Bounds on some van der Waerden numbers

Abstract For positive integers s and k 1 , k 2 , . . . , k s , the van der Waerden number w(k 1 , k 2 , . . . , k s ; s) is the minimum integer n such that for every s-coloring of set {1, 2, . . . , n}, with colors 1, 2, . . . , s, there is a k i -term arithmetic progression of color i for some i. We give an asymptotic lower bound for w(k, m; 2) for fixed m. We include a table of values of w(k, 3; 2) that are very close to this lower bound for m = 3. We also give a lower bound for w(k, k, . . . , k; s) that slightly improves previously-known bounds. Upper bounds for w(k, 4; 2) and w(4, 4, . . . , 4; s) are also provided

Characteristics of the National Applicant Pool for Clinical Informatics Fellowships (2016-2017)

We conducted a national study to assess the numbers and diversity of applicants for 2016 and 2017 clinical informatics fellowship positions. In each year, we collected data on the number of applications that programs received from candidates who were ultimately successful vs. unsuccessful. In 2017, we also conducted an anonymous applicant survey. Successful candidates applied to an average of 4.2 and 5.5 programs for 2016 and 2017, respectively. In the survey, unsuccessful candidates reported applying to fewer programs. Assuming unsuccessful candidates submitted between 2-5 applications each, the total applicant pool numbered 42-69 for 2016 (competing for 24 positions) and 52-85 for 2017 (competing for 30 positions). Among survey respondents (n=33), 24% were female, 1 was black and none were Hispanic. We conclude that greater efforts are needed to enhance interest in clinical informatics among medical students and residents, particularly among women and members of underrepresented minority groups

Ecological Thresholds in the Savanna Landscape: Developing a Protocol for Monitoring the Change in Composition and Utilisation of Large Trees

BACKGROUND: Acquiring greater understanding of the factors causing changes in vegetation structure -- particularly with the potential to cause regime shifts -- is important in adaptively managed conservation areas. Large trees (> or =5 m in height) play an important ecosystem function, and are associated with a stable ecological state in the African savanna. There is concern that large tree densities are declining in a number of protected areas, including the Kruger National Park, South Africa. In this paper the results of a field study designed to monitor change in a savanna system are presented and discussed. METHODOLOGY/PRINCIPAL FINDINGS: Developing the first phase of a monitoring protocol to measure the change in tree species composition, density and size distribution, whilst also identifying factors driving change. A central issue is the discrete spatial distribution of large trees in the landscape, making point sampling approaches relatively ineffective. Accordingly, fourteen 10 m wide transects were aligned perpendicular to large rivers (3.0-6.6 km in length) and eight transects were located at fixed-point photographic locations (1.0-1.6 km in length). Using accumulation curves, we established that the majority of tree species were sampled within 3 km. Furthermore, the key ecological drivers (e.g. fire, herbivory, drought and disease) which influence large tree use and impact were also recorded within 3 km. CONCLUSIONS/SIGNIFICANCE: The technique presented provides an effective method for monitoring changes in large tree abundance, size distribution and use by the main ecological drivers across the savanna landscape. However, the monitoring of rare tree species would require individual marking approaches due to their low densities and specific habitat requirements. Repeat sampling intervals would vary depending on the factor of concern and proposed management mitigation. Once a monitoring protocol has been identified and evaluated, the next stage is to integrate that protocol into a decision-making system, which highlights potential leading indicators of change. Frequent monitoring would be required to establish the rate and direction of change. This approach may be useful in generating monitoring protocols for other dynamic systems

Canagliflozin and renal outcomes in type 2 diabetes and nephropathy

BACKGROUND Type 2 diabetes mellitus is the leading cause of kidney failure worldwide, but few effective long-term treatments are available. In cardiovascular trials of inhibitors of sodium–glucose cotransporter 2 (SGLT2), exploratory results have suggested that such drugs may improve renal outcomes in patients with type 2 diabetes. METHODS In this double-blind, randomized trial, we assigned patients with type 2 diabetes and albuminuric chronic kidney disease to receive canagliflozin, an oral SGLT2 inhibitor, at a dose of 100 mg daily or placebo. All the patients had an estimated glomerular filtration rate (GFR) of 30 to <90 ml per minute per 1.73 m2 of body-surface area and albuminuria (ratio of albumin [mg] to creatinine [g], >300 to 5000) and were treated with renin–angiotensin system blockade. The primary outcome was a composite of end-stage kidney disease (dialysis, transplantation, or a sustained estimated GFR of <15 ml per minute per 1.73 m2), a doubling of the serum creatinine level, or death from renal or cardiovascular causes. Prespecified secondary outcomes were tested hierarchically. RESULTS The trial was stopped early after a planned interim analysis on the recommendation of the data and safety monitoring committee. At that time, 4401 patients had undergone randomization, with a median follow-up of 2.62 years. The relative risk of the primary outcome was 30% lower in the canagliflozin group than in the placebo group, with event rates of 43.2 and 61.2 per 1000 patient-years, respectively (hazard ratio, 0.70; 95% confidence interval [CI], 0.59 to 0.82; P=0.00001). The relative risk of the renal-specific composite of end-stage kidney disease, a doubling of the creatinine level, or death from renal causes was lower by 34% (hazard ratio, 0.66; 95% CI, 0.53 to 0.81; P<0.001), and the relative risk of end-stage kidney disease was lower by 32% (hazard ratio, 0.68; 95% CI, 0.54 to 0.86; P=0.002). The canagliflozin group also had a lower risk of cardiovascular death, myocardial infarction, or stroke (hazard ratio, 0.80; 95% CI, 0.67 to 0.95; P=0.01) and hospitalization for heart failure (hazard ratio, 0.61; 95% CI, 0.47 to 0.80; P<0.001). There were no significant differences in rates of amputation or fracture. CONCLUSIONS In patients with type 2 diabetes and kidney disease, the risk of kidney failure and cardiovascular events was lower in the canagliflozin group than in the placebo group at a median follow-up of 2.62 years

Albiglutide and cardiovascular outcomes in patients with type 2 diabetes and cardiovascular disease (Harmony Outcomes): a double-blind, randomised placebo-controlled trial

Background: Glucagon-like peptide 1 receptor agonists differ in chemical structure, duration of action, and in their effects on clinical outcomes. The cardiovascular effects of once-weekly albiglutide in type 2 diabetes are unknown. We aimed to determine the safety and efficacy of albiglutide in preventing cardiovascular death, myocardial infarction, or stroke. Methods: We did a double-blind, randomised, placebo-controlled trial in 610 sites across 28 countries. We randomly assigned patients aged 40 years and older with type 2 diabetes and cardiovascular disease (at a 1:1 ratio) to groups that either received a subcutaneous injection of albiglutide (30–50 mg, based on glycaemic response and tolerability) or of a matched volume of placebo once a week, in addition to their standard care. Investigators used an interactive voice or web response system to obtain treatment assignment, and patients and all study investigators were masked to their treatment allocation. We hypothesised that albiglutide would be non-inferior to placebo for the primary outcome of the first occurrence of cardiovascular death, myocardial infarction, or stroke, which was assessed in the intention-to-treat population. If non-inferiority was confirmed by an upper limit of the 95% CI for a hazard ratio of less than 1·30, closed testing for superiority was prespecified. This study is registered with ClinicalTrials.gov, number NCT02465515. Findings: Patients were screened between July 1, 2015, and Nov 24, 2016. 10 793 patients were screened and 9463 participants were enrolled and randomly assigned to groups: 4731 patients were assigned to receive albiglutide and 4732 patients to receive placebo. On Nov 8, 2017, it was determined that 611 primary endpoints and a median follow-up of at least 1·5 years had accrued, and participants returned for a final visit and discontinuation from study treatment; the last patient visit was on March 12, 2018. These 9463 patients, the intention-to-treat population, were evaluated for a median duration of 1·6 years and were assessed for the primary outcome. The primary composite outcome occurred in 338 (7%) of 4731 patients at an incidence rate of 4·6 events per 100 person-years in the albiglutide group and in 428 (9%) of 4732 patients at an incidence rate of 5·9 events per 100 person-years in the placebo group (hazard ratio 0·78, 95% CI 0·68–0·90), which indicated that albiglutide was superior to placebo (p<0·0001 for non-inferiority; p=0·0006 for superiority). The incidence of acute pancreatitis (ten patients in the albiglutide group and seven patients in the placebo group), pancreatic cancer (six patients in the albiglutide group and five patients in the placebo group), medullary thyroid carcinoma (zero patients in both groups), and other serious adverse events did not differ between the two groups. There were three (<1%) deaths in the placebo group that were assessed by investigators, who were masked to study drug assignment, to be treatment-related and two (<1%) deaths in the albiglutide group. Interpretation: In patients with type 2 diabetes and cardiovascular disease, albiglutide was superior to placebo with respect to major adverse cardiovascular events. Evidence-based glucagon-like peptide 1 receptor agonists should therefore be considered as part of a comprehensive strategy to reduce the risk of cardiovascular events in patients with type 2 diabetes. Funding: GlaxoSmithKline

INTEGERS: Electronic Journal of Combinatorial Number Theory

INTEGERS is a free online journal of combinatorial number theory. Although it is "published with the help of the State University of West Georgia, Charles University, and DIMATIA," the journal's editors are professors and mathematicians from universities around the world. INTEGERS is currently in its third year, and all research papers that have been included in the journal are archived on the Web site. Occasionally, a paper will have Maple packages associated with it, and these are also given online. A recent addition is a section for combinatorial games. The first article in this section introduces the game Chomp, which involves two players and a chocolate bar. While it might sound strange, the game is quite complex, and the author discusses a formula he developed