Crisp and Soft Computing with Hypercubical Calculus: New by Dr. Michael Zaus (auth.)

By Dr. Michael Zaus (auth.)

Three transdisciplinary mainstreams of crisp and gentle computing are offered during this e-book. (1) a completely new method of clinical modeling from scratch as in keeping with parity common sense with new operators for binary computing and the recent framework of Langlet transforms. (2) A compact evaluation of the principles of fuzzy good judgment, and a entire remedy of fuzzy nonlinear dynamical predictor platforms by way of fuzzy cognitive maps. Readers attracted to new methods of causal modeling and nonlinear forecasting are brought to fuzzy wisdom engineering as a paradigm shift in clever computing. (3) New views for evolutionary computing with an integro-differential operator from parity good judgment, and a scientific elaboration of autogenetic algorithms for seek in excessive dimensional function areas. Readers drawn to quick computing, functional purposes of causal reasoning with fuzzy good judgment, and interactive experimental regulate environments as according to evolutionary computing, will achieve major insights right into a number of computational energy tools.

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Extra info for Crisp and Soft Computing with Hypercubical Calculus: New Approaches to Modeling in Cognitive Science and Technology with Parity Logic, Fuzzy Logic, and Evolutionary Computing

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5 . 5 acts on its arguments. 3 -6 -- In particular, E9i= 1 111101 = [(1=1=1=1=0=1)=0] = [(2lo 1) = 0], and -6 -analogously for E9i= 1 100100 = [(1=0=0=1=0=0)=1] = [(2 lo 4) = 1]. Hence the binary equivalence sum determines whether x and y are each of even parity, or not. 3 for the binary scalar integral, the XOR sum, and its dual, the binary equivalence sum. 3 above. It is called unequal-scan in APL, prefix-scan in computer science, and parity integral in parity logic ([LAN92a], [ZA95b]). Chapter 2.

1 with respect to binary differentials. 20 Chapter 2. 3 x=yffiz. 1 If x, z E Bn, then there exists exactly one y E Bn such that x ffi y = z . The theorem and its corollary show that Bn has three distinguished entities: (a) vertices x E Bn, (b) directions dx E Bn, and (c) edges (x, dx) E Bn. 2b below. 2b That both tables show the truth-table of XOR is not the point. 3 for components Xi, Yi, Zi E x, y, z E Bn such that Xi and Yi are considered as independent binary variables. The proof of Yi = Xi ffi Zi is based on the implication ((xi ffi Yi = Zi) and (xi ffi Yi = zi)) ~ ((xi 1\ Yi) =(xi 1\ Zi) and (xi 1\ Yi) =(xi 1\ zi)).

This holds for any Gaussian, except that a broadly peaked Gaussian has a narrowly peaked Fourier transform, and the other way round, because the standard deviation of the Fourier transform is 1/(21ru). 6) enk -- (n) k - n(n-l)u·~n-k+l) k(k-1 ... 8) The latter is a triangle in which odd numbers are replaced by ones, and even numbers are replaced by zeroes. This is nice and it's the way it should be, but Pascal's triangle mod 2 can be completed to Pascal's square, a fairly rare construct in modulo 2 algebra, but a trade secret in parity logic.

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