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Mirror Descent and Exponentiated Gradient Algorithms Using Trace-Form Entropies [PDF]
EntropyThis paper introduces a broad class of Mirror Descent (MD) and Generalized Exponentiated Gradient (GEG) algorithms derived from trace-form entropies defined via deformed logarithms. Leveraging these generalized entropies yields MD and GEG algorithms with
Andrzej Cichocki +3 more
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NeutroGeometry & AntiGeometry are alternatives and generalizations of the Non-Euclidean Geometries [PDF]
Neutrosophic Sets and Systems, 2021 In this paper we extend the NeutroAlgebra & AntiAlgebra to the geometric spaces, by founding the NeutroGeometry & AntiGeometry.
Florentin Smarandache
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Real Examples of NeutroGeometry & AntiGeometry [PDF]
Neutrosophic Sets and Systems, 2023 For the classical Geometry, in a geometrical space, all items (concepts, axioms, theorems, etc.) are totally (100%) true. But, in the real world, many items are not totally true. The NeutroGeometry is a geometrical space that has some items that are only
Florentin Smarandache
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THE COMMON EVOLUTION OF GEOMETRY AND ARCHITECTURE FROM A GEODETIC POINT OF VIEW [PDF]
The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, 2017 Throughout history the link between geometry and architecture has been strong and while architects have used mathematics to construct their buildings, geometry has always been the essential tool allowing them to choose spatial shapes which are ...
T. Bellone, F. Fiermonte, L. Mussio
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The Digital Paradigm in Contemporary Architecture
img journal, 2023 The architecture of the 20th century has been largely affected by changes in the field of technology. In particular, the evolution of digital representation has led to new visions of contemporary architectural space. Expressive freedoms, which in the pre-
Domenico Mediati
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HERBRAND’S THEOREM AND NON-EUCLIDEAN GEOMETRY [PDF]
The Bulletin of Symbolic Logic, 2015 AbstractWe use Herbrand’s theorem to give a new proof that Euclid’s parallel axiom is not derivable from the other axioms of first-order Euclidean geometry. Previous proofs involve constructing models of non-Euclidean geometry. This proof uses a very old and basic theorem of logic together with some simple properties of ruler-and-compass constructions ...
Beeson, Michael +2 more
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Liquid crystal director fields in three-dimensional non-Euclidean geometries
New Journal of Physics, 2020 This paper investigates nematic liquid crystals in three-dimensional curved space, and determines which director deformation modes are compatible with each possible type of non-Euclidean geometry. Previous work by Sethna et al showed that double twist is
Jean-François Sadoc +2 more
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On the Euclidean action of de Sitter black holes and constrained instantons
SciPost Physics, 2023 We compute the on-shell Euclidean action of Schwarzschild-de Sitter black holes, and take their contributions in the gravitational path integral into account using the formalism of constrained instantons.
Edward K. Morvan, Jan Pieter van der Schaar, Manus R. Visser
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Journal of High Energy Physics, 2020 We construct black hole geometries in AdS3 with non-trivial values of KdV charges. The black holes are holographically dual to quantum KdV Generalized Gibbs Ensemble in 2d CFT.
Anatoly Dymarsky, Sotaro Sugishita
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