A chimera state consisting of both coherent and incoherent groups is a fascinating spatial pattern in non-locally coupled identical oscillators. It is thought that random initial conditions hardly evolve to chimera st...A chimera state consisting of both coherent and incoherent groups is a fascinating spatial pattern in non-locally coupled identical oscillators. It is thought that random initial conditions hardly evolve to chimera states. In this work, we study the dependence of chimera states on initial conditions. We show that random initial conditions may lead to chimera states and the chance of realizing chimera states becomes increasing when the model parameters axe moving away from the boundary of their stable regime.展开更多
Conditional dependence plays a crucial role in various statistical procedures,including variable selection,network analysis and causal inference.However,there remains a paucity of relevant research in the context of h...Conditional dependence plays a crucial role in various statistical procedures,including variable selection,network analysis and causal inference.However,there remains a paucity of relevant research in the context of high-dimensional conditioning variables,a common challenge encountered in the era of big data.To address this issue,many existing studies impose certain model structures,yet high-dimensional conditioning variables often introduce spurious correlations in these models.In this paper,we systematically study the estimation biases inherent in widely-used measures of conditional dependence when spurious variables are present under high-dimensional settings.We discuss the estimation inconsistency both intuitively and theoretically,demonstrating that the conditional dependencies can be either overestimated or underestimated under different scenarios.To mitigate these biases and attain consistency,we introduce a measure based on data splitting and refitting techniques for high-dimensional conditional dependence.A conditional independence test is also developed using the newly advocated measure,with a tuning-free asymptotic null distribution.Furthermore,the proposed test is applied to generating high-dimensional network graphs in graphical modeling.The superior performances of newly proposed methods are illustrated both theoretically and through simulation studies.We also utilize the method to construct the gene-gene networks using a dataset of breast invasive carcinoma,which contains interesting discoveries that are worth further scientific exploration.展开更多
We introduce the Kernel-based Partial Conditional Mean Dependence,a sca-lar-valued measure of conditional mean dependence of Y given X,while adjusting for the nonlinear dependence on Z.Here X,Y and Z are random elemen...We introduce the Kernel-based Partial Conditional Mean Dependence,a sca-lar-valued measure of conditional mean dependence of Y given X,while adjusting for the nonlinear dependence on Z.Here X,Y and Z are random elements from arbitrary separable Hilbert spaces.This measure ex-tends the Kernel-based Conditional Mean Dependence.As the estimator of the measure is developed,the concentration property of the estimator is proved.Numerical results demonstrate the effectiveness of the new dependence meas-ure in the context of dependence testing,highlighting their advantages in cap-turing nonlinear partial conditional mean dependencies.展开更多
This paper is concerned with ultrahigh dimensional data analysis,which has become increasingly important in diverse scientific fields.We develop a sure independence screening procedure via the measure of conditional m...This paper is concerned with ultrahigh dimensional data analysis,which has become increasingly important in diverse scientific fields.We develop a sure independence screening procedure via the measure of conditional mean dependence based on Copula(CC-SIS,for short).The CC-SIS can be implemented as easily as the sure independence screening procedures which respectively based on the Pearson correlation,conditional mean and distance correlation(SIS,SIRS and DC-SIS,for short)and can significantly improve the performance of feature screening.We establish the sure screening property for the CC-SIS,and conduct simulations to examine its finite sample performance.Numerical comparison indicates that the CC-SIS performs better than the other two methods in various models.At last,we also illustrate the CC-SIS through a real data example.展开更多
Let X be a compact metric space studies some relationships between stochastic and f ： X→ X be a continuous map. This paper and topological properties of dynamical systems. It is shown that if f satisfies the central...Let X be a compact metric space studies some relationships between stochastic and f ： X→ X be a continuous map. This paper and topological properties of dynamical systems. It is shown that if f satisfies the central limit theorem, then f is topologically ergodic and / is sensitively dependent on initial conditions if and only if / is neither minimal nor equicontinuous.展开更多
Conditional dependence learning with high-dimensional conditioning variables.Jianxin Bi,Xingdong Feng&Jingyuan Liu.Abstract Conditional dependence plays a crucial role in various statistical procedures,including v...Conditional dependence learning with high-dimensional conditioning variables.Jianxin Bi,Xingdong Feng&Jingyuan Liu.Abstract Conditional dependence plays a crucial role in various statistical procedures,including variable selection,network analysis and causal inference.However,there remains a paucity of relevant research in the context of high-dimensional conditioning variables,a common challenge encountered in the era of big data.To address this issue,many existing studies impose certain model structures,yet high-dimensional conditioning variables often introduce spurious correlations in these models.In this paper,we systematically study the estimation biases inherent in widely-used measures of conditional dependence when spurious variables are present under high-dimensional settings.展开更多
Conditional functional dependencies（CFDs） are important techniques for data consistency. However, CFDs are limited to 1） provide the reasonable values for consistency repairing and 2） detect potential errors. This...Conditional functional dependencies（CFDs） are important techniques for data consistency. However, CFDs are limited to 1） provide the reasonable values for consistency repairing and 2） detect potential errors. This paper presents context-aware conditional functional dependencies（CCFDs） which contribute to provide reasonable values and detect po- tential errors. Especially, we focus on automatically discov- ering minimal CCFDs. In this paper, we present context rela- tivity to measure the relationship of CFDs. The overlap of the related CFDs can provide reasonable values which result in more accuracy consistency repairing, and some related CFDs are combined into CCFDs. Moreover, we prove that discover- ing minimal CCFDs is NP-complete and we design the pre- cise method and the heuristic method. We also present the dominating value to facilitate the process in both the precise method and the heuristic method. Additionally, the context relativity of the CFDs affects the cleaning results. We will give an approximate threshold of context relativity accord- ing to data distribution for suggestion. The repairing results are approved more accuracy, even evidenced by our empirical evaluation.展开更多
We give the conditionally residual h-integrability with exponent r for an array of random variables and establish the conditional mean convergence of conditionally negatively quadrant dependent and conditionally negat...We give the conditionally residual h-integrability with exponent r for an array of random variables and establish the conditional mean convergence of conditionally negatively quadrant dependent and conditionally negative associated random variables under this integrability. These results generalize and improve the known ones.展开更多
According to current theoretical predictions, any deleterious mutations that reduce nonsexual fitness may have a negative influence on mating success. This means that sexual selection may remove deleterious mutations ...According to current theoretical predictions, any deleterious mutations that reduce nonsexual fitness may have a negative influence on mating success. This means that sexual selection may remove deleterious mutations from the populations. Males of good genetic quality should be more successful in mating, compared to the males of lower genetic quality. As mating success is a condition dependent trait, large fractions of the genome may be a target of sexual selection and many behavioral traits are likely to be condition dependent. We manipulated the genetic quality of Drosophila subobscura males by inducing mutations with ionizing radiation and observed the effects of the obtained heterozygous mutations on male mating behavior： courtship occurrence, courtship latency, mating occurrence, latency to mating and duration of mating. We found possible effects of mutations. Females mated more frequently with male progeny of nonirradiated males and that these males courted females faster compared to the male progeny of irradiated males. Our findings indicate a possible important role of sexual selection in purging deleterious mutations.展开更多
We give a summary on the recent development of chaos theory in topological dynamics, focusing on Li-Yorke chaos, Devaney chaos, distributional chaos, positive topological entropy, weakly mixing sets and so on, and the...We give a summary on the recent development of chaos theory in topological dynamics, focusing on Li-Yorke chaos, Devaney chaos, distributional chaos, positive topological entropy, weakly mixing sets and so on, and their relationships.展开更多
In this paper, we discuss the half inverse problem for Sturm–Liouville equations with boundary conditions dependent on the spectral parameter and a finite number of discontinuities inside the interval and prove the H...In this paper, we discuss the half inverse problem for Sturm–Liouville equations with boundary conditions dependent on the spectral parameter and a finite number of discontinuities inside the interval and prove the Hochstadt–Liberman type theorem for the above boundary-valued problem.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No 71301012
文摘A chimera state consisting of both coherent and incoherent groups is a fascinating spatial pattern in non-locally coupled identical oscillators. It is thought that random initial conditions hardly evolve to chimera states. In this work, we study the dependence of chimera states on initial conditions. We show that random initial conditions may lead to chimera states and the chance of realizing chimera states becomes increasing when the model parameters axe moving away from the boundary of their stable regime.
基金supported by National Natural Science Foundation of China(Grant Nos.12271456,12371270 and 71988101)the Ministry of Education Research in the Humanities and Social Sciences(Grant No.22YJA910002)Shanghai Science and Technology Development Funds(Grant No.23JC1402100)。
文摘Conditional dependence plays a crucial role in various statistical procedures,including variable selection,network analysis and causal inference.However,there remains a paucity of relevant research in the context of high-dimensional conditioning variables,a common challenge encountered in the era of big data.To address this issue,many existing studies impose certain model structures,yet high-dimensional conditioning variables often introduce spurious correlations in these models.In this paper,we systematically study the estimation biases inherent in widely-used measures of conditional dependence when spurious variables are present under high-dimensional settings.We discuss the estimation inconsistency both intuitively and theoretically,demonstrating that the conditional dependencies can be either overestimated or underestimated under different scenarios.To mitigate these biases and attain consistency,we introduce a measure based on data splitting and refitting techniques for high-dimensional conditional dependence.A conditional independence test is also developed using the newly advocated measure,with a tuning-free asymptotic null distribution.Furthermore,the proposed test is applied to generating high-dimensional network graphs in graphical modeling.The superior performances of newly proposed methods are illustrated both theoretically and through simulation studies.We also utilize the method to construct the gene-gene networks using a dataset of breast invasive carcinoma,which contains interesting discoveries that are worth further scientific exploration.
文摘We introduce the Kernel-based Partial Conditional Mean Dependence,a sca-lar-valued measure of conditional mean dependence of Y given X,while adjusting for the nonlinear dependence on Z.Here X,Y and Z are random elements from arbitrary separable Hilbert spaces.This measure ex-tends the Kernel-based Conditional Mean Dependence.As the estimator of the measure is developed,the concentration property of the estimator is proved.Numerical results demonstrate the effectiveness of the new dependence meas-ure in the context of dependence testing,highlighting their advantages in cap-turing nonlinear partial conditional mean dependencies.
基金Supported by Natural Science Foundation of Henan(Grant No.202300410066)Program for Science and Technology Development of Henan Province(Grant No.242102310350).
文摘This paper is concerned with ultrahigh dimensional data analysis,which has become increasingly important in diverse scientific fields.We develop a sure independence screening procedure via the measure of conditional mean dependence based on Copula(CC-SIS,for short).The CC-SIS can be implemented as easily as the sure independence screening procedures which respectively based on the Pearson correlation,conditional mean and distance correlation(SIS,SIRS and DC-SIS,for short)and can significantly improve the performance of feature screening.We establish the sure screening property for the CC-SIS,and conduct simulations to examine its finite sample performance.Numerical comparison indicates that the CC-SIS performs better than the other two methods in various models.At last,we also illustrate the CC-SIS through a real data example.
基金Support by the Natural Science Foundation of Anhui Educational Committee (KJ2007B123)863 Project(2007AA03Z108)
文摘Let X be a compact metric space studies some relationships between stochastic and f ： X→ X be a continuous map. This paper and topological properties of dynamical systems. It is shown that if f satisfies the central limit theorem, then f is topologically ergodic and / is sensitively dependent on initial conditions if and only if / is neither minimal nor equicontinuous.
文摘Conditional dependence learning with high-dimensional conditioning variables.Jianxin Bi,Xingdong Feng&Jingyuan Liu.Abstract Conditional dependence plays a crucial role in various statistical procedures,including variable selection,network analysis and causal inference.However,there remains a paucity of relevant research in the context of high-dimensional conditioning variables,a common challenge encountered in the era of big data.To address this issue,many existing studies impose certain model structures,yet high-dimensional conditioning variables often introduce spurious correlations in these models.In this paper,we systematically study the estimation biases inherent in widely-used measures of conditional dependence when spurious variables are present under high-dimensional settings.
文摘Conditional functional dependencies（CFDs） are important techniques for data consistency. However, CFDs are limited to 1） provide the reasonable values for consistency repairing and 2） detect potential errors. This paper presents context-aware conditional functional dependencies（CCFDs） which contribute to provide reasonable values and detect po- tential errors. Especially, we focus on automatically discov- ering minimal CCFDs. In this paper, we present context rela- tivity to measure the relationship of CFDs. The overlap of the related CFDs can provide reasonable values which result in more accuracy consistency repairing, and some related CFDs are combined into CCFDs. Moreover, we prove that discover- ing minimal CCFDs is NP-complete and we design the pre- cise method and the heuristic method. We also present the dominating value to facilitate the process in both the precise method and the heuristic method. Additionally, the context relativity of the CFDs affects the cleaning results. We will give an approximate threshold of context relativity accord- ing to data distribution for suggestion. The repairing results are approved more accuracy, even evidenced by our empirical evaluation.
基金Acknowledgements The authors thank Editor Lu and two anonymous referees for their constructive suggestions and comments which helped in significantly improving an earlier version of this paper. This work is supported by the National Natural Science Foundation of China （11171001, 11201001, 11426032）, the Natural Science Foundation of Anhui Province （1308085QA03, 1408085QA02）, the Science Fund for Distinguished Young Scholars of Anhui Province （1508085J06）, and Introduction Projects of Anhui University Academic and Technology Leaders.
文摘We give the conditionally residual h-integrability with exponent r for an array of random variables and establish the conditional mean convergence of conditionally negatively quadrant dependent and conditionally negative associated random variables under this integrability. These results generalize and improve the known ones.
文摘According to current theoretical predictions, any deleterious mutations that reduce nonsexual fitness may have a negative influence on mating success. This means that sexual selection may remove deleterious mutations from the populations. Males of good genetic quality should be more successful in mating, compared to the males of lower genetic quality. As mating success is a condition dependent trait, large fractions of the genome may be a target of sexual selection and many behavioral traits are likely to be condition dependent. We manipulated the genetic quality of Drosophila subobscura males by inducing mutations with ionizing radiation and observed the effects of the obtained heterozygous mutations on male mating behavior： courtship occurrence, courtship latency, mating occurrence, latency to mating and duration of mating. We found possible effects of mutations. Females mated more frequently with male progeny of nonirradiated males and that these males courted females faster compared to the male progeny of irradiated males. Our findings indicate a possible important role of sexual selection in purging deleterious mutations.
基金Supported by NNSF of China(Grant Nos.11371339,11431012,11401362,11471125)NSF of Guangdong province(Grant No.S2013040014084)
文摘We give a summary on the recent development of chaos theory in topological dynamics, focusing on Li-Yorke chaos, Devaney chaos, distributional chaos, positive topological entropy, weakly mixing sets and so on, and their relationships.
文摘In this paper, we discuss the half inverse problem for Sturm–Liouville equations with boundary conditions dependent on the spectral parameter and a finite number of discontinuities inside the interval and prove the Hochstadt–Liberman type theorem for the above boundary-valued problem.
