TY - GEN
N1 - It is often assumed incorrectly that Quantum Computation was introduced in 1982 and that Quantum Automata were introduced in 1997. Actually, the formal concepts of Quantum Automata and Quantum Computation were introduced in 1971, in relation to Quantum Genetics (Rosen, 1960) in a paper published in the Bulletin of Mathematical Biophysics, 33:339-354 (Baianu, 1971a). There are also numerous citations of Quantum Automata papers printed in the late 80?s and also recent quantum computation textbooks that fail to report the first introduction of the concepts of ?quantum automaton? and
?quantum computation?. Categorical computations, both algebraic and topological, were also introduced in 1971 (Baianu, 1971b) that propose to employ symbolic programming for adjoint functor pairs in the theory of categories, functors and natural transformations (Baianu, 1971b). The notions of topological semigroup, quantum automaton, or computer, were then suggested for applications and modeling, with a view to their potential applications to the analogous simulation of biological systems, and especially genetic activities and nonlinear dynamics in genetic networks. Further, detailed studies of nonlinear dynamics in genetic networks were carried out in categories of n-valued, Lukasiewicz Logic Algebras that showed significant dissimilarities (Baianu, 1977) from Boolean models of human neural networks (McCullough and Pitts,1943). Further, detailed studies of nonlinear dynamics in genetic networks were carried out in categories of n-valued, Lukasiewicz Logic Algebras that showed significant dissimilarities (Baianu, 1977; 2004a; Baianu et al, 2004b) from Boolean models of human neural networks (McCullough and Pitts, 1943).
ID - cogprints3697
UR - http://cogprints.org/3697/
A1 - Baianu, Professor I.C.
TI - Quantum Genetics in terms of Quantum Reversible Automata and
Quantum Computation of Genetic Codes and Reverse Transcription
Y1 - 2004/06//
N2 - The concepts of quantum automata and quantum computation are studied in the context of quantum genetics and genetic networks with nonlinear dynamics. In previous publications (Baianu,1971a, b) the formal concept of quantum automaton and quantum computation, respectively, were introduced and their possible implications for genetic processes and metabolic activities in living cells and organisms were considered. This was followed by a report on quantum and abstract, symbolic computation based on the theory of categories, functors and natural transformations (Baianu,1971b; 1977; 1987; 2004; Baianu et al, 2004). The notions of topological semigroup, quantum automaton, or quantum computer, were then suggested with a view to their potential applications to the analogous simulation of biological systems, and especially genetic activities and nonlinear dynamics in genetic networks. Further, detailed studies of nonlinear dynamics in genetic networks were carried out in categories of n-valued, ?ukasiewicz Logic Algebras that showed significant dissimilarities (Baianu, 1977; 2004a; Baianu et al, 2004b) from Boolean models of human neural networks (McCullough and Pitts, 1943). Molecular models in terms of categories, functors and natural transformations were then formulated for uni-molecular chemical transformations, multi-molecular chemical and biochemical transformations (Baianu, 1983, 1987, 2004a). Previous applications of computer modeling, classical automata theory, and relational biology to molecular biology, oncogenesis and medicine were extensively reviewed and several important conclusions were reached regarding both the potential and limitations of the computation-assisted modeling of biological systems, and especially complex organisms such as Homo sapiens sapiens (Baianu,1987). Novel approaches to solving the realization problems of Relational Biology models in Complex System Biology are introduced in terms of natural transformations between functors of such molecular categories. Several applications of such natural transformations of functors were then presented to protein biosynthesis, embryogenesis and nuclear transplant experiments. Topoi of ?ukasiewicz Logic Algebras and Intuitionistic Logic (Heyting) Algebras are being considered for modeling nonlinear dynamics and cognitive processes in complex neural networks that are present in the human brain, as well as stochastic modeling of genetic networks in ?ukasiewicz Logic Algebras.
AV - public
KW - Automata Theory/ Sequential Machines
KW - Bioinformatics
KW - Complex Biological Systems
KW - Complex Systems Biology
KW - Computer Simulations and Modeling
KW - Dynamical Systems
KW - Quantum Dynamics
KW - Quantum Field Theory
KW - Quantum Groups
KW - Topological Quantum Field Theory (TQFT)
KW - Quantum Automata
KW - Cognitive Systems
KW - Graph Transformations
KW - Logic
KW - Mathematical Modeling; applications of the Theory of Categories
KW - Functors and Natural Transformations; pushouts
KW - pullbacks
KW - presheaves
KW - sheaves
KW - Categories of sheaves
KW - Topos
KW - n-valued Logic
KW - N-categories/ higher dimensional algebra
KW - Homotopy theory;apllications to physical theories
KW - quantum gravity
KW - complex systems biology
KW - bioengineering
KW - informatics
KW - Bioinformatics
KW - Computer simulations
KW - Mathematical Biology of complex systems and phenomena in various types of Dynamical Systems; bioengineering
KW - Computing
KW - Neurosciences
KW - Bioinformatics
KW - biological and/or social networks; quantitative ecology and quantitative biology/
ER -