12,499 research outputs found
Unsharp Quantum Reality
The positive operator (valued) measures (POMs) allow one to generalize the notion of observable beyond the traditional one based on projection valued measures (PVMs). Here, we argue that this generalized conception of observable enables a consistent notion of unsharp reality and with it an adequate concept of joint properties. A sharp or unsharp property manifests itself as an element of sharp or unsharp reality by its tendency to become actual or to actualize a specific measurement outcome. This actualization tendency-or potentiality-of a property is quantified by the associated quantum probability. The resulting single-case interpretation of probability as a degree of reality will be explained in detail and its role in addressing the tensions between quantum and classical accounts of the physical world will be elucidated. It will be shown that potentiality can be viewed as a causal agency that evolves in a well-defined way
Design and Analysis of an Estimation of Distribution Approximation Algorithm for Single Machine Scheduling in Uncertain Environments
In the current work we introduce a novel estimation of distribution algorithm
to tackle a hard combinatorial optimization problem, namely the single-machine
scheduling problem, with uncertain delivery times. The majority of the existing
research coping with optimization problems in uncertain environment aims at
finding a single sufficiently robust solution so that random noise and
unpredictable circumstances would have the least possible detrimental effect on
the quality of the solution. The measures of robustness are usually based on
various kinds of empirically designed averaging techniques. In contrast to the
previous work, our algorithm aims at finding a collection of robust schedules
that allow for a more informative decision making. The notion of robustness is
measured quantitatively in terms of the classical mathematical notion of a norm
on a vector space. We provide a theoretical insight into the relationship
between the properties of the probability distribution over the uncertain
delivery times and the robustness quality of the schedules produced by the
algorithm after a polynomial runtime in terms of approximation ratios
"The connection between distortion risk measures and ordered weighted averaging operators"
Distortion risk measures summarize the risk of a loss distribution by means of a single value. In fuzzy systems, the Ordered Weighted Averaging (OWA) and Weighted Ordered Weighted Averaging (WOWA) operators are used to aggregate a large number of fuzzy rules into a single value. We show that these concepts can be derived from the Choquet integral, and then the mathematical relationship between distortion risk measures and the OWA and WOWA operators for discrete and nite random variables is presented. This connection oers a new interpretation of distortion risk measures and, in particular, Value-at-Risk and Tail Value-at-Risk can be understood from an aggregation operator perspective. The theoretical results are illustrated in an example and the degree of orness concept is discussed.Fuzzy systems; Degree of orness; Risk quantification; Discrete random variable JEL classification:C02,C60
The structure of classical extensions of quantum probability theory
On the basis of a suggestive definition of a classical extension of quantum mechanics in terms of statistical models, we prove that every such classical extension is essentially given by the so-called Misra–Bugajski reduction map. We consider how this map enables one to understand quantum mechanics as a reduced classical statistical theory on the projective Hilbert space as phase space and discuss features of the induced hidden-variable model. Moreover, some relevant technical results on the topology and Borel structure of the projective Hilbert space are reviewed
Improving proton-induced one-nucleon removal in intranuclear cascade
It is a well-established fact that intranuclear-cascade models generally fail
to consistently reproduce the cross sections for one-proton and one-neutron
removal from stable nuclei by a high-energy proton beam. We use simple
shell-model calculations to investigate the reasons of this deficiency. We find
that a refined description of the neutron skin and of the energy density in the
nuclear surface is crucial for the aforementioned observables, and that neither
ingredient is sufficient if taken separately. As a by-product, the predictions
for removal of several nucleons are also improved by the refined treatment.Comment: 15 pages, 11 figures. Submitted to Phys. Rev.
Stochastic domination for the Ising and fuzzy Potts models
We discuss various aspects concerning stochastic domination for the Ising
model and the fuzzy Potts model. We begin by considering the Ising model on the
homogeneous tree of degree , \Td. For given interaction parameters ,
and external field h_1\in\RR, we compute the smallest external field
such that the plus measure with parameters and dominates
the plus measure with parameters and for all .
Moreover, we discuss continuity of with respect to the three
parameters , , and also how the plus measures are stochastically
ordered in the interaction parameter for a fixed external field. Next, we
consider the fuzzy Potts model and prove that on \Zd the fuzzy Potts measures
dominate the same set of product measures while on \Td, for certain parameter
values, the free and minus fuzzy Potts measures dominate different product
measures. For the Ising model, Liggett and Steif proved that on \Zd the plus
measures dominate the same set of product measures while on \T^2 that
statement fails completely except when there is a unique phase.Comment: 22 pages, 5 figure
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