Identifying vehicular crash high risk locations along highways is important for understanding the causes of vehicle crashes and to determine effective countermeasures based on the analysis. This paper presents a GIS a...Identifying vehicular crash high risk locations along highways is important for understanding the causes of vehicle crashes and to determine effective countermeasures based on the analysis. This paper presents a GIS approach to examine the spatial patterns of vehicle crashes and determines if they are spatially clustered, dispersed, or random. Moran’s I and Getis-Ord Gi* statistic are employed to examine spatial patterns, clusters mapping of vehicle crash data, and to generate high risk locations along highways. Kernel Density Estimation (KDE) is used to generate crash concentration maps that show the road density of crashes. The proposed approach is evaluated using the 2013 vehicle crash data in the state of Indiana. Results show that the approach is efficient and reliable in identifying vehicle crash hot spots and unsafe road locations.展开更多
This article obtains an explicit expression of the heat kernels on H-type groups and then follow the estimate of heat kernels to deduce the Hardy＇s uncertainty principle on the nilpotent Lie groups.
Q-methodology was introduced more than 80 years ago to study subjective topics such as attitudes, perceptions, preferences, and feelings and there has not been much change in its statistical components since then. In ...Q-methodology was introduced more than 80 years ago to study subjective topics such as attitudes, perceptions, preferences, and feelings and there has not been much change in its statistical components since then. In Q-methodology, subjective topics are studied using a combination of qualitative and quantitative techniques. It involves development of a sample of statements and rank-ordering these statements by study participants using a grid known as Q-sort table. After completion of Q-sort tables by the participants, a by-person factor analysis (i.e., the factor analysis is performed on persons, not variables or traits) is used to analyze the data. Therefore, each factor represents a group of individuals with similar views, feelings, or preferences about the topic of the study. Then, each group (factor) is usually described by a set of statements, called distinguishing statements, or statements with high or low factor scores. In this article, we review one important statistical issue, i.e. the criteria for identifying distinguishing statements and provide a review of its mathematical calculation and statistical background. We show that the current approach for identifying distinguishing statements has no sound basis, which may result in erroneous findings and seems to be appropriate only when there are repeated evaluations of Q-sample from the same subjects. However, most Q-studies include independent subjects with no repeated evaluation. Finally, a new approach is suggested for identifying distinguishing statements based on Cohen’s effect size. We demonstrate the application of this new formula by applying the current and the suggested methods on a Q-dataset and explain the differences.展开更多
Laplace transform is one of the powerful tools for solving differential equations in engineering and other science subjects.Using the Laplace transform for solving differential equations,however,sometimes leads to sol...Laplace transform is one of the powerful tools for solving differential equations in engineering and other science subjects.Using the Laplace transform for solving differential equations,however,sometimes leads to solutions in the Laplace domain that are not readily invertible to the real domain by analyticalmeans.Thus,we need numerical inversionmethods to convert the obtained solution fromLaplace domain to a real domain.In this paper,we propose a numerical scheme based on Laplace transform and numerical inverse Laplace transform for the approximate solution of fractal-fractional differential equations with orderα,β.Our proposed numerical scheme is based on three main steps.First,we convert the given fractal-fractional differential equation to fractional-differential equation in Riemann-Liouville sense,and then into Caputo sense.Secondly,we transformthe fractional differential equation in Caputo sense to an equivalent equation in Laplace space.Then the solution of the transformed equation is obtained in Laplace domain.Finally,the solution is converted into the real domain using numerical inversion of Laplace transform.Three inversion methods are evaluated in this paper,and their convergence is also discussed.Three test problems are used to validate the inversion methods.We demonstrate our results with the help of tables and figures.The obtained results show that Euler’s and Talbot’s methods performed better than Stehfest’s method.展开更多
α-diversity describes species diversity at local scales.The Simpson’s and Shannon-Wiener indices are widely used to characterizeα-diversity based on species abundances within a fixed study site(e.g.,a quadrat or pl...α-diversity describes species diversity at local scales.The Simpson’s and Shannon-Wiener indices are widely used to characterizeα-diversity based on species abundances within a fixed study site(e.g.,a quadrat or plot).Although such indices provide overall diversity estimates that can be analyzed,their values are not spatially continuous nor applicable in theory to any point within the study region,and thus they cannot be treated as spatial covariates for analyses of other variables.Herein,we extended the Simpson’s and Shannon-Wiener indices to create point estimates ofα-diversity for any location based on spatially explicit species occurrences within different bandwidths(i.e.,radii,with the location of interest as the center).For an arbitrary point in the study region,species occurrences within the circle plotting the bandwidth were weighted according to their distance from the center using a tri-cube kernel function,with occurrences closer to the center having greater weight than more distant ones.These novel kernel-basedα-diversity indices were tested using a tree dataset from a 400 m×400 m study region comprising a 200 m×200 m core region surrounded by a 100-m width buffer zone.Our newly extendedα-diversity indices did not disagree qualitatively with the traditional indices,and the former were slightly lower than the latter by<2%at medium and large band widths.The present work demonstrates the feasibility of using kernel-basedα-diversity indices to estimate diversity at any location in the study region and allows them to be used as quantifiable spatial covariates or predictors for other dependent variables of interest in future ecological studies.Spatially continuousα-diversity indices are useful to compare and monitor species trends in space and time,which is valuable for conservation practitioners.展开更多
随着人口老龄化趋势的加剧,老年人行走的生物力学特征成为健康管理和康复领域的关键研究方向。了解不同年龄段中老年人群行走过程中下肢姿势控制的生物力学特征,对于更好地理解步态变化、预防下肢损伤以及制定有效的康复策略至关重要。...随着人口老龄化趋势的加剧,老年人行走的生物力学特征成为健康管理和康复领域的关键研究方向。了解不同年龄段中老年人群行走过程中下肢姿势控制的生物力学特征,对于更好地理解步态变化、预防下肢损伤以及制定有效的康复策略至关重要。探究中老年人群年龄变化对步态生物力学特征的影响,以减少步行时的跌倒损伤风险。采集60名40~49、50~59岁两个年龄段的受试者(30男、30女)。使用运动学采集设备Codamotion红外捕捉系统、ATMI三维测力台和Footscan压力平板同步采集受试者的运动学和动力学数据。所有数据分析采用科恩效应(Cohen s effect)进行统计分析。实验结果表明:脚跟着地时刻过渡到全脚掌着地时刻老年组女性左侧膝关节屈曲变化角度最大,为11.22°,老年组男性右侧髋关节屈曲变化角度最大,为5.99°;开始着地阶段女子中年组与老年组双侧差异均中等强效应(d=0.5、d=0.77),整足触地阶段女子老年组双侧差异具有中等效应(d=0.62);男性老年组行走时Z轴方向特征量F 1双侧差异展示出中等效应(d=0.714);结果表明,年龄增加双足效应值增大,行走过程中双足不稳定性增加。步态变化受性别差异影响,在制定个性化的康复和预防策略时,需要根据不同性别的特点进行针对性的训练和干预。另外,足底压力和冲量的变化与年龄相关,应加强足底肌肉的锻炼,以减少足底损伤和改善步态稳定性。展开更多
为全面准确地描述地震相特征,在地震相分析中引入了时频分析技术,如短时窗傅里叶变换、Cabor 变换、小波变换等。之后发展起来的 S 变换时频分析方法综合了短时窗傅里叶变换和小波变换的优点,具有线性化、无损可逆性以及高时频分辨率等...为全面准确地描述地震相特征,在地震相分析中引入了时频分析技术,如短时窗傅里叶变换、Cabor 变换、小波变换等。之后发展起来的 S 变换时频分析方法综合了短时窗傅里叶变换和小波变换的优点,具有线性化、无损可逆性以及高时频分辨率等特性。阐述了 S 变换的基本理论,并利用 S 变换对理想的地震序列模型以及实际地震资料进行了地震相分析。通过对地震相特征的连续性以及振幅和频率变化特征的分析发现,对于规模较小的地震相体,在时间剖面上很难识别其层序内的地震相特征(特别是频率)随旅行时的变化情况,但在 S 变换的时频域内可以被清楚地体现出来。因此,在进行沉积环境识别时,可以利用 S 变换来提供有效地震信息。展开更多
文摘Identifying vehicular crash high risk locations along highways is important for understanding the causes of vehicle crashes and to determine effective countermeasures based on the analysis. This paper presents a GIS approach to examine the spatial patterns of vehicle crashes and determines if they are spatially clustered, dispersed, or random. Moran’s I and Getis-Ord Gi* statistic are employed to examine spatial patterns, clusters mapping of vehicle crash data, and to generate high risk locations along highways. Kernel Density Estimation (KDE) is used to generate crash concentration maps that show the road density of crashes. The proposed approach is evaluated using the 2013 vehicle crash data in the state of Indiana. Results show that the approach is efficient and reliable in identifying vehicle crash hot spots and unsafe road locations.
基金supported by National Science Foundation of China (10571044)
文摘This article obtains an explicit expression of the heat kernels on H-type groups and then follow the estimate of heat kernels to deduce the Hardy＇s uncertainty principle on the nilpotent Lie groups.
文摘Q-methodology was introduced more than 80 years ago to study subjective topics such as attitudes, perceptions, preferences, and feelings and there has not been much change in its statistical components since then. In Q-methodology, subjective topics are studied using a combination of qualitative and quantitative techniques. It involves development of a sample of statements and rank-ordering these statements by study participants using a grid known as Q-sort table. After completion of Q-sort tables by the participants, a by-person factor analysis (i.e., the factor analysis is performed on persons, not variables or traits) is used to analyze the data. Therefore, each factor represents a group of individuals with similar views, feelings, or preferences about the topic of the study. Then, each group (factor) is usually described by a set of statements, called distinguishing statements, or statements with high or low factor scores. In this article, we review one important statistical issue, i.e. the criteria for identifying distinguishing statements and provide a review of its mathematical calculation and statistical background. We show that the current approach for identifying distinguishing statements has no sound basis, which may result in erroneous findings and seems to be appropriate only when there are repeated evaluations of Q-sample from the same subjects. However, most Q-studies include independent subjects with no repeated evaluation. Finally, a new approach is suggested for identifying distinguishing statements based on Cohen’s effect size. We demonstrate the application of this new formula by applying the current and the suggested methods on a Q-dataset and explain the differences.
文摘Laplace transform is one of the powerful tools for solving differential equations in engineering and other science subjects.Using the Laplace transform for solving differential equations,however,sometimes leads to solutions in the Laplace domain that are not readily invertible to the real domain by analyticalmeans.Thus,we need numerical inversionmethods to convert the obtained solution fromLaplace domain to a real domain.In this paper,we propose a numerical scheme based on Laplace transform and numerical inverse Laplace transform for the approximate solution of fractal-fractional differential equations with orderα,β.Our proposed numerical scheme is based on three main steps.First,we convert the given fractal-fractional differential equation to fractional-differential equation in Riemann-Liouville sense,and then into Caputo sense.Secondly,we transformthe fractional differential equation in Caputo sense to an equivalent equation in Laplace space.Then the solution of the transformed equation is obtained in Laplace domain.Finally,the solution is converted into the real domain using numerical inversion of Laplace transform.Three inversion methods are evaluated in this paper,and their convergence is also discussed.Three test problems are used to validate the inversion methods.We demonstrate our results with the help of tables and figures.The obtained results show that Euler’s and Talbot’s methods performed better than Stehfest’s method.
基金supported by Natural Science Foundation of Xinjiang Uygur Autonomous Region(2022D01A213)。
文摘α-diversity describes species diversity at local scales.The Simpson’s and Shannon-Wiener indices are widely used to characterizeα-diversity based on species abundances within a fixed study site(e.g.,a quadrat or plot).Although such indices provide overall diversity estimates that can be analyzed,their values are not spatially continuous nor applicable in theory to any point within the study region,and thus they cannot be treated as spatial covariates for analyses of other variables.Herein,we extended the Simpson’s and Shannon-Wiener indices to create point estimates ofα-diversity for any location based on spatially explicit species occurrences within different bandwidths(i.e.,radii,with the location of interest as the center).For an arbitrary point in the study region,species occurrences within the circle plotting the bandwidth were weighted according to their distance from the center using a tri-cube kernel function,with occurrences closer to the center having greater weight than more distant ones.These novel kernel-basedα-diversity indices were tested using a tree dataset from a 400 m×400 m study region comprising a 200 m×200 m core region surrounded by a 100-m width buffer zone.Our newly extendedα-diversity indices did not disagree qualitatively with the traditional indices,and the former were slightly lower than the latter by<2%at medium and large band widths.The present work demonstrates the feasibility of using kernel-basedα-diversity indices to estimate diversity at any location in the study region and allows them to be used as quantifiable spatial covariates or predictors for other dependent variables of interest in future ecological studies.Spatially continuousα-diversity indices are useful to compare and monitor species trends in space and time,which is valuable for conservation practitioners.
文摘随着人口老龄化趋势的加剧,老年人行走的生物力学特征成为健康管理和康复领域的关键研究方向。了解不同年龄段中老年人群行走过程中下肢姿势控制的生物力学特征,对于更好地理解步态变化、预防下肢损伤以及制定有效的康复策略至关重要。探究中老年人群年龄变化对步态生物力学特征的影响,以减少步行时的跌倒损伤风险。采集60名40~49、50~59岁两个年龄段的受试者(30男、30女)。使用运动学采集设备Codamotion红外捕捉系统、ATMI三维测力台和Footscan压力平板同步采集受试者的运动学和动力学数据。所有数据分析采用科恩效应(Cohen s effect)进行统计分析。实验结果表明:脚跟着地时刻过渡到全脚掌着地时刻老年组女性左侧膝关节屈曲变化角度最大,为11.22°,老年组男性右侧髋关节屈曲变化角度最大,为5.99°;开始着地阶段女子中年组与老年组双侧差异均中等强效应(d=0.5、d=0.77),整足触地阶段女子老年组双侧差异具有中等效应(d=0.62);男性老年组行走时Z轴方向特征量F 1双侧差异展示出中等效应(d=0.714);结果表明,年龄增加双足效应值增大,行走过程中双足不稳定性增加。步态变化受性别差异影响,在制定个性化的康复和预防策略时,需要根据不同性别的特点进行针对性的训练和干预。另外,足底压力和冲量的变化与年龄相关,应加强足底肌肉的锻炼,以减少足底损伤和改善步态稳定性。
文摘为全面准确地描述地震相特征,在地震相分析中引入了时频分析技术,如短时窗傅里叶变换、Cabor 变换、小波变换等。之后发展起来的 S 变换时频分析方法综合了短时窗傅里叶变换和小波变换的优点,具有线性化、无损可逆性以及高时频分辨率等特性。阐述了 S 变换的基本理论,并利用 S 变换对理想的地震序列模型以及实际地震资料进行了地震相分析。通过对地震相特征的连续性以及振幅和频率变化特征的分析发现,对于规模较小的地震相体,在时间剖面上很难识别其层序内的地震相特征(特别是频率)随旅行时的变化情况,但在 S 变换的时频域内可以被清楚地体现出来。因此,在进行沉积环境识别时,可以利用 S 变换来提供有效地震信息。
