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==Complex Systems Biophysics== ''Complex Systems Biophysics (<math>CSB</math>)'' or ...

This is a contributed new topic on [[../PhysicalMathematics2/|mathematical physics]], physical mathematics, and their various applications in: enginee ===Mathematical Physics and Physical Mathematics=== ...

==Parallel replacement systems== ...Salomaa's book<ref name="Salomaa">Arto Salomaa, Jewels in Formal Language Theory, Computer Science Press 1981</ref>. ...

.../SimilarityAndAnalogousSystemsDynamicAdjointnessAndTopologicalEquivalence/|systems]] in terms of molecular sets that vary with time (or <math>msv</math>'s, an Bartholomay, A. F.: 1960. Molecular Set Theory. A mathematical representation for chemical reaction mechanisms. ''Bull. Math. Biophys.'' , ...

.../SimilarityAndAnalogousSystemsDynamicAdjointnessAndTopologicalEquivalence/|systems]] with [[../NewtonianMechanics/|dynamics]] that is not reducible to that of ...he operational logics underlying super-complex [[../GeneralDynamicSystems/|systems dynamics]] ...

...>-systems are "Cartesian closed'' , and may be considered in a very strict mathematical sense as subcategories of the category of [[../AAT/|sequential machines]] o ...cation systems-- when extended to generalized, variable <math>(M,R)</math>-systems-- that were endowed with unique [[../CoIntersections/|algebraic]] and varia ...

...-Grothendieck Lemma and construction, or they can be directly derived by a mathematical interpretation of the first ten axioms of [[../ETACAxioms/|ETAS]], plus two ...instead of only the discrete topology of sets. Further details concerning mathematical, logical and complex modeling are provided in the following list of publica ...

...ation at different hierarchical (that is, lattice-like) levels by means of mathematical sets. The first example is that of an ''\htmladdnormallink{organismic set'' ...ogy]]. ''First order organismic sets'' , <math>S_1</math>, are then simple mathematical models of single cells in terms of both genetic (modeled by <math>S_0</math ...

\section{Topic on axioms in mathematics, logic algebra, mathematical physics and mathematical biophysics} ...

This topic entry introduces one of the most general mathematical models of living organisms ...of the axioms in ETAS- a natural extension of Lawvere's <math>elementary\; theory\; of \; abstract \; categories</math> ([[../ETACAxioms/|ETAC]]) to [[../Abe ...

.../SimilarityAndAnalogousSystemsDynamicAdjointnessAndTopologicalEquivalence/|systems]]. ...nted by Rosetta biogroupoids, together with the complex--albeit inanimate--systems with chaos. With the emergence of the ultra-complex system of the human min ...

===Organismic Set Theory and Relational Biology=== [[../NicolasRashevsky/|Nicolas Rashevsky]] defined the mathematical [[../PreciseIdea/|concept]] of ''[[../RSystemsCategory/|organismic sets]]'' ...

...hematicalFoundationsOfQuantumTheories/|mathematical foundations of quantum theory]] in physics was also closely involved with the design and building of the #Accelerator design and operational theory ...

...emsBiology/|abstract relational biology]] and its close connections to the theory of [[../Cod/|categories]], especially the concrete and abstract categories ...Nicolas Rashevsky]] were based on set theory, [[../Molecule/|molecular set theory]], and the classical logic of [[../Predicate/|predicates]] and logical prop ...

...networks'' , <math>GN</math> -- that form a living organism's genome --are mathematical models of functional genes linked through their non-linear, [[../NewtonianM ...] see, for example, ref. <ref name='ICBetal2k6'/>. Most, but not all, such mathematical models are Bayesian, and therefore involve computations for random networks ...

and other relevant mathematical [[../PreciseIdea/|concepts]] utilized to represent [[../CosmologicalConstan ===Fundamental, mathematical concepts in quantum field theory === ...

===Organismic Set Theory and Relational Biology=== .../SimilarityAndAnalogousSystemsDynamicAdjointnessAndTopologicalEquivalence/|systems]] and Ecology. ...

...d for outstanding, exceptional [[../Work/|work]] by living mathematicians, mathematical physicists or theoretical physicists. The Niels Henrik Abel (1802--1829) Me ...Prize recognizes contributions of extraordinary depth and influence to the mathematical sciences and has been awarded annually since 2003. It carries a cash award ...

...n(1987) showed that complex [[../ContinuousGroupoidHomomorphism/|dynamical systems]], dynamical systems can be thus numerically simulated. ...

.... In all of these uses it is understood that the various terms refer to a mathematical object and not the corresponding sign or syntactic expression. * Kohavi, Zvi (1978), ''Switching and Finite Automata Theory'', 1st edition, McGraw–Hill, 1970. 2nd edition, McGraw–Hill, 1978. ...