Relevant bibliographies by topics / Simplicial sets and complexes

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Simplicial sets and complexes'

Author: Grafiati
Published: 4 June 2021
Last updated: 8 February 2022

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Journal articles on the topic "Simplicial sets and complexes"

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ELTER, HERVE, and PASCAL LIENHARDT. "CELLULAR COMPLEXES AS STRUCTURED SEMI-SIMPLICIAL SETS." International Journal of Shape Modeling 01, no. 02 (1994): 191–217. http://dx.doi.org/10.1142/s021865439400013x.

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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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ARAMAYONA, JAVIER, and CHRISTOPHER J. LEININGER. "FINITE RIGID SETS IN CURVE COMPLEXES." Journal of Topology and Analysis 05, no. 02 (2013): 183–203. http://dx.doi.org/10.1142/s1793525313500076.

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We prove that curve complexes of surfaces are finitely rigid: for every orientable surface S of finite topological type, we identify a finite subcomplex 𝔛 of the curve complex [Formula: see text] such that every locally injective simplicial map [Formula: see text] is the restriction of an element of [Formula: see text], unique up to the (finite) pointwise stabilizer of 𝔛 in [Formula: see text]. Furthermore, if S is not a twice-punctured torus, then we can replace [Formula: see text] in this statement with the extended mapping class group Mod ±(S).
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Robbin, Joel W., and Dietmar A. Salamon. "Lyapunov maps, simplicial complexes and the Stone functor." Ergodic Theory and Dynamical Systems 12, no. 1 (1992): 153–83. http://dx.doi.org/10.1017/s0143385700006647.

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AbstractLet be an attractor network for a dynamical system ft: M → M, indexed by the lower sets of a partially ordered set P. Our main theorem asserts the existence of a Lyapunov map ψ:M → K(P) which defines the attractor network. This result is used to prove the existence of connection matrices for discrete-time dynamical systems.
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Buijs, Urtzi, Yves Félix, Aniceto Murillo, and Daniel Tanré. "Maurer–Cartan Elements in the Lie Models of Finite Simplicial Complexes." Canadian Mathematical Bulletin 60, no. 3 (2017): 470–77. http://dx.doi.org/10.4153/cmb-2017-003-7.

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AbstractIn a previous work, we associated a complete diòerential graded Lie algebra to any finite simplicial complex in a functorial way. Similarly, we also have a realization functor fromthe category of complete diòerential graded Lie algebras to the category of simplicial sets. We have already interpreted the homology of a Lie algebra in terms of homotopy groups of its realization. In this paper, we begin a dictionary between models and simplicial complexes by establishing a correspondence between the Deligne groupoid of the model and the connected components of the finite simplicial complex
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Fieldsteel, Nathan, and Hal Schenck. "Polynomial Interpolation in Higher Dimension: From Simplicial Complexes to GC Sets." SIAM Journal on Numerical Analysis 55, no. 1 (2017): 131–43. http://dx.doi.org/10.1137/16m1057322.

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Jardine, J. F. "Model structures for pro-simplicial presheaves." Journal of K-theory 7, no. 3 (2011): 499–525. http://dx.doi.org/10.1017/is011003012jkt149.

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AbstractThis paper displays model structures for the category of pro-objects in simplicial presheaves on an arbitrary small Grothendieck site. The first of these is an analogue of the Edwards-Hastings model structure for pro-simplicial sets, in which the cofibrations are monomorphisms and the weak equivalences are specified by comparisons of function complexes. Other model structures are built from the Edwards-Hastings structure by using Bousfield-Friedlander localization techniques. There is, in particular, an n-type structure for pro-simplicial presheaves, and also a model structure in which
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BROWN, KENNETH A., and KEVIN P. KNUDSON. "NONLINEAR STATISTICS OF HUMAN SPEECH DATA." International Journal of Bifurcation and Chaos 19, no. 07 (2009): 2307–19. http://dx.doi.org/10.1142/s0218127409024086.

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We study the structure of point clouds obtained as time delay embeddings of human speech signals by approximating the data sets with certain simplicial complexes and analyzing their persistent homology. Results for several different sounds are presented in embedding dimensions 3 and 4. The first Betti number allows a coarse classification of sounds into three groups: vowels, nasals and noise.
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Bullejos, M., and A. M. Cegarra. "Classifying Spaces for Monoidal Categories Through Geometric Nerves." Canadian Mathematical Bulletin 47, no. 3 (2004): 321–31. http://dx.doi.org/10.4153/cmb-2004-031-8.

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AbstractThe usual constructions of classifying spaces for monoidal categories produce CW-complexes withmany cells that,moreover, do not have any proper geometricmeaning. However, geometric nerves ofmonoidal categories are very handy simplicial sets whose simplices have a pleasing geometric description: they are diagrams with the shape of the 2-skeleton of oriented standard simplices. The purpose of this paper is to prove that geometric realizations of geometric nerves are classifying spaces for monoidal categories.
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Richter, Birgit, and Steffen Sagave. "A strictly commutative model for the cochain algebra of a space." Compositio Mathematica 156, no. 8 (2020): 1718–43. http://dx.doi.org/10.1112/s0010437x20007319.

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AbstractThe commutative differential graded algebra $A_{\mathrm {PL}}(X)$ of polynomial forms on a simplicial set $X$ is a crucial tool in rational homotopy theory. In this note, we construct an integral version $A^{\mathcal {I}}(X)$ of $A_{\mathrm {PL}}(X)$. Our approach uses diagrams of chain complexes indexed by the category of finite sets and injections $\mathcal {I}$ to model $E_{\infty }$ differential graded algebras (dga) by strictly commutative objects, called commutative $\mathcal {I}$-dgas. We define a functor $A^{\mathcal {I}}$ from simplicial sets to commutative $\mathcal {I}$-dgas
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Dissertations / Theses on the topic "Simplicial sets and complexes"

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Caroli, Manuel. "Triangulating Point Sets in Orbit Spaces." Phd thesis, Université de Nice Sophia-Antipolis, 2010. http://tel.archives-ouvertes.fr/tel-00552215.

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Dans cette thèse, nous étudions les triangulations définies par un ensemble de points dans des espaces de topologies différentes. Nous proposons une définition générale de la triangulation de Delaunay, valide pour plusieurs classes d'espaces, ainsi qu'un algorithme de construction. Nous fournissons une implantation pour le cas particulier du tore plat tridimensionnel. Ce travail est motivé à l'origine par le besoin de logiciels calculant des triangulations de Delaunay périodiques, dans de nombreux domaines dont l'astronomie, l'ingénierie des matériaux, le calcul biomédical, la dynamique des fl
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Jonsson, Jakob. "Simplicial Complexes of Graphs." Doctoral thesis, Stockholm, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-202.

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Jonsson, Jakob. "Simplicial complexes of graphs /." Berlin [u.a.] : Springer, 2008. http://dx.doi.org/10.1007/978-3-540-75858-7.

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Mirmohades, Djalal. "Simplicial Structure on Complexes." Licentiate thesis, Uppsala universitet, Algebra och geometri, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-221410.

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Nilsson, Viktor, and Jakob Huber. "Cyclic and Simplicial Sets in Algebraic Topology." Thesis, KTH, Skolan för teknikvetenskap (SCI), 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-231553.

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Basic properties of simplicial and cyclic sets and the geometric realization of the respective are studied. This is conducted using a category theoretical approach when reasonable and a more direct algebraic topological such when simpler. As the topics are uncommon on an undergraduate level an introduction of topological, category theoretic and simplicial notions and concepts will be included. The purpose is the understanding of the aforementioned and further exploration into the supposedly less traversed of cyclic sets.<br>Grundläggande egenskaper hos simpliciala och cykliska mängder och den
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Zhang, Zhihan. "Random walk on simplicial complexes." Electronic Thesis or Diss., université Paris-Saclay, 2020. http://www.theses.fr/2020UPASM010.

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La notion de laplacien d’un graphe peut être généralisée aux complexes simpliciaux et aux hypergraphes. Cette notion contient des informations sur la topologie de ces structures. Dans la première partie de cette thèse,nous définissons une nouvelle chaîne de Markov sur les complexes simpliciaux. Pour un degré donné k de simplexes, l’espace d’états n’est pas les k-simplexes comme dans les articles précédents sur ce sujet mais plutôt l’ensemble des k-chaines ou k-co-chaines. Ce nouveau cadre est la généralisation naturelle sur les chaînes de Markov canoniques sur des graphes. Nous montrons que le
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Petersson, Anna. "Enumeration of spanning trees in simplicial complexes." Licentiate thesis, Uppsala universitet, Matematiska institutionen, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-138976.

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Zuffi, Lorenzo. "Simplicial Complexes From Graphs Toward Graph Persistence." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/13519/.

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Persistent homology is a branch of computational topology which uses geometry and topology for shape description and analysis. This dissertation is an introductory study to link persistent homology and graph theory, the connection being represented by various methods to build simplicial complexes from a graph. The methods we consider are the complex of cliques, of independent sets, of neighbours, of enclaveless sets and complexes from acyclic subgraphs, each revealing several properties of the underlying graph. Moreover, we apply the core ideas of persistence theory in the new context of graph
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Egan, Sarah. "Nash equilibria in games and simplicial complexes." Thesis, University of Bath, 2008. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.500758.

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Nash's Theorem is a famous and widely used result in non-cooperative game theory which can be applied to games where each player's mixed strategy payoff function is defined as an expectation. Current proofs of this Theorem neither justify why this constraint is necessary or satisfactorily identifies its origins. In this Thesis we change this and prove Nash's Theorem for abstract games where, in particular, the payoff functions can be replaced by total orders. The result of this is a combinatoric proof of Nash's Theorem. We also construct a generalised simplicial complex model and demonstrate a
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Hetyei, Gábor. "Simplicial and cubical complexes : anologies and differences." Thesis, Massachusetts Institute of Technology, 1994. http://hdl.handle.net/1721.1/32610.

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Books on the topic "Simplicial sets and complexes"

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Simplicial complexes of graphs. Springer, 2008.

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Jonsson, Jakob. Simplicial Complexes of Graphs. Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-75859-4.

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Rhodes, John, and Pedro V. Silva. Boolean Representations of Simplicial Complexes and Matroids. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-15114-4.

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Mudamburi, Nolan Jatiel Zifambi. Simplicial complexes based on automorphisms of free products. University of Birmingham, 1996.

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Ghani, Razia Parvin. Presentation of the automorphism group of free groups using simplicial complexes. University of Birmingham, 1992.

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Ashley, N. Simplicial T-complexes and crossed complexes: A non-abelian version of a theorem of Dold and Kan. Państwowe Wydawn. Nauk., 1988.

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Persistence theory: From quiver representations to data analysis. American Mathematical Society, 2015.

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W, Jones David. A general theory of polyhedral sets and the corresponding T-complexes. Państwowe Wydawn. Nauk., 1988.

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Sargent, Andrew L. Basis sets for geometry optimizations of second-row transition metal inorganic and organometallic complexes. Cornell Theory Center, Cornell University, 1991.

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Pantev, Tony. Stacks and catetories in geometry, topology, and algebra: CATS4 Conference Higher Categorical Structures and Their Interactions with Algebraic Geometry, Algebraic Topology and Algebra, July 2-7, 2012, CIRM, Luminy, France. American Mathematical Society, 2015.

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Book chapters on the topic "Simplicial sets and complexes"

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Moerdijk, Ieke, and Bertrand Toën. "Inner Kan complexes and normal dendroidal sets." In Simplicial Methods for Operads and Algebraic Geometry. Springer Basel, 2010. http://dx.doi.org/10.1007/978-3-0348-0052-5_7.

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Tancer, Martin. "Intersection Patterns of Convex Sets via Simplicial Complexes: A Survey." In Thirty Essays on Geometric Graph Theory. Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-0110-0_28.

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Goerss, Paul G., and John F. Jardine. "Simplicial sets." In Simplicial Homotopy Theory. Birkhäuser Basel, 1999. http://dx.doi.org/10.1007/978-3-0348-8707-6_1.

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Gelfand, Sergei I., and Yuri I. Manin. "Simplicial Sets." In Springer Monographs in Mathematics. Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-662-12492-5_1.

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Gelfand, Sergei I., and Yuri I. Manin. "Simplicial Sets." In Methods of Homological Algebra. Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-662-03220-6_1.

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Hovey, Mark. "Simplicial sets." In Model Categories. American Mathematical Society, 2007. http://dx.doi.org/10.1090/surv/063/03.

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Goerss, Paul G., and John F. Jardine. "Simplicial sets." In Simplicial Homotopy Theory. Birkhäuser Basel, 2009. http://dx.doi.org/10.1007/978-3-0346-0189-4_1.

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Deo, Satya. "Simplicial Complexes." In Texts and Readings in Mathematics. Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-10-8734-9_3.

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McCleary, John. "Simplicial complexes." In The Student Mathematical Library. American Mathematical Society, 2006. http://dx.doi.org/10.1090/stml/031/10.

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Petersen, T. Kyle. "Simplicial complexes." In Eulerian Numbers. Springer New York, 2015. http://dx.doi.org/10.1007/978-1-4939-3091-3_8.

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Conference papers on the topic "Simplicial sets and complexes"

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Bertolotto, Michela, Leila De Floriani, and Paola Marzano. "Pyramidal simplicial complexes." In the third ACM symposium. ACM Press, 1995. http://dx.doi.org/10.1145/218013.218054.

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Popović, Jovan, and Hugues Hoppe. "Progressive simplicial complexes." In the 24th annual conference. ACM Press, 1997. http://dx.doi.org/10.1145/258734.258852.

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Vergne, A., L. Decreusefond, and P. Martins. "Reduction algorithm for simplicial complexes." In IEEE INFOCOM 2013 - IEEE Conference on Computer Communications. IEEE, 2013. http://dx.doi.org/10.1109/infcom.2013.6566818.

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Lickorish, W. B. R. "Simplicial moves on complexes and manifolds." In Low Dimensional Topology -- The Kirbyfest. Mathematical Sciences Publishers, 1999. http://dx.doi.org/10.2140/gtm.1999.2.299.

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Preti, Giulia, Gianmarco De Francisci Morales, and Francesco Bonchi. "STruD: Truss Decomposition of Simplicial Complexes." In WWW '21: The Web Conference 2021. ACM, 2021. http://dx.doi.org/10.1145/3442381.3450073.

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Costa, A., and M. Farber. "Homological Domination in Large Random Simplicial Complexes." In IMA Conference on Mathematics of Robotics. Institute of Mathematics and its Applications, 2015. http://dx.doi.org/10.19124/ima.2015.001.01.

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Misztal, Marek Krzysztof, Jakob Andreas Bærentzen, Francois Anton, and Steen Markvorsen. "Cut Locus Construction Using Deformable Simplicial Complexes." In 2011 Eighth International Symposium on Voronoi Diagrams in Science and Engineering (ISVD). IEEE, 2011. http://dx.doi.org/10.1109/isvd.2011.26.

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Gandoin, Pierre-Marie, and Olivier Devillers. "Progressive lossless compression of arbitrary simplicial complexes." In the 29th annual conference. ACM Press, 2002. http://dx.doi.org/10.1145/566570.566591.

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Barbarossa, Sergio, Stefania Sardellitti, and Elena Ceci. "LEARNING FROM SIGNALS DEFINED OVER SIMPLICIAL COMPLEXES." In 2018 IEEE Data Science Workshop (DSW). IEEE, 2018. http://dx.doi.org/10.1109/dsw.2018.8439885.

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Matoušek, Jiří, Martin Tancer та Uli Wagner. "Hardness of embedding simplicial complexes in ℝd". У Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms. Society for Industrial and Applied Mathematics, 2009. http://dx.doi.org/10.1137/1.9781611973068.93.

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Reports on the topic "Simplicial sets and complexes"

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Shkodin, Andrey. Sets of exercises for education workers in the Far North. Science and Innovation Center Publishing House, 2021. http://dx.doi.org/10.12731/shkodin.0418.15042021.

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Complexes of exercises for educational workers of the Far North is an electronic resource developed specifically for pedagogical workers living in the Far North. The selection and description of exercise complexes was developed on the basis of a study of the peculiarities of living in the Far North, common diseases characteristic of the inhabitants of the Far North and the peculiarities of the profession of a teacher. Access to the electronic resource is free, hosted on the google cloud service and youtube video hosting, contains video resources and comments on use. Available through a browser
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