Computations Neurons Perform in Networks: Inside vs. Outside & Lessons Learned from a Sixteenth Century Shoemaker

Cognitive and other neural processes emerge from the interactions between neurons. Major advances have been made in studying networks in which the interactions occur instantaneously by means of graded synapses (Guckenheirner and Rowat 1997). In other networks, the interaction between neurons involves time-delayed signals (action potentials or spikes) that activate synapses on other neurons discontinuously in a pulse-like manner. These interactions can also be treated as being graded if, when appropriate, the infomration transmitted between neurons can be measured as the average number of spikes per unit time (Freeman , 1992) ; i.e., the amount of information carried by individual spikes is relatively low. We refer to both of these types of interactions as "graded". There is a large armamentarium of mathematical and dynamical systems tools for studying the computations that such neurons perform. There is also a complementary connection between these tools and biological experimentation.

The subject of the present paper is on networks in which averaging can not be done. The generation of spikes in these neurons is significantly affected by the temporal order of spikes sent to them by other neurons. Two input spike trains, having the same average spikes per unit time but different temporal spacing between the spikes, produce different outputs in target neurons ; i.e., the amount of information carried by individual spikes is relatively high. We refer to these networks as "spike-activated". By comparison to graded networks, there is little formal or experimental work on the general principles underlying these networks.

There are many nonlinear physiological processes in spike-activated networks that need to be considered. We have begun by focusing on a single nonlinearity analysis, the threshold tansition between spiking and nonspiking behavior, and use linear perturbation to examine it. The findings indicate that there may be an epistemological distinction between graded networks and spike-activated networks. This is reminiscent of the distinction between endophysics and exophysics whose resolutions requires an external observer having information about a system and its external universe (Rôssler, 1989). Interestingly, the philosophical roots of our approach and the study of dynamics more generally may be traceable to Jacob Bôhme (1575-1624), a mystic and contemporary of Descartes. Bôhme influenced many philosophers and scientists, and may have provided Isaac Newton the metaphorical insight into his laws of physics (Mpitsos, 1995 ; Yates, 1972,1979).