MAXIMAL FUNCTION CHARACTERIZATIONS OF HARDY SPACES ASSOCIATED WITH BOTH NON-NEGATIVE SELF-ADJOINT OPERATORS SATISFYING GAUSSIAN ESTIMATES AND BALL QUASI-BANACH FUNCTION SPACES

Assume that L is a non-negative self-adjoint operator on L^(2)(ℝ^(n))with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝ^(n) satisfying some mild assumptions.Let HX,L(ℝ^(n))be the Hardy space associated with both X and L,which is defined by the Lusin area function related to the semigroup generated by L.In this article,the authors establish various maximal function characterizations of the Hardy space HX,L(ℝ^(n))and then apply these characterizations to obtain the solvability of the related Cauchy problem.These results have a wide range of generality and,in particular,the specific spaces X to which these results can be applied include the weighted space,the variable space,the mixed-norm space,the Orlicz space,the Orlicz-slice space,and the Morrey space.Moreover,the obtained maximal function characterizations of the mixed-norm Hardy space,the Orlicz-slice Hardy space,and the Morrey-Hardy space associated with L are completely new.

Improving the accuracy of precipitation estimates in a typical inland arid area of China using a dynamic Bayesian model averaging approach

Xinjiang Uygur Autonomous Region is a typical inland arid area in China with a sparse and uneven distribution of meteorological stations,limited access to precipitation data,and significant water scarcity.Evaluating and integrating precipitation datasets from different sources to accurately characterize precipitation patterns has become a challenge to provide more accurate and alternative precipitation information for the region,which can even improve the performance of hydrological modelling.This study evaluated the applicability of widely used five satellite-based precipitation products(Climate Hazards Group InfraRed Precipitation with Station(CHIRPS),China Meteorological Forcing Dataset(CMFD),Climate Prediction Center morphing method(CMORPH),Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks-Climate Data Record(PERSIANN-CDR),and Tropical Rainfall Measuring Mission Multi-satellite Precipitation Analysis(TMPA))and a reanalysis precipitation dataset(ECMWF Reanalysis v5-Land Dataset(ERA5-Land))in Xinjiang using ground-based observational precipitation data from a limited number of meteorological stations.Based on this assessment,we proposed a framework that integrated different precipitation datasets with varying spatial resolutions using a dynamic Bayesian model averaging(DBMA)approach,the expectation-maximization method,and the ordinary Kriging interpolation method.The daily precipitation data merged using the DBMA approach exhibited distinct spatiotemporal variability,with an outstanding performance,as indicated by low root mean square error(RMSE=1.40 mm/d)and high Person's correlation coefficient(CC=0.67).Compared with the traditional simple model averaging(SMA)and individual product data,although the DBMA-fused precipitation data were slightly lower than the best precipitation product(CMFD),the overall performance of DBMA was more robust.The error analysis between DBMA-fused precipitation dataset and the more advanced Integrated Multi-satellite Retrievals for Global Precipitation Measurement Final(IMERG-F)precipitation product,as well as hydrological simulations in the Ebinur Lake Basin,further demonstrated the superior performance of DBMA-fused precipitation dataset in the entire Xinjiang region.The proposed framework for solving the fusion problem of multi-source precipitation data with different spatial resolutions is feasible for application in inland arid areas,and aids in obtaining more accurate regional hydrological information and improving regional water resources management capabilities and meteorological research in these regions.

Machine learning-based comparison of factors influencing estimated glomerular filtration rate in Chinese women with or without nonalcoholic fatty liver

BACKGROUND The prevalence of non-alcoholic fatty liver(NAFLD)has increased recently.Subjects with NAFLD are known to have higher chance for renal function impairment.Many past studies used traditional multiple linear regression(MLR)to identify risk factors for decreased estimated glomerular filtration rate(eGFR).However,medical research is increasingly relying on emerging machine learning(Mach-L)methods.The present study enrolled healthy women to identify factors affecting eGFR in subjects with and without NAFLD(NAFLD+,NAFLD-)and to rank their importance.AIM To uses three different Mach-L methods to identify key impact factors for eGFR in healthy women with and without NAFLD.METHODS A total of 65535 healthy female study participants were enrolled from the Taiwan MJ cohort,accounting for 32 independent variables including demographic,biochemistry and lifestyle parameters(independent variables),while eGFR was used as the dependent variable.Aside from MLR,three Mach-L methods were applied,including stochastic gradient boosting,eXtreme gradient boosting and elastic net.Errors of estimation were used to define method accuracy,where smaller degree of error indicated better model performance.RESULTS Income,albumin,eGFR,High density lipoprotein-Cholesterol,phosphorus,forced expiratory volume in one second(FEV1),and sleep time were all lower in the NAFLD+group,while other factors were all significantly higher except for smoking area.Mach-L had lower estimation errors,thus outperforming MLR.In Model 1,age,uric acid(UA),FEV1,plasma calcium level(Ca),plasma albumin level(Alb)and T-bilirubin were the most important factors in the NAFLD+group,as opposed to age,UA,FEV1,Alb,lactic dehydrogenase(LDH)and Ca for the NAFLD-group.Given the importance percentage was much higher than the 2nd important factor,we built Model 2 by removing age.CONCLUSION The eGFR were lower in the NAFLD+group compared to the NAFLD-group,with age being was the most important impact factor in both groups of healthy Chinese women,followed by LDH,UA,FEV1 and Alb.However,for the NAFLD-group,TSH and SBP were the 5th and 6th most important factors,as opposed to Ca and BF in the NAFLD+group.

Genetic and Agronomic Parameter Estimates of Growth, Yield and Related Traits of Maize (Zea mays L.) under Different Rates of Nitrogen Fertilization

This study evaluated the genetic and agronomic parameter estimates of maize under different nitrogen rates. The trial was established at the Njala Agricultural Research Centre experimental site during 2021 and 2022 in a split block design with three maize varieties (IWCD2, 2009EVDT, and DMR-ESR-Yellow) and seven nitrogen (0, 30, 60, 90, 120, 150 and 180 kg∙N∙ha−1) rates. Findings showed that cob diameter and anthesis silking time (ASI) had intermediate heritability, ASI had high genetic advance, ASI and grain yield had high genotypic coefficient of variation (GCV), while traits with high phenotypic coefficient of variation (PCV) were plant height, ASI, grain yield, number of kernel per cob, number of kernel rows, ear length, and ear height. The PCV values were higher than GCV, indicating the influence of the environment in the studied traits. Nitrogen rates and variety significantly (p < 0.05) influenced grain yield production. Mean grain yields and economic parameter estimates increased with increasing nitrogen rates, with the 30 and 180 kg∙N∙ha−1 plots exhibiting the lowest and highest grain yields of 1238 kg∙ha−1 and 2098 kg∙ha−1, respectively. Variety and nitrogen effects on partial factor productivity (PFPN), agronomic efficiency (AEN), net returns (NR), value cost ratio (VCR) and marginal return (MR) indicated that these parameters were significantly affected (p < 0.05) by these factors. The highest PFPN (41.3 kg grain kg−1∙N) and AEN (29.4 kg grain kg−1∙N) were obtained in the 30 kg∙N∙ha−1 plots, while the highest VCR (2.8) and MR (SLL 1.8 SLL−1 spent on N) were obtained in the 180 kg∙N∙ha−1. The significant influence of variety and nitrogen on traits suggests that increasing yields and maximizing profits require use of appropriate nitrogen fertilization and improved farming practices that could be exploited for increased productivity of maize.

Method for rapid warning and activity concentration estimates in online waterγ-spectrometry systems

Onlineγ-spectrometry systems for inland waters,most of which extract samples in situ and in real time,are able to produce reliable activity concentration measurements for waterborne radionuclides only when they are distributed relatively uniformly and enter into a steady-state diffusion regime in the measurement chamber.To protect residents’health and ensure the safety of the living environment,better timeliness is required for this measurement method.To address this issue,this study established a mathematical model of the online waterγ-spectrometry system so that rapid warning and activity estimates can be obtained for water under non-steady-state(NSS)conditions.In addition,the detection efficiency of the detector for radionuclides during the NSS diffusion process was determined by applying the computational fluid dynamics technique in conjunction with Monte Carlo simulations.On this basis,a method was developed that allowed the online waterγ-spectrometry system to provide rapid warning and activity concentration estimates for radionuclides in water.Subsequent analysis of the NSS-mode measurements of^(40)K radioactive solutions with different activity concentrations determined the optimum warning threshold and measurement time for producing accurate activity concentration estimates for radionuclides.The experimental results show that the proposed NSS measurement method is able to give warning and yield accurate activity concentration estimates for radionuclides 55.42 and 69.42 min after the entry of a 10 Bq/L^(40)K radioactive solution into the measurement chamber,respectively.These times are much shorter than the 90 min required by the conventional measurement method.Furthermore,the NSS measurement method allows the measurement system to give rapid(within approximately 15 min)warning when the activity concentrations of some radionuclides reach their respective limits stipulated in the Guidelines for Drinking-water Quality of the WHO,suggesting that this method considerably enhances the warning capacity of in situ online waterγ-spectrometry systems.

Using Extreme Value Theory Approaches to Estimate High Quantiles for Stroke Data

This paper aims to explore the application of Extreme Value Theory (EVT) in estimating the conditional extreme quantile for time-to-event outcomes by examining the functional relationship between ambulatory blood pressure trajectories and clinical outcomes in stroke patients. The study utilizes EVT to analyze the functional connection between ambulatory blood pressure trajectories and clinical outcomes in a sample of 297 stroke patients. The 24-hour ambulatory blood pressure measurement curves for every 15 minutes are considered, acknowledging a censored rate of 40%. The findings reveal that the sample mean excess function exhibits a positive gradient above a specific threshold, confirming the heavy-tailed distribution of data in stroke patients with a positive extreme value index. Consequently, the estimated conditional extreme quantile indicates that stroke patients with higher blood pressure measurements face an elevated risk of recurrent stroke occurrence at an early stage. This research contributes to the understanding of the relationship between ambulatory blood pressure and recurrent stroke, providing valuable insights for clinical considerations and potential interventions in stroke management.

基于ESTIMATE算法探究TCGA数据库免疫相关基因在乳腺癌中的预后价值

目的根据ESTIMATE算法探究TCGA数据库中免疫相关基因在乳腺癌中的预后价值。方法从TCGA数据库获取606例乳腺癌患者的临床信息和肿瘤样本的转录组数据,采用edgeR方法对转录组数据进行差异表达分析,通过ESTIMATE算法筛选出基于免疫分数或间质分数高低分组的差异表达基因;使用R软件绘制差异表达基因的聚类分析热图;使用韦恩图对基于免疫分数和间质分数得到的差异表达基因进行交集分析;运用STRING数据库,搜索并预测表达显著差异基因编码蛋白质之间的相互作用;通过单因素Cox回归分析评估差异表达基因的预后作用;运用DAVID数据库对差异表达基因进行GO富集分析以及KEGG通路富集分析。结果生存分析结果显示,高免疫分数组患者的总生存期中位值943天,而低分组患者总生存期中位值860天,显著高分组患者总生存期显著高于低分组患者(P<0.05);而间质分数与乳腺癌患者总生存期之间无差异(P>0.05)。进一步对免疫分数高分组和低分组患者表达上调的951个差异表达基因进行生存分析,发现160个基因与乳腺癌患者的总生存期显著相关;对上述160个基因进行蛋白质互作分析,富集出与乳腺癌患者总生存率呈正相关的CTLA4、CD8A、CD19、CD27、CD2、IL2、GZMB、IL2RB、CD3E、CD40LG等基因。对上述160个基因进行GO富集和KEGG通路分析,结果显示免疫功能相关信号通路T细胞受体信号通路、造血细胞系、T细胞活化等通路显著富集。结论本研究发现160个具有预后价值的免疫分数相关基因,免疫分数与乳腺癌患者的总生存期、预后改善相关,将为乳腺癌预后判断和靶向治疗提供新的潜在靶点。

Global population estimate and conservation gap analysis for the Nordmann's Greenshank(Tringa guttifer)

Nordmann's Greenshank(Tringa guttifer)is a globally endangered species that has received little research attention.It is threatened by rapid habitat loss,an incomplete network of protected sites,and lack of long-term data on population dynamics.Citizen science data can be combined with survey data to support population estimation and conservation gap analysis.From 2020 to 2021,Nordmann's Greenshank was surveyed in Tiaozini,Xiaoyangkou,and Dongling on the southern coast of Jiangsu Province,China,and the global population of the species was re-evaluated using the data obtained.We integrated citizen science data from eBird and the China Bird Report from 2000 to 2020 with the survey results to identify important habitats harboring over 1%of its total population,and compared this data with existing protected areas to identify gaps in its global conservation.Our survey found that Tiaozini supported at least 1194 individuals.Consequently,its global population was reestimated to be 1500-2000.Moreover,45 important habitats were identified based on citizen data and survey results.Although 44.4%and 50.0%of the priority sites in the world and China,respectively,are located outside protected areas,the Conservation Effectiveness Index(C)is 68.4%and 71.1%,respectively,showing that the current coverage of protected areas for this part of its range is reasonable.This study presents the most complete and recent population data to date.Tiaozini is the most important migration stopover site for Nordmann's Greenshanks.The species is under threat in terms of breeding,wintering,and stopover sites.Therefore,we suggest improving monitoring,establishing new protected sites to complete the habitat protection network,and improving the effectiveness of existing habitat protection strategies,including further developing high tide roosting sites.

Stochastic Programming for Hub Energy Management Considering Uncertainty Using Two-Point Estimate Method and Optimization Algorithm

To maximize energy profit with the participation of electricity,natural gas,and district heating networks in the day-ahead market,stochastic scheduling of energy hubs taking into account the uncertainty of photovoltaic and wind resources,has been carried out.This has been done using a new meta-heuristic algorithm,improved artificial rabbits optimization(IARO).In this study,the uncertainty of solar and wind energy sources is modeled using Hang’s two-point estimating method(TPEM).The IARO algorithm is applied to calculate the best capacity of hub energy equipment,such as solar and wind renewable energy sources,combined heat and power(CHP)systems,steamboilers,energy storage,and electric cars in the day-aheadmarket.The standard ARO algorithmis developed to mimic the foraging behavior of rabbits,and in this work,the algorithm’s effectiveness in avoiding premature convergence is improved by using the dystudynamic inertia weight technique.The proposed IARO-based scheduling framework’s performance is evaluated against that of traditional ARO,particle swarm optimization(PSO),and salp swarm algorithm(SSA).The findings show that,in comparison to previous approaches,the suggested meta-heuristic scheduling framework based on the IARO has increased energy profit in day-ahead electricity,gas,and heating markets by satisfying the operational and energy hub limitations.Additionally,the results show that TPEM approach dependability consideration decreased hub energy’s profit by 8.995%as compared to deterministic planning.

SUFFICIENT AND NECESSARY CONDITIONS ON THE EXISTENCE AND ESTIMATES OF BOUNDARY BLOW-UP SOLUTIONS FOR SINGULAR p-LAPLACIAN EQUATIONS

Let?denote a smooth,bounded domain in R^(N)(N≥2).Suppose that g is a nondecreasing C^(1)positive function and assume that b(x)is continuous and nonnegative inΩ,and that it may be singular on■Ω.In this paper,we provide sufficient and necessary conditions on the existence of boundary blow-up solutions to the p-Laplacian problem△_(p)u=b(x)g(u)for x∈Ω,u(x)→+∞as dist(x,■Ω)→0.The estimates of such solutions are also investigated.Moreover,when b has strong singularity,the nonexistence of boundary blow-up(radial)solutions and infinitely many radial solutions are also considered.

基于ESTIMATE评分挖掘肝癌微环境相关的预后基因

目的基于ESTIMATE评分筛选与肝癌肿瘤微环境预后相关的基因。方法从TCGA数据库中下载肝癌转录组数据,使用ESTIMATE法计算肝癌组织的免疫和基质评分。分析肝癌基质、免疫评分与肿瘤分级、分期、生存时间的相关关系。Limma包分析差异表达基因,进行基因功能富集分析和通路富集分析。采用Cytoscape中Mcode模块筛选核心差异表达基因,并分析核心基因与肝癌预后、诊断和肿瘤免疫浸润细胞的相关关系。结果筛选出肝癌微环境相关差异表达基因329个。基因功能富集分析显示其主要参与免疫激活和调节等过程。Cytoscape筛选PPI网络核心基因CCR5、SLAMF1、TRAF3IP3,在肝癌中高表达,且基因表达量高的患者的总生存期较低表达患者长,与肿瘤免疫浸润细胞比例呈正相关关系。结论CCR5、SLAMF1、TRAF3IP3基因表达与肝癌的诊断、预后显著相关。

A Posteriori Error Estimate of Two Grid Mixed Finite Element Methods for Semilinear Elliptic Equations

In this paper, we present the a posteriori error estimate of two-grid mixed finite element methods by averaging techniques for semilinear elliptic equations. We first propose the two-grid algorithms to linearize the mixed method equations. Then, the averaging technique is used to construct the a posteriori error estimates of the two-grid mixed finite element method and theoretical analysis are given for the error estimators. Finally, we give some numerical examples to verify the reliability and efficiency of the a posteriori error estimator.

An Example of a Bounded Potential q(x) on the Half-Line, for Estimates of A(α) Amplitude

We show an example of a bounded potential on the half-line obtained as the image of an Inverse Transformation Operator of the Bessel singular potential of the Reduced Radial Schr&#246;dinger Equation, and show us the Estimates of the A(α) amplitude.

Methodology for Obtaining Optimal Sleeve Friction and Friction Ratio Estimates from CPT Data

Cone penetration testing (CPT) is a cost effective and popular tool for geotechnical site characterization. CPT consists of pushing at a constant rate an electronic penetrometer into penetrable soils and recording cone bearing (qc), sleeve friction (fc) and dynamic pore pressure (u) with depth. The measured qc, fs and u values are utilized to estimate soil type and associated soil properties. A popular method to estimate soil type from CPT measurements is the Soil Behavior Type (SBT) chart. The SBT plots cone resistance vs friction ratio, Rf [where: Rf = (fs/qc)100%]. There are distortions in the CPT measurements which can result in erroneous SBT plots. Cone bearing measurements at a specific depth are blurred or averaged due to qc values being strongly influenced by soils within 10 to 30 cone diameters from the cone tip. The qcHMM algorithm was developed to address the qc blurring/averaging limitation. This paper describes the distortions which occur when obtaining sleeve friction measurements which can in association with qc blurring result in significant errors in the calculated Rf values. This paper outlines a novel and highly effective algorithm for obtaining accurate sleeve friction and friction ratio estimates. The fc optimal filter estimation technique is referred to as the OSFE-IFM algorithm. The mathematical details of the OSFE-IFM algorithm are outlined in this paper along with the results from a challenging test bed simulation. The test bed simulation demonstrates that the OSFE-IFM algorithm derives accurate estimates of sleeve friction from measured values. Optimal estimates of cone bearing and sleeve friction result in accurate Rf values and subsequent accurate estimates of soil behavior type.

Hamilton-Souplet-Zhang's gradient estimates for two weighted nonlinear parabolic equations

In this paper, we consider gradient estimates for positive solutions to the following weighted nonlinear parabolic equations on a complete smooth metric measure space with only Bakry-émery Ricci tensor bounded below: One is $${u_t} = {\Delta _f}u + au\log u + bu$$ with a, b two real constants, and another is $${u_t} = {\Delta _f}u + \lambda {u^\alpha }$$ with λ, α two real constants. We obtain local Hamilton-Souplet-Zhang type gradient estimates for the above two nonlinear parabolic equations. In particular, our estimates do not depend on any assumption on f.

Comparisons of Maximum Likelihood Estimates and Bayesian Estimates for the Discretized Discovery Process Model

A Bayesian approach using Markov chain Monte Carlo algorithms has been developed to analyze Smith’s discretized version of the discovery process model. It avoids the problems involved in the maximum likelihood method by effectively making use of the information from the prior distribution and that from the discovery sequence according to posterior probabilities. All statistical inferences about the parameters of the model and total resources can be quantified by drawing samples directly from the joint posterior distribution. In addition, statistical errors of the samples can be easily assessed and the convergence properties can be monitored during the sampling. Because the information contained in a discovery sequence is not enough to estimate all parameters, especially the number of fields, geologically justified prior information is crucial to the estimation. The Bayesian approach allows the analyst to specify his subjective estimates of the required parameters and his degree of uncertainty about the estimates in a clearly identified fashion throughout the analysis. As an example, this approach is applied to the same data of the North Sea on which Smith demonstrated his maximum likelihood method. For this case, the Bayesian approach has really improved the overly pessimistic results and downward bias of the maximum likelihood procedure.

Accuracy of endoscopists' estimate of polyp size: A continuous dilemma

AIM: To examine the discrepancy, if any, between the endoscopist's estimate and pathologist's measurement of colonic polyp size. METHODS: We retrospectively studied 88 patients who underwent colonoscopy with a clear unequivocal documentation of polyp size by both the endoscopist and pathologist. Endoscopist measurements were based on the visual estimate of polyp size seen on high definition screens. The measurement was done by our pathologists after formalin fixation. We compared the endoscopist estimate of the polyp size to the pathologist measurement in order to explore the discordance between the two readings. Data regarding demographics and method of polypectomy(snare polypectomy vs excisional biopsy) was collected, as well. Statistical analysis software statistical software was used to analyze the data. RESULTS: Our cohort included 88 patients from which 111 polyps were removed. Fifty-two(46.8%) of the 111 polyps were excised using biopsy forceps and fiftynine(53.2%) were removed by snare. In the biopsy forceps group, the mean polyp size documented by the pathologist was 0.38 ± 0.19 cm and the mean polyp size documented by the endoscopist was 0.54 ± 0.16cm. The mean difference was 0.15 cm(P < 0.001). In the snare group, the mean polyp size documented by the pathologist was 0.54 ± 0.24 cm and the mean polyp size documented by the endoscopist 0.97 ± 0.34 cm. The mean difference was 0.42 cm(P < 0.001). Combining both groups, the mean size documented by pathologist was 0.46 ± 0.23 cm compared to 0.76 ± 0.35 cm documented by the endoscopist. The mean difference was 0.3 cm(95%CI: 0.23-0.36).CONCLUSION: Post polypectomy measurement by the pathologist are generally smaller than the endoscopist's estimate.

THE COMPRESSION LS ESTIMATE OF REGRESSION COEFFICIENT IN MULTIVARIATE LINEAR MODEL

In this paper, compression LS estimate (k) of the regression coefficient B isconsidered when the design matrix present ill-condition in multivariate linear model.The MSE (mean square error)of the estimate(k)=Vec( (k))is less than theMSE of LS estimate β￣* of the regression coefficient β= Vec(B) by choosing the pa-rameter k. Admissibility , numerical stability and relative efficiency of (k)are proved. The method of determining k value for practical use is also suggested

A NEW ESTIMATE OF SHAPE PARAMETER IN THE FAMILY OF GAMMA DISTRIBUTION

In this paper, a new estimator of the shape parameter in the family of Gamma distribution is constructed by using the moment idea, and it is proved that this estimator is strongly consistent and asymptotically normal.

AN INTEGRAL ESTIMATE AND THE EQUIVALENT NORMS ON F(p, q, s, k) SPACES IN THE UNIT BALL

In this article, the authors give a typical integral＇s bidirectional estimates for allcases. At the same time, several equivalent characterizations on the F（p, q, s, k） space in theunit ball of Cn are given.