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.

AUTOMATIC DECISION-MAKING: NEURAL FIRING AND RESPONSE

In contrast with conscious decision-making, there are numerous subconscious decisions that we make without thinking about them. Some are biological and are made by different parts of our body to keep it alive and functioning normally. Others are a result of repetition and training that we can then do without thinking about them. The mathematics of conscious decisions with the Analytic Hierarchy and Network Processes is discrete, and has been discussed in the first three parts published on the subject. The mathematics of subconscious decisions is continuous. Here, we generalize the discrete mathematics of conscious decisions to the continuous case and develop it in some depth to apply to the synthesis of firings in the brain.

Spontaneous firing in olfactory bulb neurons of Bufo bufo gargarizans in and after hibernation

Microelectrode technique was used to record the spontaneous electrical activities of the neurons in olfactory bulb of the Bufo bufo gargarizans, both in hibernation and after hibemation. This study investigated the electrophysiological characteristics of amphibian olfactory bulb in the period of hibernation and after hibernation and its effects on the start of hibernation and spontaneous awakening. The research showed four forms of spontaneous firings： single spontaneous firing, burst spontaneous firing, irregular spontaneous firing and consecutive single spontaneous firing. The single spontaneous firing includes slow depolarized spontaneous firing and fast depolarized spontaneous firing, and the slow depolarized spontaneous firing occurs only during the hibernation period. In hibernation, the low amplitude and low frequency firing with a longer duration may be relevant to maintaining the tonicity of the central nervous system in toads that are in hibernation, and this kind of firing may also provide an excited basis for their arousal from hibernation. After hibernation, the amplitude and frequency of firing increase, but the firing duration gets shorter. This form of short-term firing, which may be a phenomenon of sensory neurons fast adapting, is one of the neuronal mechanisms for the arousal of hibernating animals.

Experimental identification of a comb-shaped chaotic region in multiple parameter spaces simulated by the Hindmarsh–Rose neuron model

A comb-shaped chaotic region has been simulated in multiple two-dimensional parameter spaces using the Hindmarsh-Rose （HR） neuron model in many recent studies, which can interpret almost all of the previously simulated bifurcation processes with chaos in neural firing patterns. In the present paper, a comb-shaped chaotic region in a two- dimensional parameter space was reproduced, which presented different processes of period-adding bifurcations with chaos with changing one parameter and fixed the other parameter at different levels. In the biological experiments, different period-adding bifurcation scenarios with chaos by decreasing the extra-cellular calcium concentration were observed from some neural pacemakers at different levels of extra-cellular 4-aminopyridine concentration and from other pacemakers at different levels of extra-cellular caesium concentration. By using the nonlinear time series analysis method, the determin- istic dynamics of the experimental chaotic firings were investigated. The period-adding bifurcations with chaos observed in the experiments resembled those simulated in the comb-shaped chaotic region using the HR model. The experimental results show that period-adding bifurcations with chaos are preserved in different two-dimensional parameter spaces, which provides evidence of the existence of the comb-shaped chaotic region and a demonstration of the simulation results in dif- ferent two-dimensional parameter spaces in the HR neuron model. The results also present relationships between different firing patterns in two-dimensional parameter spaces.

A cascade model of information processing and encoding for retinal prosthesis

Retinal prosthesis offers a potential treatment for individuals suffering from photoreceptor degeneration diseases.Establishing biological retinal models and simulating how the biological retina convert incoming light signal into spike trains that can be properly decoded by the brain is a key issue.Some retinal models have been presented,ranking from structural models inspired by the layered architecture to functional models originated from a set of specific physiological phenomena.However,Most of these focus on stimulus image compression,edge detection and reconstruction,but do not generate spike trains corresponding to visual image.In this study,based on stateof-the-art retinal physiological mechanism,including effective visual information extraction,static nonlinear rectification of biological systems and neurons Poisson coding,a cascade model of the retina including the out plexiform layer for information processing and the inner plexiform layer for information encoding was brought forward,which integrates both anatomic connections and functional computations of retina.Using MATLAB software,spike trains corresponding to stimulus image were numerically computed by four steps：linear spatiotemporal filtering,static nonlinear rectification,radial sampling and then Poisson spike generation.The simulated results suggested that such a cascade model could recreate visual information processing and encoding functionalities of the retina,which is helpful in developing artificial retina for the retinally blind.