Dependency representing Markov properties of nonstationary spike trains recorded from the cat's optic tract fibers

Abstract

Here K=0.51og2e, and I/~ml is the correlation coefficient determinant obtained from the ensemble averages of sample records. When an observed value A~,, is greater than or equal to the critical value, A~=Kz2(~)/N, the null hypothesis of the (m-1)th order, A~,,--~m-N,,-*---0, is rejected at the level of significance e. Here )~2(cQ is the chi-square value with one degree of freedom at c~ and N is sample size. With these statistics it was shown that the order and the values of Markov properties of spike trains of optic tract X-and Y-fibers became higher and larger, respectively, after the light spot presentation; and that the values ~1 due to negative correlation came to increase and returned to the maintained level earlier in Y-fibers than in X-fibers, while the maximum values for X-fibers continued to the light off. It is discussed that Markov properties of spike trains of optic tract fibers in the visual pathway seem to constitute a significant component of the neural information code.

Markov dependency based on Shannon's entropy and its application to neural spike trains

“…Then simplified dependency D m is defined similarly as in (5): 2) m = |{log 2 |^m|-log 2 |^m +1 |} (21) where \R m \ is the determinant of the matrix R m . Although computation methods of simplified dependency D m for an (m 4l)-dimensional ensemble are different from those of S) m for the stationary series, &D m and the critical value AD^ are derived as follows [15]: The simphfied dependency, originally defined for the Gaussian Markov process, showed robustness for skewed distributions such as exponential distributions [20]. How ever, neuronal spike trains with more than exponential skewness were often observed, such as long-tailed or multi modal distributions.…”

“…We sought to determine the effect of light stimulation in terms of changes in the order and value of Markov properties [15], [21]. The results revealed that the light spot presentation to the centers of receptive fields of on-center optic tract fibers led to an increase of the values of the first-order Markov properties, and that the values increased and reached the maximum earlier in Y fibers than in X fibers.…”

“…This concept later evolved into some techniques for estimating the degree of the higher order Markov processes [15], [17], [20].…”

Quantitative analysis of the sympathetic efferent activity to characterize the integrative function of the sympathetic ganglion.

“…For this purpose, we have proposed dependency as one of statistical measures representing Markovian characteristics (NAKAHAMA and NISHIOKA, 1966;NAKAHAMA et al, 1972NAKAHAMA et al, , 1974NAKAHAMA et al, , 1975NAKAHAMA et al, , 1977NAKAHAMA et al, , 1979.…”

“…The latter, however, have no bearing on the analysis of the time structure. We have aimed, therefore, at description of the sympathetic activity in terms of a Markov process in order to obtain appropriate information on the intensity and consistency of time dependent patterns by determining the order and value of the Markov dependency (NAKAHAMA and NISHIOKA, 1966;NAKAHAMA et al, 1972NAKAHAMA et al, , 1974NAKAHAMA et al, , 1975NAKAHAMA et al, , 1977NAKAHAMA et al, , 1979. Comparing the results derived from the preand postganglionic activities we have made an attempt to assess integrative function of the superior cervical ganglion.…”