Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1990. / Vita. Abstract. Includes bibliographical references (leaves 82-88). Also available via the Internet.

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Thesis (M.S.)--Rochester Institute of Technology, 1983. / Typescript. Includes bibliographical references (leaves 313-316).

Thesis (Ph. D.)--Ohio University, June, 1998. / Title from PDF t.p.

In many situations in the world, the amount of resources available for use is limited. This statement is especially true in the cells of living organisms. During the translation process in protein synthesis, ribosomes move along the mRNA strand constructing proteins based on the sequence of codons that form a gene. The totally asymmetric simple exclusion process (TASEP) models well the translation process. However, these genes are constantly competing for ribosomes and other resources in the cell. To see how finite resources and competition affects such a system, we must construct a simple model to account for the limited resources. We consider coupling multiple TASEPs to a finite reservoir of particles where the entry rate of particles into the TASEPs depends on the number of particles left in the reservoir. Starting with a single TASEP connected to the reservoir, we study the system using both Monte Carlo simulations and theoretical approaches. We explore how the average overall density, density profile, and current change as a function of the number of particles initially in the reservoir for various parameters. New features arise not seen in the ordinary TASEP model, even for a single TASEP connected to the pool of particles. These features include a localized shock in the density profile. To explain what is seen in the simulations, we use an appropriately generalized version of a domain wall theory. The dynamics of the TASEPs with finite resources are also studied through the power spectra associated with the total particle occupancy of each TASEP and the reservoir. Again, we find new phenomena not seen in the power spectrum of the ordinary TASEP. For a single constrained TASEP, we find a suppression at low frequencies when compared to the power spectrum of the ordinary TASEP. The severity of this suppression is found to depend on how the entry rate changes with respect to the number of particles in the pool. For two TASEPs of different lengths, we find an enhancement of the power spectrum of the smaller TASEP when compared to the ordinary TASEP's power spectrum. We explain these findings using a linearized Langevin equation. Finally, we model competition between ten genes found in Escherichia coli using a modified version of the TASEP. This modified version includes extended objects and inhomogeneous internal hopping rates. We use the insight gained from the previous studies of finite resources and competition as well as other studies to gain some insight into how competition affects protein production. / Ph. D.

This study has been concerned specifically with the problem of estimating the power spectrum associated with a random process. It has shown how the power spectral density function φ(ω) can be used to specify completely a stationary Gaussian process. Estimation of this function is therefore one of the fundamental problems in random time-series. The power spectral density function is given by φ(ω) = [2/π] ∫₀^+∞ ρ(τ)cos ωτ dτ And must be estimated from a partial realization of the process. To accomplish this, the usual procedure is to use estimated auto-covariance functions ρ̂(τ), computed from a set of observations X(t_i) from which φ(ω) is approximated by numerical integration. This gives φ̂(ω) = 1/W [ρ̂(0)+2∑_j=1^m-1 ρ̂[jπ/W]cos(ωjπ/W) + ρ̂[mπ/W]cos(ωmπ/W)] where the ρ[jπ/W]’s are estimated from ρ̂[jπ/W] = (1/n)∑_i=1ⁿX(t_i)X(t_i + jπ/W) j = 0, 1, …, m. φ̂(ω_α) is widely used in power spectral analysis and although it can be shown to be biased, the side lobes of its spectral window can be soothed in such a way that the bias is greatly reduced. The difficulty with the estimator is not so much with its bias, but rather with the considerable numerical task it creates even when digital computing equipment is available. The primary objective of this research was to devise an estimator which would simulate the bias of the classical estimator φ̂(ω_α) but which would require much less work to compute. To this end the randomizes estimator φ*(ω_α) = (1/n)_i=1ⁿ X(t_i)X(t_i + k_iΔt)G_α(k_i) was considered. Unlike φ̂(ω_α) which was constructed by systematically forming all possible lagged products X(t_i)X(t_i + k_iΔt), i=1, 2, …, n and k=0, 1, …, m , the new estimator utilizes a random subsample of lagged products. This is made possible by choosing the k_i at random. The weighting function G_α(k_i) is determined in such a way that the bias of φ*(ω_α) is the same as the bias of φ̂(ω_α). As would be expected, the sampling variance of φ*(ω_α) is larger than the variance of φ̂(ω_α), since φ*(ω_a) is based on considerably fewer points. It was discovered, however, that the variance of φ*(ω_α) was affected by the probabilities used in the selection of the k_i. Thus, the difference between the variances of the two estimators can be minimized by an appropriate choice of the probabilities P(j). It was shown also that by selecting the integers j = 0, 1, …, m with probabilities P(j) = (√(f(j))) / ((∑_j=1^m)(√(f(j)), where f(j) = (1/n)[ρ²(0) + ρ²(jΔt)]ρ²(j)G²_α²(j), that the variance of φ*(ω_α) is minimized. For the special case, φ(ω) = λ and the point W/2, it was shown that sampling with equal probabilities is about half as efficient as with probabilities. Finally, some of the areas in which research has been carried out using power spectral analysis were considered. In particular, a problem from the field of aeronautical engineering research was used to demonstrate how the randomized estimator φ*(ω_α) would be calculated from real data. Using 900 observations on the pitching velocity of an aircraft, the power spectrum was estimated at ten points. The new estimator proved very tractable and it is felt that the loss of precision due to sampling will be more than offset by the economy and ease with which it produces estimates. This will be especially true when the need is for quick pilot estimates of spectra to be used in preliminary studies, as guidance for future research. / Ph. D.

The quality of parametric power spectral estimates is analyzed and a lower bound based on the Cramer-Rao inequality for unbiased estimators has been computed. The quality of a least squares autoregressive (AR) ladder estimator is evaluated by simulation, in terms of bias and variance of the corresponding spectral density estimates. The AR ladder estimator and classical periodogram based moving average (MA) estimators are then evaluated against the theoretical Cramer-Rao bound for AR and ARMA process realizations. / M.S.

We use a perturbation analysis to predict some of the instabilities in a single-machine quasi-infinite busbar system. The system’s behavior is described by the so-called swing equation, which is a nonlinear second-order ordinary-differential equation with additive and multiplicative harmonic terms having the frequency Ω. When Ω≈ω₀, and Ω≈2ω₀, where ω₀ is the linear natural frequency of the machine, we use digital-computer simulations to exhibit some of the complicated responses of the machine, including period-doubling bifurcations, chaotic motions, and unbounded motions (loss of synchronism). To predict the onset of these complicated behaviors, we use the method of multiple scales to develop approximate closed-form expressions for the periodic responses of the machine. Then, we use various techniques to determine the stability of the analytical solutions. The analytically predicted periodic solutions and conditions for their instability are in good agreement with the digital-computer results. / Master of Science

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Ocean Engineering, 1980. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Includes bibliographical references. / by Robert Bradlee Campbell. / Ph.D.

Thesis (Sc.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1979. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Bibliography: leaves 99-108. / by Marvin Stuart Keshner. / Sc.D.