Chan, Joseph M., Carlsson, Gunnar and Rabadan, Raul, Topology of viral evolution, Proceedings of the National Academy of Sciences, vol 110, 46, 18566–18571, 2013. link
Amit Singer, Hau-tieng Wu, “Spectral Convergence of the Connection Laplacian from random samples”, arXiv, 1306.1587. Aug 2013 link
Hau-tieng Wu, “Embedding Riemannian Manifolds by the Heat Kernel of the Connection Laplacian”, arXiv, 1305.4232. Aug 2013 link
Daniel Müllner, “fastcluster: Fast Hierarchical, Agglomerative Clustering Routines for R and Python”, Journal of Statistical Software, 53(9). Jun 2013 link
Pawin Vongmasa, Gunnar Carlsson, “Exterior Critical Series of Persistence Modules”, arXiv, 1305.4780. May 2013 link
P. Y. Lum, G. Singh, A. Lehman, T. Ishkanov, M. Vejdemo-Johansson, M. Alagappan, J. Carlsson, G. Carlsson, “Extracting insights from the shape of complex data using topology”, Scientific Reports, 3, Article number: 1236. Apr 2013 link
Reza Bosagh Zadeh, Gunnar Carlsson, “Dimension Independent Matrix Square using MapReduce”, arXiv, 1304.1467. Apr 2013 link
Huang-Wei Chang, Sergio Bacallado, Vijay S. Pande, Gunnar E. Carlsson, “Persistent Topology and Metastable State in Conformational Dynamics”, PLoS ONE, 8(4): e58699. Apr 2013 link
Gunnar Carlsson, Facundo Mémoli, “Classifying Clustering Schemes”, Foundations of Computational Mathematics, Volume 13, Issue 2, pp 221–252. Apr 2013 link
Sara Kalisnik, “Alexander Duality for Parametrized Homology”. Mar 2013 link
Jose A. Perea and Gunnar Carlsson, “A Klein-Bottle-Based Dictionary for Texture Representation”, International Journal of Computer Vision
,2013, 1-23. link
Aaron Adcock, Erik Carlsson and Gunnar Carlsson, “The Ring of Algebraic Functions on Persistence Bar Codes”. Nov 2012 link
Chen Gu, Huang-Wei Chang, Lutz Maibaum, Vijay S. Pande, Gunnar E. Carlsson and Leonidas J. Guibas, “Building Markov State Models with Solvent Dynamics”. Oct 2012 link
Aaron Adcock, Daniel Rubin and Gunnar Carlsson, “Classification of Hepatic Lesions using the Matching Metric”, ArXiv, 1210.0866. Oct 2012 link
Ryan H. Lewis and Afra Zomorodian, “Multicore Homology”. Sep 2012 link
Robert MacPherson and Benjamin Schweinhart, “Measuring Shape with Topology”. Jul 2012 link
Michael Lesnick, “Multidimensional Interleavings and Applications to Topological Inference”. Jun 2012 link
Y. Dabaghian, F. Mémoli, L. Frank, G. Carlsson, “A topological paradigm for hippocampal spatial map formation using persistent homology”, PLoS Computational Biology, 8(8): e1002581. May 2012 link
Daniel Müllner, “Modern hierarchical, agglomerative clustering algorithms”. Sep 2011 link
Gunnar Carlsson, Jackson Gorham, Matthew Kahle, Jeremy Mason, “Computational topology for configuration spaces of hard disks”, Phys. Rev. E, 85, 011303 (2012). Aug 2011 link
Michael Lesnick, “The Optimality of the Interleaving Distance on Multidimensional Persistence Modules”. Aug 2011 link
Andrew Tausz and Gunnar Carlsson, “Homological Coordinatization”. Aug 2011 link
Andrew Tausz and Gunnar Carlsson, “Applications of Zigzag Persistence to Topological Data Analysis”. Aug 2011 link
Mikael Vejdemo-Johansson, “Interleaved computation for persistent homology ”, preprint. May 2011 link
V. de Silva, D. Morozov and M. Vejdemo-Johansson, “Persistent Cohomology and Circular Coordinates”, Discrete and Computational Geometry, Special Issue: 25th Annual Symposium on Computational Geometry. Apr 2011 link
Monica Nicolau, Arnold J. Levine, and Gunnar Carlsson, “Topology based data analysis identifies a subgroup of breast cancers with a unique mutational profile and excellent survival”, Proceedings of the National Academy of Sciences. Feb 2011 link
Henry Adams, Atanas Atanasov, and Gunnar Carlsson, “Morse theory in topological data analysis”. Nov 2010 link
F. Mémoli, “A spectral notion of Gromov-Wasserstein distances and related methods”, Journal of Applied and Computational Harmonic Analysis . Jan 2010 link
M. Kahle, E. Meckes, “Limit theorems for Betti numbers of random simplicial complexes”. Jan 2010 link
J. Kloke, G. Carlsson, “Topological De-Noising: Strengthening the Topological Signal”. Jan 2010 link
G. Carlsson and A. Zomorodian, “Theory of multidimensional persistence”, Discrete and Computational Geometry, Volume 42, Number 1. Jul 2009 link
V. De Silva, M. Vejdemo-Johansson, “Persistent Cohomology and Circular Coordinates”, SOCG. Jun 2009 link
G. Carlsson, V. De Silva, D. Morozov, “Zigzag Persistent Homology and Real-valued Functions”, SOCG. Jun 2009 link
Y. Yao, J. Sun, X. Huang, G. Bowman, G. Singh, M. Lesnick, L. Guibas, V. Pande, G. Carlsson, “Topological methods for exploring low-density states in biomolecular folding pathways”, The Journal of Chemical Physics. Apr 2009 link
G. Carlsson, F. Memoli, “Characterization, stability and convergence of Hierarchical Clustering methods”, Journal of Machine Learning Research, 11(Apr):1425?1470. Apr 2009 link
G. Carlsson, G. Singh and A. Zomorodian, “Computing multidimensional persistence”, ISAAC. Jan 2009 link
G. Carlsson and F. Memoli, “Multiparameter clustering algorithms ”, IFCS. Jan 2009 link
F. Memoli, “Spectral Gromov-Wasserstein distances for shape matching”, NORDIA-ICCV. Jan 2009 link
F. Chazal, D. Cohen-Steiner, L. Guibas, F. Memoli and S. Oudot, “Gromov-Hausdorff stable signatures for shapes using persistence”, SGP. Jan 2009 link
G. Carlsson, V. De Silva, “Zigzag Persistence”, Foundations of Computational Mathematics, to appear. Jan 2009 link
G. Carlsson, “Topology and Data”, Bulletin of the American Mathematical Society, vol 46, Number 2, pp. 255−308. Jan 2009 link
X. Jiang, L.-H. Lim, Y. Yao, Y. Ye, “Learning to rank with combinatorial Hodge Theory”. Nov 2008 link
I. Onur Filiz, X. Guo, J. Morton, and B. Sturmfels, “Graphical models for correlated defaults”. Sep 2008 link
J. Morton, “Relations among conditional probabilities”. Aug 2008 link
G. Bowman, X. Huang, Y. Yao, J. Sun, G. Carlsson, L. Guibas and V. Pande, “Structural insight into RNA Hairpin Folding Intermediates”, Journal of American Chemical Society (Communications). Jul 2008 link
F. Memoli, “Gromov-Hausdorff distances in Euclidean spaces ”, NORDIA-CVPR. Jun 2008 link
G. Singh, F. Memoli, T. Ishkhanov, G. Sapiro, G. Carlsson and D. Ringach, “Topological analysis of population activity in visual cortex”, Journal of Vision. Jun 2008link
G. Carlsson and F. Memoli,, “Persistent Clustering and a Theorem of J. Kleinberg ”. Mar 2008 link
V. de Silva and R. Ghrist, “Coordinate-free coverage in sensor networks with controlled boundaries via homology”, International Journal of Robotics Research, to appear. Jan 2008 link
G. Carlsson, T. Ishkhanov, V. de Silva, and A. Zomorodian, “On the local behavior of spaces of natural images”, local preprint; see other entry for the journal version. Jan 2008 link
G. Carlsson, T. Ishkhanov, V. de Silva, and A. Zomorodian, “On the local behavior of spaces of natural images”, International Journal of Computer Vision, volume 76, number 1, pages 1−12. Jan 2008 link
G. Singh, F. Memoli, T. Ishkhanov, G. Carlsson, G. Sapiro and D. Ringach, “Topological Structure of Population Activity in Primary Visual Cortex,”. Nov 2007 link
T. Ishkhanov, “A Topological Method for Shape Comparison,”. Oct 2007 link
G. Carlsson and T. Ishkhanov, “A Topological Analysis of the Space of Natural Images”. Oct 2007 link
F. Memoli, “On the use of Gromov-Hausdorff Distances for Shape Comparison ”, Point Based Graphics 2007, Prague. Sep 2007 link
G. Singh, F. Memoli and G. Carlsson, “Topological Methods for the Analysis of High Dimensional Data Sets and 3D Object Recognition”, Point Based Graphics 2007, Prague — Paper. Sep 2007 link
G. Singh, F. Memoli and G. Carlsson, “Topological Methods for the Analysis of High Dimensional Data Sets and 3D Object Recognition”, Point Based Graphics 2007, Prague — Slides. Sep 2007 link
G. Singh, F. Memoli and G. Carlsson, “Topological Methods for the Analysis of High Dimensional Data Sets and 3D Object Recognition”, Point Based Graphics 2007, Prague — Movie. Sep 2007 link
G. Carlsson and A. Zomorodian, “The theory of multidimensional persistence”, 23rd ACM Symposium on Computational Geometry, Gyeongju, South Korea. Jun 2007 link
H. Adams and G. Carlsson, “On the non-linear statistics of range image patches,”. Jun 2007 link
A. Zomorodian and G. Carlsson, “Localized homology”, Shape Modeling International, Lyon, France . Jan 2007 link
V. de Silva and R. Ghrist, “Coordinate-free coverage in sensor networks with controlled boundaries via homology”. Jan 2006 link
E. Carlsson, G. Carlsson, and V. de Silva, “An algebraic topological method for feature identification,”, International Journal of Computational Geometry and Applications, 16 (2006), no. 4, pp. 291—314. Jan 2006 link
V. de Silva and R. Ghrist, “Coverage in sensor networks via persistent homology”. Nov 2005 link
V. de Silva, R. Ghrist, and A. Muhammad, “Blind swarms for coverage in 2-D”, Robotics: Science and Systems, I, Cambridge, MA. Jun 2005 link
G. Carlsson, “Persistent homology and the analysis of high dimensional data”, Symposium on the Geometry of Very Large Data Sets, Fields Institute for Research in Mathematical Sciences. Feb 2005 link
A. Zomorodian and G. Carlsson , “Computing persistent homology”, Discrete and Computational Geometry, 33 (2), pp. 247—274. . Jan 2005 link
G. Carlsson, A. Zomorodian, A. Collins, and L. Guibas, “Persistence barcodes for shapes”, International Journal of Shape Modeling, 11 (2005), pp. 149—187.. Jan 2005 link
P. Diaconis, S. Holmes, and R. Montgomery, “Dynamical bias in the coin toss”. Oct 2004 link
A. Collins, A. Zomorodian, G. Carlsson, and L. Guibas, “A barcode shape descriptor for curve point cloud data”, Computers & Graphics, to appear. Sep 2004 link
G. Carlsson, A. Zomorodian, A. Collins, and L. Guibas, “Persistence barcodes for shapes”, Symposium on Geometry Processing, Nice, France. Jul 2004 link
G. Carlsson and V. de Silva, “A geometric framework for sparse matrix problems”, Advances in Applied Mathematics, 33 (1), July 2004, pp. 1–25. Jul 2004 link
A. Zomorodian and G. Carlsson, “Computing persistent homology”, 20th ACM Symposium on Computational Geometry. Jun 2004 link
A. Collins, A. Zomorodian, G. Carlsson, and L. Guibas, “A barcode shape descriptor for curve point cloud data”, Symposium on Point-Based Graphics, ETH, Zürich, Switzerland. Jun 2004 link
V. de Silva and G. Carlsson, “Topological estimation using witness complexes”, Symposium on Point-Based Graphics, ETH, Zürich, Switzerland. Jun 2004 link
V. de Silva, “A weak definition of Delaunay triangulation”. Oct 2003 link
G. Carlsson and V. de Silva, “Topological approximation by small simplicial complexes”. Sep 2003 link
V. de Silva, J.B. Tenenbaum, “Unsupervised learning of curved manifolds”, Nonlinear Estimation and Classification, Lecture Notes in Statistics, 171, pp. 453–466. Jan 2003 link
V. de Silva and J.B. Tenenbaum, “Local versus global methods for nonlinear dimensionality reduction”, Advances in Neural Information Processing Systems, 15, MIT Press, pp. 705–712. Jan 2003 link
I thought it might be interested to point out that stocks prices can be twisted into braids, knots and links exactly in the same manner fluid flows form knots. The link to the paper http://arxiv.org/abs/1404.6637 .
Taking some stocks composing the Dow Jones market index, such as American Express (AXP) and Procter & Gamble (PG), their prices can be tied into knots and links. Knot formation can be followed for all 30 stocks composing Dow Jones encoding the relevant information of the stock market as a whole.
The Alexander-Conway polynomial and Jones polynomial are calculated for the knot formed in the market and could help investors (traders) to anticipate mini-flash crashes emerging from High Frequency Trading activities.