Baianu, Professor I.C. and Georgescu, Professor George and Glazebrook, Professor James F. (2010) ŁukasiewiczMoisil ManyValued Logic Algebra of HighlyComplex Systems. [Journal (Paginated)]
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Abstract
A novel approach to selforganizing, highlycomplex systems (HCS), such as living organisms and artificial intelligent systems (AIs), is presented which is relevant to Cognition, Medical Bioinformatics and Computational Neuroscience. Quantum Automata (QAs) were defined in our previous work as generalized, probabilistic automata with quantum state spaces (Baianu, 1971). Their nextstate functions operate through transitions between quantum states defined by the quantum equations of motion in the Schroedinger representation, with both initial and boundary conditions in spacetime. Such quantum automata operate with a quantum logic, or Qlogic, significantly different from either Boolean or Łukasiewicz manyvalued logic. A new theorem is proposed which states that the category of quantum automata and automatahomomorphisms has both limits and colimits. Therefore, both categories of quantum automata and classical automata (sequential machines) are bicomplete. A second new theorem establishes that the standard automata category is a subcategory of the quantum automata category. The quantum automata category has a faithful representation in the category of Generalized (M,R)Systems which are open, dynamic biosystem networks with defined biological relations that represent physiological functions of primordial organisms, single cells and higher organisms.
Item Type:  Journal (Paginated) 

Additional Information:  http://www.edusoft.ro/brain/index.php/brain/article/view/97/201 ISSN: 20673957 
Keywords:  LMalgebraic logic, LMlogic algebras, algebraic category of LMlogic algebras, fundamental theorems of LMlogic algebra, nonlinear genetic networks, nonlinear dynamics, Epigenomics, Cellular Interactomics, Immunology and hormonal regulatory systems, category theory, functors and natural transformations, toposes and Heyting logic algebras, quantum automata categories, limits and colimits, quantum automata homomorphisms, Abelian category, bicomplete categories, Quantum Relational Biology, generalised metabolicreplication, (M,R)systems, complex bionetworks, quantum logic, noncommutative lattices, Hilbert space, quantum computers, computability of complex biological systems, Cartesian closed categories, extended quantum topos, category of groupoids, dynamic realisations of generalised (M,R)systems (GMRs), category of GMRs, compact subsystems of GMR 
Subjects:  Biology > Theoretical Biology Neuroscience > Computational Neuroscience Computer Science > Complexity Theory Computer Science > Dynamical Systems Computer Science > Neural Nets Neuroscience > Neurogenetics Neuroscience > Neural Modelling Neuroscience > Neurophysiology 
ID Code:  7751 
Deposited By:  Baianu, Professor I. C. 
Deposited On:  16 Dec 2011 00:58 
Last Modified:  16 Dec 2011 00:58 
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