572 research outputs found
Practical Model-Based Diagnosis with Qualitative Possibilistic Uncertainty
An approach to fault isolation that exploits vastly incomplete models is
presented. It relies on separate descriptions of each component behavior,
together with the links between them, which enables focusing of the reasoning
to the relevant part of the system. As normal observations do not need
explanation, the behavior of the components is limited to anomaly propagation.
Diagnostic solutions are disorders (fault modes or abnormal signatures) that
are consistent with the observations, as well as abductive explanations. An
ordinal representation of uncertainty based on possibility theory provides a
simple exception-tolerant description of the component behaviors. We can for
instance distinguish between effects that are more or less certainly present
(or absent) and effects that are more or less certainly present (or absent)
when a given anomaly is present. A realistic example illustrates the benefits
of this approach.Comment: Appears in Proceedings of the Eleventh Conference on Uncertainty in
Artificial Intelligence (UAI1995
Categorical Quantum Dynamics
We use strong complementarity to introduce dynamics and symmetries within the
framework of CQM, which we also extend to infinite-dimensional separable
Hilbert spaces: these were long-missing features, which open the way to a
wealth of new applications. The coherent treatment presented in this work also
provides a variety of novel insights into the dynamics and symmetries of
quantum systems: examples include the extremely simple characterisation of
symmetry-observable duality, the connection of strong complementarity with the
Weyl Canonical Commutation Relations, the generalisations of Feynman's clock
construction, the existence of time observables and the emergence of quantum
clocks.
Furthermore, we show that strong complementarity is a key resource for
quantum algorithms and protocols. We provide the first fully diagrammatic,
theory-independent proof of correctness for the quantum algorithm solving the
Hidden Subgroup Problem, and show that strong complementarity is the feature
providing the quantum advantage. In quantum foundations, we use strong
complementarity to derive the exact conditions relating non-locality to the
structure of phase groups, within the context of Mermin-type non-locality
arguments. Our non-locality results find further application to quantum
cryptography, where we use them to define a quantum-classical secret sharing
scheme with provable device-independent security guarantees.
All in all, we argue that strong complementarity is a truly powerful and
versatile building block for quantum theory and its applications, and one that
should draw a lot more attention in the future.Comment: Thesis submitted for the degree of Doctor of Philosophy, Oxford
University, Michaelmas Term 2016 (273 pages
Coherent Price Systems and Uncertainty-Neutral Valuation
We consider fundamental questions of arbitrage pricing arising when the
uncertainty model is given by a set of possible mutually singular probability
measures. With a single probability model, essential equivalence between the
absence of arbitrage and the existence of an equivalent martingale measure is a
folk theorem, see Harrison and Kreps (1979). We establish a microeconomic
foundation of sublinear price systems and present an extension result. In this
context we introduce a prior dependent notion of marketed spaces and viable
price systems. We associate this extension with a canonically altered concept
of equivalent symmetric martingale measure sets, in a dynamic trading framework
under absence of prior depending arbitrage. We prove the existence of such sets
when volatility uncertainty is modeled by a stochastic differential equation,
driven by Peng's G-Brownian motions
The legacy of 50 years of fuzzy sets: A discussion
International audienceThis note provides a brief overview of the main ideas and notions underlying fifty years of research in fuzzy set and possibility theory, two important settings introduced by L.A. Zadeh for representing sets with unsharp boundaries and uncertainty induced by granules of information expressed with words. The discussion is organized on the basis of three potential understanding of the grades of membership to a fuzzy set, depending on what the fuzzy set intends to represent: a group of elements with borderline members, a plausibility distribution, or a preference profile. It also questions the motivations for some existing generalized fuzzy sets. This note clearly reflects the shared personal views of its authors
A framework of distributionally robust possibilistic optimization
In this paper, an optimization problem with uncertain constraint coefficients
is considered. Possibility theory is used to model the uncertainty. Namely, a
joint possibility distribution in constraint coefficient realizations, called
scenarios, is specified. This possibility distribution induces a necessity
measure in scenario set, which in turn describes an ambiguity set of
probability distributions in scenario set. The distributionally robust approach
is then used to convert the imprecise constraints into deterministic
equivalents. Namely, the left-hand side of an imprecise constraint is evaluated
by using a risk measure with respect to the worst probability distribution that
can occur. In this paper, the Conditional Value at Risk is used as the risk
measure, which generalizes the strict robust and expected value approaches,
commonly used in literature. A general framework for solving such a class of
problems is described. Some cases which can be solved in polynomial time are
identified
Two Forms of Inconsistency in Quantum Foundations
Recently, there has been some discussion of how Dutch Book arguments might be
used to demonstrate the rational incoherence of certain hidden variable models
of quantum theory (Feintzeig and Fletcher 2017). In this paper, we argue that
the 'form of inconsistency' underlying this alleged irrationality is deeply and
comprehensively related to the more familiar 'inconsistency' phenomenon of
contextuality. Our main result is that the hierarchy of contextuality due to
Abramsky and Brandenburger (2011) corresponds to a hierarchy of
additivity/convexity-violations which yields formal Dutch Books of different
strengths. We then use this result to provide a partial assessment of whether
these formal Dutch Books can be interpreted normatively.Comment: 26 pages, 5 figure
Possibilistic uncertainty analysis of a conceptual model of snowmelt runoff
This study presents the analysis of predictive uncertainty of a conceptual type snowmelt runoff model. The method applied uses possibilistic rather than probabilistic calculus for the evaluation of predictive uncertainty. Possibility theory is an information theory meant to model uncertainties caused by imprecise or incomplete knowledge about a real system rather than by randomness. A snow dominated catchment in the Chilean Andes is used as case study. Predictive uncertainty arising from parameter uncertainties of the watershed model is assessed. Model performance is evaluated according to several criteria, in order to define the possibility distribution of the parameter vector. The plausibility of the simulated glacier mass balance and snow cover are used for further constraining the model representations. Possibility distributions of the discharge estimates and prediction uncertainty bounds are subsequently derived. The results of the study indicate that the use of additional information allows a reduction of predictive uncertainty. In particular, the assessment of the simulated glacier mass balance and snow cover helps to reduce the width of the uncertainty bounds without a significant increment in the number of unbounded observations
Empirical White Noise Processes and the Subjective Probabilistic Approaches
The paper discusses the identification of the empirical white noise processes generated by deterministic numerical algorithms.The introduced fuzzy-random complementary approach can identify the inner hidden correlational patterns of the empirical white noise process if the process has a real hidden structure of this kind. We have shown how the characteristics of auto-correlated white noise processes change as the order of autocorrelation increases. Although in this paper we rely on random number generators to get approximate white noise processes, in our upcoming research we are planning to turn the focus on physical white noise processes in order to validate our hypothesis
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