Other Applied Mathematics Commons^™

A Simulation Assessment Of The 'Law Of One Price', Caleb Wilkins

Computational and Data Sciences (MS) Theses

The ‘law of one price’ is an appealing notion regarding pricing of tradeable commodities that are priced in different currencies. It states that the prices of the same good in different markets should be equal after adjustment for exchange rates and that equality should persist through exchange rate fluctuations.

My research simulates the market conditions that should precipitate the ‘law of one price.’ Data was obtained from the simulated trade between algorithmic artificial intelligence agents that operated under induced boundedly rational market behaviors. Trade took place in two initially separate markets, a high-price market with a higher equilibrium price and …

A Novel Correction For The Adjusted Box-Pierce Test, Sidy Danioko, Jianwei Zheng, Kyle Anderson, Alexander Barrett, Cyril S. Rakovski

Mathematics, Physics, and Computer Science Faculty Articles and Research

The classical Box-Pierce and Ljung-Box tests for auto-correlation of residuals possess severe deviations from nominal type I error rates. Previous studies have attempted to address this issue by either revising existing tests or designing new techniques. The Adjusted Box-Pierce achieves the best results with respect to attaining type I error rates closer to nominal values. This research paper proposes a further correction to the adjusted Box-Pierce test that possesses near perfect type I error rates. The approach is based on an inflation of the rejection region for all sample sizes and lags calculated via a linear model applied to simulated …

A Novel Correction For The Adjusted Box-Pierce Test — New Risk Factors For Emergency Department Return Visits Within 72 Hours For Children With Respiratory Conditions — General Pediatric Model For Understanding And Predicting Prolonged Length Of Stay, Sidy Danioko

Computational and Data Sciences (PhD) Dissertations

This thesis represents the results of three research projects that underline the breadth and depth of my interests.

Firstly, I devoted some efforts to the well-known Box-Pierce goodness-of-fit tests for time series models which has been an important research topic over the last few decades. All previously proposed tests are focused on changes of the test statistics. Instead, I adopted a different approach that takes the best performing test and modifying the rejection region. Thus, I developed a semiparametric correction of the Adjusted Box-Pierce test that attains the best I error rates for all sample sizes and lags and outperforms …

Image Restoration Using Automatic Damaged Regions Detection And Machine Learning-Based Inpainting Technique, Chloe Martin-King

Computational and Data Sciences (PhD) Dissertations

In this dissertation we propose two novel image restoration schemes. The first pertains to automatic detection of damaged regions in old photographs and digital images of cracked paintings. In cases when inpainting mask generation cannot be completely automatic, our detection algorithm facilitates precise mask creation, particularly useful for images containing damage that is tedious to annotate or difficult to geometrically define. The main contribution of this dissertation is the development and utilization of a new inpainting technique, region hiding, to repair a single image by training a convolutional neural network on various transformations of that image. Region hiding is also …

Realization Of Tensor Product And Of Tensor Factorization Of Rational Functions, Daniel Alpay, Izchak Lewkowicz

Mathematics, Physics, and Computer Science Faculty Articles and Research

We study the state space realization of a tensor product of a pair of rational functions. At the expense of “inflating” the dimensions, we recover the classical expressions for realization of a regular product of rational functions. Under an additional assumption that the limit at infinity of a given rational function exists and is equal to identity, we introduce an explicit formula for a tensor factorization of this function.

A More Powerful Unconditional Exact Test Of Homogeneity For 2 × C Contingency Table Analysis, Louis Ehwerhemuepha, Heng Sok, Cyril Rakovski

Mathematics, Physics, and Computer Science Faculty Articles and Research

The classical unconditional exact p-value test can be used to compare two multinomial distributions with small samples. This general hypothesis requires parameter estimation under the null which makes the test severely conservative. Similar property has been observed for Fisher's exact test with Barnard and Boschloo providing distinct adjustments that produce more powerful testing approaches. In this study, we develop a novel adjustment for the conservativeness of the unconditional multinomial exact p-value test that produces nominal type I error rate and increased power in comparison to all alternative approaches. We used a large simulation study to empirically estimate the …

Herglotz Functions Of Several Quaternionic Variables, Khaled Abu-Ghanem, Daniel Alpay, Fabrizio Colombo, Izchak Lewkowicz, Irene Sabadini

Mathematics, Physics, and Computer Science Faculty Articles and Research

We first review realizations of Herglotz functions in the unit ball of C^N and provide new insights. Then, we define the corresponding class and prove the extend the results in the case of several quaternionic variables.

Generating Species Assemblages For Restoration And Experimentation: A New Method That Can Simultaneously Converge On Average Trait Values And Maximize Functional Diversity, David C. Laughlin, Loïc Chalmandrier, Chaitanya Joshi, Michael Renton, John M. Dwyer, Jennifer L. Funk

Biology, Chemistry, and Environmental Sciences Faculty Articles and Research

1.Restoring resilient ecosystems in an era of rapid environmental change requires a flexible framework for selecting assemblages of species based on functional traits. However, current trait‐based models have been limited to algorithms that select species assemblages that only converge on specified average trait values, and could not accommodate the common desire among restoration ecologists to generate functionally diverse assemblages.

2.We have solved this problem by applying a nonlinear optimization algorithm to solve for the species relative abundances that maximize Rao's quadratic entropy (Q) subject to other linear constraints. Rao's Q is a closed‐form algebraic expression of functional diversity …

Positive Definite Functions And Dual Pairs Of Locally Convex Spaces, Daniel Alpay, Saak Gabriyelyan

Mathematics, Physics, and Computer Science Faculty Articles and Research

Using pairs of locally convex topological vector spaces in duality and topologies defined by directed families of sets bounded with respect to the duality, we prove general factorization theorems and general dilation theorems for operator-valued positive definite functions.

Evolution Of Superoscillations For Schrödinger Equation In A Uniform Magnetic Field, Fabrizio Colombo, Jonathan Gantner, Daniele C. Struppa

Mathematics, Physics, and Computer Science Faculty Articles and Research

Aharonov-Berry superoscillations are band-limited functions that oscillate faster than their fastest Fourier component. Superoscillations appear in several fields of science and technology, such as Aharonov’s weak measurement in quantum mechanics, in optics, and in signal processing. An important issue is the study of the evolution of superoscillations using the Schrödinger equation when the initial datum is a weak value. Some superoscillatory functions are not square integrable, but they are real analytic functions that can be extended to entire holomorphic functions. This fact leads to the study of the continuity of a class of convolution operators acting on suitable spaces of …