Mathematical models

Marine Hydrokinetic (MHK) energy is an alternative to address the demand for cleaner energy sources. This study advanced numerical modeling tools and uses these to evaluate the performance of both a Tidal Turbine (TT) and an Ocean Current Turbine (OCT) operating in a variety of conditions. Inflow models are derived with current speeds ranging from 1.5 to 3 m/s and Turbulence Intensities (TI) of 5-15% and integrated into a TT simulation. An OCT simulation representing a commercial scale 20 m diameter turbine moored to the seafloor via underwater cable is enhanced with the capability to ingest Acoustic Doppler Current Profiler (ADCP) data and simulate fault conditions. ADCP measurements collected off the coast of Ft. Lauderdale during Hurricanes Irma and Maria were post-processed and used to characterize the OCT performance. In addition, a set of common faults were integrated into the OCT model to assess the system response in fault-induced scenarios.

Mathematical modeling is a powerful tool to study and analyze the disease dynamics prevalent in the community. This thesis studies the dynamics of two time since infection structured vector borne models with direct transmission. We have included disease induced death rate in the first model to form the second model. The aim of this thesis is to analyze whether these two models have same or different disease dynamics. An explicit expression for the reproduction number denoted by R0 is derived. Dynamical analysis reveals the forward bifurcation in the first model. That is when the threshold value R0 < 1, disease free-equilibrium is stable locally implying that if there is small perturbation of the system, then after some time, the system will return to the disease free equilibrium. When R0 > 1 the unique endemic equilibrium is locally asymptotically stable.
For the second model, analysis of the existence and stability of equilibria reveals the existence of backward bifurcation i.e. where the disease free equilibrium coexists with the endemic equilibrium when the reproduction number R02 is less than unity. This aspect shows that in order to control vector borne disease, it is not sufficient to have reproduction number less than unity although necessary. Thus, the infection can persist in the population even if the reproduction number is less than unity. Numerical simulation is presented to see the bifurcation behaviour in the model. By taking the reproduction number as the bifurcation parameter, we find the system undergoes backward bifurcation at R02 = 1. Thus, the model has backward bifurcation and have two positive endemic equilibrium when R02 < 1 and unique positive endemic equilibrium whenever R02 > 1. Stability analysis shows that disease free equilibrium is locally asymptotically stable when R02 < 1 and unstable when R02 > 1. When R02 < 1, lower endemic equilibrium in backward bifurcation is locally unstable.

Every scheduled treatment at a radiation therapy clinic involves a series of safety
protocol to ensure the utmost patient care. Despite safety protocol, on a rare occasion
an entirely preventable medical event, an accident, may occur. Delivering a treatment
plan to the wrong patient is preventable, yet still is a clinically documented error.
This research describes a computational method to identify patients with a novel
machine learning technique to combat misadministration.The patient identification
program stores face and fingerprint data for each patient. New, unlabeled data from
those patients are categorized according to the library. The categorization of data by
this face-fingerprint detector is accomplished with new machine learning algorithms
based on Sparse Modeling that have already begun transforming the foundation of
Computer Vision. Previous patient recognition software required special subroutines
for faces and di↵erent tailored subroutines for fingerprints. In this research, the same
exact model is used for both fingerprints and faces, without any additional subroutines
and even without adjusting the two hyperparameters. Sparse modeling is a powerful tool, already shown utility in the areas of super-resolution, denoising, inpainting,
demosaicing, and sub-nyquist sampling, i.e. compressed sensing. Sparse Modeling
is possible because natural images are inherrently sparse in some bases, due to their
inherrant structure. This research chooses datasets of face and fingerprint images to
test the patient identification model. The model stores the images of each dataset as
a basis (library). One image at a time is removed from the library, and is classified by
a sparse code in terms of the remaining library. The Locally Competetive Algorithm,
a truly neural inspired Artificial Neural Network, solves the computationally difficult
task of finding the sparse code for the test image. The components of the sparse
representation vector are summed by `1 pooling, and correct patient identification is
consistently achieved 100% over 1000 trials, when either the face data or fingerprint
data are implemented as a classification basis. The algorithm gets 100% classification
when faces and fingerprints are concatenated into multimodal datasets. This suggests
that 100% patient identification will be achievable in the clinal setting.

Computers are becoming an integral part of our high school curriculum. Students use computers for computer-assisted instruction (CAI), word processing, spreadsheet and database applications, and computer programming. It is important to know the cognitive effects of each mode of computer use. The purpose of this study was to investigate transfer effects of a high school BASIC programming course on students' skills in mathematical modeling, procedural comprehension, and verbal problem solution. The sample consisted of 44 BASIC I students, 44 computer literacy students, and 44 students who had no computer training. Groups were matched on years of mathematics and on the grade received in the last mathematics course taken. Pretests and posttests were administered. Results indicated no significant differences in scores among groups for mathematical modeling or procedural comprehension; however, a significant difference was found among groups for verbal problem solution. The BASIC group scored significantly higher than the computer literacy group and the group with no exposure (p < .01). Auxiliary hypotheses examined possible interactions of group with gender, student level, prior grade received in mathematics, and years of high school mathematics. Significant main effects were found for both prior grade (p < .05) and years of mathematics (p < .05) with achievement directly related to excellence of grades and magnitude of coursework. Neither gender x treatment interaction, nor gender alone was found to be a significant source of score variance. Although the variance caused by student grade level was not significant, a significant interaction was found between group membership and grade level with respect to verbal problems. Sophomores in the literacy group scored higher than did sophomores in the nonexposure group; juniors in the nonexposure group scored higher than juniors in the computer literacy group. Suggestions for future research include studying effects (a) over an entire district, (b) on lower level mathematics students, and (c) on lower socioeconomic groups. Recommendations for computer education include teaching algebraic problem solving by computer and exposure of programming coursework to a wider population.

Pixel based and object based vegetation community classification methods were performed using 30 meter spatial resolution Landsat satellite imagery of the Arthur R. Marshall Loxahatchee National Wildlife Refuge (Refuge), a remnant of the northern Everglades. Supervised classification procedures using maximum likelihood and parallelepiped algorithms were used to produce thematic maps with the following vegetation communities : wet prairie, sawgrass, cattail, tree island, brush, aquatic/open water. Spectral data, as well as NDVI, texture and principal component data were used to produce vegetation community classification maps. The accuracy levels of the thematic maps produced were calculated and compared to one another. The pixel based approach using the parallelepiped classification algorithm on the spectral and NDVI dataset had the highest accuracy level. A generalized form of this classification using only three vegetation communities (all wet prairie, tree island/brush and aquatic/open water) was compared to a previously published classification which used 1987 SPOT imagery in order to extract information on possible vegetation community transitions that are occurring within the Refuge. Results of the study indicate that 30 meter spatial resolution may be useful for understanding broad vegetation community trends but not species level trends. Pixel based procedures provide a more accurate classification than object based procedures for this landscape when using 30 meter imagery. Lastly, since 1987 there may be a trend of tree island/brush communities replacing wet prairie communities in the northern part of the Refuge and a transition to wet prairie communities in place of tree island/brush communities in the southern portion of the Refuge.

Experimental and computational investigations addressing how various neural functions are achieved in the brain converged in recent years to a unified idea that the neural activity underlying most of the cognitive functions is distributed over large scale networks comprising various cortical and subcortical areas. Modeling approaches represent these areas and their connections using diverse models of neurocomputational units engaged in graph-like or neural field-like structures. Regardless of the manner of network implementation, simulations of large scale networks have encountered significant difficulties mainly due to the time delay introduced by the long range connections. To decrease the computational effort, it is common to assume severe approximations to simplify the descriptions of the neural dynamics associated with the system's units. In this dissertation we propose an alternative framework allowing the prevention of such strong assumptions while efficiently representing th e dynamics of a complex neural network. First, we consider the dynamics of small scale networks of globally coupled non-identical excitatory and inhibitory neurons, which could realistically instantiate a neurocomputational unit. We identify the most significant dynamical features the neural population exhibits in different parametric configuration, including multi-cluster dynamics, multi-scale synchronization and oscillator death. Then, using mode decomposition techniques, we construct analytically low dimensional representations of the network dynamics and show that these reduced systems capture the dynamical features of the entire neural population. The cases of linear and synaptic coupling are discussed in detail. In chapter 5, we extend this approach for spatially extended neural networks.

This thesis describes a methodology for mechanical fault detection and diagnostics in an ocean turbine using vibration analysis and modeling. This methodology relies on the use of advanced methods for machine vibration analysis and health monitoring. Because of some issues encountered with traditional methods such as Fourier analysis for non stationary rotating machines, the use of more advanced methods such as Time-Frequency Analysis is required. The thesis also includes the development of two LabVIEW models. The first model combines the advanced methods for on-line condition monitoring. The second model performs the modal analysis to find the resonance frequencies of the subsystems of the turbine. The dynamic modeling of the turbine using Finite Element Analysis is used to estimate the baseline of vibration signals in sensors locations under normal operating conditions of the turbine. All this information is necessary to perform the vibration condition monitoring of the turbine.

This thesis is an approach of numerical optimization of thermal design of the ocean turbine developed by the Centre of Ocean Energy and Technology (COET). The technique used here is the integrated method of finite element analysis (FEA) of heat transfer, artificial neural network (ANN) and genetic algorithm (GA) for optimization purposes.

Management of water resources has become more complex in recent years as a result of changing attitudes towards sustainability and the attribution of greater attention to environmental issues, especially under a scenario of water scarcity risk introduced by climate changes and anthropogenic pressures. This thesis addresses the conflicts in optimizing multi-purpose hydropower operations under an environment where objectives are often conflicting and uncertain. Mathematical programming formulations can be used to achieve flexible, feasible and optimal operation and planning solutions to satisfy expectations of multiple stake-holders, including regulatory environmental compliance and sustainability. Innovative optimization models using MINLP with binary variables, fuzzy set theory, partial constraint satisfaction and multi-objective formulations incorporating unit commitment problem and adaptive real-time operations are developed and applied to a real life case study. These methodologies provide advances and valuable insights on optimal operations of hydropower systems under uncertain decision making environments.

In natural systems, it has been observed that plankton exist in patches rather than in an even distribution across a body of water. However, the mechanisms behind this patchiness are not fully understood. Several previous modeling studies have examined the effects of abiotic and biotic factors on patch structure. Yet these models ignore a key point: zooplankton often undergo diel vertical migration. I have formulated a model that incorporates vertical movement into the Rosezweig-MacArthur (R-M) predator-prey model. The R-M model is stable only at a carrying capacity below a critical value. I found that adding vertical movement stabilizes the system even at a high carrying capacity. By analyzing temporal stability and spatial structure, my results show that vertical movement interacts with carrying capacity to determine patch structure.