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.

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.

The Exact Measure Functions of the Images for a Class of Self-Similar Processes

Let X= (Ω, ■, ■_t, X_t,, θ_t, p~x) be a self-similar Markov process on (0,∞) with non-decreasing path. The exact Hausdorff and Packing measure functions of the image X([0,t] ) are obtained.

ON THE EXACT HAUSDORFF MEASURE OF A CLASS OF SELF-SIMILAR SETS SATISFYING OPEN SET CONDITION

In this paper, we provide a new effective method for computing the exact value of Hausdorff measures of a class of self-similar sets satisfying the open set condition （OSC）. As applications, we discuss a self-similar Cantor set satisfying OSC and give a simple method for computing its exact Hausdorff measure.

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.

Measurement of Characteristic Self-Similarity and Self-Diversity for Complex Mechanical Systems

Based on similarity science and complex system theory,a new concept of characteristic self-diversity and corre- sponding relations between self-similarity and self-diversity for complex mechanical systems are presented in this paper.Methods of system self-similarity and self-diversity measure between main system and sub-system are studied.Numerical calculations show that the characteristic self-similarity and self-diversity measure method is validity.A new theory and method of self-similarity and self- diversity measure for complexity mechanical system is presented.

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.

THE EXACT MEASURES OF A CLASS OF SELF-SIMILAR SETS ON THE PLANE

Let S belong to R^2 be the attractor of the iterated function system {f1, f2, f3 } iterating on the unit equilateral triangle So. where fi（x） =λix ＋ bi, i = 1,2, 3, x =（x1, x2）, b1=（0, 0）, b3=（1-λ3 /2,√3/2 （1-λ3）） This paper determines the exact Hausdorff measure, centred covering measure and packing measure of S under some conditions relating to the contraction parameter.

DECAY RATE OF FOURIER TRANSFORMS OF SOME SELF-SIMILAR MEASURES

This paper is concerned with the Diophantine properties of the sequence {ξθn}, where 1 ≤ξ 〈 θ and θ is a rational or an algebraic integer. We establish a combinatorial proposition which can be used to study such two cases in the same manner. It is shown that the decay rate of the Fourier transforms of self-similar measures μλ with λ = θ-1 as the uniform contractive ratio is logarithmic. This generalizes some results of Kershner and Bufetov-Solomyak, who consider the case of Bernoulli convolutions. As an application, we prove that μλ ahaost every x is normal to any base b ≥ 2, which implies that there exist infinitely many absolute normal numbers on the corresponding self-similar set. This can be seen as a complementary result of the well-known Cassels-Schmidt theorem.

A Local Property of Hausdorff Centered Measure of Self-Similar Sets

We analyze the local behavior of the Hausdorff centered measure for self- similar sets. If E is a self-similar set satisfying the open set condition, thenC^s（E∩B（x,r））≤（2r）^sfor all x ∈ E and r〉 0, where Cs denotes the s-dimensional Hausdorff centered measure. The above inequality is used to obtain the upper bound of the Hausdorff centered measure. As the applications of above inequality, We obtained the upper bound of the Hausdorff centered measure for some self-similar sets with Hausdorff dimension equal to 1, and prove that the upper bound reach the exact Hausdorff centered measure.

FOURIER TRANSFORMATION AND SINGULAR INTEGRALS ON SELF-SIMILAR MEASURE

This paper serves two purposes. One is to modify Strichartz's results with respect to the asymptotic averages of the Fourier transform of μ on , self-similar measure defined by Hutchinson. Another purpose is to consider a singular integral operator on μ and show that this op- erator is of type (p,p)(1<p<∞).

HAUSDORFF MEASURE OF UNIFORM SELF-SIMILAR FRACTALS

Let d ≥ 1 be an integer and E a self-similar fractal set, which is the attractor of a uniform contracting iterated function system （UIFS） on R^d. Denote by D the Hausdorff dimension, by H^D（E） the Hausdorff measure and by diam（E） the diameter of E. If the UIFS is parametrised by its contracting factor c, while the set ω of fixed points of the UIFS does not depend on c, we will show the existence of a positive constant depending only on ω, such that the Hausdorff dimension is smaller than one and H^O（E） = diam（E）^D if c is smaller than this constant. We apply our result to modified versions of various classical fractals. Moreover, we present a parametrised UIFS, where ω depends on c and show the inequatily H^D（E） 〈 diam（E）^D, if c is small enough.

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.

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.

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.

THE REGULARITY OF RANDOM GRAPH DIRECTED SELF-SIMILAR SETS

A set in Rd is called regular if its Hausdorff dimension coincides with its upper box counting dimension. It is proved that a random graph-directed self-similar set is regular a.e..

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.