积分发放网络中的周期调制行波：递归速度定律与传播失败
Periodically modulated traveling waves in integrate-and-fire networks: recursive speed law and propagation failure
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中文总结 AI 辅助
本研究通过标量速度方程和递归分析，揭示了积分发放网络中周期调制行波的折叠振幅规律，区分了传播失败类型，并验证了理论结果。
中文摘要 AI 辅助
神经组织中活动的行波可被突触耦合的空间不均匀性所阻止。我们研究了一个积分发放网络，其中每个神经元只发放一次，耦合呈指数衰减。对于该模型，前沿发放映射在空间中精确简化为一个关于波速的标量方程，具有一个慢的不稳定均匀速度和一个快的稳定均匀速度，分别记为$c_1$和$c_2$，耦合的周期调制逐点进入该方程。正的周期波在折叠处终止。对于缓慢变化的调制，折叠振幅趋近于由调制波谷设定的平台，局部瓶颈速度为$\sqrt{c_1 c_2}$；趋近平台的过程由波谷的局部几何决定。对于快速变化的调制，折叠振幅随频率线性增长，斜率由积分调制剖面的全振幅平均值给出；该平均值的弱纹波截断在默认耦合下约高估斜率2.5倍。振幅的微扰递归显式给出速度剖面。我们区分周期波的丧失与特定启动的失败，并区分兴奋性区域$\epsilon\le 1$及其变号扩展。结果与简化方程的直接积分及网络的首个尖峰发放映射模拟进行了对照验证。
英文摘要
Traveling waves of activity in neural tissue can be halted by spatial inhomogeneity in synaptic coupling. We study an integrate-and-fire network in which each neuron fires once and the coupling decays exponentially. For this model the leading-edge firing map reduces exactly to a scalar equation for the wave speed in space, with a slow unstable and a fast stable homogeneous speed, $c_1$ and $c_2$, and a periodic modulation of the coupling enters this equation pointwise. Positive periodic waves terminate in folds. For slowly varying modulation the fold amplitude approaches a plateau set by the trough of the modulation, where the local bottleneck speed is $\sqrt{c_1 c_2}$; the approach to the plateau is set by the local geometry of the trough. For rapidly varying modulation the fold amplitude grows linearly with frequency, with a slope given by a full-amplitude average over the integrated modulation profile; a weak-ripple truncation of that average overestimates the slope about 2.5-fold at the default coupling. A perturbative recursion in the amplitude gives the speed profile explicitly. We distinguish loss of the periodic wave from failure of a particular launch, and the excitatory regime $ε\le 1$ from its sign-changing extension. The results are checked against direct integration of the reduced equation and first-spike firing-map simulations of the network.
发表机构
- Georgia State University（佐治亚州立大学）
- Norcliffe Foundation Center for Integrative Brain Research, Seattle Children’s Research Institute（西雅图儿童医院研究所整合脑研究中心）
- Perimeter College, Georgia State University（佐治亚州立大学边界学院）
- Universal Alloy Corporation（通用合金公司）
- Pyrsquare Analytics（Pyrsquare分析公司）
- Transylvanian Institute of Neuroscience（特兰西瓦尼亚神经科学研究所）
机构由 AI 辅助整理，请以论文原文为准。
