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.

PID Controller Design Based on the Time Domain Information of Robust IMC Controller Using Maximum Sensitivity

The IMC(Internal Model Control) controller based on robust tuning can improve the robustness and dynamic performance of the system.In this paper,the robustness degree of the control system is investigated based on Maximum Sensitivity(Ms) in depth.And the analytical relationship is obtained between the robustness specification and controller parameters,which gives a clear design criterion to robust IMC controller.Moreover,a novel and simple IMC-PID(Proportional-Integral-Derivative) tuning method is proposed by converting the IMC controller to PID form in terms of the time domain rather than the frequency domain adopted in some conventional IMC-based methods.Hence,the presented IMC-PID gives a good performance with a specific robustness degree.The new IMC-PID method is compared with other classical IMC-PID rules,showing the flexibility and feasibility for a wide range of plants.

An Interval Maximum Entropy Method for Quadratic Programming Problem

With the idea of maximum entropy function and penalty function methods, we transform the quadratic programming problem into an unconstrained differentiable optimization problem, discuss the interval extension of the maximum entropy function, provide the region deletion test rules and design an interval maximum entropy algorithm for quadratic programming problem. The convergence of the method is proved and numerical results are presented. Both theoretical and numerical results show that the method is reliable and efficient.

Application of Maximum Entropy Principle to Studying the Distribution of Wave Heights in A Random Wave Field

Based on the maximum entropy principle, a probability density function (PDF) is derived for the distribution of wave heights in a random wave field, without any more hypothesis. The present PDF, being a non-Rayleigh form, involves two parameters: the average wave height H— and the state parameter γ. The role of γ in the distribution of wave heights is examined. It is found that γ may be a certain measure of sea state. A least square method for determining γ from measured data is proposed. In virtue of the method, the values of γ are determined for three sea states from the data measured in the East China Sea. The present PDF is compared with the well known Rayleigh PDF of wave height and it is shown that it much better fits the data than the Rayleigh PDF. It is expected that the present PDF would fit some other wave variables, since its derivation is not restricted only to the wave height.

Comparison between methods for predicting maximum solid solubility of transition metals in solvent metal

It is important to know the maximum solid solubility( C max ) of various transition metals in a metal when one designs multi component alloys. There have been several semi empirical approaches to qualitatively predict the C max , such as Darken Gurry(D G) theorem, Miedema Chelikowsky(M C) theorem, electron concentration rule and the bond parameter rule. However, they are not particularly valid for the prediction of C max . It was developed on the basis of energetics of alloys as a new method to predict C max of different transition metals in metal Ti, which can be described as a semi empirical equation using the atomic parameters, i e, electronegativity difference, atomic diameter and electron concentration. It shows that the present method can be used to explain and deduce D G theorem, M C theorem and electron concentration rule.

Maximum Entropy Estimation of n-Year Extreme Waveheights

A new method for estimating the n (50 or 100) -year return-period waveheight, namely, the extreme waveheight expected to occur in n years, is presented on the basis of the maximum entropy principle. The main points of the method are as follows: (1) based on the Hamiltonian principle, a maximum entropy probability density function for the extreme waveheight H, f(H)=αHγ e -βH4 is derived from a Lagrangian function subject to some necessary and rational constraints; (2) the parameters α, β, and γ in the function are expressed in terms of the mean , variance V= (H-)2 and bias B= (H-)3 ; and (3) with , V and B estimated from observed data, the n -year return-period wave height H n is computed in accordance with the formula 11-F(H n)=n , where F(H n) is defined as F(H n)=∫ H n 0f(H) d H. Examples of estimating the 50 and 100-year return period waveheights by the present method and by some currently used method from observed data acquired from two hydrographic stations are given. A comparison of the estimated results shows that the present method is superior to the others.

Maximum likelihood spectrum estimation method and its application in seismo－magnet－icrelation

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Constraint-induced movement therapy promotes brain functional reorganization in stroke patients with hemiplegia

Stroke patients with hemiplegia exhibit flexor spasms in the upper limb and extensor spasms in the lower limb, and their movement patterns vary greatly. Constraint-induced movement therapy is an upper limb rehabilitation technique used in stroke patients with hemiplegia; however, studies of lower extremity rehabilitation are scarce. In this study, stroke patients with lower limb hemiplegia underwent conventional Bobath therapy for 4 weeks as baseline treatment, followed by constraint-induced movement therapy for an additional 4 weeks. The 10-m maximum walking speed and Berg balance scale scores significantly improved following treatment, and lower extremity motor function also improved. The results of functional MRI showed that constraint-induced movement therapy alleviates the reduction in cerebral functional activation in patients, which indicates activation of functional brain regions and a significant increase in cerebral blood perfusJon. These results demonstrate that constraint-induced movement therapy promotes brain functional reorganization in stroke patients with lower limb hemiplegia.

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.

Application of Maximum Entropy Distribution to the Statistical Properties of Wave Groups

The new distributions of the statistics of wave groups based on the maximum entropy principle are presented. The maximum entropy distributions appear to be superior to conventional distributions when applied to a limited amount of information. Its applications to the wave group properties show the effectiveness of the maximum entropy distribution. FFF filtering method is employed to obtain the wave envelope fast and efficiently. Comparisons of both the maximum entropy distribution and the distribution of Longuet-Higgins （1984） with the laboratory wind-wave data show that the former gives a better fit.

ON THE GENERALIZATION OF MAXIMUM MODULUS PRINCIPLE

We give the sufficient conditions of Retaining Region Theorem and Maximum Modulus principle, The results of this paper are generatizations of rele rant results in [1,2].

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。

三种PTFs方法获取的侵蚀黑土水分特征曲线的比较

采用3种土壤转换方程(PTFs)获取不同侵蚀程度黑土的土壤水分特征曲线(SWCC),并与实测数据进行了比较,以选择适合黑土SWCC间接获取的PTFs方法。以4种不同侵蚀程度的黑土为供试土壤,采用常用的PTFs计算机模型:Rosetta3、CalcPTF和以最大吸湿量为残余含水量(θ_(r))发展的PTFs方法(编号:PTFs3),进行了SWCC的van Genuchten (VG)模型参数的预报。Rosetta3模型的输入参数包括土壤机械组成、土壤密度、33 kPa压力下的土壤含水率(θ_(33 kPa))和1 500 kPa压力下土壤含水量(θ_(1 500 kPa));CalcPTF模型的输入参数包括土壤机械组成、土壤密度和有机碳含量;PTFs3的输入参数包括饱和含水量(θ_(0))、最大吸湿量(θ_(97%RH))、θ_(33 kPa)和θ_(1 500 kPa)。将上述3种方法获取的参数带入VG模型,得出供试土壤在不同水吸力下的土壤含水量,并与实测结果进行对比。结果显示,使用3种PTFs模型输出参数的VG模型预报值与实测值都有极显著的相关性,总体计算结果与实测结果也比较接近。PTFs3预报值与实测值的差值在±0.05 cm^(3)/cm^(3)内;CalcPTF-Var模型差值在-0.08~0.05 cm^(3)/cm^(3)之间;而Rosetta3模型的差值在-0.10~0.06 cm^(3)/cm^(3)之间。在土壤含水率压力小于33 kPa情况下时,SWCC差值相对较大。Rosetta3和PTFs3因为有θ_(33 kPa)和θ_(1 500 kPa)两点的水分进行校正,精确性比较可控,效果优于CalcPTF-Var。预报值与实测值差异的百分比也说明了这一点。具体到每个供试土壤样本,3种PTFs对剧烈侵蚀的黑土预报偏差百分比都较大,但PTFs3表现较优于其他两种模型。CalcPTF-Var在微度侵蚀样本S1的模拟上也出现了相对较大的偏差。综上,PTFs3模型是一种比较适合预报黑土SWCC的VG模型参数的PTFs方法。Rosetta3模型误差主要来源于较严重的低估了≤1 kPa SWCC的土壤含水量,而高估了6~33 kPa的土壤含水量。仅输入土壤理化性质的CalcPTF-Var模型需注意在部分黑土样本上的较大偏差。

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。