Literature on Category Theory and Biology
Hi, I was wondering if you are aware of any bibliographies, reviews, or papers relating category theory to biology - mathematical biology, systems biology, computational biology or bioinformatics. I would be interested in papers relating category theory to areas of knowledge representation or other areas of computer science used in abovementioned areas. Please feel free to email me in person if you wish not to overburden the mailing list. Regards, Deniz Kural
The first time the term "category theory" (I mean, exactly that term) appeared in Mathemtical Reviews was in the review of Rosen, R. [1961]: `A relational theory of the structural changes induced in biological systems by alterations in environment', {\em Bulletin of Mathematical Biophysics} \bf 23}, pp.~165--71. The full review reads: The author uses, among other things, some previous results from his biologico-mathematical applications of abstract category theory [#B416] in order to further develop another paper concerning relational biology [#B418]. Some biological applications are treated; e.g., an interpretation of the mitotic cycle. Rosen's earlier related works are reviewed as dealing with "the theory of categories." best, Colin ----- Original Message ----- From: Deniz Kural <kural@fas.harvard.edu> Date: Friday, May 4, 2007 8:55 pm Subject: categories: Literature on Category Theory and Biology To: categories@mta.ca
Hi,
I was wondering if you are aware of any bibliographies, reviews, or papers relating category theory to biology - mathematical biology, systems biology, computational biology or bioinformatics.
I would be interested in papers relating category theory to areas of knowledge representation or other areas of computer science used in abovementioned areas.
Please feel free to email me in person if you wish not to overburden the mailing list.
Regards, Deniz Kural
Hi, 1.You may want to look at the writings of Robert Rosen (a Google search will provide the necessary links). 2. For a different direction, and on a far more modest note, you may try looking at some of my papers on my web page: http://www.actcom.co.il/typographics/zippie Of course I will be very intrested to hear your comments about that. Good luck, Zippie -- ____________________________________________ Zippora Arzi-Gonczarowski, Ph.D. Aka:Zippie Typographics, Ltd. 46 Hehalutz St. Jerusalem 96222, ISRAEL zippie@actcom.co.il http://www.actcom.co.il/typographics/zippie Tel: +972-2-6437819 Fax: +972-2-6434252 _____________________________________________
The links: http://perso.orange.fr/vbm-ehr/ and http://alf.nbi.dk/%7Eemmeche/coPubl/97d.NABCE/ExplEmer.html and a related paper "Categorical language and hierarchical models for cell systems" by R. Brown, R. Paton and T. Porter may be of interest. I believe that Brown and Porter have other references of this nature. See also the recent work by M. Healy on neural networks. Best wishes, Ralph Wojtowicz wojtowicz@metsci.com
A new "heteromorphic" treatment of adjoint functors provides applications to biology such as an abstract characterization of selectionist (as opposed to instructionist) mechanisms as in Darwin's evolutionary theory, the selectionist theory of the immune system, and neural darwinism (e.g., Edelman's and Changeux's work). Heteromorphisms, e.g., the injection of a set of generators into the free group on the set, can be formally treated in category theory using bifunctors Het:X^op x A--> Set analogous to the usual Hom:X^op x X-->Set. When the heteromorphisms from objects in a category X to objects in a category A can represented in each of the categories, then the functors giving the representing objects are a pair of adjoint functors and the representations give a pair of natural isomorphisms: Hom_A(Fx,a) = Het(x,a) = Hom-_X(x,Ga). The usual treatment of adjoints leaves out the middle term. And all adjoint functors can be shown to arise in this manner (up to isomorphism). The applications were not available in the usual treatment of adjoints where the heteromorphisms were not explicit. The applications are outlined in a paper just published in Axiomathes (2007) 17: 19-39. A reprint can be retreived from my website: http://www.ellerman.org/Davids-Stuff/Maths/Adjoints-Axiomathes-Reprint.pdf . A rather long (and impenetrable) treatment of the math was in the recent "What is Category Theory" collection of papers (2006: Polimetrica). A short straightforward treatment of the math is available on the ArXiv: http://arxiv.org/abs/0704.2207v1 . Other applications of category theory to biology have been made by Robert Rosen (as mentioned by several posts) and by Andree Ehresmann. Best, David __________________ David Ellerman Visiting Scholar University of California at Riverside Email: david@ellerman.org Webpage: www.ellerman.org View my research on my SSRN Author page: <http://ssrn.com/author=294049> http://ssrn.com/author=294049
In answer to Deniz Kural With Jean-Paul Vanbremeersch we have been developing a model for biological and neural systems based on category theory called Memory Evolutive Systems. Since 20 years we have published a series of papers on this subject, most of which are posted on our Internet site http://perso.wanadoo.fr/vbm-ehr Recently we have written a book on this subject: Memory Evolutive sytems: hierarchy, emergence, cognition" due to appear this month in the series "Studies in Multidisciplinarity" of Elsevier (volume 4). Sincerely Andree C. Ehresmann
Regarding Deniz Kural's question about references to papers on category theory and biology, Tom Caudell and I have been investigating a semantic theory for neural networks both biological and artificial, cognitive and non-cognitive. We are designing and conducting experiments to test and refine the theory in both neuroscience and cognitive psychology working with colleagues in those disciplines. An initial paper on the theory is M. J. Healy and T. P. Caudell (2006) Ontologies and Worlds in Category Theory: Implications for Neural Systems, Axiomathes, vol. 16, nos. 1-2, pp. 165-214. The only experiment appearing in a publication to date is one on an artificial neural network application, presented at IJCNN 2005 in Montreal (the results were presented also at CT06). Regards, Mike Healy
participants (7)
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Andree Ehresmann -
Colin McLarty -
David Ellerman -
Deniz Kural -
mjhealy@ece.unm.edu -
Wojtowicz, Ralph -
Zippie Arzi-Gonczarowski