Talk:PlanetPhysics/Natural Transformations of Organismic Structures

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 \subsection{Natural Transformations of Organismic Structures}

Biological \htmladdnormallink{systems}{http://planetphysics.us/encyclopedia/SimilarityAndAnalogousSystemsDynamicAdjointnessAndTopologicalEquivalence.html}, or living organisms are characterized by relational structures and their \htmladdnormallink{dynamic}{http://planetphysics.us/encyclopedia/MathematicalFoundationsOfQuantumTheories.html} transformations which can be represented as natural transformations of heterofunctors in organismic supercategories(\htmladdnormallink{OS}{http://planetphysics.us/encyclopedia/OS.html}). Such OS-structures can be specified mathematically either by using the Yoneda-Grothendieck Lemma and construction, or they can be directly derived by a mathematical interpretation of the first ten axioms of \htmladdnormallink{ETAS}{http://planetphysics.us/encyclopedia/ETACAxioms.html}, plus two additional axioms defining both `self-repair' of metabolic components and complete reproduction in terms of \htmladdnormallink{genetic coding, translational genomics}{http://planetphysics.org/?op=getobj&from=books&id=213} and epigenetic meta-processes.

Natural transformations of organismic structures allow for the extension of both Rashevsky's \htmladdnormallink{organismic set theory}{http://planetphysics.us/encyclopedia/TheoryOfOrganismicSets.html} and Robert Rosen's Metabolic-Replication Systems Set-Categorical approach to \htmladdnormallink{relational biology}{http://planetphysics.us/encyclopedia/RSystemsCategory.html} based on the \htmladdnormallink{concepts}{http://planetphysics.us/encyclopedia/PreciseIdea.html} of \htmladdnormallink{molecular set variables}{http://planetphysics.us/encyclopedia/ChemicalTransformations.html} and variable categories; the latter concepts are generalizations of Anthony Bartholomay's definition of molecular sets, and the consideration of variable categories with structure instead of only the discrete topology of sets. 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.; \htmladdnormallink{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; \htmladdnormallink{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; \htmladdnormallink{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,
\htmladdnormallink{Abstract of Report is here available as a PDF}{http://www.ag.uiuc.edu/fs401/QAuto.pdf} and
\htmladdnormallink{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}).
\htmladdnormallink{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.
\htmladdnormallink{``DNA Molecular Models and Dynamics.''}{http://planetphysics.org/?op=getobj&from=books&id=213}


\end{thebibliography} 

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