Robert E. Lee DeVille

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Implants used for joint replacement are often cemented into place to increase stability. As the person ambulates, the implanted materials slide against each other producing small wear debris particles. There is increasing evidence that wear debris particles that are present in periprosthetic tissues have direct effects on osteoblasts. Particles resulting(More)
For large distributed systems built from inexpensive components, one expects to see incessant failures. This paper proposes two models for such faults and analyzes two well-known self-stabilizing algorithms under these fault models. For a small number of processes, the properties of interest are verified automatically using probabilistic model-checking(More)
We study the largest Lyapunov exponent of the response of a two dimensional non-Hamiltonian system driven by additive white noise. The specific system we consider is the third-order truncated normal form of the unfolding of a Hopf bifurcation. We show that in the small-noise limit the top Lyapunov exponent always approaches zero from below (and is thus(More)
For singular perturbation problems, the renormalization group (RG) method of Chen, Goldenfeld, and Oono has been shown to be an effective general approach. It has been applied to a variety of problems traditionally analyzed using disparate methods, including the method of multiple scales, boundary layer theory, the WKBJ method, the PoincareLindstedt method,(More)
We develop a new framework for the study of complex continuous time dynamical systems based on viewing them as collections of interacting control modules. This framework is inspired by and builds upon the groupoid formalism of Golubitsky, Stewart and their collaborators. Our approach uses the tools and—more importantly—the stance of category theory. This(More)
We study the size of the range of the derivatives of a smooth function between Banach spaces. We establish conditions on a pair of Banach spaces X and Y to ensure the existence of a C smooth (Fréchet smooth or a continuous Gâteaux smooth) function f from X onto Y such that f vanishes outside a bounded set and all the derivatives of f are surjections. In(More)
In this paper, we note a connection between number theory and dynamical systems, in that we will show an object which is associated to a given family of analytic maps also has an interesting number theoretic property. It was shown in [DeV01] that there is a set of irrational numbers which are associated with the complex exponential family λe. We will show(More)
We consider neuronal network models with plasticity and randomness; we show that complicated global structures can evolve even in the presence of simple local update rules. Our models are discrete in time and our analysis uses tools from the theory of Markov chains. Specifically, we propose a discrete-time model of the evolution of a neuronal network(More)