Digital Commons Network^™

Finding Torsion-Free Groups Which Do Not Have The Unique Product Property, Lindsay Jennae Soelberg

Theses and Dissertations

This thesis discusses the Kaplansky zero divisor conjecture. The conjecture states that a group ring of a torsion-free group over a field has no nonzero zero divisors. There are situations for which this conjecture is known to hold, such as linearly orderable groups, unique product groups, solvable groups, and elementary amenable groups. This paper considers the possibility that the conjecture is false and there is some counterexample in existence. The approach to searching for such a counterexample discussed here is to first find a torsion-free group that has subsets A and B such that AB has no unique product. We …

An Algorithm For Symbolic Computing Of Singular Limits Of Dynamical Systems, Dane Jordan Bjork

Theses and Dissertations

The manifold boundary approximation method, MBAM is a new technique used in approximating systems of equations using parameter reduction. This method and other approximation methods are introduced and described. Several current issues in performing MBAM are discussed in further detail. These issues significantly slow down the process of MBAM and create a barrier of entry for those wishing to use the method without a strong background in mathematics. A solution is proposed to automatically reparameterize models and evaluate specific types of variables approaching limits -- significantly speeding up the process of MBAM. An implementation of the solution is discussed.

Adding Limit Points To Bass-Serre Graphs Of Groups, Alexander Jin Shumway

Theses and Dissertations

We give a brief overview of Bass-Serre theory and introduce a method of adding a limit point to graphs of groups. We explore a basic example of this method, and find that while the fundamental theorem of Bass-Serre theory no longer applies in this case we still recover a group action on a covering space of sorts with a subgroup isomorphic to the fundamental group of our new base space with added limit point. We also quantify how much larger the fundamental group of a graph of groups becomes after this construction, and discuss the effects of adding and identifying …

Euclidean Domains, Vandy Jade Tombs

Theses and Dissertations

In the usual definition of a Euclidean domain, a ring has a norm function whose codomain is the positive integers. It was noticed by Motzkin in 1949 that the codomain could be replaced by any well-ordered set. This motivated the study of transfinite Euclidean domains in which the codomain of the norm function is replaced by the class of ordinals. We prove that there exists a (transfinitely valued) Euclidean Domain with Euclidean order type for every indecomposable ordinal. Modifying the construction, we prove that there exists a Euclidean Domain with no multiplicative norm. Following a definition of Clark and Murty, …

Use Of Phase And Amplitude Gradient Estimation For Acoustic Source Characterization And Localization, Joseph Scott Lawrence

Theses and Dissertations

Energy-based acoustic quantities provide vital information about acoustic fields and the characterization of acoustic sources. Recently, the phase and amplitude gradient estimator (PAGE) method has been developed to reduce error and extend bandwidth of energy-based quantity estimates. To inform uses and applications of the method, analytical and experimental characterizations of the method are presented. Analytical PAGE method bias errors are compared with those of traditional estimation for two- and three-microphone one-dimensional probes. For a monopole field when phase unwrapping is possible, zero bias error is achieved for active intensity using three-microphone PAGE and for specific acoustic impedance using two-microphone PAGE. …

Data Assimilation In The Boussinesq Approximation For Mantle Convection, Shane Alexander Mcquarrie

Theses and Dissertations

Many highly developed physical models poorly approximate actual physical systems due to natural random noise. For example, convection in the earth's mantle—a fundamental process for understanding the geochemical makeup of the earth's crust and the geologic history of the earth—exhibits chaotic behavior, so it is difficult to model accurately. In addition, it is impossible to directly measure temperature and fluid viscosity in the mantle, and any indirect measurements are not guaranteed to be highly accurate. Over the last 50 years, mathematicians have developed a rigorous framework for reconciling noisy observations with reasonable physical models, a technique called data assimilation. …

Congruences For Fourier Coefficients Of Modular Functions Of Levels 2 And 4, Eric Brandon Moss

Theses and Dissertations

We give congruences modulo powers of 2 for the Fourier coefficients of certain level 2 modular functions with poles only at 0, answering a question posed by Andersen and Jenkins. The congruences involve a modulus that depends on the binary expansion of the modular form's order of vanishing at infinity. We also demonstrate congruences for Fourier coefficients of some level 4 modular functions.

The Arithmetic Of Modular Grids, Grant Steven Molnar

Theses and Dissertations

Let M_k^(∞) (Gamma, nu) denote the space of weight k weakly holomorphic weight modular forms with poles only at the cusp (∞), and let widehat M_k^(∞) (Gamma, nu) subseteq M_k^(∞) (Gamma, nu) denote the space of weight k weakly holomorphic modular forms in M_k^(∞) (Gamma, nu) which vanish at every cusp other than (∞). We construct canonical bases for these spaces in terms of Maass--Poincaré series, and show that the coefficients of these bases satisfy Zagier duality.

Principles Of Productivity Revealed From Secondary Mathematics Teachers' Discussions Around The Productiveness Of Teacher Moves In Response To Teachable Moments, Kylie Victoria Palsky

Theses and Dissertations

How do teachers talk about the productiveness of teacher's in-the-moment responses to student mathematical thinking? This is a question current research does not fully answer as most research on teacher moves is focused on what teacher moves researchers have noticed teachers do rather than on what teachers think about these teacher moves. To fill the gap in the research and to answer the question, a group of 13 teachers were given ten classroom situations to compare and contrast for productivity. I analyzed (a) the content of the teachers' discussions by drawing on Teacher Response Coding (TRC) language, and (b) the …

Fundamental Investigation Of Magnesium Corrosion Using Experiments And Simulation, Dila Ram Banjade

Theses and Dissertations

Magnesium (Mg) is the lightest of all structural metals and has tremendous potential for applications in the lightweight industry. However, the corrosion of Mg is a significant barrier towards its wider use. Despite years of research, the fundamental understanding of Mg corrosion still remains short. The enhanced hydrogen evolution reaction (HER) with anodic polarization, the modeling of galvanic corrosion and the impact of hydrogen bubbles for galvanically coupled Mg are important aspects of Mg corrosion that need to be understood before any mitigation measures can be taken. The results presented in this work provide a key step in that direction. …

Strontium Isotopes-A Tracer For Dust And Flow Processes In An Alpine Catchment, Colin Andrus Hale

Theses and Dissertations

Stream chemistry changes in response to snowmelt, but does not typically reflect thechemistry of the snowpack. This suggests that flow processes between snowmelt and streamsystem, such as interactions with the soil and bedrock, have an important control on waterchemistry and highlight the complex flow pathways from the snowpack to stream. To investigateflow processes in the upper Provo River watershed, northern Utah, we sampled three sites on theriver ~20 times per year during 2016 and 2017. The sites, from highest elevations to lowest wereSoapstone, Woodland, and Hailstone, corresponding to locations of active stream gauges. Toidentify possible water sources to the stream …

Machine Learning For Inspired, Structured, Lyrical Music Composition, Paul Mark Bodily

Theses and Dissertations

Computational creativity has been called the "final frontier" of artificial intelligence due to the difficulty inherent in defining and implementing creativity in computational systems. Despite this difficulty computer creativity is becoming a more significant part of our everyday lives, in particular music. This is observed in the prevalence of music recommendation systems, co-creational music software packages, smart playlists, and procedurally-generated video games. Significant progress can be seen in the advances in industrial applications such as Spotify, Pandora, Apple Music, etc., but several problems persist. Of more general interest, however, is the question of whether or not computers can exhibit autonomous …

A Framework And Exploration Of A Cybersecurity Education Escape Room, Justin Charles Snyder

Theses and Dissertations

This thesis presents a review of educational-escape-room literature followed by a design-oriented framework (the Snyder Escape Room Framework or SERF) and demonstrates the potential efficacy of escape-rooms in cybersecurity education. Several authors have proposed frameworks and guidelines for game and educational design regarding escape rooms. This work coalesces some of those ideas into a more substantial and comprehensive framework (SERF) that designers can use when developing educational escape rooms. The Snyder Escape Room Framework provides heuristics for goals and objectives, players, activities, context, trajectory design, and evaluation. Additionally, this work describes and analyzes the novel prototyped BYU GCC escape room …

Teacher Graphing Practices For Linear Functions In A Covariation-Based College Algebra Classroom, Konda Jo Luckau

Theses and Dissertations

Graphing is a fundamental topic in algebra that is notoriously difficult for students. Much of the past research has focused on conceptions and misconceptions. This study extends past research by looking at the mathematical practices of a practitioner, specifically one instructor of a function-based covariation-focused algebra class in the linear functions unit. Considering practices in addition to conception adds dramatically to our understanding of mathematical activity because it leads to explicit descriptions of normative purposes that are connected to particular situations or problems and also specifies how tools and symbols are coordinated to achieve these purposes. The results of this …

Image Source Modeling Of Time Reversal For Room Acoustics Applications, Michael Hunter Denison

Theses and Dissertations

Time Reversal (TR) is a technique that may be used to focus an acoustic signal at a particular point in space. While many variables contribute to the quality of TR focusing of sound in a particular room, the most important have been shown to be the number of sound sources, signal bandwidth and absorption properties of the medium [Ribay et al., J. Acoust. Soc. Am. 117(5), 2866-2872 (2005)]. However, the effect of room size on TR focusing has not been explored. Using the image source method algorithm proposed by Allen and Berkley [J. Allen and D. A. Berkley, J. Acoust. …

Gekko Optimization Suite, Logan Beal, Daniel Hill, Ronald Abraham Martin, John Hedengren

Faculty Publications

This paper introduces GEKKO as an optimization suite for Python. GEKKO specializes in dynamic optimization problems for mixed-integer, nonlinear, and differential algebraic equations (DAE) problems. By blending the approaches of typical algebraic modeling languages (AML) and optimal control packages, GEKKO greatly facilitates the development and application of tools such as nonlinear model predicative control (NMPC), real-time optimization (RTO), moving horizon estimation (MHE), and dynamic simulation. GEKKO is an object-oriented Python library that offers model construction, analysis tools, and visualization of simulation and optimization. In a single package, GEKKO provides model reduction, an object-oriented library for data reconciliation/model predictive control, and …

Software Testing A Library And Restful Application Programming Interface For Ecological Pesticide Risk Assessment Models, Tom Purucker, William Eckel, Jonathan Flaishans, Tao Hong, Trip Hook, Andrew Kanarek, Jeffrey M. Minucci, Nicholas Pope, Deron Smith, Sumathy Sinnathamby, Nelson Thurman, Kurt Wolfe

International Congress on Environmental Modelling and Software

The Environmental Protection Agency (EPA) registers pesticides for use in the United States under the Federal Insecticide, Fungicide, and Rodenticide Act (FIFRA). Before a pesticide can be registered, the EPA must assess whether the pesticide can be used without being harmful to humans or posing unreasonable adverse environmental effects. We present a set of ecological risk assessment models commonly used as part of the FIFRA registration process as a software library. These mathematical models predict fate, transport and exposure of pesticides in different media and are designed to be protective of non-target ecological species. Some algorithms in this set have …

Practical Poststructuralism For Confronting Wicked Problems, Vanessa Schweizer, Ricarda Scheele, Hannah Kosow

International Congress on Environmental Modelling and Software

This paper discusses an innovative qualitative-quantitative modelling method relevant to two characteristics of wicked problems: they have no definitive formulation, and the choice of how they are defined or explained determines the nature of their resolution. Through projects conceptualizing the human dimensions of climate change, the socio-technical dynamics of the Energiewende (Germany’s low-carbon energy transition), and of water futures of a megacity (Lima), it has been found that the system-theoretic method of cross-impact balances (CIB) reveals fundamental assumptions in interdisciplinary modelling projects and opens them up for investigation. This can democratize modelling exercises while preserving scientific credibility. It can also …

Operationalizing Social Ecological Systems Resilience Analysis Using A Dynamic Index, Bruno Meirelles

International Congress on Environmental Modelling and Software

Governance of social ecological systems (SES) is a difficult task. Embrace its complexity, the coupled nature of social and ecological dimensions, feedbacks and non-linearity of its attributes and the necessity of dealing with society participation in the decision process make the challenge bigger. Resilience is a growing research field that can collaborate with this discussion. Resilience is a SES feature that enhance its capacity of maintain identity under different systems changes. This work uses system dynamics theory as foundation to build a Dynamic Resilience Index. This index uses Cobb-Douglas equation to encompass several resilience attributes as biodiversity, social networks, institutions, …

Long-Term Forecasting Of Nitrogen Dioxide Ambient Levels In Metropolitan Areas Using The Discrete-Time Markov Model, Asaf Nebenzal, Barak Fishbain

International Congress on Environmental Modelling and Software

Abstract: Air pollution management and control are key factors in maintaining sustainable societies. Air quality forecasting is a key factor in these tasks. While short-term forecasting, few days into the future, is a well-established research domain, no method exists for long-term forecasting (e.g., what will be the pollution levels distribution in the next year), which is essential for environmental planning and management as well as epidemiological and exposure studies. This research defines long-term air pollution forecasting and presents a Discrete-Time-Markov-based model for forecasting ambient nitrogen oxides patterns. Specifically, the model provides an estimate for the chance for tomorrow’s pollution level, …

An Interdisciplinary Approach For Finding Biophysically Optimal Land Use Strategies With Highest Social Welfare, Andrea Kaim, Bartosz Bartkowski, Michael Beckmann, Nele Lienhopp, Christoph Schroeter-Schlaack, Ralf Seppelt, Michael Strauch, Martin Volk

International Congress on Environmental Modelling and Software

Agricultural production needs to generate economic profits and contributes to the social welfare of a society. At the same time, it is one of the biggest threats to biodiversity. While from a narrowly economic viewpoint land should be allocated in a way that best fulfils the demand for agricultural products, ecological disciplines aim to protect nature, e.g. biodiversity. Thus, a socially optimal land use strategy should combine both perspectives. However, in the field of spatial land use allocation, there is a lack of studies that consider both aspects simultaneously. Therefore, we developed a method that finds biophysically optimal land use …

Developing An Integrated Model For Food-Energy-Water Nexus In The Pacific Northwest, Usa, Seyed Mohammad Hossien Tabatabaie, Ganti Murthy

International Congress on Environmental Modelling and Software

With growing populations and the changing climate, the importance of food, energy, and water (FEW) security has become a global issue. The competition for natural resources has caused the recognition of FEW nexus concept in which the interdependency between FEW sectors is taken into account for the effective management of resources with an enhanced understanding of underlying dynamics. In this context, developing an integrated model supported by a comprehensive quantitative framework is necessary. Although there are numerous studies on FEW nexus, limited research has been done on developing mathematical equations to model the FEW nexus. The goal of this study …

Uncertainty And Sensitivity Analysis For Reducing Greenhouse Gas Emissions From Wastewater Treatment Plant, Giorgio Mannina, Alida Cosenza, Taise Ferreira Rebouças

International Congress on Environmental Modelling and Software

This paper presents the sensitivity and uncertainty analysis of a plat-wide mathematical model for wastewater treatment plants (WWTPs). The mathematical model assesses direct and indirect (due to the energy consumption) greenhouse gases (GHG) emissions from a WWTP employing a whole-plant approach. The model includes: i. the kinetic/mass-balance based model regarding nitrogen; ii. two-step nitrification process; iii. N₂O formation both during nitrification and denitrification (as dissolved and off-gas concentration). Important model factors have been selected by using the Extended - Fourier Amplitude Sensitivity Testing (FAST) global sensitivity analysis method. A scenario analysis has been performed in order to evaluate …

Uncertainty In Drinking Water Supplies: Exploring Stochastic Source Water Quality Generation Methods, William J. Raseman, Joseph R. Kasprzyk, William Kleiber, Rajagopalan Balaji

International Congress on Environmental Modelling and Software

This work explores stochastic source water quality generation methods to aid in the characterization of uncertainty in water treatment planning. Water treatment plants (WTPs) are tasked with providing citizens safe and reliable drinking water; however, variability of surface water quality due to seasonal fluctuations and extreme events (e.g., flooding and wildfires) can overwhelm a WTP's capacity to do so. By characterizing source water uncertainty and creating realistic water quality scenarios, decision makers can adjust operating policies and make infrastructural changes to improve the reliability of their system. Building on methods from stochastic streamflow generation, including, autoregressive moving average models, vector …

An Environmental Modelling Approach Sheds New Light On A Thorny Problem: Gender Inequality In Science, Kate O'Brien, Paul Maxwell, Terrance Fitzsimmons, Brian Head, Margaret Crane

International Congress on Environmental Modelling and Software

Much has been written and said about gender inequality in Science, Technology, Engineering and Mathematics (STEM): documenting the phenomenon, proposing a myriad of causes, debating possible solutions, and, most frequently, asking why is progress so slow? In this study, we propose that gender inequality in STEM is not just one problem, but a collection of interconnected, poorly defined problems for which there are no definitive solutions. Sound familiar? The same challenges characterize other wicked problems, such as those faced in modelling and managing socio-ecological systems. Like ecosystem health, gender equality has multiple valid definitions and no single indicator of success. …

From Data Science To Hydrology: California Reservoirs During Drought, Armeen Taeb

International Congress on Environmental Modelling and Software

Water is a precious commodity, especially in the state of California. Our state frequently experiences cycles of major state-wide precipitation deficits – most notably the 2012–2015 drought which was the worst to occur in the past 1200 years. The focus of this work is to develop a state-wide model of the California reservoir network to address the following scientific questions: 1) what are the dependencies among reservoirs? 2) Are there unmodeled phenomena (denoted as latent variables) that are influencing the network globally? Could these latent variables cause a system-wide catastrophe (e.g. exhaustion of multiple large reservoirs)?

Since reservoirs are strongly …

An Interoperable Workflow-Based Framework For The Automation Of Building Intelligent Process Control Systems, Josep Pascual Pañach, Miquel Àngel Cugueró Escofet, Miquel Sànchez Marrè, Pere Aguiló Martos

International Congress on Environmental Modelling and Software

One of the major problems to design and implement a control/supervision system for a process lies in the need to establish an ad-hoc system for each process installation. On the other side, an open challenge related to the deployment of Intelligent Decision Support Systems (IDSSs) is the interoperability of the different methods used, in order to allow interaction and reuse of different data mining methods and the use of methods based on a model or an expert. Thus, this paper proposes the use of visual workflows, to enable the automation of the design task and the implementation of Intelligent Process …

Open Source Tool In R Language To Estimate The Inference Of The Fuzzy Cognitive Map In Environmental Decision Making, Zoumpolia Dikopoulou, Elpiniki Papageorgiou, Antonie Jetter, Dionysios Bochtis

International Congress on Environmental Modelling and Software

Fuzzy cognitive maps (FCMs) have gained popularity within the scientific community due to their capabilities in modeling and decision making for complex problems. However, despite the large number of papers in advances on mathematical formulation and applications of FCMs, and some recent tools for this soft computing technique, there is a lack of open source tools for FCMs in modeling and inference in diverse application domains. In this research paper, we are filling that gap. We present an open source package in R programming language, called the ‘fcm’ package to estimate the inference of the FCM and accomplish …

Integrating Data-Based And Knowledge-Based Models In An Environmental Decision Support System For The Management Of A Drinking Water Treatment Plant, Lluís Godo-Pla, Pere Emiliano, Jordi Suquet, Fernando Valero, Manel Poch, Hèctor Monclús

International Congress on Environmental Modelling and Software

Drinking Water Treatment Plants (DWTP) face complex decision-making in their daily operation. The amount of data generated along the DWTP allows developing data-driven models and knowledge-based models that can be integrated into Intelligent Environmental Decision Support Systems (IEDSS). These systems can be used for predicting the main operational parameters along the water treatment process. At the present study, the procedure for building an IEDSS has been followed with a whole-plant approach. A methodology has been purposed to choose the right modelling technique that attends to the process characteristics and whose results are in tune with the expert knowledge. As a …

The Influence Of Fisher Information In Kic Model Selection, Judith Schenk, Eileen Poeter, William Navidi

International Congress on Environmental Modelling and Software

Groundwater models are commonly constructed using a small amount of data relative to the size of the area modeled. Considering only a single groundwater model ignores the uncertainty associated with model structure. Evaluating multiple groundwater models of a system considers model structural uncertainty and provides for a more realistic assessment of prediction uncertainty. Kashyap information criteria (KIC) is an equation used in multi-model analysis (MMA) to evaluate a set of models and the probability that a model represents the true, but unknown, system. Fisher Information (FI) measures information content of a model and is an influential component in the KIC …