Degenerate neckpinches in Ricci flow

In earlier work, we derived formal matched asymptotic profiles for families of Ricci flow solutions developing Type-II degenerate neckpinches. In the present work, we prove that there do exist Ricci flow solutions that develop singularities modeled on each such profile. In particular, we show that for each positive integer $k\geq3$, there exist compact solutions in all dimensions $m\geq3$ that become singular at the rate (T-t)^{-2+2/k}$

Correlation Between Lumbopelvic and Sagittal Parameters and Health-Related Quality of Life in Adults With Lumbosacral Spondylolisthesis.

Study Design:Secondary analysis of prospective, multicenter data. Objective:To evaluate impact of sagittal parameters on health-related quality of life (HRQoL) in adults with lumbosacral spondylolisthesis. Methods:Adults with unoperated lumbosacral spondylolisthesis were identified in the Spinal Deformity Study Group database. Pearson's correlations were calculated between SF-12 (Short Form-12)/Scoliosis Research Society-30 (SRS-30) scores and radiographic parameters (C7 sagittal vertical axis [SVA] deviation, T1 pelvic angle, pelvic tilt [PT], pelvic incidence, sacral slope, slip angle, Meyerding slip grade, Labelle classification). Main effects linear regression models measured association between individual health status measures and individual radiographic predictor variables. Results:Forty-five patients were analyzed (male, 15; female, 30; average age 40.5 ± 18.7 years; 14 low-grade, 31 high-grade). For low-grade slips, SVA had strong negative correlations with SF-12 mental component score (MCS), SRS-30 appearance, mental, and satisfaction domains (r = -0.57, r = -0.60, r = -0.58, r = -0.53, respectively; P < .05). For high-grade slips, slip angle had a moderate negative correlation with SF-12 MCS (r = -0.36; P = .05) and SVA had strong negative correlations with SF-12 physical component score (PCS), SRS-30 appearance and activity domains (r = -0.48, r = -0.48, r = -0.45; P < .05) and a moderate negative correlation with SRS-30 total (r = -0.37; P < .05). T1 pelvic angle had a moderate negative correlation with SF-12 PCS and SRS-30 appearance (r = -0.37, r = -0.36; P ≤ .05). For every 1° increase in PT, there was a 0.04-point decrease in SRS appearance, 0.05-point decrease in SRS activity, 0.06-point decrease in SRS satisfaction, and 0.04-point decrease in SRS total score (P < .05). Conclusion:Lumbosacral spondylolisthesis in adults negatively affects HRQoL. Multiple radiographic sagittal parameters negatively affect HRQoLs for patients with low- and high-grade slips. Improvement of sagittal parameters is an important goal of surgery for adults with lumbosacral spondylolisthesis

Reproducibility of lymphovascular space invasion (LVSI) assessment in endometrial cancer

Aims Lymphovascular space invasion (LVSI) in endometrial cancer (EC) is an important prognostic variable impacting on a patient's individual recurrence risk and adjuvant treatment recommendations. Recent work has shown that grading the extent of LVSI further improves its prognostic strength in patients with stage I endometrioid EC. Despite this, there is little information on the reproducibility of LVSI assessment in EC. Therefore, we designed a study to evaluate interobserver agreement in discriminating true LVSI from LVSI mimics (Phase I) and reproducibility of grading extent of LVSI (Phase II). Methods and results Scanned haematoxylin and eosin (H&E) slides of endometrioid EC (EEC) with a predefined possible LVSI focus were hosted on a website and assessed by a panel of six European gynaecological pathologists. In Phase I, 48 H&E slides were included for LVSI assessment and in Phase II, 42 H&E slides for LVSI grading. Each observer was instructed to apply the criteria for LVSI used in daily practice. The degree of agreement was measured using the two-way absolute agreement average-measures intraclass correlation coefficient (ICC). Reproducibility of LVSI assessment (ICC = 0.64, P < 0.001) and LVSI grading (ICC = 0.62, P < 0.001) in EEC was substantial among the observers. Conclusions Given the good reproducibility of LVSI, this study further supports the important role of LVSI in decision algorithms for adjuvant treatment

Autonomous three-dimensional formation flight for a swarm of unmanned aerial vehicles

This paper investigates the development of a new guidance algorithm for a formation of unmanned aerial vehicles. Using the new approach of bifurcating potential fields, it is shown that a formation of unmanned aerial vehicles can be successfully controlled such that verifiable autonomous patterns are achieved, with a simple parameter switch allowing for transitions between patterns. The key contribution that this paper presents is in the development of a new bounded bifurcating potential field that avoids saturating the vehicle actuators, which is essential for real or safety-critical applications. To demonstrate this, a guidance and control method is developed, based on a six-degreeof-freedom linearized aircraft model, showing that, in simulation, three-dimensional formation flight for a swarm of unmanned aerial vehicles can be achieved

Formal matched asymptotics for degenerate Ricci flow neckpinches

Gu and Zhu have shown that Type-II Ricci flow singularities develop from nongeneric rotationally symmetric Riemannian metrics on $S^m$, for all $m\geq 3$. In this paper, we describe and provide plausibility arguments for a detailed asymptotic profile and rate of curvature blow-up that we predict such solutions exhibit

Evaluation of Dynamic Models of Distillation Columns with Emphasis on the Initial Response

The flow dynamics (tray hydraulics) are of key importance for the initial dynamic response of distillation columns. The most important parameters are the liquid holdup, the liquid hydraulic time constant and the vapor constant representing the initial effect of a change in vapor flow on liquid flow. In the paper we present methods for determining these parameters experimentally, and compare the results with estimates from available correlations such as the Francis Weir formula