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Reconstructing functions from random samples
1. | Department of Mathematics, Rutgers University, Piscataway, NJ 08854, United States |
2. | Rutgers University, 110 Frelinghusen Road, Piscataway, NJ 08854, United States |
3. | Department of Mathematics, University of Pennsylvania, Philadelphia, PA 19104, United States |
References:
[1] |
A. Bjorner, Nerves, fibers and homotopy groups,, Journal of Combinatorial Theory, 102 (2003), 88.
doi: 10.1016/S0097-3165(03)00015-3. |
[2] |
K. Borsuk, On the imbedding of systems of compacta in simplicial complexes,, Fundamenta Mathematicae, 35 (1948), 217.
|
[3] |
G. Carlsson, Topology and data,, Bulletin of the American Mathematical Society, 46 (2009), 255.
doi: 10.1090/S0273-0979-09-01249-X. |
[4] |
J.-G. Dumas, F. Heckenbach, B. D. Saunders and V. Welker, Computing simplicial homology based on efficient Smith normal form algorithms,, Proceedings of Algebra, (2003), 177.
|
[5] |
H. Edelsbrunner and J. L. Harer, Computational Topology - an Introduction,, American Mathematical Society, (2010).
|
[6] |
K. Fischer, B. Gaertner and M. Kutz, Fast-smallest-enclosing-ball computation in high dimensions,, Proceedings of the $11^{th}$ Annual European Symposium on Algorithms (ESA), 2832 (2003), 630.
doi: 10.1007/978-3-540-39658-1_57. |
[7] |
R. Ghrist, Three examples of applied and computational homology,, Nieuw Archief voor Wiskunde, 9 (2008), 122.
|
[8] |
A. Granas and J. Dugundji, Fixed Point Theory,, Springer-Verlag, (2003).
doi: 10.1007/978-0-387-21593-8. |
[9] |
S. Harker, K. Mischaikow, M. Mrozek and V. Nanda, Discrete Morse theoretic algorithms for computing homology of complexes and maps,, Foundations of Computational Mathematics, 14 (2014), 151.
doi: 10.1007/s10208-013-9145-0. |
[10] |
T. Kaczynski, K. Mischaikow and M. Mrozek, Computational Homology,, Springer-Verlag, (2004).
doi: 10.1007/b97315. |
[11] |
D. Kozlov, Combinatorial Algebraic Topology,, Springer, (2008).
doi: 10.1007/978-3-540-71962-5. |
[12] |
J. R. Munkres, Elements of Algebraic Topology,, Addison-Wesley, (1984).
|
[13] |
P. Niyogi, S. Smale and S. Weinberger, Finding the homology of submanifolds with high confidence from random samples,, Discrete and Computational Geometry, 39 (2008), 419.
doi: 10.1007/s00454-008-9053-2. |
[14] |
S. Smale, A Vietoris mapping theorem for homotopy,, Proceedings of the American mathematical society, 8 (1957), 604.
doi: 10.1090/S0002-9939-1957-0087106-9. |
[15] |
E. H. Spanier, Algebraic Topology,, Springer-Verlag, (1981).
|
show all references
References:
[1] |
A. Bjorner, Nerves, fibers and homotopy groups,, Journal of Combinatorial Theory, 102 (2003), 88.
doi: 10.1016/S0097-3165(03)00015-3. |
[2] |
K. Borsuk, On the imbedding of systems of compacta in simplicial complexes,, Fundamenta Mathematicae, 35 (1948), 217.
|
[3] |
G. Carlsson, Topology and data,, Bulletin of the American Mathematical Society, 46 (2009), 255.
doi: 10.1090/S0273-0979-09-01249-X. |
[4] |
J.-G. Dumas, F. Heckenbach, B. D. Saunders and V. Welker, Computing simplicial homology based on efficient Smith normal form algorithms,, Proceedings of Algebra, (2003), 177.
|
[5] |
H. Edelsbrunner and J. L. Harer, Computational Topology - an Introduction,, American Mathematical Society, (2010).
|
[6] |
K. Fischer, B. Gaertner and M. Kutz, Fast-smallest-enclosing-ball computation in high dimensions,, Proceedings of the $11^{th}$ Annual European Symposium on Algorithms (ESA), 2832 (2003), 630.
doi: 10.1007/978-3-540-39658-1_57. |
[7] |
R. Ghrist, Three examples of applied and computational homology,, Nieuw Archief voor Wiskunde, 9 (2008), 122.
|
[8] |
A. Granas and J. Dugundji, Fixed Point Theory,, Springer-Verlag, (2003).
doi: 10.1007/978-0-387-21593-8. |
[9] |
S. Harker, K. Mischaikow, M. Mrozek and V. Nanda, Discrete Morse theoretic algorithms for computing homology of complexes and maps,, Foundations of Computational Mathematics, 14 (2014), 151.
doi: 10.1007/s10208-013-9145-0. |
[10] |
T. Kaczynski, K. Mischaikow and M. Mrozek, Computational Homology,, Springer-Verlag, (2004).
doi: 10.1007/b97315. |
[11] |
D. Kozlov, Combinatorial Algebraic Topology,, Springer, (2008).
doi: 10.1007/978-3-540-71962-5. |
[12] |
J. R. Munkres, Elements of Algebraic Topology,, Addison-Wesley, (1984).
|
[13] |
P. Niyogi, S. Smale and S. Weinberger, Finding the homology of submanifolds with high confidence from random samples,, Discrete and Computational Geometry, 39 (2008), 419.
doi: 10.1007/s00454-008-9053-2. |
[14] |
S. Smale, A Vietoris mapping theorem for homotopy,, Proceedings of the American mathematical society, 8 (1957), 604.
doi: 10.1090/S0002-9939-1957-0087106-9. |
[15] |
E. H. Spanier, Algebraic Topology,, Springer-Verlag, (1981).
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