On the number of states of the neuronal sources

Abstract

In a previous paper (Proceedings of the World Congress on Neuroinformatics (2001)) the authors applied the socalled Lempel Á/Ziv complexity to study neural discharges (spike trains) from an information-theoretical point of view. Along with other results, it is shown there that this concept of complexity allows to characterize the responses of primary visual cortical neurons to both random and periodic stimuli. To this aim we modeled the neurons as information sources and the spike trains as messages generated by them. In this paper, we study further consequences of this mathematical approach, this time concerning the number of states of such neuronal information sources. In this context, the state of an information source means an internal degree of freedom (or parameter) which allows outputs with more general stochastic properties, since symbol generation probabilities at every time step may additionally depend on the value of the current state of the neuron. Furthermore, if the source is ergodic and Markovian, the number of states is directly related to the stochastic dependence lag of the source and provides a measure of the autocorrelation of its messages. Here, we find that the number of states of the neurons depends on the kind of stimulus and the type of preparation ( in vivo versus in vitro recordings), thus providing another way of differentiating neuronal responses. In particular, we observed that (for the encoding methods considered) in vitro sources have a higher lag than in vivo sources for periodic stimuli. This supports the conclusion put forward in the paper mentioned above that, for the same kind of stimulus, in vivo responses are more random (hence, more difficult to compress) than in vitro responses and, consequently, the former transmit more information than the latter. #

Application of Lempel–Ziv complexity to the analysis of neural discharges

“…Hence, although responses to the same stimulus Downloaded by [University of Lethbridge] at 23:08 17 June 2016 change, their complexity remains approximately constant. This invariance property of the normalized complexity was observed in Amigó et al (2003).…”

“…Normalized complexity is connected with several important concepts of information theory such as entropy, compression ratio for information of lossless sources (Ziv 1978), optimal encoding (Ziv and Lempel 1978) and randomness (Leung and Tavares 1985). Further applications concerning the number of internal states of the neuronal sources are addressed in Amigó et al (2003). Here we will pursue only its relation to entropy.…”

Characterisation of the Effects of Sleep Deprivation on the Electroencephalogram Using Permutation Lempel–Ziv Complexity, a Non-Linear Analysis Tool

“…Our PLZC results are consistent with these complexity measures. LZC was also used in other studies [64][65][66][67][68] to estimate the information content in spike trains during different brain states. To exclude external stimuli, spike trains were recorded during the dark period.…”

Artificial Neural Networks and Retinal Ganglion Cell Responses

“…This approach allows to answer questions about the relevant parameters that transmit information as well as addresses related issues such as the redundancy, the minimum number of neurons needed for coding certain group of stimuli, the efficiency of the code, the maximum information that a given code is able to transmit and the redundancy degree that exists in the population firing pattern (Borst and Theunissen, 1999;Amigo et al, 2003;Panzeri et al, 2003;Pola et al, 2003). We analysed the information about the stimulus that single cells conveyed, as well as the progression of the mutual information values after increasing the number of cells for each subpopulation.…”