To send content items to your account,
please confirm that you agree to abide by our usage policies.
If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account.
Find out more about sending content to .
To send content items to your Kindle, first ensure email@example.com
is added to your Approved Personal Document E-mail List under your Personal Document Settings
on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part
of your Kindle email address below.
Find out more about sending to your Kindle.
Note you can select to send to either the @free.kindle.com or @kindle.com variations.
‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi.
‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
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.
The development of magnetic resonance (MR) imaging systems has been extended for the entire radiotherapy process. However, MR images provide voxel values that are not directly related to electron densities, thus MR images cannot be used directly for dose calculation. The aim of this study is to investigate the feasibility of dose calculations to be performed on MR images and evaluate the necessity of re-planning.
A prostate cancer patient was imaged using both MR and computed tomography (CT). The multilevel threshold (MLT) algorithm was used to categorise voxel values in the MR images into three segments (air, water and bone) with homogeneous Hounsfield units (HU). An intensity-modulated radiation therapy plan was generated from CT images of the patient. The plan was then copied to the segmented MR datasets and the doses were recalculated using pencil beam (PB) and collapsed cone (CC) algorithms and Monte Carlo (MC) modelling.
γ Evaluation showed that the percentage of points in regions of interest with γ<1 (3%/3 mm) were more than 94% in the segmented MR. Compared with the planning CT plan, the segmented MR plan resulted in a dose difference of –0·3, 0·8 and –1·3% when using PB, CC and MC algorithms, respectively.
The segmentation and conversion of MR images into HU data using the MLT algorithm, used in this feasibility study, can be used for dose calculation. This method can be used as a dosimetric assessment tool and can be easily implemented in the clinic.
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.
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.
After the January 12, 2010, earthquake in Haiti, Project Medishare and the University of Miami organized, built, and staffed a 200-bed field hospital (the University of Miami Hospital in Haiti [UMHH] ) on the outskirts of Port-au-Prince. We describe the operational challenges of providing a safe environment at the UMHH. Furthermore, we compared how these issues were addressed at this ad hoc hospital with how they were addressed at the field hospital of the Israel Defense Force, a fully deployable hospital with an organization fine-tuned as a result of prior disaster situations, also in Haiti.
In this article we introduce a new method of mitigating the problem of long wait times for low-priority customers in a two-class queuing system. To this end, we allow class 1 customers to be upgraded to class 2 after they have been in queue for some time. We assume that there are ci servers at station i, i=1, 2. The servers at station 1 are flexible in the sense that they can work at either station, whereas the servers at station 2 are dedicated. Holding costs at rate hi are accrued per customer per unit time at station i, i=1, 2. This study yields several surprising results. First, we show that stability analysis requires a condition on the order of the service rates. This is unexpected since no such condition is required when the system does not have upgrades. This condition continues to play a role when control is considered. We provide structural results that include a c-μ rule when an inequality holds and a threshold policy when the inequality is reversed. A numerical study verifies that the optimal control policy significantly reduces holding costs over the policy that assigns the flexible server to station 1. At the same time, in most cases the optimal control policy reduces waiting times of both customer classes.