Results 11 to 20 of about 46,892 (166)
Integral geometry and holography [PDF]
Journal of High Energy Physics, 2015 We present a mathematical framework which underlies the connection between information theory and the bulk spacetime in the AdS$_3$/CFT$_2$ correspondence. A key concept is kinematic space: an auxiliary Lorentzian geometry whose metric is defined in terms of conditional mutual informations and which organizes the entanglement pattern of a CFT state ...
Czech, Bartłomiej +3 more
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INTEGRABLE SYSTEMS IN SYMPLECTIC GEOMETRY [PDF]
Glasgow Mathematical Journal, 2007 AbstractQuaternionic vector mKDV equations are derived from the Cartan structure equation in the symmetric space=Sp(n+1)/Sp(1) ×Sp(n). The derivation of the soliton hierarchy utilizes a moving parallel frame and a Cartan connection 1-form ω related to the Cartan geometry onmodelled on$(\mk{sp}_{n+1}, \mk{sp}_{1}\,{\times}\, \mk{sp}_{n})$.
Asadi, E., Sanders, J.A.
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Geometry of Information Integration [PDF]
, 2018 Information geometry is used to quantify the amount of information integration within multiple terminals of a causal dynamical system. Integrated information quantifies how much information is lost when a system is split into parts and information transmission between the parts is removed. Multiple measures have been proposed as a measure of integrated
Shun-ichi Amari +2 more
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The task of integral geometry with measure induction [PDF]
Компьютерные исследования и моделирование, 2011 A new statement of Integral Geometry problem where the image of function in each point is taken as an integral with respect to measure which depends on the point is suggested. Such Measure System is named Measure Induction.
A. V. Koganov
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Integrable Background Geometries [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2014 for Progress in Twistor Theory ...
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An Integral-Equation-Based Variance Reduction Method for Accelerated Monte Carlo Simulations
Photonics, 2023 In this work, we introduce a novel variance reduction approach utilising the integral formulation of the radiative transfer equation to calculate the radiance in a planar symmetric slab geometry.
David Hevisov +3 more
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Holographic integral geometry with time dependence
Journal of High Energy Physics, 2020 We write down Crofton formulas — expressions that compute lengths of space- like curves in asymptotically AdS3 geometries as integrals over kinematic space — which apply when the curve and/or the background spacetime is time-dependent.
Bartłomiej Czech +2 more
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Influence of Construction Joint and Bridge Geometry on Integral Abutment Bridges
Applied Sciences, 2021 Although integral abutment bridges (IABs) have become a preferred construction choice for short- to medium-length bridges, they still have unclear bridge design guidelines.
Wooseok Kim +4 more
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Qualia: The Geometry of Integrated Information
PLoS Computational Biology, 2009 According to the integrated information theory, the quantity of consciousness is the amount of integrated information generated by a complex of elements, and the quality of experience is specified by the informational relationships it generates. This paper outlines a framework for characterizing the informational relationships generated by such systems.
David Balduzzi, Giulio Tononi
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Algebraic Integral Geometry [PDF]
, 2011 A survey on recent developments in (algebraic) integral geometry is given. The main focus lies on algebraic structures on the space of translation invariant valuations and applications in integral geometry.
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