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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,
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.
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
version history HOW TO CITE THIS ENTRY
"... This document uses XHTML/Unicode to format the display. If you think special symbols are not displaying correctly, see our guide Displaying Special Characters. last substantive content change Open access to the Encyclopedia is being made possible by a worldwide funding initiative. In order to prese ..."
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This document uses XHTML/Unicode to format the display. If you think special symbols are not displaying correctly, see our guide Displaying Special Characters. last substantive content change Open access to the Encyclopedia is being made possible by a worldwide funding initiative. In order to preserve open access to the SEP for the longterm, we need the support of important users like University of Colorado/Boulder. If you would like your institution to join the growing number of contributing institutions, please let your librarians know. Backward Causation Sometimes also called retrocausation. A common feature of our world seems to be that in all cases of causation, the cause and the effect are placed in time so that the cause precedes its effect temporally. Our normal understanding of causation assumes this feature to such a degree that we intuitively have great difficulty imagining things differently. The notion of backward causation, however, stands for the idea that the temporal order of cause and effect is a mere contingent feature and that there may be cases where the cause is causally prior to its effect but where the temporal order of the cause and effect is reversed with respect to normal causation, i.e. there may be cases where the effect temporally, but not causally, precedes its cause.
CWP459 Localizing change with Coda Wave Interferometry: Derivation and validation of the sensitivity kernel
"... Coda waves have been studied extensively over the past few years. The main goal has been to characterize the transport of energy in media with strong fluctuations ..."
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Coda waves have been studied extensively over the past few years. The main goal has been to characterize the transport of energy in media with strong fluctuations
mlq header will be provided by the publisher Fast Quantum Algorithms for Handling Probabilistic and Interval Uncertainty
, 2003
"... In many reallife situations, we are interested in the value of a physical quantity y that is difficult or impossible to measure directly. To estimate y, we find some easiertomeasure quantities x1,..., xn which are related to y by a known relation y = f(x1,..., xn). Measurements are never 100 % ac ..."
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In many reallife situations, we are interested in the value of a physical quantity y that is difficult or impossible to measure directly. To estimate y, we find some easiertomeasure quantities x1,..., xn which are related to y by a known relation y = f(x1,..., xn). Measurements are never 100 % accurate; hence, the measured values ˜xi are different from xi, and the resulting estimate ˜y = f(˜x1,..., ˜xn) is different from the desired value y = f(x1,..., xn). How different can it be? Traditional engineering approach to error estimation in data processing assumes that we know the probabildef ities of different measurement errors ∆xi = ˜xi − xi. In many practical situations, we only know the upper bound ∆i for this error; hence, after the measurement, the only information that we have about xi is that it def belongs to the interval xi = [˜xi − ∆i, ˜xi + ∆i]. In this case, it is important to find the range y of all possible values of y = f(x1,..., xn) when xi ∈ xi. We start the paper with a brief overview of the computational complexity of the corresponding interval computation problems. Most of the related problems turn out to be, in general, at least NPhard. In 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. Most of the paper’s results were first presented at NAFIPS’2003 [30]. Copyright line will be provided by the publisher 1 Introduction: Data Processing