66,061 research outputs found

    Physical Logic

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    In R.D. Sorkin's framework for logic in physics a clear separation is made between the collection of unasserted propositions about the physical world and the affirmation or denial of these propositions by the physical world. The unasserted propositions form a Boolean algebra because they correspond to subsets of an underlying set of spacetime histories. Physical rules of inference, apply not to the propositions in themselves but to the affirmation and denial of these propositions by the actual world. This physical logic may or may not respect the propositions' underlying Boolean structure. We prove that this logic is Boolean if and only if the following three axioms hold: (i) The world is affirmed, (ii) Modus Ponens and (iii) If a proposition is denied then its negation, or complement, is affirmed. When a physical system is governed by a dynamical law in the form of a quantum measure with the rule that events of zero measure are denied, the axioms (i) - (iii) prove to be too rigid and need to be modified. One promising scheme for quantum mechanics as quantum measure theory corresponds to replacing axiom (iii) with axiom (iv) Nature is as fine grained as the dynamics allows.Comment: 14 pages, v2 published version with a change in the title and other minor change

    Sequential Monte Carlo Methods for Option Pricing

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    In the following paper we provide a review and development of sequential Monte Carlo (SMC) methods for option pricing. SMC are a class of Monte Carlo-based algorithms, that are designed to approximate expectations w.r.t a sequence of related probability measures. These approaches have been used, successfully, for a wide class of applications in engineering, statistics, physics and operations research. SMC methods are highly suited to many option pricing problems and sensitivity/Greek calculations due to the nature of the sequential simulation. However, it is seldom the case that such ideas are explicitly used in the option pricing literature. This article provides an up-to date review of SMC methods, which are appropriate for option pricing. In addition, it is illustrated how a number of existing approaches for option pricing can be enhanced via SMC. Specifically, when pricing the arithmetic Asian option w.r.t a complex stochastic volatility model, it is shown that SMC methods provide additional strategies to improve estimation.Comment: 37 Pages, 2 Figure

    The kindergarten-path effect revisited: children’s use of context in processing structural ambiguities

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    Research with adults has shown that ambiguous spoken sentences are resolved efficiently, exploiting multiple cues—including referential context—to select the intended meaning. Paradoxically, children appear to be insensitive to referential cues when resolving ambiguous sentences, relying instead on statistical properties intrinsic to the language such as verb biases. The possibility that children’s insensitivity to referential context may be an artifact of the experimental design used in previous work was explored with 60 4- to 11-year-olds. An act-out task was designed to discourage children from making incorrect pragmatic inferences and to prevent premature and ballistic responses by enforcing delayed actions. Performance on this task was compared directly with the standard act-out task used in previous studies. The results suggest that young children (5 years) do not use contextual information, even under conditions designed to maximize their use of such cues, but that adult-like processing is evident by approximately 8 years of age. These results support and extend previous findings by Trueswell and colleagues (Cognition (1999), Vol. 73, pp. 89–134) and are consistent with a constraint-based learning account of children’s linguistic development.</p

    Faithfulness and learning hypergraphs from discrete distributions

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    The concepts of faithfulness and strong-faithfulness are important for statistical learning of graphical models. Graphs are not sufficient for describing the association structure of a discrete distribution. Hypergraphs representing hierarchical log-linear models are considered instead, and the concept of parametric (strong-) faithfulness with respect to a hypergraph is introduced. Strong-faithfulness ensures the existence of uniformly consistent parameter estimators and enables building uniformly consistent procedures for a hypergraph search. The strength of association in a discrete distribution can be quantified with various measures, leading to different concepts of strong-faithfulness. Lower and upper bounds for the proportions of distributions that do not satisfy strong-faithfulness are computed for different parameterizations and measures of association.Comment: 23 pages, 6 figure
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