Discrete memristive neuron model and its interspike interval-encoded application in image encryption

Bursting is a diverse and common phenomenon in neuronal activation patterns and it indicates that fast action voltage spiking periods are followed by resting periods.The interspike interval(ISI)is the time between successive action voltage spikes of neuron and it is a key indicator used to characterize the bursting.Recently,a three-dimensional memristive Hindmarsh-Rose(mHR)neuron model was constructed to generate hidden chaotic bursting.However,the properties of the discrete mHR neuron model have not been investigated,yet.In this article,we first construct a discrete mHR neuron model and then acquire different hidden chaotic bursting sequences under four typical sets of parameters.To make these sequences more suitable for the application,we further encode these hidden chaotic sequences using their ISIs and the performance comparative results show that the ISI-encoded chaotic sequences have much more complex chaos properties than the original sequences.In addition,we apply these ISI-encoded chaotic sequences to the application of image encryption.The image encryption scheme has a symmetric key structure and contains plain-text permutation and bidirectional diffusion processes.Experimental results and security analyses prove that it has excellent robustness against various possible attacks.

A comparison of the spontaneous firing patterns between principal cells and fast spiking interneurons from dentate gyrus in waking guinea pigs

Objective To explore the possible mechanisms that cause the dentate gyrus （DG） neurons to play different roles in information coding. Methods In vivo extracellular single unit recording was performed on 22 waking female guinea pigs, which were positioned in a sound-attenuated recording chamber without any muscular relaxants. The spontaneous firing patterns of the DG neurons were detected and compared. Results There were two different electrophysiologi- cal populations in the DG of guinea pigs, principal cells （PCs） and fast spiking interneurons （INs）. Of the PCs, 1.3% discharged regularly, 48.1% irregularly and 50.6% in bursts ; in contrast, of the INs units, 64.1% discharged regularly, 2.6% irregularly and 33.3% in bursts. The spontaneous firing patterns of PCs were significantly different from those of INs （P 〈0.01 ）. In addition, the differences of several interspike interval （ISI） parameters also have been observed： （1） the ISI coefficients of variation of PCs （3.39 ± 3.56） were significantly higher than those of INs （1.08 ± 0.46） （P 〈0.01） ; （2） the ISI asymmetric indexes of PCs （0. 047±0. 059） were significantly lower than those of INs （0.569±0. 238） （P 〈 0.01 ）. Conclusion In the DG, the spontaneous firing patterns of PCs were significantly different from those of INs. The former were prone to fire in bursts, the latter were prone to fire regularly. The different roles in information coding between PCs and INs might be caused by their different firing patterns.

Dynamics analysis on neural firing patterns by symbolic approach

Neural firing patterns are investigated by using symbolic dynamics. Bifurcation behaviour of the Hindmarsh-Rose （HR） neuronal model is simulated with the external stimuli gradually decreasing, and various firing activities with different topological structures are orderly numbered. Through constructing first-return maps of interspike intervals, all firing patterns are described and identified by symbolic expressions. On the basis of ordering rules of symbolic sequences, the corresponding relation between parameters and firing patterns is established, which will be helpful for encoding neural information. Moreover, using the operation rule of ＊ product, generation mechanisms and intrinsic configurations of periodic patterns can be distinguished in detail. Results show that the symbolic approach is a powerful tool to study neural firing activities. In particular, such a coarse-grained way can be generalized in neural electropt/ysiological experiments to extract much valuable information from complicated experimental data.

Characterizing neural activities evoked by manual acupuncture through spiking irregularity measures

The neural system characterizes information in external stimulations by different spiking patterns. In order to examine how neural spiking patterns are related to acupuncture manipulations, experiments are designed in such a way that different types of manual acupuncture （MA） manipulations are taken at the ＇Zusanli＇ point of experimental rats, and the induced electrical signals in the spinal dorsal root ganglion are detected and recorded. The interspike interval （ISI） statistical histogram is fitted by the gamma distribution, which has two parameters： one is the time-dependent firing rate and the other is a shape parameter characterizing the spiking irregularities. The shape parameter is the measure of spiking irregularities and can be used to identify the type of MA manipulations. The coefficient of variation is mostly used to measure the spike time irregularity, but it overestimates the irregularity in the case of pronounced firing rate changes. However, experiments show that each acupuncture manipulation will lead to changes in the firing rate. So we combine four relatively rate- independent measures to study the irregularity of spike trains evoked by different types of MA manipulations. Results suggest that the MA manipulations possess unique spiking statistics and characteristics and can be distinguished according to the spiking irregularity measures. These studies have offered new insights into the coding processes and information transfer of acupuncture.

Information geometry in neural spike sequences

An information geometrical method is developed for characterizing or classifying neurons in cortical areas whose spike rates fluctuate in time.The interspike intervals(ISIs)of a spike sequence of a neuron is modeled as a gamma process with a time-variant spike rate,a fixed shape parameter and a fixed absolute refractory period.We formulate the problem of estimating the fixed parameters as semiparametric estimation and apply an information geometrical method to derive the optimal estimators from a statistical viewpoint.