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     

小世界神经网络的二次超谐波随机共振

随机共振现象是非线性系统中普遍存在的自然现象.主要通过研究小世界生物神经网络中的输出信噪比与反映小世界效应的重连概率p、耦合强度c以及输入信号振幅A之间的关系，来揭示小世界生物神经网络的二次超谐波随机共振的一些规律.发现对于Hodgkin-Huxley小世界神经网络，并不是信号越强，信噪比越大，而是输入信号的振幅A存在一个最优值A_O，此时网络信噪比最大.     

多色部分相干偏心光束在non-Kolmogorov湍流中的传输

推导了多色部分相干偏心光束在non-Kolmogorov 湍流中传输的总光强、轴上光谱、相干度的解析表达式, 研究了光束偏心参数β 、湍流广义指数α和源光谱带宽Ω对激光传输特性的影响. 研究表明: β越大, 则光束重心偏离传输轴越远, 相干度的不对称性越明显, 但是, β对轴上光谱几乎没有影响; 湍流广义指数α对总光强、 轴上光谱和相干长度的影响是非单调的, 当α=3.1时, 湍流对光束传输特性的影响最大. 值得指出的是: 在某些传输距离处, 不同α对应的轴上光谱位移量相同; 在某些传输距离处, 轴上光谱位移量为零, 且该传输距离与Ω无关, 但湍流使得该传输距离缩短. 所得结论对多色部分相干偏心光束在 湍流大气中传输的相关应用具有重要意义. 关键词： non-Kolmogorov湍流 多色部分相干偏心光束 光谱强度 相干度     

耦合小世界神经网络的随机共振

噪声广泛存在于生物神经系统中,对系统功能具有重要作用.采用神经元二维映射模型构建一个复杂神经网络,由多个小世界子网络构成,研究了Gaussian白噪声诱导的随机共振现象.研究发现,只有合适的噪声强度才能使神经网络对输入刺激信号的频率响应达到峰值.另外,网络结构对系统随机共振特性有重要影响.在固定的耦合强度下,存在一个最优的局部小世界子网络结构,使得整个系统的频率响应最佳.     

用于混沌时间序列预测的多簇回响状态网络

研究了混沌时间序列预测问题.提出了一种由五元生长因子组调控的类皮层神经网络模型,即多簇回响状态网络模型（MCESN）.研究表明该生长因子组能够有效决定模型的拓扑性质;同时具备小世界和无标度等复杂网络特征的MCESN能够获得较优的预测结果.通过Monte Carlo仿真实验表明,该模型不仅训练算法简单,而且与常规回响状态网络比较,预测结果的精度更高、标准差更小. 关键词： 混沌时间序列预测 回响状态网络 复杂网络 Ω复杂性')" href="#">Ω复杂性     

α稳定噪声驱动的非对称双稳随机共振现象

以微弱周期信号激励的非对称双稳系统为模型, 以信噪比增益为指标, 首先针对加性和乘性α 稳定噪声共同作用的随机共振现象展开了研究, 然后针对单独加性α 稳定噪声激励的随机共振现象进行了研究, 探究了α 稳定噪声特征指数α 和对称参数β 分别取不同值时, 系统结构参数a, b, 刻画双稳系统非对称性的偏度r以及α 稳定噪声强度放大系数Q或D对非对称双稳系统共振输出的作用规律. 研究结果表明, 无论在加性和乘性α 稳定噪声共同作用下还是在单独加性α 稳定噪声作用下, 通过调节a和b或者r均可诱导随机共振, 实现微弱信号的检测, 且有多个参数区间与之对应, 这些区间不随α 或β 的变化而变化; 在研究噪声诱导的随机共振现象时发现, 调节噪声强度放大系数也可使系统产生随机共振现象, 且达到共振状态时D的区间也不随α 或β 的变化而变化. 这些结论为α 稳定噪声环境下参数诱导随机共振中系统参数以及噪声诱导随机共振中噪声强度的合理选取提供了依据.     

精确求解级联型三能级原子与单模相干态光场场熵的演化特性

本文利用全量子理论,在非旋波近似下对单模相干态光场与级联型三能级原子相互作用过程中场熵随时间的演化进行了精确求解.数值计算的结果表明：随着初始时刻平均光子数n以及光场与原子的耦合强度u, v的增大,场熵的平均值先增大后减小,因此纠缠度也同样先增大后减小;随着失谐量Δ的增大,场熵的平均值逐渐减小,因此纠缠度也逐渐减小. 关键词： 相干态正交化展开 非旋波近似 场熵     

简谐噪声激励下FitzHugh-Nagumo神经元的动力学行为

研究了简谐噪声激励下的FitzHugh-Nagumo神经元模型, 其放电形式、相干共振等动力学行为均受噪声阻尼参数和频率参数的影响.选择不同的参数所得到的神经元的放电形式不同.神经元存在共振特性,对某一频率的噪声有更强的响应,在此频率参数下的峰序列更有序,出现相干共振系数的极小值.噪声的阻尼参数越大,不同的频率成分越多,神经元的响应也变得杂乱,进而导致神经元与噪声的同步变弱,峰序列相干共振系数也相应增大. 关键词： 简谐噪声 FitzHugh-Nagumo神经元 相干共振 峰峰间隔     

频率变化的光场对双光子过程中量子纠缠的调控

运用量子信息熵理论研究了二能级原子与频率随时间变化的相干态光场作用的双光子过程中纠缠度演化,主要讨论了光场频率随时间作正弦调制和脉冲调制两种情况下,纠缠随时间的演化特性. 当光场频率随时间作正弦调制时,原子与光场的纠缠度明显增大,并保持高纠缠度. 通过改变光场频率调制的频率β和振幅α,发现原子与光场纠缠度的演化过程对调制的振幅更加敏感. 当光场频率随时间作脉冲调制时,在纠缠度最大值处开始加脉冲比在最小值处加脉冲能够更快、更容易实现原子与光场纠缠度的提高和稳定. 脉冲调制的突变使 关键词： 纠缠 场熵 相干态 双光子Jaynes-Cummings模型     

基于度的正/负相关相依网络模型及其鲁棒性研究

利用典型的Barabási-Albert无标度网络构建了基于度的正/负相关相依网络模型, 该模型考虑子网络间的相依方式及相依程度, 主要定义了两个参数F和K, F表示相依节点比例, K表示相依冗余度. 在随机攻击及基于度的蓄意攻击模式下, 针对网络的级联失效问题, 研究了不同的F值和K值对该相依网络模型鲁棒性的影响, 与随机相依网络模型进行了对比研究. 仿真结果表明:无论是随机相依或是基于度的正/负相关相依网络, 其鲁棒性都是随着F的增大而减弱, 随着K的增大而增强; 在随机攻击下, 全相依模式(F=1)时, 基于度正相关相依网络模型鲁棒性最优, 部分相依模式 (F =0.2, 0.5, 0.8)时, 基于度的负相关相依网络模型则表现出更好的鲁棒性. 而在基于度的蓄意攻击下, 无论F为何值, 基于度的正相关相依网络模型表现出弱鲁棒性.     

Coherence Resonance and Noise-Induced Synchronization in Hindmarsh-Rose Neural Network with Different Topologies

In this paper, we investigate coherence resonance （CR） and noise-induced synchronization in Hindmarsh- Rose （HR） neural network with three different types of topologies： regular, random, and small-world. It is found that the additive noise can induce CR in HR neural network with different topologies and its coherence is optimized by a proper noise level. It is also found that as coupling strength increases the plateau in the measure of coherence curve becomes broadened and the effects of network topology is more pronounced simultaneously. Moreover, we find that increasing the probability p of the network topology leads to an enhancement of noise-induced synchronization in HR neurons network.     

Spatial coherence resonance on diffusive and small-world networks of Hodgkin-Huxley neurons

Spatial coherence resonance in a spatially extended system that is locally modeled by Hodgkin-Huxley (HH) neurons is studied in this paper. We focus on the ability of additive temporally and spatially uncorrelated Gaussian noise to extract a particular spatial frequency of excitatory waves in the medium, whereby examining the impact of diffusive and small-world network topology that determines the interactions amongst coupled HH neurons. We show that there exists an intermediate noise intensity that is able to extract a characteristic spatial frequency of the system in a resonant manner provided the latter is diffusively coupled, thus indicating the existence of spatial coherence resonance. However, as the diffusive topology of the medium is relaxed via the introduction of shortcut links introducing small-world properties amongst coupled HH neurons, the ability of additive Gaussian noise to evoke ordered excitatory waves deteriorates rather spectacularly, leading to the decoherence of the spatial dynamics and with it related absence of spatial coherence resonance. In particular, already a minute fraction of shortcut links suffices to substantially disrupt coherent pattern formation in the examined system.     

小世界网络与无标度网络的社区结构研究

模块性(modularity)是度量网络社区结构(community structure)的主要参数.探讨了Watts和Strogatz的小世界网络(简称W-S模型)以及Barabàsi 等的B-A无标度网络(简称B-A模型)两类典型复杂网络模块性特点.结果显示，网络模块性受到网络连接稀疏的影响，W-S模型具有显著的社区结构，而B-A模型的社区结构特征不明显.因此，应用中应该分别讨论网络的小世界现象和无标度特性.社区结构不同于小世界现象和无标度特性，并可以利用模块性区别网络类型，因此网络复杂性指标应该包括 关键词： 模块性 社区结构 小世界网络 无标度网络     

Delay-enhanced spatiotemporal order in coupled neuronal systems

In a network of noisy neuron oscillators with time-delayed coupling, we uncover a phenomenon of delay-enhanced spatiotemporal order. We find that time delay in the coupling can dramatically enhance the temporal coherence and spatial synchrony of the noise-induced spike trains. In addition, if the delay time is tuned to nearly match the intrinsic spiking period of the neuronal network, both the coherence and the synchrony reach maximum levels, demonstrating an interesting type of resonance phenomenon with delay. Such findings are shown to be robust to the change of the noise intensity and the rewiring probability of small-world network.     

Optimal network structure to induce the maximal small-world effect

In this paper, the general efficiency, which is the average of the global efficiency and the local efficiency, is defined to measure the communication efficiency of a network. The increasing ratio of the general efficiency of a small-world network relative to that of the corresponding regular network is used to measure the small-world effect quantitatively. The more considerable the small-world effect, the higher the general efficiency of a network with a certain cost is. It is shown that the small-world effect increases monotonically with the increase of the vertex number. The optimal rewiring probability to induce the best small-world effect is approximately 0.02 and the optimal average connection probability decreases monotonically with the increase of the vertex number. Therefore, the optimal network structure to induce the maximal small-world effect is the structure with the large vertex number （〉 500）, the small rewiring probability （≈0.02） and the small average connection probability （〈 0.1）. Many previous research results support our results.     

An effective method to improve the robustness of small-world networks under attack

In this study, the robustness of small-world networks to three types of attack is investigated. Global efficiency is introduced as the network coefficient to measure the robustness of a small-world network. The simulation results prove that an increase in rewiring probability or average degree can enhance the robustness of the small-world network under all three types of attack. The effectiveness of simultaneously increasing both rewiring probability and average degree is also studied, and the combined increase is found to significantly improve the robustness of the small-world network.Furthermore, the combined effect of rewiring probability and average degree on network robustness is shown to be several times greater than that of rewiring probability or average degree individually. This means that small-world networks with a relatively high rewiring probability and average degree have advantages both in network communications and in good robustness to attacks. Therefore, simultaneously increasing rewiring probability and average degree is an effective method of constructing realistic networks. Consequently, the proposed method is useful to construct efficient and robust networks in a realistic scenario.     

Harmonic stochastic resonance-enhanced signal detecting in NW small-world neural network

The harmonic stochastic resonance-enhanced signal detecting in Newman-Watts small-world neural network is studied using the Hodgkin-Huxley dynamical equation with noise.If the connection probability p,coupling strength g syn and noise intensity D matches well,higher order resonance will be found and an optimal signal-to-noise ratio will be obtained.Then,the reasons are given to explain the mechanism of this appearance.     

The networks from medical knowledge and clinical practice have small-world,scale-free,and hierarchical features

Here, we constructed and analyzed a network (henceforth, “medical knowledge network”) derived from a commonly used medical text. We show that this medical knowledge network has small-world, scale-free, and hierarchical features. We then constructed a network from data from a hospital information system that reflected actual clinical practice and found that this network also had small-world, scale-free, and hierarchical features. Moreover, we found that both the diagnosis frequency distribution of the hospital network and the diagnosis degree distribution of the medical knowledge network obeyed a similar power law. These findings suggest that the structure of clinical practice may emerge from the mutual influence of medical knowledge and clinical practice, and that the analysis of a medical knowledge network may facilitate the investigation of the characteristics of medical practice.