
Previous Article
Online learning of both state and dynamics using ensemble Kalman filters
 FoDS Home
 This Issue
 Next Article
Intrinsic disease maps using persistent cohomology
1.  CUNY Graduate Center, 365 5th Avenue, New York, NY 10016 
2.  Department of Mathematics, CUNY College of Staten Island, 2800 Victory Boulevard, Staten Island, NY 10314 
We use persistent cohomology and circular coordinates to investigate three datasets related to infectious diseases. We show that all three datasets exhibit circular coordinates that carry information about the data itself. For one of the datasets we are able to recover time post infection from the circular coordinate itself – for the other datasets, this information was not available, but in one we were able to relate the circular coordinate to red blood cell counts and weight changes in the subjects.
References:
[1] 
K. Cumnock, A. S. Gupta, M. Lissner, V. Chevee, N. M. Davis and D. S. Schneider, Host energy source is important for disease tolerance to malaria, Current Biology, 28 (2018), 16351642. doi: 10.1016/j.cub.2018.04.009. Google Scholar 
[2] 
V. de Silva, D. Morozov and M. VejdemoJohansson, Persistent cohomology and circular coordinates, Discrete Comput. Geom., 45 (2011), 737759. doi: 10.1007/s004540119344x. Google Scholar 
[3] 
F. Pedregosa, G. Varoquaux, A. Gramfort and al. et, Scikitlearn: Machine learning in {P}ython, J. Mach. Learn. Res., 12 (2011), 28252830. Google Scholar 
[4] 
B. R. Rosenberg, M. Depla, C. A. Freije, D. Gaucher and S. Mazouz, et al., Longitudinal transcriptomic characterization of the immune response to acute hepatitis c virus infection in patients with spontaneous viral clearance, PLoS Pathogens, 14 (2018). doi: 10.1371/journal. ppat. 1007290. Google Scholar 
[5] 
B. Y. Torres, J. H. M. Oliveira, A. T. Tate, P. Rath, K. Cumnock and D. S. Schneider, Tracking resilience to infections by mapping disease space, PLoS biology, 14 (2016). doi: 10.1371/journal. pbio. 1002436. Google Scholar 
[6] 
M. VejdemoJohansson and A. Leshchenko, Certified mapper: Repeated testing for acyclicity and obstructions to the nerve lemma, in Topological Data Analysis, Abel Symposia, 15, Springer, Cham, 2020, 491–515. doi: 10.1007/9783030434083_19. Google Scholar 
show all references
References:
[1] 
K. Cumnock, A. S. Gupta, M. Lissner, V. Chevee, N. M. Davis and D. S. Schneider, Host energy source is important for disease tolerance to malaria, Current Biology, 28 (2018), 16351642. doi: 10.1016/j.cub.2018.04.009. Google Scholar 
[2] 
V. de Silva, D. Morozov and M. VejdemoJohansson, Persistent cohomology and circular coordinates, Discrete Comput. Geom., 45 (2011), 737759. doi: 10.1007/s004540119344x. Google Scholar 
[3] 
F. Pedregosa, G. Varoquaux, A. Gramfort and al. et, Scikitlearn: Machine learning in {P}ython, J. Mach. Learn. Res., 12 (2011), 28252830. Google Scholar 
[4] 
B. R. Rosenberg, M. Depla, C. A. Freije, D. Gaucher and S. Mazouz, et al., Longitudinal transcriptomic characterization of the immune response to acute hepatitis c virus infection in patients with spontaneous viral clearance, PLoS Pathogens, 14 (2018). doi: 10.1371/journal. ppat. 1007290. Google Scholar 
[5] 
B. Y. Torres, J. H. M. Oliveira, A. T. Tate, P. Rath, K. Cumnock and D. S. Schneider, Tracking resilience to infections by mapping disease space, PLoS biology, 14 (2016). doi: 10.1371/journal. pbio. 1002436. Google Scholar 
[6] 
M. VejdemoJohansson and A. Leshchenko, Certified mapper: Repeated testing for acyclicity and obstructions to the nerve lemma, in Topological Data Analysis, Abel Symposia, 15, Springer, Cham, 2020, 491–515. doi: 10.1007/9783030434083_19. Google Scholar 
[1] 
Elamin H. Elbasha. Model for hepatitis C virus transmissions. Mathematical Biosciences & Engineering, 2013, 10 (4) : 10451065. doi: 10.3934/mbe.2013.10.1045 
[2] 
Tadas Telksnys, Zenonas Navickas, Miguel A. F. Sanjuán, Romas Marcinkevicius, Minvydas Ragulskis. Kink solitary solutions to a hepatitis C evolution model. Discrete & Continuous Dynamical Systems  B, 2020, 25 (11) : 44274447. doi: 10.3934/dcdsb.2020106 
[3] 
Yanyu Xiao, Xingfu Zou. On latencies in malaria infections and their impact on the disease dynamics. Mathematical Biosciences & Engineering, 2013, 10 (2) : 463481. doi: 10.3934/mbe.2013.10.463 
[4] 
Tao Feng, Zhipeng Qiu, Xinzhu Meng. Dynamics of a stochastic hepatitis C virus system with host immunity. Discrete & Continuous Dynamical Systems  B, 2019, 24 (12) : 63676385. doi: 10.3934/dcdsb.2019143 
[5] 
Jianlu Zhang. Coexistence of period 2 and 3 caustics for deformative nearly circular billiard maps. Discrete & Continuous Dynamical Systems, 2019, 39 (11) : 64196440. doi: 10.3934/dcds.2019278 
[6] 
Antonio Pumariño, José Ángel Rodríguez, Enrique Vigil. Persistent twodimensional strange attractors for a twoparameter family of Expanding Baker Maps. Discrete & Continuous Dynamical Systems  B, 2019, 24 (2) : 657670. doi: 10.3934/dcdsb.2018201 
[7] 
Julie Déserti. Jonquières maps and $SL(2;\mathbb{C})$cocycles. Journal of Modern Dynamics, 2016, 10: 2332. doi: 10.3934/jmd.2016.10.23 
[8] 
Grzegorz Graff, Piotr NowakPrzygodzki. Fixed point indices of iterations of $C^1$ maps in $R^3$. Discrete & Continuous Dynamical Systems, 2006, 16 (4) : 843856. doi: 10.3934/dcds.2006.16.843 
[9] 
Robert M. Strain. Coordinates in the relativistic Boltzmann theory. Kinetic & Related Models, 2011, 4 (1) : 345359. doi: 10.3934/krm.2011.4.345 
[10] 
Daniel N. Dore, Andrew D. Hanlon. Area preserving maps on $\boldsymbol{S^2}$: A lower bound on the $\boldsymbol{C^0}$norm using symplectic spectral invariants. Electronic Research Announcements, 2013, 20: 97102. doi: 10.3934/era.2013.20.97 
[11] 
Alejandro Adem and Jeff H. Smith. On spaces with periodic cohomology. Electronic Research Announcements, 2000, 6: 16. 
[12] 
Rui Wang, Rundong Zhao, Emily RibandoGros, Jiahui Chen, Yiying Tong, GuoWei Wei. HERMES: Persistent spectral graph software. Foundations of Data Science, 2021, 3 (1) : 6797. doi: 10.3934/fods.2021006 
[13] 
Robert Schippa. Sharp Strichartz estimates in spherical coordinates. Communications on Pure & Applied Analysis, 2017, 16 (6) : 20472051. doi: 10.3934/cpaa.2017100 
[14] 
Hui Wan, JingAn Cui. A model for the transmission of malaria. Discrete & Continuous Dynamical Systems  B, 2009, 11 (2) : 479496. doi: 10.3934/dcdsb.2009.11.479 
[15] 
Daniel Guan. Modification and the cohomology groups of compact solvmanifolds. Electronic Research Announcements, 2007, 13: 7481. 
[16] 
HuaiDong Cao and Jian Zhou. On quantum de Rham cohomology theory. Electronic Research Announcements, 1999, 5: 2434. 
[17] 
Dennise GarcíaBeltrán, José A. Vallejo, Yurii Vorobiev. Lie algebroids generated by cohomology operators. Journal of Geometric Mechanics, 2015, 7 (3) : 295315. doi: 10.3934/jgm.2015.7.295 
[18] 
Yu Gao, JianGuo Liu. The modified CamassaHolm equation in Lagrangian coordinates. Discrete & Continuous Dynamical Systems  B, 2018, 23 (6) : 25452592. doi: 10.3934/dcdsb.2018067 
[19] 
Daniel Maxin, Fabio Augusto Milner. The effect of nonreproductive groups on persistent sexually transmitted diseases. Mathematical Biosciences & Engineering, 2007, 4 (3) : 505522. doi: 10.3934/mbe.2007.4.505 
[20] 
Francis Michael Russell, J. C. Eilbeck. Persistent mobile lattice excitations in a crystalline insulator. Discrete & Continuous Dynamical Systems  S, 2011, 4 (5) : 12671285. doi: 10.3934/dcdss.2011.4.1267 
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]