natural transformations of organismic structures
NaturalTransformationsOfOrganismicStructures
2010-12-05 16:05:25
2010-12-05 16:05:25
Topic
natural transformation, organismic structures, variable molecular sets, variable category, variable topology
\subsection{Natural Transformations of Organismic Structures}
Biological systems, or living organisms are characterized by relational structures and their dynamic transformations which can be represented as natural transformations of \PMlinkname{heterofunctors in organismic supercategories}{Supercategories3}(OS). Such OS-structures can be specified mathematically either by using the \PMlinkname{Yoneda-Grothendieck Lemma and construction}{YonedaEmbedding}, or they can be directly derived by a mathematical interpretation of the first ten axioms of ETAS, plus two additional axioms defining both `self-repair' of metabolic components and complete reproduction in terms of \PMlinkexternal{genetic coding, translational genomics}{http://planetphysics.org/?op=getobj&from=books&id=213} and epigenetic meta-processes. Further details concerning mathematical, logical and complex modeling are provided in the following list of publications and related web (html) links.
\begin{thebibliography}{9}
\bibitem{ICB6}
I.C. Baianu: 1977, A Logical Model of Genetic Activities in \L ukasiewicz Algebras: The Non-linear Theory. \emph{Bulletin of Mathematical Biophysics}, \textbf{39}: 249-258.
\bibitem{ICB7}
I.C. Baianu: 1980, Natural Transformations of Organismic Structures. \emph{Bulletin of Mathematical Biophysics}
\textbf{42}: 431-446.
\bibitem{ICB8}
I.C. Baianu: 1983, Natural Transformation Models in Molecular Biology., in \emph{Proceedings of the SIAM Natl. Meet}., Denver, CO.; \PMlinkexternal{An Eprint is here available}{http://cogprints.org/3675/1/Naturaltransfmolbionu6.pdf} .
\bibitem{ICB9}
I.C. Baianu: 1984, A Molecular-Set-Variable Model of Structural and Regulatory Activities in Metabolic and Genetic Networks., \emph{FASEB Proceedings} \textbf{43}, 917.
\bibitem{ICB2}
I.C. Baianu: 1987a, Computer Models and Automata Theory in Biology and Medicine., in M. Witten (ed.),
\emph{Mathematical Models in Medicine}, vol. 7., Pergamon Press, New York, 1513-1577; \PMlinkexternal{CERN Preprint No. EXT-2004-072:}{http://documents.cern.ch/cgi-bin/setlink?base=preprint&categ=ext&id=ext-2004-067}.
\bibitem{ICB9b}
I.C. Baianu: 1987b, Molecular Models of Genetic and Organismic Structures, in \emph{Proceed. Relational Biology Symp.} Argentina; \PMlinkexternal{CERN Preprint No.EXT-2004-067:MolecularModelsICB3.doc}{http://documents.cern.ch/cgi-bin/setlink?base=preprint&categ=ext&id=ext-2004-067}.
\bibitem{Bgg2}
I.C. Baianu, Glazebrook, J. F. and G. Georgescu: 2004, Categories of Quantum Automata and
N-Valued \L ukasiewicz Algebras in Relation to Dynamic Bionetworks, \textbf{(M,R)}--Systems and
Their Higher Dimensional Algebra,
\PMlinkexternal{Abstract of Report is here available as a PDF}{http://www.ag.uiuc.edu/fs401/QAuto.pdf} and
\PMlinkexternal{html document}{http://doc.cern.ch/archive/electronic/other/ext/ext-2004-058/QuantumAutnu3_ICB.pdf}
\bibitem{BHS2}
R. Brown R, P.J. Higgins, and R. Sivera.: \emph{``Non--Abelian Algebraic Topology''},({\em in preparation}).
\PMlinkexternal{available here as PDF}{http://arxiv.org/PS_cache/math/pdf/0407/0407275v2.pdf}.
\bibitem{BGB2}
R. Brown, J. F. Glazebrook and I. C. Baianu: A categorical and higher dimensional algebra framework for complex systems and spacetime structures, \emph{Axiomathes} \textbf{17}:409-493.
(2007).
\bibitem{LO68}
L. L$\ddot{o}$fgren: 1968. On Axiomatic Explanation of Complete Self--Reproduction. \emph{Bull. Math. Biophysics},
\textbf{30}: 317-348.
\bibitem{ICBetal2k9}
Contributed Review. 2009. GNUL download.
\PMlinkexternal{``DNA Molecular Models and Dynamics.''}{http://planetphysics.org/?op=getobj&from=books&id=213}
\end{thebibliography}