When has a Gaussian distribution ( and is an invertible function of " X " ), or " Y " itself has a ( marginal ) Gaussian distribution, this explained component of variation sets a lower bound on the mutual information:
12.
Conceptually, there is no difference between a reversible " n "-bit circuit and a reversible " n "-bit logic gate : either one is just an invertible function on the space of " n " bit data.
13.
For example, supposing there are " K " basic symbols, an alternative G�del numbering could be constructed by invertibly mapping this set of symbols ( through, say, an invertible function " h " ) to the set of digits of a bijective base-" K " numeral system.
14.
Several methods are known for defining cellular automata rules that are reversible; these include the block cellular automaton method, in which each update partitions the cells into blocks and applies an invertible function separately to each block, and the second-order cellular automaton method, in which the update rule combines states from two previous steps of the automaton.
15.
Given the optimal \ mathbf { W }, the signals \ mathbf { Y } have maximum entropy and are therefore independent, which ensures that the extracted signals \ mathbf { y } = g ^ {-1 } ( \ mathbf { Y } ) are also independent . g is an invertible function, and is the signal model.
16.
Note that unlike the general linear group, which is generally defined axiomatically as " invertible functions preserving the linear ( vector space ) structure ", the projective linear group is defined " constructively, " as a quotient of the general linear group of the associated vector space, rather than axiomatically as " invertible functions preserving the projective linear structure ".
17.
Note that unlike the general linear group, which is generally defined axiomatically as " invertible functions preserving the linear ( vector space ) structure ", the projective linear group is defined " constructively, " as a quotient of the general linear group of the associated vector space, rather than axiomatically as " invertible functions preserving the projective linear structure ".
