CHomP, Computational homology project. Much of the fascination and challenge of studying nonlinear systems arises from the complicated spatial, temporal and even spatial-temporal behavior they exhibit. On the level of mathematics this complicated behavior can occur at all scales, both in the state space and in parameter space. Somewhat paradoxically, this points to the need for a coherent set of mathematical techniques that is capable of extracting coarse but robust information about the structure of these systems. Furthermore, most of our understanding of specific systems comes from experimental observation or numerical simulations and thus it is important that these techniques be computationally efficient. Algebraic Topology is the classical mathematical tool for the global analysis of nonlinear spaces and functions, within which homology is perhaps the most computable subset. In particular, it provides a well understood framework through which the information hidden in large datasets can be reduced to compact algebraic expressions that provide insight into underlying geometric structures and properties. The material described through these web pages represents our ongoing effort to develop and apply efficient and effective topologically based methods to the analysis of nonlinear systems.

References in zbMATH (referenced in 20 articles )

Showing results 1 to 20 of 20.
Sorted by year (citations)

  1. Bush, Justin; Cowan, Wes; Harker, Shaun; Mischaikow, Konstantin: Conley-Morse databases for the angular dynamics of Newton’s method on the plane (2016)
  2. Harker, Shaun; Kokubu, Hiroshi; Mischaikow, Konstantin; Pilarczyk, Paweł: Inducing a map on homology from a correspondence (2016)
  3. Haro, Àlex; Canadell, Marta; Figueras, Jordi-Lluís; Luque, Alejandro; Mondelo, Josep-Maria: The parameterization method for invariant manifolds. From rigorous results to effective computations (2016)
  4. Krčál, Marek; Pilarczyk, Paweł: Computation of cubical Steenrod squares (2016)
  5. Alexander, Zachary; Bradley, Elizabeth; Meiss, James D.; Sanderson, Nicole F.: Simplicial multivalued maps and the witness complex for dynamical analysis of time series (2015)
  6. Gameiro, Marcio; Hiraoka, Yasuaki; Izumi, Shunsuke; Kramar, Miroslav; Mischaikow, Konstantin; Nanda, Vidit: A topological measurement of protein compressibility (2015)
  7. Pilarczyk, Paweł; Real, Pedro: Computation of cubical homology, cohomology, and (co)homological operations via chain contraction (2015)
  8. Cochran, Gregory S.; Wanner, Thomas; Dłotko, Paweł: A randomized subdivision algorithm for determining the topology of nodal sets (2013)
  9. Kaczynski, Tomasz; Mrozek, Marian: The cubical cohomology ring: an algorithmic approach (2013)
  10. Pellikka, M.; Suuriniemi, S.; Kettunen, L.; Geuzaine, C.: Homology and cohomology computation in finite element modeling (2013)
  11. van den Berg, Jan Bouwe; Day, Sarah; Vandervorst, Robert: Braided connecting orbits in parabolic equations via computational homology (2013)
  12. Berciano, A.; Molina-Abril, H.; Real, P.: Searching high order invariants in computer imagery (2012)
  13. Dłotko, P.; Ghrist, R.; Juda, M.; Mrozek, M.: Distributed computation of coverage in sensor networks by homological methods (2012)
  14. Allili, Madjid; Corriveau, David; Derivière, Sara; Ethier, Marc; Kaczynski, Tomasz: Detecting critical regions in multidimensional data sets (2011)
  15. Mrozek, Marian; Wanner, Thomas: Coreduction homology algorithm for inclusions and persistent homology (2010)
  16. Pilarczyk, Paweł: Parallelization method for a continuous property (2010)
  17. Wilczak, Daniel: Uniformly hyperbolic attractor of the Smale-Williams type for a Poincaré map in the Kuznetsov system (2010)
  18. Arai, Zin; Kokubu, Hiroshi; Pilarczyk, Paweł: Recent development in rigorous computational methods in dynamical systems (2009)
  19. Mrozek, Marian; Batko, Bogdan: Coreduction homology algorithm (2009)
  20. Pilarczyk, Paweł; Stolot, Kinga: Excision-preserving cubical approach to the algorithmic computation of the discrete Conley index (2008)