The article is devoted to the evaluation of fractal properties of routing data in computer large scale networks. Implemented the study of percolation network topological structures of large dimension and made their tr...The article is devoted to the evaluation of fractal properties of routing data in computer large scale networks. Implemented the study of percolation network topological structures of large dimension and made their transformation into fractal macrostructure. An example of calculating the fractal dimension of the data path for the boundary of the phase transition between the states of network connectivity. The dependence of the fractal dimension of the percolation cluster on the size of the square δ-cover and conductivity value network of large dimension. It is shown that for the value of the fractal dimension of the route dc ≈ 1.5, network has a stable dynamics of development and size of clusters are optimized with respect to the current load on the network.展开更多
The authors define the directional hyper Hilbert transform and give ita mixed norm estimate. The similar conclusions for the directional fractional integral of one dimension are also obtained in this paper. As an appl...The authors define the directional hyper Hilbert transform and give ita mixed norm estimate. The similar conclusions for the directional fractional integral of one dimension are also obtained in this paper. As an application of the above results, the authors give the Lp-boundedness for a class of the hyper singular integrals and the fractional integrals with variable kernel. Moreover, as another application of the above results, the authors prove the dimension free estimate for the hyper Riesz transform. This is an extension of the related result obtained by Stein.展开更多
We study the properties of the Lasso in the high-dimensional partially linear model where the number of variables in the linear part can be greater than the sample size.We use truncated series expansion based on polyn...We study the properties of the Lasso in the high-dimensional partially linear model where the number of variables in the linear part can be greater than the sample size.We use truncated series expansion based on polynomial splines to approximate the nonparametric component in this model.Under a sparsity assumption on the regression coefficients of the linear component and some regularity conditions,we derive the oracle inequalities for the prediction risk and the estimation error.We also provide sufficient conditions under which the Lasso estimator is selection consistent for the variables in the linear part of the model.In addition,we derive the rate of convergence of the estimator of the nonparametric function.We conduct simulation studies to evaluate the finite sample performance of variable selection and nonparametric function estimation.展开更多
In this paper, the dimension of invariant subspaces admitted by nonlinear sys- tems is estimated under certain conditions. It is shown that if the two-component nonlinear vector differential operator F = （F1, F2） wi...In this paper, the dimension of invariant subspaces admitted by nonlinear sys- tems is estimated under certain conditions. It is shown that if the two-component nonlinear vector differential operator F = （F1, F2） with orders {k1, k2} （k1≥ k2） preserves the invariant subspace Wn1^1× Wn2^2 （n1 ≥ n2）, then n1 - n2 ≤ k2, n1 ≤2（k1 ＋ k2） ＋ 1, where Wnq^q is the space generated by solutions of a linear ordinary differential equation of order nq （q = 1, 2）. Several examples including the （1＋1）-dimensional diffusion system and Ito＇s type, Drinfel＇d-Sokolov-Wilson＇s type and Whitham-Broer-Kaup＇s type equations are presented to illustrate the result. Furthermore, the estimate of dimension for m-component nonlinear systems is also given.展开更多
文摘The article is devoted to the evaluation of fractal properties of routing data in computer large scale networks. Implemented the study of percolation network topological structures of large dimension and made their transformation into fractal macrostructure. An example of calculating the fractal dimension of the data path for the boundary of the phase transition between the states of network connectivity. The dependence of the fractal dimension of the percolation cluster on the size of the square δ-cover and conductivity value network of large dimension. It is shown that for the value of the fractal dimension of the route dc ≈ 1.5, network has a stable dynamics of development and size of clusters are optimized with respect to the current load on the network.
基金the 973 Project of China(No.G1999075105)the National Natural ScienceFoundation of China(No.19631080,No.10271016)the Zhejiang Provincial Natural ScienceFoundation of China(No.RC97017,No.197042).
文摘The authors define the directional hyper Hilbert transform and give ita mixed norm estimate. The similar conclusions for the directional fractional integral of one dimension are also obtained in this paper. As an application of the above results, the authors give the Lp-boundedness for a class of the hyper singular integrals and the fractional integrals with variable kernel. Moreover, as another application of the above results, the authors prove the dimension free estimate for the hyper Riesz transform. This is an extension of the related result obtained by Stein.
文摘We study the properties of the Lasso in the high-dimensional partially linear model where the number of variables in the linear part can be greater than the sample size.We use truncated series expansion based on polynomial splines to approximate the nonparametric component in this model.Under a sparsity assumption on the regression coefficients of the linear component and some regularity conditions,we derive the oracle inequalities for the prediction risk and the estimation error.We also provide sufficient conditions under which the Lasso estimator is selection consistent for the variables in the linear part of the model.In addition,we derive the rate of convergence of the estimator of the nonparametric function.We conduct simulation studies to evaluate the finite sample performance of variable selection and nonparametric function estimation.
基金Project supported by the National Natural Science Foundation of China for Distinguished Young Scholars (No.10925104)the National Natural Science Foundation of China (No.11001240)+1 种基金the Doctoral Program Foundation of the Ministry of Education of China (No.20106101110008)the Zhejiang Provincial Natural Science Foundation of China (Nos.Y6090359,Y6090383)
文摘In this paper, the dimension of invariant subspaces admitted by nonlinear sys- tems is estimated under certain conditions. It is shown that if the two-component nonlinear vector differential operator F = （F1, F2） with orders {k1, k2} （k1≥ k2） preserves the invariant subspace Wn1^1× Wn2^2 （n1 ≥ n2）, then n1 - n2 ≤ k2, n1 ≤2（k1 ＋ k2） ＋ 1, where Wnq^q is the space generated by solutions of a linear ordinary differential equation of order nq （q = 1, 2）. Several examples including the （1＋1）-dimensional diffusion system and Ito＇s type, Drinfel＇d-Sokolov-Wilson＇s type and Whitham-Broer-Kaup＇s type equations are presented to illustrate the result. Furthermore, the estimate of dimension for m-component nonlinear systems is also given.
