Theory of Cybernetic and Intelligent Machine Based on Lie Commutators

Fatmi, H.A.; Marcer, Peter J.; Jessel, Maurice; Resconi, Germano

doi:10.1080/03081079008935070

Cited by 12 publications

(2 citation statements)

References 20 publications

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“…In this work, we delineated a parallel development of such ideas we called "Compensative Geometry" which has old systemic roots. It is within such a context-at the crossroad of Theoretical Physics, Cybernetics, Category and Group Theory and Logical System Theory-that the constructive approach here introduced has been developed [3,7,11] (for some fundamental steps, see [15][16][17]; for the consequences on the computation concept, see [18,19]). Such class of theories is based on few principles related to different orders of commutators between covariant derivatives.…”

Section: Discussionmentioning

confidence: 99%

Beyond an Input/Output Paradigm for Systems: Design Systems by Intrinsic Geometry

Resconi¹,

Licata²

2014

Systems

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Given a stress-free system as a perfect crystal with points or atoms ordered in a three dimensional lattice in the Euclidean reference space, any defect, external force or heterogeneous temperature change in the material connection that induces stress on a previously stress-free configuration changes the equilibrium configuration. A material has stress in a reference which does not agree with the intrinsic geometry of the material in the stress-free state. By stress we mean forces between parts when we separate one part from another (tailing the system), the stress collapses to zero for any part which assumes new configurations. Now the problem is that all the new configurations of the parts are incompatible with each other. This means that close loop in the earlier configuration now is not closed and that the two paths previously joining the same two points now join different points from the same initial point so the final point is path dependent. This phenomenon is formally described by the commutators of derivatives in the new connection of the stress-free parts of the system under the control of external currents. This means that we lose the integrability property of the system and the possibility to generate global coordinates. The incompatible system can be represented by many different local references or Cartan moving Euclidean reference, one for any part of the system that is stress-free. The material under stress when is free assumes an equilibrium configuration or manifold that describes the intrinsic "shape" or geometry of the natural stress-the free state of the OPEN ACCESS Systems 2014, 2 662 material. Therefore, we outline a design system by geometric compensation as a prototypical constructive operation.

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Section: Discussionmentioning

confidence: 99%

Beyond an Input/Output Paradigm for Systems: Design Systems by Intrinsic Geometry

Resconi¹,

Licata²

2014

Systems

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“…In [12], the author attempted the introduction of a method for embedding certain automata and computational structures in a system of continuous signals. Additionally, one can notice the existence of some dispersed evidence in the literature for the existence of certain analog models of computation that appear to be of similar power with models of quantum computation (indicative references in [13] - [18]).…”

Section: Introductionmentioning

confidence: 99%

Encoding discrete quantum algebras in a hierarchy of binary words

Raptis

2019

J. Phys.: Conf. Ser.

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It is shown how to endow a hierarchy of sets of binary patterns with the structure of an abstract, normed C*-algebra. In the course we also recover an intermediate connection with the words of a Dyck language and Tempereley-Lieb algebras for which we also find that an effective arithmetic code is possible albeit of greater complexity. We also discuss possible applications associated with signal theory and waveform engineering on possible ways to embed discrete computational structures in an analog continuum substrate.

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Can Quantum Computation Provide a Physically Realistic Model of the Self and Its Brain?

Marcer

1992

Nature, Cognition and System II

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Theory of Cybernetic and Intelligent Machine Based on Lie Commutators

Cited by 12 publications

References 20 publications

Beyond an Input/Output Paradigm for Systems: Design Systems by Intrinsic Geometry

Beyond an Input/Output Paradigm for Systems: Design Systems by Intrinsic Geometry

Encoding discrete quantum algebras in a hierarchy of binary words

Can Quantum Computation Provide a Physically Realistic Model of the Self and Its Brain?

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