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Results tagged with computational-topology
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user 18263
Computational topology is the study of decidability problems in topology and the algorithms that determine decidability. Examples of area of study include Normal Surface theory and the subproblems of unknot and $S^3$ recognition.
5
votes
Accepted
Are there "geometrically nice" sets from which to construct coverings that admit "Vietoris-R...
Since the question is rather broad, the answer got unwieldy. Sorry, I hope some of this is relevant to the sort of questions you are asking.
Complexity of Approximating the Čech Complex
The computat …
- 15.5k
8
votes
Homological computations
What is the fundamental domain of the action? In case you can easily create a cubical or simplicial decomposition of this region, there is tons of software out there to help you with the grunt-work.
…
- 15.5k
11
votes
Computer-aided homology computations
I realize that this is an old question and it is likely that the OP has moved on, but let me summarize the state-of-the-art as it exists now.
The given sizes (18 million by 15 million) are pretty h …
- 15.5k
27
votes
Accepted
Inference using Topological Data Analysis: Is it worth it for a regular statistician to lear...
Let me answer the broad question first: depending on what you actually want to do, the barcode-type invariants extracted by topological data analysis could be quite useful in your work. And it doesn't …
- 15.5k
12
votes
Inference using Topological Data Analysis: Is it worth it for a regular statistician to lear...
Update: There is a now a new paper by Otter et al which went through all the trouble of comparing many software packages for performance, memory, ease-of-use etc.: http://arxiv.org/abs/1506.08903
Thi …
- 15.5k
37
votes
Accepted
Reference on Persistent Homology
Since this area is developing rather quickly, there is a dearth of canonical references that would satisfy basic pedagogical requirements. If I were teaching a course on this material right now, I wou …
- 15.5k