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2009. Categorical Ontology of Complex Systems, Metalevels and levels: The Emergence of life
 Human Consciousness and Society’. In: “Theory and Applications of Ontology.” vol.1
"... Relational structures of organisms and the human mind are naturally represented in terms of novel variable topology concepts, nonAbelian categories and Higher Dimensional Algebra – relatively new concepts that would be defined in this tutorial paper. A unifying theme of localtoglobal approaches ..."
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Relational structures of organisms and the human mind are naturally represented in terms of novel variable topology concepts, nonAbelian categories and Higher Dimensional Algebra – relatively new concepts that would be defined in this tutorial paper. A unifying theme of localtoglobal approaches to organismic development, evolution and human consciousness leads to novel patterns of relations that emerge in super and ultra complex systems in terms of compositions of local procedures [1]. The claim is defended in this paper that human consciousness is unique and should be viewed as an ultracomplex, global process of processes, at a metalevel not sub–summed by, but compatible with, human brain dynamics [2][5]. The emergence of consciousness and its existence are considered to be dependent upon an extremely complex structural and functional unit with an asymmetric network topology and connectivities–the human brain. However, the appearance of human consciousness is shown to be critically dependent upon societal coevolution, elaborate languagesymbolic communication and ‘virtual’, higher dimensional, non–commutative processes
Bioinformatics and Medicine
, 2012
"... Robert Rosen introduced metabolicrepair models, or (M,R)systems in mathematical biology (abstract relational biology) in 1957 ([4,5]); such systems will be here abbreviated assystems, (or simply 's). ..."
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Robert Rosen introduced metabolicrepair models, or (M,R)systems in mathematical biology (abstract relational biology) in 1957 ([4,5]); such systems will be here abbreviated assystems, (or simply 's).
Quantum Genetics in terms of Quantum Reversible Automata and Quantum Computation of Genetic Codes and Reverse Transcription
"... 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 po ..."
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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 nvalued, Łukasiewicz 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
Copyright © I.C. Baianu, 2004. Bulletin of Mathematical Biophysics, 33:349365 (1971). ORGANISMIC SUPERCATEGORIES AND QUALITATIVE DYNAMICS OF SYSTEMS
"... The representation of biological systems by means of organismic supercategories, developed in previous papers, is further discussed. The different approaches to relational biology, developed by Rashevsky, Rosen and by Baianu and Marinescu, are compared with Qualitative Dynamics of Systems which was ..."
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The representation of biological systems by means of organismic supercategories, developed in previous papers, is further discussed. The different approaches to relational biology, developed by Rashevsky, Rosen and by Baianu and Marinescu, are compared with Qualitative Dynamics of Systems which was initiated by Henri Poincaré (1881). On the basis of this comparison some concrete results concerning dynamics of genetic system, development, fertilization, regeneration, dynamic system analogies, and oncogenesis are derived. 1. Introduction. In previous papers (Baianu and Marinescu, 1968; Comorozan and Baianu, 1969; Baianu, 1970; herein afterwards referred to as I, II, III, respectively), a categorical representation of biological systems was introduced. This representation is different from Rosen's categorical approach to relational biology (Rosen 1958a, b; 1959). The aim of this paper is to present some concrete results which are derived on the basis of our
COMPLEX NONLINEAR BIODYNAMICS IN CATEGORIES, HIGHER DIMENSIONAL ALGEBRA AND ŁUKASIEWICZ– MOISIL TOPOS: TRANSFORMATIONS OF NEURONAL,
"... ABSTRACT. A categorical, higher dimensional algebra and generalized topos framework for Łukasiewicz–Moisil Algebraic–Logic models of nonlinear dynamics in complex functional genomes and cell interactomes is proposed. Łukasiewicz– Moisil Algebraic–Logic models of neural, genetic and neoplastic cell ..."
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ABSTRACT. A categorical, higher dimensional algebra and generalized topos framework for Łukasiewicz–Moisil Algebraic–Logic models of nonlinear 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 nonlinear dynamic systems with nstate components that allow for the generalization of previous logical models of both genetic activities and neural networks. An algebraic formulation of variable ‘nextstate functions ’ is extended to a Łukasiewicz–Moisil Topos with an nvalued Łukasiewicz–Moisil Algebraic Logic subobject classifier description that represents nonrandom and nonlinear network activities as well as their transformations in developmental processes and carcinogenesis. The unification of the theories of organismic sets, molecular sets and Robert Rosen’s (M,R)systems is also considered here in terms of natural transformations of organismal structures which generate higher dimensional algebras based on consistent axioms, thus avoiding well known logical paradoxes occurring with sets. Quantum bionetworks, such as quantum neural nets and quantum genetic networks, are also discussed and their underlying, noncommutative quantum logics are considered in the context of an emerging Quantum Relational Biology. KEY WORDS: adjoint functors and dynamically analogous systems, biogroupoids and organismal development, biological principles, nuclear equivalence and cell differentiation, categories, nvalued logics and higher dimensional algebra in neuroscience and genetics, cognitive and anticipatory processes, learning and quantum wavepattern recognition, colimits, limits and adjointness relations in biology, generalized (M,R)systems, neurocategories and consciousness, quantum automata and relational biology, quantum bionetworks and their underlying quantum logics, quantum computers 1.
Copyright IC Baianu. COMPUTER MODELS AND AUTOMATA THEORY IN BIOLOGY AND MEDICINE: COMPUTER SIMULATION AND COMPUTABILITY OF BIOLOGICAL SYSTEMS
, 1985
"... The ability to simulate a biological organism by employing a computer is related to the ability of the computer to calculate the behavior of such a dynamical system, or the "computability " of the system. * However, the two questions of computability and simulation are not equivale ..."
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The ability to simulate a biological organism by employing a computer is related to the ability of the computer to calculate the behavior of such a dynamical system, or the &quot;computability &quot; of the system. * However, the two questions of computability and simulation are not equivalent. Since the question of computability can be given a precise answer in terms of recursive functions, automata theory and dynamical systems, it will be appropriate to consider it first. The more elusive question of adequate simulation of biological systems by a computer will be then addressed and a possible connection between the two answers given will be considered. A. Are biological systems recursively computable? An answer to this question was recently given by Conrad and Rössler [219] who showed that although a system can be computation universal it may not be effectively programmable if its translator has &quot;chaotic &quot; dynamics; such chaotic dynamics were encountered in certain models of biomolecular reaction kinetics [220]. At this point, let us introduce the concepts of recursive function, recursive computer, computation and program in order to be able to formally discuss recursive computability of a system, be it biological or nonbiological. A function is called recursive if there is an effective procedure, or computation, for calculating it (p. 211 in Ref. [155]). * The contributions made to this section by an anonymous referee are gratefully acknowledged. 1 A recursive computer C [155] on the alphabet Y is a partial recursive function fc: Y b → Y b. Q = Y b is called the set of complete states of C. (The qualifier &quot;partial &quot; refers to the fact that the recursive function may not be defined for all its values.) If at an instant t the computer has n registers, the jth register containing the word Yj, one can say that the complete state of the computer is the word Y1b...bYn of Q; also if the state of the computer C is ξ ∈Q
HUMAN CONSCIOUSNESS AND ARTIFICIAL INTELLIGENCE
"... In this monograph we present a novel approach to the problems raised by higher complexity in both nature and the human society, by considering the most complex levels of objective existence as ontological metalevels, such as those present in the creative human minds and civilised, modern societies. ..."
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In this monograph we present a novel approach to the problems raised by higher complexity in both nature and the human society, by considering the most complex levels of objective existence as ontological metalevels, such as those present in the creative human minds and civilised, modern societies. Thus, a ‘theory ’ about theories is called a ‘metatheory’. In the same sense that a statement about propositions is a higherlevel 〈proposition 〉 rather than a simple proposition, a global process of subprocesses is a metaprocess, and the emergence of higher levels of reality via such metaprocesses results in the objective existence of ontological metalevels. The new concepts suggested for understanding the emergence and evolution of life, as well as human consciousness, are in terms of globalisation of multiple, underlying processes into the metalevels of their existence. Such concepts are also useful in computer aided ontology and computer science [1],[194],[197]. The selected approach for our broad– but also indepth – study of the fundamental, relational structures and functions present in living, higher organisms and of the extremely complex processes and metaprocesses of the human mind combines new concepts from three recently developed, related mathematical fields: Algebraic Topology (AT), Category Theory (CT) and Higher Dimensional Algebra
FROM SIMPLE TO HIGHLYCOMPLEX SYSTEMS: A PARADIGM SHIFT TOWARDS NONABELIAN EMERGENT SYSTEM DYNAMICS AND METALEVELS
"... Abstract. The evolution of nonlinear dynamical system theory and supercomplex systems–that are defined by classes of variable topologies and their associated transformations–is presented from a categorial and generalised, or extended topos viewpoint. A generalisation of dynamical systems, general ..."
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Abstract. The evolution of nonlinear dynamical system theory and supercomplex systems–that are defined by classes of variable topologies and their associated transformations–is presented from a categorial and generalised, or extended topos viewpoint. A generalisation of dynamical systems, general systems theory is then considered for the metalevel dynamical systems with variable topology and variable phase space, within the framework of an “universal”, or generalised Topos–a logicomathematical construction that covers both the commutative and noncommutative structures based on logic classifiers that are multivalued (MV) logic algebras. The extended topos concept was previously developed in conjunction with dynamic networks that were shown to be relevant to Complex Systems Biology. In so doing, we shall distinguish three major phases in the development of systems theory (two already completed and one currently unfolding). The three phases will be respectively called The Age of Equilibrium, The Age of Complexity and The Age of SuperComplexity. The first two may be taken as lasting from approximately 1850 to 1960, and the third which is now rapidly developing in applications to various types of systems after it began in the 1970s after the works of Rosen, Maturana and others. The mathematical theory of categories–which began in the 1940s [44],[45] with a seminal paper by Eilenberg and Mac Lane in 1945 [45] – is an unifying trend in modern mathematics [40], and has proved especially suitable for modeling the novelties raised by the third phase of systems ’ theory, which became associated with applications to system supercomplexity problems in the late 1950s and 70s [84][85],[2],[6],[8], [88][89]; it was continued by applications to logical programming involving categorical logic in computer science [58] , as well as the categorical foundations of mathematics [59][60].