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Fast Quantum Algorithms for Handling Probabilistic and Interval Uncertainty
, 2003
"... this paper, we show how the use of quantum computing can speed up some computations related to interval and probabilistic uncertainty. We end the paper with speculations on whether (and how) "hypothetic" physical devices can compute NPhard problems faster than in exponential time ..."
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this paper, we show how the use of quantum computing can speed up some computations related to interval and probabilistic uncertainty. We end the paper with speculations on whether (and how) "hypothetic" physical devices can compute NPhard problems faster than in exponential time
Multilevel Synergetic Computation in Brain
 NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
, 2001
"... Patterns of activities of neurons serve as attractors, since they are those neuronal configurations which correspond to minimal ’free energy’ of the whole system. Namely, they realize maximal possible agreement among constitutive neurons and are moststrongly correlated with some environmental patte ..."
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Patterns of activities of neurons serve as attractors, since they are those neuronal configurations which correspond to minimal ’free energy’ of the whole system. Namely, they realize maximal possible agreement among constitutive neurons and are moststrongly correlated with some environmental pattern. Neuronal patternsquaattractors have both a material and a virtual aspect. As neuronal patterns, on the one hand, patternsquaattractors are explicit carriers of informational contents. As attractors, on the other hand, patternsquaattractors are implicit mental representations which acquire a meaning in contextual relations to other possible patterns. Recognition of an external pattern is explained as a (re)construction of the pattern which is the most relevant and similar to a given environmental pattern. The identity of the processes of pattern construction, reconstruction and Hebbian shortterm storage is realized in a net. Perceptual processes are here modeled using Kohonen’s topologypreserving feature mapping onto cortex where further associative processing is continued. To model stratification of associative processing because of influence from higher brain areas, Haken’s multilevel synergetic network is found to be appropriate. The hierarchy of brain processes is of ”software”type, i.e. virtual, as well as it is of ”hardware”type, i.e. physiological. It is shown that synergetic and attractor dynamics can characterize not only neural networks,
Proof Nets as Formal Feynman Diagrams
"... Summary. The introduction of linear logic and its associated proof theory has revolutionized many semantical investigations, for example, the search for fullyabstract models of PCF and the analysis of optimal reduction strategies for lambda calculi. In the present paper we show how proof nets, a gra ..."
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Summary. The introduction of linear logic and its associated proof theory has revolutionized many semantical investigations, for example, the search for fullyabstract models of PCF and the analysis of optimal reduction strategies for lambda calculi. In the present paper we show how proof nets, a graphtheoretic syntax for linear logic proofs, can be interpreted as operators in a simple calculus. This calculus was inspired by Feynman diagrams in quantum field theory and is accordingly called the φcalculus. The ingredients are formal integrals, formal power series, a derivativelike construct and analogues of the Dirac delta function. Many of the manipulations of proof nets can be understood as manipulations of formulas reminiscent of a beginning calculus course. In particular, the “box ” construct behaves like an exponential and the nesting of boxes phenomenon is the analogue of an exponentiated derivative formula. We show that the equations for the multiplicativeexponential fragment of linear logic hold. 1
ON THE CANONICAL FORMULATION OF ELECTRODYNAMICS AND WAVE MECHANICS By
, 2004
"... Since August of 1999, I have had the privilege of conducting my Ph.D. research in the group of Prof. Yngve Öhrn and Dr. Erik Deumens at the University of Florida’s Quantum Theory Project. During my time in their group I learned a great deal on the theory of dynamics, in particular, the Hamiltonian a ..."
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Since August of 1999, I have had the privilege of conducting my Ph.D. research in the group of Prof. Yngve Öhrn and Dr. Erik Deumens at the University of Florida’s Quantum Theory Project. During my time in their group I learned a great deal on the theory of dynamics, in particular, the Hamiltonian approach to dynamics and its applications in electrodynamics and atomic and molecular collisions. I also learned a new appreciation for scientific computing, of which I was previously ignorant. Most importantly, Prof. Öhrn and Dr. Deumens taught me how to think through a physical problem, sort out its underlying dynamical equations, and solve them in a mathematically welldefined manner. I especially want to thank Dr. Erik Deumens, with whom I worked most closely during my Ph.D. research. Erik had a vision when I began my graduate studies and has promoted my work since then to successfully realize it. Along the way, he challenged my creative, mathematical, and physical intuitions and imparted on me a love for theoretical physics. Erik has always taken time to listen to and carefully answer my questions and has always respected my ideas. I thank him for being such an excellent mentor to me. My understanding of physics has also been broadened by many others. Firstly, I would like to thank Dr. Remigio CabreraTrujillo, who was a post doctoral associate in the ÖhrnDeumens group, for his guidance especially during my first few years. He has been a great source for advice on many topics from the details of quantum scattering theory to simple computer problems like clearing printer jams. I have joked on many occasions that he was my personal postdoc because he was always so willing to help when I had questions. I would also like to thank the past and
The Search for Structure in Quantum Computation
"... Abstract. I give a noncomprehensive survey of the categorical quantum mechanics program and how it guides the search for structure in quantumcomputation. Idiscuss theexampleofmeasurementbased computing which is one of the successes of such an enterprise and briefly mention topological quantum comp ..."
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Abstract. I give a noncomprehensive survey of the categorical quantum mechanics program and how it guides the search for structure in quantumcomputation. Idiscuss theexampleofmeasurementbased computing which is one of the successes of such an enterprise and briefly mention topological quantum computing which is an inviting target for future research in this area. 1
1 A FunctionAnalytic Development of Field Theory
"... I confirm that the work presented in this thesis is my own. Where information has been derived from other sources, I confirm that this has been indicated in the thesis. ..."
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I confirm that the work presented in this thesis is my own. Where information has been derived from other sources, I confirm that this has been indicated in the thesis.