Numerical Analysis and Computation Commons^™

Performance Of Numerical Methods Applied To The Black–Scholes Model, Scott Cameron Williams

UNF Graduate Theses and Dissertations

We compare five numerical approaches for approximating solutions to the Black–Scholes partial differential equation for pricing European call options: FTCS, BTCS, Crank– Nicolson, Monte Carlo simulation, and a physics–informed neural network (PINN). These methods span finite difference techniques, probabilistic simulation, and machine learning. Performance is evaluated based on computational efficiency and accuracy relative to the analytical Black–Scholes solution.

Among the methods, Crank–Nicolson and the PINN demonstrated the strongest overall performance. Crank–Nicolson achieved the highest accuracy but exhibited increased runtime as the number of underlying stock price grid points grew. In contrast, the PINN produced slightly less accurate results but with …

Property Testing Ai: An Efficient Frontier, Paul Sopher Lintilhac

Dartmouth College Ph.D Dissertations

In this dissertation, we take a step towards addressing the major problem of a lack of standardized and rigorous approaches to testing and evaluation of AI systems. Taking inspiration from both the fields of Property Testing and Property Based Testing (for programs), we develop a novel taxonomy of partially overlapping classes of properties of AI systems, including simple properties, compound properties, higher order properties, data relation properties, and architecture-utility properties. We argue that this taxonomy categorizes a diverse set of AI traits -- including accuracy, fairness, robustness, monotonicity, point-wise and global privacy properties, sensitivity, and more -- according to the …

A Novel Preprocessing Model For Multi Modal Brain Mri Image Classification For Stroke Prognosis, Alwin Joseph, Chandra J

Northeast Journal of Complex Systems (NEJCS)

Magnetic Resonance Imaging (MRI) is an imaging technique used for the diagnosis and observing the progression in various neurological disorders. Stroke is one of the prominent neurological disorders that creates significant impacts in the patients. It occurs when the blood supply to part of the brain is interrupted or reduced, preventing brain tissues from getting oxygen and nutrients. Multimodal data from various modalities help clinicians in proper prognosis of stroke. Ischemic Stroke Lesion Segmentation Challenge (ISLES22) provides data of stroke data for various stroke patients, the dataset consists of three modalities of data – Fluid Attenuated Inversion Recovery (FLAIR), Apparent …

Chatgpt As Metamorphosis Designer For The Future Of Artificial Intelligence (Ai): A Conceptual Investigation, Amarjit Kumar Singh (Library Assistant), Dr. Pankaj Mathur (Deputy Librarian)

Library Philosophy and Practice (e-journal)

Abstract

Purpose: The purpose of this research paper is to explore ChatGPT’s potential as an innovative designer tool for the future development of artificial intelligence. Specifically, this conceptual investigation aims to analyze ChatGPT’s capabilities as a tool for designing and developing near about human intelligent systems for futuristic used and developed in the field of Artificial Intelligence (AI). Also with the helps of this paper, researchers are analyzed the strengths and weaknesses of ChatGPT as a tool, and identify possible areas for improvement in its development and implementation. This investigation focused on the various features and functions of ChatGPT that …

Computational Models To Detect Radiation In Urban Environments: An Application Of Signal Processing Techniques And Neural Networks To Radiation Data Analysis, Jose Nicolas Gachancipa

Beyond: Undergraduate Research Journal

Radioactive sources, such as uranium-235, are nuclides that emit ionizing radiation, and which can be used to build nuclear weapons. In public areas, the presence of a radioactive nuclide can present a risk to the population, and therefore, it is imperative that threats are identified by radiological search and response teams in a timely and effective manner. In urban environments, such as densely populated cities, radioactive sources may be more difficult to detect, since background radiation produced by surrounding objects and structures (e.g., buildings, cars) can hinder the effective detection of unnatural radioactive material. This article presents a computational model …

Quadratic Neural Network Architecture As Evaluated Relative To Conventional Neural Network Architecture, Reid Taylor

Senior Theses

Current work in the field of deep learning and neural networks revolves around several variations of the same mathematical model for associative learning. These variations, while significant and exceptionally applicable in the real world, fail to push the limits of modern computational prowess. This research does just that: by leveraging high order tensors in place of 2nd order tensors, quadratic neural networks can be developed and can allow for substantially more complex machine learning models which allow for self-interactions of collected and analyzed data. This research shows the theorization and development of mathematical model necessary for such an idea to …

Optimal Analytical Methods For High Accuracy Cardiac Disease Classification And Treatment Based On Ecg Data, Jianwei Zheng

Computational and Data Sciences (PhD) Dissertations

This work constitutes six projects. In the first project, a newly inaugurated research database for 12-lead electrocardiogram signals was created under the auspices of Chapman University and Shaoxing People's Hospital (Shaoxing Hospital Zhejiang University School of Medicine). This database aims to enable the scientific community in conducting new studies on arrhythmia and other cardiovascular conditions. In the second project, we created a new 12-lead ECG database under the auspices of Chapman University and Ningbo First Hospital of Zhejiang University that aims to provide high quality data enabling detection of the distinctions between idiopathic ventricular arrhythmia from right ventricular outflow tract …

Cover Song Identification - A Novel Stem-Based Approach To Improve Song-To-Song Similarity Measurements, Lavonnia Newman, Dhyan Shah, Chandler Vaughn, Faizan Javed

SMU Data Science Review

Music is incorporated into our daily lives whether intentional or unintentional. It evokes responses and behavior so much so there is an entire study dedicated to the psychology of music. Music creates the mood for dancing, exercising, creative thought or even relaxation. It is a powerful tool that can be used in various venues and through advertisements to influence and guide human reactions. Music is also often "borrowed" in the industry today. The practices of sampling and remixing music in the digital age have made cover song identification an active area of research. While most of this research is focused …

Sensor Data Analysis In Smart Buildings, Manuel A. Mane Penton

Publications and Research

Data analysis and Machine Learning are destined to evolve the current technology infrastructure by solving technology and economy demands present mainly in developed cities like New York. This research proposes a machine learning (ML) based solution to alleviate one of the main issues that big buildings such as CUNY campuses have, that is the waste of energy resources. The analysis of data coming from the readings of different deployed sensors such as CO2, humidity and temperature can be used to estimate occupancy in a specific room and building in general. The outcome of this research established a relationship between the …

Orthogonal Recurrent Neural Networks And Batch Normalization In Deep Neural Networks, Kyle Eric Helfrich

Theses and Dissertations--Mathematics

Despite the recent success of various machine learning techniques, there are still numerous obstacles that must be overcome. One obstacle is known as the vanishing/exploding gradient problem. This problem refers to gradients that either become zero or unbounded. This is a well known problem that commonly occurs in Recurrent Neural Networks (RNNs). In this work we describe how this problem can be mitigated, establish three different architectures that are designed to avoid this issue, and derive update schemes for each architecture. Another portion of this work focuses on the often used technique of batch normalization. Although found to be successful …

Predicting Win Rates In Competitive Overwatchtm, Andrea Sibley

Mathematics Senior Capstone Papers

OverwatchTM is a video game published by Blizzard Entertainment R where two teams comprised of six people each compete against one another to accomplish a specific goal. The goal of each game is dependent on which map is being played. The maps are divided into four categories: Assault, Escort, Control, and Hybrid. A data set comprised of 3000 games of competitive OverwatchTM is used to determine how likely a team is to win their match. The factors used to determine the likelihood of winning are the map type and the skill ranking for each team. The data set is pre-processed …

Randomized Algorithms For Preconditioner Selection With Applications To Kernel Regression, Conner Dipaolo

HMC Senior Theses

The task of choosing a preconditioner M to use when solving a linear system Ax=b with iterative methods is often tedious and most methods remain ad-hoc. This thesis presents a randomized algorithm to make this chore less painful through use of randomized algorithms for estimating traces. In particular, we show that the preconditioner stability || I - M^-1A ||_F, known to forecast preconditioner quality, can be computed in the time it takes to run a constant number of iterations of conjugate gradients through use of sketching methods. This is in spite of folklore which …

Information Theoretic Study Of Gaussian Graphical Models And Their Applications, Ali Moharrer

LSU Doctoral Dissertations

In many problems we are dealing with characterizing a behavior of a complex stochastic system or its response to a set of particular inputs. Such problems span over several topics such as machine learning, complex networks, e.g., social or communication networks; biology, etc. Probabilistic graphical models (PGMs) are powerful tools that offer a compact modeling of complex systems. They are designed to capture the random behavior, i.e., the joint distribution of the system to the best possible accuracy. Our goal is to study certain algebraic and topological properties of a special class of graphical models, known as Gaussian graphs. First, …

Daily Traffic Flow Pattern Recognition By Spectral Clustering, Matthew Aven

CMC Senior Theses

This paper explores the potential applications of existing spectral clustering algorithms to real life problems through experiments on existing road traffic data. The analysis begins with an overview of previous unsupervised machine learning techniques and constructs an effective spectral clustering algorithm that demonstrates the analytical power of the method. The paper focuses on the spectral embedding method’s ability to project non-linearly separable, high dimensional data into a more manageable space that allows for accurate clustering. The key step in this method involves solving a normalized eigenvector problem in order to construct an optimal representation of the original data.

While this …