MIXED SELF-CONFORMAL MULTIFRACTAL MEASURES

Mixed multifractal analysis studies the simultaneous scaling behavior of finitely many measures. A self-conformal measure is a measure invariant under a set of conformal mappings. In this paper, we provide a descript.ion of the mixed multifractal theory of finitely many self-conformal measures.

DIMENSIONS FOR RANDOM SELF-CONFORMAL SETS

A set is called regular if its Hausdorff dimension and upper box-counting dimension coincide. In this paper,we prove that the random self-conformal set is regular almost surely. Also we determine the dimensions for a class of random self-conformal sets.

Passive target tracking with intermittent measurement based on random finite set

In the tracking problem for the maritime radiation source by a passive sensor,there are three main difficulties,i.e.,the poor observability of the radiation source,the detection uncertainty(false and missed detections)and the uncertainty of the target appearing/disappearing in the field of view.These difficulties can make the establishment or maintenance of the radiation source target track invalid.By incorporating the elevation information of the passive sensor into the automatic bearings-only tracking(BOT)and consolidating these uncertainties under the framework of random finite set(RFS),a novel approach for tracking maritime radiation source target with intermittent measurement was proposed.Under the RFS framework,the target state was represented as a set that can take on either an empty set or a singleton; meanwhile,the measurement uncertainty was modeled as a Bernoulli random finite set.Moreover,the elevation information of the sensor platform was introduced to ensure observability of passive measurements and obtain the unique target localization.Simulation experiments verify the validity of the proposed approach for tracking maritime radiation source and demonstrate the superiority of the proposed approach in comparison with the traditional integrated probabilistic data association(IPDA)method.The tracking performance under different conditions,particularly involving different existence probabilities and different appearance durations of the target,indicates that the method to solve our problem is robust and effective.

A random forest algorithm based on similarity measure and dynamic weighted voting

The random forest model is universal and easy to understand, which is often used for classification and prediction. However, it uses non-selective integration and the majority rule to judge the final result, thus the difference between the decision trees in the model is ignored and the prediction accuracy of the model is reduced. Taking into consideration these defects, an improved random forest model based on confusion matrix (CM-RF)is proposed. The decision tree cluster is selectively constructed by the similarity measure in the process of constructing the model, and the result is output by using the dynamic weighted voting fusion method in the final voting session. Experiments show that the proposed CM-RF can reduce the impact of low-performance decision trees on the output result, thus improving the accuracy and generalization ability of random forest model.

Outcome measures in clinical trials of traditional Chinese medicine for stable angina pectoris

Objective:This work aimed to present a descriptive analysis of the outcome measures used in clinical trials of traditional Chinese medicine(TCM)for patients with stable angina pectoris,and to provide baseline data for the development of core outcome sets(COSs)for relevant clinical trials.Methods:Medical databases were searched to identify randomized trials of the effects of TCM for the treatment of stable angina pectoris.Outcome measures of each trial were extracted.Descriptive statistics were used to analyze the baseline characteristics of outcomes in clinical trials of TCM.Results:94 randomized trials(with 9,111 participants)involving 79 different outcomes were identified.The mean number of outcomes was 5(1-21 per trial).The 5 most commonly reported outcomes were efficacy rate of electrocardiogram,efficacy rate of angina pectoris,efficacy rate of TCM syndrome,fasting lipid indices,and withdrawal rate of nitroglycerin.Several challenges were identified:(1)significant heterogeneity of outcomes and differences in the technique and timing of the measurement of the same outcome;(2)transformation of continuous data into categorical data and presented as such in>90% of trials;(3)few trials on the outcomes associated with the advantages and characteristics of TCM;and(4)selective reporting of outcomes.Conclusions:The outcomes used are excessively heterogenous,and the choice of some outcomes(timing and techniques)for measurement is confusing or inappropriate.Hence,developing and implementing a COS is necessary for greater consistency.

The Construction of Statisticaly Self-similar Measures

We have studied statistically self similar measures together with statistically self similar sets in this paper.A special kind of statistically self similar measures has been constructed and a class of statistically self similar sets as well.

A New Probe: AFM Measurements for Random Disorder Systems

We study the quenched random disorder(QRD) effects created by aerosil dispersion in the octylcyanobiphenyl(8CB) liquid crystal(LC) using atomic force microscopy technique. Gelation process in the 8CB+aerosil gels yields a QRD network which also changes the surface topography. By increasing the aerosil concentration, the original smooth pattern of LC sample surfaces is suppressed by the emergence of a fractal aerosil surface effect and these surfaces become more porous, rougher and they have more and larger crevices. The dispersed aerosil also serves as pinning centers for the liquid crystal molecules. It is observed that via the diffusion-limitedaggregation process, aerosil nano-particles yield a fractal-like surface pattern for the less disordered samples. As the aerosil dispersion increases, the surface can be described by more aggregated regions, which also introduces more roughness. Using this fact, we show that there is a net correlation between the short-range ordered x-ray peak widths(the results of previous x-ray diffraction experiments) and the calculated surface roughness. In other words, we show that these QRD gels can also be characterized by their surface roughness values.

Centrality Measures Based on Matrix Functions

Network is considered naturally as a wide range of different contexts, such as biological systems, social relationships as well as various technological scenarios. Investigation of the dynamic phenomena taking place in the network, determination of the structure of the network and community and description of the interactions between various elements of the network are the key issues in network analysis. One of the huge network structure challenges is the identification of the node(s) with an outstanding structural position within the network. The popular method for doing this is to calculate a measure of centrality. We examine node centrality measures such as degree, closeness, eigenvector, Katz and subgraph centrality for undirected networks. We show how the Katz centrality can be turned into degree and eigenvector centrality by considering limiting cases. Some existing centrality measures are linked to matrix functions. We extend this idea and examine the centrality measures based on general matrix functions and in particular, the logarithmic, cosine, sine, and hyperbolic functions. We also explore the concept of generalised Katz centrality. Various experiments are conducted for different networks generated by using random graph models. The results show that the logarithmic function in particular has potential as a centrality measure. Similar results were obtained for real-world networks.

Variable Importance Measure System Based on Advanced Random Forest

The variable importance measure(VIM)can be implemented to rank or select important variables,which can effectively reduce the variable dimension and shorten the computational time.Random forest(RF)is an ensemble learning method by constructing multiple decision trees.In order to improve the prediction accuracy of random forest,advanced random forest is presented by using Kriging models as the models of leaf nodes in all the decision trees.Referring to the Mean Decrease Accuracy(MDA)index based on Out-of-Bag(OOB)data,the single variable,group variables and correlated variables importance measures are proposed to establish a complete VIM system on the basis of advanced random forest.The link of MDA and variance-based sensitivity total index is explored,and then the corresponding relationship of proposed VIM indices and variance-based global sensitivity indices are constructed,which gives a novel way to solve variance-based global sensitivity.Finally,several numerical and engineering examples are given to verify the effectiveness of proposed VIM system and the validity of the established relationship.

Martingales and Super-Martingales Relative to a Convex Set of Equivalent Measures

In the paper, the martingales and super-martingales relative to a convex set of equivalent measures are systematically studied. The notion of local regular super-martingale relative to a convex set of equivalent measures is introduced and the necessary and sufficient conditions of the local regularity of it in the discrete case are founded. The description of all local regular super-martingales relative to a convex set of equivalent measures is presented. The notion of the complete set of equivalent measures is introduced. We prove that every bounded in some sense super-martingale relative to the complete set of equivalent measures is local regular. A new definition of the fair price of contingent claim in an incomplete market is given and the formula for the fair price of Standard Option of European type is found. The proved Theorems are the generalization of the famous Doob decomposition for super-martingale onto the case of super-martingales relative to a convex set of equivalent measures.

Indicator Selection for Quality Measurement in Maternal Neonatal and Child Health Services: Application of Random Forest Classifier

Quality of Maternal, Neonatal and Child (MNCH) care is an important aspect in ensuring healthy outcomes and survival of mothers and children. To maintain quality in health services provided, organizations and other stakeholders in maternal and child health recommend regular quality measurement. Quality indicators are the key components in the quality measurement process. However, the literature shows neither an indicator selection process nor a set of quality indicators for quality measurement that is universally accepted. The lack of a universally accepted quality indicator selection process and set of quality indicators results in the establishment of a variety of quality indicator selection processes and several sets of quality indicators whenever the need for quality measurement arises. This adds extra processes that render quality measurement process. This study, therefore, aims to establish a set of quality indicators from a broad set of quality indicators recommended by the World Health Organization (WHO). The study deployed a machine learning technique, specifically a random forest classifier to select important indicators for quality measurement. Twenty-nine indicators were identified as important features and among those, eight indicators namely maternal mortality ratio, still-birth rate, delivery at a health facility, deliveries assisted by skilled attendants, proportional breach delivery, normal delivery rate, born before arrival rate and antenatal care visit coverage were identified to be the most important indicators for quality measurement.

Robustness self-testing of states and measurements in the prepare-and-measure scenario with 3 → 1 random access code

Recently, Tavakoli et al.proposed a self-testing scheme in the prepare-and-measure scenario, showing that self-testing is not necessarily based on entanglement and violation of a Bell inequality [Phys.Rev.A 98 062307(2018)].They realized the self-testing of preparations and measurements in an N → 1(N ≥ 2) random access code(RAC), and provided robustness bounds in a 2 → 1 RAC.Since all N → 1 RACs with shared randomness are combinations of 2 → 1 and 3 → 1 RACs, the3 → 1 RAC is just as important as the 2 → 1 RAC.In this paper, we find a set of preparations and measurements in the3 → 1 RAC, and use them to complete the robustness self-testing analysis in the prepare-and-measure scenario.The method is robust to small but inevitable experimental errors.

远隔缺血后适应治疗对急性缺血性卒中超时间窗患者临床预后的影响:一项随机对照试验

背景急性缺血性卒中(AIS)高发,及时恢复脑血流是治疗的关键,超时间窗就诊患者无更多促进脑血流恢复的治疗手段。研究远隔缺血后适应(RIPostC)治疗对AIS超时间窗就诊患者的临床疗效、并发症和预后,具有重要的临床意义。目的探究RIPostC治疗对AIS超时间窗患者干预的影响,为超时间窗就诊的AIS患者寻求安全、有效的脑血流恢复治疗方式。方法本研究采用随机、分组、安慰剂对照法进行试验。选取2021-09-02—2022-08-31于北京航天总医院神经内科病房住院治疗的超溶栓时间窗(发病时间>6 h)的AIS患者为研究对象。依据随机数字表法将患者分为对照组和试验组。试验期+随访期共90 d,均使用同等的一般治疗、脑血管病常规治疗,试验组在此基础上给予RIPostC治疗14 d(28次),对照组给予模拟的RIPostC治疗14 d(28次)。在干预前和干预后30 d、干预后90 d,采用改良Rankin量表(mRS)、美国国立卫生研究院卒中量表(NIHSS)评估两组患者神经功能,简易精神状态检查量表(MMSE)、蒙特利尔认知评估量表(MoCA)评估患者认知功能,工具性日常生活能力量表(IADL)评估日常生活能力,焦虑自评量表(SAS)、抑郁自评量表(SDS)评估精神状态,经颅多普勒超声(TCD)评估脑血流速度,以白介素(IL)-6反映炎症情况。结果122例患者中,最终完成试验及随访99例,其中试验组49例,对照组50例。两组患者性别、年龄、基础疾病(高血压、糖尿病、冠心病)及基线NIHSS评分比较,差异无统计学意义(P>0.05)。重复测量方差分析结果示,时间与组别对MMSE、MoCA、mRS、NIHSS、脑血流速度、IL-6存在交互作用(P<0.05),时间和组别对MMSE、MoCA、NIHSS、脑血流速度、IL-6主效应显著(P<0.05),时间对mRS、SAS、SDS、IADL主效应显著(P<0.05)。试验组干预后30、90 d MMSE、MoCA评分及脑血流速度均高于对照组,mRS、NIHSS评分均低于对照组(P<0.05);试验组干预后30、90 d SDS、IADL评分低于对照组(P<0.05);试验组干预后30 d SAS评分高于对照组,IL-6低于对照组(P<0.05)。99例患者中共有23例患者发生不良反应,其中试验组17例,对照组6例,两组皮肤瘀点、头晕、心慌、胸闷发生率比较,差异无统计学意义(P>0.05);对照组患者皮肤瘀斑发生率[4.00%(2/50)与12.24%(6/49)]、总不良反应发生率[12.00%(6/50)与34.69%(17/49)]低于试验组(P<0.05)。结论RIPostC治疗可降低AIS患者的炎症反应,对神经功能、认知功能抑郁情绪及颅内血流速度可起到积极的改善效果。

Residual lifetime prediction model of nonlinear accelerated degradation data with measurement error

For the product degradation process with random effect (RE), measurement error (ME) and nonlinearity in step-stress accelerated degradation test (SSADT), the nonlinear Wiener based degradation model with RE and ME is built. An analytical approximation to the probability density function (PDF) of the product's lifetime is derived in a closed form. The process and data of SSADT are analyzed to obtain the relation model of the observed data under each accelerated stress. The likelihood function for the population-based observed data is constructed. The population-based model parameters and its random coefficient prior values are estimated. According to the newly observed data of the target product in SSADT, an analytical approximation to the PDF of its residual lifetime (RL) is derived in accordance with its individual degradation characteristics. The parameter updating method based on Bayesian inference is applied to obtain the posterior value of random coefficient of the RL model. A numerical example by simulation is analyzed to verify the accuracy and advantage of the proposed model.

MATHEMATICAL FOUNDATION OF A NEW COMPLEXITY MEASURE

For many continuous bio-medieal signals with both strong nonlinearity and non-stationarity, two criterions were proposed for their complexity estimation ： （1） Only a short data set is enough for robust estimation; （2） No over-coarse graining preproeessing, such as transferring the original signal into a binary time series, is needed. Co complexity measure proposed by us previously is one of such measures. However, it lacks the solid mathematical foundation and thus its use is limited. A modified version of this measure is proposed, and some important properties are proved rigorously. According to these properties, this measure can be considered as an index of randomness of time series in some senses, and thus also a quantitative index of complexity under the meaning of randomness finding complexity. Compared with other similar measures, this measure seems more suitable for estimating a large quantity of complexity measures for a given task, such as studying the dynamic variation of such measures in sliding windows of a long process, owing to its fast speed for estimation.

THE RANDOM SHIFT SET AND RANDOM SUB-SELF-SIMILAR SET

First of all the authors introduce the concepts of random sub-self-similar set and random shift set and then construct the random sub-self-similar set by a random shift set and a collection of statistical contraction operators.

Methods for predicting the remaining useful life of equipment in consideration of the random failure threshold

The value range of the failure threshold will generate an uncertain influence on the prediction results for the remaining useful life(RUL) of equipment. Most of the existing studies on the RUL prediction assume that the failure threshold is a fixed value,as they have difficulty in reflecting the random variation of the failure threshold. In connection with the inadequacies of the existing research, an in-depth analysis is carried out to study the effect of the random failure threshold(RFT) on the prediction results for the RUL. First, a nonlinear degradation model with unit-to-unit variability and measurement error is established based on the nonlinear Wiener process. Second, the expectation-maximization(EM) algorithm is used to solve the estimated values of the parameters of the prior degradation model, and the Bayesian method is used to iteratively update the posterior distribution of the random coefficients. Then, the effects of three types of RFT constraint conditions on the prediction results for the RUL are analyzed, and the probability density function(PDF) of the RUL is derived. Finally,the degradation data of aero-turbofan engines are used to verify the correctness and advantages of the method.

THE DIMENSION FOR RANDOM SUB-SELF-SIMILAR SET

In this article, the Hausdorff dimension and exact Hausdorff measure function of any random sub-self-similar set are obtained under some reasonable conditions. Several examples are given at the end.

A pixel-level local contrast measure for infrared small target detection

Infrared(IR) small target detection is one of the key technologies of infrared search and track(IRST)systems. Existing methods have some limitations in detection performance, especially when the target size is irregular or the background is complex. In this paper, we propose a pixel-level local contrast measure(PLLCM), which can subdivide small targets and backgrounds at pixel level simultaneously.With pixel-level segmentation, the difference between the target and the background becomes more obvious, which helps to improve the detection performance. First, we design a multiscale sliding window to quickly extract candidate target pixels. Then, a local window based on random walker(RW) is designed for pixel-level target segmentation. After that, PLLCM incorporating probability weights and scale constraints is proposed to accurately measure local contrast and suppress various types of background interference. Finally, an adaptive threshold operation is applied to separate the target from the PLLCM enhanced map. Experimental results show that the proposed method has a higher detection rate and a lower false alarm rate than the baseline algorithms, while achieving a high speed.

Magnetic imaging-assisted colonoscopy vs conventional colonoscopy: A randomized controlled trial

AIM: To compare magnetic imaging-assisted colonoscopy (MIC) with conventional colonoscopy (CC).