With big science projects like the human genome project, [2], and preliminary
attempts to seriously study brain activity, e.g. [9], mathematical biology
has come of age, employing formalisms and tools from most branches of
mathematics.
Recent results, [51] and [53], have extended the relational (or categorical)
approach of Rosen [44], to demonstrate that (in a very general class of systems)
cellular self-organization/self-replication is implicit in metabolism and
repair/stability. This is a powerful philosophical statement and removes the
need of teleological argument. However, the result carries a technical limitation
to Cartesian closed categories, which excludes many mathematical
languages.
We review the relevant literature on metabolic-repair pathways, category
theory and systems theory, before performing a critique of this work. We
find that the restriction to Cartesian closed categories is purely for simplicity,
and describe how equivalent arguments may be built for monoidal closed
categories. Moreover, any symmetric monoidal category may be "embedded"
in a closed one. We discuss how these constructions/techniques provide the
formal structure to treat self-organization/self-replication in most contemporary
mathematical (modelling) languages. These results signicantly soften
the impact on current modelling paradigms while extending the philosophical
implications. / Thesis (M.Sc.)-University of KwaZulu-Natal, Durban, 2012.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:ukzn/oai:http://researchspace.ukzn.ac.za:10413/10617 |
| Date | 23 April 2014 |
| Creators | Songa, Maurine Atieno. |
| Contributors | Banasiak, Jacek., Amery, Gareth. |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | English |
| Type | Thesis |
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