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Set Theory and Physics
 FOUNDATIONS OF PHYSICS, VOL. 25, NO. 11
, 1995
"... Inasmuch as physical theories are formalizable, set theory provides a framework for theoretical physics. Four speculations about the relevance of set theoretical modeling for physics are presented: the role of transcendental set theory (i) hr chaos theory, (ii) for paradoxical decompositions of soli ..."
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Cited by 8 (7 self)
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Inasmuch as physical theories are formalizable, set theory provides a framework for theoretical physics. Four speculations about the relevance of set theoretical modeling for physics are presented: the role of transcendental set theory (i) hr chaos theory, (ii) for paradoxical decompositions of solid threedimensional objects, (iii) in the theory of effective computability (ChurchTurhrg thesis) related to the possible "solution of supertasks," and (iv) for weak solutions. Several approaches to set theory and their advantages and disadvatages for" physical applications are discussed: Cantorian "naive" (i.e., nonaxiomatic) set theory, contructivism, and operationalism, hr the arrthor's ophrion, an attitude of "suspended attention" (a term borrowed from psychoanalysis) seems most promising for progress. Physical and set theoretical entities must be operationalized wherever possible. At the same thne, physicists shouM be open to "bizarre" or "mindboggling" new formalisms, which treed not be operationalizable or testable at the thne of their " creation, but which may successfully lead to novel fields of phenomenology and technology.
Fundamental Physical Limits on Computation
 NEC Research Technical Report
, 1995
"... Current (May 1995) revision of 1992 report. We consider limitations on the performance of computers arising from thermodynamics and the laws of physics. We provide upper bounds on three quantities: sustained information flux, information storage density, and sustained computational speed. All of the ..."
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Cited by 2 (0 self)
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Current (May 1995) revision of 1992 report. We consider limitations on the performance of computers arising from thermodynamics and the laws of physics. We provide upper bounds on three quantities: sustained information flux, information storage density, and sustained computational speed. All of these upper bounds are "tight" in the sense that they could be approached by plausiblesounding physical systems, and they all arise from a single unified point of view. We also make a conjecture about the rate of inevitable decay of stored information. This conjecture may be thought of as a quantitative extension of the second law of thermodynamics. It leads to a bound on the density of stable information. We carefully elucidate the assumptions behind these bounds. We give a list of 4 open problems at the end. KEYWORDS: thermodynamics, computation, reversible Turing machines, blackbody radiation, decay of information, physics, entropy, information transmission and storage, cooling requirement...
Recurrent Supervised Neural Computation and LMI Model Transformation for Order ReductionBased Control of Linear TimeIndependent Closed Quantum Computing Systems
"... Abstract This paper introduces a new method of intelligent control for closed quantum computation timeindependent systems. The new method uses recurrent supervised neural network to identify certain parameters of the transformed system matrix [ A ~]. Linear matrix inequality is then used to determ ..."
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Abstract This paper introduces a new method of intelligent control for closed quantum computation timeindependent systems. The new method uses recurrent supervised neural network to identify certain parameters of the transformed system matrix [ A ~]. Linear matrix inequality is then used to determine the permutation matrix [P] so that a complete system transformation { [ B ~], [ C ~], [ D ~]} is achieved. The transformed model is then reduced using the method of singular perturbation and state feedback control is applied to enhance system performance. In quantum computing and mechanics, a closed system is an isolated system that can’t exchange energy or matter with its surroundings and doesn’t interact with other quantum systems. In contrast to open quantum systems, closed quantum systems obey the unitary evolution and thus are information lossless (i.e., reversible). The experimental simulation results show that the new hierarchical control methodology simplifies the model of the quantum computing system and thus uses a simpler controller that produces the desired system response for performance enhancement.