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This paper is an analytical study of Boolean networks. The motivation is our desire to understand the large, complicated, and interconnected pathways which comprise intracellular biochemical signal transduction networks. The simplest possible conceptual model that mimics signal transduction with sigmoidal kinetics is the n-node Boolean network each of whose(More)
OBJECTIVE To investigate the nature of variability present in time series generated from gait parameters of two different age groups via a nonlinear analysis. DESIGN Measures of nonlinear dynamics were used to compare kinematic parameters between elderly and young females. BACKGROUND Aging may lead to changes in motor variability during walking, which(More)
The complexity of biochemical intracellular signal transduction networks has led to speculation that the high degree of interconnectivity that exists in these networks transforms them into an information processing network. To test this hypothesis directly, a large scale model was created with the logical mechanism of each node described completely to allow(More)
One way of coping with the complexity of biological systems is to use the simplest possible models which are able to reproduce at least some nontrivial features of reality. Although two value Boolean models have a long history in technology, it is perhaps a little bit surprising that they can also represent important features of living organizms. In this(More)
This paper considers a simple Boolean network with N nodes, each node's state at time t being determined by a certain number of parent nodes, which may vary from one node to another. This is an extension of a model studied by Andrecut and Ali [Int. J. Mod. Phys. B 15, 17 (2001)]], who consider the same number of parents for all nodes. We make use of the(More)
This paper considers a simple Boolean network with N nodes, each node's state at time t being determined by a certain number k of parent nodes, which is fixed for all nodes. The nodes, with randomly assigned neighborhoods, are updated based on various asynchronous schemes. We make use of a Boolean rule that is a generalization of rule 126 of elementary(More)
Here we propose six open problems in dynamical systems and chaos theory. The first open problem is concern with rigorous proof of a collection of quadratic ODE systems being non-chaotic. The second problem is for a universal definition of non-chaotic solutions. The third problem is about the number of systems that can have chaotic solutions when the right(More)
In this paper we apply Theorem 2.1 in [Heidel J, Zhang F. Nonchaotic and chaotic behaviour in the three-dimensional quadratic systems: five-one conservative cases, in press] to some simple chaotic jerk functions listed in [Sprott JC. Simple chaotic systems and circuits. Am J Phys 2000;68(8):758–63; Sprott JC. Algebraically simple chaotic flows. Int J Chaos(More)
Dynamic Spread of Social Behavior in Boolean Networks Elizabeth Ball, M.A. University of Nebraska, 2011 Advisor: Dora Matache, Ph.D. A variety of systems evolve towards achieving a global organization or coordination without a centralized process or control. As the systems evolve they tend to reach a certain level of harmony and may exhibit a significant(More)