期刊：
Physica A-Statistical Mechanics and its Applications,2020年546:123765 ISSN：0378-4371
通讯作者：
Jin, Zhen
作者机构：
[Song, Haitao; Jin, Jun; Jin, Zhen; Zhou, Zhidong] Shanxi Univ, Complex Syst Res Ctr, Taiyuan 030006, Peoples R China.;[Zhou, Zhidong] Hengyang Normal Univ, Coll Math & Stat, Hengyang 421002, Peoples R China.;[Song, Haitao; Jin, Jun; Jin, Zhen; Zhou, Zhidong] Shanxi Univ, Shanxi Key Lab Math Tech & Big Data Anal Dis Cont, Taiyuan 030006, Peoples R China.
通讯机构：
[Jin, Zhen] S;Shanxi Univ, Complex Syst Res Ctr, Taiyuan 030006, Peoples R China.
关键词：
Complex network;Hypernetwork;Stationary average hyperdegree distribution;Degree distribution;Scale-free;Power-law distribution
摘要：
Based on hypernetwork theory, we construct a new evolving hypernetwork, which incorporating new nodes and new hyperedges growing, old nodes and old hyperedges disappearing, or rewiring of hyperedges from some nodes to anothers. Besides the growth of hyperedges by adding new nodes, it is also possible that a new hyperedge can be constructed between old nodes in hypernetworks. This evolving hypernetwork model with both increasing and decreasing is more realistic than the evolving model only with increasing. By employing Poisson process theory and continuous method, we obtain stationary average hyperdegree distribution and degree distribution of the hypernetwork. Analytical result shows that the evolving hypernetwork following a generalized power-law distribution, has a phenomenon of "the rich get richer'' and a wide range of universality. The theoretical prediction of the stationary average hyperdegree distribution and degree distribution are in good agreement with the real numerical simulation results. (C) 2020 The Authors. Published by Elsevier B.V.
作者机构：
[Li, Linyan; Huang, Haiwu] Hengyang Normal Univ, Coll Math & Stat, Hengyang 421002, Peoples R China.;[Huang, Haiwu] Hunan Prov Key Lab Intelligent Informat Proc & Ap, Hengyang 421002, Peoples R China.;[Lu, Xuewen] Univ Calgary, Dept Math & Stat, Calgary, AB T2N 1N4, Canada.
通讯机构：
[Huang, Haiwu] H;Hengyang Normal Univ, Coll Math & Stat, Hengyang 421002, Peoples R China.;Hunan Prov Key Lab Intelligent Informat Proc & Ap, Hengyang 421002, Peoples R China.
关键词：
negatively orthant dependent random variables;the tail probability;strong convergence
摘要：
In this research, strong convergence properties of the tail probability for weighted sums of negatively orthant dependent random variables are discussed. Some sharp theorems for weighted sums of arrays of rowwise negatively orthant dependent random variables are established. These results not only extend the corresponding ones of Cai [4], Wang et al. [19] and Shen [13], but also improve them, respectively.
作者机构：
[Li, Long; Long, Zuqiang] Hengyang Normal Univ, Coll Math & Stat, Hengyang 421008, Hunan, Peoples R China.;[Qiao, Zhijun] Univ Texas Rio Grande Valley, Dept Math, Edinburg, TX 78539 USA.
通讯机构：
[Li, Long] H;Hengyang Normal Univ, Coll Math & Stat, Hengyang 421008, Hunan, Peoples R China.
摘要：
In this paper, a smoothing algorithm with constant learning rate is presented for training two kinds of fuzzy neural networks (FNNs): max-product and max-min FNNs. Some weak and strong convergence results for the algorithm are provided with the error function monotonically decreasing, its gradient going to zero, and weight sequence tending to a fixed value during the iteration. Furthermore, conditions for the constant learning rate are specified to guarantee the convergence. Finally, three numerical examples are given to illustrate the feasibility and efficiency of the algorithm and to support the theoretical findings.
摘要：
For $$b\in L_{\mathrm{loc}}({\mathbb {R}}^n)$$ and $$0<\alpha <1$$, we use fractional differentiation to define a new type of commutator of the Littlewood-Paley g-function operator, namely $$\begin{aligned} g_{\Omega ,\alpha ;b}(f )(x) =\bigg (\int _0^\infty \bigg |\frac{1}{t} \int _{|x-y|\le t}\frac{\Omega (x-y)}{|x-y|^{n+\alpha -1}}(b(x)-b(y))f(y)\,dy\bigg |^2\frac{dt}{t}\bigg )^{1/2}. \end{aligned}$$Here, we obtain the necessary and sufficient conditions for the function b to guarantee that $$g_{\Omega ,\alpha ;b}$$ is a bounded operator on $$L^2({\mathbb {R}}^n)$$. More precisely, if $$\Omega \in L(\log ^+ L)^{1/2}{(S^{n-1})}$$ and $$b\in I_{\alpha }(BMO)$$, then $$g_{\Omega ,\alpha ;b}$$ is bounded on $$L^2({\mathbb {R}}^n)$$. Conversely, if $$g_{\Omega ,\alpha ;b}$$ is bounded on $$L^2({\mathbb {R}}^n)$$, then $$b \in Lip_\alpha ({\mathbb {R}}^n)$$ for $$0<\alpha < 1$$.
