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Integral representations provide a useful framework of study and simulation of fractional Browian motion, which has been used in modeling of many natural situations. In this thesis we extend an integral representation of fractional Brownian motion that is supported on a bounded interval of ℝ to integral representation that is supported on bounded subset of ℝ[superscript d]. These in turn can be used to give new series representations of fractional Brownian motion. / Graduation date: 2013

Nanoscale biological systems operate in the presence of overwhelming viscous drag and thermal diffusion, thus invalidating the use of macroscopically oriented thinking to explain such systems. Rectified Brownian motion (RBM), in contrast, is a distinctly nanoscale approach that thrives in thermal environments. The thesis discusses both the foundations and applications of RBM, with an emphasis on nano-biology. Results from stochastic non-equilibrium steady state theory are used to motivate a compelling definition for RBM. It follows that RBM is distinct from both the so-called power stroke and Brownian ratchet approaches to nanoscale mechanisms. Several physical examples provide a concrete foundation for these theoretical arguments. Notably, the molecular motors kinesin and myosin V are proposed to function by means of a novel RBM mechanism: strain-induced bias amplification. The conclusion is reached that RBM is a versatile and robust approach to nanoscale biology.

Thesis (M.S. in Electrical Engineering)--Naval Postgraduate School, March 2004. / Thesis advisor(s): Murali Tummala, Roberto Cristi. Includes bibliographical references (p. 127-129). Also available online.

This thesis discusses the efficient and accurate generation of self-similar traffic for ATM networks. ATM networks have been developed to carry multiple service categories. Since the traffic on a number of existing networks is bursty, much research focuses on how to capture the characteristics of traffic to reduce the impact of burstiness. Conventional traffic models do not represent the characteristics of burstiness well, but self-similar traffic models provide a closer approximation. Self-similar traffic models have two fundamental properties, long-range dependence and infinite variance, which have been found in a large number of measurements of real traffic. Therefore, generation of self-similar traffic is vital for the accurate simulation of ATM networks. The main starting point for self-similar traffic generation is the production of fractional Brownian motion (FBM) or fractional Gaussian noise (FGN). In this thesis six algorithms are brought together so that their efficiency and accuracy can be assessed. It is shown that the discrete FGN (dPGN) algorithm and the Weierstrass-Mandelbrot (WM) function are the best in terms of accuracy while the random midpoint displacement (RMD) algorithm, successive random addition (SRA) algorithm, and the WM function are superior in terms of efficiency. Three hybrid approaches are suggested to overcome the inefficiency or inaccuracy of the six algorithms. The combination of the dFGN and RMD algorithm was found to be the best in that it can generate accurate samples efficiently and on-the-fly. After generating FBM sample traces, a further transformation needs to be conducted with either the marginal distribution model or the storage model to produce self-similar traffic. The storage model is a better transformation because it provides a more rigorous mathematical derivation and interpretation of physical meaning. The suitability of using selected Hurst estimators, the rescaled adjusted range (R/S) statistic, the variance-time (VT) plot, and Whittle's approximate maximum likelihood estimator (MLE), is also covered. Whittle's MLE is the better estimator, the R/S statistic can only be used as a reference, and the VT plot might misrepresent the actual Hurst value. An improved method for the generation of self-similar traces and their conversion to traffic has been proposed. This, combined with the identification of reliable methods for the estimators of the Hurst parameter, significantly advances the use of self-similar traffic models in ATM network simulation.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1984. / Typescript. Vita. Includes bibliographical references.

Thesis--University of Wisconsin--Madison. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 126-128).

Thesis (Ph. D.)--University of Wisconsin--Madison, 1984. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 191-197).

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