Analytical and NumericalMethods to Study the MFPT and SR of a Stochastic Tumor-Immune Model

The Mean First-Passage Time (MFPT) and Stochastic Resonance (SR) of a stochastic tumor-immune model withnoise perturbation are discussed in this paper. Firstly, considering environmental perturbation, Gaussian whitenoise and Gaussian colored noise are introduced into a tumor growth model under immune surveillance. Asfollows, the long-time evolution of the tumor characterized by the Stationary Probability Density (SPD) and MFPTis obtained in theory on the basis of the Approximated Fokker-Planck Equation (AFPE). Herein the recurrenceof the tumor from the extinction state to the tumor-present state is more concerned in this paper. A moreefficient algorithmof Back-Propagation Neural Network (BPNN) is utilized in order to testify the correction of thetheoretical SPDandMFPT.With the existence of aweak signal, the functional relationship between Signal-to-NoiseRatio (SNR), noise intensities and correlation time is also studied. Numerical results show that both multiplicativeGaussian colored noise and additive Gaussian white noise can promote the extinction of the tumors, and themultiplicative Gaussian colored noise can lead to the resonance-like peak on MFPT curves, while the increasingintensity of the additiveGaussian white noise results in theminimum of MFPT. In addition, the correlation timesare negatively correlated with MFPT. As for the SNR, we find the intensities of both the Gaussian white noise andthe Gaussian colored noise, as well as their correlation intensity can induce SR. Especially, SNR is monotonouslyincreased in the case ofGaussian white noisewith the change of the correlation time.At last, the optimal parametersin BPNN structure are analyzed for MFPT from three aspects: the penalty factors, the number of neural networklayers and the number of nodes in each layer.

Median-of-Means方法在偏度系数中的应用

传统偏度系数的定义涉及样本均值和三阶矩,使其对离群值十分敏感。本文在偏度系数的估计中引入Median-of-Means方法,提出偏度系数的新估计量,并证明其相合性和渐近正态性。此外,基于经验似然方法提出一种新的偏度系数检验统计量,证明其渐近性质并进行数值模拟。结果表明,本文提出的估计量具有一定稳健性,检验统计量表现也优于传统方法。最后将所提出的估计与检验方法应用于实际数据分析发现,估计结果比较稳健,进一步表明原有的偏度系数估计方法并不适用。

Estimation of the Stress-Strength Reliability for Exponentiated Pareto Distribution Using Median and Ranked Set Sampling Methods

In reliability analysis,the stress-strength model is often used to describe the life of a component which has a random strength(X)and is subjected to a random stress(Y).In this paper,we considered the problem of estimating the reliability𝑅𝑅=P[Y<X]when the distributions of both stress and strength are independent and follow exponentiated Pareto distribution.The maximum likelihood estimator of the stress strength reliability is calculated under simple random sample,ranked set sampling and median ranked set sampling methods.Four different reliability estimators under median ranked set sampling are derived.Two estimators are obtained when both strength and stress have an odd or an even set size.The two other estimators are obtained when the strength has an odd size and the stress has an even set size and vice versa.The performances of the suggested estimators are compared with their competitors under simple random sample via a simulation study.The simulation study revealed that the stress strength reliability estimates based on ranked set sampling and median ranked set sampling are more efficient than their competitors via simple random sample.In general,the stress strength reliability estimates based on median ranked set sampling are smaller than the corresponding estimates under ranked set sampling and simple random sample methods.Keywords:Stress-Strength model,ranked set sampling,median ranked set sampling,maximum likelihood estimation,mean square error.corresponding estimates under ranked set sampling and simple random sample methods.

Estimation of Population Variance Using the Coefficient of Kurtosis and Median of an Auxiliary Variable under Simple Random Sampling

In this study we have proposed a modified ratio type estimator for population variance of the study variable y under simple random sampling without replacement making use of coefficient of kurtosis and median of an auxiliary variable x. The estimator’s properties have been derived up to first order of Taylor’s series expansion. The efficiency conditions derived theoretically under which the proposed estimator performs better than existing estimators. Empirical studies have been done using real populations to demonstrate the performance of the developed estimator in comparison with the existing estimators. The proposed estimator as illustrated by the empirical studies performs better than the existing estimators under some specified conditions i.e. it has the smallest Mean Squared Error and the highest Percentage Relative Efficiency. The developed estimator therefore is suitable to be applied to situations in which the variable of interest has a positive correlation with the auxiliary variable.

The Mean Deviation from the Median of the Dagum Distribution

The Dagum model is particularly suitable for the analysis of the distributions of economic quantities, such as income, assets and consumption. The purpose of this note is to derive the expression of the mean deviation from the median of the Dagum distribution to study the behavior of the scale and shape parameters in terms of absolute variability and in terms of relative variability.

Discussion about the Mean,Median,Mode and their Validity,and the Representative Number

The mean,median and mode are statistical means often used in statistics to describe the concentrative trend of a group of data.However,the three kinds of data are not only different in definition,but also different in application.For the same group of data,there is no definite and strict standard for which one should be used.What's more,different data may even lead to diametrically opposite conclusions.Even if we finally choose one,what extent the data can describe the concentrative trend of the group of data?Is there any statistical method that can describe the concentrative trend of a group of data more objectively and fairly?It is not only a very interesting issue,but also an issue including great research value.

RELATIONSHIP BETWEEN INCLUSION IN THE RAPE CROP-QINGYOU Ⅱ AND ALATE RATIO OF MYZUS PERSICAE

AlateratioofMyzuspersicaeSulzerwasgreatlycloserinrelationshiptocertaininclusionintherapecrop-QingyouⅡ,suchastryptophan,ratioofcontentsofsolublesugartoproteinandmeancrowdingnessunderconditionsofvariedmateproportionoffertilizers-N,P,K.Thefollowinginclusionintherapecropwerealsorelatedtotheratioofalatate:asperticacid,troeoninie,serine,glutancicacid,phenylalanine,lysine,histidine,valine,methionine,isoleucine,leucine,solublesugarandwater-solubleprotein.

The relationship of blood cell-associated inflammatory indices and diabetic retinopathy: a Meta-analysis and systematic review

AIM: To explore the correlation between several blood cell-associated inflammatory indices including mean platelet volume(MPV), platelet distribution width(PDW), neutrophil to lymphocyte ratio(NLR) and platelet-lymphocyte ratio(PLR), and the presence and severity of diabetic retinopathy(DR). METHODS: We searched for eligible studies from PubMed, EMBASE, Web of Science and CNKI up to December 13, 2017. Standardized mean difference(SMD) calculated with confidence interval(CI) of 95% was used to estimate the values of those indices. RESULTS: A total of 31 studies were included in the present Meta-analysis. As compared with type 2 diabetes mellitus(T2 DM) patients without DR, the values of MPV, PDW, NLR, and PLR were higher in patients with DR(SMD=0.67; 95%CI: 0.36 to 0.98; SMD=0.51; 95%CI: 0.27 to 0.75; SMD=0.77; 95%CI: 0.49 to 1.05 and SMD=1.18; 95%CI: 0.07 to 2.28). Additionally, it was also observed that MPV was closely correlated with the severity of DR. CONCLUSION: MPV, PDW, NLR, and PLR could be recommended as diagnostic biomarkers for DR, and MPV could be applied to assess the severity of DR.

Ratio of In-Sphere Volume to Polyhedron Volume of the Great Pyramid Compared to Selected Convex Polyhedral Solids

The architecture of the Great Pyramid at Giza is based on fascinating golden mean geometry. Recently the ratio of the in-sphere volume to the pyramid volume was calculated. One yields as result RV = π ⋅ φ5, where is the golden mean. It is important that the number φ5 is a fundamental constant of nature describing phase transition from microscopic to cosmic scale. In this contribution the relatively small volume ratio of the Great Pyramid was compared to that of selected convex polyhedral solids such as the Platonic solids respectively the face-rich truncated icosahedron (bucky ball) as one of Archimedes’ solids leading to effective filling of the polyhedron by its in-sphere and therefore the highest volume ratio of the selected examples. The smallest ratio was found for the Great Pyramid. A regression analysis delivers the highly reliable volume ratio relation , where nF represents the number of polyhedron faces and b approximates the silver mean. For less-symmetrical solids with a unique axis (tetragonal pyramids) the in-sphere can be replaced by a biaxial ellipsoid of maximum volume to adjust the RV relation more reliably.

A Class of Estimators for Population Ratio in Simple Random Sampling Using Variable Transformation

This paper is an extension and generalization of the study carried out by [1] on the estimation of the population ratio (R) of the population means of two variables (y and x) under Simple Random Sampling (SRS) scheme, using a variable transformation of the auxiliary variable, x. All the six estimators proposed by [1] are easily identified as special cases of the proposed class of estimators. Asymptotic properties of the proposed class of estimators are derived theoretically and subsequently verified using empirical illustrations. Some of the proposed estimators are found to have relatively large gains in efficiency over the customary ratio estimator, ?for the given data set.

Sample geometric mean versus sample median in closed form framework of seismic reliability evaluation: a case study comparison

Earthquake engineers have made a lot of efforts to derive a comprehensive set of closed form expressions for performance evaluation of frames, which are already presented in guidelines such as SAC/FEMA. These analytical expressions have been developed to estimate the annual probability of exceeding a limit state. In the process of such seismic assessments, some essential assumptions are adopted to simplify the process. One of these fundamental assumptions declares that drift demand at any seismic intensity level follows a lognormal distribution around its median. To investigate the validity of this assumption, this paper describes a case study of the types of errors that could be produced by using the sample median as the central tendency. Based on the Maximum Likelihood Estimation method as well as other statistical evidence, this paper proposes the use of the sample geometric mean instead of the sample median for the central tendency. Further, the results of seismic reliability evaluations of 4 sample frames are compared based on utilizing both the geometric mean and the sample median. In this process, both first and second order power law fits of the hazard curve are implemented to compare the effects of hazard estimation and the selection of the central tendency on the final results. It is observed in the application example that the sample geometric mean could lead to more accurate results.

Determination of a novel ACE inhibitor in the presence of alkaline and oxidative degradation products using smart spectrophotometric and chemometric methods

Simple, accurate, sensitive and validated UV spectrophotometric and chemometric methods were developed for the determination of imidapril hydrochloride （IMD） in the presence of both its alkaline （AKN） and oxidative （OXI） degradation products and in its pharmaceutical formulation. Method A is the fourth derivative spectra （D4） which allows the determination of IMD in the presence of both AKN and OXD, in pure form and in tablets by measuring the peak amplitude at 243.0 nm. Methods B, C and D, manipulating ratio spectra, were also developed. Method B is the double divisor-ratio difference spectrophotometric one （DD-RD） by computing the difference between the amplitudes of IMD ratio spectra at 232 and 256.3 nm. Method C is the double divisor-first derivative of ratio spectra method （DD-DR1） at 243.2 nm, while method D is the mean centering of ratio spectra （MCR） at 288.0 nm. Methods A, B, C and D could successfully determine IMD in a concentration range of 4.0-32.0 mg/mL. Methods E and F are principal component regression （PCR） and partial least-squares （PLS）, respectively, for the simultaneous determination of IMD in the presence of both AKN and OXI, in pure form and in its tablets. The developed methods have the advantage of simultaneous determination of the cited components without any pre-treatment. The accuracy, precision and linearity ranges of the developed methods were determined. The results obtained were statistically compared with those of a reported HPLC method, and there was no significant difference between the proposed methods and the reported method regarding both accuracy and precision.

Axonal degeneration of the ulnar nerve secondary to carpal tunnel syndrome: fact or fiction?

The distribution of sensory symptoms in carpal tunnel syndrome is strongly dependent on the degree of electrophysiological dysfunction of the median nerve. The association between carpal tunnel syndrome and ulnar nerve entrapment is still unclear. In this study, we measured ulnar nerve function in 82 patients with carpal tunnel syndrome. The patients were divided into group I with minimal carpal tunnel syndrome （n = 35） and group II with mild to moderate carpal tunnel syndrome （n = 47） according to electrophysiological data. Sixty-one age- and sex-matched subjects without carpal tunnel syndrome were used as a control group. There were no significant differences in ulnar sensory nerve peak latencies or conduction velocities from the 4th and 5th fingers between patients with carpal tunnel syndrome and the control group. The ulnar sensory nerve action potential amplitudes from the 4th and 5th fingers were lower in patients with carpal tunnel syndrome than in the control group. The ratios of the ulnar sensory nerve action potential amplitudes from the 4th and 5th fingers were almost the same in patients with carpal tunnel syndrome as in the control group. These findings indicate that in patients with minimal to moderate carpal tunnel syndrome, there is some electrophysiological evidence of traction on the adjacent ulnar nerve fibers. The findings do not indicate axonal degeneration of the ulnar nerve.

Effects of grassland management on the community structure, aboveground biomass and stability of a temperate steppe in Inner Mongolia, China

Plant community structure responds strongly to anthropogenic disturbances, which greatly influence community stability. The changes in community structure, aboveground biomass（AGB）, biodiversity and community stability associated with different management practices were studied with a three-year field investigation in a temperate steppe of Inner Mongolia, China. The species richness, Shannon-Wiener index, evenness, plant functional type abundance, AGB, temporal community stability, summed covariance, scaling coefficient and dominant species stability were compared among areas subjected to long-term reservation（R）, long-term grazing（G）, mowing since enclosure in 2008（M） and grazing enclosure since 2008（E）. Site R had higher perennial grass abundance and lower species richness than sites G, M and E, although the AGB was not significantly different among the four sites. The species structure varied from a single dominant species at site R to multiple dominant species at sites G, M and E. The long-term reservation grassland had lower biodiversity but higher stability, whereas the enclosed grassland with/without mowing had higher biodiversity but lower stability. Different stability mechanisms, such as the compensatory dynamics, mean-variance scaling and dominant species stability were examined. Results showed that community stability was most closely related to the relative stability of the dominant species, which supports the biomass ratio hypothesis proposed by Grime.

Usefulness of white blood cell count to mean platelet volume ratio for predicting long-term prognosis after primary percutaneous coronary intervention in patients with acute coronary syndrome

Background and Objective The white blood cell count to mean platelet volume ratio(WMR)has recently been described as a predictor of cardiovascular events in patients who undergo percutaneous coronary intervention(PCI).The aim of this study was to investigate the usefulness of admission WMR in predicting outcomes in patients with acute coronary syndrome(ACS).

Growth of Douglas-fir （Pseudotsuga menziesii （Mirb.） Franco） in the Region of Yundola Training and Experimental Forest Range, Bulgaria

The aim of the article was to study the growth of Douglas-fir plantations in the region of the Training Experimental Forest Enterprise, Yundola （Central South Bulgaria）. The study sites were three Douglas-fir plantations, ranging between 50 and 55 years of age at altitudinal range between 1,400 m and 1,600 m above sea level （masl）. The mean height, diameter at breast height, site class, stem volume as well as the mechanical resistance （H/D ratio） of Douglas-fir were measured for each plantation. The results showed that Douglas-fir had the best height growth of the studied plantations on slope facing South at altitude 1,600 masl and Douglas-fir with age 55 years old reached a mean height of 32.4 m. The average diameter at breast height of the studied plantations reaches approximately 30 cm, which shows that they are suitable for large scale wood harvesting. The average stem volume of Douglas-fir in the observed plantations up to age of 55 is within the range of 400-600 m3/ha, with an average annual volume increment from 7 m3/ha to 12 m3/ha each year. The high index of mechanical resistance （H/D ratio） indicated a risk for abiotic damages, which implicated the need for the immediate implementation of felling.

Determination Multipole Mixing Ratios and Transition Strengths of Gamma Rays from Level Studies of 93Mo （p, nγ） Reaction

The multipole mixing ratios have been calculated by a2-ratio method, from levels of 93Mo（p, nγ） reaction. The branching ratios of such γ-transitions are used to calculate the total gamma widths. Besides, the transition strengths and probabilities have been calculated for γ-transitions from excited states whose life times have been reported previously. The results are found to be in general in good agreement with the previous results populated from the previous work.

OFDM系统中一种A-MMSE信道估计算法

针对正交频分复用(Orthogonal Frequency Division Multiplexing,OFDM)系统中最小均方误差(Minimum Mean Squared Error,MMSE)信道估计算法误码率(BER)高的问题,提出一种平均最小均方误差(Averaged-Minimum Mean Squared Error,A-MMSE)信道估计算法。该算法首先基于802.11n标准而构造了一种新的导频结构,收发两端分别进行降采样和过采样处理,利用已知训练序列和导频获得信道频域响应。仿真结果表明,所提出的A-MMSE信道估计算法与传统的MMSE算法相比,在BER为10^(-3)时,信噪比改善了约8dB。因而所提出的信道估计算法能明显改善系统的BER性能。

Towards an evaluation of alcoholic liver cirrhosis and nonalcoholic fatty liver disease patients with hematological scales

BACKGROUND Seeking potentially novel blood markers of liver fibrosis and steatosis is constantly of crucial importance.Despite a growing number of studies in this field of hepatology,a certain role of hematological indices in the course of liver disorders has not been fully elucidated,yet.AIM To evaluate a diagnostic accuracy of neutrophil-to-lymphocyte ratio(NLR),platelet-to-lymphocyte ratio(PLR)and mean platelet volume-to-platelet-ratio(MPR)in the course of alcoholic liver cirrhosis(ALC)and nonalcoholic fatty liver disease(NAFLD).METHODS One hundred forty-two patients with ALC,92 with NAFLD and 68 persons in control group were enrolled in the study.Hematological indices(NLR,PLR and MPR),indirect and direct markers of liver fibrosis(aspartate transaminase to alkaline transaminase ratio,aspartate transaminase to platelet ratio index,fibrosis-4,gamma-glutamyl transpeptidase to platelet ratio,procollagen Ⅰ carboxyterminal propeptide,procollagen Ⅲ aminoterminal propeptide,transforming growth factor-α,platelet-derived growth factor AB,laminin)were measured in each person.Model for end-stage liver disease(MELD)score in ALC group and NAFLD fibrosis score together with BARD score were calculated in NAFLD patients.Receiver operating characteristic(ROC)curves and area under the curve(AUC)values were applied to assess the sensitivity and specificity of examined markers and to evaluate proposed cut-offs of measured indices in the course of ALC and NAFLD.RESULTS MPR and NLR values in ALC patients were significantly higher in comparison to control group;PLR level was significantly lower.MPR and PLR correlated with assessed indirect and direct markers of liver fibrosis.MPR,NLR and PLR correlated with MELD score.NLR level in NAFLD patients was significantly higher in comparison to controls.MPR correlated with indirect markers of liver fibrosis and NAFLD fibrosis score.AUC values and proposed cut-offs for NLR,PLR and MPR in ALC patients were:0.821(>2.227),0.675(<70.445)and 0.929(>0.048),respectively.AUC values and proposed cut-offs for NLR,PLR and MPR in NAFLD group were:0.725(>2.034),0.528(>97.101)and 0.547(>0.038),respectively.CONCLUSION Hematological markers are inseparably connected with serological indices of liver fibrosis in ALC and NAFLD patients.MPR and NLR turned out to be the most powerful parameters in ALC patients.