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摘要翻译：
分析计算了随机门限网络(RTN)在齐次和非齐次门限下的临界连通度，并通过数值模拟验证了结果。我们发现$k_c$随（平均）绝对阈值$h$的超线性增长，对于大的$h$逼近$k_c(h)\sim h^2/(2\ln{h}）$,并证明了这种渐近标度对于具有泊松分布连通性和门限分布且方差增长慢于$h^2$的RTN是普遍的。有趣的是，对于稀疏连通网络，阈值的非均匀分布导致扰动传播增加，而对于密集连通网络，损伤减小；交叉点产生了一种新颖的、特征性的连通性$K_D$，这在布尔网络中是没有的。最后，引入了节点阈值与度之间的局部相关性。在这里，数值模拟表明，即使是微弱的（反）关联也能导致从有序动力学到混沌动力学的转变，反之亦然。结果表明，在这种情况下，退火近似中典型的朴素平均场假设导致了错误的预测，因为阈值和超出程度之间的相关性作为一种副作用强烈地改变了损伤传播行为。
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英文标题：
《Critical Line in Random Threshold Networks with Inhomogeneous Thresholds》
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作者：
Thimo Rohlf
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最新提交年份：
2008
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分类信息：
一级分类：Physics 物理学
二级分类：Disordered Systems and Neural Networks 无序系统与神经网络
分类描述：Glasses and spin glasses; properties of random, aperiodic and quasiperiodic systems; transport in disordered media; localization; phenomena mediated by defects and disorder; neural networks
眼镜和旋转眼镜；随机、非周期和准周期系统的性质；无序介质中的传输；本地化；由缺陷和无序介导的现象；神经网络
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一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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一级分类：Physics 物理学
二级分类：Cellular Automata and Lattice Gases 元胞自动机与格子气体
分类描述：Computational methods, time series analysis, signal processing, wavelets, lattice gases
计算方法，时间序列分析，信号处理，小波，格子气体
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一级分类：Quantitative Biology 数量生物学
二级分类：Molecular Networks 分子网络
分类描述：Gene regulation, signal transduction, proteomics, metabolomics, gene and enzymatic networks
基因调控、信号转导、蛋白质组学、代谢组学、基因和酶网络
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英文摘要：
We calculate analytically the critical connectivity $K_c$ of Random Threshold Networks (RTN) for homogeneous and inhomogeneous thresholds, and confirm the results by numerical simulations. We find a super-linear increase of $K_c$ with the (average) absolute threshold $|h|$, which approaches $K_c(|h|) \sim h^2/(2\ln{|h|})$ for large $|h|$, and show that this asymptotic scaling is universal for RTN with Poissonian distributed connectivity and threshold distributions with a variance that grows slower than $h^2$. Interestingly, we find that inhomogeneous distribution of thresholds leads to increased propagation of perturbations for sparsely connected networks, while for densely connected networks damage is reduced; the cross-over point yields a novel, characteristic connectivity $K_d$, that has no counterpart in Boolean networks. Last, local correlations between node thresholds and in-degree are introduced. Here, numerical simulations show that even weak (anti-)correlations can lead to a transition from ordered to chaotic dynamics, and vice versa. It is shown that the naive mean-field assumption typical for the annealed approximation leads to false predictions in this case, since correlations between thresholds and out-degree that emerge as a side-effect strongly modify damage propagation behavior.
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PDF链接：
https://arxiv.org/pdf/707.3621
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