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Full-Text Articles in Physical Sciences and Mathematics
Paper Structure Formation Simulation, Tyler R. Seekins
Paper Structure Formation Simulation, Tyler R. Seekins
Electronic Theses and Dissertations
On the surface, paper appears simple, but closer inspection yields a rich collection of chaotic dynamics and random variables. Predictive simulation of paper product properties is desirable for screening candidate experiments and optimizing recipes but existing models are inadequate for practical use. We present a novel structure simulation and generation system designed to narrow the gap between mathematical model and practical prediction. Realistic inputs to the system are preserved as randomly distributed variables. Rapid fiber placement (~1 second/fiber) is achieved with probabilistic approximation of chaotic fluid dynamics and minimization of potential energy to determine flexible fiber conformations. Resulting digital packed …
Spatio-Temporal Cluster Detection And Local Moran Statistics Of Point Processes, Jennifer L. Matthews
Spatio-Temporal Cluster Detection And Local Moran Statistics Of Point Processes, Jennifer L. Matthews
Mathematics & Statistics Theses & Dissertations
Moran's index is a statistic that measures spatial dependence, quantifying the degree of dispersion or clustering of point processes and events in some location/area. Recognizing that a single Moran's index may not give a sufficient summary of the spatial autocorrelation measure, a local indicator of spatial association (LISA) has gained popularity. Accordingly, we propose extending LISAs to time after partitioning the area and computing a Moran-type statistic for each subarea. Patterns between the local neighbors are unveiled that would not otherwise be apparent. We consider the measures of Moran statistics while incorporating a time factor under simulated multilevel Palm distribution, …
Exploring The Variance Of The Sample Variance Through Estimation And Simulation, Christina Stradwick
Exploring The Variance Of The Sample Variance Through Estimation And Simulation, Christina Stradwick
Theses, Dissertations and Capstones
In this thesis, we examine properties of the variance of the sample variance, which we will denote V (S 2 ). We derive a formula for this variance and show that it only depends on the sample size, variance, and kurtosis of the underlying distribution. We also derive the maximum likelihood estimators for this parameter, Vˆ (S 2 ), under the normal, exponential, Bernoulli, and Poisson distributions and end the thesis with simulations demonstrating the distributions of these estimators.