# Complex Non-linear Biodynamics in Categories, Higher Dimensional Algebra and Łukasiewicz–Moisil Topos: Transformations of Neuronal, Genetic and Neoplastic Networks

@article{Bianu2006ComplexNB, title={Complex Non-linear Biodynamics in Categories, Higher Dimensional Algebra and Łukasiewicz–Moisil Topos: Transformations of Neuronal, Genetic and Neoplastic Networks}, author={Ion C. Băianu and R. Brown and George Georgescu and James F. Glazebrook}, journal={Axiomathes}, year={2006}, volume={16}, pages={65-122} }

A categorical, higher dimensional algebra and generalized topos framework for Łukasiewicz–Moisil Algebraic–Logic models of non-linear dynamics in complex functional genomes and cell interactomes is proposed. Łukasiewicz–Moisil Algebraic–Logic models of neural, genetic and neoplastic cell networks, as well as signaling pathways in cells are formulated in terms of non-linear dynamic systems with n-state components that allow for the generalization of previous logical models of both genetic… Expand

#### 34 Citations

N-Valued Logics and Łukasiewicz–Moisil Algebras

- Mathematics
- 2006

AbstractFundamental properties of N-valued logics are compared and eleven theorems are presented for their Logic Algebras, including Łukasiewicz–Moisil Logic Algebras represented in terms of… Expand

A Conceptual Construction of Complexity Levels Theory in Spacetime Categorical Ontology: Non-Abelian Algebraic Topology, Many-Valued Logics and Dynamic Systems

- Computer Science
- 2007

A paradigm shift towards non-commutative, or non-Abelian, theories of highly complex dynamics—which is presently unfolding in physics, mathematics, life and cognitive sciences—may be implemented through realizations of higher dimensional algebras in neurosciences and psychology, as well as in human genomics, bioinformatics and interactomics. Expand

Categorical Ontology of Complex Spacetime Structures: The Emergence of Life and Human Consciousness

- Computer Science
- 2007

The claim is defended in this essay that human consciousness is unique and should be viewed as an ultra-complex, global process of processes. Expand

Quantum Genetics and Quantum Automata Models of Quantum-Molecular Selection Processes Involved in the Evolution of Organisms and Species

- Biology
- 2012

The theoretical framework introduced in this article paves the way to a Quantitative Biology approach to biological evolution at the quantum-molecular, as well as at the organismal and species levels. Expand

Robert Rosen’s Work and Complex
Systems Biology

- Computer Science
- 2006

Complex Systems Biology approaches are here considered from the viewpoint of Robert Rosen’s (M,R)-systems, Relational Biology and Quantum theory, as well as from the standpoint of computer modeling.… Expand

From Simple to Complex and Ultra-complex Systems: A Paradigm Shift Towards Non-Abelian Systems Dynamics

- Psychology
- 2010

Atoms, molecules, organisms distinguish layers of reality because of the causal links that govern their behavior, both horizontally (atom-atom, molecule-molecule, organism-organism) and vertically… Expand

A Non-Abelian, Categorical Ontology of Spacetimes and Quantum Gravity

- Mathematics
- 2007

A non-Abelian, Universal SpaceTime Ontology is introduced in terms of Categories, Functors, Natural Transformations, Higher Dimensional Algebra and the Theory of Levels. A Paradigm shift towards… Expand

Metabolic, Replication and Genomic Category of Systems in Biology, Bioinformatics and Medicine

- Biology
- 2012

Theoreticians of life’s origins postulated that Life on Earth has begun with the simplest possible organism, called the primordial, and mathematicians interested in biology attempted to answer this important question of the minimal living organism by defining the functional relations that would have made life possible in such a minimal system. Expand

files: Acomarev34TAO1pt10 .tex CATEGORICAL ONTOLOGY OF COMPLEX SYSTEMS, META–SYSTEMS AND LEVELS: THE EMERGENCE OF LIFE, HUMAN CONSCIOUSNESS AND SOCIETY

- Psychology
- 2009

The task of developing novel and improved methodological tools for a categorical ontology of complex spacetime structures and the ontological theory of levels is here considered from several… Expand

Category of Metabolic-Replication Systems in Biology and Medicine

- Computer Science
- 2012

Metabolic-repair models, or (M,R)-systems were introduced in Relational Biology by Robert Rosen in terms of categories of sets, deliberately selected without any structure other than the discrete topology of sets. Expand

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