[1]
|
C. Bandt and B. Pompe, Permutation entropy: A natural complexity measure for time series, Phys. Rev. Lett., 88 (2002), 174102.
doi: 10.1103/PhysRevLett.88.174102.
|
[2]
|
R. Belton, B. Cummins and R. R. Narem, Computing and comparing extremal event dags, https://github.com/breecummins/min_interval_posets, 2021.
|
[3]
|
P. Bendich, H. Edelsbrunner, D. Morozov and A. Patel, Homology and Robustness of Level and Interlevel sets, Homology, Homotopy and Applications, 15 (2013), 51-72.
doi: 10.4310/HHA.2013.v15.n1.a3.
|
[4]
|
P. Bendich and J. Harer, Persistent intersection homology, Foundations of Computational Mathematics, 11 (2010), 305-336.
|
[5]
|
E. Berry, B. Cummins, R. R. Narem, L. M. Smith, S. B. Haase and T. Gedeon, Using extremal events to characterize noisy time series, Journal of Mathematical Biology, 80 (2020), 1523-1557.
doi: 10.1007/s00285-020-01471-4.
|
[6]
|
J. Berwald and M. Gidea, Critical transitions in a model of a genetic regulatory system, Mathematical Biosciences & Engineering, 11 (2014), 723-740.
doi: 10.3934/mbe.2014.11.723.
|
[7]
|
S. Boll, Suppression of acoustic noise in speech using spectral subtraction, IEEE Transactions on Acoustics, Speech, and Signal Processing, 27 (1979), 113-120.
doi: 10.1109/TASSP.1979.1163209.
|
[8]
|
S. L. Bristow, A. R. Leman, L. A. Simmons Kovacs, A. Deckard, J. Harer and S. B. Haase, Checkpoints couple transcription network oscillator dynamics to cell-cycle progression, Genome Biology, 15 (2014).
|
[9]
|
G. Carlsson and V. de Silva, Zigzag persistence, Foundations of Computational Mathematics, 10 (2010), 367-405.
doi: 10.1007/s10208-010-9066-0.
|
[10]
|
C. Chen, X. Ni, Q. Bai and Y. Wang, A topological regularizer for classifiers via persistent homology, In AISTATS, 2019.
|
[11]
|
C.-Y. Cho, C. M. Kelliher and S. B. Haase, The cell-cycle transcriptional network generates and transmits a pulse of transcription once each cell cycle, Cell Cycle, 18 (2019), 363-378.
doi: 10.1080/15384101.2019.1570655.
|
[12]
|
C.-Y. Cho, F. C. Motta, C. M. Kelliher and S. B. Haase, Reconciling conflicting models for global control of cell-cycle transcription, Cell Cycle, 16 (2017), 1965-1978.
doi: 10.1080/15384101.2017.1367073.
|
[13]
|
D. Cohen-Steiner, H. Edelsbrunner and J. Harer, Stability of persistence diagrams, Discrete and Computational Geometry, 37 (2007), 103-120.
doi: 10.1007/s00454-006-1276-5.
|
[14]
|
D. Cohen-Steiner, H. Edelsbrunner and D. Morozov, Vines and vineyards by updating persistence in linear time, In SoCG 2006: Proceedings of the Twenty-Second Annual Symposium on Computational Geometry, 2006,119-126.
doi: 10.1145/1137856.1137877.
|
[15]
|
T. H. Cormen, C. E. Leiserson, R. L. Rivest and C. Stein, Introduction to Algorithms, Third Edition, 3rd edition, The MIT Press, 2009.
|
[16]
|
B. Cummins, T. Gedeon, S. Harker and K. Mischaikow, Model rejection and parameter reduction via time series, SIAM Journal of Applied Dynamical Systems, 17 (2018), 1589-1616.
doi: 10.1137/17M1134548.
|
[17]
|
M. Dindin, Y. Umeda and F. Chazal, Topological data analysis for arrhythmia detection through modular neural networks, In CanadianAI 2020 - 33rd Canadian Conference on Artificial Intelligence, Proc. 33rd Canadian Conference on Artificial Intelligence, May 2020., Ottawa, Canada, May 2020. 7 pages, 4 figures.
doi: 10.1007/978-3-030-47358-7_17.
|
[18]
|
H. Edelsbrunner and J. Harer, Persistent homology - a survey, Surveys on Discrete and Computational Geometry: Twenty Years Later, 2008,257-282.
doi: 10.1090/conm/453/08802.
|
[19]
|
H. Edelsbrunner and J. L. Harer, Computational Topology: An Introduction, Applied Mathematics. American Mathematical Society, 2010.
doi: 10.1090/mbk/069.
|
[20]
|
M. Feng and M. A. Porter, Persistent homology of geospatial data: A case study with voting, SIAM Review, 63 (2021), 67-99.
doi: 10.1137/19M1241519.
|
[21]
|
S. Gholizadeh and W. Zadrozny, A short survey of topological data analysis in time series and system analysis, arXiv: 1809.10745, 2018.
|
[22]
|
R. Ghrist., The persistent topology of data, American Mathematical Society, Bulletin. New Series., 45 (2008), 61-75.
doi: 10.1090/S0273-0979-07-01191-3.
|
[23]
|
D. Günther, J. Salmon and J. Tierny, Mandatory critical points of 2d uncertain scalar fields, Computer Graphics Forum, 33 (2014), 31-40.
doi: 10.1111/cgf.12359.
|
[24]
|
S. B. Haase and C. Wittenberg, Topology and control of the cell-cycle-regulated transcriptional circuitry, Genetics, 196 (2014), 65-90.
doi: 10.1534/genetics.113.152595.
|
[25]
|
A. Hatcher, Algebraic Topology, Cambridge University Press, 2002.
|
[26]
|
T. Kaczynski, K. Mischaikow and M. Mrozek, Computational Homology, volume 157. Springer-Verlag, 2004.
doi: 10.1007/b97315.
|
[27]
|
S. Kamath and P. Loizou, A multi-band spectral subtraction method for enhancing speech corrupted by colored noise, 2002 IEEE International Conference on Acoustics, Speech, and Signal Processing, 4, 2002.
doi: 10.1109/ICASSP.2002.5745591.
|
[28]
|
F. A. Khasawneh and E. Munch, Topological data analysis for true step detection in periodic piecewise constant signals, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 474 (2018), 20180027, 24 pp.
doi: 10.1098/rspa.2018.0027.
|
[29]
|
W. Kim and F. Mémoli, Stable signatures for dynamic metric spaces via zigzag persistent homology, 2017. arXiv: 1712.04064.
|
[30]
|
W. Kim and F. Mémoli, Spatiotemporal persistent homology for dynamic metric spaces, Discrete Computational Geometry, 66 (2021), 831-875.
doi: 10.1007/s00454-019-00168-w.
|
[31]
|
L. A. S. Kovacs, M. B. Mayhew, D. A. Orlando, Y. Jin, Q. Li, C. Huang, S. I. Reed, S. Mukherjee and S. B. Haase, Cyclin-dependent kinases are regulators and effectors of oscillations driven by transcription factor network, Molecular Cell, 45 (2012), 669-679.
doi: 10.1016/j.molcel.2011.12.033.
|
[32]
|
L. A. S. Kovacs, D. A. Orlando and S. B. Haase, Transcription networks and cyclin/cdks: The yin and yang of cell cycle oscillators, Cell Cycle, 7 (2008), 2626-2629.
doi: 10.4161/cc.7.17.6515.
|
[33]
|
P. Lawson, A. B. Sholl, J. Quincy Brown, B. Terese Fasy and C. Wenk, Persistent homology for the quantitative evaluation of architectural features in prostate cancer, Scientific Reports, 9 (2019).
|
[34]
|
Y. Lee, S. D. Barthel, P. Dłotko, S. M. Moosavi, K. Hess and B. Smit, High-throughput screening approach for nanoporous materials genome using topological data analysis: Application to zeolites, Journal of Chemical Theory and Computation, 14 (2018), 4427-4437.
doi: 10.1021/acs.jctc.8b00253.
|
[35]
|
D. Ma, T. Liu, L. Chang, C. Rui, Y. Xiao, S. Li, J. B. Hogenesch, Y. E. Chen and J. D. Lin, The liver clock controls cholesterol homeostasis through trib1 protein-mediated regulation of pcsk9/low density lipoprotein receptor (ldlr) axis*, Journal of Biological Chemistry, 290 (2015), 31003-31012.
doi: 10.1074/jbc.M115.685982.
|
[36]
|
J. Milnor, Morse Theory, Princeton University Press, New Jersey, 1963.
|
[37]
|
D. Morozov, K. Beketayev and G. H. Weber, Interleaving distance between merge trees, Discrete Computational Geometry, 49 (2013), 22-45.
|
[38]
|
D. Morozov and G. Weber, Distributed merge trees, In Proceedings of the Annual Symposium on Principles and Practice of Parallel Programming, 93-102. ACM, February 2013.
doi: 10.1145/2442516.2442526.
|
[39]
|
J. R. Munkres, Elements of Algebraic Topology, Addison-Wesley, 1984.
|
[40]
|
L. S. Mure, H. D. Le, G. Benegiamo, M. W. Chang, L. Rios, N. Jillani, M. Ngotho, T. Kariuki, O. Dkhissi-Benyahya, H. M. Cooper and S. Panda, Diurnal transcriptome atalas of primate across major neural and peripheral tissues, Science, 359 (2018).
|
[41]
|
A. Myers and F. A. Khasawneh, On the automatic parameter selection for permutation entropy, Chaos: An Interdisciplinary Journal of Nonlinear Science, 30 (2020).
|
[42]
|
A. Myers, F. A. Khasawneh and B. T. Fasy, Separating persistent homology of noise from time series data using topological signal processing, arXiv: 2012.04039, 2020.
|
[43]
|
S. B. Needleman and C. D. Wunsch, A general method applicable to the search for similarities in the amino acid sequence of two proteins, Journal of Molecular Biology, 48 (1970), 443-453.
doi: 10.1016/B978-0-12-131200-8.50031-9.
|
[44]
|
R. R. Nerem, P. Crawford-Kahrl, B. Cummins and T. Gedeon, A poset metric from the directed maximum common edge subgraph, 2019. arXiv: 1910.14638.
|
[45]
|
D. A. Orlando, C. Y. Lin, A. Bernard, J. Y. Wang, J. E. S. Socolar, E. S. Iversen, A. J. Hartemink and S. B. Haase, Global control of cell cycle transcription by coupled cdk and network oscillators, Nature, 453 (2008), 944-947.
doi: 10.1038/nature06955.
|
[46]
|
N. Otter, M. A. Porter, U. Tillmann, P. Grindrod and H. A. Harrington, A roadmap for the computation of persistent homology, EPJ Data Science, 6 (2017).
|
[47]
|
J. A. Perea, A brief history of persistence, Morfismos, 23 (2019), 1-16.
|
[48]
|
J. A. Perea, A. Deckard, S. B. Haase and J. Harer, Sw1pers: Sliding windows and 1-persistence scoring; discovering periodicity in gene expression time series data, BMC Bioinformatics, 16 (2015).
|
[49]
|
G. Petri, P. Expert, F. Turkheimer, R. Carhart-Harris, D. Nutt, P. J. Hellyer and F. Vaccarino, Homological scaffolds of brain functional networks, Journal of the Royal Society Interface, 11 (2014).
|
[50]
|
S. J. Rahi, K. Pecani, A. Ondracka and C. Oikonomou, The cdk-apc/c oscillator predominantly entrains periodic cell-cycle transcription, Cell, 165 (2016), 475-487.
doi: 10.1016/j.cell.2016.02.060.
|
[51]
|
M. D. Ruben, G. Wu, D. F. Smith, R. E. Schmidt, L. J. Francey, Y. Y. Lee, R. C. Anafi and J. B. Hogenesch, A database of tissue-specific rhythmically expressed human genes has potential applications in circadian medicine, Science Translational Medicine, 10 (2018).
|
[52]
|
N. F. Sanderson, E. Shugerman, S. Molnar, J. D. Meiss and E. Bradley, Computational topology techniques for characterizing time-series data, In Niall Adams, Allan Tucker, and David Weston, editors, Advances in Intelligent Data Analysis XVI. Springer, 2017.
doi: 10.1007/978-3-319-68765-0_24.
|
[53]
|
K. Shedden and S. Cooper, Analysis of cell-cycle gene expression in saccharomyces cerevisiae using microarrays and multiple synchronization methods, Nucleic Acids Research, 30 (2002), 2920-2929.
doi: 10.1093/nar/gkf414.
|
[54]
|
I. Simon, J. Barnett, N. Hannett, C. T. Harbison, N. J. Rinaldi, T. L. Volkert, J. J. Wyrick, J. Zeitlinger, D. K. Gifford, T. S. Jaakkola and R. A. Young, Serial regulation of transcriptional regulators in the yeast cell cycle, Cell, 106 (2001), 697-708.
doi: 10.1016/S0092-8674(01)00494-9.
|
[55]
|
M. Small, Complex networks from time series: Capturing dynamics, In 2013 IEEE International Symposium on Circuits and Systems (ISCAS), 2013, 2509-2512.
doi: 10.1109/ISCAS.2013.6572389.
|
[56]
|
D. Smirnov and D. Morozov, Triplet merge trees, Topological Methods in Data Analysis and Visualization V (TopoInVis'17), 2020.
doi: 10.1007/978-3-030-43036-8_2.
|
[57]
|
L. M. Smith, F. C. Motta, G. Chopra, J. Kathleen Moch, R. R. Nerem, B. Cummins, K. E. Roche, C. M. Kelliher, A. R. Leman, J. Harer, T. Gedeon, N. C. Waters and S. B. Haase, An intrinsic oscillator drives the blood stage cycle of the malaria parasite plasmodium falciparum, Science, 368 (2020), 754-759.
doi: 10.1126/science.aba4357.
|
[58]
|
B. J. Stolz, H. A. Harrington and M. A. Porter, Persistent homology of time-dependent functional networks constructed from coupled time series, Chaos, 27 (2017).
|
[59]
|
F. Takens, Detecting strange attractors in turbulence, Dynamical Systems and Turbulence, Warwick 1980, Lecture Notes in Mathematics, 898 (1981), 366-381.
|
[60]
|
C. M. Topaz, L. Ziegelmeier and T. Halverson, Topological data analysis of biological aggregation models, PLoS ONE, (2015).
doi: 10.1371/journal.pone.0126383.
|
[61]
|
R. S. Tsay, Multivariate Time Series Analysis: With R and Financial Applications, Wiley, 1st edition, 2013.
|
[62]
|
M. Ulmer, L. Ziegelmeier and C. M. Topaz, A topological approach to selecting models of biological experiments, PLoS ONE, (2019).
doi: 10.1371/journal.pone.0213679.
|
[63]
|
O. Vipond, J. A. Bull, P. S. Macklin, U. Tillmann, C. W. Pugh, H. M. Byrne and H. A. Harrington, Multiparameter persistent homology landscapes identify immune cell spatial patterns in tumors, Proceedings of the National Academy of Sciences, 118 (2021).
doi: 10.1073/pnas.2102166118.
|
[64]
|
R. A. Wagner and M. J. Fischer, The string-to-string correction problem, Journal of the ACM, 21 (1974), 168-173.
doi: 10.1145/321796.321811.
|
[65]
|
W. W. S. Wei, Multivariate Time Series Analysis and Applications, Wiley, 1st edition, 2019.
|
[66]
|
L. Xian, H. Adams, C. M. Topaz and L. Ziegelmeier, Capturing dynamics of time-varying data via topology, Foundations of Data Science, 4 (2022), 1-36.
doi: 10.3934/fods.2021033.
|
[67]
|
R. Zhang, N. F. Lahens, H. I. Ballance, M. E. Hughes and J. B. Hogenesch, A circadian gene expression atlas in mammals: Implications for biology and medicine, Proceedings of the National Academy of Sciences of the United States of America, 111 (2014), 16219-16224.
doi: 10.1073/pnas.1408886111.
|
[68]
|
A. Zomorodian and G. Carlsson, Computing persistent homology, Discrete Computational Geometry, 33 (2005), 249-274.
doi: 10.1007/s00454-004-1146-y.
|