Applied Mathematics Commons^™

An Exploration Of Controlling The Content Learned By Deep Neural Networks, Liqun Yang

FIU Electronic Theses and Dissertations

With the great success of the Deep Neural Network (DNN), how to get a trustworthy model attracts more and more attention. Generally, people intend to provide the raw data to the DNN directly in training. However, the entire training process is in a black box, in which the knowledge learned by the DNN is out of control. There are many risks inside. The most common one is overfitting. With the deepening of research on neural networks, additional and probably greater risks were discovered recently. The related research shows that unknown clues can hide in the training data because of the …

Geometric Quantizations Related To The Laplace Eigenspectra Of Compact Riemannian Symmetric Spaces Via Borel-Weil-Bott Theory, Camilo Montoya

FIU Electronic Theses and Dissertations

The purpose of this thesis is to suggest a geometric relation between the Laplace-Beltrami spectra and eigenfunctions on compact Riemannian symmetric spaces and the Borel-Weil theory using ideas from symplectic geometry and geometric quantization. This is done by associating to each compact Riemannian symmetric space, via Marsden-Weinstein reduction, a generalized flag manifold which covers the space parametrizing all of its maximal totally geodesic tori. In the process we notice a direct relation between the Satake diagram of the symmetric space and the painted Dynkin diagram of its associated flag manifold. We consider in detail the examples of the classical simply-connected …

Evaluation Of Parametric And Nonparametric Statistical Models In Wrong-Way Driving Crash Severity Prediction, Sajidur Rahman Nafis

FIU Electronic Theses and Dissertations

Wrong-way driving (WWD) crashes result in more fatalities per crash, involve more vehicles, and cause extended road closures compared to other types of crashes. Although crashes involving wrong-way drivers are relatively few, they often lead to fatalities and serious injuries. Researchers have been using parametric statistical models to identify factors that affect WWD crash severity. However, these parametric models are generally based on several assumptions, and the results could generate numerous errors and become questionable when these assumptions are violated. On the other hand, nonparametric methods such as data mining or machine learning techniques do not use a predetermined functional …

Singularities And Global Solutions In The Schrodinger-Hartree Equation, Anudeep Kumar

FIU Electronic Theses and Dissertations

In 1922, Louis de Broglie proposed wave-particle duality and introduced the idea of matter waves. In 1925, Erwin Schrodinger, proposed a wave equation for de Broglie’s matter waves. The Schrodinger equation is described using the de Broglie’s matter wave, which takes the wave function, and describes its quantum state over time.

Herein, we study the generalized Hartree (gHartree) equation, which is a nonlinear Schrodinger type equation except now the nonlinearities are a nonlocal (convolution) type. In the gHartree equation, the influence on the behavior of the solutions is global as opposed to the case of local (power type) nonlinearities.

Our …

Modeling Drought, Drought Teleconnection, And Its Effect On Groundwater Level Dynamics In The Biscayne Aquifer, Anteneh Z. Abiy

FIU Electronic Theses and Dissertations

Developing a self-sufficient water supply system in Southeast Florida is one input to the success of the ongoing restoration effort in the Everglades. Maintaining a high groundwater level in the urban side of the Biscayne Aquifer (BA) is important to sustain the urban water supply. However, the long-term groundwater table condition in the Biscayne Aquifer (BA) is threatened by a combination of drought, groundwater pumping, and sea-level rise. Further, the long-term drought pattern, drought drivers, and the aquifer’s response to drought and other stress conditions are not well known. As a result, options that would help to maintain a high …

A Mathematical Framework On Machine Learning: Theory And Application, Bin Shi

FIU Electronic Theses and Dissertations

The dissertation addresses the research topics of machine learning outlined below. We developed the theory about traditional first-order algorithms from convex opti- mization and provide new insights in nonconvex objective functions from machine learning. Based on the theory analysis, we designed and developed new algorithms to overcome the difficulty of nonconvex objective and to accelerate the speed to obtain the desired result. In this thesis, we answer the two questions: (1) How to design a step size for gradient descent with random initialization? (2) Can we accelerate the current convex optimization algorithms and improve them into nonconvex objective? For application, …

Sabermetrics - Statistical Modeling Of Run Creation And Prevention In Baseball, Parker Chernoff

FIU Electronic Theses and Dissertations

The focus of this thesis was to investigate which baseball metrics are most conducive to run creation and prevention. Stepwise regression and Liu estimation were used to formulate two models for the dependent variables and also used for cross validation. Finally, the predicted values were fed into the Pythagorean Expectation formula to predict a team’s most important goal: winning.

Each model fit strongly and collinearity amongst offensive predictors was considered using variance inflation factors. Hits, walks, and home runs allowed, infield putouts, errors, defense-independent earned run average ratio, defensive efficiency ratio, saves, runners left on base, shutouts, and walks per …

Development Of A Two-Fluid Drag Law For Clustered Particles Using Direct Numerical Simulation And Validation Through Experiments, Ahmadreza Abbasi Baharanchi

FIU Electronic Theses and Dissertations

This dissertation focused on development and utilization of numerical and experimental approaches to improve the CFD modeling of fluidization flow of cohesive micron size particles. The specific objectives of this research were: (1) Developing a cluster prediction mechanism applicable to Two-Fluid Modeling (TFM) of gas-solid systems (2) Developing more accurate drag models for Two-Fluid Modeling (TFM) of gas-solid fluidization flow with the presence of cohesive interparticle forces (3) using the developed model to explore the improvement of accuracy of TFM in simulation of fluidization flow of cohesive powders (4) Understanding the causes and influential factor which led to improvements and …

Gis-Integrated Mathematical Modeling Of Social Phenomena At Macro- And Micro- Levels—A Multivariate Geographically-Weighted Regression Model For Identifying Locations Vulnerable To Hosting Terrorist Safe-Houses: France As Case Study, Elyktra Eisman

FIU Electronic Theses and Dissertations

Adaptability and invisibility are hallmarks of modern terrorism, and keeping pace with its dynamic nature presents a serious challenge for societies throughout the world. Innovations in computer science have incorporated applied mathematics to develop a wide array of predictive models to support the variety of approaches to counterterrorism. Predictive models are usually designed to forecast the location of attacks. Although this may protect individual structures or locations, it does not reduce the threat—it merely changes the target. While predictive models dedicated to events or social relationships receive much attention where the mathematical and social science communities intersect, models dedicated to …

An Assessment Of The Performances Of Several Univariate Tests Of Normality, James Olusegun Adefisoye

FIU Electronic Theses and Dissertations

The importance of checking the normality assumption in most statistical procedures especially parametric tests cannot be over emphasized as the validity of the inferences drawn from such procedures usually depend on the validity of this assumption. Numerous methods have been proposed by different authors over the years, some popular and frequently used, others, not so much. This study addresses the performance of eighteen of the available tests for different sample sizes, significance levels, and for a number of symmetric and asymmetric distributions by conducting a Monte-Carlo simulation. The results showed that considerable power is not achieved for symmetric distributions when …

Theoretical Investigation Of Intra- And Inter-Cellular Spatiotemporal Calcium Patterns In Microcirculation, Jaimit B. Parikh

FIU Electronic Theses and Dissertations

Microcirculatory vessels are lined by endothelial cells (ECs) which are surrounded by a single or multiple layer of smooth muscle cells (SMCs). Spontaneous and agonist induced spatiotemporal calcium (Ca²⁺) events are generated in ECs and SMCs, and regulated by complex bi-directional signaling between the two layers which ultimately determines the vessel tone. The contractile state of microcirculatory vessels is an important factor in the determination of vascular resistance, blood flow and blood pressure. This dissertation presents theoretical insights into some of the important and currently unresolved phenomena in microvascular tone regulation. Compartmental and continuum models of isolated EC …

Numerical Modeling Of The Effects Of Hydrologic Conditions And Sediment Transport On Geomorphic Patterns In Wetlands, Mehrnoosh Mahmoudi

FIU Electronic Theses and Dissertations

This dissertation focused on developing a numerical model of spatial and temporal changes in bed morphology of ridge and slough features in wetlands with respect to hydrology and sediment transport when a sudden change in hydrologic condition occurs. The specific objectives of this research were: (1) developing a two-dimensional hydrology model to simulate the spatial distribution of flow depth and velocity over time when a pulsed flow condition is applied, (2) developing a process-based numerical model of sediment transport coupled with flow depth and velocity in wetland ecosystems, and (3) use the developed model to explore how sediment transport may …

Development Of A Methodology That Couples Satellite Remote Sensing Measurements To Spatial-Temporal Distribution Of Soil Moisture In The Vadose Zone Of The Everglades National Park, Luis G. Perez

FIU Electronic Theses and Dissertations

Spatial-temporal distribution of soil moisture in the vadose zone is an important aspect of the hydrological cycle that plays a fundamental role in water resources management, including modeling of water flow and mass transport. The vadose zone is a critical transfer and storage compartment, which controls the partitioning of energy and mass linked to surface runoff, evapotranspiration and infiltration. This dissertation focuses on integrating hydraulic characterization methods with remote sensing technologies to estimate the soil moisture distribution by modeling the spatial coverage of soil moisture in the horizontal and vertical dimensions with high temporal resolution.

The methodology consists of using …

A Modified Resource Distribution Fairness Measure, Zhenmin Chen

Department of Mathematics and Statistics

An important issue of resource distribution is the fairness of the distribution. For example, computer network management wishes to distribute network resource fairly to its users. To describe the fairness of the resource distribution, a quantitative fairness score function was proposed in 1984 by Jain et al. The purpose of this paper is to propose a modified network sharing fairness function so that the users can be treated differently according to their priority levels. The mathematical properties are discussed. The proposed fairness score function keeps all the nice properties of and provides better performance when the network users have different …

Fibrations And Contact Structures, Hamidou Dathe, Philippe Rukimbira

Department of Mathematics and Statistics

We prove that a closed 3-dimensional manifold is a torus bundle over the circle if and only if it carries a closed nonsingular 1-form which is linearly deformable into contact forms.