H5) quadrangle of which we are currently producing a 1:2M scale geological map. Here, we describe our first observations of Rustaveli

Tele-autonomous control involving contacts: The applications of a high precision laser line range sensor

The object localization algorithm based on line-segment matching is presented. The method is very simple and computationally fast. In most cases, closed-form formulas are used to derive the solution. The method is also quite flexible, because only few surfaces (one or two) need to be accessed (sensed) to gather necessary range data. For example, if the line-segments are extracted from boundaries of a planar surface, only parameters of one surface and two of its boundaries need to be extracted, as compared with traditional point-surface matching or line-surface matching algorithms which need to access at least three surfaces in order to locate a planar object. Therefore, this method is especially suitable for applications when an object is surrounded by many other work pieces and most of the object is very difficult, is not impossible, to be measured; or when not all parts of the object can be reached. The theoretical ground on how to use line range sensor to located an object was laid. Much work has to be done in order to be really useful

Preliminary findings from geological mapping of the Hokusai (H5) quadrangle of Mercury

Quadrangle geological maps from Mariner 10 data cover 45% of the surface of Mercury at 1:5M scale. Orbital MESSENGER data, which cover the entire planetary surface, can now be used to produce finer scale geological maps, including regions unseen by Mariner 10. Hokusai quadrangle (0–90° E; 22.5–66° N) is in the hemisphere unmapped by Mariner 10. It contains prominent features which are already being studied, including: Rachmaninoff basin, volcanic vents within and around Rachmaninoff, much of the Northern Plains and abundant wrinkle ridges. Its northern latitude makes it a prime candidate for regional geological mapping since compositional and topographical data, as well as Mercury Dual Imaging System (MDIS) data, are available for geological interpretation. This work aims to produce a map at 1:2M scale, compatible with other new quadrangle maps and to complement a global map now in progress

Neutron activation analysis traces copper artifacts to geographical point of origin

Impurities remaining in the metallic copper are identified and quantified by spectrographic and neutron activation analysis. Determination of the type of ore used for the copper artifact places the geographic point of origin of the artifact

Dynamical Quantum Phase Transitions in the Transverse Field Ising Model

A phase transition indicates a sudden change in the properties of a large system. For temperature-driven phase transitions this is related to non-analytic behavior of the free energy density at the critical temperature: The knowledge of the free energy density in one phase is insufficient to predict the properties of the other phase. In this paper we show that a close analogue of this behavior can occur in the real time evolution of quantum systems, namely non-analytic behavior at a critical time. We denote such behavior a dynamical phase transition and explore its properties in the transverse field Ising model. Specifically, we show that the equilibrium quantum phase transition and the dynamical phase transition in this model are intimately related.Comment: 4+4 pages, 4 figures, Appendix adde