Applications of Some Elliptic Equations in Riemannian Manifolds

Let $(M^{n+1}, g)$ be a compact Riemannian manifold with smooth boundary B and nonnegative Bakry-Emery Ricci curvature. In this paper, we use the solvability of some elliptic equations to prove some estimates of the weighted mean curvature and some related rigidity theorems. As their applications, we obtain some lower bound estimate of the first nonzero eigenvalue of the drifting Laplacian acting on functions on B and some corresponding rigidity theorems

A Generic Conceptual Model for Risk Analysis in a Multi-agent Based Collaborative Design Environment

Organised by: Cranfield UniversityThis paper presents a generic conceptual model of risk evaluation in order to manage the risk through related constraints and variables under a multi-agent collaborative design environment. Initially, a hierarchy constraint network is developed to mapping constraints and variables. Then, an effective approximation technique named Risk Assessment Matrix is adopted to evaluate risk level and rank priority after probability quantification and consequence validation. Additionally, an Intelligent Data based Reasoning Methodology is expanded to deal with risk mitigation by combining inductive learning methods and reasoning consistency algorithms with feasible solution strategies. Finally, two empirical studies were conducted to validate the effectiveness and feasibility of the conceptual model.Mori Seiki – The Machine Tool Compan

Composition law and Nodal genus-2 curves in P^2

Recently, there has been great interest in the application of composition laws to problems in enumerative geometry. Using the moduli space of stable maps, we compute the number of irreducible, reduced, nodal, degree-$d$ genus-$2$ plane curves whose normalization has a fixed complex structure and which pass through $3d - 2$ general points in $\Bbb P^2$.Comment: 13 pages, AMS-Te

MiR-338-3p Is a Biomarker in Neonatal Acute Respiratory Distress Syndrome (ARDS) and Has Roles in the Inflammatory Response of ARDS Cell Models

To investigate the association between serum miR-338-3p levels and neonatal acute respiratory distress syndrome (ARDS) and its mechanism. The relative miR-338-3p expression in serum was detected by quantitative real-time RT-PCR. Interleukin-1beta (IL-1β), IL-6, and tumor necrosis factor-alpha (TNF-α) levels were detected by ELISAs. A receiver operating characteristic (ROC) curve analysis of serum miR-338-3p evaluated the diagnosis of miR-338-3p in neonatal ARDS. Pearson’s correlation analysis evaluated the correlation between serum miR-338-3p and neonatal ARDS clinical factors. Flow cytometry evaluated apoptosis, and a CCK-8 assay assessed cell viability. A luciferase assay evaluated the miR-338-3p/AKT3 relationship. The miR- 338-3p expression was decreased in neonatal ARDS patients and in lipopolysaccharide (LPS)-treated cells. The ROC curve showed the accuracy of miR-338-3p for evaluating neonatal ARDS patients. The correlation analysis demonstrated that miR-338-3p was related to PRISM-III, PaO2/FiO2, oxygenation index, IL-1β, IL-6, and TNF-α in neonatal ARDS patients. MiR-338-3p overexpression inhibited the secretion of inflammatory components, stifled cell apoptosis, and LPS-induced advanced cell viability. The double-luciferase reporter gene experiment confirmed that miR-338-3p negatively regulates AKT3 mRNA expression. Serum miR-338-3p levels were related to the diagnosis and severity of neonatal ARDS, which may be attributed to its regulatory effect on inflammatory response in ARDS

Exponential Stability of Stochastic Nonlinear Dynamical Price System with Delay

Based on Lyapunov stability theory, Itô formula, stochastic analysis, and matrix theory, we study the exponential stability of the stochastic nonlinear dynamical price system. Using Taylor's theorem, the stochastic nonlinear system with delay is reduced to an n-dimensional semilinear stochastic differential equation with delay. Some sufficient conditions of exponential stability and corollaries for such price system are established by virtue of Lyapunov function. The time delay upper limit is solved by using our theoretical results when the system is exponentially stable. Our theoretical results show that if the classical price Rayleigh equation is exponentially stable, so is its perturbed system with delay provided that both the time delay and the intensity of perturbations are small enough. Two examples are presented to illustrate our results

Value of segmental myocardial strain by 2-dimensional strain echocardiography for assessment of scar area induced in a rat model of myocardial infarction

<p>Abstract</p> <p>Objectives</p> <p>Two-dimensional strain echocardiography (2DSE) technique has enabled accurate quantification of regional myocardial function. This experimental study was aimed to investigate the value of 2DSE in detection of segmental regional myocardial dysfunction induced by fibrosis following myocardial infarction in a small animal (rat) model.</p> <p>Methods</p> <p>A rat model of myocardial infarction was established by ligation of the proximal left anterior descending coronary artery in 17 SD rats. Regional myocardial function was detected by 2DSE at baseline and 4-weeks post-infarction, including end-systolic radial strain and strain rate (SR and SrR) and end-systolic circumferential strain and strain rate (SC and SrC) of each of six segments at papillary level. According to the size of scar found by histologic Masson staining, the optimal cutoff points of parameters for detecting scar area were analyzed and the sensitivity and specificity of every parameter to detect myocardial scar were obtained using ROC.</p> <p>Results</p> <p>(1) Comparing with parameters measured at baseline, there were significant decreases in SR, SrR, SC and SrC of each segment at 4 weeks post-infarction, with the worst in the infarct area (32.90 ± 8.79 vs 11.18 ± 3.89, 6.28 ± 1.35 vs 3.18 ± 0.47, -14.46 ± 2.21 vs <it>-</it>6.30 ± 2.17 and 4.93 ± 0.95 vs 2.59 ± 1.16, respectively) (all <it>P </it>< 0.05). (2)By 4 weeks, the myocardium of infarct area (anteroseptum, anterior and anterolateral) had fibrosis (31.33 ± 9.89, 73.42 ± 13.21 and 13.99 ± 3.24%, respectively) with minimal fibrosis in inferoseptal segment (0.32 ± 0.19%), no fibrosis was found in the inferior and inferolateral segments. (3)Significant negative correlations were found between the size of segmental scar and 2DSE parameters (r-value -0.61 ~ -0.80, all <it>P </it>< 0.01) with the strongest correlation in SR. SR less than 10% has 84% sensitivity and 98% specificity for detecting segments of scar area greater than 30% with AUC = 0.97.</p> <p>Conclusions</p> <p>2DSE is able to assess regional myocardial dysfunction in a rat model of myocardial infarction and has high accuracy in detecting infarct segments with scar area greater than 30%.</p

Risk assessment of critical time to renewable operation with steady-state security region

PS10: Risk Assessment in Power System Operation: ID 371Uncertain and variable characteristics of renewable energy resources introduce challenges to power system operation. A normal operating point might be drifted towards an unreliable operating point due to stochastic outputs od renewables. This paper proposes a novel method for estimating critical time to unreliable operating point with steady-state constraints. In this work, a stochastic differential equation is employed to describe the distribution of renewables with predictable tendency and stochastic errors of prediction; meanwhile, the DC power flow based steady-state security region is used to restrict the injected space. To find the critical time that uncontrollable renewables leave the security region, according the flexibility requirements defined by NERC, the uncontrollable region is identified with the Fourier-Motzkin elimination first. And then, by solving the Chebychev center problem, the critical distance for variable renewable outputs is obtained. Finally, an analytical solution of expected exit-time for renewable outputs leaving the security region is given with the Martingale stopping theorem. The proposed method can be used to construct the condition-driven risk indicators. An illustrative example is employed to demonstrate and validate the proposed method.postprin