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Sep, 2019
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Biology and Topology

There is an article “ Can biology lead to new theorems? ” by Sturmfels on biology and mathematics.

Phylogenetic trees are now studied by using mathematical tools.

Other biological structures such as RNAs and proteins are studied mathematically. For example, [ JQR PKWA ] . A more topological one is [ DLV ] .

I learned the word phylogenomics in [ PS ] . Statistics, combinatorics , probability , and algebraic geometry are related to this subject.

According to Carr, Devadoss, and Forcey [ ? ] , graph associahedra appear in biological statistics [ MPS + ] .

Oriented matroids appear in biochemistry. For example, [ OBJOD01 BGO ] .

The structure called branched polymer introduced as models in chemistry and biology seems to be interesting. See, for example, Brydges and Imbre [ BI03 ] , Kenyon and Winkler [ KW ] , and Meszaros and Postnikov [ MP ] . Meszaros and Postnikov found a relation to hyperplane arrangements

When we apply Leinster’s definition of the Euler characteristic of small categories to metric spaces regarded as enriched categories, we obtain the notion of magnitude. It appeared in a paper on biodiversity [ SP94 ] independently.

References

[BGO]     C. G. Bailey, D. W. Gull, and J. S. Oliveira. Hypergraphic Oriented Matroid Relational Dependency Flow Models of Chemical Reaction Networks, arXiv:0902.0847 .

[BI03]     David C. Brydges and John Z. Imbrie. Branched polymers and dimensional reduction. Ann. of Math. (2) , 158(3):1019–1039, 2003, http://dx.doi.org/10.4007/annals.2003.158.1019 .

[DLV]     Isabel K. Darcy, John Luecke, and Mariel Vazquez. Tangle analysis of difference topology experiments: applications to a Mu protein-DNA complex, arXiv:0710.4150 .

[JQR]     Emma Y. Jin, Jing Qin, and Christian M. Reidys. Combinatorics Of RNA Structures With Pseudoknots, arXiv:0704.2518 .

[KW]     Richard Kenyon and Peter Winkler. Branched Polymers, arXiv:0709.2325 .

[MP]     Karola Meszaros and Alexander Postnikov. Branched polymers and hyperplane arrangements, arXiv:0909.4547 .

[MPS + ]     Jason Morton, Lior Pachter, Anne Shiu, Bernd Sturmfels, and Oliver Wienand. Convex Rank Tests and Semigraphoids, arXiv:math/0702564 .

[OBJOD01]     Joseph Oliveira, Colin Bailey, Janet Jones-Oliveira, and David Dixon. An algebraic-combinatorial model for the identification and mapping of biochemical pathways. Bulletin of Mathematical Biology , 63(6):1163–1196, November 2001.

[PKWA]     R. C. Penner, Michael Knudsen, Carsten Wiuf, and Joergen Ellegaard Andersen. Fatgraph Models of Proteins, arXiv:0902.1025 .

[PS]     Lior Pachter and Bernd Sturmfels. The Mathematics of Phylogenomics, arXiv:math/0409132 .

[SP94]     A. Solow and S. Polasky. Measuring biological diversity. Environmental and Ecological Statistics , 1:95–107, 1994.