The first demonstration of laser action in ruby was made in 1960 by T. H. Maiman of Hughes Research Laboratories, USA. Many laboratories worldwide began the search for lasers using different materials, operating at different wavelengths. In the UK, academia, industry and the central laboratories took up the challenge from the earliest days to develop these systems for a broad range of applications. This historical review looks at the contribution the UK has made to the advancement of the technology, the development of systems and components and their exploitation over the last 60 years.

Let G be a finite group, and let cs(G) be the set of conjugacy class sizes of G. Recalling that an element g of G is called a vanishing element if there exists an irreducible character of G taking the value 0 on g, we consider one particular subset of cs(G), namely, the set vcs(G) whose elements are the conjugacy class sizes of the vanishing elements of G. Motivated by the results inBianchi et al. (2020, J. Group Theory, 23, 79–83), we describe the class of the finite groups G such that vcs(G) consists of a single element under the assumption that G is supersolvable or G has a normal Sylow 2-subgroup (in particular, groups of odd order are covered). As a particular case, we also get a characterization of finite groups having a single vanishing conjugacy class size which is either a prime power or square-free.

We consider an M/M/1 queue with a removable server that dynamically chooses its service rate from a set of finitely many rates. If the server is off, the system must warm up for a random, exponentially distributed amount of time, before it can begin processing jobs. We show under the average cost criterion, that work conserving policies are optimal. We then demonstrate the optimal policy can be characterized by a threshold for turning on the server and the optimal service rate increases monotonically with the number in system. Finally, we present some numerical experiments to provide insights into the practicality of having both a removable server and service rate control.

OBJECTIVES/SPECIFIC AIMS: Clostridium difficile infection (CDI) is the most common cause of antibiotic-associated diarrhea and an increasingly common infection in children in both hospital and community settings. Between 20% and 30% of pediatric patients will have a recurrence of symptoms in the days to weeks following an initial infection. Multiple recurrences have been successfully treated with fecal microbiota transplantation (FMT), though the body of evidence in pediatric patients is limited primarily to case reports and case series. The goal of our study was to better understand practices, success, and safety of FMT in children as well as identify risk factors associated with a failed FMT in our pediatric patients. METHODS/STUDY POPULATION: This multicenter retrospective analysis included 373 patients who underwent FMT for CDI between January 1, 2006 and January 1, 2017 from 18 pediatric centers. Demographics, baseline characteristics, FMT practices, C. difficile outcomes, and post-FMT complications were collected through chart abstraction. Successful FMT was defined as no recurrence of CDI within 60 days after FMT. Of the 373 patients in the cohort, 342 had known outcome data at two months post-FMT and were included in the primary analysis evaluating risk factors for recurrence post-FMT. An additional six patients who underwent FMT for refractory CDI were excluded from the primary analysis. Unadjusted analysis was performed using Wilcoxon rank-sum test, Pearson χ2 test, or Fisher exact test where appropriate. Stepwise logistic regression was utilized to determine independent predictors of success. RESULTS/ANTICIPATED RESULTS: The median age of included patients was 10 years (IQR; 3.0, 15.0) and 50% of patients were female. The majority of the cohort was White (89.0%). Comorbidities included 120 patients with inflammatory bowel disease (IBD) and 14 patients who had undergone a solid organ or stem cell transplantation. Of the 336 patients with known outcomes at two months, 272 (81%) had a successful outcome. In the 64 (19%) patients that did have a recurrence, 35 underwent repeat FMT which was successful in 20 of the 35 (57%). The overall success rate of FMT in preventing further episodes of CDI in the cohort with known outcome data was 87%. Unadjusted predictors of a primary FMT response are summarized. Based on stepwise logistic regression modeling, the use of fresh stool, FMT delivery via colonoscopy, the lack of a feeding tube, and a lower number of CDI episodes before undergoing FMT were independently associated with a successful outcome. There were 20 adverse events in the cohort assessed to be related to FMT, 6 of which were felt to be severe. There were no deaths assessed to be related to FMT in the cohort. DISCUSSION/SIGNIFICANCE OF IMPACT: The overall success of FMT in pediatric patients with recurrent or severe CDI is 81% after a single FMT. Children without a feeding tube, who receive an early FMT, FMT with fresh stool, or FMT via colonoscopy are less likely to have a recurrence of CDI in the 2 months following FMT. This is the first large study of FMT for CDI in a pediatric cohort. These findings, if confirmed by additional prospective studies, will support alterations in the practice of FMT in children.

We consider the problem of routing and admission control in a loss system featuring two classes of arriving jobs (high-priority and low-priority jobs) and two types of servers, in which decision-making for high-priority jobs is forced, and rewards influence the desirability of each of the four possible routing decisions. We seek a policy that maximizes expected long-run reward, under both the discounted reward and long-run average reward criteria, and formulate the problem as a Markov decision process. When the reward structure favors high-priority jobs, we demonstrate that there exists an optimal monotone switching curve policy with slope of at least −1. When the reward structure favors low-priority jobs, we demonstrate that the value function, in general, lacks structure, which complicates the search for structure in optimal policies. However, we identify conditions under which optimal policies can be characterized in greater detail. We also examine the performance of heuristic policies in a brief numerical study.

Flea beetle (Chrysomelidae) egg deposition has been found on three impressions of alder (Alnus parvifolia) leaves collected at a roadcut in Republic, Washington. These fossils were discovered by Wes Wehr (University of Washington, Burke Museum) during investigations of fossil plants from the Republic, Washington, area. These impressions represent a yet to be determined species, belonging to the genus Altica GeofFroy (1762). They represent the first member of this genus to be described from the Eocene of North America. The fossils were found in lacustrine rocks from the lower part of the Klondike Mountain Formation. Figure 1 represents the Republic fossil locality and the distribution of this Formation. A brief description of the geologic history of this region can be found in Wolfe and Wehr (1987). The Klondike Mountain Formation has a radiometric age that ranges from 42.3 ± 2.0 to 50.3 ± 1.7 m.y. (Pearson and Obradovich, 1977).

The redshifted 21cm line of neutral hydrogen (Hi), potentially observable at low radio frequencies (~50–200 MHz), should be a powerful probe of the physical conditions of the inter-galactic medium during Cosmic Dawn and the Epoch of Reionisation (EoR). The sky-averaged Hi signal is expected to be extremely weak (~100 mK) in comparison to the foreground of up to 104 K at the lowest frequencies of interest. The detection of such a weak signal requires an extremely stable, well characterised system and a good understanding of the foregrounds. Development of a nearly perfectly (~mK accuracy) calibrated total power radiometer system is essential for this type of experiment. We present the BIGHORNS (Broadband Instrument for Global HydrOgen ReioNisation Signal) experiment which was designed and built to detect the sky-averaged Hi signal from the EoR at low radio frequencies. The BIGHORNS system is a mobile total power radiometer, which can be deployed in any remote location in order to collect radio frequency interference (RFI) free data. The system was deployed in remote, radio quiet locations in Western Australia and low RFI sky data have been collected. We present a description of the system, its characteristics, details of data analysis, and calibration. We have identified multiple challenges to achieving the required measurement precision, which triggered two major improvements for the future system.