Lattices and lattice-valued relations in biology |
| |
Authors: | M W Warner |
| |
Institution: | (1) Department of Mathematics, The City University, London, UK |
| |
Abstract: | Rashevsky's treatment of general binary relations between sets of biological elements is extended using the novel mathematical
concept of lattice-valued relation (l.v.r.). This yields a quantitative measure of the strength of the relations between components
of a biological organism, and some illustrative examples are given. Specific l.v.r.'s are used to define (more precisely than
in Rashevsky's preliminary theory of binary relations) the biologically important relationships amongst hormones, metabolism
and energy exchange involved in metabolic reactions. The ‘strongest link’ between the set of hormones and the set of metabolic
reactions is quantified using a special l.v.r., and other specific biological realisations of lattice-valued relations in
abstract-relational biology are presented. L.v.r.'s may also be regarded as a form ofG-relation in relational biology, or as a particular case of generating diagrams. Further possible developments of this approach,
using more complex tools of the newly developed mathematical theory of lattice-valued relations, such as function space l.v.r.,
group l.v.r., l.v.r. morphisms, l.v.r. homology andn-ary l.v.r.'s are suggested. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|