探究功能多样性如何影响商圈活力,可为城市用地功能结构优化调整和商圈功能改造提供理论支撑,进而促进城市混合功能有序开发、提升城市活力。已有关于功能多样性与活力的研究,大多集中在城市、街道活力等方面,对于商圈活力研究很少涉及...探究功能多样性如何影响商圈活力,可为城市用地功能结构优化调整和商圈功能改造提供理论支撑,进而促进城市混合功能有序开发、提升城市活力。已有关于功能多样性与活力的研究,大多集中在城市、街道活力等方面,对于商圈活力研究很少涉及,且大多利用单一的熵指数反映功能多样性。在利用夜光数据对活力的研究中,大多选取城市或更大区域尺度作为研究单元,无法精准地从多角度、多层面理解功能多样性与城市内部活力的关系。因此,本文以广州市主城区为例,以商圈作为基本研究单元,融合城市设施兴趣点(Point of Interest,POI)和珞珈一号夜间灯光数据,利用希尔数模型从多维视角测度商圈功能多样性特征,并以此来探究其与商圈活力的定量化关系。主要结论如下:①仅用熵指数来反映多样性是不足的,其与商圈活力在0.1的显著性水平下无相关性,需结合希尔数多样性指数从多视角度量商圈功能多样性,以弥补单一熵指数测度方法的不足;②广州商圈功能丰富度指数与其活力净相关系数为0.382,提高功能丰富度以增加商圈各功能间互补性、异质性或混合性,从而具备足够的功能多样性,促进各类功能间的协同与竞争,形成良好的兼容性混合,以更好的满足多数人的消费需求,激发商圈活力;③广州商圈规模效应与其活力净相关系数为0.507,对比大于集聚效应的0.371,表明广州商圈发展遵循新经济地理学的规模报酬递增规律,即商圈规模越大对于提升商圈活力的效用越大,而商圈功能集聚度对于提升商圈活力的效用相对较小。展开更多
We will introduce a type of Fredholm operators which are shown to have a certain con- tinuity in weak topologies.From this,we will prove that the fundamental matrix solutions of k-th, k≥2,order linear systems of ordi...We will introduce a type of Fredholm operators which are shown to have a certain con- tinuity in weak topologies.From this,we will prove that the fundamental matrix solutions of k-th, k≥2,order linear systems of ordinary differential equations are continuous in coefficient matrixes with weak topologies.Consequently,Floquet multipliers and Lyapunov exponents for periodic systems are continuous in weak topologies.Moreover,for the scalar Hill’s equations,Sturm-Liouville eigenvalues, periodic and anti-periodic eigenvalues,and rotation numbers are all continuous in potentials with weak topologies.These results will lead to many interesting variational problems.展开更多
Due to the tremendous diversity of microbial organisms in topsoil,the estimation of saturated richness in a belowground ecosystem is still challenging.Here,we intensively surveyed the 16S rRNA gene in four 1 m2 sampli...Due to the tremendous diversity of microbial organisms in topsoil,the estimation of saturated richness in a belowground ecosystem is still challenging.Here,we intensively surveyed the 16S rRNA gene in four 1 m2 sampling quadrats in a typical grassland,with 141 biological or technical replicates generating over 11 million sequences per quadrat.Through these massive data sets and using both non-asymptotic extrapolation and non-parametric asymptotic approaches,results revealed that roughly 15919±193,27193±1076 and 56985±2347 prokaryotic species inhabited in 1 m2 topsoil,classifying by DADA2,UPARSE(97%cutoff)and Deblur,respectively,and suggested a huge difference among these clustering tools.Nearly 500000 sequences were required to catch 50%species in 1 m2,while any estimator based on 500000 sequences would still lose about a third of total richness.Insufficient sequencing depth will greatly underestimate both observed and estimated richness.At least~911000,~3461000,and~1878000 sequences were needed for DADA2,UPARSE,and Deblur,respectively,to catch 80%species in 1 m2 topsoil,and the numbers of sequences would be nearly twice to three times on this basis to cover 90%richness.In contrast,α-diversity indexes characterized by higher order of Hill numbers,including Shannon entropy and inverse Simpson index,reached saturation with fewer than 100000 sequences,suggesting sequencing depth could be varied greatly when focusing on exploring differentα-diversity characteristics of a microbial community.Our findings were fundamental for microbial studies that provided benchmarks for the extending surveys in large scales of terrestrial ecosystems.展开更多
文摘探究功能多样性如何影响商圈活力,可为城市用地功能结构优化调整和商圈功能改造提供理论支撑,进而促进城市混合功能有序开发、提升城市活力。已有关于功能多样性与活力的研究,大多集中在城市、街道活力等方面,对于商圈活力研究很少涉及,且大多利用单一的熵指数反映功能多样性。在利用夜光数据对活力的研究中,大多选取城市或更大区域尺度作为研究单元,无法精准地从多角度、多层面理解功能多样性与城市内部活力的关系。因此,本文以广州市主城区为例,以商圈作为基本研究单元,融合城市设施兴趣点(Point of Interest,POI)和珞珈一号夜间灯光数据,利用希尔数模型从多维视角测度商圈功能多样性特征,并以此来探究其与商圈活力的定量化关系。主要结论如下:①仅用熵指数来反映多样性是不足的,其与商圈活力在0.1的显著性水平下无相关性,需结合希尔数多样性指数从多视角度量商圈功能多样性,以弥补单一熵指数测度方法的不足;②广州商圈功能丰富度指数与其活力净相关系数为0.382,提高功能丰富度以增加商圈各功能间互补性、异质性或混合性,从而具备足够的功能多样性,促进各类功能间的协同与竞争,形成良好的兼容性混合,以更好的满足多数人的消费需求,激发商圈活力;③广州商圈规模效应与其活力净相关系数为0.507,对比大于集聚效应的0.371,表明广州商圈发展遵循新经济地理学的规模报酬递增规律,即商圈规模越大对于提升商圈活力的效用越大,而商圈功能集聚度对于提升商圈活力的效用相对较小。
基金the National Natural Science Foundation of China(Grant Nos.10325102,10531010)the National Basic Research Program of China(Grant No.2006CB805903)Teaching and Research Award Program for Outstanding Young Teachers,Ministry of Education of China(2001)
文摘We will introduce a type of Fredholm operators which are shown to have a certain con- tinuity in weak topologies.From this,we will prove that the fundamental matrix solutions of k-th, k≥2,order linear systems of ordinary differential equations are continuous in coefficient matrixes with weak topologies.Consequently,Floquet multipliers and Lyapunov exponents for periodic systems are continuous in weak topologies.Moreover,for the scalar Hill’s equations,Sturm-Liouville eigenvalues, periodic and anti-periodic eigenvalues,and rotation numbers are all continuous in potentials with weak topologies.These results will lead to many interesting variational problems.
基金the National Natural Science Foundation of China(NSFC Grant No.U1906223)the National Key Research and Development Program(Grant No.2019YFC1905001)。
文摘Due to the tremendous diversity of microbial organisms in topsoil,the estimation of saturated richness in a belowground ecosystem is still challenging.Here,we intensively surveyed the 16S rRNA gene in four 1 m2 sampling quadrats in a typical grassland,with 141 biological or technical replicates generating over 11 million sequences per quadrat.Through these massive data sets and using both non-asymptotic extrapolation and non-parametric asymptotic approaches,results revealed that roughly 15919±193,27193±1076 and 56985±2347 prokaryotic species inhabited in 1 m2 topsoil,classifying by DADA2,UPARSE(97%cutoff)and Deblur,respectively,and suggested a huge difference among these clustering tools.Nearly 500000 sequences were required to catch 50%species in 1 m2,while any estimator based on 500000 sequences would still lose about a third of total richness.Insufficient sequencing depth will greatly underestimate both observed and estimated richness.At least~911000,~3461000,and~1878000 sequences were needed for DADA2,UPARSE,and Deblur,respectively,to catch 80%species in 1 m2 topsoil,and the numbers of sequences would be nearly twice to three times on this basis to cover 90%richness.In contrast,α-diversity indexes characterized by higher order of Hill numbers,including Shannon entropy and inverse Simpson index,reached saturation with fewer than 100000 sequences,suggesting sequencing depth could be varied greatly when focusing on exploring differentα-diversity characteristics of a microbial community.Our findings were fundamental for microbial studies that provided benchmarks for the extending surveys in large scales of terrestrial ecosystems.
