The brain computes! This is accepted as a truism by the majority of neuroscientists engaged in discovering the principles employed in the design and operation of nervous systems. What is meant here is that any brain takes the incoming sensory data, encodes them into various biophysical variables, such as the membrane potential or neuronal firing rates, and subsequently performs a very large number of ill-specified operations, frequently termed computations, on these variables to extract relevant features from the input. The outcome of some of these computations can be stored for later access and will, ultimately, control the motor output of the animal in appropriate ways. The present book is dedicated to understanding in detail the biophysical mechanisms responsible for these computations. Its scope is the type of information processing underlying perception and motor control, occurring at the millisecond to fraction of a second time scale. When you look at a pair of stereo images trying to fuse them into a binocular percept, your brain is busily computing away trying to find the “best” solution. What are the computational primitives at the neuronal and subneuronal levels underlying this impressive performance, unmatched by any machine? Naively put and using the language of the electronic circuit designer, the book asks: “What are the diodes and the transistors of the brain?” and “What sort of operations do these elementary circuit elements implement?” Contrary to received opinion, nerve cells are considerably more complex than suggested by work in the neural network community. Like morons, they are reduced to computing nothing but a thresholded sum of their inputs. We know, for instance, that individual nerve cells in the locust perform an operation akin to a multiplication. Given synapses, ionic channels, and membranes, how is this actually carried out? How do neurons integrate, delay, or change their output gain? What are the relevant variables that carry information? The membrane potential? The concentration of intracellular Ca2+ ions? What is their temporal resolution? And how large is the variability of these signals that determines how accurately they can encode information? And what variables are used to store the intermediate results of these computations? And where does long-term memory reside? Natural philosophers and scientists in the western world have always compared the brain to the most advanced technology of the day.
On the exponents of primitive, ministrong digraphs with shortest elementary circuit length s
