Throughout this paper,let(Ω,ι,μ)be a probability space,D the collection of allleft-continuous distribution functions,and D^+={F(0)=0|F∈D},and L(Ω)the collec-tion of all random variables which is a.s.finite on Ω,...Throughout this paper,let(Ω,ι,μ)be a probability space,D the collection of allleft-continuous distribution functions,and D^+={F(0)=0|F∈D},and L(Ω)the collec-tion of all random variables which is a.s.finite on Ω,and L^+={ξ≥0 a.s.|ξ∈L(Ω)}.For random metric (normed) spaces,see [1]or[2].Theorem 1 Let(M,d)be a complete metric space f:M→M,a contract mappingwith contract coefficient α∈[0,1),L(Ω,m)the collection of all M-valued random vari-展开更多
In this paper,we obtain some tripled common random fixed point and tripled random fixed point theorems with several generalized Lipschitz constants in such spaces.We consider the obtained assertions without the assump...In this paper,we obtain some tripled common random fixed point and tripled random fixed point theorems with several generalized Lipschitz constants in such spaces.We consider the obtained assertions without the assumption of normality of cones.The presented results generalize some coupled common fixed point theorems in the existing literature.展开更多
In this paper, we shall present the strong laws of large numbers for fuzzy set-valued random variables in the sense of d<sup>∞</sup><sub>H</sub> . The results are based on the result ...In this paper, we shall present the strong laws of large numbers for fuzzy set-valued random variables in the sense of d<sup>∞</sup><sub>H</sub> . The results are based on the result of single-valued random variables obtained by Taylor [1] and set-valued random variables obtained by Li Guan [2].展开更多
In this paper, we shall represent a strong law of large numbers (SLLN) for weighted sums of set- valued random variables in the sense of the Hausdorff metric dH, based on the result of single-valued random variable ob...In this paper, we shall represent a strong law of large numbers (SLLN) for weighted sums of set- valued random variables in the sense of the Hausdorff metric dH, based on the result of single-valued random variable obtained by Taylor [1].展开更多
First of all the authors introduce the concepts of random sub-self-similar set and random shift set and then construct the random sub-self-similar set by a random shift set and a collection of statistical contraction ...First of all the authors introduce the concepts of random sub-self-similar set and random shift set and then construct the random sub-self-similar set by a random shift set and a collection of statistical contraction operators.展开更多
In this article, the Hausdorff dimension and exact Hausdorff measure function of any random sub-self-similar set are obtained under some reasonable conditions. Several examples are given at the end.
Quantitative headspace analysis of volatiles emitted by plants or any other living organisms in chemical ecology studies generates large multidimensional data that require extensive mining and refining to extract usef...Quantitative headspace analysis of volatiles emitted by plants or any other living organisms in chemical ecology studies generates large multidimensional data that require extensive mining and refining to extract useful information. More often the number of variables and the quantified volatile compounds exceed the number of observations or samples and hence many traditional statistical analysis methods become inefficient. Here, we employed machine learning algorithm, random forest (RF) in combination with distance-based procedure, similarity percentage (SIMPER) as preprocessing steps to reduce the data dimensionality in the chemical profiles of volatiles from three African nightshade plant species before subjecting the data to non-metric multidimensional scaling (NMDS). In addition, non-parametric methods namely permutational multivariate analysis of variance (PERMANOVA) and analysis of similarities (ANOSIM) were applied to test hypothesis of differences among the African nightshade species based on the volatiles profiles and ascertain the patterns revealed by NMDS plots. Our results revealed that there were significant differences among the African nightshade species when the data’s dimension was reduced using RF variable importance and SIMPER, as also supported by NMDS plots that showed S. scabrum being separated from S. villosum and S. sarrachoides based on the reduced data variables. The novelty of our work is on the merits of using data reduction techniques to successfully reveal differences in groups which could have otherwise not been the case if the analysis were performed on the entire original data matrix characterized by small samples. The R code used in the analysis has been shared herein for interested researchers to customise it for their own data of similar nature.展开更多
文摘Throughout this paper,let(Ω,ι,μ)be a probability space,D the collection of allleft-continuous distribution functions,and D^+={F(0)=0|F∈D},and L(Ω)the collec-tion of all random variables which is a.s.finite on Ω,and L^+={ξ≥0 a.s.|ξ∈L(Ω)}.For random metric (normed) spaces,see [1]or[2].Theorem 1 Let(M,d)be a complete metric space f:M→M,a contract mappingwith contract coefficient α∈[0,1),L(Ω,m)the collection of all M-valued random vari-
基金supported by the Foundation of Education Ministry,Hubei Province,China(Q20122203)
文摘In this paper,we obtain some tripled common random fixed point and tripled random fixed point theorems with several generalized Lipschitz constants in such spaces.We consider the obtained assertions without the assumption of normality of cones.The presented results generalize some coupled common fixed point theorems in the existing literature.
文摘In this paper, we shall present the strong laws of large numbers for fuzzy set-valued random variables in the sense of d<sup>∞</sup><sub>H</sub> . The results are based on the result of single-valued random variables obtained by Taylor [1] and set-valued random variables obtained by Li Guan [2].
文摘In this paper, we shall represent a strong law of large numbers (SLLN) for weighted sums of set- valued random variables in the sense of the Hausdorff metric dH, based on the result of single-valued random variable obtained by Taylor [1].
基金Supported by the National Natural Science Foundation of China (10371092)the Foundation of Wuhan University
文摘First of all the authors introduce the concepts of random sub-self-similar set and random shift set and then construct the random sub-self-similar set by a random shift set and a collection of statistical contraction operators.
基金supported by the National Natural Science Foundation of China(10371092)Foundation of Ningbo University(8Y0600036).
文摘In this article, the Hausdorff dimension and exact Hausdorff measure function of any random sub-self-similar set are obtained under some reasonable conditions. Several examples are given at the end.
文摘Quantitative headspace analysis of volatiles emitted by plants or any other living organisms in chemical ecology studies generates large multidimensional data that require extensive mining and refining to extract useful information. More often the number of variables and the quantified volatile compounds exceed the number of observations or samples and hence many traditional statistical analysis methods become inefficient. Here, we employed machine learning algorithm, random forest (RF) in combination with distance-based procedure, similarity percentage (SIMPER) as preprocessing steps to reduce the data dimensionality in the chemical profiles of volatiles from three African nightshade plant species before subjecting the data to non-metric multidimensional scaling (NMDS). In addition, non-parametric methods namely permutational multivariate analysis of variance (PERMANOVA) and analysis of similarities (ANOSIM) were applied to test hypothesis of differences among the African nightshade species based on the volatiles profiles and ascertain the patterns revealed by NMDS plots. Our results revealed that there were significant differences among the African nightshade species when the data’s dimension was reduced using RF variable importance and SIMPER, as also supported by NMDS plots that showed S. scabrum being separated from S. villosum and S. sarrachoides based on the reduced data variables. The novelty of our work is on the merits of using data reduction techniques to successfully reveal differences in groups which could have otherwise not been the case if the analysis were performed on the entire original data matrix characterized by small samples. The R code used in the analysis has been shared herein for interested researchers to customise it for their own data of similar nature.
