混沌神经网络的动态阈值控制

提出了混沌神经网络的动态阈值控制方法, 将大脑脑电波的主要成分, 正弦信号作为控制变量实现对混沌神经网络内部状态的阈值动态改变, 从而达到了控制混沌神经网络混沌的目的. 利用该方法可以将混沌神经网络的输出稳定在一个与网络初始模式相关的存储模式和其反相模式上, 从而使混沌神经网络在模式识别、信息搜索等信息处理功能得以实现. 该控制方法不需要事先指定阈值, 是一种自适应方法, 符合实际人脑的思维运动. 关键词： 混沌控制 混沌神经网络 动态阈值控制 信息处理     

Kauffman networks with threshold functions

We investigate Threshold Random Boolean Networks with K = 2 inputs per node, which are equivalent to Kauffman networks, with only part of the canalyzing functions as update functions. According to the simplest consideration these networks should be critical but it turns out that they show a rich variety of behaviors, including periodic and chaotic oscillations. The analytical results are supported by computer simulations.     

Epidemic threshold and immunization on generalized networks

The susceptible–infected–susceptible (SIS) model is widely adopted in the studies of epidemic dynamics. When it is applied on contact networks, these networks mostly consist of nodes connected by undirected and unweighted edges following certain statistical properties, whereas in this article we consider the threshold and immunization problem for the SIS model on generalized networks that may contain different kinds of nodes and edges which are very possible in the real situation. We proved that an epidemic will become extinct if and only if the spectral radius of the corresponding parameterized adjacent matrix (PAM) is smaller than 1. Based on this result, we can evaluate the efficiency of immune strategies and take several prevailing ones as examples. In addition, we also develop methods that can precisely find the optimal immune strategies for networks with the given PAM.     

Invasion threshold in heterogeneous metapopulation networks

We study the dynamics of epidemic and reaction-diffusion processes in metapopulation models with heterogeneous connectivity patterns. In susceptible-infected-removed-like processes, along with the standard local epidemic threshold, the system exhibits a global invasion threshold. We provide an explicit expression of the threshold that sets a critical value of the diffusion/mobility rate below, which the epidemic is not able to spread to a macroscopic fraction of subpopulations. The invasion threshold is found to be affected by the topological fluctuations of the metapopulation network. The results presented provide a general framework for the understanding of the effect of travel restrictions in epidemic containment.     

Comparing the evolution of canalyzing and threshold networks

We study the influence of the type of update functions on the evolution of Boolean networks under selection for dynamical robustness. The chosen types of functions are canalyzing functions and threshold functions. Starting from a random initial network, we evolve the network by an adaptive walk. During the first time period, where the networks evolve to the plateau of 100 percent fitness, we find that both type of update functions give the same behavior, albeit for different network sizes and connectedness. However, on the long run, as the networks continue to evolve on the fitness plateau, the different types of update functions give rise to different network structure, due to their different mutational robustness. When both types of update functions occur together, none of them is preferred under long-term evolution.     

A novel 2D-OCDMA system with dynamic optimum decision threshold by estimating the number of active users

A novel two dimensional optical code division multiple access (2D-OCDMA) system with dynamic optimum decision threshold by estimating the number of active users is proposed. The bit-error rates (BER) of the system is analyzed. By using one wavelength as the estimator of the number of active users, which is not assigned to any address code, the number of active users can be obtained. The dynamic optimum decision threshold can be obtained according to the multiple user interference (MUI), which can be obtained by cross-correlation characteristics between address codes and the number of active users.     

Elementary models of dynamic networks

Inspecting the dynamics of networks opens a new dimension in understanding the interactions among the components of complex systems. Our goal is to understand the baseline properties expected from elementary random changes over time, in order to be able to assess the various effects found in longitudinal data. We created elementary dynamic models from classic random and preferential networks. Focusing on edge dynamics, we defined several processes for changing networks of a fixed size. We applied simple rules, including random, preferential and assortative modifications of existing edges – or a combination of these. Starting from initial Erdos-Rényi networks, we examined various basic network properties (e.g., density, clustering, average path length, number of components, degree distribution, etc.) of both snapshot and cumulative networks (for various lengths of aggregation time windows). Our results provide a baseline for changes to be expected in dynamic networks. We found universalities in the dynamic behavior of most network statistics. Furthermore, our findings suggest that certain network properties have a strong, non-trivial dependence on the length of the sampling window.     

Spectral narrowing and lasing threshold in self-assembled active photonic crystal

Laser-induced emission from rhodamine-B dye embedded in pseudo band gap opaline photonic crystals is discussed. The photonic crystals are fabricated using rhodamine-B doped polystyrene colloids and show 65% reflectance at the stop band centered at 604 nm. The reflectance of the crystal is increased to 74% by coating with a thin layer of gold. Both spontaneous and stimulated emissions of the dye are observed in the photonic stop band environment by exciting the crystal with the second harmonic (532 nm) of a Q-switched Nd:YAG laser. The thin layer of gold functioned as a high reflecting end mirror to the dye-doped cavity when the crystal is pumped from the substrate side. Angle-dependent suppression at the stop band wavelength is observed in the spontaneous emission of the dye. Spectrally narrow stimulated emission and lasing is achieved in the gold coated dyed PhC at a threshold pump power of 60 mW in a selective direction of 22° from the direction of excitation. By studying emission from several photonic crystals with different number of layers, it is concluded that a sharp threshold for lasing is not observed in uncoated photonic crystals when they contained fewer than 30 ordered layers and lesser than 70% reflectance.     

The classification and analysis of dynamic networks

In this paper we, firstly, classify the complex networks in which the nodes are of the lifetime distribution. Secondly, in order to study complex networks in terms of queuing system and homogeneous Markov chain, we establish the relation between the complex networks and queuing system, providing a new way of studying complex networks. Thirdly, we prove that there exist stationary degree distributions of M--G--P network, and obtain the analytic expression of the distribution by means of Markov chain theory. We also obtain the average path length and clustering coefficient of the network. The results show that M--G--P network is not only scale-free but also of a small-world feature in proper conditions.     

Hyperparameter on-line learning of stochastic resonance based threshold networks

Aiming at training the feed-forward threshold neural network consisting of nondifferentiable activation functions, the approach of noise injection forms a stochastic resonance based threshold network that can be optimized by various gradient-based optimizers. The introduction of injected noise extends the noise level into the parameter space of the designed threshold network, but leads to a highly non-convex optimization landscape of the loss function. Thus, the hyperparameter on-line learning procedure with respective to network weights and noise levels becomes of challenge. It is shown that the Adam optimizer, as an adaptive variant of stochastic gradient descent, manifests its superior learning ability in training the stochastic resonance based threshold network effectively. Experimental results demonstrate the significant improvement of performance of the designed threshold network trained by the Adam optimizer for function approximation and image classification.     

Epidemic threshold and phase transition in scale-free networks with asymmetric infection

We study the SIS epidemic dynamics on scale-freeweighted networks with asymmetric infection, by both analysis andnumerical simulations, with focus on the epidemic threshold aswell as critical behaviors. It is demonstrated that the asymmetryof infection plays an important role: we could redistribute theasymmetry to balance the degree heterogeneity of the network andthen to restore the epidemic threshold to a fnite value. On theother hand, we show that the absence of the epidemic threshold isnot so bad as commented previously since the prevalence grows veryslowly in this case and one could only protect a few vertices toprevent the diseases propagation.     

Toward cell circuitry: Topological analysis of enzyme reaction networks via reaction route graphs

The first step toward developing complete cell circuitry is to build quantitative networks for enzyme reactions. The conventional King-Altman-Hill (KAH) algorithm for topological analysis of enzyme networks, adapted from electrical networks, is based on “Reaction Graphs” that, unlike electrical circuits, are not quantitative, being straightforward renderings of conventional schematics of reaction mechanisms. Therefore, we propose the use of “Reaction Route (RR) Graphs” instead, as a more suitable graph-theoretical representation for topological analysis of enzyme reaction networks. The RR Graphs are drawn such that they are not only useful for visualizing the various reaction routes or pathways, but unlike Reaction Graphs possess network properties consistent with requisite kinetic, mass balance, and thermodynamic constraints. Therefore, they are better than the conventional Reaction Graphs for topological representation and analysis of enzyme reactions, both via the KAH methodology as well as via numerical matrix inversion. The difference between the two is highlighted based on the example of a single enzyme reaction network for the conversion of 7,8-dihydrofolate and NADPH into 5,6,7,8-tetrahydrofolate and NADP⁺, catalyzed by the enzyme dihydrofolate reductase.     

Distance measures for dynamic citation networks

Acyclic digraphs arise in many natural and artificial processes. Among the broader set, dynamic citation networks represent an important type of acyclic digraph. For example, the study of such networks includes the spread of ideas through academic citations, the spread of innovation through patent citations, and the development of precedent in common law systems. The specific dynamics that produce such acyclic digraphs not only differentiate them from other classes of graphs, but also provide guidance for the development of meaningful distance measures. In this article, we develop and apply our sink distance measure together with the single-linkage hierarchical clustering algorithm to both a two-dimensional directed preferential attachment model as well as empirical data drawn from the first quarter-century of decisions of the United States Supreme Court. Despite applying the simplest combination of distance measure and clustering algorithm, analysis reveals that more accurate and more interpretable clusterings are produced by this scheme.     

动态复杂网络中节点影响力的研究进展

节点影响力的识别和预测具有重要的理论意义和应用价值,是复杂网络的热点研究领域.目前大多数研究方法都是针对静态网络或动态网络某一时刻的快照进行的,然而在实际应用场景中,社会、生物、信息、技术等复杂网络都是动态演化的.因此在动态复杂网络中评估节点影响力以及预测节点未来影响力,特别是在网络结构变化之前的预测更具意义.本文系统地总结了动态复杂网络中节点影响力算法面临的三类挑战,即在增长网络中,节点影响力算法的计算复杂性和时间偏见;网络实时动态演化时,节点影响力算法的适应性;网络结构微扰或突变时,节点影响力算法的鲁棒性,以及利用网络结构演变阐释经济复杂性涌现的问题.最后总结了这一研究方向几个待解决的问题并指出未来可能的发展方向.     

Random graph models for dynamic networks

Recent theoretical work on the modeling of network structure has focused primarily on networks that are static and unchanging, but many real-world networks change their structure over time. There exist natural generalizations to the dynamic case of many static network models, including the classic random graph, the configuration model, and the stochastic block model, where one assumes that the appearance and disappearance of edges are governed by continuous-time Markov processes with rate parameters that can depend on properties of the nodes. Here we give an introduction to this class of models, showing for instance how one can compute their equilibrium properties. We also demonstrate their use in data analysis and statistical inference, giving efficient algorithms for fitting them to observed network data using the method of maximum likelihood. This allows us, for example, to estimate the time constants of network evolution or infer community structure from temporal network data using cues embedded both in the probabilities over time that node pairs are connected by edges and in the characteristic dynamics of edge appearance and disappearance. We illustrate these methods with a selection of applications, both to computer-generated test networks and real-world examples.     

Influence and dynamic behavior in random boolean networks

We present a rigorous mathematical framework for analyzing dynamics of a broad class of boolean network models. We use this framework to provide the first formal proof of many of the standard critical transition results in boolean network analysis, and offer analogous characterizations for novel classes of random boolean networks. We show that some of the assumptions traditionally made in the more common mean-field analysis of boolean networks do not hold in general. For example, we offer evidence that imbalance (internal inhomogeneity) of transfer functions is a crucial feature that tends to drive quiescent behavior far more strongly than previously observed.     

Learning and control with large dynamic neural networks

This paper is a presentation of neuronal control systems in the terms of the dynamical systems theory, where (1) the controller and its surrounding environment are seen as two co-dependent controlled dynamical systems (2) the behavioral transitions that take place under adaptation processes are analyzed in terms of phase-transitions. We present in the second section a generic method for the construction of multi-population random recurrent neural networks. The third section gives an overview of the various phase transitions that take place under an external forcing signal, or under internal parametric changes. The section 4 presents some applications in the domain of sequence identification and active perception modeling. The section 5 presents some applications in the domain of closed-loop control systems and reinforcement learning.