Finite Abelian Groups in which the Probability of an Automorphism Fixing an Element is Large

Let G be a finite group and let A be its automorphism group. We obtain various results on the probability that a random element of A fixes a random element of G

Undergraduates, the Right Questions, and Cayley Produce Results

During the summers of 1989, 1990, and 1991, eighteen undergraduates participated in a National Science Foundation Research Experiences for Undergraduates program at Rose-Hulman for which the author was the principal investigator. This paper provides some examples of the mathematics discovered during these three summers and discusses the philosophy, environment and process which made these discoveries possible

Counting Centralizers in Finite Groups

We discuss various results on the number of commuting pairs and the sizes of the centralizers of a group

Simulation of Blood Flow and Nanoparticle Transport in a Stenosed Carotid Bifurcation and Pseudo-Arteriole

Numerical simulation of flow through a realistic bifurcated carotid artery geometry with a stenosis has been conducted for comparison to experimental measurements. The behaviour of simplified therapeutic nanoparticles in relatively low concentration was observed using a discrete particle approach. The role of size (diameters from 500 nm to 50 nm) in determining particle residence time and the potential for both desirable and undesirable wall interactions was investigated. It was found that mean particle residence time reduced with decreasing particle diameter, and the percentage of particles experiencing one or more wall interactions increased simultaneously. Further simulations were conducted on a scaled-down version of the geometry which approximated the size and flow conditions of an arteriole with capillary branches, and in this instance the mean residence time increased with decreasing particle diameter, owing largely to the greater influence of Brownian motion. 33% of all 50 nm particles were involved in wall interactions, indicating that smaller particles would have a greater ability to target, for instance, cancerous tumours in such regions

Synergistic Monitoring – Addressing the Threats and Identifying Opportunities

For many years, land managers and scientists have been applying a variety of land treatments to improve or protect rangeland ecosystems. Collectively, we have studied the response of these treatments and wildfire events to identify opportunities for maintaining or improving Nevada sagebrush ecosystem health and functionality. In partnership with collaborators, we initiated a State-wide effort to capture, consolidate, and summarize implementation, monitoring, and research information for these events. We are conducting field studies to identify and fill information gaps. We seek a new and expanded information base that is available to Nevada land managers, scientists, and others interested in healthy and resilient sagebrush sites. We plan to identify the consequences of passive and active management; develop predictive tools for adaptive management; identify research needs; and increase accessibility to location, implementation and monitoring information for these events. Through the collaborative integration of our field study results with historic and current research and monitoring information, we seek to increase knowledge of landscape-level and site-specific ecological processes. This will further develop our ability to manage and predict rangeland health, integrity, resilience (after disturbance), and resistance (to undesired change under significant disturbance regimes) in the context of multiple-use management

The Interaction of Testosterone and Cortisol Is Associated With Attained Status in Male Executives.

Are hormone levels associated with the attainment of social status? Although endogenous testosterone predicts status-seeking social behaviors, research suggests that the stress hormone cortisol may inhibit testosterone’s effects. Thus, individuals with both high testosterone and low cortisol may be especially likely to occupy high-status positions in social hierarchies while individuals with high testosterone and high cortisol may not. We tested this hypothesis by recruiting a sample of real executives and examining testosterone, cortisol, and a concrete indicator of attained status: the number of subordinates over which the executive has authority. Despite the myriad nonhormonal factors that determine organizational promotion, the executives’ endogenous testosterone and cortisol interacted to significantly predict hierarchical position: Testosterone positively predicted executives’ number of subordinates, but only among low-cortisol executives. The results imply that reducing cortisol levels via stress reduction may be a critical goal not only because doing so will improve health but also because doing so may enhance leadership potential

Universal Gelation of Metal Oxide Nanocrystals via Depletion Attractions

Nanocrystal gelation provides a powerful framework to translate nanoscale properties into bulk materials and to engineer emergent properties through the assembled microstructure. However, many established gelation strategies rely on chemical reactions and specific interactions, e.g., stabilizing ligands or ions on the surface of the nanocrystals, and are therefore not easily transferrable. Here, we report a general gelation strategy via non-specific and purely entropic depletion attractions applied to three types of metal oxide nanocrystals. The gelation thresholds of two compositionally distinct spherical nanocrystals agree quantitatively, demonstrating the adaptability of the approach for different chemistries. Consistent with theoretical phase behavior predictions, nanocrystal cubes form gels at a lower polymer concentration than nanocrystal spheres, allowing shape to serve as a handle to control gelation. These results suggest that the fundamental underpinnings of depletion-driven assembly, traditionally associated with larger colloidal particles, are also applicable at the nanoscale

Reporting randomised trials of social and psychological interventions: the CONSORT-SPI 2018 Extension

Background: Randomised controlled trials (RCTs) are used to evaluate social and psychological interventions and inform policy decisions about them. Accurate, complete, and transparent reports of social and psychological intervention RCTs are essential for understanding their design, conduct, results, and the implications of the findings. However, the reporting of RCTs of social and psychological interventions remains suboptimal. The CONSORT Statement has improved the reporting of RCTs in biomedicine. A similar high-quality guideline is needed for the behavioural and social sciences. Our objective was to develop an official extension of the Consolidated Standards of Reporting Trials 2010 Statement (CONSORT 2010) for reporting RCTs of social and psychological interventions: CONSORT-SPI 2018. Methods: We followed best practices in developing the reporting guideline extension. First, we conducted a systematic review of existing reporting guidelines. We then conducted an online Delphi process including 384 international participants. In March 2014, we held a 3-day consensus meeting of 31 experts to determine the content of a checklist specifically targeting social and psychological intervention RCTs. Experts discussed previous research and methodological issues of particular relevance to social and psychological intervention RCTs. They then voted on proposed modifications or extensions of items from CONSORT 2010. Results: The CONSORT-SPI 2018 checklist extends 9 of the 25 items from CONSORT 2010: background and objectives, trial design, participants, interventions, statistical methods, participant flow, baseline data, outcomes and estimation, and funding. In addition, participants added a new item related to stakeholder involvement, and they modified aspects of the flow diagram related to participant recruitment and retention. Conclusions: Authors should use CONSORT-SPI 2018 to improve reporting of their social and psychological intervention RCTs. Journals should revise editorial policies and procedures to require use of reporting guidelines by authors and peer reviewers to produce manuscripts that allow readers to appraise study quality, evaluate the applicability of findings to their contexts, and replicate effective interventions

AFP, PIVKAII, GP3, SCCA-1 and follisatin as surveillance biomarkers for hepatocellular cancer in non-alcoholic and alcoholic fatty liver disease

<p>Abstract</p> <p>Background</p> <p>The incidence and mortality of hepatocellular cancer (HCC) complicating alcoholic and non-alcoholic fatty liver diseases (ALD and NAFLD) is rising in western societies. Despite knowing the at risk populations for HCC development, the lack of sensitive and specific means of surveillance hampers disease detection at curable stages. The most widely used serum HCC marker is alpha-fetoprotein (AFP), while PIVKA-II, glypican-3 (GP3) and Squamous Cell Carcinoma Antigen -1 (SCCA-1) have been proposed as new biomarkers. Assessment of these HCC biomarkers has largely been performed in patients with viral hepatitis. We conducted a cross sectional study assessing the value of these serum proteins, as well a novel candidate biomarker -follistatin – in patients with HCC arising on a background of ALD or NAFLD.</p> <p>Methods</p> <p>Pre-treatment serum samples from 50 patients with HCC arising on a background of ALD (n = 31) or NAFLD (n = 19) were assessed by specific ELISA assay for PIVKAII, Glypican-3, SCCA-1 and Follistatin. Results were compared and contrasted with a control patient group with biopsy proven steatohepatitis-related cirrhosis (n = 41). The diagnostic accuracy of each of the candidate biomarkers was evaluated using receiver operating characteristic (ROC) curve analysis, reporting the area under the curve (AUC) and its 95% confidence interval (CI). Performance was compared to that of the established biomarker, AFP.</p> <p>Results</p> <p>Serum levels of all proteins were assessed by specific ELISA assays. GP3, SCCA-1 and follistatin had no HCC surveillance benefit in these patients. AFP and PIVKAII were superior to the other markers, particularly in combination.</p> <p>Conclusion</p> <p>We conclude that while novel means of surveillance are urgently required, the combination of AFP and PIVKAII for HCC is an improvement on AFP alone in ALD/NAFLD patients. Furthermore, our data in this homogenous subset of patients- particularly that confirming no role for SCCA-1 – suggests that the choice of optimal biomarkers for HCC surveillance may be determined by the aetiology of underlying chronic liver disease.</p