A Block-Based Adaptive Decoupling Framework for Graph Neural Networks

Graph neural networks (GNNs) with feature propagation have demonstrated their power in handling unstructured data. However, feature propagation is also a smooth process that tends to make all node representations similar as the number of propagation increases. To address this problem, we propose a novel Block-Based Adaptive Decoupling (BBAD) Framework to produce effective deep GNNs by utilizing backbone networks. In this framework, each block contains a shallow GNN with feature propagation and transformation decoupled. We also introduce layer regularizations and flexible receptive fields to automatically adjust the propagation depth and to provide different aggregation hops for each node, respectively. We prove that the traditional coupled GNNs are more likely to suffer from over-smoothing when they become deep. We also demonstrate the diversity of outputs from different blocks of our framework. In the experiments, we conduct semi-supervised and fully supervised node classifications on benchmark datasets, and the results verify that our method can not only improve the performance of various backbone networks, but also is superior to existing deep graph neural networks with less parameters.     

Neural networks and chaos: construction, evaluation of chaotic networks, and prediction of chaos with multilayer feedforward networks

Many research works deal with chaotic neural networks for various fields of application. Unfortunately, up to now, these networks are usually claimed to be chaotic without any mathematical proof. The purpose of this paper is to establish, based on a rigorous theoretical framework, an equivalence between chaotic iterations according to Devaney and a particular class of neural networks. On the one hand, we show how to build such a network, on the other hand, we provide a method to check if a neural network is a chaotic one. Finally, the ability of classical feedforward multilayer perceptrons to learn sets of data obtained from a dynamical system is regarded. Various boolean functions are iterated on finite states. Iterations of some of them are proven to be chaotic as it is defined by Devaney. In that context, important differences occur in the training process, establishing with various neural networks that chaotic behaviors are far more difficult to learn.     

A New Chaotic Parameters Disturbance Annealing Neural Network for Solving Global Optimization Problems

Since there were few chaotic neural networks applicable to the global optimization, in this paper, we proposea new neural network model - chaotic parameters disturbance annealing (CPDA) network, which is superior to otherexisting neural networks, genetic algorithms, and simulated annealing algorithms in global optimization. In the presentCPDA network, we add some chaotic parameters in the energy function, which make the Hopfield neural network escapefrom the attraction of a local minimal solution and with the parameter p1 annealing, our model will converge to theglobal optimal solutions quickly and steadily. The converge ability and other characters are also analyzed in this paper.The benchmark examples show the present CPDA neuralnetwork's merits in nonlinear global optimization.     

基于邻域粗糙集和并行神经网络的故障诊断

针对目前使用神经网络诊断故障时出现的输入向量选择困难、网络结构复杂、对并发故障诊断效果不好等问题,提出了基于邻域粗糙集和并行神经网络的故障诊断方法。先利用邻域粗糙集对初始征兆进行约简,留下有价值的征兆作为神经网络的输入向量,然后针对每种故障类型设计一个神经网络。用多个训练好的神经网络来并行诊断故障,综合每个神经网络的结果给出最终的诊断结论。用转子实验台的实验数据对这种故障诊断方法进行验证,结果显示该方法能优化神经网络结构,且神经网络具有训练速度快、诊断正确率高的特点。     

Quantum mechanics of Klein-Gordon fields II: Relativistic coherent states

We use the formulation of the quantum mechanics of first-quantized Klein-Gordon fields given in the first of this series of papers to study relativistic coherent states. In particular, we offer an explicit construction of coherent states for both charged and neutral (real) free Klein-Gordon fields as well as for charged fields interacting with a constant magnetic field. Our construction is free from the problems associated with charge-superselection rule that complicated the previous studies. We compute various physical quantities associated with our coherent states and present a detailed investigation of their classical (nonquantum) and nonrelativistic limits.     

少节点基因调控网络的控制

近年来,自组织振荡网络受到越来越多科学家的关注,对生物体的生长、发育起调控作用的基因调控网络即是其中的一种.本文研究了少节点基因调控网络的控制问题.运用多相位超前驱动方法对该种网络进行调控,可以有效地提高对网络的控制效率.通过数值模拟,发现对于少节点基因调控网络,当系统参数确定时,网络的有效控制率可以达到95％以上(10节点网络);当系统参数不确定时,控制的效率也非常高.     

Reproducible sequence generation in random neural ensembles

Little is known about the conditions that neural circuits have to satisfy to generate reproducible sequences. Evidently, the genetic code cannot control all the details of the complex circuits in the brain. In this Letter, we give the conditions on the connectivity degree that lead to reproducible and robust sequences in a neural population of randomly coupled excitatory and inhibitory neurons. In contrast to the traditional theoretical view we show that the sequences do not need to be learned. In the framework proposed here just the averaged characteristics of the random circuits have to be under genetic control. We found that rhythmic sequences can be generated if random networks are in the vicinity of an excitatory-inhibitory synaptic balance. Reproducible transient sequences, on the other hand, are found far from a synaptic balance.     

Large-scale structure of time evolving citation networks

In this paper we examine a number of methods for probing and understanding the large-scale structure of networks that evolve over time. We focus in particular on citation networks, networks of references between documents such as papers, patents, or court cases. We describe three different methods of analysis, one based on an expectation-maximization algorithm, one based on modularity optimization, and one based on eigenvector centrality. Using the network of citations between opinions of the United States Supreme Court as an example, we demonstrate how each of these methods can reveal significant structural divisions in the network and how, ultimately, the combination of all three can help us develop a coherent overall picture of the network's shape.     

Direct calculation of time varying Aharonov-Bohm effect

The Aharonov-Bohm effect (ABE) for steady magnetic fields is a well known phenomenon. However, if the current in the infinite solenoid that creates the magnetic field is time-dependent, that is in the presence of both magnetic and electric fields, there is no agreement whether the effect would be present. In this note, we try to investigate time varying ABE by a direct calculation in a set-up with a weak time dependent magnetic field. We find that the electric field arising out of the time-varying magnetic field in the path of the electrons does not enter the action integral but only changes the path of the electron from the source to the slits and then on to the detector. We find a frequency dependent AB phase shift. At low frequencies the result smoothly approaches the one for a constant field as the frequency tends towards zero. On the other hand, for high frequencies such that the AB-phase induced in the path of the wave packet oscillates rapidly, the net effect will be very small which is borne out by our results.     

Dissipation of ‘dark energy’ by cortex in knowledge retrieval

We have devised a thermodynamic model of cortical neurodynamics expressed at the classical level by neural networks and at the quantum level by dissipative quantum field theory. Our model is based on features in the spatial images of cortical activity newly revealed by high-density electrode arrays. We have incorporated the mechanism and necessity for so-called dark energy in knowledge retrieval. We have extended the model first using the Carnot cycle to define our measures for energy, entropy and temperature, and then using the Rankine cycle to incorporate criticality and phase transitions. We describe the dynamics of two interactive fields of neural activity that express knowledge, one at high and the other at low energy density, and the two operators that create and annihilate the fields. We postulate that the extremely high density of energy sequestered briefly in cortical activity patterns can account for the vividness, richness of associations, and emotional intensity of memories recalled by stimuli.     

基于自归一化神经网络的脉冲星候选体选择

脉冲星候选体选择是脉冲星搜寻任务中的重要步骤.为了提高脉冲星候选体选择的准确率,提出了一种基于自归一化神经网络的候选体选择方法.该方法采用自归一化神经网络、遗传算法、合成少数类过采样这三种技术提升对脉冲星候选体的筛选能力.利用自归一化神经网络的自归一化性质克服了深层神经网络训练中梯度消失和爆炸的问题,大大加快了训练速度.为了消除样本数据的冗余性,利用遗传算法对脉冲星候选体的样本特征进行选择,得到了最优特征子集.针对数据中真实脉冲星样本数极少带来的严重类不平衡性,采用合成少数类过采样技术生成脉冲星候选体样本,降低了类不平衡率.以分类精度为评价指标,在3个脉冲星候选体数据集上的实验结果表明,本文提出的方法能有效提升脉冲星候选体选择的性能.     

Minimal attractors in digraph system models of neuronal networks

We study a class of discrete dynamical systems models of neuronal networks. In these models, each neuron is represented by a finite number of states and there are rules for how a neuron transitions from one state to another. In particular, the rules determine when a neuron fires and how this affects the state of other neurons. In an earlier paper [D. Terman, S. Ahn, X. Wang, W. Just, Reducing neuronal networks to discrete dynamics, Physica D 237 (2008) 324-338], we demonstrate that a general class of excitatory-inhibitory networks can, in fact, be rigorously reduced to the discrete model. In the present paper, we analyze how the connectivity of the network influences the dynamics of the discrete model. For randomly connected networks, we find two major phase transitions. If the connection probability is above the second but below the first phase transition, then starting in a generic initial state, most but not all cells will fire at all times along the trajectory as soon as they reach the end of their refractory period. Above the first phase transition, this will be true for all cells in a typical initial state; thus most states will belong to a minimal attractor of oscillatory behavior (in a sense that is defined precisely in the paper). The exact positions of the phase transitions depend on intrinsic properties of the cells including the lengths of the cells’ refractory periods and the thresholds for firing. Existence of these phase transitions is both rigorously proved for sufficiently large networks and corroborated by numerical experiments on networks of moderate size.     

Controlling the evolution of nondiffracting speckle by complex amplitude modulation on a phase-only spatial light modulator

In this work we investigate the structure of nondiffracting speckle fields, both experimentally and theoretically. We are able to produce very good agreement between the experimentally recorded and theoretically calculated fields by using complex amplitude modulation on a phase-only spatial light modulator to implement controlled ring-slit experiments for the generation of nondiffracting speckle fields. The structure of the nondiffracting speckle due to binary and continuous phase modulations for both a uniform and a normal distribution is investigated. We find that we are able to engineer whether the nondiffracting field will appear as speckle or a structured zero-order Bessel beam by adjusting the standard deviation in the distribution. Having the ability to control where in the spectrum, from fully-developed nondiffracting speckle to a symmetric zero-order Bessel beam, the nondiffracting field will exist can prove to be a useful resource in the non-destructive testing of materials.     

Evolving complex dynamics in electronic models of genetic networks

Ordinary differential equations are often used to model the dynamics and interactions in genetic networks. In one particularly simple class of models, the model genes control the production rates of products of other genes by a logical function, resulting in piecewise linear differential equations. In this article, we construct and analyze an electronic circuit that models this class of piecewise linear equations. This circuit combines CMOS logic and RC circuits to model the logical control of the increase and decay of protein concentrations in genetic networks. We use these electronic networks to study the evolution of limit cycle dynamics. By mutating the truth tables giving the logical functions for these networks, we evolve the networks to obtain limit cycle oscillations of desired period. We also investigate the fitness landscapes of our networks to determine the optimal mutation rate for evolution.     

Calculated signal-to-noise ratio of MRI detected with SQUIDs and Faraday detectors in fields from 10 microT to 1.5 T

We examine the calculated signal-to-noise ratio (SNR) achievable with different MRI detection modalities in precession fields ranging from 10 microT to 1.5 T. In particular, we compare traditional Faraday detectors with both tuned and untuned detectors based on superconducting quantum interference devices (SQUIDs). We derive general expressions for the magnetic field noise due to the samples and the detectors, and then calculate the SNR achievable for a specific geometry with each modality with and without prepolarization. We show that each of the three modalities is superior in one of the three field ranges. SQUID-based detection is superior to conventional Faraday detection for MRI in precession fields below 250 mT for a 65 mm diameter surface coil placed a distance of 25 mm from the voxel of interest embedded in a cylinder of tissue 50 mm tall and of radius 50 mm. This crossover field, however, is sensitive to the geometry.     

An empirical study of Chinese language networks

Chinese is spoken by the largest number of people in the world, and it is regarded as one of the most important languages. In this paper, we explore the statistical properties of Chinese language networks (CLNs) within the framework of complex network theory. Based on one of the largest Chinese corpora, i.e. People’s Daily Corpus, we construct two networks (CLN1 and CLN2) from two different respects, with Chinese words as nodes. In CLN1, a link between two nodes exists if they appear next to each other in at least one sentence; in CLN2, a link represents that two nodes appear simultaneously in a sentence. We show that both networks exhibit small-world effect, scale-free structure, hierarchical organization and disassortative mixing. These results indicate that in many topological aspects Chinese language shapes complex networks with organizing principles similar to other previously studied language systems, which shows that different languages may have some common characteristics in their evolution processes. We believe that our research may shed some new light into the Chinese language and find some potentially significant implications.     

Stochastic resonance and synchronization behaviors of excitatory-inhibitory small-world network subjected to electromagnetic induction

The phenomenon of stochastic resonance and synchronization on some complex neuronal networks have been investigated extensively.These studies are of great significance for us to understand the weak signal detection and information transmission in neural systems.Moreover,the complex electrical activities of a cell can induce time-varying electromagnetic fields,of which the internal fluctuation can change collective electrical activities of neuronal networks.However,in the past there have been a few corresponding research papers on the influence of the electromagnetic induction among neurons on the collective dynamics of the complex system.Therefore,modeling each node by imposing electromagnetic radiation on the networks and investigating stochastic resonance in a hybrid network can extend the interest of the work to the understanding of these network dynamics.In this paper,we construct a small-world network consisting of excitatory neurons and inhibitory neurons,in which the effect of electromagnetic induction that is considered by using magnetic flow and the modulation of magnetic flow on membrane potential is described by using memristor coupling.According to our proposed network model,we investigate the effect of induced electric field generated by magnetic stimulation on the transition of bursting phase synchronization of neuronal system under electromagnetic radiation.It is shown that the intensity and frequency of the electric field can induce the transition of the network bursting phase synchronization.Moreover,we also analyze the effect of magnetic flow on the detection of weak signals and stochastic resonance by introducing a subthreshold pacemaker into a single cell of the network and we find that there is an optimal electromagnetic radiation intensity,where the phenomenon of stochastic resonance occurs and the degree of response to the weak signal is maximized.Simulation results show that the extension of the subthreshold pacemaker in the network also depends greatly on coupling strength.The presented results may have important implications for the theoretical study of magnetic stimulation technology,thus promoting further development of transcranial magnetic stimulation(TMS) as an effective means of treating certain neurological diseases.     

Mutual and intermittent enhancements of synchronization transitions by autaptic and synaptic delay in scale-free neuron networks

In neural networks, there exist both synaptic delays among different neurons and autaptic self-feedback delays in a neuron itself. In this paper, we study synchronization transitions induced by synaptic and autaptic delays in scale-free neuron networks, mainly exploring how these two time delays affect synchronization transitions induced by each other. It is found that the synchronization transitions induced by synaptic (autaptic) delay are intermittently enhanced when autaptic (synaptic) delay is varied. There are optimal autaptic strength and synaptic coupling strength by which the synchronization transitions induced by autaptic and synaptic delays become strongest. The underlying mechanisms are briefly discussed in terms of the relationships of autaptic delay, synaptic delay, and inter-burst interval. These results show that synaptic and autaptic delays could contribute to each other and enhance synchronization transitions in the neuronal networks. This implies that autaptic and synaptic delays could play a vital role for the information transmission in neural systems.