Processing of Information in Synchroneously Firing Chains in Networks of Neurons

The Abeles model of cortical activity assumes that in absence of stimulation neural activity in zero order can be described by a Poisson process. Here the model is extended to describe information processing by synfire chains within a network of activity uncorrelated to the synfire chain. A quantitative derivation of the transfer function from this concept is given. Two seminal concepts were introduced by Abeles [1, 2, 3]: A quantitative model for uncorrelated activity in the cortex in absence of external stimulation, and the concept of the synfire chain, a spatiotemporal pattern of synchroneous activity of neurons being active in the same cortical task. Synchroneous spiking, as a refinement of averaged firing rates, has been used as an equivalent mathematical basis for neural models [4, 5]. The experimental and theoretical aspects of synfire chains remain a field of active research [6, 7] and also provide a conceptual basis for neural computing architectures [8]. This paper analyzes the extension to formulate processing and propagation of information in such a network. 1 The Abeles model of cortical activity The model of uncorrelated cortical activity given by Abeles [1], here referred to as Abeles Model, is a direct approach to understand why randomly firing by selfexcitation can be a stationary and robust firing mode in a neural network. The underlying experiments are interpreted in the following way: Even if the cortex is not excited by sensory input, the neurons are firing randomly (Poisson process) and excite each other. Obviously, this is to be interpreted as a “ground state” of the cortical network. An interesting question is whether random firing is a stable mode of a network or not. Because 99% of the inputs to the cortex are coming from the same or other cortical areas [9], we shall at first neglect the 1% (sensory) input and therefore consider a network with 100% feedback.