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Full-Text Articles in Physical Sciences and Mathematics
The Deep Bsde Method, Daniel Kovach
The Deep Bsde Method, Daniel Kovach
Masters Theses
"The curse of dimensionality is the non-linear growth in computing time as the dimension of a problem increases. Using the Deep Backwards Stochastic Differential Equation (Deep BSDE) method developed in [HJE18], I approximate the solution at an initial time to a one-dimensional diffusion equation. Although we only approximate a one-dimensional equation, this method extends well to higher dimensions because it overcomes the curse of dimensionality by evaluating the given partial differential equation along "random characteristics''. In addition to the implementation, I also present most of the mathematical theory needed to understand this method"-- Abstract, p. iii
A Deep Learning Model To Predict Traumatic Brain Injury Severity And Outcome From Mr Images, Dacosta Yeboah, Hung Nguyen, Daniel B. Hier, Gayla R. Olbricht, Tayo Obafemi-Ajayi
A Deep Learning Model To Predict Traumatic Brain Injury Severity And Outcome From Mr Images, Dacosta Yeboah, Hung Nguyen, Daniel B. Hier, Gayla R. Olbricht, Tayo Obafemi-Ajayi
Chemistry Faculty Research & Creative Works
For Many Neurological Disorders, Including Traumatic Brain Injury (TBI), Neuroimaging Information Plays a Crucial Role Determining Diagnosis and Prognosis. TBI is a Heterogeneous Disorder that Can Result in Lasting Physical, Emotional and Cognitive Impairments. Magnetic Resonance Imaging (MRI) is a Non-Invasive Technique that Uses Radio Waves to Reveal Fine Details of Brain Anatomy and Pathology. Although MRIs Are Interpreted by Radiologists, Advances Are Being Made in the Use of Deep Learning for MRI Interpretation. This Work Evaluates a Deep Learning Model based on a Residual Learning Convolutional Neural Network that Predicts TBI Severity from MR Images. the Model Achieved a …
A Multi-Step Nonlinear Dimension-Reduction Approach With Applications To Bigdata, R. Krishnan, V. A. Samaranayake, Jagannathan Sarangapani
A Multi-Step Nonlinear Dimension-Reduction Approach With Applications To Bigdata, R. Krishnan, V. A. Samaranayake, Jagannathan Sarangapani
Mathematics and Statistics Faculty Research & Creative Works
In this paper, a multi-step dimension-reduction approach is proposed for addressing nonlinear relationships within attributes. In this work, the attributes in the data are first organized into groups. In each group, the dimensions are reduced via a parametric mapping that takes into account nonlinear relationships. Mapping parameters are estimated using a low rank singular value decomposition (SVD) of distance covariance. Subsequently, the attributes are reorganized into groups based on the magnitude of their respective singular values. The group-wise organization and the subsequent reduction process is performed for multiple steps until a singular value-based user-defined criterion is satisfied. Simulation analysis is …