Applied Mathematics Commons^™

A Brief On Characteristic Functions, Austin G. Vandegriffe

Graduate Student Research & Creative Works

Characteristic functions (CFs) are often used in problems involving convergence in distribution, independence of random variables, infinitely divisible distributions, and stochastics. The most famous use of characteristic functions is in the proof of the Central Limit Theorem, also known as the Fundamental Theorem of Statistics. Though less frequent, CFs have also been used in problems of nonparametric time series analysis and in machine learning. Moreover, CFs uniquely determine their distribution, much like the moment generating functions (MGFs), but the major difference is that CFs always exists, whereas MGFs can fail, e.g. the Cauchy distribution. This makes CFs more robust in …

Development Of An Effect Size To Classify The Magnitude Of Dif In Dichotomous And Polytomous Items, James D. Weese

Graduate Theses and Dissertations

A standardized effect size for the SIBTEST/POLYSIBTEST procedure is proposed, allowing for Differential Item Functioning (DIF) to be classified with a single set of DIF heuristics regardless of whether data are dichotomous or polytomous. This proposed standardized effect size accounts for both variability in responses and whether participants are included in the SIBTEST/POLYSIBTEST calculations. First, a new set of unstandardized effect size heuristics are established for dichotomous data that are more aligned with Educational Testing Service (ETS) standards using two and three parameter logistic (2PL and 3PL) models. Second, a standardized effect size is proposed and compared to other DIF …

Impatient Customers In An Markovian Queue With Bernoulli Schedule Working Vacation Interruption And Setup Time, P. Manoharan, T. Jeeva

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, using probability generating function method, Impatient customers in an Markovian queue with Bernoulli schedule working vacation interruption and setup time is discussed. Customers impatience is due to the servers vacation. During the working vacation period, if there are customers in the queue, the vacation can be interrupted at a service completion instant and the server begins a regular service period with probability (1 - b) or continues the vacation with probability b. We obtain the probability generating functions of the stationary state probabilities, performance measures, sojourn time of a customer and stochastic decomposition of the queue length, …

On A Multiserver Queueing System With Customers’ Impatience Until The End Of Service Under Single And Multiple Vacation Policies, Mokhtar Kadi, Amina A. Bouchentouf, Lahcene Yahiaoui

Applications and Applied Mathematics: An International Journal (AAM)

This paper deals with a multiserver queueing system with Bernoulli feedback and impatient customers (balking and reneging) under synchronous multiple and single vacation policies. Reneged customers may be retained in the system. Using probability generating functions (PGFs) technique, we formally obtain the steady-state solution of the proposed queueing system. Further, important performance measures and cost model are derived. Finally, numerical examples are presented.

Analysis Of Map/Ph/1 Queueing Model With Breakdown, Instantaneous Feedback And Server Vacation, G. Ayyappan, K. Thilagavathy

Applications and Applied Mathematics: An International Journal (AAM)

In this article, we analyze a single server queueing model with feedback, a single vacation under Bernoulli schedule, breakdown and repair. The arriving customers follow the Markovian Arrival Process (MAP) and service follow the phase-type distribution. When the server returns from vacation, if there is no one present in the system, the server will wait until the customer’s arrival. When the service completion epoch if the customer is not satisfied then that customer will get the service immediately. Under the steady-state probability vector that the total number of customers are present in the system is probed by the Matrix-analytic method. …

Inference And Estimation In Change Point Models For Censored Data, Kristine Gierz

Mathematics & Statistics Theses & Dissertations

In general, the change point problem considers inference of a change in distribution for a set of time-ordered observations. This has applications in a large variety of fields and can also apply to survival data. With improvements to medical diagnoses and treatments, incidences and mortality rates have changed. However, the most commonly used analysis methods do not account for such distributional changes. In survival analysis, change point problems can concern a shift in a distribution for a set of time-ordered observations, potentially under censoring or truncation.

In this dissertation, we first propose a sequential testing approach for detecting multiple change …

Viewing Ode Models Through A New Lens: The Generalized Linear Chain Trick, Paul Hurtado, Cameron Richards

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Stochastic Analysis And Statistical Inference For Seir Models Of Infectious Diseases, Andrés Ríos-Gutiérrez, Viswanathan Arunachalam, Anuj Mubayi

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Pharmacokinetics And Pharmacodynamics Models Of Tumor Growth And Anticancer Effects In Discrete Time, Ngoc Nguyen, Ferhan M. Atici

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

From Wave Propagation To Spin Dynamics: Mathematical And Computational Aspects, Oleksii Beznosov

Mathematics & Statistics ETDs

In this work we concentrate on two separate topics which pose certain numerical challenges. The first topic is the spin dynamics of electrons in high-energy circular accelerators. We introduce a stochastic differential equation framework to study spin depolarization and spin equilibrium. This framework allows the mathematical study of known equations and new equations modelling the spin distribution of an electron bunch. A spin distribution is governed by a so-called Bloch equation, which is a linear Fokker-Planck type PDE, in general posed in six dimensions. We propose three approaches to approximate solutions, using analytical and modern numerical techniques. We also present …

A Data Analytic Framework For Physical Fatigue Management Using Wearable Sensors, Zahra Sedighi Maman, Ying-Ju Chen, Amir Baghdadi, Seamus Lombardo, Lora A. Cavuoto, Fadel M. Megahed

Mathematics Faculty Publications

The use of expert systems in optimizing and transforming human performance has been limited in practice due to the lack of understanding of how an individual's performance deteriorates with fatigue accumulation, which can vary based on both the worker and the workplace conditions. As a first step toward realizing the human-centered approach to artificial intelligence and expert systems, this paper lays the foundation for a data analytic approach to managing fatigue in physically-demanding workplaces. The proposed framework capitalizes on continuously collected human performance data from wearable sensor technologies, and is centered around four distinct phases of fatigue: (a) detection, where …

A Two-Stage Machine Learning Framework To Predict Heart Transplantation Survival Probabilities Over Time With A Monotonic Probability Constraint, Hamidreza Ahady Dolatsaraa, Ying-Ju (Tessa) Chen, Christy Evans, Ashish Gupta, Fadel M. Megahed

Mathematics Faculty Publications

The overarching goal of this paper is to develop a modeling framework that can be used to obtain personalized, data-driven and monotonically constrained probability curves. This research is motivated by the important problem of improving the predictions for organ transplantation outcomes, which can inform updates made to organ allocation protocols, post-transplantation care pathways, and clinical resource utilization. In pursuit of our overarching goal and motivating problem, we propose a novel two-stage machine learning-based framework for obtaining monotonic probabilities over time. The first stage uses the standard approach of using independent machine learning models to predict transplantation outcomes for each time-period …

Analysis Of Surface Temperature Trends Of Global Lakes Using Satellite Remote Sensing And In Situ Observations, Christal Jean Soverall, Zahida Yasmin, Mahoutin Godnou, Wen Yong Huang, Ryan Chen, Abdou Bah, Hamidreza Norouzi, Reginald Blake

Publications and Research

Even though lakes make up a small percentage of the water bodies on the global land surface, lakes provide critically important ecosystem services. Unfortunately, however, several lake surface areas around the globe have been changing with many of them drastically decreasing due to climate variability and local mismanagement at the basin-scale level. Lake Surface Water Temperature (LSWT) is recognized as a critical indicator of climate change in lakes. The changes in water and the surrounding land temperatures may be an indicator of climate variability if there is consistency between changes in both temperatures. This project focuses on the application of …

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 …

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 …

Linear Methods For Regression With Small Sample Sizes Relative To The Number Of Variables., Rajesh Sikder

Electronic Theses and Dissertations

In data sets where there are a small number of observations but a large number of variables observed for each observation, ordinary least squares estimation cannot be used for regression models. There are many alternative including stepwise regression, penalized methods such as ridge regression and the LASSO, and methods based on derived inputs such as principal components regression and partial least squares regression. In this thesis, these five methods are described. K-fold cross validation is also discussed as a way for determining regularization parameters for each method. The performance of these methods in estimation and prediction is also examined through …

Statistical Methods For Resolving Intratumor Heterogeneity With Single-Cell Dna Sequencing, Alexander Davis

Dissertations and Theses (Open Access)

Tumor cells have heterogeneous genotypes, which drives progression and treatment resistance. Such genetic intratumor heterogeneity plays a role in the process of clonal evolution that underlies tumor progression and treatment resistance. Single-cell DNA sequencing is a promising experimental method for studying intratumor heterogeneity, but brings unique statistical challenges in interpreting the resulting data. Researchers lack methods to determine whether sufficiently many cells have been sampled from a tumor. In addition, there are no proven computational methods for determining the ploidy of a cell, a necessary step in the determination of copy number. In this work, software for calculating probabilities from …

Lattice Of Maximal-Primary Ideals In Quadratic Orders, Ryan Bridges

Mathematics & Statistics ETDs

An order is a subring of the ring of integers of an algebraic extension, Peruginelli and Zanardo classified the lattices of orders with prime index inside te ring of integers of quadratic extensions of the rational numbers. The lattices are quite striking and have different layered structure depending on whether the prime is inert, split, or ramified. This thesis considers the orders which have prime power index inside the Gaussian integers. This is a nice generalization of the work of Peruginelli and Zanardo, and succeeds in a few classifications of specific instances of orders derived from inert primes.

"A Comparison Of Variable Selection Methods Using Bootstrap Samples From Environmental Metal Mixture Data", Paul-Yvann Djamen

Mathematics & Statistics ETDs

In this thesis, I studied a newly developed variable selection method SODA, and three customarily used variable selection methods: LASSO, Elastic net, and Random forest for environmental mixture data. The motivating datasets have neuro-developmental status as responses and metal measurements and demographic variables as covariates. The challenges for variable selections include (1) many measured metal concentrations are highly correlated, (2) there are many possible ways of modeling interactions among the metals, (3) the relationships between the outcomes and explanatory variables are possibly nonlinear, (4) the signal to noise ratio in the real data may be low. To compare these methods …

Quantitatively Motivated Model Development Framework: Downstream Analysis Effects Of Normalization Strategies, Jessica M. Rudd

Doctor of Data Science and Analytics Dissertations

Through a review of epistemological frameworks in social sciences, history of frameworks in statistics, as well as the current state of research, we establish that there appears to be no consistent, quantitatively motivated model development framework in data science, and the downstream analysis effects of various modeling choices are not uniformly documented. Examples are provided which illustrate that analytic choices, even if justifiable and statistically valid, have a downstream analysis effect on model results. This study proposes a unified model development framework that allows researchers to make statistically motivated modeling choices within the development pipeline. Additionally, a simulation study is …

Methods Of Uncertainty Quantification For Physical Parameters, Kellin Rumsey

Mathematics & Statistics ETDs

Uncertainty Quantification (UQ) is an umbrella term referring to a broad class of methods which typically involve the combination of computational modeling, experimental data and expert knowledge to study a physical system. A parameter, in the usual statistical sense, is said to be physical if it has a meaningful interpretation with respect to the physical system. Physical parameters can be viewed as inherent properties of a physical process and have a corresponding true value. Statistical inference for physical parameters is a challenging problem in UQ due to the inadequacy of the computer model. In this thesis, we provide a comprehensive …

Assessing The Validity Of Sentiment Analysis Measures Through Polychoric Correlation, Kelli N. Kasper

Mathematics & Statistics ETDs

Sentiment analysis methods extract the attitude of a text via systematic algorithms. To evaluate the validity of common sentiment analysis methods, we use polychoric correlation to compare computer-mediated methods and human-rated analogues. Our main topics of interest are the internal consistency of the raters' scores, the level of consensus among raters, and how well raters' scores correlate with those given by sentiment analysis methods for randomly collected Twitter data.

Our analysis found that there is good validity for methods that measure negative and positive sentiments in short texts, both in terms of inter-rater consistency and when comparing raters to computer-mediated …

An Investigation Of Gene Regulatory Network State Space Variability, Sara Faye Liesman

Theses and Dissertations

Genes are segments of DNA that provide a blueprint for cells and organisms to effectively control processes and regulations within individuals. There have been many attempts to quantify these processes, as a greater understanding of how genes operate could have large impacts on both personalized and precision medicine. Gene interactions are of particular interest, however, current biological methods can not easily reveal the details of these interactions. Therefore, we infer networks of interactions from gene expression data which we call a gene regulatory network, or GRN. Due to the robust behavior of genes and the inherent variability within interactions, models …

An Improved Method For Spectroscopic Quality Classification, Elizabeth G. Mayer

Mathematics & Statistics ETDs

Spectral quality classification is a vital step in data cleaning before the

analysis of magnetic resonance spectroscopy (MRS) data can be done. This

analysis compares five methods of quality classification; three of these are

legacy methods, Maudsley et al. (2006), Zhang et al. (2018), and

Bustillo et al. (2020), and two newly created methods that used a random forests

classifier (RFC) to inform their classifications. We found that the random forest

classifier was the most accurate at predicting spectra quality (balanced

accuracy for RF of 88% vs legacy of 70%, 72%, or 72%). A

Random-Forests-Informed Filtering method (RFIFM) for quality …

A Study Of The Efficacy Of Machine Learning For Diagnosing Obstructive Coronary Artery Disease In Non-Diabetic Patients, Demond Larae Handley

Theses and Dissertations

According to the Centers for Disease Control and Prevention, about 18.2 million adults age 20 and older have Coronary Artery Disease in the United States. Early diagnosis is therefore of crucial importance to help prevent debilitating consequences, and principally death for many patients. In this study we use data containing gene expression values from peripheral blood samples in 198 non-diabetic patients, with the goal of developing an age and sex gene expression model for diagnosis of Coronary Artery Disease. We employ machine learning methods to obtain a classification based on genetic information, age and sex. Our implementation uses feed forward …

Dividend Maximization Under A Set Ruin Probability Target In The Presence Of Proportional And Excess-Of-Loss Reinsurance, Christian Kasumo, Juma Kasozi, Dmitry Kuznetsov

Applications and Applied Mathematics: An International Journal (AAM)

We study dividend maximization with set ruin probability targets for an insurance company whose surplus is modelled by a diffusion perturbed classical risk process. The company is permitted to enter into proportional or excess-of-loss reinsurance arrangements. By applying stochastic control theory, we derive Volterra integral equations and solve numerically using block-by-block methods. In each of the models, we have established the optimal barrier to use for paying dividends provided the ruin probability does not exceed a predetermined target. Numerical examples involving the use of both light- and heavy-tailed distributions are given. The results show that ruin probability targets result in …

Inventory Models For Deteriorating Items With Power Pattern Demand Rate, Olalekan Adaraniwon Amos

Student Works (2020-2029)

Inventory management has become a prevalent topic in the field of operational research over some decades now. It cuts across many areas like management sciences, statistics and engineering. However, research focusing on inventory model with power demand pattern is quite limited. Demand patterns are defined as different ways by which products are removed out of inventory to supply customers demand during the schedule period. Power demand pattern permits suiting the demand to a more practical situation. In this research, four deterministic inventory model for deteriorating items with power demand pattern has been developed. We considered in the first models an …

Multilevel Asymptotic Parallel-In-Time Techniques For Temporally Oscillatory Pdes, Nicholas Abel

Mathematics & Statistics ETDs

As the clock speeds of individual processors level off and the amount of parallel resources continue to increase rapidly, further exploitation of parallelism is necessary to improve compute times. For time-dependent differential equations, the serial computation of time-stepping presents a bottleneck, but parallel-in-time integration methods offer a way to compute the solution in parallel along the time domain. Parallel-in-time methods have been successful in achieving speedup when computing solutions for parabolic problems; however, for problems with large hyperbolic terms and no strong diffusivity, parallel-in-time methods have traditionally struggled to offer speedup. While work has been done to understand why parallel-in-time …

A Statistical Analysis Of The Unm Facets Design Identity & Beliefs Survey Data, Clarissa A. Sorensen-Unruh

Mathematics & Statistics ETDs

The NSF-funded FACETS (Formation of Accomplished Chemical Engineers for Transforming Society, NSF Award 1623105) grant aims to transform the undergraduate engineering experience in the Department of Chemical and Biological Engineering at the University of New Mexico to address attrition within engineering majors, especially among underserved populations (Brainard & Carlin, 1998). The UNM FACETS Design Identity & Beliefs survey, an assessment tool used as part of the research of the grant, generated the dataset used in this study. I performed several different statistical analyses on the dataset, including confirmatory factor analysis (CFA), principal component analysis (PCA), and cluster analysis. The …

Decision Tree For Predicting The Party Of Legislators, Afsana Mimi

Publications and Research

The motivation of the project is to identify the legislators who voted frequently against their party in terms of their roll call votes using Office of Clerk U.S. House of Representatives Data Sets collected in 2018 and 2019. We construct a model to predict the parties of legislators based on their votes. The method we used is Decision Tree from Data Mining. Python was used to collect raw data from internet, SAS was used to clean data, and all other calculations and graphical presentations are performed using the R software.