Exact Distribution of Difference of Two Sample Proportions and Its Inferences

Comparing two population proportions using confidence interval could be misleading in many cases, such as the sample size being small and the test being based on normal approximation. In this case, the only one option that we have is to collect a large sample. Unfortunately, the large sample might not be possible. One example is a person suffering from a rare disease. The main purpose of this journal is to derive a closed formula for the exact distribution of the difference between two independent sample proportions, and use it to perform related inferences such as a confidence interval, regardless of the sample sizes and compare with the existing Wald, Agresti-Caffo and Score. In this journal, we have derived a closed formula for the exact distribution of the difference between two independent sample proportions. This distribution doesn’t need any requirements, and can be used to perform inferences such as: a hypothesis test for two population proportions, regardless of the nature of the distribution and the sample sizes. We claim that exact distribution has the least confidence width among Wald, Agresti-Caffo and Score, so it is suitable for inferences of the difference between the population proportion regardless of sample size.

Effects of Different Hormone Proportions on Differentiation and Regeneration of Prtmus avium L. Adventitious Buds

In order to screen the appropriate culture condition for the differentiation and regeneration of Prtmus avium L. adventitious buds, in this study, the effect of different hormone proportions on differentiation and regeneration of shoot tip explants were investigated using Gisela No. 5 and Gisela No. 6 as experimental materi- als. The results showed that, different hormone proportions had extremely significant effects （ P 〈0.01 ） on the differentiation rate of P. avium adventitious buds; the appropriate hormone proportions for Gisela No. 5 and Gisela No. 6 to induce dedifferentiation of adventitious buds were 6-BA 3.0 mg/L ＋ IBA 0.5 mg/L ＋ KT O. 1 mg/L and 6-BA 1.0 mg/L ＋ IBA 0.5 mg/L ＋ KT 0.2 rag/L, respectively. In addition, different hormone proportions had extremely significant effects （P 〈 0.01 ） on the regeneration coefficient and regeneration rate of P. avium adventitious buds; with the hormone proportion of 6-BA 1.0 mg/L ＋ IBA 1.0 mg/L ＋ KT 0.3mg/L, the number of regenerated adventitious buds reached the maximum for both varieties.

ISO International Standards—a“toolbox”of Olympic proportions for major sporting,cultural and social events

How are the winners determined in most of the events that make up the Olympic Games? Theyare,of course,the athletes who run or swim faster,jump higher,lift heavier,throw further.But how is their prowess measured? By the SI (Système inter-national) International System of Units,which

Effects of different proportions of two Bacillus sp. on the growth performance, small intestinal morphology, caecal microbiota and plasma biochemical profile of Chinese Huainan Partridge Shank chickens

A total of 900 one-d-old Chinese Huainan Partridge Shank chickens were randomly allocated into nine groups with five replicates of 20 each.Birds were fed with basal diet,basal diet supplemented with 150 mg kg^（–1） aureomycin,basal diet supplemented with different proportions of Bacillus licheniformis and Bacillus subtilis,which was 0：1.0×10~6,2.5×10~5：7.5×10~5,3.3×10~5：6.6×10~5,5.0×10~5：5.0×10~5,6.6×10~5：3.3×10~5,7.5×10~5：2.5×10~5 and 1.0×10~6：0,respectively.The duration of the experiment was 56 d.The results indicated that dietary supplementation of 6.6×10~5：3.3×10~5 of B.lichenifornis：B.subtilis improved final body weight,increased the average daily gain,and reduced feed/gain ratio（P〈0.05）.The numbers of total Lactobacillus and Bifidobacterium sp.in the caecum significantly increased,and the numbers of Escherichia coli and Salmonella sp.significantly declined compared to that of the control（P〈0.05）.Intestinal villous height and villous height to crypt depth ratio of the duodenum,jejunum,and ileum were significantly higher than that of the control,and intestinal crypt depth of the duodenum and ileum was significantly lower（P〈0.05）.The total antioxidant capacity,total superoxide dismutase,and glutathione peroxidase ability in plasma significantly improved,while the malondialdehyde concentration in plasma decreased（P〈0.05）.Compared to the control,plasma concentrations of ammonia,uric acid and urea nitrogen and the activity of xanthine oxidase were reduced（P〈0.05）.In conclusion,an inclusion of 6.6×10~5：3.3×10~5 of B.licheniformis：B.subtilis to the diet improved the growth performance,caecal microbiota,plasma biochemical profile,and significantly improved the small intestine morphology,while reducing the mortality rate.

Mixing planting proportions in a plantation affects functional traits and biomass allocation of Cunninghamia lanceolata and Phoebe bournei seedlings

Functional traits of trees are significantly associated with their adaptation strategies and productivity.However,the effects of species composition and mixing proportion on the functional traits of trees grown in mixed plantations have not been studied extensively.In this study,planting experiments(duration about seven months)were used to study variations in functional traits and biomass allocation of C unninghamia lanceolata(Lamb.)Hook and Phoebe bournei(Hemsley)Yang seedlings in five different mixes(0C:4P,1C:3P,1C:1P,3C:1P,and 4C:0P).Total leaf area per seedling increased in each species as its respective proportion in the mixture decreased.However,the specific leaf area decreased for P.bournei under low percent composition,and the specific leaf area for C.lanceolata differed only marginally among the plantings.The net photosynthetic rates of the two species were higher in the mixed plantings than in their corresponding monocultures,whereas the transpiration rate,stomatal conductance,and instantaneous water use efficiency were not different among the plantings.The average root length and root surface area of C.lanceolata and P.bournei were higher in the mixed plantings than in their monocultures.Specifically,root surface area of C.lanceolate and both root length and surface area of P.bournei increased significantly in the 1C:3P and 2C:2P mixed plantings.Leaf,stem,root,and total dry mass per seedling for C.lanceolata decreased with its increasing percent composition in the mixed plantings,while these variables varied less for P.bournei.The plasticity of biomass allocation was relatively low for both species.Total biomass per planting was higher in the mixed plantings than in the monocultures.Our study indicates that species composition and mixing proportion can considerably affect the functional traits of C.lanceolata and P.bournei.The increase in productivity in the mixed plantings may be partially attributed to low rates of competition between the two species,and future studies should examine the different interspecies relationships.The results of this study can be used to improve plantation productivity and ultimately increase the sustainability of tree products and help to better understand the adaptation strategies of plant coexistence.

Compositions,Proportions,and Equilibrium Temperature of Coexisting Two-feldspar in Crystalline Rocks

Compositions, proportions, and equilibrium temperature of coexisting two-feldspar in crystalline rocks are of great importance to classification in petrography and interpretation of petrogenesis. Crystalline rocks are usually composed of 4-6 minerals （phases）, depending on their independent chemical components and the equilibrium temperature of crystallizations. In general, number of mineral phases can be determined by the ＂Phase Rule＂. According to the mass balance principle, bulk composition of coexisting two-feldspar could be evaluated from the bulk chemistry of a rock, provided that the compositions of the coexisting mafic mineral phases containing calcium, sodium, and potassium oxides are determined, e.g., by microprobe analysis. The compositions, proportions, and temperature of two-feldspar in equilibrium can thus be simultaneously resolved numerically from bulk composition of the rock, by incorporating the activity/composition relations of the ternary feldspars with the mass balance constraints. Upon the numerical approximation method presented in this paper, better-quality, internally consistent data on feldspar group could usually be obtained, which would be expected more realistic and accurate in consideration of thermodynamic equilibria in the system of crystalline rocks, as well as bulk chemistry of a rock and the composing minerals.

Representative heights for assessing whole-tree values of cell-type proportions in Eucalyptus camaldulensis and E. globulus

Eucalyptus camaldulensis Dehnh. and E. globulus Labill. are economically important species for wood and pulpwood materials. Representative heights for assessing whole-tree values of cell-type proportions(vessels, fibers, ray and axial parenchyma percentages) using increment cores were examined by analysis of within-tree variations. Pattern differences were evaluated between trees and species in both radial and axial directions by statistical data analysis(Moses test). In E. camaldulensis,within-tree variation of vessel percentage was generally higher in the upper and outer regions of the trunk. In contrast, E. globulus within-tree variation was unclear. In both species, although no clear pattern of fiber percentages was observed, within-tree variations of ray and axial parenchyma levels were higher in the lower and inner regions.Significant differences in patterns were observed in the axial variation between species for vessel percentages and in the radial variation between trees of E. camaldulensis for ray parenchyma percentages. The representative heights for assessing whole-tree cell-type proportions were 0.8 mabove the ground for E. camaldulensis and 2.8 m for E.globulus, regardless of differences in tree height and pattern of within-tree variation of cell-type proportions.

Inferences on the Difference of Two Proportions: A Bayesian Approach

Let π=π1-π2 be the difference of two independent proportions related to two populations. We study the test H0:π≥0 against different alternatives, in the Bayesian context. The various Bayesian approaches use standard beta distributions, and are simple to derive and compute. But the more general test H0:π≥η, with η>0, requires more advanced mathematical tools to carry out the computations. These tools, which include the density of the difference of two general beta variables, are presented in the article, with numerical examples for illustrations to facilitate comprehension of results.

Reduction of NO_(x)emission based on optimized proportions of mill scale and coke breeze in sintering process

Reducing NO_(x) emission of iron ore sintering process in a cost effective manner is a challenge for the iron and steel industry at present.Effects of the proportion of mill scale and coke breeze on the NO_(x) emission,strength of sinter,and sinter indexes were studied by com-bustion and sinter pot tests.Results showed that the peak value of NO concentration,total of NO emission,and fuel-N conversion rate gradu-ally decreased as the proportions of the mill scale increased because NO was reduced to N_(2) by Fe_(3)O_(4),FeO,and Fe in the mill scale.The strength of sinter reached the highest value at 8.0wt%mill scale due to the formation of minerals with low melting point.The fuel-N conver-sion rate slightly fluctuated and total NO_(x) emission significantly decreased with the decreased proportions of coke breeze because CO forma-tion and content of N element in the sintered mixture decreased.However,the sinter strength also decreased due to the decrease in the amount of the melting minerals.Furthermore,results of the sinter pot tests indicated that NO_(x) emission decreased.The sinter indexes performed well when the proportions of mill scale and coke breeze were 8.0wt%and 3.70wt%respectively in the sintered mixture.

Geometric investigation of entrance proportions of houses from the Qajar to the beginning of the early Pahlavi in Dezful City(1789—1979)

Due to the importance of the historical context of Dezful City,investigating historic buildings is necessary.But unfortunately,a large part of it is being destroyed.For this reason,it is essential to discover the guidelines and logic behind the architectural design of these buildings to help their reconstruction or restoration.Regrettably,there is no logical information about the components of this context and the reconstructions are usually done according to taste and based on architecture tested or personal preference.Therefore,it is necessary to find a logic behind these critical components that support the whole plan or parts of it in a particular style.The purpose of this research is to discover and find the logic behind the design of this building in the historical context of Dezful.Finding geometrical proportions can significantly help to reconstruct buildings better and more accurately.For this purpose,30 historical houses of Dezful were randomly selected,and their input information was drawn in 2D form in AutoCAD.Then,the length,width,and height proportions were measured,and the obtained ratios were compared with the golden proportions and dynamic rectangles.This paper studies entrance based on ratios of√2,√3,√4,√4,√1.25 andφ(the golden section).The results show that golden proportions and proportions derived from dynamic rectangles are present in the wording of all cases.Moreover,the range of ratios in the plan is from 1.34 to 2,and the content of changes in the section is from 1.22 to 2.The results can help architects,and particularly building owners,to reconstruct based on existing logic by discovering the proportions of the entrances of the houses.It is possible to administer a part of the damaged tissue and estimate its dimensions and sizes because the proportions’completeness can help revive half-destroyed historical buildings.

Uncertainties of landslide susceptibility prediction:Influences of different spatial resolutions,machine learning models and proportions of training and testing dataset

This study aims to reveal the impacts of three important uncertainty issues in landslide susceptibility prediction(LSP),namely the spatial resolution,proportion of model training and testing datasets and selection of machine learning models.Taking Yanchang County of China as example,the landslide inventory and 12 important conditioning factors were acquired.The frequency ratios of each conditioning factor were calculated under five spatial resolutions(15,30,60,90 and 120 m).Landslide and non-landslide samples obtained under each spatial resolution were further divided into five proportions of training and testing datasets(9:1,8:2,7:3,6:4 and 5:5),and four typical machine learning models were applied for LSP modelling.The results demonstrated that different spatial resolution and training and testing dataset proportions induce basically similar influences on the modeling uncertainty.With a decrease in the spatial resolution from 15 m to 120 m and a change in the proportions of the training and testing datasets from 9:1 to 5:5,the modelling accuracy gradually decreased,while the mean values of predicted landslide susceptibility indexes increased and their standard deviations decreased.The sensitivities of the three uncertainty issues to LSP modeling were,in order,the spatial resolution,the choice of machine learning model and the proportions of training/testing datasets.

An expectation–maximization algorithm for estimating proportions of deletions among bacterial populations with application to study antibiotic resistance gene transfer in Enterococcus faecalis

The emergence of antibiotic resistance in bacteria limits the availability of antibiotic choices for treatment and infection control,thereby representing a major threat to human health.The de novo mutation of bacterial genomes is an essential mechanism by which bacteria acquire antibiotic resistance.Previously,deletion mutations within bacterial immune systems,ranging from dozens to thousands of base pairs(bps)in length,have been associated with the spread of antibiotic resistance.Most current methods for evaluating genomic structural variations(SVs)have concentrated on detecting them,rather than estimating the proportions of populations that carry distinct SVs.A better understanding of the distribution of mutations and subpopulations dynamics in bacterial populations is needed to appreciate antibiotic resistance evolution and movement of resistance genes through populations.Here,we propose a statistical model to estimate the proportions of genomic deletions in a mixed population based on Expectation–Maximization(EM)algorithms and next-generation sequencing(NGS)data.The method integrates both insert size and split-read mapping information to iteratively update estimated distributions.The proposed method was evaluated with three simulations that demonstrated the production of accurate estimations.The proposed method was then applied to investigate the horizontal transfers of antibiotic resistance genes in concert with changes in the CRISPR-Cas system of E.faecalis.

Cumulative effects of excess high-normal alanine aminotransferase levels in relation to new-onset metabolic dysfunction-associated fatty liver disease in China

BACKGROUND Within the normal range,elevated alanine aminotransferase(ALT)levels are associated with an increased risk of metabolic dysfunction-associated fatty liver disease(MAFLD).AIM To investigate the associations between repeated high-normal ALT measurements and the risk of new-onset MAFLD prospectively.METHODS A cohort of 3553 participants followed for four consecutive health examinations over 4 years was selected.The incidence rate,cumulative times,and equally and unequally weighted cumulative effects of excess high-normal ALT levels(ehALT)were measured.Cox proportional hazards regression was used to analyse the association between the cumulative effects of ehALT and the risk of new-onset MAFLD.RESULTS A total of 83.13%of participants with MAFLD had normal ALT levels.The incidence rate of MAFLD showed a linear increasing trend in the cumulative ehALT group.Compared with those in the low-normal ALT group,the multivariate adjusted hazard ratios of the equally and unequally weighted cumulative effects of ehALT were 1.651[95%confidence interval(CI):1.199-2.273]and 1.535(95%CI:1.119-2.106)in the third quartile and 1.616(95%CI:1.162-2.246)and 1.580(95%CI:1.155-2.162)in the fourth quartile,respectively.CONCLUSION Most participants with MAFLD had normal ALT levels.Long-term high-normal ALT levels were associated with a cumulative increased risk of new-onset MAFLD.

Geometric proportions： The underlying structure of design process for Islamic geometric patterns

This paper discusses geometric proportions which serve as a design toot, especially for IsLamic pattern design. The key rote of geometry in Islamic patterns is discussed with relation to proportions which act as the underlying structure of the design process. Evaluations based on spatial structure and esthetic criteria are integrated into the conceptual phase of the design process. Proportions serve two objectives; firstly, in pattern design, proportions are strongly linked to geometry, which can be viewed as a self-guiding method of esthetically proven design. SecondLy, geometric proportions regulate primarily the order of patterns; while at the same time they mediate between the two poles of order and diversity as wetl as among different esthetic revels. This paper anatyzes geometric principles and design features of traditional Istamic patterns, involving geometric proportion anatysis. It also describes the syntheses of Islamic patterns from the perspectives of Islamic cosmology, philosophy and metaphysics of geometry, which can be seen as following a pre-established principle of geometric and proportional design with high accuracy and great precision. Furthermore, the underlying relationship between cosmology and geometry is manifested in Islamic patterns where geometry acts as the vocabulary underpinning the pattern language. These findings support the argument that geometry was independently discovered and applied by Islamic culture as a universal language, constituting one of the most important multicultural symbols in design.

Event-based nonfragile state estimation for memristive recurrent neural networks with stochastic cyber-attacks and sensor saturations

This paper addresses the issue of nonfragile state estimation for memristive recurrent neural networks with proportional delay and sensor saturations. In practical engineering, numerous unnecessary signals are transmitted to the estimator through the networks, which increases the burden of communication bandwidth. A dynamic event-triggered mechanism,instead of a static event-triggered mechanism, is employed to select useful data. By constructing a meaningful Lyapunov–Krasovskii functional, a delay-dependent criterion is derived in terms of linear matrix inequalities for ensuring the global asymptotic stability of the augmented system. In the end, two numerical simulations are employed to illustrate the feasibility and validity of the proposed theoretical results.

Intelligent Fractional-Order Controller for SMES Systems in Renewable Energy-Based Microgrid

An autonomous microgrid that runs on renewable energy sources is presented in this article.It has a supercon-ducting magnetic energy storage(SMES)device,wind energy-producing devices,and an energy storage battery.However,because such microgrids are nonlinear and the energy they create varies with time,controlling and managing the energy inside them is a difficult issue.Fractional-order proportional integral(FOPI)controller is recommended for the current research to enhance a standalone microgrid’s energy management and performance.The suggested dedicated control for the SMES comprises two loops:the outer loop,which uses the FOPI to regulate the DC-link voltage,and the inner loop,responsible for regulating the SMES current,is constructed using the intelligent FOPI(iFOPI).The FOPI+iFOPI parameters are best developed using the dandelion optimizer(DO)approach to achieve the optimum performance.The suggested FOPI+iFOPI controller’s performance is contrasted with a conventional PI controller for variations in wind speed and microgrid load.The optimal FOPI+iFOPI controller manages the voltage and frequency of the load.The behavior of the microgrid as a reaction to step changes in load and wind speed was measured using the proposed controller.MATLAB simulations were used to evaluate the recommended system’s performance.The results of the simulations showed that throughout all interruptions,the recommended microgrid provided the load with AC power with a constant amplitude and frequency.In addition,the required load demand was accurately reduced.Furthermore,the microgrid functioned incredibly well despite SMES and varying wind speeds.Results obtained under identical conditions were compared with and without the best FOPI+iFOPI controller.When utilizing the optimal FOPI+iFOPI controller with SMES,it was found that the microgrid performed better than the microgrid without SMES.

Monitoring shear deformation of sliding zone via fiber Bragg grating and particle image velocimetry

Monitoring shear deformation of sliding zones is of great significance for understanding the landslide evolution mechanism,in which fiber optic strain sensing has shown great potential.However,the cor-relation between strain measurements of quasi-distributed fiber Bragg grating(FBG)sensing arrays and shear displacements of surrounding soil remains elusive.In this study,a direct shear model test was conducted to simulate the shear deformation of sliding zones,in which the soil internal deformation was captured using FBG strain sensors and the soil surface deformation was measured by particle image velocimetry(PIV).The test results show that there were two main slip surfaces and two secondary ones,developing a spindle-shaped shear band in the soil.The formation of the shear band was successfully captured by FBG sensors.A sinusoidal model was proposed to describe the fiber optic cable deformation behavior.On this basis,the shear displacements and shear band widths were calculated by using strain measurements.This work provides important insight into the deduction of soil shear deformation using soil-embedded FBG strain sensors.

The burden of upper motor neuron involvement is correlated with the bilateral limb involvement interval in patients with amyotrophic lateral sclerosis:a retrospective observational study

Amyotrophic lateral sclerosis is a rare neurodegenerative disease characterized by the involvement of both upper and lower motor neurons.Early bilateral limb involvement significantly affects patients'daily lives and may lead them to be confined to bed.However,the effect of upper and lower motor neuron impairment and other risk factors on bilateral limb involvement is unclear.To address this issue,we retrospectively collected data from 586 amyotrophic lateral sclerosis patients with limb onset diagnosed at Peking University Third Hospital between January 2020 and May 2022.A univariate analysis revealed no significant differences in the time intervals of spread in different directions between individuals with upper motor neuron-dominant amyotrophic lateral sclerosis and those with classic amyotrophic lateral sclerosis.We used causal directed acyclic graphs for risk factor determination and Cox proportional hazards models to investigate the association between the duration of bilateral limb involvement and clinical baseline characteristics in amyotrophic lateral sclerosis patients.Multiple factor analyses revealed that higher upper motor neuron scores(hazard ratio[HR]=1.05,95%confidence interval[CI]=1.01–1.09,P=0.018),onset in the left limb(HR=0.72,95%CI=0.58–0.89,P=0.002),and a horizontal pattern of progression(HR=0.46,95%CI=0.37–0.58,P<0.001)were risk factors for a shorter interval until bilateral limb involvement.The results demonstrated that a greater degree of upper motor neuron involvement might cause contralateral limb involvement to progress more quickly in limb-onset amyotrophic lateral sclerosis patients.These findings may improve the management of amyotrophic lateral sclerosis patients with limb onset and the prediction of patient prognosis.

Partitioning Calculation Method of Short-Circuit Current for High Proportion DG Access to Distribution Network

Aiming at the problemthat the traditional short-circuit current calculationmethod is not applicable to Distributed Generation(DG)accessing the distribution network,the paper proposes a short-circuit current partitioning calculation method considering the degree of voltage drop at the grid-connected point of DG.Firstly,the output characteristics of DG in the process of low voltage ride through are analyzed,and the equivalent output model of DG in the fault state is obtained.Secondly,by studying the network voltage distribution law after fault in distribution networks under different DG penetration rates,the degree of voltage drop at the grid-connected point of DG is used as a partition index to partition the distribution network.Then,iterative computation is performed within each partition,and data are transferred between partitions through split nodes to realize the fast partition calculation of short-circuit current for high proportion DG access to distribution network,which solves the problems of long iteration time and large calculation error of traditional short-circuit current.Finally,a 62-node real distribution network model containing a high proportion of DG access is constructed onMATLAB/Simulink,and the simulation verifies the effectiveness of the short-circuit current partitioning calculation method proposed in the paper,and its calculation speed is improved by 48.35%compared with the global iteration method.

Influence of donor age on liver transplantation outcomes: A multivariate analysis and comparative study

BACKGROUND The growing disparity between the rising demand for liver transplantation(LT)and the limited availability of donor organs has prompted a greater reliance on older liver grafts.Traditionally,utilizing livers from elderly donors has been associated with outcomes inferior to those achieved with grafts from younger donors.By accounting for additional risk factors,we hypothesize that the utili-zation of older liver grafts has a relatively minor impact on both patient survival and graft viability.AIM To evaluate the impact of donor age on LT outcomes using multivariate analysis and comparing young and elderly donor groups.METHODS In the period from April 2013 to December 2018,656 adult liver transplants were performed at the University Hospital Merkur.Several multivariate Cox propor-tional hazards models were developed to independently assess the significance of donor age.Donor age was treated as a continuous variable.The approach involved univariate and multivariate analysis,including variable selection and assessment of interactions and transformations.Additionally,to exemplify the similarity of using young and old donor liver grafts,the group of 87 recipients of elderly donor liver grafts(≥75 years)was compared to a group of 124 recipients of young liver grafts(≤45 years)from the dataset.Survival rates of the two groups were estimated using the Kaplan-Meier method and the log-rank test was used to test the differences between groups.RESULTS Using multivariate Cox analysis,we found no statistical significance in the role of donor age within the constructed models.Even when retained during the entire model development,the donor age's impact on survival remained insignificant and transformations and interactions yielded no substantial effects on survival.Consistent insigni-ficance and low coefficient values suggest that donor age does not impact patient survival in our dataset.Notably,there was no statistical evidence that the five developed models did not adhere to the proportional hazards assumption.When comparing donor age groups,transplantation using elderly grafts showed similar early graft function,similar graft(P=0.92),and patient survival rates(P=0.86),and no significant difference in the incidence of postoperative complications.CONCLUSION Our center's experience indicates that donor age does not play a significant role in patient survival,with elderly livers performing comparably to younger grafts when accounting for other risk factors.