Geodesic
A random Bockstein operator
Algebra and discrete mathematics, Tome 25 (2018) no. 2, pp. 311-321.

Voir la notice de l'article provenant de la source Math-Net.Ru

As more of topology's tools become popular in analyzing high-dimensional data sets, the goal of understanding the underlying probabilistic properties of these tools becomes even more important. While much attention has been given to understanding the probabilistic properties of methods that use homological groups in topological data analysis, the probabilistic properties of methods that employ cohomology operations remain unstudied. In this paper, we investigate the Bockstein operator with randomness in a strictly algebraic setting.
Keywords: random cohomology operations, topological data analysis, Bockstein operation. 
@article{ADM_2018_25_2_a10,
     author = {Matthew Zabka},
     title = {A random {Bockstein} operator},
     journal = {Algebra and discrete mathematics},
     pages = {311--321},
     publisher = {mathdoc},
     volume = {25},
     number = {2},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2018_25_2_a10/}
}
TY  - JOUR
AU  - Matthew Zabka
TI  - A random Bockstein operator
JO  - Algebra and discrete mathematics
PY  - 2018
SP  - 311
EP  - 321
VL  - 25
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2018_25_2_a10/
LA  - en
ID  - ADM_2018_25_2_a10
ER  - 
%0 Journal Article
%A Matthew Zabka
%T A random Bockstein operator
%J Algebra and discrete mathematics
%D 2018
%P 311-321
%V 25
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2018_25_2_a10/
%G en
%F ADM_2018_25_2_a10
Matthew Zabka. A random Bockstein operator. Algebra and discrete mathematics, Tome 25 (2018) no. 2, pp. 311-321. http://geodesic.mathdoc.fr/item/ADM_2018_25_2_a10/

[1] G. Carlsson, “Topology and data”, Bulletin of the American Mathematical Society, 2 (2009), 255–308 | DOI | MR | Zbl

[2] M. Kahle, “Topology of random clique complexes”, Discrete Mathematics, 6 (2009), 1658–1671 | DOI | MR | Zbl

[3] M. Kahle, “Random geometric complexes”, Discrete Computational Geometry, 3 (2011), 553–573 | DOI | MR | Zbl

[4] Robert E. Mosher and Martin C. Tangora, Cohomology Operations and Applications in Homotopy Theory, Dover, 2008 | MR

[5] Michael F. Atiyah and Ian G. Macdonald, Introduction to Commutative Algebra, Addison-Wesley, Reading, 1969 | MR | Zbl