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Articles 1 - 3 of 3
Full-Text Articles in Applied Mathematics
An Exploration Of Controlling The Content Learned By Deep Neural Networks, Liqun Yang
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
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
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 …