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

Uniqueness of two-convex closed ancient solutions to the mean curvature flow

In this paper we consider closed non-collapsed ancient solutions to the mean curvature flow ($n \ge 2$) which are uniformly two-convex. We prove that any two such ancient solutions are the same up to translations and scaling. In particular, they must coincide up to translations and scaling with the rotationally symmetric closed ancient non-collapsed solution constructed by Brian White in (2000), and by Robert Haslhofer and Or Hershkovits in (2016).Comment: 74 pages, 5 figure

Bony ingrowth potential of 3D-printed porous titanium alloy: a direct comparison of interbody cage materials in an in vivo ovine lumbar fusion model.

Background contextThere is significant variability in the materials commonly used for interbody cages in spine surgery. It is theorized that three-dimensional (3D)-printed interbody cages using porous titanium material can provide more consistent bone ingrowth and biological fixation.PurposeThe purpose of this study was to provide an evidence-based approach to decision-making regarding interbody materials for spinal fusion.Study designA comparative animal study was performed.MethodsA skeletally mature ovine lumbar fusion model was used for this study. Interbody fusions were performed at L2-L3 and L4-L5 in 27 mature sheep using three different interbody cages (ie, polyetheretherketone [PEEK], plasma sprayed porous titanium-coated PEEK [PSP], and 3D-printed porous titanium alloy cage [PTA]). Non-destructive kinematic testing was performed in the three primary directions of motion. The specimens were then analyzed using micro-computed tomography (µ-CT); quantitative measures of the bony fusion were performed. Histomorphometric analyses were also performed in the sagittal plane through the interbody device. Outcome parameters were compared between cage designs and time points.ResultsFlexion-extension range of motion (ROM) was statistically reduced for the PTA group compared with the PEEK cages at 16 weeks (p-value=.02). Only the PTA cages demonstrated a statistically significant decrease in ROM and increase in stiffness across all three loading directions between the 8-week and 16-week sacrifice time points (p-value≤.01). Micro-CT data demonstrated significantly greater total bone volume within the graft window for the PTA cages at both 8 weeks and 16 weeks compared with the PEEK cages (p-value<.01).ConclusionsA direct comparison of interbody implants demonstrates significant and measurable differences in biomechanical, µ-CT, and histologic performance in an ovine model. The 3D-printed porous titanium interbody cage resulted in statistically significant reductions in ROM, increases in the bone ingrowth profile, as well as average construct stiffness compared with PEEK and PSP

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

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