Statistics and Probability Commons^™

Maximum Likelihood Estimation Of Species Trees And Anomaly Zone Detection Using Ranked Gene Trees, Anastasiia Kim

Mathematics & Statistics ETDs

A phylogenetic tree represents the evolutionary relationships among a set of organisms. Gene trees can be used to reconstruct phylogenetic trees. The methods in this dissertation focus on the gene tree topologies with emphasis on ranked gene tree topologies. A ranked tree depicts the order in which nodes appear in the tree together with topological relationships among gene lineages. One challenge that arises during phylogenetic inference is the existence of the anomaly zones, the regions of branch-length space in the species tree that can produce gene trees that have topologies differing from the species tree topology but are more probable …

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 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 …

Side-Channel Power Resistance For Encryption Algorithms Using Implementation Diversity, Ivan M. Bow

Electrical and Computer Engineering ETDs

This thesis paper investigates countermeasures to hardware side-channel attacks and proposes a new solution to this ever growing threat against data integrity and security. The side-channel attack methods, differential power analysis and correlation power analysis, are both very powerful techniques and are used to gain access to secrets inside of a field programmable gate array that are otherwise inaccessible, in particular the cryptographic key for the Advanced Encryption Standard algorithm. To counter these attacks, we propose a method of changing the internal hardware configuration of the field programmable gate array using dynamic partial reconfiguration. Using this method, we change the …

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 …

Nonlinear Least Squares 3-D Geolocation Solutions Using Time Differences Of Arrival, Michael V. Bredemann

Mathematics & Statistics ETDs

This thesis uses a geometric approach to derive and solve nonlinear least squares minimization problems to geolocate a signal source in three dimensions using time differences of arrival at multiple sensor locations. There is no restriction on the maximum number of sensors used. Residual errors reach the numerical limits of machine precision. Symmetric sensor orientations are found that prevent closed form solutions of source locations lying within the null space. Maximum uncertainties in relative sensor positions and time difference of arrivals, required to locate a source within a maximum specified error, are found from these results. Examples illustrate potential requirements …

Neutroalgebra Is A Generalization Of Partial Algebra, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we recall, improve, and extend several definitions, properties and applications of our previous 2019 research referred to NeutroAlgebras and AntiAlgebras (also called NeutroAlgebraic Structures and respectively AntiAlgebraic Structures). Let be an item (concept, attribute, idea, proposition, theory, etc.). Through the process of neutrosphication, we split the nonempty space we work on into three regions {two opposite ones corresponding to and , and one corresponding to neutral (indeterminate) (also denoted ) between the opposites}, which may or may not be disjoint – depending on the application, but they are exhaustive (their union equals the whole space). A NeutroAlgebra …

How We Can Extend The Standard Deviation Notion With Neutrosophic Interval And Quadruple Neutrosophic Numbers, Victor Christianto, Florentin Smarandache, Muhammad Aslam

Branch Mathematics and Statistics Faculty and Staff Publications

During scientific demonstrating of genuine specialized framework we can meet any sort and rate model vulnerability. Its reasons can be incognizance of modelers or information mistake. In this way, characterization of vulnerabilities, as for their sources, recognizes aleatory and epistemic ones. The aleatory vulnerability is an inalienable information variety related with the researched framework or its condition. Epistemic one is a vulnerability that is because of an absence of information on amounts or procedures of the framework or the earth [7]. Right now, we examine fourfold neutrosophic numbers and their potential application for practical displaying of physical frameworks, particularly in …

A Pedagogic Analysis Of Linear Algebra Courses, Andrew Taylor

Mathematics & Statistics ETDs

This project is concerned with investigating the question, "Do our applied linear algebra courses (at the University of New Mexico) adequately prepare STEM students for future work in their respective fields?" In order to explore this, surveys were issued to three groups (sections) of students (among two different instructors) at the conclusion of their applied linear algebra course, as well as STEM professors/instructors from a variety of STEM fields. Students were surveyed regarding their perceived mastery of given topics/ideas from the course and professors/instructors were surveyed about the level of mastery they felt was necessary (referred to as ``desired mastery") …

Implications Of The Modifiable Areal Unit Problem For Wildfire Analyses, Timothy P. Nagle-Mcnaughton, Xi Gong, Jose A. Constantine

Geography and Environmental Studies Faculty Publications

Wildfires pose a danger to both ecologies and communities. To this end, many large-scale analyses of wildfire patterns and behavior rely on the aggregation of point data to polygons, typically those based on distinct disparate ecological areas. However, the sizes, shapes, andorientations of the polygons to which data are aggregated are not neutral factors in the resulting analysis. The influence of the aggregation polygons on calculated results is known as the modifiable areal unit problem (MAUP), which is well-documented in the spatial statistics literature. Despite the documentation of the MAUP, relatively few wildfire studies consider the effects of the MAUP …

Practical Modelling Of The Vanilla Option Volatility Smile, Jacob E. Shanley

Mathematics & Statistics ETDs

Many discussions on how best to model the standard American Option derivative focus solely upon the volatility smile modelling itself from a mathematical perspective. This thesis instead closely examines both the practical and mathematical implications of processing market data, modelling the volatility smile, and making real-world trading decisions from the results. In particular, it contains an analysis of market data processing algorithms, new volatility smile models, multiple empirically-driven weighting schemes, Gauss-Newton and Levenberg-Marquardt optimization algorithms, and various trading strategies. The top performing combinations found were those that involved the Smile and Twist volatility smile models, Volatility Width Vega Multiplier weighting …

Constraining The Oxygen Values Of The Late Cretaceous Western Interior Seaway Using Marine Bivalves, Camille H. Dwyer

Earth and Planetary Sciences ETDs

The Western Interior Seaway (WIS) remains an oceanographic enigma, including its circulation, similarity to the open ocean, and the fidelity of geochemical proxies to reconstruct paleoenvironments. Across the late Campanian and early Maastrichtian I test whether: 1) the WIS had unique δ¹⁸O_VPDB compared to other marine settings, 2) increasing oceanographic restriction changed the stable isotope composition, and 3) biases, e.g., taxonomy or diagenesis, influenced stable isotope compositions. Results indicate distinct δ¹⁸O_VPDB in the WIS compared to other marine settings. δ¹⁸O_VPDB values were stable through time, suggesting insignificant oceanographic restriction and a …

A Deep Learning Approach To Uncertainty Quantification, Mst Afroja Akter

Mathematics & Statistics ETDs

In this thesis we consider ordinary differential equations (ODEs) with random parameters. We focus on Monte Carlo (MC) sampling for computing the statistics of some quantities of interest (QoIs) given by the solution of the ODE problems. We use the 4th order accurate Runge-Kutta (RK4) method as the deterministic ODE solver. We then develop a hybrid MC sampling method that combines RK4 with neural network models to efficiently compute the statistics of QoIs within a desired accuracy. We present several numerical examples to verify the accuracy and efficiency of the proposed hybrid method compared to classical MC sampling. The hybrid …

Assessing The Efficacy Of Home-Based Renal Care Using Propensity Scores, Eunice Choi

Mathematics & Statistics ETDs

This study investigated the efficacy of Home-Based Renal Care (HBRC) in diabetic Zuni Indians with Chronic Kidney Disease (CKD) in New Mexico using propensity scores. Home based intervention as opposed to standard clinical care is a pragmatic treatment approach that incorporates the preference of population in hopes of addressing a cultural barrier to healthcare in this high risk population. This study uses a logistic regression model and a linear regression model to estimate the average effect of HBRC on increasing the likelihood of participants taking a more active role in the management of their chronic condition compared to the control …

Neutrosophic Set Is A Generalization Of Intuitionistic Fuzzy Set, Inconsistent Intuitionistic Fuzzy Set (Picture Fuzzy Set, Ternary Fuzzy Set), Pythagorean Fuzzy Set, Q-Rung Orthopair Fuzzy Set, Spherical Fuzzy Set, And N-Hyperspherical Fuzzy Set, While Neutrosophication Is A Generalization Of Regret Theory, Grey System Theory, And Three-Ways Decision (Revisited), Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we prove that Neutrosophic Set (NS) is an extension of Intuitionistic Fuzzy Set (IFS) no matter if the sum of single-valued neutrosophic components is < 1, or > 1, or = 1. For the case when the sum of components is 1 (as in IFS), after applying the neutrosophic aggregation operators one gets a different result from that of applying the intuitionistic fuzzy operators, since the intuitionistic fuzzy operators ignore the indeterminacy, while the neutrosophic aggregation operators take into consideration the indeterminacy at the same level as truth-membership and falsehood-nonmembership are taken. NS is also more flexible and effective because it …

Learning Statistics Through Guided Block Play: A Pre-Curriculum In Statistical Literacy, Robert P. Giebitz

Organization, Information and Learning Sciences ETDs

Learning to use data to investigate the world and make decisions has become an essential skill for all citizens. Play and curiosity are powerful motivators for learning. Inquiry – the process of asking questions and seeking answers – can engage the natural curiosity of young learners and motivate early learning. Recent research in statistics education has shown that children as young as 4 and 5 years old can learn to collect, organize, and interpret data they acquire through observation, counting, and measuring in a process of guided inquiry. Guided block play has been used for over 100 years to enable …

The Compensation For Few Clusters In Clustered Randomized Trials With Binary Outcomes, Lily Stalter

Mathematics & Statistics ETDs

Cluster randomized trials are increasingly popular in epidemiological and medical research. When analyzing the data from such studies it is imperative that the hierarchical structure of the data be taken into account. Multilevel logistic regression is used to analyze clustered data with binary outcomes. Previous literature shows that a greater number of clusters is more important than a large number of subjects per cluster. This paper investigates if it is possible to compensate for the increased bias found for parameter estimates when the number of clusters is decreased. A simulation study was conducted where the absolute percent relative bias for …

Genome-Wide Analysis Of Alternative Rna Splicing In Children With Acute Myeloid Leukemia (Aml), Xichen Li

Shared Knowledge Conference

The pediatric Acute Myeloid Leukemia (AML) is a high-risk and hard-to-treat childhood cancer that originates in the bone marrow from immature white blood cells. Recently, more and more evidence indicates that aberrant splicing of genes is a common characteristic for AML. Gene expression profiles have proved extremely useful for identifying genes that are associated with clinical characteristics and survival outcome of cancer patients. However, conventional gene expression profiles do not account for the differences observed in expressed isoforms when alternative RNA splicing is analyzed. Alternative RNA splicing can generate dozens of distinct transcripts from individual genes and the expressions of …

Analysis Of Ranked Gene Tree Probability Distributions Under The Coalescent Process For Detecting Anomaly Zones, Anastasiia Kim

Shared Knowledge Conference

In phylogenetic studies, gene trees are used to reconstruct species tree. Under the multispecies coalescent model, gene trees topologies may differ from that of species trees. The incorrect gene tree topology (one that does not match the species tree) that is more probable than the correct one is termed anomalous gene tree (AGT). Species trees that can generate such AGTs are said to be in the anomaly zone (AZ). In this region, the method of choosing the most common gene tree as the estimate of the species tree will be inconsistent and will converge to an incorrect species tree when …

Crustal Seismic Anisotropy Of The Ruby Mountains Core Complex And Surrounding Northern Basin And Range, Justin T. Wilgus

Earth and Planetary Sciences ETDs

Metamorphic core complexes (MCC) are distinctive uplifts that expose deeply exhumed and deformed crustal rocks due to localized extensional deformation. Consequently, their detailed structure provide a window into deep crustal mechanics. The North American Cordillera contains numerous MCC, one of which is the Ruby Mountains core complex (RMCC) located in the highly extended northern Basin and Range. To constrain the extent to which anisotropy below the RMCC deviates from the regional Basin and Range average and test the depth dependence of crustal anisotropy we conduct a radial anisotropy investigation below the RMCC and surrounding northern Basin and Range. Data from …

Quantitative Validation Of Simulated Sea Ice Displacements, Bryan R. Mccormick

Mathematics & Statistics ETDs

Accurate simulations of Arctic sea ice are important for forecasting as well as for understanding the global climate. However, quantitative measures for simulation displacements are underutilized. We present five such measures proposed as being useful in the validation of simulated sea ice displacements. Using drifting buoy and satellite measurements of sea ice motion as observation, we apply the metrics in a comparison of observed displacements and predicted displacements from the Arctic sea ice simulation MPM\_ice. We find the metric scores are useful for comparing simulations and observations. The metrics also brought to light problems in the simulation MPM_ice, demonstrating their …

Which Factors Influence Student Success In Intermediate Algebra, Math 101-102-103?, Linh T. Ward

Mathematics & Statistics ETDs

At The University of New Mexico (UNM), Intermediate Algebra (MATH 120 and MATH 101-102-103) has historically been a so-called “killer course”, with very low pass rates: approximately 40% in Fall 2009 to Spring 2011 and about 50% from Fall 2011 to Spring 2013. Furthermore, many students failed the class multiple times. Since 2013, a computer system called ALEKS has been used to teach the course and, along with some additional interventions, on Albuquerque/Main campus success rates for MATH 101 have increased to roughly 80% and MATH 102 to about 70%. This thesis provides a strategy to identify those 20-30% as-risk …

Trace Formulas For Perturbations Of Operators With Hilbert-Schmidt Resolvents, Bishnu Prasad Sedai

Mathematics & Statistics ETDs

In this dissertation, we study Taylor approximations of functions of operators with Hilbert-Schmidt resolvents. We obtain integral representations for traces of the respective Taylor remainders that are analogous to trace formulas obtained in the case of Schatten perturbations in [10, 11, 16].

High Order Hermite And Sobolev Discontinuous Galerkin Methods For Hyperbolic Partial Differential Equations, Adeline Kornelus

Mathematics & Statistics ETDs

Many real-world problems involving dynamics of solid or fluid bodies can be modeled by hyperbolic partial differential equations (PDEs). Up to this point, only solutions to selected PDEs are available. Many PDEs are physically or geometrically complex, resulting in difficulties computing the analytical solutions. In this thesis, we focus on numerical methods for approximating solutions to hyperbolic PDEs. Long-term simulation for the motion of the body described by the PDE requires a method that is not only robust and efficient, but also produces small error because the error will be propagated and accumulated over the course of the simulation. Therefore, …

Comparison Of Two Methods In Estimating Standard Error Of Simulated Moments Estimators For Generalized Linear Mixed Models, Danielle K. Duran

Mathematics & Statistics ETDs

We consider standard error of the method of simulated moment (MSM) estimator for generalized linear mixed models (GLMM). Parametric bootstrap (PB) has been used to estimate the covariance matrix, in which we use the estimates to generate the simulated moments. To avoid the bias introduced by estimating the parameters and to deal with the correlated observations, (Lu, 2012) proposed a multi-stage block nonparametric bootstrap to estimate the standard errors. In this research, we compare PB and nonparametric bootstrap methods (NPB) in estimating the standard errors of MSM estimators for GLMM. Simulation results show that when the group size is large, …

Multidataset Independent Subspace Analysis: A Framework For Analysis Of Multimodal, Multi-Subject Brain Imaging Data, Rogers F. Silva

Electrical and Computer Engineering ETDs

Mental illnesses are serious disorders of the brain that have devastating effects on individuals and society. In addition to their disabling and impairing effects, mental illnesses have deep social and economical implications, accounting for an estimated loss of 12 billion working days and a care cost surge to $6 trillion a year by 2030. For diseases such as depression and anxiety, enhancing preventive programs and treatment accessibility, in combination with accurate early diagnosis and personalized treatments, are projected to result in a four-fold return on every dollar invested, a strategy that can drastically help curtail those losses. Notably, within the …

Using Statistical Techniques To Estimate Rooted Species Trees From Unrooted Gene Trees, Ayed Rheal Alanzi

Mathematics & Statistics ETDs

Methods for inferring species trees from gene trees motivated by incomplete lineage

sorting typically use either rooted gene trees to infer a rooted species tree, or use

unrooted gene trees to infer an unrooted species tree, which is then typically rooted

using one or more outgroups. Theoretically, however, it has been known since 2011

that it is possible to infer the root of the species tree directly from unrooted gene

trees without assuming an outgroup. The present work is the first that we know of

which attempts to infer the root of a species tree using unrooted gene trees as …

Optimal Experimental Design To Characterize A Wave Source Using Dosimeter Measurements, Renee L. Gooding

Mathematics & Statistics ETDs

When modeling physical phenomena we want to solve the inverse problem by estimating the parameters that characterize the source model that we are interested in. In this thesis, we focus on the optimal placement of a finite number of individual sensors, called dosimeters, in two and three dimensions with a time dependent Gaussian wave source. Using a computational model along with experimental data, we design an iterative process to determine the optimal placement of an additional sensor such that the noise in the measurements has a minimal effect on the parameter estimation. First, we estimate the parameters that characterize the …

Deterministic And Probabilistic Methods For Seismic Source Inversion, Juan Pablo Madrigal Cianci

Mathematics & Statistics ETDs

The national Earthquake Information Center (NEIC) reports an occurrence of about 13,000 earthquakes every year, spanning different values on the Richter scale from very mild (2) to "giant earthquakes'' (8 and above). Being able to study these earthquakes provides useful information for a wide range of applications in geophysics. In the present work we study the characteristics of an earthquake by performing seismic source inversion; a mathematical problem that, given some recorded data, produces a set of parameters that when used as input in a mathematical model for the earthquake generates synthetic data that closely resembles the measured data. There …