Relevant bibliographies by topics / Vietoris construction

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Conference papers

Academic literature on the topic 'Vietoris construction'

Author: Grafiati
Published: 4 June 2021
Last updated: 18 February 2022

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Journal articles on the topic "Vietoris construction"

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Zomorodian, Afra. "Fast construction of the Vietoris-Rips complex." Computers & Graphics 34, no. 3 (2010): 263–71. http://dx.doi.org/10.1016/j.cag.2010.03.007.

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VENEMA, YDE, STEVE VICKERS, and JACOB VOSMAER. "Generalised powerlocales via relation lifting." Mathematical Structures in Computer Science 23, no. 1 (2012): 142–99. http://dx.doi.org/10.1017/s0960129512000229.

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This paper introduces an endofunctor VT on the category of frames that is parametrised by an endofunctor T on the category Set that satisfies certain constraints. This generalises Johnstone's construction of the Vietoris powerlocale in the sense that his construction is obtained by taking for T the finite covariant power set functor. Our construction of the T-powerlocale VT out of a frame is based on ideas from coalgebraic logic and makes explicit the connection between the Vietoris construction and Moss's coalgebraic cover modality.We show how to extend certain natural transformations between
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Gehrke, Mai, Daniela Petrişan, and Luca Reggio. "Quantifiers on languages and codensity monads." Mathematical Structures in Computer Science 30, no. 10 (2020): 1054–88. http://dx.doi.org/10.1017/s0960129521000074.

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AbstractThis paper contributes to the techniques of topo-algebraic recognition for languages beyond the regular setting as they relate to logic on words. In particular, we provide a general construction on recognisers corresponding to adding one layer of various kinds of quantifiers and prove a corresponding Reutenauer-type theorem. Our main tools are codensity monads and duality theory. Our construction hinges on a measure-theoretic characterisation of the profinite monad of the free S-semimodule monad for finite and commutative semirings S, which generalises our earlier insight that the Viet
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Jardine, John F. "Fuzzy sets and presheaves." Compositionality 1 (December 20, 2019): 3. http://dx.doi.org/10.32408/compositionality-1-3.

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This paper presents a presheaf theoretic approach to the construction of fuzzy sets, which builds on Barr's description of fuzzy sets as sheaves of monomorphisms on a locale. Presheaves are used to give explicit descriptions of limit and colimit descriptions in fuzzy sets on an interval. The Boolean localization construction for sheaves on a locale specializes to a theory of stalks for sheaves and presheaves on an interval.The system V∗(X) of Vietoris-Rips complexes for a data set X is both a simplicial fuzzy set and a simplicial sheaf in this general framework. This example is explicitly disc
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Loday, Jean-Louis. "Algebraic K-theory and cyclic homology." Journal of K-theory 11, no. 3 (2013): 553–57. http://dx.doi.org/10.1017/is012011006jkt200.

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The following are personal reminiscences of my research years in algebraic K-theory and cyclic homology during which Dan Quillen was everyday present in my professional life.In the late sixties (of the twentieth century) the groups K0;K1;K2 were known and well-studied. The group K0 had been introduced by Alexander Grothendieck, then came K1 by Hyman Bass [2] (as a variation of the Whitehead group), permitting one to generalize the notion of determinant, and finally K2 by John Milnor [9] and Michel Kervaire. The big problem was: how about Kn? Having in mind topological K-theory and all the othe
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Corob Cook, Ged. "Eilenberg–Mac Lane Spaces for Topological Groups." Axioms 8, no. 3 (2019): 90. http://dx.doi.org/10.3390/axioms8030090.

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In this paper, we establish a topological version of the notion of an Eilenberg–Mac Lane space. If X is a pointed topological space, π 1 ( X ) has a natural topology coming from the compact-open topology on the space of maps S 1 → X . In general, the construction does not produce a topological group because it is possible to create examples where the group multiplication π 1 ( X ) × π 1 ( X ) → π 1 ( X ) is discontinuous. This discontinuity has been noticed by others, for example Fabel. However, if we work in the category of compactly generated, weakly Hausdorff spaces, we may retopologise bot
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VICKERS, STEVEN. "Constructive points of powerlocales." Mathematical Proceedings of the Cambridge Philosophical Society 122, no. 2 (1997): 207–22. http://dx.doi.org/10.1017/s0305004196001636.

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Results of Bunge and Funk and of Johnstone, providing constructively sound descriptions of the global points of the lower and upper powerlocales, are extended here to describe the generalized points and proved in a way that displays in a symmetric fashion two complementary treatments of frames: as suplattices and as preframes. Also described here are the points of the Vietoris powerlocale.In each of two special cases, an exponential $D ($ being the Sierpiński locale) is shown to be homeomorphic to a powerlocale: to the lower powerlocale when D is discrete, and to the upper powerlocale when D i
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Erovenko, Igor V. "On bounded cohomology of amalgamated products of groups." International Journal of Mathematics and Mathematical Sciences 2004, no. 40 (2004): 2103–21. http://dx.doi.org/10.1155/s0161171204311142.

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We investigate the structure of the singular part of the second bounded cohomology group of amalgamated products of groups by constructing an analog of the initial segment of the Mayer-Vietoris exact cohomology sequence for the spaces of pseudocharacters.
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Bunk, Severin, and Richard J. Szabo. "Topological insulators and the Kane–Mele invariant: Obstruction and localization theory." Reviews in Mathematical Physics 32, no. 06 (2019): 2050017. http://dx.doi.org/10.1142/s0129055x20500178.

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We present homotopy theoretic and geometric interpretations of the Kane–Mele invariant for gapped fermionic quantum systems in three dimensions with time-reversal symmetry. We show that the invariant is related to a certain 4-equivalence which lends it an interpretation as an obstruction to a block decomposition of the sewing matrix up to non-equivariant homotopy. We prove a Mayer–Vietoris Theorem for manifolds with [Formula: see text]-actions which intertwines Real and [Formula: see text]-equivariant de Rham cohomology groups, and apply it to derive a new localization formula for the Kane–Mel
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Paliulionis, Viktoras. "Aerodromų kliūtis ribojančių paviršių modeliavimas geoinformacinių technologijų priemonėmis." Informacijos mokslai 56 (January 1, 2011): 119–27. http://dx.doi.org/10.15388/im.2011.0.3145.

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Trijų matavimų (3D) erdvinių duomenų modeliavimas, analizė ir vizualizavimas naudojami daugelyje sričių. Šiame straipsnyje nagrinėjami klausimai, susiję su aerodromų kliūtis ribojančių paviršių (apsaugos zonų) modeliavimu, siekiant nustatyti kliūtis, kurios gali kelti pavojų orlaivių skrydžiams. Pademonstruota, kaip šiuos klausimus galima spręsti naudojantis skaitmeniniu reljefo, vietovės ir kliūtis ribojančių paviršių modeliavimu, 3D vizualizavimu ir analize. Siūlomas skaitmeninių vietovės modeliųsudarymo algoritmas leidžia efektyviai naudoti lazerinio skenavimo (LIDAR) taškų duomenis. Aprašy
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Dissertations / Theses on the topic "Vietoris construction"

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Tête, Claire. "Profondeur, dimension et résolutions en algèbre commutative : quelques aspects effectifs." Thesis, Poitiers, 2014. http://www.theses.fr/2014POIT2288/document.

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Cette thèse d'algèbre commutative porte principalement sur la théorie de la profondeur. Nous nous efforçons d'en fournir une approche épurée d'hypothèse noethérienne dans l'espoir d'échapper aux idéaux premiers et ceci afin de manier des objets élémentaires et explicites. Parmi ces objets, figurent les complexes algébriques de Koszul et de Cech dont nous étudions les propriétés cohomologiques grâce à des résultats simples portant sur la cohomologie du totalisé d'un bicomplexe. Dans le cadre de la cohomologie de Cech, nous avons établi la longue suite exacte de Mayer-Vietoris avec un traitement
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Jakl, Tomáš. "d-Framy jako algebraické duály bitopologických prostorů." Doctoral thesis, 2018. http://www.nusl.cz/ntk/nusl-373804.

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Achim Jung and Drew Moshier developed a Stone-type duality theory for bitopological spaces, amongst others, as a practical tool for solving a particular problem in the theory of stably compact spaces. By doing so they discovered that the duality of bitopological spaces and their algebraic counterparts, called d-frames, covers several of the known dualities. In this thesis we aim to take Jung's and Moshier's work as a starting point and fill in some of the missing aspects of the theory. In particular, we investigate basic categorical properties of d-frames, we give a Vietoris construction for d
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Books on the topic "Vietoris construction"

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Valiulytė, Elena. Dabartinės lietuvių kalbos sintaksiniai sinonimai: Vietos, laiko ir priežasties raiška. Mokslo ir enciklopedijų leidybos institutas, 1998.

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Conference papers on the topic "Vietoris construction"

1

Upadhyay, Aakriti, Weifu Wang, and Chinwe Ekenna. "Approximating Cfree Space Topology by Constructing Vietoris-Rips Complex." In 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE, 2019. http://dx.doi.org/10.1109/iros40897.2019.8968148.

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