Precise Asymptotics for Random Matrices and Random Growth Models

The author considers the largest eigenvaiues of random matrices from Gaussian unitary ensemble and Laguerre unitary ensemble, and the rightmost charge in certain random growth models. We obtain some precise asymptotics results, which are in a sense similar to the precise asymptotics for sums of independent random variables in the context of the law of large numbers and complete convergence. Our proofs depend heavily upon the upper and lower tail estimates for random matrices and random growth models. The Tracy-Widom distribution plays a central role as well.

Efficacy and safety of nerve growth factor for the treatment of neurological diseases:a meta-analysis of 64 randomized controlled trials involving 6,297 patients

OBJECTIVE： China is the only country where nerve growth factor is approved for large-scale use as a clinical medicine. More than 10 years ago, in 2003, nerve growth factor injection was listed as a national drug. The goal of this article is to evaluate comprehensively the efficacy and safety of nerve growth factor for the treatment of neurological diseases. DATA RETRIEVAL： A computer-based retrieval was performed from six databases, including the Cochrane Library, PubMed, EMBASE, Sino Med, CNKI, and the VIP database, searching from the clinical establishment of nerve growth factor for treatment until December 31, 2013. The key words for the searches were ＂nerve growth factor, randomized controlled trials＂ in Chinese and in English. DATA SELECTION： Inclusion criteria： any study published in English or Chinese referring to randomized controlled trials of nerve growth factor; patients with neurological diseases such as peripheral nerve injury, central nerve injury, cranial neuropathy, and nervous system infections; patients older than 7 years; similar research methods and outcomes assessing symptoms; and measurement of nerve conduction velocities. The meta-analysis was conducted using Review Manager 5.2.3 software. MAIN OUTCOME MEASURES： The total effective rate, the incidence of adverse effects, and the nerve conduction velocity were recorded for each study. RESULTS： Sixty-four studies involving 6,297 patients with neurological diseases were included. The total effective rate in the group treated with nerve growth factor was significantly higher than that in the control group （P 〈 0.0001, RR： 1.35, 95%CI： 1.30-1.40）. The average nerve conduction velocity in the nerve growth factor group was significantly higher than that in the control group （P 〈 0.00001, MD. 4.59 m/s, 95%CI： 4.12-5.06）. The incidence of pain or sclero- ma at the injection site in the nerve growth factor group was also higher than that in the control group （P 〈 0.00001, RR： 6.30, 95%CI： 3.53-11.27）, but such adverse effects were mild. CONCLUSION： Nerve growth factor can significantly improve nerve function in patients with nervous system disease and is safe and effective.

THE GROWTH OF RANDOM DIRICHLET SERIES (I)

Under the conditions(without independence): (i) There Exists alpha > 0, such that sup E\Z(n)\(alpha) < +infinity, (ii) There Exists beta > 0, such that sup E\Z(n)\(-beta) < +infinity, the random series Sigma a(n) Z(n)e(-lambda n) and series' Sigma a(n)e(-lambda ns) a.s. have the same abscissa of convergence, the (R) order, lower order and type.

The asymptotic stability analysis in stochastic logistic model with Poisson growth coefficient

The asymptotic stability of a discrete logistic model with random growth coefficient is studied in this paper. Firstly, the discrete logistic model with random growth coefficient is built and reduced into its deterministic equivalent system by orthogonal polynomial approximation. Then, the linear stability theory and the Jury criterion of nonlinear deterministic discrete systems are applied to the equivalent one. At last, by mathematical analysis, we find that the parameter interval for asymptotic stability of nontrivial equilibrium in stochastic logistic system gets smaller as the random intensity or statistical parameters of random variable is increased and the random parameter’s influence on asymptotic stability in stochastic logistic system becomes prominent.

Influencing factors and growth state classification of a natural Metasequoia population

By analyzing the importance of influencing factors and conducting a comparative study of the effects of different sorting algorithms, a new method is proposed that is suitable for classifying the growth state of a natural Metasequoia glyptostroboides Hu and W.C. Cheng population. We studied 2817 M. glyptostroboides trees over 100 years old and analyzed their growth state by measuring 15 factors from stumpage, site condition, and environmental data. The dimensionality of all factors were reduced using the random forest algorithm, and we classified the remaining factors using the following algorithms: random forest, back-propagation(BP) neural networks, and support vector machine(SVM). The applicability of each sorting algorithm was analyzed. When all the d factors are used for classification and modeling, the model's overall accuracy,kappa coefficient and test accuracy were 85.5%, 0.739 and 85.8%, respectively. By reducing the dimensionality of the factors using the random forest algorithm, 11 factors most strongly influenced the classifications of the growth state of the Metasequoia population: diameter at breast height,height, crown width, age from stumpage data; longitude,latitude, elevation, slope aspect, gradient and slope position from the site condition data; and the edge of the field from the environmental data. For classifying the Metasequoia population, the random forest algorithm has the highest overall accuracy at 87.2%, which is 3.4 and 2.3% higher than the BP neural networks and SVM algorithms,respectively. The SVM algorithm is superior to the random forest algorithm with respect to classifying the state of mortality. The combination of the random forest and SVM algorithms and their combined information can be used to classify and predict the growth state of this natural M.glyptostroboides population to provide a scientific basis for its effective protection.

基于Spark的FP-Growth伴随车辆发现与应用

随着大数据技术在交通管理中的广泛应用,在海量车牌数据中检测伴随车辆,引起了研究者们的关注。但目前大多数方法在庞大的数据量下运行效率低,且停留在理论研究阶段,并未与实际应用相结合。提出了一种针对于此应用的新颖方法。采用Spark分布式并行计算框架提高运行速度,利用负载均衡原理对数据进行均衡化处理,再提出基于改进的FP-Growth的伴随车辆发现算法,利用置信度对结果进行后处理,剔除车辆随机伴随的情况,提高了检测正确率。该方法应用于长沙市交警大联合交管中心系统,其中将海量车牌识别数据存储在Hadoop大数据平台下的Hive数据库中,在交通PGIS(Police Geographic Information System)上可视化分析结果,实验证明了方法的高效性和可行性。

STOCHASTIC MODELLING OF FATIGUE CRACK GROWTH UNDER CONSTANT AMPLITUDE LOADING

Two stochastic models of fatigue crack growth under constant amplitude cyclic loading are proposed and studied by using the stochastic averaging method and total probability theorem to account for high frequency component and low frequency component, respectively, of the irregular nature of fatigue crack growth observed in Virkler's experiment. Particular attention is paid to the prediction performance of the models under a change in the initial crack length. It is shown that the models proposed in the present paper yields better agreement with experimental data than other models available in literature.

ON THE DISTRIBUTION OF VALUES AND DEFICIENT FUNCTION OF A GENERAL RANDOM INTEGRAL FUNCTION

Under suitable conditions on {X-n}, the author obtains the important results: it is almost sure that the random integral function f(w) = Sigma (infinity)(n=0) X(n)z(n) (of finite positive order) has no deficient function, and any direction is a Borel direction (without finite exceptional value) of f(w).

Model Selection in Estimation of Covariance Functions for Growth of Angora Goats

Covariance functions have been proposed as an alternative to model longitudinal data in animal breeding because of their various merits in comparison to the classical analytical methods.In practical estimation,different models and polynomial orders fitted can influence the estimates of covariance functions and thus genetic parameters.The objective of this study was to select model for estimation of covariance functions for body weights of Angora goats at 7 time points.Covariance functions were estimated by fitting 6 random regression models with birth year,birth month,sex,age of dam,birth type,and relative birth date as fixed effects.Random effects involved were direct and maternal additive genetic,and animal and maternal permanent environmental effects with different orders of fit.Selection of model and orders of fit were carried out by likelihood ratio test and 4 types of information criteria.The results showed that model with 6 orders of polynomial fit for direct additive genetic and animal permanent environmental effects and 4 and 5 orders for maternal genetic and permanent environmental effects,respectively,were preferable for estimation of covariance functions.Models with and without maternal effects influenced the estimates of covariance functions greatly.Maternal permanent environmental effect does not explain the variation of all permanent environments,well suggesting different sources of permanent environmental effects also has large influence on covariance function estimates.

PROBABILITY OF RANDOM EVENTS OF INSPECTION AND REPAIR AND MAINTAINING RELIABILITY OF STRUCTURES

Reliability analysis of the inspected and repaired structure requires dealing with a large number of complex random events. Considering many kinds of random factors, a probability of these random events existing possibly in the inspection and repair process and reliability analysis methodologies are proposed. A systematic dynamic reliability model is given for structures in service under the scheduled inspection and repair.

Random Dirichlet Series with Coefficients Satisfying only a Moment Condition

This note implies only a moment condition upon the coefficients of random Dirichlet series to study the convergence and growth of the series. The condition needs the coefficients to satisfy the so-called inverse H?lder inequality, which need not be independent. The note uses a method whose feature is to compare the convergence of two series, and obtains two theorems, one dealing with the convergence of the random Dirichlet series, another the growth of the random analytic function represented by the series. These results can be used to improve essentially some known conclusions.

On Random Taylor Series

This paper deals with random Taylor series whose coefficients consist of independent random variables {X n} with the property: αE 1/2 {|X n| 2}≤E{|X n|}<∞, E{X n}=0 (n ) for some positive constant α. The convergence, growth, and value distribution of the series are investigated.

Variation in growth potential between hybrid clones of Eucalyptus trees in eastern South Africa

Growth of commercial forestry is highly dependent on the availability of fast-growing planting materials. Consequently, the efficient utilization of fastgrowing plantations can greatly impact productivity. The objectives of this study were to evaluate variations in the growth potential of two clones and to estimate the average stem radial growth advantage of a fast-growing clone using data obtained from Sappi landholdings in eastern South Africa and a mixed modelling approach that permits the incorporation of covariance structure into the statistical model. During the first 2 years of growth, the stem radius of nine trees each of two clones was measured using dendrometer attached to the tree. A second-degree fractional polynomial model was chosen to show the functional relationship between stem radius and tree age. Growth of the two hybrid clones differed significantly. The Eucalyptus grandis×Eucalyptus urophylla clone grew faster than the E. grandis×camaldulensis clone, indicating better genetic potential for rapid growth and yield. This study can be considered as starting point to further compare the potential for rapid growth of several hybrid clones using the longitudinal data modelling approach.

Construction of Clonal Growth Models in Trifolium repens

The suitability of models for describing the clonal growth of Trifolium repens population was discussed. The results showed that deterministic models were inadequate for describing its clonal growth, but the diffusion models and the randomwalk models suited for the clonal growth characteristics of the population. And it was found that random-walk models were better than diffusion models for describing a population in an environment with rich natural resources, and the latter was better in a poor environment.

基于森林资源清查资料的盈江县森林生物量和生长量分析

为确定盈江县森林碳储量和碳汇潜力的变化特征及其影响因子,以便更好地分析盈江县森林生物量和生长量。基于盈江县2012年和2017年森林资源清查数据,利用生物量换算因子连续函数法和异速生长方程,评估盈江县森林碳储量和碳汇潜力的变化特征及其影响因子。结果显示:(1)盈江县森林生物量储量丰富,达85.55 t/hm^(2)。其中:栎类林最大,为168.3 t/hm^(2);核桃林最低,为7.10 t/hm^(2)。(2)不同林龄林分生物量差异较大,近熟林最高,其次分别为中龄林、成熟林、过熟林、幼龄林。(3)常绿阔叶林的林分生长量最大,其次是落叶阔叶林和针叶林。结果表明:盈江县森林生物量储量丰富且以阔叶林为主;林龄和年均气温是影响林分生长和生物量的主要因素。

缺口悬臂梁振动疲劳裂纹扩展行为研究

航空飞行器在服役过程中会经受大量复杂的随机振动载荷,其结构易发生振动疲劳进而导致损伤甚至失效,造成严重损失。以铝合金悬臂梁结构件为对象,开展振动疲劳试验与理论分析,研究随机振动载荷下含裂纹梁的应力强度因子求解方法,提出一种基于Hudson理论的时域法,结合经典的Paris公式估算振动疲劳裂纹扩展寿命。结果表明:本文提出的基于Hudson理论的时域法的寿命预测结果优于试验对比估算结果,验证了该方法能够有效描述随机振动裂纹扩展行为。

基于随机森林算法的桉树人工林单木生物量预估模型

单木生物量模型是估测森林生物量的基础。通过标准木法实测雷州半岛地区90株桉树单株生物量数据,随机划分60个样本数据作为训练集,30个样本数据作为验证集。以林龄、树高和胸径为自变量,单木生物量为因变量,使用岭回归模型、异速生长模型和随机森林算法构建模型,采用决定系数(R^(2))、均方根误差(RMSE)和平均绝对误差(MAE)对模型进行评价。结果表明:随机森林模型的R~2、RMSE和MAE无论在训练集还是验证集均高于岭回归模型和异速生长模型。由随机森林模型的因子重要值可知,胸径是影响单木生物量的主要因子。引入林龄因子后的随机森林模型可以提高单木生物量的预测精度,为碳汇计量提供基础数据和模型支撑。

健康焦虑的移动网络化解释偏向矫正:一项随机对照试验

本研究旨在考察移动网络化解释偏向矫正(internet-based Cognitive Bias Modification-Interpretation,iCBM-I)对健康焦虑的干预效果、影响因素及灾难化解释在干预起效中的机制作用。采用随机对照试验,将符合健康焦虑标准的被试(N=228)随机分配到iCBM-I干预组(100%积极反馈,N=76)、注意控制组(50%积极50%消极反馈,N=76)以及等待组(N=76)。干预组和注意控制组进行为期12天的在线任务训练,等待组不做训练。在干预前、干预后及干预后一个月对被试的健康焦虑、灾难化解释、一般焦虑和抑郁进行测量。结果发现:与等待组相比,iCBM-I干预对健康焦虑个体的灾难化解释、一般焦虑和抑郁症状存在显著的即时效果和一个月后的追踪效果;基于潜在增长曲线模型的纵向中介检验显示,相对于注意控制组,iCBM-I干预通过降低个体的灾难化解释进而改善健康焦虑。本研究为健康焦虑的网络化干预提供了新视角,未来研究可以考虑联合“自上而下”和“自下而上”的干预方法,以提高健康焦虑的干预效果。

天然云冷杉林树木生长与树木大小、竞争和树种多样性的关系

【目的】林分内林木大小、竞争和树种多样性等多方面因素影响着林木的生长,而胸高断面积生长量通常被用来描述树木生长状态。本文利用长白山云冷杉针阔混交林主要树种的单木胸高断面积生长量建立随机森林模型,研究和量化影响树木生长的环境因素,旨在为该地区的云冷杉针阔混交林生长预估提供理论依据。【方法】连续24年(1987—2010年)对总样木数为6903株的固定样地进行数据调查,应用随机森林算法,选取单木、竞争因子、多样性和气候方面共11个调查因子,对混交林中6个主要树种建立胸高断面积生长量模型,并使用10折交叉验证法来优化超参数mtry和评估模型结果。【结果】(1)臭冷杉、云杉、红松、椴树、枫桦、白桦6个主要树种胸高断面积生长量模型的决定系数分别为0.663、0.683、0.695、0.459、0.384和0.568。(2)单木胸高断面积是最重要的因子,对树木生长有着很强的正向影响;竞争因子和树木大小多样性是影响树木生长的主要因素,单木胸高断面积生长量随着竞争因子、树木大小多样性增加而下降。(3)树种多样性对树木生长的影响比较有限,树种多样性指数和混交度的增加会一定程度加快云杉、臭冷杉和红松的生长速度;而气候因子对树木生长的影响则相对较小。【结论】树木生长在很大程度上依赖于其自身的生长潜力,在外界环境中主要受到来自林木间竞争和树木大小多样性的抑制,而树种多样性的增加也能在一定程度促进林内优势树种的生长;随机森林模型能够很好地量化和显出各变量与单木胸高断面积生长量之间复杂的关系,可以作为森林管理评价工具,为森林生长收获预估提供新的方法。

鼠神经生长因子治疗NAION疗效及安全性的Meta分析

目的对鼠神经生长因子(mNGF)治疗非动脉炎性前部缺血性视神经病变(NAION)的有效性和安全性进行Meta分析。方法检索PubMed、Web of Science、The Cochrane Library、中国知网、万方、维普和中国生物医学文献数据库建库至2023年2月报道的mNGF治疗NAION的随机对照试验(RCT),根据是否使用mNGF治疗分为治疗组和对照组。由2名研究者独立筛选文献、提取资料,评价纳入文献的偏倚风险,采用RevMan 5.3软件对总有效率、视力、视野、电生理P100峰潜时、视神经平均纤维层厚度进行Meta分析,并进行安全性评价。结果共纳入18篇文献,1,507例患者(1,573只眼),其中治疗组759例(797只眼),对照组748例(776只眼)。使用mNGF的治疗组总有效率[OR=4.810,95%CI(3.480,6.650),Z=9.540,P=0.000]、视力[MD=0.120,95%CI(0.080,0.170),Z=5.430,P=0.000]、视野平均缺损度[MD=-1.960,95%CI(-2.560,-1.360),Z=6.400,P=0.000]、电生理P100峰潜时[MD=-8.650,95%CI(-11.610,-5.700),Z=5.740,P=0.000]、视神经平均纤维层厚度[MD=10.420,95%CI(8.300,12.540),Z=9.650,P=0.000]均优于对照组,差异均有统计学意义。不良反应主要为局部注射mNGF后出现的局部刺激、疼痛、硬结,症状较轻。结论MNGF治疗NAION具有一定的疗效,可提高患者总有效率、视力,降低视野平均缺损度和视神经平均纤维层厚度,临床应用安全可靠。