The Experts below are selected from a list of 318 Experts worldwide ranked by ideXlab platform
Anthony S. Maida - One of the best experts on this subject based on the ideXlab platform.
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Reliability Measure Theory
1993Co-Authors: Anthony S. MaidaAbstract:Abstmct- This paper develops a new semantic framework for nonmonotonic reasoning. Specifically this paper proposes a reliability Measure Theory based on multivalued logics that view a knowledge base as a set of contexts, and compares the contexts according to some reliability Measure. The proposed Theory shows higher precision of nonmonotonic reasoning than other approaches. In particular, the qualification problem does not occur and many unwanted conflicts are eliminated.
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Reliability Measure Theory: a nonmonotonic semantics
IEEE Transactions on Knowledge and Data Engineering, 1993Co-Authors: Anthony S. MaidaAbstract:A semantic framework for nonmonotonic reasoning is developed. Specifically, a reliability Measure Theory based on multivalued logics that view a knowledge base as a set of contexts is proposed, and the contexts are compared according to some reliability Measure. The proposed Theory shows higher precision of nonmonotonic reasoning than other approaches. In particular, the qualification problem does not occur and many unwanted conflicts are eliminated.
Maya R Gupta - One of the best experts on this subject based on the ideXlab platform.
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A Measure Theory Tutorial (Measure Theory for Dummies)
2020Co-Authors: Maya R GuptaAbstract:This tutorial is an informal introduction to Measure Theory for people who are interested in reading papers that use Measure Theory. The tutorial assumes one has had at least a year of college-level calculus, some graduate level exposure to random processes, and familiarity with terms like “closed” and “open.” The focus is on the terms and ideas relevant to applied probability and information Theory. There are no proofs and no exercises. Measure Theory is a bit like grammar, many people communicate clearly without worrying about all the details, but the details do exist and for good reasons. There are a number of great texts that do Measure Theory justice. This is not one of them. Rather this is a hack way to get the basic ideas down so you can read through research papers and follow what’s going on. Hopefully, you’ll get curious and excited enough about the details to check out some of the references for a deeper understanding.
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A Measure Theory Tutorial (Measure Theory for Dummies)
Tutorial, 2006Co-Authors: Maya R GuptaAbstract:This tutorial is an informal introduction to Measure Theory for people who are interested in reading papers that use Measure Theory. The tutorial assumes one has had at least a year of college-level calculus, some graduate level exposure to random processes, and familiarity with terms like “closed” and “open.” The focus is on the terms and ideas relevant to applied probability and information Theory. There are no proofs and no exercises.
Petros Wallden - One of the best experts on this subject based on the ideXlab platform.
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Quantum Covers in Quantum Measure Theory
Foundations of Physics, 2010Co-Authors: Sumati Surya, Petros WalldenAbstract:Sorkin’s recent proposal for a realist interpretation of quantum Theory, the anhomomorphic logic or coevent approach, is based on the idea of a “quantum Measure” on the space of histories. This is a generalisation of the classical Measure to one which admits pair-wise interference and satisfies a modified version of the Kolmogorov probability sum rule. In standard Measure Theory the Measure on the base set Ω is normalised to one, which encodes the statement that “Ω happens”. Moreover, the Kolmogorov sum rule implies that the Measure of any subset A is strictly positive if and only if A cannot be covered by a countable collection of subsets of zero Measure. In quantum Measure Theory on the other hand, simple examples suffice to demonstrate that this is no longer true. We propose an appropriate generalisation, the quantum cover, which in addition to being a cover of A, satisfies the property that if the quantum Measure of A is non-zero then this is also the case for at least one of the elements in the cover. Our work implies a non-triviality result for the coevent interpretation for Ω of finite cardinality, and allows us to cast the Peres-Kochen-Specker theorem in terms of quantum covers.
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Quantum Covers in Quantum Measure Theory
arXiv: Quantum Physics, 2008Co-Authors: Sumati Surya, Petros WalldenAbstract:In standard Measure Theory the Measure on the base set Omega is normalised to one, which encodes the statement that "Omega happens". Moreover, the rules imply that the Measure of any subset A of Omega is strictly positive if and only if A cannot be covered by a collection of subsets of zero Measure. In quantum Measure Theory on the other hand, simple examples suffice to demonstrate that this is no longer true. We propose an appropriate generalisation of a cover to quantum Measure Theory, the {\sl quantum cover}, which in addition to being a cover of A, satisfies the property that if every one of its elements has zero quantum Measure, then so does A. We show that a large class of inextendible antichains in the associated powerset lattice provide quantum covers for Omega, for a quantum Measure that derives from a strongly positive decoherence functional. Quantum covers, moreover, give us a new perspective on the Peres-Kochen-Specker theorem and its role in the anhomomorphic logic approach to quantum interpretation.
D. Sivakumar - One of the best experts on this subject based on the ideXlab platform.
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FOCS - Pseudorandom generators, Measure Theory, and natural proofs
Proceedings of IEEE 36th Annual Foundations of Computer Science, 1995Co-Authors: K.w. Regan, D. SivakumarAbstract:We prove that if strong pseudorandom number generators exist, then the class of languages that have polynomial-sized circuits (P/poly) is not measurable within exponential time, in terms of the resource-bounded Measure Theory of Lutz. We prove our result by showing that if P/poly has Measure zero in exponential time, then there is a natural proof against P/poly, in the terminology of Razborov and Rudich (1994). We also provide a partial converse of this result.
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Pseudorandom generators, Measure Theory, and natural proofs
Proceedings of IEEE 36th Annual Foundations of Computer Science, 1995Co-Authors: K.w. Regan, D. SivakumarAbstract:We prove that if strong pseudorandom number generators exist, then the class of languages that have polynomial-sized circuits (P/poly) is not measurable within exponential time, in terms of the resource-bounded Measure Theory of Lutz. We prove our result by showing that if P/poly has Measure zero in exponential time, then there is a natural proof against P/poly, in the terminology of Razborov and Rudich (1994). We also provide a partial converse of this result.
Eduardo Guendelman - One of the best experts on this subject based on the ideXlab platform.
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String model with mesons and baryons in modified Measure Theory
International Journal of Modern Physics A, 2019Co-Authors: T. O. Vulfs, Eduardo GuendelmanAbstract:We consider string meson and string baryon models in the framework of the modified Measure Theory, the Theory that does not use the determinant of the metric to construct the invariant volume eleme...
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String Model with Baryons in Modified Measure Theory
arXiv: High Energy Physics - Theory, 2018Co-Authors: T. O. Vulfs, Eduardo GuendelmanAbstract:We consider string baryon model in the framework of modified Measure Theory, a Theory that does not use the determinant of the metric to construct the invariant volume element. A baryon is modeled by two strings with a charge at each endpoint that represent a quark. It is shown that the discontinuity of the tension leads to the termination of a string, and Neumann boundary conditions naturally arise at these endpoints. We connect the endpoint of one string with the internal part of the other one. That way a system of three effective strings is constructed. Dirichlet and Neumann boundary conditions are obtained dynamically in the point of intersection. When tensions are chosen in such way that two of them are much greater than the third one then a diquark is obtained. In that case two quarks are tightly bound while the third quark is bound by a tension which is smaller to the vertex of the interaction.
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Lorentz-covariant four-vector formalism for two-Measure Theory
Physical Review D, 2013Co-Authors: Eduardo Guendelman, Hitoshi Nishino, Subhash RajpootAbstract:In the conventional two-Measure Theory, the scalar density function $\ensuremath{\Phi}$ is taken to be $\ensuremath{\Phi}\ensuremath{\equiv}{ϵ}^{\ensuremath{\mu}\ensuremath{\nu}\ensuremath{\rho}\ensuremath{\sigma}}{ϵ}_{abcd}({\ensuremath{\partial}}_{\ensuremath{\mu}}{\ensuremath{\varphi}}^{a})({\ensuremath{\partial}}_{\ensuremath{\nu}}{\ensuremath{\varphi}}^{b})({\ensuremath{\partial}}_{\ensuremath{\rho}}{\ensuremath{\varphi}}^{c})({\ensuremath{\partial}}_{\ensuremath{\sigma}}{\ensuremath{\varphi}}^{d})$, where the indices $a,b,c,d=1$, 2, 3, 4 are internal-space indices. It is more natural to replace the four scalars ${\ensuremath{\varphi}}^{a}$ by a Lorentz-covariant four-vector ${\ensuremath{\varphi}}^{m}$ with a local Lorentz index $m=(0)$, (1), (2), (3). We entertain this possibility, and show that the newly proposed Lagrangian respects not only Lorentz covariance, but also global-scale invariance. The crucial equation ${\ensuremath{\partial}}_{\ensuremath{\mu}}L=0$ in the conventional two-Measure Theory also arises in our new formulation, as the ${\ensuremath{\varphi}}^{m}$-field equation.