Eigenvalue spectra of random matrices for neural networks

The dynamics of neural networks is influenced strongly by the spectrum of eigenvalues of the matrix describing their synaptic connectivity. In large networks, elements of the synaptic connectivity matrix can be chosen randomly from appropriate distributions, making results from random matrix theory highly relevant. Unfortunately, classic results on the eigenvalue spectra of random matrices do not apply to synaptic connectivity matrices because of the constraint that individual neurons are either excitatory or inhibitory. Therefore, we compute eigenvalue spectra of large random matrices with excitatory and inhibitory columns drawn from distributions with different means and equal or different variances.     

基于抑制性突触可塑性的反馈神经回路兴奋性与抑制性动态平衡

大脑皮层的兴奋性与抑制性平衡是维持正常脑功能的前提, 而其失衡会诱发癫痫、帕金森、抑郁症等多种神经疾病, 因此兴奋性与抑制性平衡的研究是脑科学领域的核心科学问题. 反馈神经回路是脑皮层网络的典型连接模式, 抑制性突触可塑性在兴奋性与抑制性平衡中扮演关键角色. 本文首先构建具有抑制性突触可塑性的反馈神经回路模型; 然后通过计算模拟研究揭示在抑制性突触可塑性的调控下反馈神经回路的兴奋性与抑制性可取得较高程度的动态平衡, 并且二者的平衡对输入扰动具有较强的鲁棒性; 其次给出了基于抑制性突触可塑性的反馈神经回路兴奋性与抑制性平衡机理的解释; 最后发现反馈回路神经元数目有利于提高兴奋性与抑制性平衡的程度, 这在一定程度上解释了为何神经元之间会存在较多的连接. 本文的研究对于理解脑皮层的兴奋性与抑制性动态平衡机理具有重要的参考价值.     

Dynamics of Hopfield-Type Neural Networks with Modulo Periodic Unpredictable Synaptic Connections,Rates and Inputs

In this paper, we rigorously prove that unpredictable oscillations take place in the dynamics of Hopfield-type neural networks (HNNs) when synaptic connections, rates and external inputs are modulo periodic unpredictable. The synaptic connections, rates and inputs are synchronized to obtain the convergence of outputs on the compact subsets of the real axis. The existence, uniqueness, and exponential stability of such motions are discussed. The method of included intervals and the contraction mapping principle are applied to attain the theoretical results. In addition to the analysis, we have provided strong simulation arguments, considering that all the assumed conditions are satisfied. It is shown how a new parameter, degree of periodicity, affects the dynamics of the neural network.     

Field coupling-induced synchronization via a capacitor and inductor

Resistor-based voltage coupling is often used to realize complete synchronization between identical nonlinear circuits while phase synchronization is investigated between non-identical nonlinear circuits (periodic or chaotic oscillation). Indeed, the coupling resistor used to consume certain Joule heat and energy before reaching the synchronization target when continuous current passed across the coupling device. In this paper, capacitor and inductor is paralleled with one coupling resistor, respectively, and the coupling devices are used bridge connection between two LC hyperchaotic circuits for investigating synchronization problems. As a result, the coupling channel can be activated to propagate energy and balance the outputs voltage from the two circuits. The dimensionless dynamical equations are obtained by applying scale transformation on the circuit equations when field coupling is switched on. It is found that the threshold of coupling intensity for reaching synchronization and the power consumption of controller can be decreased when the coupling resistor is paralleled with on capacitor or inductor. The mechanism could be that involvement of coupling capacitor(or inductor) can trigger time-varying electric field (or magnetic field), and the energy flow of field coupling via coupling capacitor (or inductor) can contribute the exchange of energy in the coupled nonlinear circuits. It can give insights to investigate synchronization on chaotic systems, neural circuits and neural networks including synapse coupling and field coupling. Finally, the experimental results on circuits are also supplied for further verification.     

Self-sustained firing activities of the cortical network with plastic rules in weak AC electrical fields

Both external and endogenous electrical fields widely exist in the environment of cortical neurons. The effects of a weak alternating current (AC) field on a neural network model with synaptic plasticity are studied. It is found that self-sustained rhythmic firing patterns, which are closely correlated with the cognitive functions, are significantly modified due to the self-organizing of the network in the weak AC field. The activities of the neural networks are affected by the synaptic connection strength, the external stimuli, and so on. In the presence of learning rules, the synaptic connections can be modulated by the external stimuli, which will further enhance the sensitivity of the network to the external signal. The properties of the external AC stimuli can serve as control parameters in modulating the evolution of the neural network.     

A few strong connections: optimizing information retention in neuronal avalanches

Background  

How living neural networks retain information is still incompletely understood. Two prominent ideas on this topic have developed in parallel, but have remained somewhat unconnected. The first of these, the "synaptic hypothesis," holds that information can be retained in synaptic connection strengths, or weights, between neurons. Recent work inspired by statistical mechanics has suggested that networks will retain the most information when their weights are distributed in a skewed manner, with many weak weights and only a few strong ones. The second of these ideas is that information can be represented by stable activity patterns. Multineuron recordings have shown that sequences of neural activity distributed over many neurons are repeated above chance levels when animals perform well-learned tasks. Although these two ideas are compelling, no one to our knowledge has yet linked the predicted optimum distribution of weights to stable activity patterns actually observed in living neural networks.     

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.     

Synaptic behaviors of a single metal–oxide–metal resistive device

The mammalian brain is far superior to today’s electronic circuits in intelligence and efficiency. Its functions are realized by the network of neurons connected via synapses. Much effort has been extended in finding satisfactory electronic neural networks that act like brains, i.e., especially the electronic version of synapse that is capable of the weight control and is independent of the external data storage. We demonstrate experimentally that a single metal–oxide–metal structure successfully stores the biological synaptic weight variations (synaptic plasticity) without any external storage node or circuit. Our device also demonstrates the reliability of plasticity experimentally with the model considering the time dependence of spikes. All these properties are embodied by the change of resistance level corresponding to the history of injected voltage-pulse signals. Moreover, we prove the capability of second-order learning of the multi-resistive device by applying it to the circuit composed of transistors. We anticipate our demonstration will invigorate the study of electronic neural networks using non-volatile multi-resistive device, which is simpler and superior compared to other storage devices.     

Stochastic Resonance in Neural Systems with Small-World Connections

We study the stochastic resonance （SR） in Hodgkin-Huxley （HH） neural systems with small-world （SW） connections under the noise synaptic current and periodic stimulus, focusing on the dependence of properties of SR on coupling strength c. It is found that there exists a critical coupling strength c^＊ such that if c 〈 c^＊, then the SR can appear on the SW neural network. Especially, dependence of the critical coupling strength c^＊ on the number of neurons N shows the monotonic even almost linear increase of c^＊ as N increases and c^＊ on the SW network is smaller than that on the random network. For the effect of the SW network on the phenomenon of SR, we show that decreasing the connection-rewiring probability p of the network topology leads to an enhancement of SR. This indicates that the SR on the SW network is more prominent than that on the random network （p = 1.0）. In addition, it is noted that the effect becomes remarkable as coupling strength increases. Moreover, it is found that the SR weakens but resonance range becomes wider with the increase of c on the SW neural network.     

Mean Field Theory of Self-Organizing Memristive Connectomes

Biological neuronal networks are characterized by nonlinear interactions and complex connectivity. Given the growing impetus to build neuromorphic computers, understanding physical devices that exhibit structures and functionalities similar to biological neural networks is an important step toward this goal. Self-organizing circuits of nanodevices are at the forefront of the research in neuromorphic computing, as their behavior mimics synaptic plasticity features of biological neuronal circuits. However, an effective theory to describe their behavior is lacking. This study provides for the first time an effective mean field theory for the emergent voltage-induced polymorphism of circuits of a nanowire connectome, showing that the behavior of these circuits can be explained by a low-dimensional dynamical equation. The equation can be derived from the microscopic dynamics of a single memristive junction in analytical form. The effective model is tested on experiments of nanowire networks and show that it fits both the potentiation and depression of these synapse-mimicking circuits. It is shown that this theory applies beyond the case of nanowire networks by formulating a general mean-field theory of conductance transitions in self-organizing memristive connectomes.     

Optimal control of neuronal activity

We investigate the optimal control of neuronal spiking activity for neurons receiving a class of random synaptic inputs, characterized by a positive parameter alpha. Optimal control signals and optimal variances are found exactly for the diffusion process approximating an integrate and fire model. When synaptic inputs are "sub-Poisson" (alpha<0.5), we find that the optimal synaptic input is a delta function (corresponding to bang-bang control) and the optimal signal is not unique. Poisson synaptic input is the critical case: The control signal is unique, but the control signal is still a delta function. For "supra-Poisson" (alpha>0.5) inputs, the optimal control is smooth and unique. The optimal variance obtained in the current paper sets the lowest possible bound in controlling the stochasticity of neuronal activity. We also discuss how to implement the optimal control signal for certain model neurons.     

Enhance sensitivity to illumination and synchronization in light-dependent neurons

When a phototube is activated to connect a neural circuit, the output voltage becomes sensitive to external illumination because the photocurrent across the phototube can be controlled by external electromagnetic wave. The channel currents from different branch circuits have different impacts on the outputs voltage of the neural circuit. In this paper, a phototube is incorporated into different branch circuits in a simple neural circuit, and then a light-controlled neuron is obtained for further nonlinear analysis. Indeed, the phototube is considered as exciting source when it is activated by external illumination, and two kinds of light-sensitive neurons are obtained when the phototube is connected to capacitor or induction coil, respectively. Electric synapse coupling is applied to detect possible synchronization between two functional neurons, and the energy consumption along the coupling channel via resistor is estimated. The analog circuits for the two kinds of light-sensitive neurons are supplied for further confirmation by using Multisim. It is found that two light-sensitive neurons and neural circuits can be synchronized by taming the coupling intensity carefully. It provides possible clues to understand the synchronization mechanism for eyes and artificial sensors which are sensitive to illumination. Finally, a section for open problems is supplied for further investigation about its collective behaviors in the network with/without synapse coupling.     

混沌映射和神经网络互扰的新型复合流密码

提出了一种将新型的神经网络互学习模型和常见的多混沌系统融合互扰的复合流密码方案. 首先利用三个Logistics混沌映射产生的随机序列作为神经网络互学习模型中三个 隐含层神经元的随机输入, 神经网络交互学习达到内部权值同步后, 再将同步权值映射为随机序列并与三个Logistics序列复合产生最终的密钥流. 实验表明, 产生的密钥流具有更好的随机性, 混沌流加密应用效果好. 关键词： 混沌映射 神经网络 权值同步 随机密钥流     

Designing neural networks that process mean values of random variables

We develop a class of neural networks derived from probabilistic models posed in the form of Bayesian networks. Making biologically and technically plausible assumptions about the nature of the probabilistic models to be represented in the networks, we derive neural networks exhibiting standard dynamics that require no training to determine the synaptic weights, that perform accurate calculation of the mean values of the relevant random variables, that can pool multiple sources of evidence, and that deal appropriately with ambivalent, inconsistent, or contradictory evidence.     

The Biophysical Basis of Excitability,by H.G. Fereira and M.W. Marshall

Cellular behaviour is governed by gene regulatory processes that are intrinsically dynamic and nonlinear, and are subject to non-negligible amounts of random fluctuations. Such conditions are ubiquitous in physical systems, where they have been studied for decades using the tools of statistical and nonlinear physics. The goal of this introductory tutorial is to show how approaches traditionally used in physics can help in reaching a systems-level understanding of living cells. To that end, we present an overview of the dynamical phenomena exhibited by genetic circuits and their functional significance. We also describe the theoretical and experimental approaches that are being used to unravel the relationship between circuit structure and function in dynamical cellular processes under the influence ofnoise. Studies are discussed both at the single-cell level and in cellular populations, where intercellular coupling plays an important role.     

Statistical methods in nonlinear dynamics

Sensitivity to initial conditions in nonlinear dynamical systems leads to exponential divergence of trajectories that are initially arbitrarily close, and hence to unpredictability. Statistical methods have been found to be helpful in extracting useful information about such systems. In this paper, we review briefly some statistical methods employed in the study of deterministic and stochastic dynamical systems. These include power spectral analysis and aliasing, extreme value statistics and order statistics, recurrence time statistics, the characterization of intermittency in the Sinai disorder problem, random walk analysis of diffusion in the chaotic pendulum, and long-range correlations in stochastic sequences of symbols.     

基于分块离散小波变换的图像信息隐藏与盲提取算法

提出了一种在小波域中图像信息隐藏与盲提取算法. 该算法首先对载体图像进行分块两层离散小波变换, 找到每块第二级分解子带中的最大值即最重要小波系数, 然后根据小波特征树的对应关系将其在第一级分解子带中的对应区域作为嵌入区域, 在该区域嵌入由秘密信息生成的伪随机序列. 提取过程中, 同样按照小波系数对应关系寻找到嵌入区域并判断其与伪随机序列的相关性即可解密, 不需要提供原始图像. 实验结果表明, 该算法能实现二值图像的嵌入与盲提取, 且提取出的图像质量较好并具备一定的抗攻击能力, 尤其对于剪切攻击的鲁棒性较好.     

Reliable computing with unreliable components: Using separable environments to stabilize long-term information storage

How, in the face of both intrinsic and extrinsic volatility, can unconventional computing fabrics store information over arbitrarily long periods? Here, we argue that the predictable structure of many realistic environments, both natural and artificial, can be used to maintain useful categorical boundaries even when the computational fabric itself is inherently volatile and the inputs and outputs are partially stochastic. As a concrete example, we consider the storage of binary classifications in connectionist networks, although the underlying principles should be applicable to other unconventional computing paradigms. Specifically, we demonstrate that an unsupervised, activity dependent plasticity rule, AHAH (Anti-Hebbian-And-Hebbian), allows binary classifications to remain stable even when the underlying synaptic weights are subject to random noise. When embedded in environments composed of separable features, the weight vector is restricted by the AHAH rule to local attractors representing stable partitions of the input space, allowing unsupervised recovery of stored binary classifications following random perturbations that leave the system in the same basin of attraction. We conclude that the stability of long-term memories may depend not so much on the reliability of the underlying substrate, but rather on the reproducible structure of the environment itself, suggesting a new paradigm for reliable computing with unreliable components.     

Physical random access signal design for 5G mobile satellite communication systems

In view of the distinctive characteristics of satellite communication, the physical random access signals used in the terrestrial mobile communication system have to be modified or redesigned for the satellite communication system. In this paper, we boost the random access signal energy by repeating the short Zadoff–Chu (ZC) sequence based preamble signal used in the terrestrial system. Different long ZC sequences are used to scramble this cascaded sequence to distinguish different random access signals for multiple random access user equipments. For correlation performance optimization, properties of the roots for both the short and long ZC sequences are mathematically analyzed and derived. Finally, we illustrate how to construct a root set for these different long ZC sequences based on the obtained propositions in a practical way. This analytical framework provides a useful insight into ZC sequence-based random access signal design and performance analysis in mobile satellite communication systems.