Bounds on \"{U}bercrossing and Petal Numbers for Knots

An $n$-crossing is a point in the projection of a knot where $n$ strands cross so that each strand bisects the crossing. An \"ubercrossing projection has a single $n$-crossing and a petal projection has a single $n$-crossing such that there are no loops nested within others. The \"ubercrossing number, $\text{\"u}(K)$, is the smallest $n$ for which we can represent a knot $K$ with a single $n$-crossing. The petal number is the number of loops in the minimal petal projection. In this paper, we relate the \"{u}bercrossing number and petal number to well-known invariants such as crossing number, bridge number, and unknotting number. We find that the bounds we have constructed are tight for $(r, r+1)$-torus knots. We also explore the behavior of \"{u}bercrossing number under composition.Comment: 13 pages, 8 figure

Meandering river dynamics

Meandering channels are dynamic landforms that arise as a result of fluid mechanic and sedimentary processes. Their evolution has been described by the meander morphodynamic equations, which dictate that channel curvature and bed topology give rise to local perturbations in streamwise fluid velocity, prompting the preferential erosion and sediment deposition that constitute meander behavior. Previous theoretical work has been based on simplified periodic systems. Here we determine the mathematical conditions required for unique solutions to the meander morphodynamics equations. Our predictions for non-periodic finite-domains constitute the first correct explanation of behavior observed in flumes, where a fixed inlet leads to the long-term decay of all meanders. We show that a continuous perturbation is required for sustained meandering. With a driven perturbation at the inlet, we find that high (low) frequency driving results in spatial decay (growth). We present original scaling arguments for the dependence of the meander migration rate on geological parameters, showing that the rate of migration increases with increased width, down-reach slope, and bank erodibility, and decreases with increased volumetric flow rate. The meander equations involve a single dimensionless parameter alpha, which characterizes the ratio of secondary to irrotational flow. We show that variations in alpha have significant impact on spatial and temporal scaling, and on the degree of upstream skewing in meander shapes. For numerical simulations, we develop a rigorous mathematical description of the relationship between spatial discretization schemes and numerical stability, and we present a robust, stable numerical algorithm. We introduce a parametric Lagrangian variable for improved stability and adaptive spatial resolution. Our implicit numerical solver facilitates a time-step size which is limited by accuracy instead of stability, leading to a significant improvement in computational speed. We present the first demonstrably accurate, converged solutions for the meander morphodynamics equations. Our nonlinear work has focused on the evolution of initially quiescent systems with boundary driving. We find that finite-domain theory accurately describes behavior close to the upstream boundary, whereas standard period-domain behavior dominates downstream. In the instance of clamped upstream boundaries, nonlinear simulation leads to a significantly longer progression of the initial disturbance relative to linear theory before subsiding into a straight channel. We find that upstream perturbations will cause the excitation of temporally growing waves downstream. Finally, we provide rigorous scaling analysis to determine the appropriate length of experimental flumes, the appropriate duration of experimental runs, and the necessary properties of sediment. We present simulations of previous experimental work and find good heuristic agreement, and we provide recommendations for experimental conditions for the observation of sustained meandering in laboratory flumes

Total hip replacement for the treatment of end stage arthritis of the hip : a systematic review and meta-analysis

Background: Evolvements in the design, fixation methods, size, and bearing surface of implants for total hip replacement (THR) have led to a variety of options for healthcare professionals to consider. The need to determine the most optimal combinations of THR implant is warranted. This systematic review evaluated the clinical effectiveness of different types of THR used for the treatment of end stage arthritis of the hip. Methods: A comprehensive literature search was undertaken in major health databases. Randomised controlled trials (RCTs) and systematic reviews published from 2008 onwards comparing different types of primary THR in patients with end stage arthritis of the hip were included. Results: Fourteen RCTs and five systematic reviews were included. Patients experienced significant post-THR improvements in Harris Hip scores, but this did not differ between impact types. There was a reduced risk of implant dislocation after receiving a larger femoral head size (36 mm vs. 28 mm; RR = 0.17, 95% CI: 0.04, 0.78) or cemented cup (vs. cementless cup; pooled odds ratio: 0.34, 95% CI: 0.13, 0.89). Recipients of cross-linked vs. conventional polyethylene cup liners experienced reduced femoral head penetration and revision. There was no impact of femoral stem fixation and cup shell design on implant survival rates. Evidence on mortality and complications (aseptic loosening, femoral fracture) was inconclusive. Conclusions: The majority of evidence was inconclusive due to poor reporting, missing data, or uncertainty in treatment estimates. The findings warrant cautious interpretation given the risk of bias (blinding, attrition), methodological limitations (small sample size, low event counts, short follow-up), and poor reporting. Long-term pragmatic RCTs are needed to allow for more definitive conclusions. Authors are encouraged to specify the minimal clinically important difference and power calculation for their primary outcome(s) as well CONSORT, PRISMA and STROBE guidelines to ensure better reporting and more reliable production and assessment of evidence

Aspirin for prophylactic use in the primary prevention of cardiovascular disease and cancer : a systematic review and overview of reviews

Background: Prophylactic aspirin has been considered to be beneficial in reducing the risks of heart disease and cancer. However, potential benefits must be balanced against the possible harm from side effects, such as bleeding and gastrointestinal (GI) symptoms. It is particularly important to know the risk of side effects when aspirin is used as primary prevention - that is when used by people as yet free of, but at risk of developing, cardiovascular disease (CVD) or cancer. In this report we aim to identify and re-analyse randomised controlled trials (RCTs), systematic reviews and meta-analyses to summarise the current scientific evidence with a focus on possible harms of prophylactic aspirin in primary prevention of CVD and cancer. Objectives: To identify RCTs, systematic reviews and meta-analyses of RCTs of the prophylactic use of aspirin in primary prevention of CVD or cancer. To undertake a quality assessment of identified systematic reviews and meta-analyses using meta-analysis to investigate study-level effects on estimates of benefits and risks of adverse events; cumulative meta-analysis; exploratory multivariable meta-regression; and to quantify relative and absolute risks and benefits. Methods: We identified RCTs, meta-analyses and systematic reviews, and searched electronic bibliographic databases (from 2008 September 2012) including MEDLINE, Cochrane Central Register of Controlled Trials, Database of Abstracts of Reviews of Effects, NHS Centre for Reviews and Dissemination, and Science Citation Index. We limited searches to publications since 2008, based on timing of the most recent comprehensive systematic reviews. Results: In total, 2572 potentially relevant papers were identified and 27 met the inclusion criteria. Benefits of aspirin ranged from 6% reduction in relative risk (RR) for all-cause mortality [RR 0.94, 95% confidence interval (CI) 0.88 to 1.00] and 10% reduction in major cardiovascular events (MCEs) (RR 0.90, 95% CI 0.85 to 0.96) to a reduction in total coronary heart disease (CHD) of 15% (RR 0.85, 95% CI 0.69 to 1.06). Reported pooled odds ratios (ORs) for total cancer mortality ranged between 0.76 (95% CI 0.66 to 0.88) and 0.93 (95% CI 0.84 to 1.03). Inclusion of the Women's Health Study changed the estimated OR to 0.82 (95% CI 0.69 to 0.97). Aspirin reduced reported colorectal cancer (CRC) incidence (OR 0.66, 95% CI 0.90 to 1.02). However, including studies in which aspirin was given every other day raised the OR to 0.91 (95% CI 0.74 to 1.11). Reported cancer benefits appeared approximately 5 years from start of treatment. Calculation of absolute effects per 100,000 patient-years of follow-up showed reductions ranging from 33 to 46 deaths (all-cause mortality), 60-84 MCEs and 47-64 incidents of CHD and a possible avoidance of 34 deaths from CRC. Reported increased RRs of adverse events from aspirin use were 37% for GI bleeding (RR 1.37, 95% CI 1.15 to 1.62), between 54% (RR 1.54, 95% CI 1.30 to 1.82) and 62% (RR 1.62, 95% CI 1.31 to 2.00) for major bleeds, and between 32% (RR 1.32, 95% CI 1.00 to 1.74) and 38% (RR 1.38, 95% CI 1.01 to 1.82) for haemorrhagic stroke. Pooled estimates of increased RR for bleeding remained stable across trials conducted over several decades. Estimates of absolute rates of harm from aspirin use, per 100,000 patient-years of follow-up, were 99-178 for non-trivial bleeds, 46-49 for major bleeds, 68-117 for GI bleeds and 8-10 for haemorrhagic stroke. Meta-analyses aimed at judging risk of bleed according to sex and in individuals with diabetes were insufficiently powered for firm conclusions to be drawn. Limitations: Searches were date limited to 2008 because of the intense interest that this subject has generated and the cataloguing of all primary research in so many previous systematic reviews. A further limitation was our potential over-reliance on study-level systematic reviews in which the person-years of follow-up were not accurately ascertainable. However, estimates of number of events averted or incurred through aspirin use calculated from data in study-level meta-analyses did not differ substantially from estimates based on individual patient data-level meta-analyses, for which person-years of follow-up were more accurate (although based on less-than-complete assemblies of currently available primary studies). Conclusions: We have found that there is a fine balance between benefits and risks from regular aspirin use in primary prevention of CVD. Effects on cancer prevention have a long lead time and are at present reliant on post hoc analyses. All absolute effects are relatively small compared with the burden of these diseases. Several potentially relevant ongoing trials will be completed between 2013 and 2019, which may clarify the extent of benefit of aspirin in reducing cancer incidence and mortality. Future research considerations include expanding the use of IPD meta-analysis of RCTs by pooling data from available studies and investigating the impact of different dose regimens on cardiovascular and cancer outcomes

Aspirin in primary prevention of cardiovascular disease and cancer : a systematic review of the balance of evidence from reviews of randomized trials

Background: Aspirin has been recommended for primary prevention of cardiovascular disease (CVD) and cancer, but overall benefits are unclear. We aimed to use novel methods to re-evaluate the balance of benefits and harms of aspirin using evidence from randomised controlled trials, systematic reviews and meta-analyses. Methods and Findings: Data sources included ten electronic bibliographic databases, contact with experts, and scrutiny of reference lists of included studies. Searches were undertaken in September 2012 and restricted to publications since 2008. Of 2,572 potentially relevant papers 27 met the inclusion criteria. Meta-analysis of control arms to estimate event rates, modelling of all-cause mortality and L'Abbé plots to estimate heterogeneity were undertaken. Absolute benefits and harms were low: 60-84 major CVD events and 34-36 colorectal cancer deaths per 100,000 person-years were averted, whereas 46-49 major bleeds and 68-117 gastrointestinal bleeds were incurred. Reductions in all-cause mortality were minor and uncertain (Hazard Ratio 0.96; 95% CI: 0.90-1.02 at 20 years, Relative Risk [RR] 0.94, 95% CI: 0.88-1.00 at 8 years); there was a non-significant change in total CVD (RR 0.85, 95% CI: 0.69-1.06) and change in total cancer mortality ranged from 0.76 (95% CI: 0.66-0.88) to 0.93 (95% CI: 0.84-1.03) depending on follow-up time and studies included. Risks were increased by 37% for gastrointestinal bleeds (RR 1.37, 95% CI: 1.15-1.62), 54%-66% for major bleeds (Rate Ratio from IPD analysis 1.54, 95% CI: 1.30-1.82, and RR 1.62, 95% CI: 1.31-2.00), and 32%-38% for haemorrhagic stroke (Rate Ratio from IPD analysis 1.32; 95% CI: 1.00-1.74; RR 1.38; 95% CI: 1.01-1.82). Conclusions: Findings indicate small absolute effects of aspirin relative to the burden of these diseases. When aspirin is used for primary prevention of CVD the absolute harms exceed the benefits. Estimates of cancer benefit rely on selective retrospective re-analysis of RCTs and more information is needed

Horizon Report Europe - 2014 Schools Edition

The NMC Horizon Project from the New Media Consortium is a long-term investigation launched in 2002 that identifies and describes emerging technologies likely to have a large impact over the coming five years in education around the globe. The NMC Horizon Report Europe: 2014 Schools Edition, the first of its kind for Europe, examines six key trends, six significant challenges and six important developments in educational technology that are very likely to impact educational change processes in European schools over the next five years (2014-2018). The topics within each section were carefully selected by the Horizon Project Europe Expert Panel, a body of 53 experts in European education, technology, and other fields. They come from 22 European countries, as well as international organisations and European networks. Throughout the report, references and links are made to more than 150 European publications (reports, articles, policy documents, blog posts etc.), projects (both EU-funded and national initiatives) and various policy initiatives from all over Europe. The Creative Classrooms multidimensional framework, developed by European Commission’s JRC-IPTS on behalf of DG EAC, was used for analysing the trends, challenges and technologies impacting European schools over the next five years. The analysis reveals that a systemic approach is needed for integrating new technologies in European schools and impacting educational change over the next five years.JRC.J.3-Information Societ

Monitoring changes in circulating tumour cells as a prognostic indicator of overall survival and treatment response in patients with metastatic melanoma

Background: New effective treatments for metastatic melanoma greatly improve survival in a proportion of patients. However biomarkers to identify patients that are more likely to benefit from a particular treatment are needed. We previously reported on a multimarker approach for the detection of heterogenous melanoma circulating tumour cells (CTCs). Here we evaluated the prognostic value of this multimarker quantification of CTCs and investigated whether changes in CTC levels during therapy can be used as a biomarker of treatment response and survival outcomes.Methods: CTCs were captured by targeting the melanoma associated markers MCSP and MCAM as well as the melanoma stem cell markers ABCB5 and CD271. CTCs were quantified in 27 metastatic melanoma patients treated by surgery or with vemurafenib, ipilimumab or dacarbazine. Patients were enrolled prospectively and CTC counts performed at baseline (prior to treatment), during and after treatment.Results: Baseline CTC numbers were not found to be prognostic of overall survival nor of progression free survival. However, a low baseline CTC number was associated with a rapid response to vemurafenib therapy. A decrease in CTCs after treatment initiation was associated with response to treatment and prolonged overall survival in vemurafenib treated patients.Conclusions: Measuring changes in CTC numbers during treatment is useful for monitoring therapy response in melanoma patients and for providing prognostic information relating to overall survival. Further studies with larger sample sizes are required to confirm the utility of CTC quantification as a companion diagnostic for metastatic melanoma treatment

Trading in your spindles for blebs: the amoeboid tumor cell phenotype in prostate cancer

Prostate cancer (PCa) remains a principal cause of mortality in developed countries. Because no clinical interventions overcome resistance to androgen ablation therapy, management of castration resistance and metastatic disease remains largely untreatable. Metastasis is a multistep process in which tumor cells lose cell-cell contacts, egress from the primary tumor, intravasate, survive shear stress within the vasculature and extravasate into tissues to colonize ectopic sites. Tumor cells reestablish migratory behaviors employed during nonneoplastic processes such as embryonic development, leukocyte trafficking and wound healing. While mesenchymal motility is an established paradigm of dissemination, an alternate, ‘amoeboid’ phenotype is increasingly appreciated as relevant to human cancer. Here we discuss characteristics and pathways underlying the phenotype, and highlight our findings that the cytoskeletal regulator DIAPH3 governs the mesenchymal-amoeboid transition. We also describe our identification of a new class of tumor-derived microvesicles, large oncosomes, produced by amoeboid cells and with potential clinical utility in prostate and other cancers