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SPSS中英文对照词典

SPSS中英文对照词典SPSS中英文对照词典发表日期：2005年11月22日出处：社会学吧Absolute deviation, 绝对离差Absolute number, 绝对数Absolute residuals, 绝对残差Acceleration array, 加速度立体阵Acceleration in an arbitrary direction, 任意方向上的加速度Acceleration normal, 法向加速度Acceleration space dimension, 加速度空间的维数Acceleration tangential, 切向加速度Acceleration vector, 加速度向量Acceptable hypothesis,可接受假设Accumulation, 累积Accuracy, 准确度Actual frequency, 实际频数Adaptive estimator, 自适应估计量Addition, 相加Addition theorem, 加法定理Additivity, 可加性Adjusted rate, 调整率Adjusted value, 校正值Admissible error, 容许误差Aggregation, 聚集性Alternative hypothesis, 备择假设Among groups, 组间Amounts, 总量Analysis of correlation, 相关分析Analysis of covariance, 协方差分析Analysis of regression, 回归分析Analysis of time series, 时间序列分析Analysis of variance, 方差分析Angular transformation, 角转换ANOVA （analysis of variance）, 方差分析ANOVA Models, 方差分析模型Arcing, 弧/弧旋Arcsine transformation,反正弦变换Area under the curve, 曲线面积AREG , 评估从一个时间点到下一个时间点回归相关时的误差 ARIMA, 季节和非季节性单变量模型的极大似然估计 Arithmetic grid paper, 算术格纸Arithmetic mean, 算术平均数Arrhenius relation, 艾恩尼斯关系Assessing fit, 拟合的评估Associative laws, 结合律Asymmetric distribution, 非对称分布Asymptotic bias, 渐近偏倚Asymptotic efficiency, 渐近效率Asymptotic variance, 渐近方差Attributable risk, 归因危险度Attribute data, 属性资料Attribution, 属性Autocorrelation, 自相关Autocorrelation of residuals,残差的自相关Average, 平均数Average confidence interval length, 平均置信区间长度Average growth rate, 平均增长率Bar chart, 条形图Bar graph, 条形图Base period, 基期Bayes‘ theorem , Bayes定理Bell-shaped curve, 钟形曲线Bernoulli distribution, 伯努力分布Best-trim estimator,最好切尾估计量Bias, 偏性Binary logistic regression, 二元逻辑斯蒂回归Binomial distribution, 二项分布Bisquare, 双平方Bivariate Correlate, 二变量相关Bivariate normal distribution, 双变量正态分布Bivariate normal population, 双变量正态总体Biweight interval, 双权区间Biweight M-estimator, 双权M估计量Block, 区组/配伍组BMDP(Biomedical computer programs), BMDP统计软件包Boxplots, 箱线图/箱尾图Breakdown bound, 崩溃界/崩溃点Canonical correlation, 典型相关Caption, 纵标目Case-control study, 病例对照研究Categorical variable, 分类变量Catenary, 悬链线Cauchy distribution, 柯西分布Cause-and-effect relationship, 因果关系Cell,单元Censoring, 终检Center of symmetry, 对称中心Centering and scaling, 中心化和定标Central tendency, 集中趋势Central value, 中心值CHAID -χ2 Automatic Interaction Detector,卡方自动交互检测Chance, 机遇Chance error, 随机误差Chance variable, 随机变量Characteristic equation, 特征方程Characteristic root, 特征根Characteristic vector, 特征向量Chebshev criterion of fit, 拟合的切比雪夫准则Chernoff faces, 切尔诺夫脸谱图Chi-square test, 卡方检验/χ2检验Choleskey decomposition, 乔洛斯基分解Circle chart, 圆图 Class interval, 组距Class mid-value, 组中值Class upper limit, 组上限Classified variable, 分类变量Cluster analysis, 聚类分析Cluster sampling, 整群抽样Code, 代码Coded data, 编码数据Coding,编码Coefficient of contingency, 列联系数Coefficient of determination, 决定系数Coefficient of multiple correlation, 多重相关系数Coefficient of partial correlation, 偏相关系数Coefficient of production-moment correlation, 积差相关系数Coefficient of rank correlation, 等级相关系数Coefficient of regression, 回归系数Coefficient of skewness, 偏度系数Coefficient of variation, 变异系数Cohort study, 队列研究Column, 列Column effect, 列效应Column factor, 列因素Combination pool, 合并Combinative table, 组合表Common factor, 共性因子Common regression coefficient, 公共回归系数Common value, 共同值Common variance, 公共方差Common variation, 公共变异Communality variance, 共性方差Comparability, 可比性Comparison of bathes, 批比较Comparison value, 比较值Compartment model, 分部模型Compassion, 伸缩Complement of an event, 补事件Complete association, 完全正相关Complete dissociation, 完全不相关Complete statistics, 完备统计量Completely randomized design, 完全随机化设计Composite event, 联合事件Composite events, 复合事件Concavity, 凹性Conditional expectation, 条件期望Conditional likelihood, 条件似然Conditional probability,条件概率Conditionally linear, 依条件线性Confidence interval, 置信区间Confidence limit, 置信限Confidence lower limit, 置信下限Confidence upper limit, 置信上限Confirmatory Factor Analysis , 验证性因子分析Confirmatory research, 证实性实验研究Confounding factor, 混杂因素Conjoint, 联合分析Consistency, 相合性Consistency check, 一致性检验Consistent asymptotically normal estimate, 相合渐近正态估计Consistent estimate, 相合估计Constrained nonlinear regression, 受约束非线性回归Constraint, 约束Contaminated distribution, 污染分布Contaminated Gausssian, 污染高斯分布Contaminated normal distribution, 污染正态分布Contamination, 污染Contamination model, 污染模型Contingency table, 列联表Contour, 边界线Contribution rate, 贡献率Control, 对照Controlled experiments, 对照实验Conventional depth, 常规深度Convolution, 卷积Corrected factor, 校正因子Corrected mean, 校正均值Correction coefficient, 校正系数Correctness, 正确性Correlation coefficient, 相关系数Correlation index, 相关指数Correspondence, 对应Counting, 计数Counts, 计数/频数Covariance, 协方差Covariant, 共变 Cox Regression, Cox回归Criteria for fitting, 拟合准则Criteria of least squares, 最小二乘准则Critical ratio, 临界比Critical region, 拒绝域Critical value,临界值Cross-over design, 交叉设计Cross-section analysis, 横断面分析Cross-section survey,横断面调查Crosstabs , 交叉表 Cross-tabulation table, 复合表Cube root, 立方根Cumulative distribution function, 分布函数Cumulative probability, 累计概率Curvature, 曲率/弯曲Curvature, 曲率Curve fit , 曲线拟和 Curve fitting, 曲线拟合Curvilinear regression, 曲线回归Curvilinear relation, 曲线关系Cut-and-try method, 尝试法Cycle, 周期Cyclist, 周期性D test, D检验Data acquisition, 资料收集Data bank, 数据库Data capacity, 数据容量Data deficiencies, 数据缺乏Data handling, 数据处理Data manipulation, 数据处理Data processing, 数据处理Data reduction, 数据缩减Data set, 数据集Data sources, 数据来源Data transformation, 数据变换Data validity, 数据有效性Data-in, 数据输入Data-out, 数据输出Dead time, 停滞期Degree of freedom, 自由度Degree of precision, 精密度Degree of reliability, 可靠性程度Degression, 递减Density function, 密度函数Density of data points, 数据点的密度Dependent variable, 应变量/依变量/因变量Dependent variable, 因变量Depth, 深度Derivative matrix, 导数矩阵Derivative-free methods, 无导数方法Design, 设计Determinacy, 确定性Determinant, 行列式Determinant,决定因素Deviation, 离差Deviation from average, 离均差Diagnostic plot, 诊断图Dichotomous variable, 二分变量Differential equation, 微分方程Direct standardization, 直接标准化法Discrete variable, 离散型变量DISCRIMINANT, 判断 Discriminant analysis, 判别分析Discriminant coefficient, 判别系数Discriminant function, 判别值Dispersion, 散布/分散度Disproportional, 不成比例的Disproportionate sub-class numbers, 不成比例次级组含量Distribution free, 分布无关性/免分布Distribution shape, 分布形状Distribution-free method, 任意分布法Distributive laws,分配律Disturbance, 随机扰动项Dose response curve, 剂量反应曲线Double blind method, 双盲法Double blind trial, 双盲试验Double exponential distribution, 双指数分布Double logarithmic,双对数Downward rank, 降秩Dual-space plot, 对偶空间图DUD, 无导数方法Duncan‘s new multiple range method, 新复极差法/Duncan新法Effect, 实验效应Eigenvalue, 特征值Eigenvector, 特征向量Ellipse, 椭圆Empirical distribution, 经验分布Empirical probability, 经验概率单位Enumeration data, 计数资料Equal sun-class number, 相等次级组含量Equally likely, 等可能Equivariance, 同变性Error, 误差/错误Error of estimate, 估计误差Error type I, 第一类错误Error type II, 第二类错误Estimand, 被估量Estimated error mean squares, 估计误差均方Estimated error sum of squares, 估计误差平方和Euclidean distance, 欧式距离Event, 事件Event, 事件Exceptional data point, 异常数据点Expectation plane, 期望平面Expectation surface, 期望曲面Expected values, 期望值Experiment, 实验Experimental sampling, 试验抽样Experimental unit, 试验单位Explanatory variable, 说明变量Exploratory data analysis, 探索性数据分析Explore Summarize, 探索-摘要Exponential curve, 指数曲线Exponential growth, 指数式增长EXSMOOTH, 指数平滑方法 Extended fit, 扩充拟合Extra parameter, 附加参数Extrapolation, 外推法Extreme observation, 末端观测值Extremes, 极端值/极值F distribution, F 分布F test, F检验Factor, 因素/因子Factor analysis, 因子分析Factor Analysis, 因子分析Factor score, 因子得分Factorial, 阶乘Factorial design, 析因试验设计False negative, 假阴性False negative error, 假阴性错误Family of distributions, 分布族Family of estimators, 估计量族Fanning, 扇面Fatality rate, 病死率Field investigation, 现场调查Field survey, 现场调查Finite population, 有限总体Finite-sample, 有限样本First derivative, 一阶导数First principal component, 第一主成分First quartile, 第一四分位数Fisher information, 费雪信息量Fitted value, 拟合值Fitting a curve, 曲线拟合Fixed base, 定基Fluctuation, 随机起伏Forecast, 预测Four fold table, 四格表Fourth, 四分点Fraction blow, 左侧比率Fractional error, 相对误差Frequency, 频率Frequency polygon, 频数多边图Frontier point, 界限点Function relationship,泛函关系Gamma distribution, 伽玛分布Gauss increment, 高斯增量Gaussian distribution, 高斯分布/正态分布Gauss-Newton increment, 高斯-牛顿增量General census, 全面普查GENLOG (Generalized liner models), 广义线性模型 Geometric mean, 几何平均数Gini‘s mean difference,基尼均差GLM (General liner models), 一般线性模型 Goodness of fit, 拟和优度/配合度Gradient of determinant, 行列式的梯度Graeco-Latin square, 希腊拉丁方Grand mean, 总均值Gross errors, 重大错误Gross-error sensitivity, 大错敏感度Group averages, 分组平均Grouped data,分组资料Guessed mean, 假定平均数Half-life, 半衰期Hampel M-estimators, 汉佩尔M估计量Happenstance, 偶然事件Harmonic mean, 调和均数Hazard function, 风险均数Hazard rate, 风险率Heading, 标目 Heavy-tailed distribution, 重尾分布Hessian array, 海森立体阵Heterogeneity, 不同质Heterogeneity of variance, 方差不齐 Hierarchical classification, 组内分组Hierarchical clustering method, 系统聚类法High-leverage point, 高杠杆率点HILOGLINEAR,多维列联表的层次对数线性模型Hinge, 折叶点Histogram, 直方图Historical cohort study, 历史性队列研究 Holes, 空洞HOMALS, 多重响应分析Homogeneity of variance, 方差齐性Homogeneity test, 齐性检验Huber M-estimators, 休伯M估计量Hyperbola, 双曲线Hypothesis testing, 假设检验Hypothetical universe, 假设总体Impossible event, 不可能事件Independence,独立性Independent variable, 自变量Index, 指标/指数Indirect standardization, 间接标准化法Individual, 个体Inference band, 推断带Infinite population, 无限总体Infinitely great, 无穷大Infinitely small, 无穷小Influence curve, 影响曲线Information capacity, 信息容量Initial condition,初始条件Initial estimate, 初始估计值Initial level, 最初水平Interaction, 交互作用Interaction terms, 交互作用项Intercept, 截距Interpolation, 内插法Interquartile range, 四分位距Interval estimation, 区间估计Intervals of equal probability, 等概率区间Intrinsic curvature, 固有曲率Invariance, 不变性Inverse matrix, 逆矩阵Inverse probability, 逆概率Inverse sine献花(0)。

SPSS术语中英文对照

SPSS术语中英文对照【常用软件】SPSS术语中英文对照Absolute deviation, 绝对离差Absolute number, 绝对数Absolute residuals, 绝对残差Acceleration array, 加速度立体阵Acceleration in an arbitrary direction, 任意方向上的加速度Acceleration normal, 法向加速度Acceleration space dimension, 加速度空间的维数Acceleration tangential, 切向加速度Acceleration vector, 加速度向量Acceptable hypothesis, 可接受假设Accumulation, 累积Accuracy, 准确度Actual frequency, 实际频数Adaptive estimator, 自适应估计量Addition, 相加Addition theorem, 加法定理Additivity, 可加性Adjusted rate, 调整率Adjusted value, 校正值Admissible error, 容许误差Aggregation, 聚集性Alternative hypothesis, 备择假设Among groups, 组间Amounts, 总量Analysis of correlation, 相关分析Analysis of covariance, 协方差分析Analysis of regression, 回归分析Analysis of time series, 时间序列分析Analysis of variance, 方差分析Angular transformation, 角转换ANOVA （analysis of variance）, 方差分析ANOVA Models, 方差分析模型Arcing, 弧/弧旋Arcsine transformation, 反正弦变换Area under the curve, 曲线面积AREG , 评估从一个时间点到下一个时间点回归相关时的误差ARIMA, 季节和非季节性单变量模型的极大似然估计Arithmetic grid paper, 算术格纸Arithmetic mean, 算术平均数Arrhenius relation, 艾恩尼斯关系Assessing fit, 拟合的评估Associative laws, 结合律Asymmetric distribution, 非对称分布Asymptotic bias, 渐近偏倚Asymptotic efficiency, 渐近效率Asymptotic variance, 渐近方差Attributable risk, 归因危险度Attribute data, 属性资料Attribution, 属性Autocorrelation, 自相关Autocorrelation of residuals, 残差的自相关Average, 平均数Average confidence interval length, 平均置信区间长度Average growth rate, 平均增长率Bar chart, 条形图Bar graph, 条形图Base period, 基期Bayes' theorem , Bayes定理Bell-shaped curve, 钟形曲线Bernoulli distribution, 伯努力分布Best-trim estimator, 最好切尾估计量Bias, 偏性Binary logistic regression, 二元逻辑斯蒂回归Binomial distribution, 二项分布Bisquare, 双平方Bivariate Correlate, 二变量相关Bivariate normal distribution, 双变量正态分布Bivariate normal population, 双变量正态总体Biweight interval, 双权区间Biweight M-estimator, 双权M估计量Block, 区组/配伍组BMDP(Biomedical computer programs), BMDP统计软件包Boxplots, 箱线图/箱尾图Breakdown bound, 崩溃界/崩溃点Canonical correlation, 典型相关Caption, 纵标目Case-control study, 病例对照研究Categorical variable, 分类变量Catenary, 悬链线Cauchy distribution, 柯西分布Cause-and-effect relationship, 因果关系Cell, 单元Censoring, 终检Center of symmetry, 对称中心Centering and scaling, 中心化和定标Central tendency, 集中趋势Central value, 中心值CHAID -χ2 Automatic Interac tion Detector, 卡方自动交互检测Chance, 机遇Chance error, 随机误差Chance variable, 随机变量Characteristic equation, 特征方程Characteristic root, 特征根Characteristic vector, 特征向量Chebshev criterion of fit, 拟合的切比雪夫准则Chernoff faces, 切尔诺夫脸谱图Chi-square test, 卡方检验/χ2检验Choleskey decomposition, 乔洛斯基分解Circle chart, 圆图Class interval, 组距Class mid-value, 组中值Class upper limit, 组上限Classified variable, 分类变量Cluster analysis, 聚类分析Cluster sampling, 整群抽样Code, 代码Coded data, 编码数据Coding, 编码Coefficient of contingency, 列联系数Coefficient of determination, 决定系数Coefficient of multiple correlation, 多重相关系数Coefficient of partial correlation, 偏相关系数Coefficient of production-moment correlation, 积差相关系数Coefficient of rank correlation, 等级相关系数Coefficient of regression, 回归系数Coefficient of skewness, 偏度系数Coefficient of variation, 变异系数Cohort study, 队列研究Column, 列Column effect, 列效应Column factor, 列因素Combination pool, 合并Combinative table, 组合表Common factor, 共性因子Common regression coefficient, 公共回归系数Common value, 共同值Common variance, 公共方差Common variation, 公共变异Communality variance, 共性方差Comparability, 可比性Comparison of bathes, 批比较Comparison value, 比较值Compartment model, 分部模型Compassion, 伸缩Complement of an event, 补事件Complete association, 完全正相关Complete dissociation, 完全不相关Complete statistics, 完备统计量Completely randomized design, 完全随机化设计Composite event, 联合事件Composite events, 复合事件Concavity, 凹性Conditional expectation, 条件期望Conditional likelihood, 条件似然Conditional probability, 条件概率Conditionally linear, 依条件线性Confidence interval, 置信区间Confidence limit, 置信限Confidence lower limit, 置信下限Confidence upper limit, 置信上限Confirmatory Factor Analysis , 验证性因子分析Confirmatory research, 证实性实验研究Confounding factor, 混杂因素Conjoint, 联合分析Consistency, 相合性Consistency check, 一致性检验Consistent asymptotically normal estimate, 相合渐近正态估计Consistent estimate, 相合估计Constrained nonlinear regression, 受约束非线性回归Constraint, 约束Contaminated distribution, 污染分布Contaminated Gausssian, 污染高斯分布Contaminated normal distribution, 污染正态分布Contamination, 污染Contamination model, 污染模型Contingency table, 列联表Contour, 边界线Contribution rate, 贡献率Control, 对照Controlled experiments, 对照实验Conventional depth, 常规深度Convolution, 卷积Corrected factor, 校正因子Corrected mean, 校正均值Correction coefficient, 校正系数Correctness, 正确性Correlation coefficient, 相关系数Correlation index, 相关指数Correspondence, 对应Counting, 计数Counts, 计数/频数Covariance, 协方差Covariant, 共变Cox Regression, Cox回归Criteria for fitting, 拟合准则Criteria of least squares, 最小二乘准则Critical ratio, 临界比Critical region, 拒绝域Critical value, 临界值Cross-over design, 交叉设计Cross-section analysis, 横断面分析Cross-section survey, 横断面调查Crosstabs , 交叉表Cross-tabulation table, 复合表Cube root, 立方根Cumulative distribution function, 分布函数Cumulative probability, 累计概率Curvature, 曲率/弯曲Curvature, 曲率Curve fit , 曲线拟和Curve fitting, 曲线拟合Curvilinear regression, 曲线回归Curvilinear relation, 曲线关系Cut-and-try method, 尝试法Cycle, 周期Cyclist, 周期性D test, D检验Data acquisition, 资料收集Data bank, 数据库Data capacity, 数据容量Data deficiencies, 数据缺乏Data handling, 数据处理Data manipulation, 数据处理Data processing, 数据处理Data reduction, 数据缩减Data set, 数据集Data sources, 数据来源Data transformation, 数据变换Data validity, 数据有效性Data-in, 数据输入Data-out, 数据输出Dead time, 停滞期Degree of freedom, 自由度Degree of precision, 精密度Degree of reliability, 可靠性程度Degression, 递减Density function, 密度函数Density of data points, 数据点的密度Dependent variable, 应变量/依变量/因变量Dependent variable, 因变量Depth, 深度Derivative matrix, 导数矩阵Derivative-free methods, 无导数方法Design, 设计Determinacy, 确定性Determinant, 行列式Determinant, 决定因素Deviation, 离差Deviation from average, 离均差Diagnostic plot, 诊断图Dichotomous variable, 二分变量Differential equation, 微分方程Direct standardization, 直接标准化法Discrete variable, 离散型变量DISCRIMINANT, 判断Discriminant analysis, 判别分析Discriminant coefficient, 判别系数Discriminant function, 判别值Dispersion, 散布/分散度Disproportional, 不成比例的Disproportionate sub-class numbers, 不成比例次级组含量Distribution free, 分布无关性/免分布Distribution shape, 分布形状Distribution-free method, 任意分布法Distributive laws, 分配律Disturbance, 随机扰动项Dose response curve, 剂量反应曲线Double blind method, 双盲法Double blind trial, 双盲试验Double exponential distribution, 双指数分布Double logarithmic, 双对数Downward rank, 降秩Dual-space plot, 对偶空间图DUD, 无导数方法Duncan's new multiple range method, 新复极差法/Duncan新法Effect, 实验效应Eigenvalue, 特征值Eigenvector, 特征向量Ellipse, 椭圆Empirical distribution, 经验分布Empirical probability, 经验概率单位Enumeration data, 计数资料Equal sun-class number, 相等次级组含量Equally likely, 等可能Equivariance, 同变性Error, 误差/错误Error of estimate, 估计误差Error type I, 第一类错误Error type II, 第二类错误Estimand, 被估量Estimated error mean squares, 估计误差均方Estimated error sum of squares, 估计误差平方和Euclidean distance, 欧式距离Event, 事件Event, 事件Exceptional data point, 异常数据点Expectation plane, 期望平面Expectation surface, 期望曲面Expected values, 期望值Experiment, 实验Experimental sampling, 试验抽样Experimental unit, 试验单位Explanatory variable, 说明变量Exploratory data analysis, 探索性数据分析Explore Summarize, 探索-摘要Exponential curve, 指数曲线Exponential growth, 指数式增长EXSMOOTH, 指数平滑方法Extended fit, 扩充拟合Extra parameter, 附加参数Extrapolation, 外推法Extreme observation, 末端观测值Extremes, 极端值/极值F distribution, F分布F test, F检验Factor, 因素/因子Factor analysis, 因子分析Factor Analysis, 因子分析Factor score, 因子得分Factorial, 阶乘Factorial design, 析因试验设计False negative, 假阴性False negative error, 假阴性错误Family of distributions, 分布族Family of estimators, 估计量族Fanning, 扇面Fatality rate, 病死率Field investigation, 现场调查Field survey, 现场调查Finite population, 有限总体Finite-sample, 有限样本First derivative, 一阶导数First principal component, 第一主成分First quartile, 第一四分位数Fisher information, 费雪信息量Fitted value, 拟合值Fitting a curve, 曲线拟合Fixed base, 定基Fluctuation, 随机起伏Forecast, 预测Four fold table, 四格表Fourth, 四分点Fraction blow, 左侧比率Fractional error, 相对误差Frequency, 频率Frequency polygon, 频数多边图Frontier point, 界限点Function relationship, 泛函关系Gamma distribution, 伽玛分布Gauss increment, 高斯增量Gaussian distribution, 高斯分布/正态分布Gauss-Newton increment, 高斯-牛顿增量General census, 全面普查GENLOG (Generalized liner models), 广义线性模型Geometric mean, 几何平均数Gini's mean difference, 基尼均差GLM (General liner models), 一般线性模型Goodness of fit, 拟和优度/配合度Gradient of determinant, 行列式的梯度Graeco-Latin square, 希腊拉丁方Grand mean, 总均值Gross errors, 重大错误Gross-error sensitivity, 大错敏感度Group averages, 分组平均Grouped data, 分组资料Guessed mean, 假定平均数Half-life, 半衰期Hampel M-estimators, 汉佩尔M估计量Happenstance, 偶然事件Harmonic mean, 调和均数Hazard function, 风险均数Hazard rate, 风险率Heading, 标目Heavy-tailed distribution, 重尾分布Hessian array, 海森立体阵Heterogeneity, 不同质Heterogeneity of variance, 方差不齐Hierarchical classification, 组内分组Hierarchical clustering method, 系统聚类法High-leverage point, 高杠杆率点HILOGLINEAR, 多维列联表的层次对数线性模型Hinge, 折叶点Histogram, 直方图Historical cohort study, 历史性队列研究Holes, 空洞HOMALS, 多重响应分析Homogeneity of variance, 方差齐性Homogeneity test, 齐性检验Huber M-estimators, 休伯M估计量Hyperbola, 双曲线Hypothesis testing, 假设检验Hypothetical universe, 假设总体Impossible event, 不可能事件Independence, 独立性Independent variable, 自变量Index, 指标/指数Indirect standardization, 间接标准化法Individual, 个体Inference band, 推断带Infinite population, 无限总体Infinitely great, 无穷大Infinitely small, 无穷小Influence curve, 影响曲线Information capacity, 信息容量Initial condition, 初始条件Initial estimate, 初始估计值Initial level, 最初水平Interaction, 交互作用Interaction terms, 交互作用项Intercept, 截距Interpolation, 内插法Interquartile range, 四分位距Interval estimation, 区间估计Intervals of equal probability, 等概率区间Intrinsic curvature, 固有曲率Invariance, 不变性Inverse matrix, 逆矩阵Inverse probability, 逆概率Inverse sine transformation, 反正弦变换Iteration, 迭代Jacobian determinant, 雅可比行列式Joint distribution function, 分布函数Joint probability, 联合概率Joint probability distribution, 联合概率分布K means method, 逐步聚类法Kaplan-Meier, 评估事件的时间长度Kaplan-Merier chart, Kaplan-Merier图Kendall's rank correlation, Kendall等级相关Kinetic, 动力学Kolmogorov-Smirnove test, 柯尔莫哥洛夫-斯米尔诺夫检验Kruskal and Wallis test, Kruskal及Wallis检验/多样本的秩和检验/H检验Kurtosis, 峰度Lack of fit, 失拟Ladder of powers, 幂阶梯Lag, 滞后Large sample, 大样本Large sample test, 大样本检验Latin square, 拉丁方Latin square design, 拉丁方设计Leakage, 泄漏Least favorable configuration, 最不利构形Least favorable distribution, 最不利分布Least significant difference, 最小显著差法Least square method, 最小二乘法Least-absolute-residuals estimates, 最小绝对残差估计Least-absolute-residuals fit, 最小绝对残差拟合Least-absolute-residuals line, 最小绝对残差线Legend, 图例L-estimator, L估计量L-estimator of location, 位置L估计量L-estimator of scale, 尺度L估计量Level, 水平Life expectance, 预期期望寿命Life table, 寿命表Life table method, 生命表法Light-tailed distribution, 轻尾分布Likelihood function, 似然函数Likelihood ratio, 似然比line graph, 线图Linear correlation, 直线相关Linear equation, 线性方程Linear programming, 线性规划Linear regression, 直线回归Linear Regression, 线性回归Linear trend, 线性趋势Loading, 载荷Location and scale equivariance, 位置尺度同变性Location equivariance, 位置同变性Location invariance, 位置不变性Location scale family, 位置尺度族Log rank test, 时序检验Logarithmic curve, 对数曲线Logarithmic normal distribution, 对数正态分布Logarithmic scale, 对数尺度Logarithmic transformation, 对数变换Logic check, 逻辑检查Logistic distribution, 逻辑斯特分布Logit transformation, Logit转换LOGLINEAR, 多维列联表通用模型Lognormal distribution, 对数正态分布Lost function, 损失函数Low correlation, 低度相关Lower limit, 下限Lowest-attained variance, 最小可达方差LSD, 最小显著差法的简称Lurking variable, 潜在变量Main effect, 主效应Major heading, 主辞标目Marginal density function, 边缘密度函数Marginal probability, 边缘概率Marginal probability distribution, 边缘概率分布Matched data, 配对资料Matched distribution, 匹配过分布Matching of distribution, 分布的匹配Matching of transformation, 变换的匹配Mathematical expectation, 数学期望Mathematical model, 数学模型Maximum L-estimator, 极大极小L 估计量Maximum likelihood method, 最大似然法Mean, 均数Mean squares between groups, 组间均方Mean squares within group, 组内均方Means (Compare means), 均值-均值比较Median, 中位数Median effective dose, 半数效量Median lethal dose, 半数致死量Median polish, 中位数平滑Median test, 中位数检验Minimal sufficient statistic, 最小充分统计量Minimum distance estimation, 最小距离估计Minimum effective dose, 最小有效量Minimum lethal dose, 最小致死量Minimum variance estimator, 最小方差估计量MINITAB, 统计软件包Minor heading, 宾词标目Missing data, 缺失值Model specification, 模型的确定Modeling Statistics , 模型统计Models for outliers, 离群值模型Modifying the model, 模型的修正Modulus of continuity, 连续性模Morbidity, 发病率Most favorable configuration, 最有利构形Multidimensional Scaling (ASCAL), 多维尺度/多维标度Multinomial Logistic Regression , 多项逻辑斯蒂回归Multiple comparison, 多重比较Multiple correlation , 复相关Multiple covariance, 多元协方差Multiple linear regression, 多元线性回归Multiple response , 多重选项Multiple solutions, 多解Multiplication theorem, 乘法定理Multiresponse, 多元响应Multi-stage sampling, 多阶段抽样Multivariate T distribution, 多元T分布Mutual exclusive, 互不相容Mutual independence, 互相独立Natural boundary, 自然边界Natural dead, 自然死亡Natural zero, 自然零Negative correlation, 负相关Negative linear correlation, 负线性相关Negatively skewed, 负偏Newman-Keuls method, q检验NK method, q检验No statistical significance, 无统计意义Nominal variable, 名义变量Nonconstancy of variability, 变异的非定常性Nonlinear regression, 非线性相关Nonparametric statistics, 非参数统计Nonparametric test, 非参数检验Nonparametric tests, 非参数检验Normal deviate, 正态离差Normal distribution, 正态分布Normal equation, 正规方程组Normal ranges, 正常范围Normal value, 正常值Nuisance parameter, 多余参数/讨厌参数Null hypothesis, 无效假设Numerical variable, 数值变量Objective function, 目标函数Observation unit, 观察单位Observed value, 观察值One sided test, 单侧检验One-way analysis of variance, 单因素方差分析Oneway ANOVA , 单因素方差分析Open sequential trial, 开放型序贯设计Optrim, 优切尾Optrim efficiency, 优切尾效率Order statistics, 顺序统计量Ordered categories, 有序分类Ordinal logistic regression , 序数逻辑斯蒂回归Ordinal variable, 有序变量Orthogonal basis, 正交基Orthogonal design, 正交试验设计Orthogonality conditions, 正交条件ORTHOPLAN, 正交设计Outlier cutoffs, 离群值截断点Outliers, 极端值OVERALS , 多组变量的非线性正规相关Overshoot, 迭代过度Paired design, 配对设计Paired sample, 配对样本Pairwise slopes, 成对斜率Parabola, 抛物线Parallel tests, 平行试验Parameter, 参数Parametric statistics, 参数统计Parametric test, 参数检验Partial correlation, 偏相关Partial regression, 偏回归Partial sorting, 偏排序Partials residuals, 偏残差Pattern, 模式Pearson curves, 皮尔逊曲线Peeling, 退层Percent bar graph, 百分条形图Percentage, 百分比Percentile, 百分位数Percentile curves, 百分位曲线Periodicity, 周期性Permutation, 排列P-estimator, P估计量Pie graph, 饼图Pitman estimator, 皮特曼估计量Pivot, 枢轴量Planar, 平坦Planar assumption, 平面的假设PLANCARDS, 生成试验的计划卡Point estimation, 点估计Poisson distribution, 泊松分布Polishing, 平滑Polled standard deviation, 合并标准差Polled variance, 合并方差Polygon, 多边图Polynomial, 多项式Polynomial curve, 多项式曲线Population, 总体Population attributable risk, 人群归因危险度Positive correlation, 正相关Positively skewed, 正偏Posterior distribution, 后验分布Power of a test, 检验效能Precision, 精密度Predicted value, 预测值Preliminary analysis, 预备性分析Principal component analysis, 主成分分析Prior distribution, 先验分布Prior probability, 先验概率Probabilistic model, 概率模型probability, 概率Probability density, 概率密度Product moment, 乘积矩/协方差Profile trace, 截面迹图Proportion, 比/构成比Proportion allocation in stratified random sampling, 按比例分层随机抽样Proportionate, 成比例Proportionate sub-class numbers, 成比例次级组含量Prospective study, 前瞻性调查Proximities, 亲近性Pseudo F test, 近似F检验Pseudo model, 近似模型Pseudosigma, 伪标准差Purposive sampling, 有目的抽样QR decomposition, QR分解Quadratic approximation, 二次近似Qualitative classification, 属性分类Qualitative method, 定性方法Quantile-quantile plot, 分位数-分位数图/Q-Q图Quantitative analysis, 定量分析Quartile, 四分位数Quick Cluster, 快速聚类Radix sort, 基数排序Random allocation, 随机化分组Random blocks design, 随机区组设计Random event, 随机事件Randomization, 随机化Range, 极差/全距Rank correlation, 等级相关Rank sum test, 秩和检验Rank test, 秩检验Ranked data, 等级资料Rate, 比率Ratio, 比例Raw data, 原始资料Raw residual, 原始残差Rayleigh's test, 雷氏检验Rayleigh's Z, 雷氏Z值Reciprocal, 倒数Reciprocal transformation, 倒数变换Recording, 记录Redescending estimators, 回降估计量Reducing dimensions, 降维Re-expression, 重新表达Reference set, 标准组Region of acceptance, 接受域Regression coefficient, 回归系数Regression sum of square, 回归平方和Rejection point, 拒绝点Relative dispersion, 相对离散度Relative number, 相对数Reliability, 可靠性Reparametrization, 重新设置参数Replication, 重复Report Summaries, 报告摘要Residual sum of square, 剩余平方和Resistance, 耐抗性Resistant line, 耐抗线Resistant technique, 耐抗技术R-estimator of location, 位置R估计量R-estimator of scale, 尺度R估计量Retrospective study, 回顾性调查Ridge trace, 岭迹Ridit analysis, Ridit分析Rotation, 旋转Rounding, 舍入Row, 行Row effects, 行效应Row factor, 行因素RXC table, RXC表Sample, 样本Sample regression coefficient, 样本回归系数Sample size, 样本量Sample standard deviation, 样本标准差Sampling error, 抽样误差SAS(Statistical analysis system ), SAS统计软件包Scale, 尺度/量表Scatter diagram, 散点图Schematic plot, 示意图/简图Score test, 计分检验Screening, 筛检SEASON, 季节分析Second derivative, 二阶导数Second principal component, 第二主成分SEM (Structural equation modeling), 结构化方程模型Semi-logarithmic graph, 半对数图Semi-logarithmic paper, 半对数格纸Sensitivity curve, 敏感度曲线Sequential analysis, 贯序分析Sequential data set, 顺序数据集Sequential design, 贯序设计Sequential method, 贯序法Sequential test, 贯序检验法Serial tests, 系列试验Short-cut method, 简捷法Sigmoid curve, S形曲线Sign function, 正负号函数Sign test, 符号检验Signed rank, 符号秩Significance test, 显著性检验Significant figure, 有效数字Simple cluster sampling, 简单整群抽样Simple correlation, 简单相关Simple random sampling, 简单随机抽样Simple regression, 简单回归simple table, 简单表Sine estimator, 正弦估计量Single-valued estimate, 单值估计Singular matrix, 奇异矩阵Skewed distribution, 偏斜分布Skewness, 偏度Slash distribution, 斜线分布Slope, 斜率Smirnov test, 斯米尔诺夫检验Source of variation, 变异来源Spearman rank correlation, 斯皮尔曼等级相关Specific factor, 特殊因子Specific factor variance, 特殊因子方差Spectra , 频谱Spherical distribution, 球型正态分布Spread, 展布SPSS(Statistical package for the social science), SPSS统计软件包Spurious correlation, 假性相关Square root transformation, 平方根变换Stabilizing variance, 稳定方差Standard deviation, 标准差Standard error, 标准误Standard error of difference, 差别的标准误Standard error of estimate, 标准估计误差Standard error of rate, 率的标准误Standard normal distribution, 标准正态分布Standardization, 标准化Starting value, 起始值Statistic, 统计量Statistical control, 统计控制Statistical graph, 统计图Statistical inference, 统计推断Statistical table, 统计表Steepest descent, 最速下降法Stem and leaf display, 茎叶图Step factor, 步长因子Stepwise regression, 逐步回归Storage, 存Strata, 层（复数）Stratified sampling, 分层抽样Stratified sampling, 分层抽样Strength, 强度Stringency, 严密性Structural relationship, 结构关系Studentized residual, 学生化残差/t化残差Sub-class numbers, 次级组含量Subdividing, 分割Sufficient statistic, 充分统计量Sum of products, 积和Sum of squares, 离差平方和Sum of squares about regression, 回归平方和Sum of squares between groups, 组间平方和Sum of squares of partial regression, 偏回归平方和Sure event, 必然事件Survey, 调查Survival, 生存分析Survival rate, 生存率Suspended root gram, 悬吊根图Symmetry, 对称Systematic error, 系统误差Systematic sampling, 系统抽样Tags, 标签Tail area, 尾部面积Tail length, 尾长Tail weight, 尾重Tangent line, 切线Target distribution, 目标分布Taylor series, 泰勒级数Tendency of dispersion, 离散趋势Testing of hypotheses, 假设检验Theoretical frequency, 理论频数Time series, 时间序列Tolerance interval, 容忍区间Tolerance lower limit, 容忍下限Tolerance upper limit, 容忍上限Torsion, 扰率Total sum of square, 总平方和Total variation, 总变异Transformation, 转换Treatment, 处理Trend, 趋势Trend of percentage, 百分比趋势Trial, 试验Trial and error method, 试错法Tuning constant, 细调常数Two sided test, 双向检验Two-stage least squares, 二阶最小平方Two-stage sampling, 二阶段抽样Two-tailed test, 双侧检验Two-way analysis of variance, 双因素方差分析Two-way table, 双向表Type I error, 一类错误/α错误Type II error, 二类错误/β错误UMVU, 方差一致最小无偏估计简称Unbiased estimate, 无偏估计Unconstrained nonlinear regression , 无约束非线性回归Unequal subclass number, 不等次级组含量Ungrouped data, 不分组资料Uniform coordinate, 均匀坐标Uniform distribution, 均匀分布Uniformly minimum variance unbiased estimate, 方差一致最小无偏估计Unit, 单元Unordered categories, 无序分类Upper limit, 上限Upward rank, 升秩Vague concept, 模糊概念Validity, 有效性VARCOMP (Variance component estimation), 方差元素估计Variability, 变异性Variable, 变量Variance, 方差Variation, 变异Varimax orthogonal rotation, 方差最大正交旋转Volume of distribution, 容积W test, W检验Weibull distribution, 威布尔分布Weight, 权数Weighted Chi-square test, 加权卡方检验/Cochran检验Weighted linear regression method, 加权直线回归Weighted mean, 加权平均数Weighted mean square, 加权平均方差Weighted sum of square, 加权平方和Weighting coefficient, 权重系数Weighting method, 加权法W-estimation, W估计量W-estimation of location, 位置W估计量Width, 宽度Wilcoxon paired test, 威斯康星配对法/配对符号秩和检验Wild point, 野点/狂点Wild value, 野值/狂值Winsorized mean, 缩尾均值Withdraw, 失访Youden's index, 尤登指数Z test, Z检验Zero correlation, 零相关Z-transformation, Z变换。

A Microscopic Convexity Principle for Nonlinear Partial Differential Equations

In general, ∇2 u may not be separated from the rest of the arguments. The similar situation also arises in the case of geometric ﬂow for hypersurfaces. In this paper, we study the microscopic convexity property for equation in the form of (1.2) and related geometric nonlinear equations of elliptic and parabolic type. The core for the microscopic convexity principle is to establish a strong maximum principle for appropriate constructed functions. The key is to control ceratin gradient terms of the symmetric tensor to show that they are vanishing at the end. There have been signiﬁcant development of analysis techniques in literature [7, 27, 17, 16, 18, 8] for this purpose, in particular the method introduced in [8]. They are very eﬀective to control quadratic terms of the gradient of the symmetric tensor. For equation (1.2), linear terms of such gradient of symmetric tensor will emerge. All the previous methods break down for these terms. The main contribution of this paper is the introduction of new analytic techniques to handle these linear terms. This type new analysis involves quotients of elementary symmetric functions near the null set of det(uij ), even though equation (1.2) itself may not be symmetric with respect to the curvature tensor. The analysis is delicate and has to be balanced as both symmetric functions in the quotient will vanish at the null set. This is a novel feature of this paper, it is another indication that these quotient functions are naturally embedded with fully nonlinear equations. In a diﬀerent context, the importance of quotient functions has been demonstrated in the beautiful work of Huisken-Sinestrari [22]. We believe the techniques in this paper will ﬁnd way to solve other problems in geometric analysis. To illustrate our main results, we ﬁrst consider the equations in ﬂat domain. Let Ω is a domain in Rn , S n denotes the space of real symmetric n × n matrices, and F = F (r, p, u, x) is a given function in S n × Rn × R × Ω and elliptic in the sense that (1.3) ( ∂F (∇2 u, ∇u, u, x)) > 0, ∂rαβ ∀x ∈ Ω.

Advances in Prospect Theory-Cumulative Representation of Uncertainty

Letting πi = πi+ if i ≥ 0, and πi = πi− if i ≤ 0, (1) becomes V ( f ) = ∑πiv(xi )
i =−m n
(2)
and
Note that • •
∑π
i =0
n
+ i
=1
i =− m
∑π
0
− i
= 1.
If W is additive and hence a probability measure then πi is simply the probability of Ai. If f = ( xi , Ai ) is given by a probability distribution p(Ai) = pi , then it can be viewed as a probabilistic or risky prospect (xi, pi). then the decision weights are defined by:
+ πn = w + ( pn ), − − π− m = w ( p−m )
2
πi+ = w+ ( pi + ......+ pn ) − w+ ( pi+1 + ......+ pn ),0 ≤ i ≤ n −1,
where w+ and w- are strictly increasing functions from [0,1] into [0,1] with w+(0) = w-(0), and w+(1) = w-(1). Ex: Roll a dice. If x is even, you receive $x, if x is odd you pay $x. f= (-5, -3, -1; 2, 4, 6), f + = (0,1/2 ; 2,1/6 ; 4,1/6 ; 6,1/6), f - = (-5,1/6; -3,1/6; -1,1/6; 0,1/2). Then, V ( f ) = V ( f + ) +V ( f − )

斯威齐模型概念

斯威齐模型概念解析1. 概念定义斯威齐模型（Pareto distribution），又称为洛伦兹曲线（Lorenz curve），是一种描述不平等分布的概率分布模型。

该模型是由意大利经济学家维尔弗雷多·斯威齐（Vilfredo Pareto）于1896年提出的，用于描述经济和社会领域中收入、财富、权力等指标的分布情况。

斯威齐模型的数学表达为：f(x)=k x k+1其中，x是一个正数，k是一个正参数，f(x)是x的概率密度函数。

2. 关键概念2.1 洛伦兹曲线洛伦兹曲线是斯威齐模型的可视化表示方法，用于展示不平等分布情况。

在洛伦兹曲线上，横坐标表示累积人口或累积收入比例（从小到大排列），纵坐标表示相应累积总收入比例。

通过绘制洛伦兹曲线可以直观地看出不同群体之间收入或财富的分布情况。

2.2 基尼系数基尼系数是衡量不平等程度的指标，通常与洛伦兹曲线一起使用。

基尼系数的取值范围为0到1，数值越大表示不平等程度越高。

基尼系数通过计算洛伦兹曲线下方面积与对角线下方面积的比值得到，公式如下：G=A A+B其中，A表示洛伦兹曲线下方面积，B表示对角线下方面积。

2.3 斯威齐指数斯威齐指数是斯威齐模型中的一个重要参数，用于描述分布的形状。

斯威齐指数越大，说明不平等程度越高。

斯威齐指数可以通过对斯威齐模型进行参数估计得到。

2.4 少部分财富或收入集中现象斯威齐模型描述了财富或收入在社会中的不平等分布情况。

根据该模型，少部分人拥有了大部分的财富或收入，而大多数人只能分享剩余的少部分。

这种现象被称为少部分财富或收入集中现象，也是斯威齐模型的核心概念之一。

3. 重要性3.1 揭示社会不平等问题斯威齐模型能够客观地描述经济和社会领域中财富、收入、权力等指标的分布情况。

通过洛伦兹曲线和基尼系数，可以直观地展示出不同群体之间的不平等程度，揭示出社会中存在的不公平现象。

3.2 政策制定依据斯威齐模型为政策制定提供了重要依据。

《孟德尔随机化研究指南》中英文版

《孟德尔随机化研究指南》中英文版全文共3篇示例，供读者参考篇1Randomized research is a vital component of scientific studies, allowing researchers to investigate causal relationships between variables and make accurate inferences about the effects of interventions. One of the most renowned guides for conducting randomized research is the "Mendel Randomization Research Guide," which provides detailed instructions and best practices for designing and implementing randomized controlled trials.The Mendel Randomization Research Guide offers comprehensive guidance on all aspects of randomized research, from study design and sample selection to data analysis and interpretation of results. It emphasizes the importance of randomization in reducing bias and confounding effects, thus ensuring the validity and reliability of study findings. With clear and practical recommendations, researchers can feel confident in the quality and rigor of their randomized research studies.The guide highlights the key principles of randomization, such as the use of random assignment to treatment groups, blinding of participants and researchers, and intent-to-treat analysis. It also discusses strategies for achieving balance in sample characteristics and minimizing the risk of selection bias. By following these principles and guidelines, researchers can maximize the internal validity of their studies and draw accurate conclusions about the causal effects of interventions.In addition to the technical aspects of randomized research, the Mendel Randomization Research Guide also addresses ethical considerations and practical challenges that researchers may face. It emphasizes the importance of obtaining informed consent from participants, protecting their privacy and confidentiality, and ensuring the safety and well-being of study subjects. The guide also discusses strategies for overcoming common obstacles in randomized research, such as recruitment and retention issues, data collection problems, and statistical challenges.Overall, the Mendel Randomization Research Guide is a valuable resource for researchers looking to improve the quality and validity of their randomized research studies. By following its recommendations and best practices, researchers can conductstudies that produce reliable and actionable findings, advancing scientific knowledge and contributing to evidence-based decision making in various fields.篇2Mendel Randomization Study GuideIntroductionMendel Randomization Study Guide is a comprehensive and informative resource for researchers and students interested in the field of Mendel randomization. This guide provides anin-depth overview of the principles and methods of Mendel randomization, as well as practical advice on how to design and conduct Mendel randomization studies.The guide is divided into several sections, each covering a different aspect of Mendel randomization. The first section provides a brief introduction to the history and background of Mendel randomization, tracing its origins to the work of Gregor Mendel, the father of modern genetics. It also discusses the theoretical foundations of Mendel randomization and its potential applications in causal inference.The second section of the guide focuses on the methods and techniques used in Mendel randomization studies. This includesa detailed explanation of how Mendel randomization works, as well as guidelines on how to select instrumental variables and control for potential confounders. It also discusses the strengths and limitations of Mendel randomization, and provides practical tips on how to deal with common challenges in Mendel randomization studies.The third section of the guide is dedicated to practical considerations in Mendel randomization studies. This includes advice on how to design a Mendel randomization study, collect and analyze data, and interpret the results. It also provides recommendations on how to report Mendel randomization studies and publish research findings in scientific journals.In addition, the guide includes a glossary of key terms and concepts related to Mendel randomization, as well as a list of recommended readings for further study. It also includes case studies and examples of Mendel randomization studies in practice, to illustrate the principles and techniques discussed in the guide.ConclusionIn conclusion, the Mendel Randomization Study Guide is a valuable resource for researchers and students interested in Mendel randomization. It provides a comprehensive overview ofthe principles and methods of Mendel randomization, as well as practical advice on how to design and conduct Mendel randomization studies. Whether you are new to Mendel randomization or looking to deepen your understanding of the field, this guide is an essential reference for anyone interested in causal inference and genetic epidemiology.篇3"Guide to Mendelian Randomization Studies" English VersionIntroductionMendelian randomization (MR) is a method that uses genetic variants to investigate the causal relationship between an exposure and an outcome. It is a powerful tool that can help researchers to better understand the underlying mechanisms of complex traits and diseases. The "Guide to Mendelian Randomization Studies" provides a comprehensive overview of MR studies and offers practical guidance on how to design and carry out these studies effectively.Chapter 1: Introduction to Mendelian RandomizationThis chapter provides an overview of the principles of Mendelian randomization, including the assumptions andlimitations of the method. It explains how genetic variants can be used as instrumental variables to estimate the causal effect of an exposure on an outcome, and outlines the key steps involved in conducting an MR study.Chapter 2: Choosing Genetic InstrumentsIn this chapter, the guide discusses the criteria for selecting appropriate genetic instruments for Mendelian randomization. It covers issues such as the relevance of the genetic variant to the exposure of interest, the strength of the instrument, and the potential for pleiotropy. The chapter also provides practical tips on how to search for suitable genetic variants in public databases.Chapter 3: Data Sources and ValidationThis chapter highlights the importance of using high-quality data sources for Mendelian randomization studies. It discusses the different types of data that can be used, such asgenome-wide association studies and biobanks, and offers advice on how to validate genetic instruments and ensure the reliability of the data.Chapter 4: Statistical MethodsIn this chapter, the guide explains the various statistical methods that can be used to analyze Mendelian randomization data. It covers techniques such as inverse variance weighting, MR-Egger regression, and bi-directional Mendelian randomization, and provides guidance on how to choose the most appropriate method for a given study.Chapter 5: Interpretation and ReportingThe final chapter of the guide focuses on the interpretation and reporting of Mendelian randomization results. It discusses how to assess the strength of causal inference, consider potential biases, and communicate findings effectively in research papers and presentations.ConclusionThe "Guide to Mendelian Randomization Studies" is a valuable resource for researchers who are interested in using genetic data to investigate causal relationships in epidemiological studies. By following the guidance provided in the guide, researchers can enhance the rigor and validity of their Mendelian randomization studies and contribute to a better understanding of the determinants of complex traits and diseases.。

A solvent extraction process for the preparation of ultrahigh purity scandium oxide

1. Introduction It is well known that scandium is a rare and very expensive metal. A number of new applications for scandium have been developed in recent years, including laser crystals
48
P. Zhang et al. / Hydrometallurgy 47 (1997147-56
and coatings, cathode materials for color cathode-ray tubes, advanced ceramics, nuclear materials and catalysts for automobiles [ll. In addition, attention has been paid to the application of scandium in the optical industry [2]. The application of scandium in high temperature superconducting materials is also under investations have heightened the demand for scandium in both quantity and quality, it is difficult to recover scandium because it is associated in trace amounts (from 1O-3 to 10p4%) with natural minerals such as wolframite, titaniferous magnetites, tinstone @no,>, bauxite and uranium ore. Scandium is generally obtained as a by-product in the form of oxide from the processing of these ores [ll. A literature survey revealed that little data is available with respect to the purification of scandium oxide. Herchenroeder et al. [3,4] investigated the process for preparing kilogram quantities of scandium oxide of ultrahigh purity by ion exchange chromatography at 93°C. Guo et al. [5] developed a technique for producing 99.99% pure scandium oxide from starting materials containing about 70% scandium oxide by extraction chromatography with more than 90% recovery. Although the process [5] has a number of advantages, its usefulness as a large-scale production method might be restricted owing to the low scandium concentration in the stock solution used and the long operating period. In previous work [6], the authors have also described an extraction chromatography process using columns containing tributyl phosphate (TBP) supported on polystyrene-divinylbenzene copolymer from hydrochloric acid system by which scandium oxide could be purified from approximately 99% to 99.99% purity with an over 92% recovery. So far, however, no information regarding preparation of ultrahigh purity scandium oxide by solvent extraction has been found. For this reason, the authors investigated in the current work a process for the purification of scandium oxide by means of two-step solvent extraction. Using this process, scandium oxide of ultrahigh purity can be prepared with a recovery greater than 93% from the starting materials containing about 99% scandium oxide.

SPSS词汇

SPSS词汇(中英文对照L-Z)Lack of fit, 失拟Ladder of powers, 幂阶梯Lag, 滞后Large sample, 大样本Large sample test, 大样本检验Latin square, 拉丁方Latin square design, 拉丁方设计Leakage, 泄漏Least favorable configuration, 最不利构形Least favorable distribution, 最不利分布Least significant difference, 最小显著差法Least square method, 最小二乘法Least-absolute-residuals estimates, 最小绝对残差估计Least-absolute-residuals fit, 最小绝对残差拟合Least-absolute-residuals line, 最小绝对残差线Legend, 图例L-estimator, L估计量L-estimator of location, 位置L估计量L-estimator of scale, 尺度L估计量Level, 水平Life expectance, 预期期望寿命Life table, 寿命表Life table method, 生命表法Light-tailed distribution, 轻尾分布Likelihood function, 似然函数Likelihood ratio, 似然比line graph, 线图Linear correlation, 直线相关Linear equation, 线性方程Linear programming, 线性规划Linear regression, 直线回归Linear Regression, 线性回归Linear trend, 线性趋势Loading, 载荷Location and scale equivariance, 位置尺度同变性Location equivariance, 位置同变性Location invariance, 位置不变性Location scale family, 位置尺度族Log rank test, 时序检验Logarithmic curve, 对数曲线Logarithmic normal distribution, 对数正态分布Logarithmic scale, 对数尺度Logarithmic transformation, 对数变换Logic check, 逻辑检查Logistic distribution, 逻辑斯特分布Logit transformation, Logit转换LOGLINEAR, 多维列联表通用模型Lognormal distribution, 对数正态分布Lost function, 损失函数Low correlation, 低度相关Lower limit, 下限Lowest-attained variance, 最小可达方差LSD, 最小显著差法的简称Lurking variable, 潜在变量Main effect, 主效应Major heading, 主辞标目Marginal density function, 边缘密度函数Marginal probability, 边缘概率Marginal probability distribution, 边缘概率分布Matched data, 配对资料Matched distribution, 匹配过分布Matching of distribution, 分布的匹配Matching of transformation, 变换的匹配Mathematical expectation, 数学期望Mathematical model, 数学模型Maximum L-estimator, 极大极小L 估计量Maximum likelihood method, 最大似然法Mean, 均数Mean squares between groups, 组间均方Mean squares within group, 组内均方Means (Compare means), 均值-均值比较Median, 中位数Median effective dose, 半数效量Median lethal dose, 半数致死量Median polish, 中位数平滑Median test, 中位数检验Minimal sufficient statistic, 最小充分统计量Minimum distance estimation, 最小距离估计Minimum effective dose, 最小有效量Minimum lethal dose, 最小致死量Minimum variance estimator, 最小方差估计量MINITAB, 统计软件包Minor heading, 宾词标目Missing data, 缺失值Model specification, 模型的确定Modeling Statistics , 模型统计Models for outliers, 离群值模型Modifying the model, 模型的修正Modulus of continuity, 连续性模Morbidity, 发病率Most favorable configuration, 最有利构形Multidimensional Scaling (ASCAL), 多维尺度/多维标度Multinomial Logistic Regression , 多项逻辑斯蒂回归Multiple comparison, 多重比较Multiple correlation , 复相关Multiple covariance, 多元协方差Multiple linear regression, 多元线性回归Multiple response , 多重选项Multiple solutions, 多解Multiplication theorem, 乘法定理Multiresponse, 多元响应Multi-stage sampling, 多阶段抽样Multivariate T distribution, 多元T分布Mutual exclusive, 互不相容Mutual independence, 互相独立Natural boundary, 自然边界Natural dead, 自然死亡Natural zero, 自然零Negative correlation, 负相关Negative linear correlation, 负线性相关Negatively skewed, 负偏Newman-Keuls method, q检验NK method, q检验No statistical significance, 无统计意义Nominal variable, 名义变量Nonconstancy of variability, 变异的非定常性Nonlinear regression, 非线性相关Nonparametric statistics, 非参数统计Nonparametric test, 非参数检验Nonparametric tests, 非参数检验Normal deviate, 正态离差Normal distribution, 正态分布Normal equation, 正规方程组Normal ranges, 正常范围Normal value, 正常值Nuisance parameter, 多余参数/讨厌参数Null hypothesis, 无效假设Numerical variable, 数值变量Objective function, 目标函数Observation unit, 观察单位Observed value, 观察值One sided test, 单侧检验One-way analysis of variance, 单因素方差分析Oneway ANOVA , 单因素方差分析Open sequential trial, 开放型序贯设计Optrim, 优切尾Optrim efficiency, 优切尾效率Order statistics, 顺序统计量Ordered categories, 有序分类Ordinal logistic regression , 序数逻辑斯蒂回归Ordinal variable, 有序变量Orthogonal basis, 正交基Orthogonal design, 正交试验设计Orthogonality conditions, 正交条件ORTHOPLAN, 正交设计Outlier cutoffs, 离群值截断点Outliers, 极端值OVERALS , 多组变量的非线性正规相关Overshoot, 迭代过度Paired design, 配对设计Paired sample, 配对样本Pairwise slopes, 成对斜率Parabola, 抛物线Parallel tests, 平行试验Parameter, 参数Parametric statistics, 参数统计Parametric test, 参数检验Partial correlation, 偏相关Partial regression, 偏回归Partial sorting, 偏排序Partials residuals, 偏残差Pattern, 模式Pearson curves, 皮尔逊曲线Peeling, 退层Percent bar graph, 百分条形图Percentage, 百分比Percentile, 百分位数Percentile curves, 百分位曲线Periodicity, 周期性Permutation, 排列P-estimator, P估计量Pie graph, 饼图Pitman estimator, 皮特曼估计量Pivot, 枢轴量Planar, 平坦Planar assumption, 平面的假设PLANCARDS, 生成试验的计划卡Point estimation, 点估计Poisson distribution, 泊松分布Polishing, 平滑Polled standard deviation, 合并标准差Polled variance, 合并方差Polygon, 多边图Polynomial, 多项式Polynomial curve, 多项式曲线Population, 总体Population attributable risk, 人群归因危险度Positive correlation, 正相关Positively skewed, 正偏Posterior distribution, 后验分布Power of a test, 检验效能Precision, 精密度Predicted value, 预测值Preliminary analysis, 预备性分析Principal component analysis, 主成分分析Prior distribution, 先验分布Prior probability, 先验概率Probabilistic model, 概率模型probability, 概率Probability density, 概率密度Product moment, 乘积矩/协方差Profile trace, 截面迹图Proportion, 比/构成比Proportion allocation in stratified random sampling, 按比例分层随机抽样Proportionate, 成比例Proportionate sub-class numbers, 成比例次级组含量Prospective study, 前瞻性调查Proximities, 亲近性Pseudo F test, 近似F检验Pseudo model, 近似模型Pseudosigma, 伪标准差Purposive sampling, 有目的抽样QR decomposition, QR分解Quadratic approximation, 二次近似Qualitative classification, 属性分类Qualitative method, 定性方法Quantile-quantile plot, 分位数-分位数图/Q-Q图Quantitative analysis, 定量分析Quartile, 四分位数Quick Cluster, 快速聚类Radix sort, 基数排序Random allocation, 随机化分组Random blocks design, 随机区组设计Random event, 随机事件Randomization, 随机化Range, 极差/全距Rank correlation, 等级相关Rank sum test, 秩和检验Rank test, 秩检验Ranked data, 等级资料Rate, 比率Ratio, 比例Raw data, 原始资料Raw residual, 原始残差Rayleigh's test, 雷氏检验Rayleigh's Z, 雷氏Z值Reciprocal, 倒数Reciprocal transformation, 倒数变换Recording, 记录Redescending estimators, 回降估计量Reducing dimensions, 降维Re-expression, 重新表达Reference set, 标准组Region of acceptance, 接受域Regression coefficient, 回归系数Regression sum of square, 回归平方和Rejection point, 拒绝点Relative dispersion, 相对离散度Relative number, 相对数Reliability, 可靠性Reparametrization, 重新设置参数Replication, 重复Report Summaries, 报告摘要Residual sum of square, 剩余平方和Resistance, 耐抗性Resistant line, 耐抗线Resistant technique, 耐抗技术R-estimator of location, 位置R估计量R-estimator of scale, 尺度R估计量Retrospective study, 回顾性调查Ridge trace, 岭迹Ridit analysis, Ridit分析Rotation, 旋转Rounding, 舍入Row, 行Row effects, 行效应Row factor, 行因素RXC table, RXC表Sample, 样本Sample regression coefficient, 样本回归系数Sample size, 样本量Sample standard deviation, 样本标准差Sampling error, 抽样误差SAS(Statistical analysis system ), SAS统计软件包Scale, 尺度/量表Scatter diagram, 散点图Schematic plot, 示意图/简图Score test, 计分检验Screening, 筛检SEASON, 季节分析Second derivative, 二阶导数Second principal component, 第二主成分SEM (Structural equation modeling), 结构化方程模型Semi-logarithmic graph, 半对数图Semi-logarithmic paper, 半对数格纸Sensitivity curve, 敏感度曲线Sequential analysis, 贯序分析Sequential data set, 顺序数据集Sequential design, 贯序设计Sequential method, 贯序法Sequential test, 贯序检验法Serial tests, 系列试验Short-cut method, 简捷法Sigmoid curve, S形曲线Sign function, 正负号函数Sign test, 符号检验Signed rank, 符号秩Significance test, 显著性检验Significant figure, 有效数字Simple cluster sampling, 简单整群抽样Simple correlation, 简单相关Simple random sampling, 简单随机抽样Simple regression, 简单回归simple table, 简单表Sine estimator, 正弦估计量Single-valued estimate, 单值估计Singular matrix, 奇异矩阵Skewed distribution, 偏斜分布Skewness, 偏度Slash distribution, 斜线分布Slope, 斜率Smirnov test, 斯米尔诺夫检验Source of variation, 变异来源Spearman rank correlation, 斯皮尔曼等级相关Specific factor, 特殊因子Specific factor variance, 特殊因子方差Spectra , 频谱Spherical distribution, 球型正态分布Spread, 展布SPSS(Statistical package for the social science), SPSS统计软件包Spurious correlation, 假性相关Square root transformation, 平方根变换Stabilizing variance, 稳定方差Standard deviation, 标准差Standard error, 标准误Standard error of difference, 差别的标准误Standard error of estimate, 标准估计误差Standard error of rate, 率的标准误Standard normal distribution, 标准正态分布Standardization, 标准化Starting value, 起始值Statistic, 统计量Statistical control, 统计控制Statistical graph, 统计图Statistical inference, 统计推断Statistical table, 统计表Steepest descent, 最速下降法Stem and leaf display, 茎叶图Step factor, 步长因子Stepwise regression, 逐步回归Storage, 存Strata, 层（复数）Stratified sampling, 分层抽样Strength, 强度Stringency, 严密性Structural relationship, 结构关系Studentized residual, 学生化残差/t化残差Sub-class numbers, 次级组含量Subdividing, 分割Sufficient statistic, 充分统计量Sum of products, 积和Sum of squares, 离差平方和Sum of squares about regression, 回归平方和Sum of squares between groups, 组间平方和Sum of squares of partial regression, 偏回归平方和Sure event, 必然事件Survey, 调查Survival, 生存分析Survival rate, 生存率Suspended root gram, 悬吊根图Symmetry, 对称Systematic error, 系统误差Systematic sampling, 系统抽样Tags, 标签Tail area, 尾部面积Tail length, 尾长Tail weight, 尾重Tangent line, 切线Target distribution, 目标分布Taylor series, 泰勒级数Tendency of dispersion, 离散趋势Testing of hypotheses, 假设检验Theoretical frequency, 理论频数Time series, 时间序列Tolerance interval, 容忍区间Tolerance lower limit, 容忍下限Tolerance upper limit, 容忍上限Torsion, 扰率Total sum of square, 总平方和Total variation, 总变异Transformation, 转换Treatment, 处理Trend, 趋势Trend of percentage, 百分比趋势Trial, 试验Trial and error method, 试错法Tuning constant, 细调常数Two sided test, 双向检验Two-stage least squares, 二阶最小平方Two-stage sampling, 二阶段抽样Two-tailed test, 双侧检验Two-way analysis of variance, 双因素方差分析Two-way table, 双向表Type I error, 一类错误/α错误Type II error, 二类错误/β错误UMVU, 方差一致最小无偏估计简称Unbiased estimate, 无偏估计Unconstrained nonlinear regression , 无约束非线性回归Unequal subclass number, 不等次级组含量Ungrouped data, 不分组资料Uniform coordinate, 均匀坐标Uniform distribution, 均匀分布Uniformly minimum variance unbiased estimate, 方差一致最小无偏估计Unit, 单元Unordered categories, 无序分类Upper limit, 上限Upward rank, 升秩Vague concept, 模糊概念Validity, 有效性VARCOMP (Variance component estimation), 方差元素估计Variability, 变异性Variable, 变量Variance, 方差Variation, 变异Varimax orthogonal rotation, 方差最大正交旋转Volume of distribution, 容积W test, W检验Weibull distribution, 威布尔分布Weight, 权数Weighted Chi-square test, 加权卡方检验/Cochran检验Weighted linear regression method, 加权直线回归Weighted mean, 加权平均数Weighted mean square, 加权平均方差Weighted sum of square, 加权平方和Weighting coefficient, 权重系数Weighting method, 加权法W-estimation, W估计量W-estimation of location, 位置W估计量Width, 宽度Wilcoxon paired test, 威斯康星配对法/配对符号秩和检验Wild point, 野点/狂点Wild value, 野值/狂值Winsorized mean, 缩尾均值Withdraw, 失访Youden's index, 尤登指数Z test, Z检验Zero correlation, 零相关Z-transformation, Z变换。

chauvenet肖维纳准则

chauvenet肖维纳准则
Chauvenet肖维纳准则是数据分析和实验设计中的一项经典原则。

该原则可以用于判断和排除异常值。

首先，我们需要了解什么是异常值。

在统计学中，异常值是指与其它观察值明显不同的数值。

这种情况通常是由于实验设计或实验记录中的错误、测量设备故障或未知因素导致的。

异常值对于数据分析可能会产生影响，影响总体结论的可靠性。

因此，排除异常值是非常重要的。

Chauvenet肖维纳准则提供了一个判断异常值的标准。

具体步骤如下：
步骤1：计算样本的平均值和标准偏差。

步骤2：计算每个观察值与平均值的偏差，并将它们除以标准偏差。

这将得到一个称为“偏差比”的值。

步骤3：使用正态分布的标准化表，找到一个使得小于它的值出现的概率为1/n（其中n是样本大小）的值。

这个值通常称为Chauvenet准则值。

步骤4：比较每个观察值对应的偏差比和Chauvenet准则值。

如果某个观察值的偏差比大于Chauvenet准则值，就将它视为异常值。

虽然Chauvenet肖维纳准则提供了一个简单的方法来检测异常值，但它也存在一些局限性。

首先，它假设数据服从正态分布。

如果数据不符合正态分布，则这个方法就不适用。

其次，Chauvenet准则值的选择也可能会影响结果。

不同的选择可能会导致不同的结果。

总之，Chauvenet肖维纳准则是一种常用的检测和排除异常值的方法。

在使用时，需要注意其适用的前提条件和选择Chauvenet准则值的不确定性。

医学科研方法效应指标名词解释

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The divergence of fluctuations for the shape on first passage percolation

a r X i v :m a t h /0501095v 1 [m a t h .P R ] 6 J a n 2005The divergence of ﬂuctuations for the shape on ﬁrst passage percolation Yu Zhang ∗,Department of Mathematics,University of Colorado Abstract Consider the ﬁrst passage percolation model on Z d for d ≥2.In this model we assign independently to each edge the value zero with probability p and the value one with probability 1−p .We denote by T (0,v )the passage time from the origin to v for v ∈R d and B (t )={v ∈R d :T (0,v )≤t }and G (t )={v ∈R d :ET (0,v )≤t }.It is well known that if p 0tB d (1−ǫ)⊂B (t )⊂tB d (1+ǫ)and G (t )(1−ǫ)⊂B (t )⊂G (t )(1+ǫ)eventually w.p.1.We denote the ﬂuctuations of B (t )from tB d and G (t )by F (B (t ),tB d )=inf l :tB d 1−l t F (B (t ),G (t ))=inf l :G (t ) 1−l t .The means of the ﬂuctuations E [F (B (t ),tB d ]and E [F (B (t ),G (t ))]have been conjec-tured ranging from divergence to non-divergence for large d ≥2by physicists.In this paper,we show that for all d ≥2with a high probability,the ﬂuctuations F (B (t ),G (t ))and F (B (t ),tB d )diverge with a rate of at least C log t for some constant C .The proof of this argument depends on the linearity between the number of pivotal edges of all minimizing paths and the paths themselves.This linearity is also indepen-dently interesting.Key words and phrases:ﬁrst passage percolation,shape,ﬂuctuations.AMS classiﬁcation:60K 35.1Introduction of the model and results.We consider Z d,d≥2,as a graph with edges connecting each pair of vertices x=(x1,···,x d)and y=(y1,···,y d)with d(x,y)=1,where d(x,y)is the distance between x and y.For anytwo vertex sets A,B⊂Z d,the distance between A and B is also deﬁned byd(A,B)=min{d(u,v):u∈A and v∈B}.(1.0) We assign independently to each edge the value zero with a probability p or one with prob-ability1−p.More formally,we consider the following probability space.As sample space,we takeΩ= e∈Z d{0,1},points of which are represented as conﬁgurations.Let P=P p be the corresponding product measure onΩ.The expectation with respect to P is denotedby E=E p.For any two vertices u and v,a pathγfrom u to v is an alternating sequence(v0,e1,v1,...,e n,v n)of vertices v i and edges e i in Z d with v0=u and v n=v.Given a pathγ,we deﬁne the passage time ofγasT(γ)=ni=1t(e i).(1.1)For any two sets A and B we deﬁne the passage time from A to B asT(A,B)=inf{T(γ):γis a path from some vertex of A to some vertex in B}, where the inﬁmum takes over all possibleﬁnite paths.A pathγfrom A to B with t(γ)= T(A,B)is called the route of T(A,B).If we focus on a special conﬁgurationω,we may write T(A,B)(ω)instead of T(A,B).When A={u}and B={v}are single vertex sets, T(u,v)is the passage time from u to v.We may extend the passage times over R d.If x and y are in R d,we deﬁne T(x,y)=T(x′,y′),where x′(resp.,y′)is the nearest neighbor of x(resp.,y)in Z d.Possible indetermination can be dropped by choosing an order on the vertices of Z d and taking the smallest nearest neighbor for this order.In particular,the point-point passage time wasﬁrst introduced by Hammersley and Welsh (1965)as follows:a m,n=inf{t(γ):γis a path from(m,···,0)to(n,···0)}.By Kingman’s subadditive argument we havelimn→∞1where p c=p c(d)is the critical probability for Bernoulli(bond)percolation on Z d and the non-random constantµp is called the time constant.Given a unit vector x∈R d,by the same argument in(1.2)1limn→∞1+xtχ(2)t ⊂B(t)⊂tB21+xtχ(2)t ⊂B(t)⊂G(t)are close to one or zero for large x or for small x≥0.In words,theﬂuctuations of B(t) diverge with a rate t1/3.There have been varying in discussions about the nature of the ﬂuctuations of B(t)for large d ranging from the possible independence ofχ(d)on d(Kar-dar and Zhang(1987))through the picture ofχ(d)decreasing with d but always remaining strictly positive(see Wolf and Kertesz(1987)and Kim and Kosterlitz(1989))to the possi-bility that for d above some d c,χ(d)=0and perhaps theﬂuctuations do not even diverge (see Natterman and Renz(1988),Haplin-Healy(1989)and Cook and Derrida(1990)).Mathematicians have also made signiﬁcant eﬀorts in this direction.Before we introduce mathematical estimates,let us give a precise deﬁnition of theﬂuctuation of B(t)from some set.For a connected setΓof R d containing the origin,letΓ+l={v∈R d:d(v,Γ)≤l}andΓ−l={v∈Γ:d(v,∂Γ)≥l}.Note thatΓ−l⊂ΓandΓ⊂Γ+l.Note also thatΓ−l might be empty even thoughΓis non-empty.We say B(t)has aﬂuctuation fromΓifF(B(t),Γ)=F(B(t)(ω),Γ)=inf{l:Γ−l⊂B(t)(ω)⊂Γ+l}.(1.10) If we setΓ=tB d for d=2,the conjecture in(1.8)is equivalent to ask ifF(B(t),tB2)≈t1/3with a high probability.When p≥p c(d),B d is unbounded and so is B(t).Also,when p=0,there are no ﬂuctuations so we require in this paper that0<P(t(e)=0)=p<p c(d).(1.11) The mathematical estimates for the upper bound of theﬂuctuation F(B(t),Γ),when Γ=tB d andΓ=G(t),are quite promising.Kesten(1993)and Alexander(1993,1996) showed that for p<p c(d)and all d≥2,there is a constant C such that√F(B(t),tB d)≤Ct)B d,where log denotes the natural logarithm.In this paper C and C i are always positive con-stants that may depend on p or d,but not t,and their values are not signiﬁcant and change from appearance to appearance.On the other hand,the estimates for the lower bound of theﬂuctuations are quite un-satisfactory.Under(1.11)it seems that the only result for all d≥2(see Kesten(1993)) isF(B(t),tB d)≥a non-zero constant eventually w.p.1.(1.13)For d=2,Piza and Newman(1995)showed thatF(B(t),tB d)≥t1/8and F(B(t),G(t))≥t1/8eventually w.p.1.(1.14) Clearly,one of most intriguing questions in thisﬁeld is to ask if theﬂuctuations of B(t) diverge as some statistical physicists believed to be true while others did not.In this paper we answer the conjecture aﬃrmatively to show that theﬂuctuations of B(t)always diverge for all d≥2.We can even tell that the divergence rate for B(t)is at least C log t.Theorem1.If0<p0and any deterministic setΓ,there exist positive constantsδ=δ(p,d)C1=C1(p,d)such thatP(F(B(t),Γ)≥δlog t)≥1−C1t−d+2−2δlog p.Remark 1.If we setΓ=tB d orΓ=G(t),together with(1.14),theﬂuctuations F(B(t),tB d)and F(B(t),G(t))are at leastδlog t with a large probability.Also,it follows from this probability estimate thatE(F(B(t),Γ))≥C log t(1.15) for a constant C=C(p,d)>0.Remark2.We are unable to estimate whether F(tB d,G(t))diverges even though we believe it does.The proof of Theorem1is constructive.In fact,if F(B(t),Γ)≤δlog t,then we can construct t d−1+2δlog p zero paths from∂B(t)toΓ+δlog t.For each such path,we can use the geometric property introduced in section2to show that the path contains a pivotal edge deﬁned in section3.Therefore,we can construct about t d−1−2δlog t pivotal edges.However, in section3,we can also show the number of pivotal edges is of order t.Therefore,for a suitableδwe cannot have as many pivotal edges as we constructed.The contradiction tells us that F(B(t),Γ)≥δlog t.With these estimates for pivotal edges in section3,we can also estimate the number of the total vertices in all routes.This estimate is independently interesting.For a connected setΓ⊂R d withα1tB d⊂Γ⊂α2tB d for some constants0<α1<1<α2,letRΓ= γt,whereγt is a route for T(0,∂Γ).Theorem2.If0<p0,there exists C(p,d,α1,α2)such thatE(|RΓ|)≤Ct,where|A|denotes the cardinality of A for some set A.Remark3.Kesten(1986)showed that there exists a route for T(0,Γ)with length Ct for some positive constant C.Theorem2gives a stronger result with the number of ver-tices in all routes for T(0,∂Γ)also in order t.For quite some time,the author believed that the routes of T(0,∂Γ)resembled a spiderweb centered at the origin so the number of the vertices in the routes should be of order t d.However,Theorem2negates this assumption.Remark4.Clearly,there might be many routes for the passage time T(0,∂Γ).As a consequence of Theorem2,each route contains at most Ct vertices.Speciﬁcally,let M x,t=sup{k:there exists a route of TΓ(0,∂Γ)containing k edges}.If0<p0,there exists a positive constant C=C(p,d)such thatE(M x,t)≤Ct.(1.16) Remark5.We may also consider Theorem2for a point-point passage time.LetR x,t= γn,whereγn is a route for T(0,xt)for a unit vector x.We may use the same argument of Theorem2to show if0<p0,there exists a positive constant C(p,d)such thatE(|R x,t|)≤Ct.(1.17) Remark6.The condition p>0in Theorem2is crucial.As p↓0,the constant C in Theorem2,(1.16)and(1.17)may go to inﬁnity.When p=0,all edges have to take value one.If we takeΓas the diamond shape with a diagonal length2t both in vertical and horizontal directions,it is easy to say that all edges inside the diamond belong to RΓso|RΓ|=O(t d).(1.18) This tells us that Theorem2will not work when p=0.2Geometric properties of B(t)In this section we would like to introduce a few geometric properties for B(t).We let B′(t)be the largest vertex set in B(t)∩Z d and G′(t)be the largest vertex set in G(t)∩Z d.Similarly, given a setΓ⊂R d,we also letΓ′be the largest vertex set inΓ.It is easy to see thatΓ′⊂Γ⊂{v+[−1/2,1/2]d:v∈Γ′}.(2.0)As we mentioned in the last section,both B(t)and G(t)areﬁnite as well as B′(t)and G′(t). We now show that B′(t)and G′(t)are also connected.Here a set A is said to be connected in Z d if any two vertices of A are connected by a path in A.Proposition1.B′(t)and G′(t)are connected.Proof.Since T(0,0)=0≤t,0∈B′(t).We pick a vertex v∈B′(t),so T(0,v)≤t. This tells us that there exists a pathγsuch thatT(γ)≤t.Therefore,for any u∈γ,T(0,u)≤t so u∈B′(t).This implies thatγ⊂B′(t),so we know B′(t)is connected.The same argument shows that G′(t)is connected.2Given aﬁnite setΓof Z d we may deﬁne its vertex boundary as follows.For each v∈Γ, v∈Γis said to be a boundary vertex ofΓif there exists u∈Γbut u is adjacent to v. We denote by∂Γall boundary vertices ofΓ.We also let∂oΓbe all vertices not inΓ,but adjacent to∂Γ.With these deﬁnitions,we have the following Proposition.Proposition2.For all v∈∂B′(t),T(0,v)=t and for all u∈∂o B′(t)T(0,u)=t+1.Proof.We pick v∈∂B′(t).By the deﬁnition of the boundary,v∈∂B′(t)so T(0,v)≤t. Now we show T(0,v)≥t for all v∈∂B′(t).If we suppose that T(0,v)<t for some v∈∂B′(t),then T(0,v)≤t−1,since T(0,v)is an integer.Note that t(e)only takes zero and one values so there exists u∈∂o B(t)and u is adjacent to v such that T(0,u)≤t.This tells us that u∈B′(t).But we know as we deﬁned that∂o B′(t)∩B(t)=∅.This contradiction tells us that T(0,v)≥t for all v∈∂B′(t).Now we will prove the second part of Proposition2.We pick a vertex u∈∂o B′(t).Since u is adjacent to v∈B′(t),T(0,u)≤1+T(0,v)≤1+t.On the other hand,any path from0to u has to pass through a vertex of∂B′(t)before reaching∂o B′(t).We denote the vertex by v.As we proved,T(0,v)=t.The passage time of the rest of the path from v to u has to be greater or equal to one,otherwise,u∈B′(t). Therefore,any path from0to u has a passage time larger or equal to t+1,that isT(0,u)≥t+1.Therefore,T(0,∂o B′(t))=t+1.2Given aﬁxed connected setκ=κt containing the origin,deﬁne the event{B′(t)=κ}={ω:B′(t)(ω)=κ}.Proposition3.The event that{B′(t)=κ}only depends on the zeros and ones of the edges ofκ∪∂oκ.Proposition2for d=2has been proven by Kesten and Zhang(1998).In fact,they gave a precise structure of B′(t).We may adapt their idea to prove Proposition2for d≥3by using the plaquette surface(see the deﬁnition in section12.4Grimmett(1999)).To avoid the complicated deﬁnition of the plaquette surface,we would rather give the following direct proof.Proof of Proposition3.LetκC denote the vertices of Z d\κand{ω(κ)}= edge inκ{0,1}and{ω(κC)}= edge inκC{0,1},where edges inκare the edges whose two vertices belong toκ∪∂oκand the edges inκC are the other edges.For eachω∈Ω,we may rewriteωasω=(ω(κ),ω(κC)).Suppose that Proposition3is not true,so the zeros and ones inω(κC)can aﬀect the event {B′(t)=κ}.In other words,there exist two diﬀerentω1,ω2∈Ωwithω1=(ω(κ),ω1(κC))andω2=(ω(κ),ω2(κC))such thatB′(t)(ω1)=κbut B′(t)(ω2)=κ.(2.4) From(2.4)there are two cases:(a)there exists u such that u∈B′(t)(ω2),but u∈κ.(b)there exists u such that u∈κ,but u∈B′(t)(ω2).If(a)holds,T(0,u)(ω2)≤t.(2.5) There exists a pathγfrom0to u such thatT(γ)(ω2)≤t.(2.6)Since u∈κ,any path from0to u has to pass through∂oκ=∂o B′(t)(ω1).Letγ′be the subpath ofγfrom0to∂oκ=∂o B′(t)(ω1).Then by Proposition2,T(γ′)(ω1)≥t+1.Note that the zeros and ones in bothω2=(ω(κ),ω2(κC)andω1=(ω(κ),ω1(κC)are the same sot+1≤T(γ′)(ω1)=T(γ′)(ω2)≤T(γ)(ω2).(2.7) By(2.6)and(2.7)(a)cannot hold.Now we assume that(b)holds.Since any path from0to u has to pass through ∂o B′(t)(ω2),by Proposition2,T(0,u)(ω2)≥t+1.(2.8) But since u∈κand B′(t)(ω1)=κ,there exists a pathγinside B′(t)(ω1)from0to u such thatT(γ)(ω1)≤t.Therefore,T(0,u)(ω2)≤T(γ)(ω2)≤t,(2.9) sinceγ⊂κand the zeros and ones in bothω2=(ω(κ),ω2(κC)andω1=(ω(κ),ω1(κC)are the same.The contradiction of(2.8)and(2.9)tells us that(b)cannot hold.23The linearity of a number of pivotal edgesIn this section we will discuss aﬁxed value0<p<p c and aﬁxed interval open I p⊂(0,p c) centered at p.First we show that the length of a route from the origin to∂B′(t)is of order t.Lemma1.For a small interval I p⊂(0,p c)centered at p,there exist positive constants α=α(I p,d),C1=C1(I p,d)and C2=C2(I p,d)such that for all t and all p′∈I p, P(∃a routeγfrom the origin to∂B′(t)with|γ|≥αt)≤C1exp(−C2t). Proof.By Theorem5.2and5.8in Kesten(1986)for all p′∈I p and for all t there exist C3=C3(I p,d)and C4=C4(I p,d)such thatP(2t/3B d⊂B(t))≤C3exp(−C4t)and P(B(t)⊂3t/2B d)≤C3exp(−C4t).(3.0) If we put these two inequalities from(3.0)together,we have for all p′∈I p and all t, P(t/2B d)⊂B′(t)⊂2tB d)for all large t)≥1−C3exp(−C4t).(3.1)On the event of{a routeγfrom the origin to∂B(t)with|γ|≥αt}∩{t/2B d)⊂B(t)⊂2tB d}we assume that there exists a routeγfrom the origin to some vertex u∈∂B′(t)witht/2≤d(0,u)≤2t and|γ|≥αtsuch thatt=T(0,∂B′(t))=T(γ)=T(0,u).Therefore,by(3.1)P(∃a routeγfrom the origin to∂B′(t)with T(γ)≤t,|γ|≥αt)≤ t/2≤d(0,u)≤2t P(∃a routeγfrom the origin to u with T(γ)≤t,|γ|≥αt)+C3exp(−C4t).Proposition5.8in Kesten(1986)tells us that there exist positive constantsβ(I p,d),C5= C5(I p,d)and C6=C6(I p,d)such that for all p′∈I p and tP(∃a self avoiding pathγfrom(0,0)to y contains n edges,but with T(γ)≤βn)≤C5exp(−C6n),(3.2) where n is the largest integer less than t.Together with these two observations if we take a suitableα=α(I p,d),we have for all p′∈I pP(∃a routeγfrom the origin to∂B′(t)with|γ|≥αt)≤(2t)d C5exp(−C6t). Lemma1follows.2To show Theorems we may concentrate to a“regular”set satisfying(3.1).Here we give the following precise deﬁnition.Given a deterministic connectedﬁnite setΓ=Γt⊂R d,Γis said to be regular if there exists t such that1/2tB d⊂Γ⊂2tB d.(3.3) For a regular setΓwe denote byTΓ(0,∂Γ)=inf{T(γ):γ⊂Γ′is a path from the origin to some vertex of∂Γ′}.Now we try to compute the derivative of ETΓ(0,∂Γ)in p for a regular setΓ.As a result,we haveETΓ(0,∂Γ)= i≥1P(TΓ((0,0),∂Γ)≥i).Note that t(e)takes zero with probability p and one with probability1−p.But we know that the standard Bernoulli random variable takes zero with probability1−p and one with probability p.Hence we have to deﬁne an increasing event(see the deﬁnition in section2of Grimmett(1999))in reverse.An event A is said to be increasing if1−I A(ω)≤1−I A(ω′)wheneverω≤ω′,where I A is the indicator of A.Note thatΓis aﬁnite set,so dETΓ(0,∂Γ)= i≥1dP(TΓ(0,∂Γ)≥i)dp=− i≥1 e∈ΓP({TΓ(0,∂Γ)≥i}(e)),(3.6)dpwhere{TΓ(0,∂Γ)≥i}(e)is the event that e is a pivotal for{TΓ(0,∂Γ)≥i}.In fact,given a conﬁgurationω,e is said to be a pivotal edge for{TΓ(0,∂Γ)(ω)≥i}if t(e)(ω)=1andTΓ(0,∂Γ)(ω′)=i−1where w′is the conﬁguration that t(b)(ω)=t(b)(ω′)for all edges b∈Γexcept e and t(e)(ω′)=0.The event{TΓ(0,∂Γ)≥i}(e)is equivalent to the event that there exists a route of TΓ(0,∂Γ)with passage time i passing through e and t(e)=1.With this observation, dETΓ(0,∂Γ)=E(KΓ).(3.7)dpNow we give an upper bound for E(KΓ)by giving an upper bound for−dETΓ(0,∂Γ)We show that the size of NΓcannot be more than Ct for some constant C.Lemma2.For a regular setΓand the interval I p,there exist positive constants C i= C i(I p,d)(i=1,2,3)such that for all p′∈I p and tP(NΓ≥C1t)≤C2exp(−C3t).Proof.We follow the proof of Theorem8.2in Smythe and Wierman(1979).Letω+r denote the time state of the lattice obtained by adding the r to t(e)for each edge e.It follows from the deﬁnitions of the passage time and NΓTΓ(0,∂Γ)(ω+r)≤TΓ(0,∂Γ)(ω)+rNΓ(ω).(3.8) If we take a negative r in(3.8),we haveNΓ(ω)≤TΓ(0,∂Γ)(ω+r)−TΓ(0,∂Γ)r≤−T(L)µr.(3.10)If we can show that for some r<0,there exist constants C4=C4(I p,d)and C5=C5(I p,d) such that for all p′∈I p and all tP(TΓ(0,∂Γ)(ω+r)≤0)≤C4exp(−C5t),(3.11) then by(3.9)and(3.10),Lemma2holds.Therefore,to show Lemma2,it remains to show (3.11).Note thatΓis aﬁnite connected set so for eachωthere exists x=x(ω)∈∂Γsuch thatTΓ(0,∂Γ)(ω+r)=TΓ(0,x)(ω+r)≥T(0,x)(ω+r).Since x∈∂ΓandΓis regular,thent/2≤d(0,x)≤2t.We haveP(TΓ(0,∂Γ)(ω+r)≤0)≤P(T(0,x(ω))(ω+r)≤0)≤ t/2≤d(0,y)≤2t P(T(0,y)(ω+r)≤0).(3.12)Therefore,by(3.2)and(3.12)we takeβand|r|small with r<0andβ>|r|>0to obtain for all p′∈I pt/2≤d(0,y)≤2t P(T(0,y)(ω+r)≤0)≤ t/2≤d(0,y)≤2t P(∃a self avoiding pathγfrom0to y contains n edges,but with T(γ)(ω)≤2βn)≤C6t d exp(−C7t),(3.13) where n is the largest integer less than t.Therefore,(3.11)follows from(3.13).2 With Lemma2we are ready to give an upper bound for−dETΓ(0,∂Γ)dp≤Ct.Proof.We assign s(e)≥t(e)either zero or one independently from edge to edge with probabilities p−h or1−(p−h)for a small number h>0,respectively.With this deﬁnition, P(s(e)=1,t(e)=0)=P(s(e)=1)−P(s(e)=1,t(e)=1)=P(s(e)=1)−P(t(e)=1)=1−(p−h)−(1−p)=h.(3.14) Letγt be a route for T tΓ(0,Γ)with time state t(e)and letγs be a route for T sΓ(0,Γ)with time state s(e).Here we pickγt such that|γt|=NΓ.For each edge e∈γt,if t(e)=1,then s(e)=1.If t(e)=0but s(e)=1,we just add one for this edge.Therefore,T sΓ(0,Γ)≤T(γt)+ e∈γt I(t(e)=0,s(e)=1).(3.15)Clearly,γt may not be unique,so we select a route from theseγt in a unique way.We still writeγt for the unique route without loss of generality.By(3.15)and this selectionET sΓ(0,Γ)≤ET(γt)+ β e∈βP(t(e)=0,s(e)=1,γt=β),(3.16)where theﬁrst sum in(3.16)takes over all possible pathsβfrom0to∂Γ′.Let us estimateβ e∈βP(t(e)=0,s(e)=1,γt=β).SinceΓis regular,the longest path from(0,0)to∂Γ′is less than(2t)d.By Lemma2,there exist C1=C1(I p,d),C2(I p,d)and C3(I p,d)such thatβ e∈βP(t(e)=0,s(e)=1,γt=β)≤ |β|≤C1t e∈βP(t(e)=0,s(e)=1,γt=β)+C2t d exp(−C3t).(3.17)Note that the value of s(e)may depend on the value of t(e),but not the other values of t(b) for b=e,so by(3.14)P(t(e)=0,s(e)=1,γt=β)=P(s(e)=1|t(e)=0,γt=β)P(t(e)=0,γt=β)≤P(s(e)=1|t(e)=0)P(γt=β)=hp−1P(γt=β).(3.18) By(3.18)we have|β|≤C1 e∈βP(t(e)=0,s(e)=1,γt=β)≤ |β|≤C1t e∈βhp−1P(γt=β)≤C1htp−1.(3.19) By(3.17)and(3.19)there exists C4=C4(I p,d)such thatE(T sΓ(0,∂Γ))≤E(T tΓ(0,∂Γ)+C4th.(3.20) If we setf(p)=E(TΓ(0,∂Γ))for time state t(e)with P(t(e)=0)=p,then by(3.20)−d f(p)−h≤C4t.(3.21) Therefore,we have−dETΓ(0,∂Γ)dp≤C4t.(3.22). Therefore,Lemma3follows from(3.22).2Together with(3.7)and Lemmas3,we have the following proposition.Proposition4.If0<p3can be adapted directly.Given aﬁxed setΓ⊂R3deﬁned in section2,Γ′⊂Z3is the largest vertex set in Γ,whereΓ′⊂Γ⊂{v+[1/2,1/2]3:v∈Γ′}.(4.0) Suppose that there exists a deterministic setΓsuch thatF(B(t),Γ)≤δlog t.(4.1) (4.1)means thatΓ−δlog t⊂B(t)⊂Γ+δlog t,whereΓ+l={v∈R3:d(v,Γ)≤l}andΓ−l={v∈Γ:d(v,∂Γ)≥l}.Weﬁrst show that ifΓ+δlog t does not satisfy the regularity condition in(3.3),then the probability of the event in(4.1)is exponentially small.We assume thatΓ+δlog t⊂2tB d.(4.2)IftF(B(t),Γ)≤δlog t withδlog t<B d.(4.4)2To see(4.4),note that3tB(t)⊂'%&%'$S mt ¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡∂(Γ+δlog t )′∂B ′(t )Figure 1:The graphs:S mt ,∂B ′(t ),Γ+δlog t ,the cylinder T s i with the center at L s i ,pivotal edge e v i ,zigzag path γv i from v i to ∂(Γ+δlog t )′.Now we focus on Γ+δlog t satisfying (3.3).We need to show that under (4.1)there are of order t 2disjoint zero paths from ∂B (t )to Γ+δlog t .To accomplish this,let S mt denote a sphere with the center at the origin and a radius tm for small but positive number m .Then by (3.1)for a suitable m >0P (S mt ⊂B (t )⊂2tB d )≥1−C 1exp(−C 2t ).(4.9)Here we select the sphere S mt without a special purpose since the sphere is easy to describe.For each s ∈∂S mt ,let L s be the normal line passing though s ,that is the line orthogonal to the tangent plane of S mt at s .We denote the cylinder with center at L s by (see Fig.1)T s (M )={(x,y,z )∈R 3:d ((x,y,z ),L s )≤M }for some constant M >0.Now we work on the regular polyhedron with ct 2faces embedded on S mt ,where ct 2is an integer and c =c (m,M )is a small number such that the radius of each face of the regular polyhedron is larger than M .We denote the center of each face in the regular polyhedron by {s i }ct 2i =1.By this construction,we have at least ct 2disjoint cylinders {T s (M )}.We denote them by {T s i (M )}ct 2i =1.For each s i ,we may take M large such that there exists a path γs i ⊂Z d ∩T s i (M )from some vertex of Z 3in S mt to ∞.To see the existence of such a path if L s i is the ray going along the coordinate axis,we just use L s i as the path.If it is not,we can construct a zigzag path in Z d next to L s i from s i to ∞(see Figure 1).In fact,we may take M =2to keepour zigzag path inside T s i (M ).For simplicity,we use T s i to denote T s i (2).There might be many such zigzag paths,so we just select one in a unique manner.We denote by u i ∈Z d with d (u i ,s i )≤2the initial vertex in γs i .Since γs i is next to L s i ,for any point x on the ray L s i ,there is v in γs i with d (v,y )≤2.Furthermore,by a simple induction we conclude thatthe number of vertices from u i to v along γs i is less than 2d (s i ,x ).(4.10)(4.10)tells us that the length of γs i is linear to the length of L s i .Since γs i is from S mt to∂(Γ+δlog t )′,it has to come outside of B ′(t )from its inside.Let v i be the vertex in ∂o B ′(t )andγv i be the piece of γs i outside B ′(t )from v i to ∂(Γ+δlog t )′(see Figure 1).On F (B (t ),Γ)≤δlog tfor a regular Γ,we know B ′(t )⊂(Γ+δlog t )′.Therefore,by our construction (see Figure 1)γv i ⊂(Γ+δlog t )′.(4.11)Also,by our special construction in (4.10),we have|γv i |≤2δlog t.(4.12)When B ′(t )=κfor a ﬁxed vertex set κ,then γv i is a ﬁxed path from ∂o κto ∂(Γ+δlog t )′with a length less than 2δlog t .Therefore,on B ′(t )=κP (γv i is a zero path)≥p 2δlog t .(4.13)We say T s i is good if there exists such a zero path γv i .On B ′(t )=κ,let M (Γ,κ)be the number of such good cylinders T s i .By (4.13),we haveEM (Γ,κ)≥(ct 2)p 2δlog t =ct 2−2δlog p .(4.14)On B ′(t )=κ,note that the event that T s i is good depends on zeros and ones of the edges inside T s i ,but outside of ∂o κ.Note also that T s i and T s j are disjoint for i =j ,so by a standard Hoeﬀding inequality there exist C 1=C 1(p,d )and C 2=C 2(p,d )such thatP (M (Γ,κ)≤ct (2−2δlog p )/2)≤C 1exp(−C 2ct −2+2δlog p ).(4.15)We denote byD (Γ,κ)={M (Γ,κ)≥ct (2+2δlog p )/2}.Note that D (Γ,κ)only depends zeros and ones outside ∂o κ.(4.16)By Proposition 3and (4.16),{B ′(t )=κ}and D (Γ,κ)are independent.(4.17)By Proposition 2,any route from (0,0,0)to v i in B ′(t )∪∂o B ′(t )has a passage time t +1.We just pick one from these routes and denote it by γ(0,v i ).On F (B (t ),Γ)≤δlog t if T s i is good,there exists a zero path γv i from v i to ∂(Γ+δlog t )′.This implies that there exists a pathγ(0,∂Γ+δlog t )=γ(0,v i )∪γv ifrom (0,0,0)to ∂(Γ+δlog t )′with a passage time t +1and the path passes through the edgeadjacent v i between ∂B (t )and ∂o B (t ).On the other hand,note that any path from theorigin to ∂(Γ+δlog t )′has to pass through ∂o B ′(t )ﬁrst,so by Proposition 2it has to spend atleast passage time t +1.Therefore,if we denote by e v i the edge adjacent v i from ∂B (t )to ∂o B (t ),then the path γ(0,∂Γ+δlog t )with passage time T ((0,0,0),∂Γ+δlog t )passes through e v i and t (e v i )=1.By (4.11)and B ′(t )⊂(Γ+δlog t )′,the path γ(0,∂Γ+δlog t )has to stay inside (Γ+δlog t )′.These observations tell us that e v i is a pivotal edge for T Γ+δlog t((0,0),Γ+δlog t ).Therefore,on F (B (t ),Γ)≤δlog t if T s i is good,T s i contains at least one pivotal edge for T Γ+δlog t ((0,0),Γ+δlog t ).(4.18)With these preparations we now show Theorem 1.Proof of Theorem 1.If Γ+δlog t is not regular,1/2tB d ⊂Γ+δlog t or Γ+δlog t ⊂2tB d ,by (4.8)there are C 1=C (p,d )and C 2(p,d )such thatP p (F (B (t ),Γ)≤δlog t )≤C 1exp(−C 2t ).(4.19)Now we only need to focus on a regular Γ+δlog t .P p (F (B (t ),Γ)≤δlog t )= ΓP (F (B (t ),Γ)≤δlog t,B ′(t )=κ),(4.20)where the sum takes over all possible sets κ.For each ﬁxed κ,by (4.17)and (4.15)there exist C 3=C 3(p,d )and C 4=C 4(p,d )such thatκP (F (B (t ),Γ)≤δlog t,B ′(t )=κ)≤κP (F (B (t ),Γ)≤δlog t,B ′(t )=κ,D (Γ,κ))+C 3exp(−C 4t 2+2δlog p ).By (4.18)κP (F (B (t ),Γ)≤δlog t,B ′(t )=κ,D (Γ,κ))≤ κPK Γ+δlog t ≥ct 2+2δlog pWe combine(4.20)-(4.21)together to haveP(F(B(t),Γ)≤δlog t)≤P KΓ+δlog t≥ct2+2δlog p.(5.3)k dFor each cube B k(u),it has at most4d neighbor cubes,where we count its diagonal neigh-bor cubes.We say these neighbors are connected to B k(u)and denote by¯B k(u)the vertex set of B k(u)and all of its neighbor cubes.Note that,by the deﬁnition,RΓis a connected set that contains the origin,soˆRΓ(k)is also connected in the sense of the connection of two of its diagonal vertices.IfΓis regular,then|RΓ|≥t/2.By(5.3),we haveP(|RΓ|≥Mt)= m≥Mt/(2k d)P(|RΓ|≥MKΓ,|ˆRΓ(k)|=m).(5.4)We say a cube B k(u)for u∈ˆRΓ(k)is bad,if there does not exist an edge e∈¯B k(u)∩RΓsuch that t(e)=1.Otherwise,we say the cube is good.Let B k(u)be the event that B k(u) is bad and let DΓbe the number of bad cubes B k(u)for u∈ˆRΓ.If B k(u)occurs,there is a zero pathγk⊂RΓfrom∂B k(u)to∂¯B k(u).By Theorem5.4 in Grimmett(1999),there exist C1=C1(p,d)and C2=C2(p,d)such that forﬁxed B k(u)P(B k(u))≤C1exp(−C2k).(5.5) On{|ˆRΓ(k)|=m,|RΓ|≥MKΓ},if2(4k)d<M,we claimDΓ≥mpivotal edges.Therefore,4d2KΓ>mM|ˆRΓ(k)|4d2≥As we mentioned,ˆRΓis connected,so there are at most(4)dm choices for all possibleκm. With this observation and(5.11)we haveP(|RΓ|≥MKΓ)= m≥Mt/(2k d)(4)dm m m m/2 exp(−C2km/2)≤C1 m≥Mt/k d m[4d2exp(−C2k/2)]m.(5.12) We choose k large to make4d2exp(−C2k/2)<1/2.By(5.12),there are C3=C3(p,d)and C4=C4(p,d)such thatP(|RΓ|≥MKΓ)≤C3exp(−C4t).(5.13) Therefore,by(5.2)note that there are at most t2d vertices onΓ,so there exists C5=C5(p,d) such thatE|RΓ|=C3t2d exp(−C4t)+MCt≤C5t.(5.14) Theorem2follows from(5.14).。

基于转录组的赤斑门条天牛嗅觉相关基因分析

基于转录组的赤斑门条天牛嗅觉相关基因分析作者：杨华芳张祖兵朱家颖柏天琦张宏瑞来源：《南方农业学报》2024年第03期摘要：【目的】鉴定赤斑白条天牛（Batocera rufomaculata）嗅觉相关基因，筛选其中的差异表达基因（DEGs），为探明赤斑白条天牛嗅觉机制和基于嗅觉识别的天牛生物防治新途径研究提供理论支撑。

【方法】采用Illumina NovaSeq 6000测序平台对赤斑白条天牛触角、跗节和残体进行转录组测序，利用测序数据组装、注释、数据库序列检索、序列比对及差异基因分析等生物信息学分析方法挖掘嗅觉相关基因。

【结果】转录组测序共获得137405条Unigenes，平均长度774 bp，N50为1462bp，GC含量42.93%。

通过同源比对共鉴定出289个嗅觉基因，包括45个OBPs、22个CSPs、50 个ORs、20个IRs、26个GRs、7个SNMPs、8个CXEs、82个CYPs、19个AOXs和10个GSTs基因。

通过比较所有样本的转录组，共筛选到8861个DEGs，其中2713个上调表达、6148个下调表达。

基因功能注释和信号通路富集分析结果表明，有3613个DEGs注释到GO功能的生物学过程、细胞组分和分子功能，其中以生物学过程的占比最高，为34.87%；有4002个DEGs注释到KEGG数据库，参与96条通路。

进一步对嗅觉基因进行分析发现，有114个嗅觉基因表达差异显著，其中79个上调表达、35个下调表达；OBP22、OBP29、CSP10、CSP15、SNMP1、OR41、CXE2和CYP10基因在触角中的表达量均高于其他组织，CSP10和CSP15基因在雌虫中偏好表达，CYP34基因在雄性中偏好表达，且在跗节中高表达。

【结论】筛选到赤斑白条天牛OBPs、CSPs、ORs、IRs、GRs、SNMPs、CXEs、CYPs、AOXs和GSTs等嗅觉相关基因。

推测触角中高表达的OBPs和CSPs基因对赤斑白条天牛雌雄虫识别同类异性释放的信息素或寄主植物释放的挥发物起关键作用，在雌虫中偏好表达的CSPs基因可能在雌虫寻找产卵场所过程中发挥重要作用。

空心莲子草叶片特征及生长期对莲草直胸跳甲产卵选择的影响

51卷空心莲子草叶片特征及生长期对莲草直胸跳甲产卵选择的影响史梦竹1，李建宇2，3，池丽霞1，马妍丽3，郑丽祯2，傅建炜1，3*（1福建省农业科学院农业质量标准与检测技术研究所/福建省农产品质量安全重点实验室，福州350001；2福建省农业科学院植物保护研究所/福建省作物有害生物监测与治理重点实验室/农业农村部福州作物有害生物科学观测实验站，福州350013；3福建农林大学/闽台作物有害生物防控国家重点实验室，福州350002）摘要：【目的】明确空心莲子草叶片特征及生长期对莲草直胸跳甲产卵选择的影响，为莲草直胸跳甲的大量繁殖及空心莲子草的生物防治提供指导。

【方法】采用选择性试验，接虫后24h 测定莲草直胸跳甲对空心莲子草的叶位、叶片性状（长宽比和表皮毛密度）的产卵选择情况；采用笼罩试验，测定空心莲子草生长期（苗期、生长期和老叶期）以及原有落卵量（0、1、2和4块/株）对莲草直胸跳甲产卵选择的影响。

【结果】莲草直胸跳甲成虫喜好产卵在叶位3和叶位4上，在叶位3和叶位4上的卵块数和卵粒数分别占总数的81.52%和81.10%，显著高于叶位1和叶位2（P <0.05，下同），且这2个叶位的平均叶片长宽比显著大于叶位1和叶位2；偏好在叶背表皮毛密度适中的叶片产卵。

莲草直胸跳甲对空心莲子草叶片背面（95.65%）和靠近叶片端部（61.96%）位置的产卵选择率显著高于叶片正面（4.35%）和叶片基部（38.04%）位置。

莲草直胸跳甲对生长期植株和未被产卵的空心莲子草叶片的产卵选择率分别为55.09%和45.26%，显著高于其他处理。

【结论】莲草直胸跳甲喜好将卵产在叶片长宽比较大的空心莲子草的叶位3和叶位4，被产卵叶片表皮毛密度适中；莲草直胸跳甲对空心莲子草叶片背面和靠近叶片端部的位置产卵选择率高，且偏好在生长期植株和未被产卵的空心莲子草叶片上产卵。

关键词：莲草直胸跳甲；空心莲子草；产卵选择；叶片特征；生长期；落卵量中图分类号：S476文献标志码：A 文章编号：2095-1191（2020）09-2174-07收稿日期：2020-02-18基金项目：国家自然科学基金项目（31901951）；国家自然科学基金项目延伸研究项目（GJYS2019002）；福建省农业科技重大专项（2017NZ0003-1-1）；福建省农业科学院科技创新团队建设项目（STIT2017-1-12）作者简介：*为通讯作者，傅建炜（1974-），博士，研究员，主要从事生物安全和农产品质量安全研究工作，E-mail ：fjw9238@163.com 。

经济心理学偏好与框架效应PPT课件

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组高获胜概率
期望值高获胜金额
期望值
1 99%的概率获得4 $ 3.95 33%的概率获得 $3.94
美元,1%的概率输
16美元，67%的
掉1美元
概率输掉2美元
2
95%的概率获得 2.5美元，5%的概
$ 2.34
40%的概率获得 8.5美元，60%的
$2.5
率输掉0.75美元
概率输掉1.5美元
• A1>A2即
• U（100）>0.01U(0)+0.89U(100)+0.10U(500)转换为：0.11U(100)>0.01U(0)+0.10U(500)
第4页/共47页
• Ｌ2：A3=10％的概率得到500万法朗
•
A3=90％的概率不得利
•
A4=11％的概率得到100万法朗
•
A4=89％的概率不得利
第14页/共47页
短视损失厌恶（myopic loss aversion, MLA）
• 在股票投资者中，长期收益可能会周期性地被短期损失所打断，短视的投资者把股票市场视同赌场，过分强调潜在的短期损失，投资者不愿意接受这种短期损失的现象被称为MLA.
• 如果损失厌恶的投资者不去频繁评估他们的投资绩效，则他们会更愿意承担风险，即评估期越长，风险资产越有吸引力，风险溢价也就越低。
• WTA/WTP作为衡量指标 • 不同类型的商品都存在WTP-WTA缺口现象
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第19页/共47页
影响WTP-WTA缺口的因素
• 实际检验和假设检验差异不显著 • 交易商品的类型
• 越是市场上普及的商品，其WTA/WTP比值越低。 • 替代效应：缺少替代品而造成的主观评价价值的上升。 • 诸如是市场商品还是非市场商品，替代品是存在或者是否易于获得等。

一天内7篇SCI文章被举报，囊括多种造假方式！这谁受得了？

⼀天内7篇SCI⽂章被举报，囊括多种造假⽅式！这谁受得了？解螺旋公众号·陪伴你科研的第2032天打假⽃⼠Elisabeth⼜⼀成果排名世界千强的印度本地治⾥⼤学（Pondicherry University），其⽣物技术实验室的教授Hannah R Vasanthi，最近被爆学术造假丑闻。

Hannah R Vasanthi也是位学术“体⾯”⼈，兼任业内杂志编委会成员，发表过不少⾼引⽂章，拿过INDO-US Raman Fellowship、Tamil Nadu Young Women Scientist Award等不少奖项。

⼀天之内7篇⽂章被Pubpeer上的学者指出各种花样造假，以后还怎么晋升主管、院长，⾛上学术巅峰？这段时间⼋成焦虑得睡不着觉了。

这些花样造假包括内容抄袭、条带复制拼接、数据粘贴、图像颠倒等等，且随⼩编来具体看看这7篇⽂章：第⼀篇⽂章“Potential health benefits of broccoli- a chemico-biological overview”，于2009年6⽉，发表在影响因⼦2.842分的Mini-Reviews in Medicinal Chemistry杂志上，⽬前已被引⽤109次。

该⽂系Hannah在康涅狄格⼤学医学院学习期间发表，涉嫌对其他⽂章⼤篇幅的内容抄袭，⽐如下⾯这篇 Fahey 等于2002年在名刊PNAS杂志上发表的原创⽂章“Sulforaphaneinhibits extracellular, intracellular, and antibiotic-resistant strains of Helicobacter pyloriand prevents benzo[a]pyrene-induced stomach tumors”，图左：另有其他学者的7篇早期⽂章被Hannah不同程度抄袭，可以这么说，Hannah的⽂章内容⼏乎就是东抄⼀段、西凑⼀段拼出来的。

翻译——精选推荐

翻译⾯板数据模型中的后模拟和贝叶斯因⼦摘要本⽂所关注的问题是关于泊松⾯板数据模型与多个随机效应的后模拟和模型选择的问题。

已经被发展了的有效算法是以马尔可夫链蒙特卡罗⽅法为基础的，⽽马尔可夫链蒙特卡罗这种⽅法主要⽤于后验分布的抽样。

数学家提出了⼀种新的参数化的随机效应和固定效应，且与常⽤的参数作⽐较；并且也认可了通过Chib⽅法的边缘似然和贝叶斯因⼦的计算。

这些⽅法可以通过两个涉及⼤样本和多个随机效应的真实数据来论证。

关键词：贝叶斯因⼦；计数数据；Gibbs抽样；重要性抽样；边缘似然；Metropolis-Dhastings算法；马尔科夫链蒙特卡罗；泊松回归1.引⾔本⽂涉及的问题是带有多个随机效应的⾯板数据模型与估计的问题。

虽然我们专注于数据资料，但是我们的很多讨论也适⽤于⼆进制数据和⼴义线性模型。

我们感兴趣的是程序，这些程序允许那些（似然函数通常不可得到的）模型和⽅法具有⼀个⾼效的估计，那些⽅法是被⽤来⽐较替换、潜在的⾮嵌套、模型的⽅法。

从各种数值的⾓度来看，越来越多的⽂献已经开始出现在⼀些问题中，这些问题主要是围绕马尔可夫链蒙特卡罗算法（Albert，1992 ；Bennett等，1996 ; Gamerman，1994; Wakefield等，1994；Zeger 和Karim，1991）。

它也已经开始了解到某种特定的识别问题会严重的损害现有模拟⽅法的性能。

Gelfand等⼈（1996）讨论了⼀种⽅法来处理这个问题，但是这种⽅法对于我们所研究的模型看起来在计算上不是那么简单的。

本⽂在三个重要⽅向推进现有的⽂献。

⾸先，我们提出了⼀种参数化模型，关系到Gelfand 等⼈（1996），这种模型实现起来⽐较简单。

固定效应时的参数协变量矩阵和随机效应时的参数协变量矩阵是完全不同的，⽽且随机效应具有⾮零平均值。

其次，我们开发基于马尔科夫链蒙特卡罗⽅法的⾼效算法，这个⽅法⽤在参数的后验分布的抽样和随机效应中。

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