35,899 research outputs found
Quantum Genetics, Quantum Automata and Quantum Computation
The concepts of quantum automata and quantum computation are studied in the context of quantum genetics and genetic networks with nonlinear dynamics. In a previous publication (Baianu,1971a) the formal concept of quantum automaton was introduced and its possible implications for genetic 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). 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, Lukasiewicz Logic Algebras that showed significant dissimilarities (Baianu, 1977) from Bolean models of human neural networks (McCullough and Pitts,1945). 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, 1983,2004a). 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. Other possible realizations in Molecular Biology and Relational Biology of Organisms are here suggested in terms of quantum automata models of Quantum Genetics and Interactomics. Future developments of this novel approach are likely to also include: Fuzzy Relations in Biology and Epigenomics, Relational Biology modeling of Complex Immunological and Hormonal regulatory systems, n-categories and Topoi of Lukasiewicz Logic Algebras and Intuitionistic Logic (Heyting) Algebras 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 Lukasiewicz Logic Algebras
On the number of attractors of Boolean automata circuits
In line with fields of theoretical computer science and biology that study Boolean automata networks often seen as models of regulation networks, we present some results concerning the dynamics of networks whose underlying interaction graphs are circuits, that is Boolean automata circuits. In the context of biological regulation, former studies have highlighted the importance of circuits on the asymptotic dynamical behaviour of the biological networks that contain them. Our work focuses on the number of attractors of Boolean automata circuits. We prove how to obtain formally the exact value of the total number of attractors of a circuit of arbitrary size n as well as, for every positive integer p, the number of its attractors of period p depending on whether the circuit has an even or an odd number of inhibitions. As a consequence, we obtain that both numbers depend only on the parity of the number of inhibitions and not on their distribution along the circuit
A Survey on Continuous Time Computations
We provide an overview of theories of continuous time computation. These
theories allow us to understand both the hardness of questions related to
continuous time dynamical systems and the computational power of continuous
time analog models. We survey the existing models, summarizing results, and
point to relevant references in the literature
Model Creation and Equivalence Proofs of Cellular Automata and Artificial Neural Networks
Computational methods and mathematical models have invaded arguably every
scientific discipline forming its own field of research called computational
science. Mathematical models are the theoretical foundation of computational
science. Since Newton's time, differential equations in mathematical models
have been widely and successfully used to describe the macroscopic or global
behaviour of systems. With spatially inhomogeneous, time-varying, local
element-specific, and often non-linear interactions, the dynamics of complex
systems is in contrast more efficiently described by local rules and thus in an
algorithmic and local or microscopic manner. The theory of mathematical
modelling taking into account these characteristics of complex systems has to
be established still. We recently presented a so-called allagmatic method
including a system metamodel to provide a framework for describing, modelling,
simulating, and interpreting complex systems. Implementations of cellular
automata and artificial neural networks were described and created with that
method. Guidance from philosophy were helpful in these first studies focusing
on programming and feasibility. A rigorous mathematical formalism, however, is
still missing. This would not only more precisely describe and define the
system metamodel, it would also further generalise it and with that extend its
reach to formal treatment in applied mathematics and theoretical aspects of
computational science as well as extend its applicability to other mathematical
and computational models such as agent-based models. Here, a mathematical
definition of the system metamodel is provided. Based on the presented
formalism, model creation and equivalence of cellular automata and artificial
neural networks are proved. It thus provides a formal approach for studying the
creation of mathematical models as well as their structural and operational
comparison.Comment: 13 pages, 1 tabl
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