Statistical Classification Using the Maximum Function

The maximum of k numerical functions defined on , , by , ??is used here in Statistical classification. Previously, it has been used in Statistical Discrimination [1] and in Clustering [2]. We present first some theoretical results on this function, and then its application in classification using a computer program we have developed. This approach leads to clear decisions, even in cases where the extension to several classes of Fisher’s linear discriminant function fails to be effective.

A New Maximum Entropy Probability Function for the Surface Elevation of Nonlinear Sea Waves

Based on the maximum entropy principle a new probability density function （PDF） f（x） for the surface elevation of nonlinear sea waves, X, is derived through performing a coordinate transform of X and solving a variation problem subject to three constraint conditions of f（ x ）. Compared with the maximum entropy PDFs presented previously, the new PDF has the following merits： （1） it has four parameters to be determined and hence can give more refined fit to observed data and has wider suitability for nonlinear waves in different conditions; （2） these parameters are expressed in terms of distribution moments of X in a relatively simple form and hence are easy to be determined from observed data; （3） the PDF is free of the restriction of weak nonlinearity and possible to be used for sea waves in complicated conditions, such as those in shallow waters with complicated topography; and （4） the PDF is simple in form and hence convenient for theoretical and practical uses. l.aboratory wind-wave experiments have been conducted to test the competence of the new PDF for the surface elevation of nonlinear waves. The experimental results manifest that the new PDF gives somewhat better fit to the laboratory wind-wave data than the well-known Gram-Charlier PDF and beta PDF.

Receiver function estimated by maximum entropy deconvolution

Maximum entropy deconvolution is presented to estimate receiver function, with the maximum entropy as the rule to determine auto-correlation and cross-correlation functions. The Toeplitz equation and Levinson algorithm are used to calculate the iterative formula of error-predicting filter, and receiver function is then estimated. During extrapolation, reflective coefficient is always less than 1, which keeps maximum entropy deconvolution stable. The maximum entropy of the data outside window increases the resolution of receiver function. Both synthetic and real seismograms show that maximum entropy deconvolution is an effective method to measure receiver function in time-domain.

ε-OPTIMAL SOLUTION FOR CONTINUOUS MINIMAX PROBLEMS WITH MAXIMUM-ENTROPY FUNCTION

This paper describes and explores a maximum-entropy approach to continuous minimax problem, which is applicable in many fields, such as transportation planning and game theory. It illustrates that the maximum entropy approcach has easy framework and proves that every accumulation of {x_k} generated by maximum-entropy programming is -optimal solution of initial continuous minimax problem. The paper also explains BFGS or TR method for it. Two numerical exam.ples for continuous minimax problem are

Maximum tolerated volume in drinking tests with water and a nutritional beverage for the diagnosis of functional dyspepsia

AIM: Recently, drinking load tests with water or nutritional beverages have been proposed as diagnostic tools for functional dyspepsia (FD), therefore we sought to reproduce if these tests can discriminate between FD patients and controls in a Mexican population. METHODS: Twenty FD-Rome Ⅱ patients were matched by age and gender with 20 healthy controls. All underwent both drinking tests at a 15 mL/min rate, randomly, 7 d apart. Every 5 min within each test, four symptoms were evaluated (satiety, bloating, nausea and pain) by Likert scales. Maximum tolerated volume (MTV) was defined as the ingested volume when a score of 5 was reached for any symptom or when the test had to be stopped because the patients could not tolerate more volume. Sensitivity and specificity were analyzed. RESULTS: FD patients had higher symptom scores for both tests compared to controls (water: t= 4.1, P= 0.001 ＜0.01; Nutren(R): t= 5.2, P= 0.001＜0.01). The MTV forwater and Nutren(R) were significantly lower in FD (water: 1014±288 vs 1749±275 mL; t = 7.9, P = 0.001＜0.01;Nutren(R): 652±168 vs 1278±286 mL; t= 6.7, P = 0.001＜0.01). With the volume tolerated by the controls, the percentile 10 was determined as the lower limit fortolerance. Sensitivity and specificity were 0.90, 0.95 for water and 0.95, 0.95 for Nutren(R) tests.CONCLUSION: A drinking test with water or a nutritional beverage can discriminate between FD patients and healthy subjects in Mexico, with high sensitivity and specificity. These tests could be used as objective, noninvasive, and safe diagnostic approaches for FD patients.

Treatment of Skeletal CL II Patient with Maximum Lower Incisor Protrusion and Minimum Overjet with Rahhal Functional Appliance

Treatment of skeletal Cl II includes functional orthopedic treatment, head-gears, extraction of the upper premolars and orthognathic surgery. To treat any patient with functional appliances (bite jumping) an adequate overjet is necessary. In this case an 11 years old female patient has skeletal CLII due to mandibular deficiency with ANB angle 8 degrees, overbite: 3 mm, overjet: 1 mm, extremely convex profile and underdeveloped chin due to the hyper muscle contraction of the lower lip to obtain oral seal. To obtain an adequate overjet lower first premolars were extracted and maximum retraction using mini screws (for maximum anchorage) was applied. Afterwards Rahhal functional appliance was used by the patient 16 hours a day for 6 months and 10 hours a day for another 6 months for retention. After that fixed orthodontic treatment was completed. Lateral cephalometrics were taken, traced and analyzed. In the result Skeletal CLI was obtained (ANB 4 degree), straight facial profile, normal over bite overjet and particular chin development were noticed. As a conclusion, in skeletal CLII malocclusions, lower incisor protrusion will cause a contraindication for functional treatment. Extraction of the lower premolars and retraction of the lower incisors followed by functional orthopedic treatment is an efficient method to treat these cases instead of waiting for orthognathic surgery, also reducing the muscle pressure on the chin will change the development characteristics of it.

柯西-施瓦茨不等式在多元函数最值中的应用

利用柯西-施瓦茨不等式,给出了一种求解含约束条件的多元函数最值问题的简便方法,并通过几个典型例题加以说明,以验证方法的便捷性与有效性.

关节松动术配合针刺治疗颞下颌关节紊乱综合征

目的探讨关节松动术配合针刺治疗颞下颌关节紊乱综合征(TMJDS)临床疗效。方法选择颞下颌关节紊乱综合征患者144例,按照随机数表法分成观察组与对照组。对照组给予单纯针刺治疗,观察组在针刺治疗基础上配合关节松动术治疗4周。比较2组口腔健康影响程度量表(OHIP-14)评分、国际常用视觉模拟评分量表(VAS)评分、最大张口度、中文版颞下颌功能受损评分(MFIQ)及Fricton颞下颌关节紊乱指数,比较2组临床疗效和安全性。结果2组治疗后OHIP-14评分,VAS评分,MFIQ评分,功能障碍指数(DI)、肌肉触压痛指数(PI)、颞下颌关节指数(CMI)评分均降低(P<0.05),且观察组低于对照组(P<0.05);2组治疗后最大张口度均升高(P<0.05),且观察组高于对照组(P<0.05);观察组总有效率高于对照组(P<0.05);2组均未发生与治疗相关的不良事件。结论关节松动术配合针刺能够改善颞下颌关节紊乱综合征患者疼痛和颞下颌功能活动,提高最大张口度,疗效明显。

基于CB-RRT^(*)算法的滩涂履带车路径规划

针对滩涂履带车在受潮汐影响的滩涂环境中进行长时间勘测作业的需求,提出柯西贝塞尔快速搜索随机树星(Cauchy Bessel Rapidly-exploring Random Tree Star,CB-RRT^(*))算法进行路径规划。为规划出安全路径,基于全局地图和潮汐数据,并通过滩涂履带车到分界区的距离构建出滩涂预测模型;为提高滩涂履带车移动到目标点需进行多次路径规划的速度,对初始路径的关键树节点使用柯西概率密度函数进行采样缩小采样范围来提高节点的利用率,进而提高算法的收敛性;在重选父节点过程中考虑最大转角约束设定相应系数,并使用连续二次贝塞尔曲线进行拼接的方式来生成路径,达到提高路径平滑度的目的和解决平滑后路径与原路径偏差过大造成的安全性问题。仿真实验结果表明,CB-RRT^(*)算法在静态滩涂环境和动态滩涂环境中,能大大提高算法的收敛性和路径的平滑性,且保证路径长度最优,研究内容可以保证滩涂履带车在各种滩涂环境中进行长时间安全作业。

基于fminimax优化函数的圆度误差评定

依据圆度误差标注代号和附加符号的含义,基于最小外接法、最大内切法和最小区域法分别建立了参考圆的圆心坐标优化目标函数和圆度误差评定模型,采用MATLAB软件编写了参考圆的圆心坐标优化目标函数子程序和圆度误差评定子程序,给出了圆度误差评定中fminimax优化函数调用方法。用Talyrond 585LT圆柱度测量仪对三个试样的圆周轮廓进行了提取,基于最小二乘法、最小外接法、最大内切法和最小区域法对提取的圆周轮廓分别进行了圆度误差评定。研究了优化搜索范围对圆度误差评定结果的影响,并将fminimax优化函数圆度误差评定的优化符合度与其他优化方法圆度误差评定的优化符合度进行了比较。fminimax优化函数的应用结果表明,评定结果精度高于或等于其他优化方法评定结果的精度,可满足圆度误差评定的需要。

基于图常量条件函数依赖的图修复规则发现

数据一致性是数据质量管理的一个重要内容。为了提升图数据一致性,大量关系型数据库中的数据依赖理论被引入到图数据库,包括图函数依赖、图关联规则等。图修复规则是最新提出的一种针对图数据的数据依赖规则,具有强大的修复能力,但目前尚无有效的挖掘算法。为了自动生成图修复规则并提高图数据修复的可靠性,提出一种将图常量条件函数依赖转化为图修复规则的方法(GenGRR)。通过图模式在图中匹配同构子图并映射成节点-属性二维表,从表中相应属性域中抽取错误模式把图常量条件函数依赖转化成图属性值修复规则;删去图模式中常量条件函数依赖RHS对应的节点与相连边生成图属性补充规则。基于最大公共同构子图筛选并验证生成图修复规则的一致性。在多个真实数据集上进行测试,验证相比图常量条件函数直接修复图数据,通过转化生成的图修复规则具有更好的修复效果。

青年人躯干压力生物反馈与膈肌功能参数的相关性

背景:躯干压力生物反馈被认为是评估核心肌肉力量的一个可靠指标,其不仅能反映个体躯干力量状况,而且与呼吸肌功能有着密切关系。目的:探讨青年人躯干压力生物反馈与膈肌功能之间的相关性。方法:选择上饶师范学院80名大学生为研究对象,男34名,女46名,年龄(19.83±1.45)岁,采用床旁肌骨超声系统测量受试者膈肌厚度和移动度,便携式肺功能检测仪检测受试者最大吸气压,压力生物反馈仪测试受试者俯卧与仰卧位的腰部及腹部压力。采用Pearson或Spearman相关系数确定躯干压力生物反馈与膈肌功能之间的相关程度,多元线性回归分析确定膈肌功能的预测模型。结果与结论:①以性别分组,男子组年龄、身高、体质量、躯干压力生物反馈数值、平静吸气末膈肌厚度、平静呼气末膈肌厚度、平静呼吸膈肌增厚率、深吸气末膈肌厚度、深呼气末膈肌厚度、深吸气膈肌移动度、最大吸气压均大于女子组(P均<0.05);②以体力活动水平分组,久坐组躯干压力生物反馈数值及最大吸气压均低于运动组(P均<0.05);③相关性分析显示,躯干压力生物反馈(俯卧)、躯干压力生物反馈(仰卧)与平静吸气末膈肌厚度、平静呼气末膈肌厚度、平静呼吸膈肌增厚率、深吸气末膈肌厚度、深呼气末膈肌厚度、深呼吸膈肌增厚率、深吸气膈肌移动度、最大吸气压均具有显著性相关关系(P均<0.01);④多元线性回归分析显示,躯干压力生物反馈(俯卧)进入平静吸气末膈肌厚度的预测模型(F=27.228,P<0.001),躯干压力生物反馈(俯卧)进入深吸气末膈肌厚度的预测模型(F=38.615,P<0.001),躯干压力生物反馈(仰卧)、年龄进入深吸气膈肌移动度的预测模型(F=15.408,P<0.001),躯干压力生物反馈(俯卧)、体质量、年龄进入最大吸气压的预测模型(F=22.314,P<0.001);⑤结果显示,躯干压力生物反馈与膈肌厚度、膈肌移动度和最大吸气压的相关性较强,快速简便的躯干压力生物反馈测量可以作为筛查健康青年人膈肌功能的一种方法。

自然增长条件下具有BMO系数的椭圆方程Calderón-Zygmund型估计

本文主要研究自然增长条件的一类非线性椭圆方程-divA (x,▽u)=divF+B (x,u,▽u)弱解梯度的全局BMO估计.在A(x,▽u)满足充分小的BMO系数条件下,利用扰动讨论和极大函数等方法,完成了一类非线性Calderón-Zygmund型全局BMO估计.

基于能量模型的最大熵生成对抗网络

生成对抗网络(Generative Adversarial Network,GAN)是目前深度学习领域的一个研究热点。针对GAN生成模型存在模式坍塌和训练不稳定的问题,提出一种全新的能量函数意义下的生成式对抗网络模型(Energy Maximum Entropy GAN,E-MEGAN)。该模型的最终目标是最大化生成样本的熵来解决模式坍塌问题,使用非参数互信息估计量计算该熵。为了稳定对抗的训练过程,还使用了以零为中心的梯度惩罚技巧。通过在MNIST和CelebA数据集上进行大量实验,表明该模型可以生成清晰高质量的图像,其IS(Inception Scores)和FID(Frechet Inception Distance)与WGAN-GP技术相比具有同等竞争力,并且不会遭受模式的损失。

面向防振锤更换的无人机-机器人协同控制

防振锤更换现场变动因素较多、存在多种信号干扰,抓取力与防振锤重力间的平衡难度大,稳定性较差,由此,提出一种无人机-机器人协同控制算法。明确防振锤内部结构,考虑线路重量和抗振力需求,计算抓取力和防振锤重力,分析不平衡因素,根据构建的无人机-刚柔耦合系统动力学模型,计算不同时间点的最佳的旋转中心值,用于约束机器人运行的最大偏离范围。根据无人机的非线性动态反演关系,以内环控制求得机器人运动轨线与目标轨迹之间的贴合能力,以外环控制获得无人机出现转弯、上升、下降以及停滞状态下的一阶和二阶导数输出数值,采用二阶求导的控制阈值,完成无人机-机器人协同控制。实验结果表明,关节柔性变化轨迹控制稳定性强,无人机姿态角和位置偏差较小,实用价值高。

基于最大熵Copula方法的古黄河宿迁段流域月降雨量模拟

为了解决Copula函数方法在拟合过程中要先选择函数类型和多变量水文模拟中保留相关性的问题,基于最大熵原理(POME),直接构建Copula函数,而无需进行Copula函数类型的优选,简化了联合概率分布函数的拟合过程。以古黄河宿迁段流域的皂河站、金锁站和泗阳站3个雨量站点39年(1980~2018年)的月降雨量实测资料为研究对象,进行实例分析。通过建立不同站点间的降雨量联合分布,检验最大熵Copula方法的有效性,并利用Gibbs采样法对月降雨量进行随机模拟。结果表明,基于最大熵Copula方法能保留各站点降雨序列的统计特性,以及不同站点间的降雨相关性,验证了该方法的有效性,可为流域多站点间的降雨量相关性分析和水资源规划与利用提供参考。

高阶声学相对传递函数的参数化辨识

针对声学相对传递函数的模型阶次高以及辨识数据信噪比低的问题,文章运用频域系统辨识方法,建立了一种相对传递函数的高精度参数化辨识方法。首先建立变量带误差辨识框架,采用周期扫频信号作为声源激励,给出声学相对传递函数的极大似然算法。然后使用正交福赛斯(Forsythe)多项式解决高阶系统带来的雅克比矩阵条件数过高的数值问题,并建立了极大似然方法所需初始值的生成策略。最后通过仿真算例和实验测试,验证文中方法在混响声场下辨识声学相对传递函数的有效性。

积分限函数∫_(x)^(x+a)|sin t|dt的最值及图形的拐点

研究了一类特殊的积分限函数f(x)=∫_(x)^(x+a)|sin t|dt。首先分析得到函数f(x)是一个周期为π的周期可导函数,再利用微积分基本公式和积分限函数求导公式两种方法,分别研究函数f(x)的最值问题,然后利用拐点的判定方法得到曲线f(x)的拐点坐标,最后对此积分限函数进行推广,并利用MATLAB软件画图验证,旨在更深入地理解和掌握积分限函数的性态。

基于改进YOLOv7的密集行人检测算法

针对密集场景中的行人目标往往存在重叠、遮挡、体积较小等问题,导致在检测过程中容易出现漏检、误检、特征提取困难、定位不准确等现象。提出一种改进YOLOv7的密集行人检测算法,首先在YOLOv7主干网络的ELAN结构上融合CBAM注意力机制,使主干网络更加关注特征的语义信息,以增强遮挡物和小目标的特征提取能力;其次在检测头的卷积中引入CoordConv模块,充分利用此模块的位置信息,有效改善了目标定位不准确的问题,提高模型对空间位置的感受能力和泛化能力;然后将原YOLOv7网络模型中的CIoU损失函数替换为Focal-EIoU损失函数,可以有效缓解正负样本不均衡的问题,在边界框回归过程中,该损失函数更注重于高质量锚框,从而加快网络的收敛速度;最后在模型中用非极大值抑制Soft-NMS算法替换传统的NMS算法,有效降低了重叠、遮挡目标的漏检率,提升模型的召回率和精度。在公开密集行人数据集WiderPerson上进行验证本模型,实验结果表明,改进后的检测算法对密集行人目标检测的准确率、召回率及平均精度mAP值相较原基线模型分别提升了2.3%、3.3%与2.6%,FPS值提升了2.3 f/s。

基于Copula函数的区域雨潮遭遇风险概率分析

随着气候变化、人类活动影响加剧以及城市化进程等一系列事件的加快,我国的城市内涝问题日渐突出。以扬州市仪邗区域为例,由于扬州南濒长江,受长江洪水、潮水顶托,当面临暴雨等灾害时,仪邗区域无法快速外排,进而增大了内涝风险,针对内涝灾害的研究也因此成为了重要内容。本文利用Copula函数构建了研究区域最大三日面雨量和长江最大三日平均潮位的联合概率分布函数,并对不同雨潮组合情况下的遭遇概率进行分析,最终得到了雨潮的联合风险概率和同现风险概率。最终结果显示,Copula函数在雨潮联合概率分布方面拟合良好。这一拟合结果不仅可以为解决仪邗山洪在长江高水位时出路不足的问题提供一定的理论支持和科学依据,也可以为其他感潮河段的防洪决策提供参考。