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A generating set for a finite group G is minimal if no proper subset generates G, and $m(G)$ denotes the maximal size of a minimal generating set for G. We prove a conjecture of Lucchini, Moscatiello and Spiga by showing that there exist $a,b> 0$ such that any finite group G satisfies $m(G) \leqslant a \cdot \delta (G)^b$ , for $\delta (G) = \sum _{p \text { prime}} m(G_p)$ , where $G_p$ is a Sylow p-subgroup of G. To do this, we first bound $m(G)$ for all almost simple groups of Lie type (until now, no nontrivial bounds were known except for groups of rank $1$ or $2$ ). In particular, we prove that there exist $a,b> 0$ such that any finite simple group G of Lie type of rank r over the field $\mathbb {F}_{p^f}$ satisfies $r + \omega (f) \leqslant m(G) \leqslant a(r + \omega (f))^b$ , where $\omega (f)$ denotes the number of distinct prime divisors of f. In the process, we confirm a conjecture of Gill and Liebeck that there exist $a,b> 0$ such that a minimal base for a faithful primitive action of an almost simple group of Lie type of rank r over $\mathbb {F}_{p^f}$ has size at most $ar^b + \omega (f)$ .

To successfully operate in a harsh environment like the Arctic Ocean, one must be able to understand and predict how that environment will evolve over different spatial and temporal scales. This is particularly challenging given the on-going and significant environmental changes that are occurring in the region. Access to the most recent environmental information provides timely knowledge that enables ship-based operations to proceed efficiently, effectively and safely in this difficult arena. Knowledge of the evolving environmental conditions during a field campaign is critical for effective planning, optimal execution of sampling strategies, and to provide a broader context to data collected at specific times and places. We describe the collaborations and processes that enabled an operational system to be developed to provide a remote field-team, located on USCGC Healy in the Beaufort Sea, with near real-time situational awareness information regarding the weather, sea ice conditions, and oceanographic processes. The developed system included the punctual throughput of near real-time products such as satellite imagery, meteorological forecasts, ice charts, model outputs, and up to date locations of key sea ice and ocean-based assets. Science and operational users, as well as onshore personnel, used this system for real-time practical considerations such as ship navigation, and to time scientific operations to ensure the appropriate sea ice and weather conditions prevailed. By presenting the outputs of the system within the context of case studies our results clearly demonstrate the benefits that improved situational awareness brings to ship-based operations in the Arctic Ocean, both today and in the future.

A popular cigarette advertisement from the 1960s exclaimed, "You've come a long way, Baby!" That sentiment could be applied to Naval Oceanography. The US Navy has navigated the course of developing prediction technology over many fundamental shifts in global geopolitics while addressing the evolving challenges at the forefront of the oceanography mission to ensure the safety of the nation's armed forces. Originally motivated by Soviet-era submarine programs, accurate acoustic prediction necessitated forecasting the positions of ocean fronts and eddies. Since then, the scope of Naval Oceanography has expanded to encompass a littoral focus, including applications that assist Navy SEa Air and Land (SEAL) teams, amphibious vehicle landings, and mine warfare. The fundamental physics governing the universe remains unchanged and so has the Navy's need to understand ocean physics, build numerical representations, connect to data streams, and assimilate observations in order to provide forecasts addressing the challenges of today and tomorrow. A well-planned course is no accident, and the Navy's leading edge in ocean prediction is the result. This paper provides a description of the path to this leading edge, a synthesis of the current operational architecture that enables Naval Oceanography, an analysis of the triumphs of the last 10 years that are part of today's oceanography portfolio, and a prediction of what the next 10 years holds for Naval Oceanography.

On October 15, 2001, a U.S. Senate staff member opened an envelope containing Bacillus anthracis spores. Chemoprophylaxis was promptly initiated and nasal swabs obtained for all persons in the immediate area. An epidemiologic investigation was conducted to define exposure areas and identify persons who should receive prolonged chemoprophylaxis, based on their exposure risk. Persons immediately exposed to B. anthracis spores were interviewed; records were reviewed to identify additional persons in this area. Persons with positive nasal swabs had repeat swabs and serial serologic evaluation to measure antibodies to B. anthracis protective antigen (anti-PA). A total of 625 persons were identified as requiring prolonged chemoprophylaxis; 28 had positive nasal swabs. Repeat nasal swabs were negative at 7 days; none had developed anti-PA antibodies by 42 days after exposure. Early nasal swab testing is a useful epidemiologic tool to assess risk of exposure to aerosolized B. anthracis. Early, wide chemoprophylaxis may have averted an outbreak of anthrax in this population.