The optimization problem to minimize the weighted sum ofα-z Bures-Wasserstein quantum divergences to given positive definite Hermitian matrices has been solved.We call the unique minimizer theα-z weighted right mean...The optimization problem to minimize the weighted sum ofα-z Bures-Wasserstein quantum divergences to given positive definite Hermitian matrices has been solved.We call the unique minimizer theα-z weighted right mean,which provides a new non-commutative version of generalized mean(H?lder mean).We investigate its fundamental properties,and give many interesting operator inequalities with the matrix power mean including the Cartan mean.Moreover,we verify the trace inequality with the Wasserstein mean and provide bounds for the Hadamard product of two right means.展开更多
Based on the martingale difference divergence,a recently proposed metric for quantifying conditional mean dependence,we introduce a consistent test of U-type for the goodness-of-fit of linear models under conditional ...Based on the martingale difference divergence,a recently proposed metric for quantifying conditional mean dependence,we introduce a consistent test of U-type for the goodness-of-fit of linear models under conditional mean restriction.Methodologically,our test allows heteroscedastic regression models without imposing any condition on the distribution of the error,utilizes effectively important information contained in the distance of the vector of covariates,has a simple form,is easy to implement,and is free of the subjective choice of parameters.Theoretically,our mathematical analysis is of own interest since it does not take advantage of the empirical process theory and provides some insights on the asymptotic behavior of U-statistic in the framework of model diagnostics.The asymptotic null distribution of the proposed test statistic is derived and its asymptotic power behavior against fixed alternatives and local alternatives converging to the null at the parametric rate is also presented.In particular,we show that its asymptotic null distribution is very different from that obtained for the true error and their differences are interestingly related to the form expression for the estimated parameter vector embodied in regression function and a martingale difference divergence matrix.Since the asymptotic null distribution of the test statistic depends on data generating process,we propose a wild bootstrap scheme to approximate its null distribution.The consistency of the bootstrap scheme is justified.Numerical studies are undertaken to show the good performance of the new test.展开更多
Internet services and web-based applications play pivotal roles in various sensitive domains, encompassing e-commerce, e-learning, e-healthcare, and e-payment. However, safeguarding these services poses a significant ...Internet services and web-based applications play pivotal roles in various sensitive domains, encompassing e-commerce, e-learning, e-healthcare, and e-payment. However, safeguarding these services poses a significant challenge, as the need for robust security measures becomes increasingly imperative. This paper presented an innovative method based on differential analyses to detect abrupt changes in network traffic characteristics. The core concept revolves around identifying abrupt alterations in certain characteristics such as input/output volume, the number of TCP connections, or DNS queries—within the analyzed traffic. Initially, the traffic is segmented into distinct sequences of slices, followed by quantifying specific characteristics for each slice. Subsequently, the distance between successive values of these measured characteristics is computed and clustered to detect sudden changes. To accomplish its objectives, the approach combined several techniques, including propositional logic, distance metrics (e.g., Kullback-Leibler Divergence), and clustering algorithms (e.g., K-means). When applied to two distinct datasets, the proposed approach demonstrates exceptional performance, achieving detection rates of up to 100%.展开更多
We discussed a totally real Riemannian foliations with parallel mean curvature on a complex projective space.We carried out the divergence of a vector field on it and obtained a formula of Simons’type.
It is well known in the literature that the logarithmic means 1/logn ^n-1∑k=1 Sk（f）/k of Walsh or trigonometric Fourier series converge a.e. to the function for each integrable function on the unit interval. This i...It is well known in the literature that the logarithmic means 1/logn ^n-1∑k=1 Sk（f）/k of Walsh or trigonometric Fourier series converge a.e. to the function for each integrable function on the unit interval. This is not the case if we take the partial sums. In this paper we prove that the behavior of the so-called NSrlund logarithmic means 1/logn ^n-1∑k=1 Sk（f）/n-k is closer to the properties of partial sums in this point of view.展开更多
基金supported by the National Re-search Foundation of Korea(NRF)grant funded by the Korea government(MSIT)(NRF-2022R1A2C4001306)supported by Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education(NRF-2022R1I1A1A01068411)。
文摘The optimization problem to minimize the weighted sum ofα-z Bures-Wasserstein quantum divergences to given positive definite Hermitian matrices has been solved.We call the unique minimizer theα-z weighted right mean,which provides a new non-commutative version of generalized mean(H?lder mean).We investigate its fundamental properties,and give many interesting operator inequalities with the matrix power mean including the Cartan mean.Moreover,we verify the trace inequality with the Wasserstein mean and provide bounds for the Hadamard product of two right means.
基金supported by the National Natural Science Foundation of China(No.12271005 and No.11901006)Natural Science Foundation of Anhui Province(2308085Y06,1908085QA06)+2 种基金Young Scholars Program of Anhui Province(2023)Anhui Provincial Natural Science Foundation(Grant No.2008085MA08)Foundation of Anhui Provincial Education Department(Grant No.KJ2021A1523)。
文摘Based on the martingale difference divergence,a recently proposed metric for quantifying conditional mean dependence,we introduce a consistent test of U-type for the goodness-of-fit of linear models under conditional mean restriction.Methodologically,our test allows heteroscedastic regression models without imposing any condition on the distribution of the error,utilizes effectively important information contained in the distance of the vector of covariates,has a simple form,is easy to implement,and is free of the subjective choice of parameters.Theoretically,our mathematical analysis is of own interest since it does not take advantage of the empirical process theory and provides some insights on the asymptotic behavior of U-statistic in the framework of model diagnostics.The asymptotic null distribution of the proposed test statistic is derived and its asymptotic power behavior against fixed alternatives and local alternatives converging to the null at the parametric rate is also presented.In particular,we show that its asymptotic null distribution is very different from that obtained for the true error and their differences are interestingly related to the form expression for the estimated parameter vector embodied in regression function and a martingale difference divergence matrix.Since the asymptotic null distribution of the test statistic depends on data generating process,we propose a wild bootstrap scheme to approximate its null distribution.The consistency of the bootstrap scheme is justified.Numerical studies are undertaken to show the good performance of the new test.
文摘Internet services and web-based applications play pivotal roles in various sensitive domains, encompassing e-commerce, e-learning, e-healthcare, and e-payment. However, safeguarding these services poses a significant challenge, as the need for robust security measures becomes increasingly imperative. This paper presented an innovative method based on differential analyses to detect abrupt changes in network traffic characteristics. The core concept revolves around identifying abrupt alterations in certain characteristics such as input/output volume, the number of TCP connections, or DNS queries—within the analyzed traffic. Initially, the traffic is segmented into distinct sequences of slices, followed by quantifying specific characteristics for each slice. Subsequently, the distance between successive values of these measured characteristics is computed and clustered to detect sudden changes. To accomplish its objectives, the approach combined several techniques, including propositional logic, distance metrics (e.g., Kullback-Leibler Divergence), and clustering algorithms (e.g., K-means). When applied to two distinct datasets, the proposed approach demonstrates exceptional performance, achieving detection rates of up to 100%.
文摘We discussed a totally real Riemannian foliations with parallel mean curvature on a complex projective space.We carried out the divergence of a vector field on it and obtained a formula of Simons’type.
基金the Hungarian National Foundation for Scientific Research(OTKA)(Grant No.T048780)the Georgian National Foundation for Scientific Research(Grant No.GNSF/ST07/3-171)
文摘It is well known in the literature that the logarithmic means 1/logn ^n-1∑k=1 Sk（f）/k of Walsh or trigonometric Fourier series converge a.e. to the function for each integrable function on the unit interval. This is not the case if we take the partial sums. In this paper we prove that the behavior of the so-called NSrlund logarithmic means 1/logn ^n-1∑k=1 Sk（f）/n-k is closer to the properties of partial sums in this point of view.
