Other Statistics and Probability Commons^™

Fluid Flow In Micro-Channels: A Stochastic Approach, Hilda Marino Black

Doctoral Dissertations

In this study free molecular flow in a micro-channel was modeled using a stochastic approach, namely the Kolmogorov forward equation in three dimensions. Model equations were discretized using Central Difference and Backward Difference methods and solved using the Jacobi method. Parameters were used that reflect the characteristic geometry of experimental work performed at the Louisiana Tech University Institute for Micromanufacturing.

The solution to the model equations provided the probability density function of the distance traveled by a particle in the micro-channel. From this distribution we obtained the distribution of the residence time of a particle in the micro-channel. Knowledge of …

Simpson's Paradox Can Emerge From The N-Player Prisoner's Dilemma: Implications For The Evolution Of Altruistic Behavior, Jeffrey Alan Fletcher, Martin Zwick

Systems Science Faculty Publications and Presentations

Simulations of the n-player Prisoner’s Dilemma in multiple populations reveal that Simpson’s paradox can emerge in such game-theoretic situations. The relative proportion of cooperators can decrease in each separate sub-population, while the proportion of cooperators in the total population can nonetheless increase, at least transiently. Factors that determine the longevity of this effect are under investigation. The increase of altruistic behavior exhibited in these simulations is not based on reciprocal altruism, as there are no strategies conditional on other players’ past actions, nor does it depend on kin selection via inclusive fitness, as there are no genes. This model is …

Cramer-Rao Bound And Optimal Amplitude Estimator Of Superimposed Sinusoidal Signals With Unknown Frequencies, Shaohui Jia

Doctoral Dissertations

This dissertation addresses optimally estimating the amplitudes of superimposed sinusoidal signals with unknown frequencies. The Cramer-Rao Bound of estimating the amplitudes in white Gaussian noise is given, and the maximum likelihood estimator of the amplitudes in this case is shown to be asymptotically efficient at high signal to noise ratio but finite sample size. Applying the theoretical results to signal resolutions, it is shown that the optimal resolution of multiple signals using a finite sample is given by the maximum likelihood estimator of the amplitudes of signals.