go site https://themusicuniverse.com/music/maths-studies-ib-coursework/45/ source url enter site silagra reviews example cover letter for office administrator job medicamentos contraindicados con el viagra sms jokes on viagra oxford thesis guidelines https://optionsrehab.org/generic/cymbalta-with-free-shipping/60/ source link enter site viagra falls the show how to write a resume objective for college celebrity definition essay outline sample thesis cooperative learning se puede tomar paracetamol con viagra phd thesis catalog https://hobcawbarony.org/coursework/6-paragraph-comparative-essay-sample/27/ frankenstein real monster essay enter http://cappuccino.ucsd.edu/how/se-tomar-cialis-posso-beber/100/ write essay on internet here go to link cialis online denmark click here viagra from boots career plan essay sea turtle essay Computing the topological type, or homology, of a given a simplicial complex is straight forward, but not always computationally feasible. The bottleneck is in computing the Smith Normal Form, which is a polynomial time algorithm [Kannan-Bachem], but still too slow on large examples (about cubic).
Discrete Morse theory [Whitehead, Forman] provides a tool set which can be used to find reasonable upper bounds. A randomized search for small discrete Morse vectors was introduced by Benedetti and Lutz, which we implemented as a client for the topological software package polymake.
I gave a workshop on
Random_Discrete_Morse at the Homology: Theoretical and Computational Aspects (HTCA 2015) conference in Genoa, Italy.
While experimenting with
Random_Discrete_Morse, we discovered a whole family of contractible, yet non-collapsible simplicial 2-complexes. We call them the sawblade complexes. Read more about the sawblade complexes here.
- B Benedetti and FH Lutz. Random discrete Morse theory and a new library of triangulations. Exp. Math., 23:66–94, 2014.
- R Forman. A user’s guide to discrete Morse theory. Sémin. Lothar. Comb., 48:B48c, 35 p., electronic only, 2002.
- R Kannan and A Bachem. Polynomial algorithms for computing the Smith and Hermite normal forms of an integer matrix. SIAM J. Comput., 8(4):499–507, 1979.
- JHC Whitehead. Simplicial spaces, nuclei and m-groups. Proc. Lond. Math. Soc., II. Ser., 45:243–327, 1939.