期刊：
Cognitive Systems Research,2021年68:62-72 ISSN：1389-0417
通讯作者：
Gao, T.;Wang, J.
作者机构：
[Li, Long] Hengyang Normal Univ, Coll Math & Stat, Henyang 421001, Peoples R China.;[Xie, Xuetao] Sichuan Univ, Coll Comp Sci, Chengdu 610065, Peoples R China.;[Gao, Tao] Beihang Univ, Sch Comp Sci & Engn, Beijing 100191, Peoples R China.;[Wang, Jian] China Univ Petr, Coll Sci, Qingdao 266580, Peoples R China.
通讯机构：
[Gao, T.] S;[Wang, J.] C;School of Computer Science and Engineering, Beihang University, Beijing 100191, China
关键词：
Armijo;Conjugate gradient;Convergence;Elman
摘要：
Elman recurrent network is a representative model with feedback mechanism. Although gradient descent method has been widely used to train Elman network, it frequently leads to slow convergence. According to optimization theory, conjugate gradient method is an alternative strategy in searching the descent direction during training. In this paper, an efficient conjugate gradient method has been presented to reach the optimal solution in two ways: (1) constructing a more effective conjugate coefficient, (2) determining adaptive learning rates in terms of the generalized Armijo search method. Experiments show that the performance of the new algorithm is superior to traditional algorithms, such as gradient descent method and conjugate gradient method. In particular, the new algorithm has better performance than the evolutionary algorithm. Finally, we prove the weak and strong convergence of the presented algorithm, i.e., the gradient norm of the error function with respect to the weight vectors converges to zero and the weight sequence approaches a fixed optimal point. (C) 2021 Elsevier B.V. All rights reserved.
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.
期刊：
JOURNAL OF EXPERIMENTAL BOTANY,2019年70(15):3969-3979 ISSN：0022-0957
通讯作者：
Tang, Kexuan;Chen, Wansheng;Zhang, Lei
作者机构：
[Ma, Yanan; Li, Ling; Fu, Xueqing; Shen, Qian; Zhang, Fangyuan; Hao, Xiaolong; Zhang, Lida; Lv, Zongyou; Shi, Pu; Chen, Minghui; Tang, Kexuan; Yan, Tingxiang] Shanghai Jiao Tong Univ, Joint Int Res Lab Metab & Dev Sci, Key Lab Urban Agr South, Minist Agr,Plant Biotechnol Res Ctr,Fudan SJTU No, Shanghai 200240, Peoples R China.;[Chen, Wansheng; Lv, Zongyou] Second Mil Med Univ, Changzheng Hosp, Dept Pharm, Shanghai 200003, Peoples R China.;[Chen, Wansheng; Lv, Zongyou] Shanghai Univ Tradit Chinese Med, Res & Dev Ctr Chinese Med Resources & Biotechnol, Shanghai 201203, Peoples R China.;[Zhang, Lei; Guo, Zhiying] Second Mil Med Univ, Sch Pharm, Dept Pharmaceut Bot, Shanghai 200433, Peoples R China.;[Jiang, Weimin] Hengyang Normal Univ, Coll Life Sci & Environm, Hengyang 421008, Hunan, Peoples R China.
通讯机构：
[Tang, Kexuan; Chen, Wansheng; Zhang, Lei] S;[Zhang, Lei] Z;Shanghai Jiao Tong Univ, Joint Int Res Lab Metab & Dev Sci, Key Lab Urban Agr South, Minist Agr,Plant Biotechnol Res Ctr,Fudan SJTU No, Shanghai 200240, Peoples R China.;Second Mil Med Univ, Changzheng Hosp, Dept Pharm, Shanghai 200003, Peoples R China.;Shanghai Univ Tradit Chinese Med, Res & Dev Ctr Chinese Med Resources & Biotechnol, Shanghai 201203, Peoples R China.
摘要：
Artemisinin is a sesquiterpene lactone produced by the Chinese traditional herb Artemisia annua and is used for the treatment of malaria. It is known that salicylic acid (SA) can enhance artemisinin content but the mechanism by which it does so is not known. In this study, we systematically investigated a basic leucine zipper family transcription factor, AaTGA6, involved in SA signaling to regulate artemisinin biosynthesis. We found specific in vivo and in vitro binding of the AaTGA6 protein to a 'TGACG' element in the AaERF1 promoter. Moreover, we demonstrated that AaNPR1 can interact with AaTGA6 and enhance its DNA-binding activity to its cognate promoter element 'TGACG' in the promoter of AaERF1, thus enhancing artemisinin biosynthesis. The artemisinin contents in AaTGA6-overexpressing and RNAi transgenic plants were increased by 90-120% and decreased by 20-60%, respectively, indicating that AaTGA6 plays a positive role in artemisinin biosynthesis. Importantly, heterodimerization with AaTGA3 significantly inhibits the DNA-binding activity of AaTGA6 and plays a negative role in target gene activation. In conclusion, we demonstrate that binding of AaTGA6 to the promoter of the artemisinin-regulatory gene AaERF1 is enhanced by AaNPR1 and inhibited by AaTGA3. Based on these findings, AaTGA6 has potential value in the genetic engineering of artemisinin production.
摘要：
In order to broaden the study of the most popular and general Takagi-Sugeno (TS) system, we propose a complex-valued neuro-fuzzy inference system which realises the zero-order TS system in the complex-valued network architecture and develop it. In the complex domain, boundedness and analyticity cannot be achieved together. The splitting strategy is given by computing the gradients of the real-valued error function with respect to the real and the imaginary parts of the weight parameters independently. Specifically, this system has four layers: in the Gaussian layer, the L-dimensional complex-valued input features are mapped to a Q-dimensional real-valued space, and in the output layer, complex-valued weights are employed to project it back to the complex domain. Hence, split-complex valued gradients of the real-valued error function are obtained, forming the split-complex valued neuro-fuzzy (split-CVNF) learning algorithm based on gradient descent. Another contribution of this paper is that the deterministic convergence of the split-CVNF algorithm is analysed. It is proved that the error function is monotone during the training iteration process, and the sum of gradient norms tends to zero. By adding a moderate condition, the weight sequence itself is also proved to be convergent.
摘要：
While the existence of conformal mappings between doubly connected domains is characterized by their conformal moduli, no such characterization is available for harmonic dilfeomorphisms. Intuitively, one expects their existence if the domain is not too thick compared to the codomain. We make this intuition precise by showing that for a Dini-smooth doubly connected domain Omega* there exists a epsilon> 0 such that for every doubly connected domain Omega with Mod Omega* < Mod Omega < Mod Omega* + epsilon there exists a harmonic dilfeomorphism from Omega onto Omega*.
摘要：
Conjugate gradient methods can be used with advantages such as fast convergence and low memory requirement in real applications. A conjugate gradient-based neuro-fuzzy learning algorithm for zero-order Takagi-Sugeno inference systems is proposed in this paper. Compared with the existing gradient-based algorithm, this method enhances the learning performance.
摘要：
This paper investigates the split complex gradient descent based neuro-fuzzy algorithm with self-adaptive momentum and L-2 regularizer for training TSK (Takagi-Sugeno-Kang) fuzzy inference models. The major threat for disposing complex data with fuzzy system is contradiction of boundedness and analyticity in the complex domain, as expressed by Liouville's theorem. The proposed algorithm operates a couple of real-valued functions and splits the complex variables into real part and imaginary part. Dynamical momentum is included in the learning mechanism to promote learning speed. L-2 regularizer is also added to control the magnitude of the weight parameters. Furthermore, a detailed convergence analysis of the proposed algorithm is fully studied. The monotonic decreasing property of the error function and convergence of the weight sequence are guaranteed. Plus a mild condition, strong convergence of the weight sequence is deduced. Finally, the simulation results are also demonstrated to verify the theoretical analysis results. (C) 2018 Elsevier B.V. All rights reserved.
摘要：
During past few years, some lightweight block ciphers have been proposed. These lightweight block ciphers take single encryption method that either uses Substitution-Permutation (SP) network structure or Feistel network structure to encrypt. In this paper, we have designed a different encryption method that takes both SP network structure and Feistel network structure to encrypt. Current SP network has a limitation that the encryption and decryption processes are dissimilar. To solve this problem, we have employed involution related properties of the nonlinear and linear components to modify SP network structure. The modified one enables the encryption and decryption program or circuit to work as the Feistel network structure. Additionally, we have implemented a MixRows in SP network structure. Then we instantiate these three novel ideas into the lightweight block cipher called SFN. We have carried out the security evaluation and the hardware and software experiments to it. The result shows that compared to other lightweight block ciphers, SFN has more advantages in terms of being immune to attacks. Also, SFN is not only compact in hardware environment but also efficient in software platforms.
摘要：
In this paper, by constructing a generalized Armijo search method, a novel conjugate gradient (CG) model has been proposed to training a common three-layer backpropagation (BP) neural network. Compared with the classical gradient descent method, this algorithm efficiently accelerates the convergence speed due to the existence of the additional conjugate direction. Essentially, the optimal learning rate of each epoch is determined by the given inexact line search strategy. The presented model does not significantly increase the computational cost in dealing with real applications. Two benchmark simulations have been performed to illustrate the promising advantages of the proposed algorithm.
作者机构：
[Chen, Yuan; Li, Long] Hengyang Normal Univ, Coll Math & Stat, Hengyang 421008, Peoples R China.;[Qiao, Zhijun] Univ Texas Rio Grande Valley, Sch Math & Stat Sci, Edinburg, TX 78539 USA.;[Liu, Yan] Dalian Polytech Univ, Dept Appl Math, Dalian 116034, Peoples R China.
通讯机构：
[Li, Long] H;Hengyang Normal Univ, Coll Math & Stat, Hengyang 421008, Peoples R China.
摘要：
In this paper, a smooth function is constructed to approximate the nonsmooth output of max-min fuzzy neural networks (FNNs) and its approximation is also presented. In place of the output of max-min FNNs by its smoothing approximation function, the error function, defining the discrepancy between the actual outputs and desired outputs of max-min FNNs, becomes a continuously differentiable function. Then, a smoothing gradient decent-based algorithm with Armijo-Goldstein step size rule is formulated to train max-min FNNs. Based on the existing convergent result, the convergence of our proposed algorithm can easily be obtained. Furthermore, the proposed algorithm also provides a feasible procedure to solve fuzzy relational equations with max-min composition. Finally, some numerical examples are implemented to support our results and demonstrate that the proposed smoothing algorithm has better learning performance than other two gradient decent-based algorithms. (C) 2017 Elsevier B.V. All rights reserved.
作者机构：
[龙祖强; 许岳兵; 李龙] College of Physics and Electronic Engineering, Hengyang Normal University, Hengyang, Hunan, 421002, China;[龙祖强] Department of Computers and Electronic Engineering, Wayne State University, Detroit, MI, 48202, United States
通讯机构：
College of Physics and Electronic Engineering, Hengyang Normal University, Hengyang, Hunan, China
作者机构：
[Li, L.] Hengyang Normal Univ, Coll Math & Stat, Hengyang 421002, Hunan, Peoples R China.;[Ponnusamy, S.] Indian Stat Inst, Chennai Ctr, Soc Elect Transact & Secur, MGR Knowledge City, CIT Campus, Madras 600113, Tamil Nadu, India.;[Qiao, J.] Hebei Univ, Dept Math, Baoding 071002, Hebei, Peoples R China.
关键词：
univalent;starlike;convex and close-to-convex function;extreme point;closed convex hull and subordination;Zalcman conjecture
摘要：
Let
$${\mathcal S}$$
denote the class of all functions of the form
$${f(z)=z+a_2z^2+a_3z^3+\cdots}$$
which are analytic and univalent in the open unit disk
$${{\mathbb{D}} }$$
and, for
$${\lambda > 0}$$
, let
$${\Phi_\lambda (n,f)=\lambda a_n^2-a_{2n-1}}$$
denote the generalized Zalcman coefficient functional. Zalcman conjectured that if
$${f\in \mathcal S}$$
, then
$${|\Phi_1 (n,f)|\leq (n-1)^2}$$
for
$${{n\ge 3}}$$
. The functional of the form
$${\Phi_\lambda (n,f)}$$
is indeed related to Fekete–Szegő functional of the
$${n}$$
-th root transform of the corresponding function in
$${\mathcal S}$$
. This conjecture has been verified for a certain special geometric subclasses of
$${\mathcal S}$$
but it remains open for
$${f\in {\mathcal S}}$$
and for
$${n > 6}$$
. In the present paper, we prove sharp bounds on
$${|\Phi_\lambda (n,f)|}$$
for
$${f\in \mathcal{F}(\alpha )}$$
and for all
$${n\geq 3}$$
, in the case that
$${\lambda}$$
is a positive real parameter, where
$${ \mathcal{F}(\alpha )}$$
denotes the family of all functions
$${f\in {\mathcal S}}$$
satisfying the condition
$${\rm{Re}} \Big( 1+\frac{zf''(z)}{f'(z)}
\Big) > \alpha \quad \mbox{for } z\in {\mathbb{D}} ,$$
where
$${-1/2\leq \alpha < 1}$$
. Thus, the present article proves the generalized Zalcman conjecture for convex functions of order
$${\alpha}$$
,
$${\alpha \in [-1/2,1)}$$
.
