变权小世界生物神经网络的兴奋及优化特性

根据实际生物神经网络具有小世界连接和神经元之间的连接强度随时间变化的特点,首先构造了一个以Hodgkin-Huxley方程为节点动力学模型的动态变权小世界生物神经网络模型,然后研究了该模型神经元的兴奋特性、权值变化特点和不同的学习系数对神经元的兴奋统计特性的影响.最有意义的结果是,在同样的网络结构、网络参数及外部刺激信号的条件下,学习系数b存在一个最优值b^*,使生物神经网络的兴奋度在b=b^*时达到最大. 关键词： 动态变权生物神经网络 小世界网络 Hodgkin-Huxley方程     

Representation Learning for Dynamic Functional Connectivities via Variational Dynamic Graph Latent Variable Models

Latent variable models (LVMs) for neural population spikes have revealed informative low-dimensional dynamics about the neural data and have become powerful tools for analyzing and interpreting neural activity. However, these approaches are unable to determine the neurophysiological meaning of the inferred latent dynamics. On the other hand, emerging evidence suggests that dynamic functional connectivities (DFC) may be responsible for neural activity patterns underlying cognition or behavior. We are interested in studying how DFC are associated with the low-dimensional structure of neural activities. Most existing LVMs are based on a point process and fail to model evolving relationships. In this work, we introduce a dynamic graph as the latent variable and develop a Variational Dynamic Graph Latent Variable Model (VDGLVM), a representation learning model based on the variational information bottleneck framework. VDGLVM utilizes a graph generative model and a graph neural network to capture dynamic communication between nodes that one has no access to from the observed data. The proposed computational model provides guaranteed behavior-decoding performance and improves LVMs by associating the inferred latent dynamics with probable DFC.     

Topology and dynamics of attractor neural networks: The role of loopiness

We derive an exact representation of the topological effect on the dynamics of sequence processing neural networks within signal-to-noise analysis. A new network structure parameter, loopiness coefficient, is introduced to quantitatively study the loop effect on network dynamics. A large loopiness coefficient means a high probability of finding loops in the networks. We develop recursive equations for the overlap parameters of neural networks in terms of their loopiness. It was found that a large loopiness increases the correlation among the network states at different times and eventually reduces the performance of neural networks. The theory is applied to several network topological structures, including fully-connected, densely-connected random, densely-connected regular and densely-connected small-world, where encouraging results are obtained.     

Associative memory on a small-world neural network

We study a model of associative memory based on a neural network with small-world structure. The efficacy of the network to retrieve one of the stored patterns exhibits a phase transition at a finite value of the disorder. The more ordered networks are unable to recover the patterns, and are always attracted to non-symmetric mixture states. Besides, for a range of the number of stored patterns, the efficacy has a maximum at an intermediate value of the disorder. We also give a statistical characterization of the spurious attractors for all values of the disorder of the network.Received: 12 January 2004, Published online: 28 May 2004PACS: 84.35. + i Neural networks - 89.75.Hc Networks and genealogical trees - 87.18.Sn Neural networks     

The influence of long-range links on spiral waves and their application for control

The influence of long-range links on spiral waves in an excitable medium has been investigated.Spatiotemporal dynamics in an excitable small-world network transform remarkably when we increase the long-range connection probability P.Spiral waves with few perturbations,broken spiral waves,pseudo spiral turbulence,synchronous oscillations,and homogeneous rest state are discovered under different network structures.Tip number is selected to detect non-equilibrium phase transition between different spatiotemporal patterns.The Kuramoto order parameter is used to identify these patterns and explain the emergence of the rest state.Finally,we use long-range links to successfully control spiral waves and spiral turbulence.     

The influence of long-range links on spiral waves and its application for control

The influence of long-range links on spiral waves in excitable medium has been investigated. Spatiotemporal dynamics in excitable small-world network transforms remarkably when we increase the long-range connection probability P. Spiral waves with few perturbations, broken spiral waves, pseudo spiral turbulence, synchronous oscillations, and homogeneous rest state are discovered under different network structures. Tip number is selected to detect non-equilibrium phase transition between different spatiotemporal patterns. The Kuramoto order parameter is used to identify these patterns and explain the emergence of the rest state. Finally, we use long-range links to control spiral wave and spiral turbulence successfully.     

Dynamics of organizational rumor communication on connecting multi-small-world networks

We study the dynamics of an epidemic-like model for the spread of a rumor on a connecting multi-small-world-network (CM-SWN) model, which represents organizational communication in the real world. It has been shown that this model exhibits a transition between regimes of localization and propagation at a finite value of network randomness. Here, by numerical means, we perform a quantitative characterization of the evolution in the three groups under two evolution rules, namely the conformity and obeying principles. The variant of a dynamic CM-SWN, where the quenched disorder of small-world networks is replaced by randomly changing connections between individuals in a single network and stable connection by star nodes between networks, is also analysed in detail and compared with a mean-field approximation.     

Dynamics of organizational rumor communication on connecting multi-small-world networks

We study the dynamics of an epidemic-like model for the spread of a rumor on a connecting multi-small-world-network (CM-SWN) model, which represents organizational communication in the real world. It has been shown that this model exhibits a transition between regimes of localization and propagation at a finite value of network randomness. Here, by numerical means, we perform a quantitative characterization of the evolution in the three groups under two evolution rules, namely the conformity and obeying principles. The variant of a dynamic CM-SWN, where the quenched disorder of small-world networks is replaced by randomly changing connections between individuals in a single network and stable connection by star nodes between networks, is also analysed in detail and compared with a mean-field approximation.     

Topological probability and connection strength induced activity in complex neural networks

Recent experimental evidence suggests that some brain activities can be assigned to small-world networks. In this work, we investigate how the topological probability p and connection strength C affect the activities of discrete neural networks with small-world (SW) connections. Network elements are described by two-dimensional map neurons (2DMNs) with the values of parameters at which no activity occurs. It is found that when the value of p is smaller or larger, there are no active neurons in the network, no matter what the value of connection strength is; for a given appropriate connection strength, there is an intermediate range of topological probability where the activity of 2DMN network is induced and enhanced. On the other hand, for a given intermediate topological probability level, there exists an optimal value of connection strength such that the frequency of activity reaches its maximum. The possible mechanism behind the action of topological probability and connection strength is addressed based on the bifurcation method. Furthermore, the effects of noise and transmission delay on the activity of neural network are also studied.     

Learning and structure of neuronal networks

We study the effect of learning dynamics on network topology. Firstly, a network of discrete dynamical systems is considered for this purpose and the coupling strengths are made to evolve according to a temporal learning rule that is based on the paradigm of spike-time-dependent plasticity (STDP). This incorporates necessary competition between different edges. The final network we obtain is robust and has a broad degree distribution. Then we study the dynamics of the structure of a formal neural network. For properly chosen input signals, there exists a steady state with a residual network. We compare the motif profile of such a network with that of the real neural network of C. elegans and identify robust qualitative similarities. In particular, our extensive numerical simulations show that this STDP-driven resulting network is robust under variations of model parameters.     

Nonlinear Dynamical Behavior in BS Evolution Model Based on Small-World Network Added with Mechanism of Preferential Connection

In this paper, we introduce a modified small-world network added with new links with preferential connection instead of adding randomly, then we apply Bak-Sneppen (BS) evolution model on this network. Several dynamical character of the model such as the evolution graph, f₀ avalanche, the critical exponent D and τ, and the distribution of mutation times of all the nodes, show particular behaviors different from those of the model based on the regular network and the small-world network.     

Fastest learning in small-world neural networks

We investigate supervised learning in neural networks. We consider a multi-layered feed-forward network with back propagation. We find that the network of small-world connectivity reduces the learning error and learning time when compared to the networks of regular or random connectivity. Our study has potential applications in the domain of data-mining, image processing, speech recognition, and pattern recognition.     

Avalanche dynamics of idealized neuron function in the brain on an uncorrelated random scale-free network

We study a simple model for a neuron function in a collective brain system. The neural network is composed of an uncorrelated configuration model (UCM) for eliminating the degree correlation of dynamical processes. The interaction of neurons is assumed to be isotropic and idealized. These neuron dynamics are similar to biological evolution in extremal dynamics with locally isotropic interaction but has a different time scale. The functioning of neurons takes place as punctuated patterns based on avalanche dynamics. In our model, the avalanche dynamics of neurons exhibit self-organized criticality which shows power-law behavior of the avalanche sizes. For a given network, the avalanche dynamic behavior is not changed with different degree exponents of networks, γ≥2.4 and various refractory periods referred to the memory effect, T_r. Furthermore, the avalanche size distributions exhibit power-law behavior in a single scaling region in contrast to other networks. However, return time distributions displaying spatiotemporal complexity have three characteristic time scaling regimes Thus, we find that UCM may be inefficient for holding a memory.     

Automatic Search Dense Connection Module for Super-Resolution

The development of display technology has continuously increased the requirements for image resolution. However, the imaging systems of many cameras are limited by their physical conditions, and the image resolution is often restrictive. Recently, several models based on deep convolutional neural network (CNN) have gained significant performance for image super-resolution (SR), while extensive memory consumption and computation overhead hinder practical applications. For this purpose, we present a lightweight network that automatically searches dense connection (ASDCN) for image super-resolution (SR), which effectively reduces redundancy in dense connection and focuses on more valuable features. We employ neural architecture search (NAS) to model the searching of dense connections. Qualitative and quantitative experiments on five public datasets show that our derived model achieves superior performance over the state-of-the-art models.     

The architectonic fold similarity network in protein fold space

By constructing the fold similarity network (FSN), we present an alternative approach to the characteristic and architecture of protein fold space. The degree distribution P(k) of FSN differs far from that of the random network with the same number of nodes and connections. The investigation shows that FSN possesses small-world property and broad-scale feature. In order to access to the assumption of the dynamics behavior for FSN, we design a simple evolutionary dynamics model based on the duplication and variation fashions of protein folds. The simulation network generated by this model is a small-world one and reproduces the broad-scale degree distribution consistent with that of FSN. It seems that this model can be used to depict the divergent evolution and expanding progress of protein fold space.     

Symbiotic relationship between brain structure and dynamics

Background  

Brain structure and dynamics are interdependent through processes such as activity-dependent neuroplasticity. In this study, we aim to theoretically examine this interdependence in a model of spontaneous cortical activity. To this end, we simulate spontaneous brain dynamics on structural connectivity networks, using coupled nonlinear maps. On slow time scales structural connectivity is gradually adjusted towards the resulting functional patterns via an unsupervised, activity-dependent rewiring rule. The present model has been previously shown to generate cortical-like, modular small-world structural topology from initially random connectivity. We provide further biophysical justification for this model and quantitatively characterize the relationship between structure, function and dynamics that accompanies the ensuing self-organization.     

Dynamics-driven evolution to structural heterogeneity in complex networks

The mutual influence of dynamics and structure is a central issue in complex systems. In this paper we study by simulation slow evolution of network under the feedback of a local-majority-rule opinion process. If performance-enhancing local mutations have higher chances of getting integrated into its structure, the system can evolve into a highly heterogeneous small-world with a global hub (whose connectivity is proportional to the network size), strong local connection correlations and power-law-like degree distribution. Networks with better dynamical performance are achieved if structural evolution occurs much slower than the network dynamics. Structural heterogeneity of many biological and social dynamical systems may also be driven by various dynamics-structure coupling mechanisms.     

Dynamic synchronization and chaos in an associative neural network with multiple active memories

Associative memory dynamics in neural networks are generally based on attractors. Retrieval based on fixed-point attractors works if only one memory pattern is retrieved at the time, but cannot enable the simultaneous retrieval of more than one pattern. Stable phase-locking of periodic oscillations or limit cycle attractors leads to incorrect feature bindings if the simultaneously retrieved patterns share some of their features. We investigate retrieval dynamics of multiple active patterns in a network of chaotic model neurons. Several memory patterns are kept simultaneously active and separated from each other by a dynamic itinerant synchronization between neurons. Neurons representing shared features alternate their synchronization between patterns, thus multiplexing their binding relationships. Our model includes a mechanism for self-organized readout or decoding of memory pattern coherence in terms of short-term potentiation and short-term depression of synaptic weights.     

A switching mechanism of the default-mode network in the brain at criticality

Many works confirm the anti-correlations between the default mode network (DMN) and the central-executive network (CEN) in the brain. However, the switching mechanism of the DMN itself is still lack of understanding from the viewpoint of neural network dynamics. Here we simulate the DMN with the Hindmarsh-Rose (HR) neuron model on the small-world network. We model the state of oscillator death and oscillatory firing as the inhibitory state and the activated state, respectively. We find that the DMN can regenerate from the inhibitory state when the input current of only one synapse is cut off at criticality.     

Self-organized Criticality in a Model Based on Neural Network

Based on the LISSOM neural network model, we introduce a model to investigate self-organized criticality in the activity of neural populations. The influence of connection (synapse) between neurons has been adequately considered in this model. It is found to exhibit self-organized criticality (SOC) behavior under appropriate conditions. We also find that the learning process has promotive influence on emergence of SOC behavior. In addition, we analyze the influence of various factors of the model on the SOC behavior, which is characterized by the power-law behavior of the avalanche size distribution.