Improvement of Similarity Measure： Pearson Product-Moment Correlation Coefficient

Aim To study the reason of the insensitiveness of Pearson product-momentcorrelation coefficient as a similarity measure and the method to improve its sensitivity. MethodsExperimental and simulated data sets were used. Results The distribution range of the data setsinfluences the sensitivity of Pearson product-moment correlation coefficient. Weighted Pearsonproduct-moment correlation coefficient is more sensitive when the range of the data set is large.Conclusion Weighted Pearson product-moment correlation coefficient is necessary when the range ofthe data set is large.

On Weighted Possibilistic Mean,Variance and Correlation of Interval-valued Fuzzy Numbers

In this paper, the concept of weighted possibilistic mean of interval- valued fuzzy number is first introduced. Further, the notions of weighted possibilistic variance, covariance and correlation of interval-valued fuzzy numbers are presented. Meantime, some important properties of them and relationships between them are studied.

Exact Statistical Distribution and Correlation of Human Height and Weight: Analysis and Experimental Confirmation

The statistical relationship between human height and weight is of especial importance to clinical medicine, epidemiology, and the biology of human development. Yet, after more than a century of anthropometric measurements and analyses, there has been no consensus on this relationship. The purpose of this article is to provide a definitive statistical distribution function from which all desired statistics (probabilities, moments, and correlation functions) can be determined. The statistical analysis reported in this article provides strong evidence that height and weight in a diverse population of healthy adults constitute correlated bivariate lognormal random variables. This conclusion is supported by a battery of independent tests comparing empirical values of 1) probability density patterns, 2) linear and higher order correlation coefficients, 3) statistical and hyperstatistics moments up to 6th order, and 4) distance correlation (dCor) values to corresponding theoretical quantities: 1) predicted by the lognormal distribution and 2) simulated by use of appropriate random number generators. Furthermore, calculation of the conditional expectation of weight, given height, yields a theoretical power law that specifies conditions under which body mass index (BMI) can be a valid proxy of obesity. The consistency of the empirical data from a large, diverse anthropometric survey partitioned by gender with the predictions of a correlated bivariate lognormal distribution was found to be so extensive and close as to suggest that this outcome is not coincidental or approximate, but may be a consequence of some underlying biophysical mechanism.

Improving constraint onΩ_(m)from SDSS using marked correlation functions

Large-scale structure(LSS)surveys will increasingly provide stringent constraints on our cosmological models.Recently,the density-marked correlation function(MCF)has been introduced,offering an easily computable density-correlation statistic.Simulations have demonstrated that MCFs offer additional,independent constraints on cosmological models beyond the standard two-point correlation(2PCF).In this study,we apply MCFs for the first time to SDSS CMASS data,aiming to investigate the statistical information regarding clustering and anisotropy properties in the Universe and assess the performance of various weighting schemes in MCFs,and finally obtain constraints onΩ_(m).Upon analyzing the CMASS data,we observe that,by combining different weights(α=[-0.2,0,0.2,0.6]),the MCFs provide a tight and independent constraint on the cosmological parameterΩ_(m),yieldingΩ_(m)=0.293±0.006 at the 1σlevel,which represents a significant reduction in the statistical error by a factor of 3.4 compared to that from 2PCF.Our constraint is consistent with recent findings from the small-scale clustering of BOSS galaxies(Zhai et al.Astronphys.J.948,99(2023))within the 1σlevel.However,we also find that our estimate is lower than the Planck measurements by about 2.6σ,indicating the potential presence of new physics beyond the standard cosmological model if all the systematics are fully corrected.The method outlined in this study can be extended to other surveys and datasets,allowing for the constraint of other cosmological parameters.Additionally,it serves as a valuable tool for forthcoming emulator analysis on the Chinese Space Station Telescope(CSST).

A Note on Some Methods Suitable for Verifying and Correcting the Prediction of Climatic Anomaly

The weighted correlation coefficient of the predicted and observed anomalies and the ratio of the weighted norm of predicted anomaly to the observed one, both together, are suggested to be suitable for the estimating of the correctness of climate prediction. The former shows the similarity of the two patterns, and the later indicates the correctness of the predicted intensity of the anomaly. The weighting function can be different for different emphasis, for example, a constant weight means that the correlation coefficient is the conventional one, but some non-uniform weight leads to the ratio of correct sign of the anomaly, the stepwise weight leads to the formulation of correctness of prediction represented by grades of the anomaly, and so on. Three methods for making correction to the prediction are given in this paper. After subtracting the mean error of the prediction, one method is developed for maximizing the similarity between the predicted and observed patterns, based on the transformation of the spatial coordinates. Another method is to minimize the mean difference between the two fields. This method can also be simplified as similar to the 'optimum interpolation' in the objective analysis of weather chart. The third method is based on the expansion of the anomaly into series of EOF, where the coefficients are the predicted but the EOFs are taken as the 'observed' calculated from historical samples.

ADAPTIVE FUSION ALGORITHMS BASED ON WEIGHTED LEAST SQUARE METHOD

Weighted fusion algorithms, which can be applied in the area of multi-sensor data fusion, are advanced based on weighted least square method. A weighted fusion algorithm, in which the relationship between weight coefficients and measurement noise is established, is proposed by giving attention to the correlation of measurement noise. Then a simplified weighted fusion algorithm is deduced on the assumption that measurement noise is uncorrelated. In addition, an algorithm, which can adjust the weight coefficients in the simplified algorithm by making estimations of measurement noise from measurements, is presented. It is proved by emulation and experiment that the precision performance of the multi-sensor system based on these algorithms is better than that of the multi-sensor system based on other algorithms.

Exact Statistical Distribution of the Body Mass Index (BMI): Analysis and Experimental Confirmation

Body Mass Index (BMI), defined as the ratio of individual mass (in kilograms) to the square of the associated height (in meters), is one of the most widely discussed and utilized risk factors in medicine and public health, given the increasing obesity worldwide and its relation to metabolic disease. Statistically, BMI is a composite random variable, since human weight (converted to mass) and height are themselves random variables. Much effort over the years has gone into attempts to model or approximate the BMI distribution function. This paper derives the mathematically exact BMI probability density function (PDF), as well as the exact bivariate PDF for human weight and height. Taken together, weight and height are shown to be correlated bivariate lognormal variables whose marginal distributions are each lognormal in form. The mean and variance of each marginal distribution, together with the linear correlation coefficient of the two distributions, provide 5 nonadjustable parameters for a given population that uniquely determine the corresponding BMI distribution, which is also shown to be lognormal in form. The theoretical analysis is tested experimentally by gender against a large anthropometric data base, and found to predict with near perfection the profile of the empirical BMI distribution and, to great accuracy, individual statistics including mean, variance, skewness, kurtosis, and correlation. Beyond solving a longstanding statistical problem, the significance of these findings is that, with knowledge of the exact BMI distribution functions for diverse populations, medical and public health professionals can then make better informed statistical inferences regarding BMI and public health policies to reduce obesity.

Characteristics of Atmospheric Fine Particulate Matter(PM2.5)Induced Differentially Expressed Proteins Determined by Proteomics and Bioinformatics Analyses

Objective To screen the differentially expressed proteins(DEPs)in human bronchial epithelial cells(HBE)treated with atmospheric fine particulate matter(PM2.5).Methods HBE cells were treated with PM2.5 samples from Shenzhen and Taiyuan for 24 h.To detect overall protein expression,the Q Exactive mass spectrometer was used.Gene ontology(GO),Kyoto encyclopedia of genes and genomes(KEGG),and Perseus software were used to screen DEPs.Results Overall,67 DEPs were screened in the Shenzhen sample-treated group,of which 46 were upregulated and 21 were downregulated.In total,252 DEPs were screened in the Taiyuan sampletreated group,of which 134 were upregulated and 118 were downregulated.KEGG analysis demonstrated that DEPs were mainly enriched in ubiquitin-mediated proteolysis and HIF-1 signal pathways in Shenzhen PM2.5 samples-treated group.The GO analysis demonstrated that Shenzhen sample-induced DEPs were mainly involved in the biological process for absorption of various metal ions and cell components.The Taiyuan PM2.5-induced DEPs were mainly involved in biological processes of protein aggregation regulation and molecular function of oxidase activity.Additionally,three important DEPs,including ANXA2,DIABLO,and AIMP1,were screened.Conclusion Our findings provide a valuable basis for further evaluation of PM2.5-associated carcinogenesis.

Bioinformatics Analysis Revealed Potential Tumor Suppressors (KLF4/CGN), Oncogenes (SHH/LIF) and Biomarkers of Asian Stomach Adenocarcinoma

Stomach adenocarcinoma (STAD) is the fifth most prevalent cancer and the third leading cause of cancer-related death in the world and is more common in Asia than in most Western countries. There is an urgent need to identify potential novel oncogenes and tumor suppressor genes, and biomarkers for STAD. 6652 differentially expressed genes were identified between STAD and normal samples based on the transcriptome data analysis of the TCGA and GEO databases. 13 key modules were identified in STAD by WGCNA analysis. 293 potential STAD associated genes were identified from intersection by Venn Diagram. The 293 intersected genes were enriched in cell cortex and infection by GO and KEGG analysis. 10 hub genes were identified from PPI and Cytoscape analyses of the intersected genes. KLF4/CGN low and SHH/LIF high expression were associated with short overall survival of Asian STAD patients. Bioinformatics analysis revealed potential novel tumor suppressors (KLF4/CGN), oncogenes (SHH/LIF) and biomarkers for diagnosis, therapy and prognosis of STAD, specifically for Asian patients.

Regional Economic Vitality Based on Weighted Grey Relational Analysis

The future development of cities has a great relationship with economic vitality.To determine the size of the economic vitality and its main influencing factors.This article takes some cities in China as examples.First,determine the main factors.Aiming at many factors,this paper starts from the perspective of population changes in different cities and changes in corporate vitality.After applying the rough set theory to objectively evaluate index weights,the main factors are screened out.Then,the weights of the corresponding evaluation indexes of each group of cities are calculated by a multiple linear regression to a weighted index system,and then the cities are ranked using the gray correlation analysis method.Finally,we get the ranking of the economic vitality level of different cities.Finally,suggestions are made based on the weighting factors of major factors and economic vitality.

Weighted spectral correlation angle target detection method for land‑based hyperspectral imaging

In land-based spectral imaging,the spectra of ground objects are inevitably afected by the imaging conditions(weather conditions,atmospheric conditions,light conditions,zenith and azimuth angle conditions)and spatial distribution of targets,leading to uncertainties featured by“same object diferent spectrum”.That is,the spectrum of a ground object may change within a certain range under diferent imaging conditions.Traditional target detection(TD)methods are mainly based on similarity measurements and do not fully account for the spectral uncertainties.These detection methods are prone to false detections or missed detections.Therefore,reducing the impact of spectral uncertainties on TD is an important research topic in hyperspectral imaging.In this paper,we frst review traditional TD methods and compare their principles and characteristics.It is found that the spectral correlation angle(SCA)method has good adaptability in land-based imaging.The shortcoming of the SCA method that it cannot refect the local spectrum characteristics,is also analyzed.As the efect of spectral uncertainties cannot be completely overcome by the SCA method,a new similarity measurement method,the weighted spectral correlation angle(WSCA)method,is proposed.It can reduce the infuence of spectral uncertainties on TD by increasing the weight of particular bands.Finally,we use two sets of experiments to analyze the efect of the WSCA method on TD.Its performance in overcoming spectral uncertainties caused by variations in imaging conditions or uneven spatial distributions of targets is tested.The results show that the WSCA method can efectively reduce the infuence of spectral uncertainties and obtain a good detection result.

Deciphering Ascorbic Acid Regulatory Pathways in Ripening Tomato Fruit Using a Weighted Gene Correlation Network Analysis Approach

Genotype is generally determined by the co-expression of diverse genes and multiple regulatory pathways in plants. Gene co-expression analysis combining with physiological trait data provides very important information about the gene function and regulatory mechanism. L-Ascorbic acid （AsA）, which is an essential nutrient component for human health and plant metabolism, plays key roles in diverse biological processes such as cell cycle, cell expansion, stress resistance, hormone synthesis, and signaling. Here, we applied a weighted gene correlation network analysis approach based on gene expression values and AsA content data in ripening tomato （Solanum lycopersicum L.） fruit with different AsA content levels, which leads to identification of AsA relevant modules and vital genes in AsA regulatory pathways. Twenty- four modules were compartmentalized according to gene expression profiling. Among these modules, one negatively related module containing genes involved in redox processes and one positively related module enriched with genes involved in AsA biosynthetic and recycling pathways were further analyzed. The present work herein indicates that redox pathways as well as hormone-signal pathways are closely correlated with AsA accumulation in ripening tomato fruit, and allowed us to prioritize candidate genes for follow-up studies to dissect this interplay at the biochemical and molecular level.

Combinatorial analysis of transcription and metabolism reveals the regulatory network associated with antioxidant substances in waxy corn

Maize is an essential source of nutrition for humans and animals and is rich in various metabolites that determine its quality.Different maize varieties show significant differences in metabolite content.Two kinds of waxy maize parental materials,S181 and 49B,created by the Chongqing Academy of Agricultural Sciences,are widely grown in China.S181 shows higher starch and sugar contents than 49B.This study generated metabolic profiles to assess the differences between the two varieties.A total of 674 metabolites that were significantly differentially expressed between the two varieties were identified by gas chromatography and untargeted metabolomics technology.These metabolites were associated with 21 categories,including antioxidant metabolites.Moreover,6415 differentially expressed genes(DEGs)were identified by RNA-seq.Interestingly,these DEGs comprised starch and sugar synthesis pathway genes and 72 different transcription factor families.Among these,six families that were reported to play an essential role in plant antioxidant action accounted for 39.2%of the transcription factor families.Using the Kyoto Encyclopedia of Genes and Genomes(KEGG)classification,the DEGs were mainly involved in amino acid biosynthesis,glycolysis/glucose metabolism,and the synthetic and metabolic pathways of antioxidant active substances.Furthermore,the correlation analysis of transcriptome and metabolomics identified five key transcription factors(ZmbHLH172,ZmNAC44,ZmNAC-like18,ZmS1FA2,ZmERF172),one ubiquitin ligase gene(ZmE25A)and one sucrose synthase gene(ZmSS1).They likely contribute to the quality traits of waxy corn through involvement in the metabolic regulatory network of antioxidant substances.Thus,our results provide new insights into maize quality-related antioxidant metabolite networks and have potential applications for waxy corn breeding.