arXiv subjects

Zhong-Qi Kyle Tian

Publications and source records attributed to Zhong-Qi Kyle Tian.

4 recordsLinked to original sources

arXiv2021

Design Fast Algorithms For Hodgkin-Huxley Neuronal Networks

The stiffness of the Hodgkin-Huxley (HH) equations during an action potential (spike) limits the use of large time steps. We observe that the neurons can be evolved independently between spikes, $i.e.,$ different neurons can be evolved with different methods and different time steps. This observation motivates us to design fast algorithms to raise efficiency. We present an adaptive method, an exponential time differencing (ETD) method and a library-based method to deal with the stiff period. All the methods can use time steps one order of magnitude larger than the regular Runge-Kutta methods to raise efficiency while achieving precise statistical properties of the original HH neurons like the largest Lyapunov exponent and mean firing rate. We point out that the ETD and library methods can stably achieve maximum 8 and 10 times of speedup, respectively.

q-bio.NC↗

arXiv2021

Library-based Fast Algorithm for Simulating the Hodgkin-Huxley Neuronal Networks

We present a modified library-based method for simulating the Hodgkin-Huxley (HH) neuronal networks. By pre-computing a high resolution data library during the interval of an action potential (spike), we can avoid evolving the HH equations during the spike and can use a large time step to raise efficiency. The library method can stably achieve at most 10 times of speedup compared with the regular Runge-Kutta method while capturing most statistical properties of HH neurons like the distribution of spikes which data is widely used in the statistical analysis like transfer entropy and Granger causality. The idea of library method can be easily and successfully applied to other HH-type models like the most prominent \textquotedblleft regular spiking\textquotedblright , \textquotedblleft fast spiking\textquotedblright , \textquotedblleft intrinsically bursting\textquotedblright{} and \textquotedblleft low-threshold spike\textquotedblright{} types of HH models.

q-bio.NC↗

arXiv2019

Design Efficient Exponential Time Differencing method For Hodgkin-Huxley Neural Networks

The exponential time differencing (ETD) method allows using a large time step to efficiently evolve the stiff system such as Hodgkin-Huxley (HH) neural networks. For pulse-coupled HH networks, the synaptic spike times cannot be predetermined and are convoluted with neuron's trajectory itself. This presents a challenging issue for the design of an efficient numerical simulation algorithm. The stiffness in the HH equations are quite different between the spike and non-spike regions. Here, we design a second-order adaptive exponential time differencing algorithm (AETD2) for the numerical evolution of HH neural networks. Compared with the regular second-order Runge-Kutta method (RK2), our AETD2 method can use time steps one order of magnitude larger and improve computational efficiency more than ten times while excellently capturing accurate traces of membrane potentials of HH neurons. This high accuracy and efficiency can be robustly obtained and do not depend on the dynamical regimes, connectivity structure or the network size.

q-bio.NC↗

arXiv2019

Digital System Reconstruction by Pairwise Transfer Entropy

Transfer entropy (TE) is an attractive model-free method to detect causality and infer structural connectivity of general digital systems. However it relies on high dimensions used in its definition to clearly remove the memory effect and distinguish the direct causality from the indirect ones which makes it almost inoperable in practice. In this work, we try to use a low order and pairwise TE framework with binary data suitably filtered from the recorded signals to avoid the high dimensional problem. Under this setting, we find and explain that the TE values from the connected and unconnected pairs have a significant difference of magnitude, which can be easily classified by cluster methods. This phenomenon widely and robustly holds over a wide range of systems and dynamical regimes. In addition, we find the TE value is quadratically related to the coupling strength and thus we can establish a quantitative mapping between the causal and structural connectivity.

q-bio.QM↗