Perfect Hash Families: The Generalization to Higher Indices

Perfect hash families are often represented as combinatorial arrays encoding partitions of kitems into v classes, so that every t or fewer of the items are completely separated by at least a specified number of chosen partitions. This specified number is the index of the hash family. The case when each t-set must be separated at least once has been extensively researched; they arise in diverse applications, both directly and as fundamental ingredients in a column replacement strategy for a variety of combinatorial arrays. In this paper, construction techniques and algorithmic methods for constructing perfect hash families are surveyed, in order to explore extensions to the situation when each t-set must be separated by more than one partition.https://digitalcommons.usmalibrary.org/books/1029/thumbnail.jp

Healthcare professionals' intentions to use wiki-based reminders to promote best practices in trauma care: a survey protocol

<p>Abstract</p> <p>Background</p> <p>Healthcare professionals are increasingly using wikis as collaborative tools to create, synthesize, share, and disseminate knowledge in healthcare. Because wikis depend on collaborators to keep content up-to-date, healthcare professionals who use wikis must adopt behaviors that foster this collaboration. This protocol describes the methods we will use to develop and test the metrological qualities of a questionnaire that will assess healthcare professionals' intentions and the determinants of those intentions to use wiki-based reminders that promote best practices in trauma care.</p> <p>Methods</p> <p>Using the Theory of Planned Behavior, we will conduct semi-structured interviews of healthcare professionals to identify salient beliefs that may affect their future use of wikis. These beliefs will inform our questionnaire on intended behavior. A test-retest of the survey will verify the questionnaire's stability over time. We will interview 50 healthcare professionals (25 physicians and 25 allied health professionals) working in the emergency departments of three trauma centers in Quebec, Canada. We will analyze the content of the interviews and construct and pilot a questionnaire. We will then test the revised questionnaire with 30 healthcare professionals (15 physicians and 15 allied health professionals) and retest it two weeks later. We will assess the internal consistency of the questionnaire constructs using Cronbach's alpha coefficients and determine their stability with the intra-class correlation (ICC).</p> <p>Discussion</p> <p>To our knowledge, this study will be the first to develop and test a theory-based survey that measures healthcare professionals' intentions to use a wiki-based intervention. This study will identify professionals' salient beliefs qualitatively and will quantify the psychometric capacities of the questionnaire based on those beliefs.</p

Multi-messenger observations of a binary neutron star merger

On 2017 August 17 a binary neutron star coalescence candidate (later designated GW170817) with merger time 12:41:04 UTC was observed through gravitational waves by the Advanced LIGO and Advanced Virgo detectors. The Fermi Gamma-ray Burst Monitor independently detected a gamma-ray burst (GRB 170817A) with a time delay of ~1.7 s with respect to the merger time. From the gravitational-wave signal, the source was initially localized to a sky region of 31 deg2 at a luminosity distance of 40+8-8 Mpc and with component masses consistent with neutron stars. The component masses were later measured to be in the range 0.86 to 2.26 Mo. An extensive observing campaign was launched across the electromagnetic spectrum leading to the discovery of a bright optical transient (SSS17a, now with the IAU identification of AT 2017gfo) in NGC 4993 (at ~40 Mpc) less than 11 hours after the merger by the One- Meter, Two Hemisphere (1M2H) team using the 1 m Swope Telescope. The optical transient was independently detected by multiple teams within an hour. Subsequent observations targeted the object and its environment. Early ultraviolet observations revealed a blue transient that faded within 48 hours. Optical and infrared observations showed a redward evolution over ~10 days. Following early non-detections, X-ray and radio emission were discovered at the transient’s position ~9 and ~16 days, respectively, after the merger. Both the X-ray and radio emission likely arise from a physical process that is distinct from the one that generates the UV/optical/near-infrared emission. No ultra-high-energy gamma-rays and no neutrino candidates consistent with the source were found in follow-up searches. These observations support the hypothesis that GW170817 was produced by the merger of two neutron stars in NGC4993 followed by a short gamma-ray burst (GRB 170817A) and a kilonova/macronova powered by the radioactive decay of r-process nuclei synthesized in the ejecta

A sequence approach to linear perfect hash families

A linear (q d, q, t)-perfect hash family of size s in a vector space V of order q d over a field F of order q consists of a set S = {φ1, ⋯, φs} of linear functionals from V to F with the following property: for all t subsets X\subseteq V there exists φi ∈ S such that φi is injective when restricted to F. A linear (q d, q, t)-perfect hash family of minimal size d(t - 1) is said to be optimal. In this paper, we extend the theory for linear perfect hash families based on sequences developed by Blackburn and Wild. We develop techniques which we use to construct new optimal linear (q 2, q, 5)-perfect hash families and (q 4, q, 3)-perfect hash families. The sequence approach also explains a relationship between linear (q 3, q, 3)-perfect hash families and linear (q 2, q, 4)-perfect hash families. © 2007 Springer Science+Business Media, LLC.Susan G. Barwick and Wen-Ai Jackso