Lattices due to increasing low energy relational processes
The problem is how two parts in biology qualitatively -- and algebraically -- interact producing an enhancement of complexity. This interaction is seen through the atoms of a lattice, whose order was defined by a constructive relational process which corresponds with increasing energies from element 0 to element 1. The paper is devoted to obtain how the lattices -- and their algebras -- change because of the complexity changes, and also which is the ordination of these algebraic structures when the energy values imposed on one of the atoms increase. In addition, different responses derived from each lattice structure also correlate with increasing energy values. Relationships among lattices and energy values concerning with appeared from the algebraic relational theory [see \textit{C. A. Leguizamón}, Bull. Math., Biol. 37, 565-572 (1975; Zbl 0318.92009)]. Because their abstract mathematical elements are defined in terms of concrete concepts used in biology, the present developments are very useful to distinguish when -- in energy terms -- an algebra is given; and as a consequence, which behaviors appear from the processes.
scientific article; zbMATH DE number 1067132