For a two-dimensional complex vector space, the spin matrices can be
calculated directly from the angular momentum commutator definition. The 3
Pauli matrices are retrieved and 23 other triplet solutions are found. In the
three-dimensional space, we show that no matrix fulfills the spin equations and
preserves the norm of the vectors. By using a Clifford geometric algebra it is
possible in the four-dimensional spacetime (STA) to retrieve the 24 different
spins 1/2. In this framework, spins 1/2 are rotations characterized by multivectors
composed of 3 vectors and 3 bivectors. Spins 1 can be defined as rotations
characterized by 4 vectors, 6 bivectors and 4 trivectors which result in unit
multivectors which preserve the norm. Let us note that this simple derivation
retrieves the main spin properties of particle physics.
In this paper, we continue
the efforts of the Computational Theory of Intelligence (CTI) by extending concepts
to include computational processes in terms of Genetic Algorithms (GA’s) and
Turing Machines (TM’s). Active, Passive, and Hybrid Computational Intelligence processes
are also introduced and discussed. We consider the ramifications of the assumptions
of CTI with regard to the qualities of reproduction and virility. Applications
to Biology, Computer Science and Cyber Security are also discussed.
We present a numerical study of the resolution power of Padé
Approximations to the Z-transform,
compared to the Fourier transform. As signals are represented as isolated poles
of the Padé Approximant to the Z-transform,
resolution depends on the relative position of signal poles in the complex plane i.e.
not only the difference in frequency (separation in angular position) but also
the difference in the decay constant (separation in radial position) contributes
to the resolution. The frequency resolution increase reported by other authors
is therefore an upper limit: in the case of signals with different decay rates
frequency resolution can be further increased.