Nonnegative Ricci curvature and escape rate gap

Let M be an open n-manifold of nonnegative Ricci curvature and let p ∈ M {p\in M} . We show that if ( M , p ) {(M,p)} has escape rate less than some positive constant ϵ ⁢ ( n ) {\epsilon(n)} , that is, minimal representing geodesic loops of π 1 ⁢ ( M , p ) {\pi_{1}(M,p)} escape from any bounded balls at a small linear rate with respect to their lengths, then π 1 ⁢ ( M , p ) {\pi_{1}(M,p)} is virtually abelian. This generalizes the author’s previous work [J. Pan, On the escape rate of geodesic loops in an open manifold with nonnegative Ricci curvature, Geom. Topol. 25 2021, 2, 1059–1085], where the zero escape rate is considered.

Carbon Dioxide Changes during High-flow Nasal Oxygenation in Apneic Patients: A Single-center Randomized Controlled Noninferiority Trial

Background Anesthesia studies using high-flow, humidified, heated oxygen delivered via nasal cannulas at flow rates of more than 50 l · min–1 postulated a ventilatory effect because carbon dioxide increased at lower levels as reported earlier. This study investigated the increase of arterial partial pressure of carbon dioxide between different flow rates of 100% oxygen in elective anesthetized and paralyzed surgical adults before intubation. Methods After preoxygenation and standardized anesthesia induction with nondepolarizing neuromuscular blockade, all patients received 100% oxygen (via high-flow nasal oxygenation system or circuit of the anesthesia machine), and continuous jaw thrust/laryngoscopy was applied throughout the 15-min period. In this single-center noninferiority trial, 25 patients each, were randomized to five groups: (1) minimal flow: 0.25 l · min–1, endotracheal tube; (2) low flow: 2 l · min–1, continuous jaw thrust; (3) medium flow: 10 l · min–1, continuous jaw thrust; (4) high flow: 70 l · min–1, continuous jaw thrust; and (5) control: 70 l · min–1, continuous laryngoscopy. Immediately after anesthesia induction, the 15-min apnea period started with oxygen delivered according to the randomized flow rate. Serial arterial blood gas analyses were drawn every 2 min. The study was terminated if either oxygen saturation measured by pulse oximetry was less than 92%, transcutaneous carbon dioxide was greater than 100 mmHg, pH was less than 7.1, potassium level was greater than 6 mmol · l–1, or apnea time was 15 min. The primary outcome was the linear rate of mean increase of arterial carbon dioxide during the 15-min apnea period computed from linear regressions. Results In total, 125 patients completed the study. Noninferiority with a predefined noninferiority margin of 0.3 mmHg · min–1 could be declared for all treatments with the following mean and 95% CI for the mean differences in the linear rate of arterial partial pressure of carbon dioxide with associated P values regarding noninferiority: high flow versus control, –0.0 mmHg · min–1 (–0.3, 0.3 mmHg · min–1, P = 0.030); medium flow versus control, –0.1 mmHg · min–1 (–0.4, 0.2 mmHg · min–1, P = 0.002); low flow versus control, –0.1 mmHg · min–1 (–0.4, 0.2 mmHg · min–1, P = 0.003); and minimal flow versus control, –0.1 mmHg · min–1 (–0.4, 0.2 mmHg · min–1, P = 0.004). Conclusions Widely differing flow rates of humidified 100% oxygen during apnea resulted in comparable increases of arterial partial pressure of carbon dioxide, which does not support an additional ventilatory effect of high-flow nasal oxygenation. Editor’s Perspective What We Already Know about This Topic What This Article Tells Us That Is New

Fast Algorithms for LS and LAD-Collaborative Regression

With the development of modern science and technology, it is easy to obtain a large number of high-dimensional datasets, which are related but different. Classical unimodel analysis is less likely to capture potential links between the different datasets. Recently, a collaborative regression model based on least square (LS) method for this problem has been proposed. In this paper, we propose a robust collaborative regression based on the least absolute deviation (LAD). We give the statistical interpretation of the LS-collaborative regression and LAD-collaborative regression. Then we design an efficient symmetric Gauss–Seidel-based alternating direction method of multipliers algorithm to solve the two models, which has the global convergence and the Q-linear rate of convergence. Finally we report numerical experiments to illustrate the efficiency of the proposed methods.

Design and Experimental Study of Progressive Spring for Formula Student Race Car

The purpose of carrying out the present work is to design, manufacture & test the progressive springs on an FS vehicle. This is one type of helical spring with a variable spring rate. The main purpose of designing progressive springs is to avail all the advantages of the variable spring rate over the linear spring rate and better ride quality along with roll control, compared to linear rate springs. We took several factors of vehicle dynamics under consideration before settling on progressive springs. Before starting with the design procedure, we had set objectives and followed the standard methodology of spring design to get the required output. Along with that, we took design philosophy under consideration. We reviewed all the parameters before finalizing the spring material as it is one of the major factors. We carried out all the necessary design calculations to complete the dimensions and stiffness of the spring. The conclusion helped us to achieve better ride quality and roll control accompanying the optimized spring design satisfying all the necessities such as load, stiffness, and deflection of progressive springs.

Maximum Likelihood Estimation for an Inhomogeneous Gamma Process with a Log-linear Rate Function

An inhomogeneous gamma process is a compromise between a renewal process and a nonhomogeneous Poisson process, since its failure probability at a given time depends both on the age of the system and on the distance from the last failure time. The inhomogeneous gamma process with a log-linear rate function is often used in modelling of recurrent event data. In this paper, it is proved that the suitably non-uniform scaled maximum likelihood estimator of the three-dimensional parameter of this model is asymptotically normal, but it enjoys the curious property that the covariance matrix of the asymptotic distribution is singular. A simulation study is presented to illustrate the behaviour of the maximum likelihood estimators in finite samples. Obtained results are also applied to real data analysis.

Differential Phase Shift Quantum Secret Sharing Using a Twin Field with Asymmetric Source Intensities

As an essential application of quantum mechanics in classical cryptography, quantum secret sharing has become an indispensable component of quantum internet. Recently, a differential phase shift quantum secret sharing protocol using a twin field has been proposed to break the linear rate-distance boundary. However, this original protocol has a poor performance over channels with asymmetric transmittances. To make it more practical, we present a differential phase shift quantum secret sharing protocol with asymmetric source intensities and give the security proof of our protocol against individual attacks. Taking finite-key effects into account, our asymmetric protocol can theoretically obtain the key rate two orders of magnitude higher than that of the original protocol when the difference in length between Alice’s channel and Bob’s is fixed at 14 km. Moreover, our protocol can provide a high key rate even when the difference is quite large and has great robustness against finite-key effects. Therefore, our work is meaningful for the real-life applications of quantum secret sharing.

On the linear convergence of the general first order primal-dual algorithm

<p style='text-indent:20px;'>In this paper, we consider the general first order primal-dual algorithm, which covers several recent popular algorithms such as the one proposed in [Chambolle, A. and Pock T., A first-order primal-dual algorithm for convex problems with applications to imaging, J. Math. Imaging Vis., 40 (2011) 120-145] as a special case. Under suitable conditions, we prove its global convergence and analyze its linear rate of convergence. As compared to the results in the literature, we derive the corresponding results for the general case and under weaker conditions. Furthermore, the global linear rate of the linearized primal-dual algorithm is established in the same analytical framework.</p>

Monitoring of the ice caps area changes on Galindez, Winter and Skua Islands (Argentine Islands, West Antarctica)

Due to global warming, the glaciers and ice systems of Antarctica and the Antarctic Peninsula have been significantly changing in shape and size in recent decades. Therefore, to control, forecast and prevent such processes, it is necessary to constantly monitor and analyse changes in the basic parameters of glaciers and ice systems. This paper proposes a study of changes in the area of ice caps located on the Galindez, Winter and Skua islands (Argentine Islands, West Antarctica). The study is based on the integration of different spatio-temporal datasets into a single system for retrospective geographical monitoring of changes in the area of Galindez, Winter and Skua islands ice caps. The system for integrating space-time datasets is the UTM coordinate system (zone 20, South). Using transformed archival cartographic materials, as well as recently obtained orthophotos, the boundaries of the glaciers in different periods of research were digitized. Based on the identified boundaries, the significance of changes in the area of island glaciers, as well as the rate of their change during 1935–2019, were determined. Based on the integration of different spatio-temporal datasets into a single system, retrospective-geographical monitoring of changes in icecaps area during 1935–2019 was performed. The ice caps were found to be experiencing systematic decrease in area with average linear rate of decrease from –0.30%/year to –0.37%/year. A detailed analysis of all integrated spatio-temporal data sets including determination of the cause of changes in the area of the Galindez, Winter and Skua islands' ice caps is a promising topic for further research.

Statins in preventing stroke

Abstact. The results of a comprehensive analysis of Simvastatin (at a dose of 20 mg per day) on the functional state of the brain in patients with atherothrombotic ischemic stroke are presented. Simvastatin provokes vasoactive action (increases linear rate of systolic blood flow velocity (LBFVsys) and decreases peripheral resistance in separate vessels of the carotid and vertebra-basilar basins), posseses antiatherogenic action (a drug decrease in the intima size, in the frequency of the atherosclerotic plagues, in the level of cholesterol, triglycerides and low density lipoproteids (LDLs). This medication leads to a positive reorganization of the bioelectric activity of the brain (increases the frequency of alpha rhythm and decreases the power of the slow rhythms), being more marked in the patients with a left-sided ischemic localization. Complex positive effects of the Simvastatin on the cerebral hemodynamic, bioelectric activity of the brain and lipid metabolism in the patients after athrothrombotic ischemic stroke allow us to recommend Simvastatin not only for the secondary prevention of stroke but also for the correction of CNS functioning in stroke patients during their rehabilitation. Key words: ischemic stroke; statins; bioelectric activity of the brain; cerebral blood flow; atherothrombotic ischemic stroke