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We offer a new account of recursive definitions for both types and partial functions. The computational requirements of the theory restrict recursive type definitions involving the total function-space constructor (→) to those with only positive occurrences of the defined typed. But we show that arbitrary recursive definitions with respect to the partial function-space constructor are sensible. The...
Synapses are the primary means for transmitting information from one neuron to the next. They are formed during the development of the nervous system, and the formation of appropriate synapses is crucial for the establishment of neuronal circuits that underlie behavior and cognition. Understanding how synapses form and are maintained will allow us to address developmental disorders such as autism,...
Let Φ be any abstract measure of computational complexity, and let L denote the specific measure of memory resource (tape) on one tape Turing machines. Denote by Rt( )Φ the class of all total functions whose Φ-complexity is bounded by the function t( ) almost everywhere. Call such classes Φ-complexity classes. We are interested in relationships among these classes, under proper set inclusion (⊂)....
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