Other Applied Mathematics Commons^™

Cdt-1d Cnn Integration With Simpson-Sobolev Regularization For High-Frequency Options Trading: With Fem-Based Heston Option Pricing, Daniel M. Margolis, Johannes Tausch, Arthur K. Selender

Mathematics Theses and Dissertations

This dissertation presents a computational framework for high-frequency options trading that combines Cross-Data-Type 1-D Convolutional Neural Networks (CDT-1D CNN) with Simpson-Sobolev regularization for directional prediction, and finite element methods (FEM) for realistic option pricing during backtesting. The core innovation lies in developing a mathematically rigorous regularization approach that maintains the adaptability of modern deep learning while enabling accurate evaluation through stochastic volatility models. The primary contribution is the Simpson-Sobolev regularization scheme, which extends traditional Sobolev regularization by incorporating Simpson’s rule for numerical integration. This approach achieves higher-order accuracy in approximating the Sobolev norms that control function smoothness. Simpson’s rule attains …

Viscous Thin-Film Models Of Nanoscale Self-Organization Under Ion Bombardment, Tyler Evans

Mathematics Theses and Dissertations

For decades, it has been observed that broad-beam irradiation of semiconductor surfaces can lead to spontaneous self-organization into highly regular patterns, sometimes at length scales of only a few nanometers. Initial theory was largely based on erosion and redistribution of material occurring on fast time scales, which are able to produce good agreement with certain aspects of surface evolution. However, further experimental and theoretical work eventually led to the realization that numerous effects are active in the irradiated target, including stresses associated with ion-implantation and the accumulation of damage leading to the development of a disordered, amorphous layer atop the …

Practical Implementation Of The Immersed Interface Method With Triangular Meshes For 3d Rigid Solids In A Fluid Flow, Norah Hakami

Mathematics Theses and Dissertations

When employing the immersed interface method (IIM) to simulate a fluid flow around a moving rigid object, the immersed object can be replaced by a virtual fluid enclosed by singular forces on the interface between the real and virtual fluids. These forces represent the impact of the rigid motion on the fluid flow and cause jump discontinuities across the interface in the whole flow field. Then, the IIM resolves the fluid flow on a fixed computational domain by directly incorporating the jump conditions across the interface into numerical schemes. Previous development of the method is limited to simple smooth boundaries. …

Modeling Fluid Phenomena In The Context Of The Constrained Vapor Bubble System, James Barrett

Mathematics Theses and Dissertations

This thesis focuses on the fluid phenomena observed within what is known as the constrained vapor bubble system. The constrained vapor bubble system is a closed system consisting of a quartz cuvette partially filled with liquid and used as a coolant device. Heat is applied to the heater end which causes the liquid to evaporate and condense on the cooled end of the cuvette. Liquid travels back to the heated end via capillary flow in the corners. A pure vapor bubble is formed in the center of the cuvette giving rise to the name of the experiment. The constrained vapor …

Cell Assembly Detection In Low Firing-Rate Spike Train Data, Phan Minh Duc Truong

Mathematics Theses and Dissertations

Cell assemblies, defined as groups of neurons forming temporal spike coordination, are thought to be fundamental units supporting major cognitive functions. However, detecting cell assemblies is challenging since they can occur at a range of time scales and with a range of precisions, from synchronous spikes to co-variations in firing rate. In this dissertation, we use a recently published cell assembly detection (CAD) algorithm that is capable of detecting assemblies at a range of time scales and precisions. We first showed that the CAD method can be applied to sparser spike train data than what have previously been reported. This …

Model Selection And Experimental Design Of Biological Networks With Algebraic Geometry, Anyu Zhang

Mathematics Theses and Dissertations

Model selection based on experimental data is an essential challenge in biological data science. In decades, the volume of biological data from varied sources, including laboratory experiments, field observations, and patient health records has seen an unprecedented increase. Mainly when collecting data is expensive or time-consuming, as it is often in the case with clinical trials and biomolecular experiments, the problem of selecting information-rich data becomes crucial for creating relevant models.

Motivated by certain geometric relationships between data, we partitioned input data sets, especially data sets that correspond to a unique basis, into equivalence classes with the same basis to …

A Data Driven Approach To Forecast Demand, Hannah Kosinovsky, Sita Daggubati, Kumar Ramasundaram, Brent Allen

SMU Data Science Review

Abstract. In this paper, we present a model and methodology for accurately predicting the following quarter’s sales volume of individual products given the previous five years of sales data. Forecasting product demand for a single supplier is complicated by seasonal demand variation, business cycle impacts, and customer churn. We developed a novel prediction using machine learning methodology, based upon a Dense neural network (DNN) model that implicitly considers cyclical demand variation and explicitly considers customer churn while minimizing the least absolute error between predicted demand and actual sales. Using parts sales data for a supplier to the oil and gas …