# 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…

## 35 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…

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

- Philosophy
- 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.

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

- Philosophy
- 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.

Robert Rosen’s Work and Complex
Systems Biology

- Philosophy
- 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.…

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

- Biology
- 2010

It is proposed that super-complexity requires at least four different categorical frameworks, provided by the theories of levels of reality, chronotopoids, (generalized) interactions, and anticipation.

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…

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

- Philosophy
- 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…

Category of Metabolic-Replication Systems in Biology and Medicine

- Medicine
- 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.

Integral Biomathics: A Post-Newtonian View into the Logos of Bios (On the New Meaning, Relations and Principles of Life in Science)

- Computer ScienceProgress in biophysics and molecular biology
- 2010

Symetries and asymetries of the immune system response: A categorification approach

- Mathematics2017 IEEE International Conference on Bioinformatics and Biomedicine (BIBM)
- 2017

A new modeling approach and conceptual framework to the immune system response and its dual role with respect to cancer is proposed based on Applied Category Theory, based on Marco Grandis and Rober Paré theory of Intercategories.

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