Portable random number generators

Computers are deterministic devices, and a computer-generated random number is a contradiction in terms. As a result, computer-generated pseudorandom numbers are fraught with peril for the unwary. We summarize much that is known about the most well-known pseudorandom number generators: congruential generators. We also provide machine-independent programs to implement the generators in any language that has 32-bit signed integers-for example C, C++, and FORTRAN. Based on an extensive search, we provide parameter values better than those previously available.Programming (Mathematics) ; Computers

Unimodular integer circulants associated with trinomials

The n � n circulant matrix associated with the polynomial [image removed] (with d < n) is the one with first row (a0 ? ad 0 ? 0). The problem as to when such circulants are unimodular arises in the theory of cyclically presented groups and leads to the following question, previously studied by Odoni and Cremona: when is Res(f(t), tn-1) = �1? We give a complete answer to this question for trinomials f(t) = tm � tk � 1. Our main result was conjectured by the author in an earlier paper and (with two exceptions) implies the classification of the finite Cavicchioli?Hegenbarth?Repov? generalized Fibonacci groups, thus giving an almost complete answer to a question of Bardakov and Vesnin

Fibonacci type semigroups

We study "Fibonacci type" groups and semigroups. By establishing asphericity of their presentations we show that many of the groups are infinite. We combine this with Adjan graph techniques and the classification of the finite Fibonacci semigroups (in terms of the finite Fibonacci groups) to extend it to the Fibonacci type semigroups

Groups of Fibonacci type revisited

This article concerns a class of groups of Fibonacci type introduced by Johnson and Mawdesley that includes Conway?s Fibonacci groups, the Sieradski groups, and the Gilbert-Howie groups. This class of groups provides an interesting focus for developing the theory of cyclically presented groups and, following questions by Bardakov and Vesnin and by Cavicchioli, Hegenbarth, and Repov?s, they have enjoyed renewed interest in recent years. We survey results concerning their algebraic properties, such as isomorphisms within the class, the classification of the finite groups, small cancellation properties, abelianizations, asphericity, connections with Labelled Oriented Graph groups, and the semigroups of Fibonacci type. Further, we present a new method of proving the classification of the finite groups that deals with all but three groups

Portable random number generators

Computers are deterministic devices, and a computer-generated random number is a contradiction in terms. As a result, computer-generated pseudorandom numbers are fraught with peril for the unwary. We summarize much that is known about the most well-known pseudorandom number generators: congruential generators. We also provide machine-independent programs to implement the generators in any language that has 32-bit signed integers-for example C, C++, and FORTRAN. Based on an extensive search, we provide parameter values better than those previously available

The aspherical Cavicchioli-Hegenbarth-Repovš generalized Fibonacci groups

The Cavicchioli–Hegenbarth–Repovš generalized Fibonacci groups are defined by the presentations Gn (m, k) = 〈x 1, … , xn | xixi+m = xi+k (1 ⩽ i ⩽ n)〉. These cyclically presented groups generalize Conway's Fibonacci groups and the Sieradski groups. Building on a theorem of Bardakov and Vesnin we classify the aspherical presentations Gn (m, k). We determine when Gn (m, k) has infinite abelianization and provide sufficient conditions for Gn (m, k) to be perfect. We conjecture that these are also necessary conditions. Combined with our asphericity theorem, a proof of this conjecture would imply a classification of the finite Cavicchioli–Hegenbarth–Repovš groups

Time and Energy, Exploring Trajectory Options Between Nodes in Earth-Moon Space

The Global Exploration Roadmap (GER) was released by the International Space Exploration Coordination Group (ISECG) in September of 2011. It describes mission scenarios that begin with the International Space Station and utilize it to demonstrate necessary technologies and capabilities prior to deployment of systems into Earth-Moon space. Deployment of these systems is an intermediate step in preparation for more complex deep space missions to near-Earth asteroids and eventually Mars. In one of the scenarios described in the GER, "Asteroid Next", there are activities that occur in Earth-Moon space at one of the Earth-Moon Lagrange (libration) points. In this regard, the authors examine the possible role of an intermediate staging point in an effort to illuminate potential trajectory options for conducting missions in Earth-Moon space of increasing duration, ultimately leading to deep space missions. This paper will describe several options for transits between Low Earth Orbit (LEO) and the libration points, transits between libration points, and transits between the libration points and interplanetary trajectories. The solution space provided will be constrained by selected orbital mechanics design techniques and physical characteristics of hardware to be used in both crewed missions and uncrewed missions. The relationships between time and energy required to transfer hardware between these locations will provide a better understanding of the potential trade-offs mission planners could consider in the development of capabilities, individual missions, and mission series in the context of the ISECG GER

Discovering Software Reliability Patterns Based On Multiple Software Projects

Discovering patterns that indicate software reliability provides valuable information to software project managers. Software Quality Classification (SQC) modeling is a methodology that can be used to discover reliability patterns of large software projects. However, the patterns found by SQC modeling may not be accurate and robust owing to insufficient information used in the training process. This study compares two genetic programming-based SQC models using different volumes of data. These data were extracted from seven different NASA software projects. The results demonstrate that combining data from different projects can produce more accurate and reliable patterns

Antibiotic Spacers in Shoulder Arthroplasty: Comparison of Stemmed and Stemless Implants.

Background: Antibiotic spacers in shoulder periprosthetic joint infection deliver antibiotics locally and provide temporary stability. The purpose of this study was to evaluate differences between stemmed and stemless spacers. Methods: All spacers placed from 2011 to 2013 were identified. Stemless spacers were made by creating a spherical ball of cement placed in the joint space. Stemmed spacers had some portion in the humeral canal. Operative time, complications, reimplantation, reinfection, and range of motion were analyzed. Results: There were 37 spacers placed: 22 were stemless and 15 were stemmed. The stemless spacer population was older (70.9 ± 7.8 years vs. 62.8 ± 8.4 years, p = 0.006). The groups had a similar percentage of each gender (stemless group, 45% male vs. stemmed group, 40% male; p = 0.742), body mass index (stemless group, 29.1 ± 6.4 kg/m2 vs. stemmed group, 31.5 ± 8.3 kg/m2; p = 0.354) and Charlson Comorbidity Index (stemless group, 4.2 ± 1.2 vs. stemmed group, 4.2 ± 1.7; p = 0.958). Operative time was similar (stemless group, 127.5 ± 37.1 minutes vs. stemmed group, 130.5 ± 39.4 minutes). Two stemless group patients had self-resolving radial nerve palsies. Within the stemless group, 15 of 22 (68.2%) underwent reimplantation with 14 of 15 having forward elevation of 109° ± 23°. Within the stemmed group, 12 of 15 (80.0%, p = 0.427) underwent reimplantation with 8 of 12 having forward elevation of 94° ± 43° (range, 30° to 150°; p = 0.300). Two stemmed group patients had axillary nerve palsies, one of which self-resolved but the other did not. One patient sustained dislocation of reverse shoulder arthroplasty after reimplantation. One stemless group patient required an open reduction and glenosphere exchange of dislocated reverse shoulder arthroplasty at 6 weeks after reimplantation. Conclusions: Stemmed and stemless spacers had similar clinical outcomes. When analyzing all antibiotic spacers, over 70% were converted to revision arthroplasties. The results of this study do not suggest superiority of either stemmed or stemless antibiotic spacers