Abstract
In this article several practical applications of algebraic topology are presented. After a short technical review of the necessary theory applications to sensor networks are presented. A very short reference of applications to data analysis follows.
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References
Y. Baryshnikov, R. Ghrist, Target enumeration via Euler characteristic integrals, SIAM J. Appl. Math. 70(3) (2009), 825–844.
Y. Baryshnikov, R. Ghrist, Target enumeration via integration over planar sensor networks, Proc. Robotics: Science and Systems, 2008.
G. Carlsson, Topology and Data, Bull. of the AMS Vol. 46 N. 2 (2009), 255–308.
H. Chintakunta, H. Krim, Topological Fidelity in Sensor Networks, arXiv:1106.6069.
H. Edelsbrunner, J. L. Harer, Computational Homology, AMS, 2010.
D. Freedman, C. Chen, Algebraic topology for computer vision, HP Laboratories HPL-2009-375, 2009.
A. Hatcher, Algebraic Topology, Cambridge Un. Press, 2002, also available at http://www.math.cornell.edu/~hatcher/AT/ATpage.html.
M. Y. Malik, An Outline of Security in Wireless Sensor Networks: Threats, Countermeasures and Implementations, arXiv:1301.3022.
D. Panagopoulos, Homology and Lazy Learning, 1st National conference of HMS and HSOR 2011, 2011.
K. S. J. Pister, Smart Dust, BAA97-43 Proposal Abstract
V. de Silva, R. Ghrist, Homological Sensor Networks, Notices of the AMS Vol. 54 N. 1 (2007), 10–17.
V. de Silva, R. Ghrist,A. Muhammad, Blind Swarms for Coverage in 2-D, Conference: Robotics: Science and Systems - RSS, 2005, 335–342.
G. Singh, F. M\(\acute{e}\) moli, G. Carlsson, Topological Methods for the analysis of high dimensional data sets and 3D object recognition, Point Based Graphics 2007, Prague - Slides. Sep 2007.
A. J. Zomorodian, Topology for computing, Cambridge Un. Press, 2005.
H. Wagner, Computational topology in text mining, ATMCS 2012, 2012.
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Panagopoulos, D., Hassapis, S. (2014). A Short Exposition of Topological Applications to Security Systems. In: Daras, N. (eds) Applications of Mathematics and Informatics in Science and Engineering. Springer Optimization and Its Applications, vol 91. Springer, Cham. https://doi.org/10.1007/978-3-319-04720-1_12
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DOI: https://doi.org/10.1007/978-3-319-04720-1_12
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