4 ms·

I was skeptical about the “applied” part, but glancing through it, the examples are really interesting! Discussing magnetic fields in the same chapter as lambda

I was skeptical about the “applied” part, but glancing through it, the examples are really interesting! Discussing magnetic fields in the same chapter as lambda calculus, very cool! Seems a bit light on details though...

nikofeyn 8y ago
why skeptical when he is a top applied mathematician? and he explains in the preface why it is seemingly light on details. it's because the details (the math) are elsewhere. the applications (as isolated entities) are also out there to a degree. what isn't out there is the bridge connecting the math to the applications, and so that is what his book sets out to do. > Discussing magnetic fields in the same chapter as lambda calculus where did you see this? i don't remember seeing it and couln't find it.
- soVeryTired 8y ago
  > why skeptical when he is a top applied mathematician? I see a lot of mathematics in the book, but from skimming it, I can't see a 'killer application' as such. I'd like to see an example of a practical problem that can be solved using reasonably deep topolgical methods (beyond, say the Euler characteristic) that can't be solved in any other way. Ghrist was championing persistent homology for network analysis as such an application a few years ago, but I'm not sure if it ever progressed beyond 'toy' problems to give state-of-the-art results.
  - improbable22 8y ago
    From skimming, it looks to me like the examples are facing the other way: they're there to help you grasp the mathematics. Would also be curious to hear of practical applications of heavy-duty topology, if anyone can think of some.
    - nikofeyn 8y ago
      just look at his research papers.
  - ajudson 8y ago
    Here is a paper for you: "Topology based data analysis identifies a subgroup of breast cancers with a unique mutational profile and excellent survival" https://www.pnas.org/content/108/17/7265 https://www.pnas.org/content/108/17/7265
    - improbable22 8y ago
      Thanks. I skimmed the linked "Mapper" article they cite as their method, and it looks about as topological as t-SNE, i.e. in the sense of caring about local nearness but not global distance. But did I miss any heavier stuff? Is this all people mean when they talk about topological data analysis?
      - ajudson 8y ago
        The other famous TDA technique is persistent homology, this paper is a good intro https://www.math.upenn.edu/~ghrist/preprints/barcodes.pdf https://www.math.upenn.edu/~ghrist/preprints/barcodes.pdf
        soVeryTired 8y ago
        But now: persistent homology. Same question as above.
        kaitai 8y ago
        Progress has been slower than expected, in some ways. But I think that persistent homology and topological methods like Mapper are slowly allowing interesting research. My favorite recent application: two-parameter persistent homology for drug discovery (link to pdf of talk: https://www.ima.umn.edu/materials/2017-2018/SW8.13-15.18/27458/Bryn-Keller_Two-Parameter-Persistence-for-Virtual-Ligand-Screening.pdf https://www.ima.umn.edu/materials/2017-2018/SW8.13-15.18/274...). Frankly I find two-parameter persistence very hard to interpret, though I hope to spend some time on it this summer. But it's undeniable that the work described in the link is an application that can't be reduced to clustering. I also feel that describing Mapper as 'just a clustering tool' is not really accurate; I'm getting good results from using Mapper for feature discovery in some specific domains where clustering has truly failed because traits lie on continua in a way that renders usual clustering muddy and useless. Edited to add: here's another interesting paper, about subgroups of type 2 diabetes patients: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4780757/ https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4780757/ They use Mapper to find 'clusters' and then go back to more traditional statistics to test significance. I don't have the data so I don't know if clustering alone would have worked.
ajudson 8y ago
I am also interested in where the lambda calculus is referenced, I do not see it in the index.

nikofeyn 8y ago

why skeptical when he is a top applied mathematician? and he explains in the preface why it is seemingly light on details. it's because the details (the math) are elsewhere. the applications (as isolated entities) are also out there to a degree. what isn't out there is the bridge connecting the math to the applications, and so that is what his book sets out to do. > Discussing magnetic fields in the same chapter as lambda calculus where did you see this? i don't remember seeing it and couln't find it.

soVeryTired 8y ago
> why skeptical when he is a top applied mathematician? I see a lot of mathematics in the book, but from skimming it, I can't see a 'killer application' as such. I'd like to see an example of a practical problem that can be solved using reasonably deep topolgical methods (beyond, say the Euler characteristic) that can't be solved in any other way. Ghrist was championing persistent homology for network analysis as such an application a few years ago, but I'm not sure if it ever progressed beyond 'toy' problems to give state-of-the-art results.
- improbable22 8y ago
  From skimming, it looks to me like the examples are facing the other way: they're there to help you grasp the mathematics. Would also be curious to hear of practical applications of heavy-duty topology, if anyone can think of some.
  - nikofeyn 8y ago
    just look at his research papers.
- ajudson 8y ago
  Here is a paper for you: "Topology based data analysis identifies a subgroup of breast cancers with a unique mutational profile and excellent survival" https://www.pnas.org/content/108/17/7265 https://www.pnas.org/content/108/17/7265
  - improbable22 8y ago
    Thanks. I skimmed the linked "Mapper" article they cite as their method, and it looks about as topological as t-SNE, i.e. in the sense of caring about local nearness but not global distance. But did I miss any heavier stuff? Is this all people mean when they talk about topological data analysis?
    - ajudson 8y ago
      The other famous TDA technique is persistent homology, this paper is a good intro https://www.math.upenn.edu/~ghrist/preprints/barcodes.pdf https://www.math.upenn.edu/~ghrist/preprints/barcodes.pdf
      - soVeryTired 8y ago
        But now: persistent homology. Same question as above.
        kaitai 8y ago
        Progress has been slower than expected, in some ways. But I think that persistent homology and topological methods like Mapper are slowly allowing interesting research. My favorite recent application: two-parameter persistent homology for drug discovery (link to pdf of talk: https://www.ima.umn.edu/materials/2017-2018/SW8.13-15.18/27458/Bryn-Keller_Two-Parameter-Persistence-for-Virtual-Ligand-Screening.pdf https://www.ima.umn.edu/materials/2017-2018/SW8.13-15.18/274...). Frankly I find two-parameter persistence very hard to interpret, though I hope to spend some time on it this summer. But it's undeniable that the work described in the link is an application that can't be reduced to clustering. I also feel that describing Mapper as 'just a clustering tool' is not really accurate; I'm getting good results from using Mapper for feature discovery in some specific domains where clustering has truly failed because traits lie on continua in a way that renders usual clustering muddy and useless. Edited to add: here's another interesting paper, about subgroups of type 2 diabetes patients: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4780757/ https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4780757/ They use Mapper to find 'clusters' and then go back to more traditional statistics to test significance. I don't have the data so I don't know if clustering alone would have worked.

ajudson 8y ago

I am also interested in where the lambda calculus is referenced, I do not see it in the index.