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

===Highly-complex systems=== Modeling the emergence of the ultra-complex system of the ...

.../SimilarityAndAnalogousSystemsDynamicAdjointnessAndTopologicalEquivalence/|systems]]. ...alDiagramsDefinedByFunctors/|categorical diagrams]] the emergence of ultra-complex ...

...sAndTopologicalEquivalence/|systems]], as well as complex or super-complex systems (biodynamics). ...Subsequently, a complex class of categorical, dynamic <math>(M,R)</math>--systems representing the categorical dynamics involved in metabolic--replication pr ...

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

...of the axioms in ETAS- a natural extension of Lawvere's <math>elementary\; theory\; of \; abstract \; categories</math> ([[../ETACAxioms/|ETAC]]) to [[../Abe dimensional algebra applications to [[../SystemsBiology/|complex systems biology]] (<ref name='Bgg2'/>, <ref name='BBGG1'/> and references cited the ...

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

...estrictive. It turns out however that the categories of <math>(M,R)</math>-systems are "Cartesian closed'' , and may be considered in a very strict mathematic ...cation systems-- when extended to generalized, variable <math>(M,R)</math>-systems-- that were endowed with unique [[../CoIntersections/|algebraic]] and varia ...

...rAlgebra4/|operators]] #[[../CosmologicalConstant/|Algebraic Quantum Field Theory]] #[[../TriangulationMethodsForQuantizedSpacetimes2/|Quantum Algebraic Topo #Conformal Map theory (CMT) ...

.../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. Ma ...

.../SimilarityAndAnalogousSystemsDynamicAdjointnessAndTopologicalEquivalence/|systems]], or living organisms are characterized by relational structures and their ...ete topology of sets. Further details concerning mathematical, logical and complex modeling are provided in the following list of publications and related web ...

...<math>S_0</math> in the simpler, Rashevsky's [[../TheoryOfOrganismicSets/|theory of organismic sets]]. ...ographyOfCategoryTheory.html [14] to [34] in the "bibliography of category theory and algebraic topology"] ...

===Dynamic Adjointness, Similarity and Analogous Systems.=== #''Comparing Systems: Similarity [[../Bijective/|relations]]''; ...

...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 ...

===Metabolic-Replication Systems=== ...ologicalEquivalence/|systems]] will be here abbreviated as <math>MR</math>-systems, (or simply <math>MR</math>'s). Rosen, then represented the <math>MR</math> ...

.../SimilarityAndAnalogousSystemsDynamicAdjointnessAndTopologicalEquivalence/|systems]] and societies. ...bras]] ([[../2Groupoid2/|HDA]]). Therefore, [[../TrivialGroupoid/|category theory]] in higher dimensions/HDA ...

...Predicate/|proposition]] that is neither proven nor demonstrated (within a theory) "but considered to be self-evident"; furthermore, the choice of an axiom o *Axioms of Set theory ...

...e system's environment, or as a [[../SuperCategory6/|supercategory]] for a complex system consisting of subsystems, or components, with internal boundaries am ...r-system'' of (sub)systems, as it is the case of ''emergent super-complex systems'' or organisms). ...

...ex analysis, functional analysis, partial differential equations, Lebesgue theory, calculus on manifolds, and the integration of differential forms. Our course begins with some fundamental observations about other number systems that we have dealt with in the past. ...

# Statistical Mechanics of Interacting Particle Systems ...y-Electron Systems, Hartree-Fock Approximation|Properties of Many-Electron Systems, Hartree-Fock Approximation]]</li> ...