Stability Analysis for Stochastic Delayed High-order Neural Networks

In this paper, the global asymptotic stability analysis problem is considered for a class of stochastic high-order neural networks with tin.delays. Based on a Lyapunov-Krasovskii functional and the stochastic stability analysis theory, several sufficient conditions are derived in order to guarantee the global asymptotic convergence of the equilibtium paint in the mean square. Investigation shows that the addressed stochastic highorder delayed neural networks are globally asymptotically stable in the mean square if there are solutions to some linear matrix inequalities （LMIs）. Hence, the global asymptotic stability of the studied stochastic high-order delayed neural networks can be easily checked by the Matlab LMI toolbox. A numerical example is given to demonstrate the usefulness of the proposed global stability criteria.

Important edge identification in complex networks based on local and global features

Identifying important nodes and edges in complex networks has always been a popular research topic in network science and also has important implications for the protection of real-world complex systems.Finding the critical structures in a system allows us to protect the system from attacks or failures with minimal cost.To date,the problem of identifying critical nodes in networks has been widely studied by many scholars,and the theory is becoming increasingly mature.However,there is relatively little research related to edges.In fact,critical edges play an important role in maintaining the basic functions of the network and keeping the integrity of the structure.Sometimes protecting critical edges is less costly and more flexible in operation than just focusing on nodes.Considering the integrity of the network topology and the propagation dynamics on it,this paper proposes a centrality measure based on the number of high-order structural overlaps in the first and second-order neighborhoods of edges.The effectiveness of the metric is verified by the infection-susceptibility(SI)model,the robustness index R,and the number of connected branchesθ.A comparison is made with three currently popular edge importance metrics from two synthetic and four real networks.The simulation results show that the method outperforms existing methods in identifying critical edges that have a significant impact on both network connectivity and propagation dynamics.At the same time,the near-linear time complexity can be applied to large-scale networks.

Four optimal design approaches of high-order finite-impulse response filters based on neural network

Four optimal approaches of high-order finite-impulse response(FIR) digital filters were developed for designing four types filters using neural network algorithms. The solutions were presented as parallel algorithms to approximate the desired frequency response specification. Therefore, these methods avoid matrix inversion, and make a fast calculation of the filter’s coefficients possible. The convergence theorems of these proposed algorithms were presented and proved to illustrate them stable, and the implementation of these methods was described together with some design guidelines. The simulation results show that the ripples of the designed FIR filters are significantly little in the pass-band and stop-band, and the proposed algorithms are of fast convergence.

New Stability Criteria for High-Order Neural Networks with Proportional Delays

This paper is concerned with high-order neural networks with proportional delays. The proportional delay is a time-varying unbounded delay which is different from the constant delay, bounded time-varying delay and distributed delay. By the nonlinear transformation yi(t) = ui( et)(i = 1, 2,..., n), we transform a class of high-order neural networks with proportional delays into a class of high-order neural networks with constant delays and timevarying coefficients. With the aid of Brouwer fixed point theorem and constructing the delay differential inequality, we obtain some delay-independent and delay-dependent sufficient conditions to ensure the existence, uniqueness and global exponential stability of equilibrium of the network. Two examples with their simulations are given to illustrate the theoretical findings. Our results are new and complement previously known results.

Estimating Functional Brain Network with Low-Rank Structure via Matrix Factorization for MCI/ASD Identification

Functional brain networks (FBNs) provide a potential way for understanding the brain organizational patterns and diagnosing neurological diseases. Due to its importance, many FBN construction methods have been proposed currently, including the low-order Pearson’s correlation (PC) and sparse representation (SR), as well as the high-order functional connection (HoFC). However, most existing methods usually ignore the information of topological structures of FBN, such as low-rank structure which can reduce the noise and improve modularity to enhance the stability of networks. In this paper, we propose a novel method for improving the estimated FBNs utilizing matrix factorization (MF). More specifically, we firstly construct FBNs based on three traditional methods, including PC, SR, and HoFC. Then, we reduce the rank of these FBNs via MF model for estimating FBN with low-rank structure. Finally, to evaluate the effectiveness of the proposed method, experiments have been conducted to identify the subjects with mild cognitive impairment (MCI) and autism spectrum disorder (ASD) from norm controls (NCs) using the estimated FBNs. The results on Alzheimer’s Disease Neuroimaging Initiative (ADNI) dataset and Autism Brain Imaging Data Exchange (ABIDE) dataset demonstrate that the classification performances achieved by our proposed method are better than the selected baseline methods.

Identifying Vital Nodes in Social Networks Using an Evidential Methodology Combining with High-Order Analysis

Identifying vital nodes is a basic problem in social network research.The existing theoretical framework mainly focuses on the lowerorder structure of node-based and edge-based relations and often ignores important factors such as interactivity and transitivity between multiple nodes.To identify the vital nodes more accurately,a high-order structure,named as the motif,is introduced in this paper as the basic unit to evaluate the similarity among the node in the complex network.It proposes a notion of high-order degree of nodes in complex network and fused the effect of the high-order structure and the lower-order structure of nodes,using evidence theory to determine the vital nodes more efficiently and accurately.The algorithm was evaluated from the function of network structure.And the SIR model was adopted to examine the spreading influence of the nodes ranked.The results of experiments in different datasets demonstrate that the algorithm designed can identify vital nodes in the social network accurately.

BHONEM:Binary High-Order Network Embedding Methods for Net worked-Guarantee Loans

Networked-guarantee loans may cause systemic risk related concern for the government and banks in China.The prediction of the default of enterprise loans is a typical machine learning based classification problem, and the networked guarantee makes this problem very difficult to solve. As we know, a complex network is usually stored and represented by an adjacency matrix. It is a high-dimensional and sparse matrix, whereas machine-learning methods usually need lowdimensional dense feature representations. Therefore, in this paper, we propose a binary higher-order network embedding method to learn the low-dimensional representations of a guarantee network. We first set vertices of this heterogeneous economic network by binary roles (guarantor and guarantee), and then define high-order adjacent measures based on their roles and economic domain knowledge. Afterwards, we design a penalty parameter in the objective function to balance the importance of network structure and adjacency. We optimize it by negative sampling based gradient descent algorithms,which solve the limitation of stochastic gradient descent on weighted edges without compromising efficiency. Finally, we test our proposed method on three real-world network datasets. The result shows that this method outperforms other start-of-the-art algorithms for both classification accuracy and robustness, especially in a guarantee network.

语义特征造型的特征识别策略

特征识别是语义特征造型系统面临的一个难题。尤其是当遇到复杂的拓扑结构或是较多的特征数量时,如何提高特征识别的效率以及采取何种识别方法,成为该技术领域的热门课题之一。通过运用BAM神经网络检测技术,提出了一种全新的特征识别策略,有效解决了CAD/CAM系统的性能瓶颈问题。

A deep learning method for solving high-order nonlinear soliton equations

We propose an effective scheme of the deep learning method for high-order nonlinear soliton equations and explore the influence of activation functions on the calculation results for higherorder nonlinear soliton equations. The physics-informed neural networks approximate the solution of the equation under the conditions of differential operator, initial condition and boundary condition. We apply this method to high-order nonlinear soliton equations, and verify its efficiency by solving the fourth-order Boussinesq equation and the fifth-order Korteweg–de Vries equation. The results show that the deep learning method can be used to solve high-order nonlinear soliton equations and reveal the interaction between solitons.

变时滞高阶BAM神经网络的稳定性

文章研究高阶BAM神经网络的稳定性,运用Brouwer不动点定理以及Lyapunov泛函方法,得到周期解的存在唯一性和稳定性.

Analysis of Gene Networks for Arabidopsis Flowering

The flowering time of Arabidopsis is sensitive to climate variability, with lighting conditions being a major determinant of the flowering time. Long-days induce early flowering, while short-days induce late flowering or even no flowers. This study investigates the intrinsic mechanisms for Arabidopsis flowering in different lighting conditions using mutual information networks and logic networks. The structure parameters of the mutual information networks show that the average degree and the average core clearly distinguish these networks. A method is then given to find the key structural genes in the mutual information networks and the logic networks respectively. Ten genes are found to possibly promote flowering with three genes that may restrain flowering. The sensitivity of this method to find the genes that promote flowering is 80%, while the sensitivity of the method to find the genes that restrain flowering is 100%.

High-Order Two-Dimension Cluster Competitive Activation Mechanisms Used for Performing Symbolic Logic Algorithms of Problem Solving

This paper presents a neural network approach, based on high-order two-dimension temporal and dynamically clustering competitive activation mecha-nisms, to implement parallel searching algorithm and many other symbolic logicalgorithms. This approach is superior in many respects to both the commonsequential algorithms of symbolic logic and the common neura.l network usedfor optimization problems. Simulations of problem solving examples prove theeffectiveness of the approach.

Generalized Embedding Machines for Recommender Systems

Factorization machine (FM) is an effective model for feature-based recommendation that utilizes inner products to capture second-order feature interactions. However, one of the major drawbacks of FM is that it cannot capture complex high-order interaction signals. A common solution is to change the interaction function, such as stacking deep neural networks on the top level of FM. In this work, we propose an alternative approach to model high-order interaction signals at the embedding level, namely generalized embedding machine (GEM). The embedding used in GEM encodes not only the information from the feature itself but also the information from other correlated features. Under such a situation, the embedding becomes high-order. Then we can incorporate GEM with FM and even its advanced variants to perform feature interactions. More specifically, in this paper, we utilize graph convolution networks (GCN) to generate high-order embeddings. We integrate GEM with several FM-based models and conduct extensive experiments on two real-world datasets. The results demonstrate significant improvement of GEM over the corresponding baselines.

Convergence of neutral type proportional-delayed HCNNs with D operators

This paper is concerned with neutral type high-order cellular neural networks(HCNNs)involving proportional delays and D operators.Some criteria are established for the global exponential convergence of the addressed models by using differential inequality techniques.Moreover,an example and its numerical simulations are employed to illustrate the main results.