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1 files changed, 33 insertions, 8 deletions
diff --git a/biblio/bibliography.bib b/biblio/bibliography.bib index 9fc01a5d..29fc5650 100644 --- a/biblio/bibliography.bib +++ b/biblio/bibliography.bib @@ -25,7 +25,8 @@ year={2014}, issn={0178-4617}, journal={Algorithmica}, doi={10.1007/s00453-014-9887-3}, -title={\href{http://dx.doi.org/10.1007/s00453-014-9887-3}{The Simplex Tree: An Efficient Data Structure for General Simplicial Complexes}}, +title={The Simplex Tree: An Efficient Data Structure for General Simplicial Complexes}, +url={http://dx.doi.org/10.1007/s00453-014-9887-3}, publisher={Springer US}, keywords={Simplicial complexes; Data structure; Computational topology; Flag complexes; Witness complexes}, author={Boissonnat, Jean-Daniel and Maria, Cl\'ement}, @@ -74,8 +75,9 @@ language={English}, author = {Jean-Daniel Boissonnat and Tamal K. Dey and Cl{\'e}ment Maria}, - title = {\href{http://dx.doi.org/10.1007/978-3-642-40450-4_59}{The Compressed Annotation Matrix: An Efficient Data Structure - for Computing Persistent Cohomology}}, + title = {The Compressed Annotation Matrix: An Efficient Data Structure for Computing Persistent Cohomology}, + url = {http://dx.doi.org/10.1007/978-3-642-40450-4_59}, + doi = {10.1007/978-3-642-40450-4_59}, booktitle = {ESA}, year = {2013}, pages = {695-706}, @@ -93,8 +95,9 @@ language={English}, @inproceedings{DBLP:conf/esa/BoissonnatM12, author = {Jean-Daniel Boissonnat and Cl{\'e}ment Maria}, - title = {\href{http://dx.doi.org/10.1007/978-3-642-33090-2_63}{The Simplex Tree: An Efficient Data Structure for General - Simplicial Complexes}}, + title = {The Simplex Tree: An Efficient Data Structure for General Simplicial Complexes}, + url = {http://dx.doi.org/10.1007/978-3-642-33090-2_63}, + doi = {10.1007/978-3-642-33090-2_63}, booktitle = {ESA}, year = {2012}, pages = {731-742}, @@ -108,7 +111,7 @@ language={English}, @techreport{boissonnat:hal-00922572, hal_id = {hal-00922572}, url = {http://hal.inria.fr/hal-00922572}, - title = {\href{http://hal.inria.fr/hal-00922572}{Computing Persistent Homology with Various Coefficient Fields in a Single Pass}}, + title = {Computing Persistent Homology with Various Coefficient Fields in a Single Pass}, author = {Boissonnat, Jean-Daniel and Maria, Cl{\'e}ment}, abstract = {{In this article, we introduce the multi-field persistence diagram for the persistence homology of a filtered complex. It encodes compactly the superimposition of the persistence diagrams of the complex with several field coefficients, and provides a substantially more precise description of the topology of the filtered complex. Specifically, the multi-field persistence diagram encodes the Betti numbers of integral homology and the prime divisors of the torsion coefficients of the underlying shape. Moreover, it enjoys similar stability properties as the ones of standard persistence diagrams, with the appropriate notion of distance. These properties make the multi-field persistence diagram a useful tool in computational topology.}}, keywords = {Computational Topology, Persistent homology, Modular reconstruction}, @@ -176,7 +179,7 @@ language={English}, @article{RS62, author={J. B. Rosser and L. Schoenfeld}, title={Approximate Formulas for some Functions of Prime Numbers}, - journal= ijm, + journal= {ijm}, volume= 6, year= 1962, pages={64-94}, @@ -306,6 +309,21 @@ language={English}, bibsource = {DBLP, http://dblp.uni-trier.de} } +%------------------------------------------------------------------ +@article{tangentialcomplex2014, +author="Boissonnat, Jean-Daniel and Ghosh, Arijit", +title="Manifold Reconstruction Using Tangential Delaunay Complexes", +journal="Discrete {\&} Computational Geometry", +year="2014", +volume="51", +number="1", +pages="221--267", +abstract="We give a provably correct algorithm to reconstruct a k-dimensional smooth manifold embedded in d-dimensional Euclidean space. The input to our algorithm is a point sample coming from an unknown manifold. Our approach is based on two main ideas: the notion of tangential Delaunay complex defined in Boissonnat and Fl{\"o}totto (Comput. Aided Des. 36:161--174, 2004), Fl{\"o}totto (A coordinate system associated to a point cloud issued from a manifold: definition, properties and applications. Ph.D. thesis, 2003), Freedman (IEEE Trans. Pattern Anal. Mach. Intell. 24(10), 2002), and the technique of sliver removal by weighting the sample points (Cheng et al. in J. ACM 47:883--904, 2000). Differently from previous methods, we do not construct any subdivision of the d-dimensional ambient space. As a result, the running time of our algorithm depends only linearly on the extrinsic dimension d while it depends quadratically on the size of the input sample, and exponentially on the intrinsic dimension k. To the best of our knowledge, this is the first certified algorithm for manifold reconstruction whose complexity depends linearly on the ambient dimension. We also prove that for a dense enough sample the output of our algorithm is isotopic to the manifold and a close geometric approximation of the manifold.", +issn="1432-0444", +doi="10.1007/s00454-013-9557-2", +url="http://dx.doi.org/10.1007/s00454-013-9557-2" +} + %BOOKS %------------------------------------------------------------------ @book{DBLP:tibkat_237559129, @@ -939,7 +957,7 @@ misc{jplex_cite, publisher={Springer New York} } -@ARTICLE{peikert2012topological, +@inbook{peikert2012topological, year={2012}, isbn={978-3-642-23174-2}, booktitle={Topological Methods in Data Analysis and Visualization II}, @@ -954,3 +972,10 @@ pages={91-106}, language={English} } +@article{de2004topological, + title={Topological estimation using witness complexes}, + author={De Silva, Vin and Carlsson, Gunnar}, + journal={Proc. Sympos. Point-Based Graphics}, + pages={157-166}, + year={2004} +} |