To Infinity and Beyond

We prove that if a group generated by a bireversible Mealy automaton contains an element of infinite order, then it must have exponential growth. As a direct consequence, no infinite virtually nilpotent group can be generated by a bireversible Mealy automaton

A1_9 To Infinity and Beyond!

This paper investigates the conditions under which Toy Storys Buzz Lightyear could take flight. At an optimum angle of attack of = 13Ëš, a firework powering Buzz would approximately need to provide a force of 165.5N for a minimum burn time of 0.82s to allow a minimum velocity of 90.68m/s to be reached for Buzz to take off

Time-dependent density functional theory of high excitations: To infinity, and beyond

We review the theoretical background for obtaining both quantum defects and scattering phase shifts from time-dependent density functional theory. The quantum defect on the negative energy side of the spectrum and the phase shift on the positive energy side merge continuously at E=0, allowing both to be found by the same method. We illustrate with simple one-dimensional examples: the spherical well and the delta well potential. As an example of a real system, we study in detail elastic electron scattering from the He${}^{+}$ ion. We show how the results are influenced by different approximations to the unknown components in (time-dependent) density functional theory: the ground state exchange-correlation potential and time-dependent kernel. We also revisit our previously obtained results for $e$-H scattering. Our results are remarkably accurate in may cases, but fail qualitatively in others.Comment: Resubmitted version, Changed acknowledgments, 17 pages including supplementary table, submitted to PCCP themed issue on time-dependent density-functional theor

crisscrossing Science Episode 071: To Infinity and Beyond

In this episode, Mike Crosser (professor of physics at Linfield College) and Chad Tillberg (professor of biology at Linfield College) invite Dr. Chuck Dunn (professor of mathematics at Linfield College) into the studio to talk about infinity. Dunn uses some analogies to describe real mathematical contexts in which infinity comes up

Pathogenic Acinetobacter: From the cell surface to infinity and beyond

The genus Acinetobacter encompasses multiple nosocomial opportunistic pathogens that are of increasing worldwide relevance because of their ability to survive exposure to various antimicrobial and sterilization agents. Among these, Acinetobacter baumannii, Acinetobacter nosocomialis, and Acinetobacter pittii are the most frequently isolated in hospitals around the world. Despite the growing incidence of multidrug-resistant Acinetobacter spp., little is known about the factors that contribute to pathogenesis. New strategies for treating and managing infections caused by multidrug-resistant Acinetobacter strains are urgently needed, and this requires a detailed understanding of the pathobiology of these organisms. In recent years, some virulence factors important for Acinetobacter colonization have started to emerge. In this review, we focus on several recently described virulence factors that act at the bacterial surface level, such as the capsule, O-linked protein glycosylation, and adhesins. Furthermore, we describe the current knowledge regarding the type II and type VI secretion systems present in these strains

To Infinity and Beyond: Scaling Economic Theories via Logical Compactness

Many economic-theoretic models incorporate finiteness assumptions that, while introduced for simplicity, play a real role in the analysis. Such assumptions introduce a conceptual problem, as results that rely on finiteness are often implicitly nonrobust; for example, they may depend upon edge effects or artificial boundary conditions. Here, we present a unified method that enables us to remove finiteness assumptions, such as those on market sizes, time horizons, and datasets. We then apply our approach to a variety of matching, exchange economy, and revealed preference settings. The key to our approach is Logical Compactness, a core result from Propositional Logic. Building on Logical Compactness, in a matching setting, we reprove large-market existence results implied by Fleiner's analysis, and (newly) prove both the strategy-proofness of the man-optimal stable mechanism in infinite markets and an infinite-market version of Nguyen and Vohra's existence result for near-feasible stable matchings with couples. In a trading-network setting, we prove that the Hatfield et al. result on existence of Walrasian equilibria extends to infinite markets. In a dynamic matching setting, we prove that Pereyra's existence result for dynamic two-sided matching markets extends to a doubly infinite time horizon. Finally, beyond existence and characterization of solutions, in a revealed-preference setting we reprove Reny's infinite-data version of Afriat's theorem and (newly) prove an infinite-data version of McFadden and Richter's characterization of rationalizable stochastic datasets

To infinity and beyond: Strategies for fabricating medicines in outer space

Recent advancements in next generation spacecrafts have reignited public excitement over life beyond Earth. However, to safeguard the health and safety of humans in the hostile environment of space, innovation in pharmaceutical manufacturing and drug delivery deserves urgent attention. In this review/commentary, the current state of medicines provision in space is explored, accompanied by a forward look on the future of pharmaceutical manufacturing in outer space. The hazards associated with spaceflight, and their corresponding medical problems, are first briefly discussed. Subsequently, the infeasibility of present-day medicines provision systems for supporting deep space exploration is examined. The existing knowledge gaps on the altered clinical effects of medicines in space are evaluated, and suggestions are provided on how clinical trials in space might be conducted. An envisioned model of on-site production and delivery of medicines in space is proposed, referencing emerging technologies (e.g. Chemputing, synthetic biology, and 3D printing) being developed on Earth that may be adapted for extra-terrestrial use. This review concludes with a critical analysis on the regulatory considerations necessary to facilitate the adoption of these technologies and proposes a framework by which these may be enforced. In doing so, this commentary aims to instigate discussions on the pharmaceutical needs of deep space exploration, and strategies on how these may be met