Doctor of Philosophy, The Ohio State University, 2021, Psychology

Trait impulsivity, defined by actions taken without forethought and a consistent preference for immediate over delayed rewards, confers vulnerability to all externalizing spectrum disorders. This includes all disorders along the common developmental progression of attention-deficit/hyperactivity disorder (ADHD) in early childhood to conduct disorder (CD) and delinquency in later childhood and adolescence, to substance use disorders (SUDs) and antisocial personality disorder (ASPD) in adulthood. Such externalizing progression derives from complex interactions among individual-level vulnerabilities and environmental risk factors over time. Specifying how such mechanisms interact across development is a burgeoning area of research. Although trait-level mechanisms have long been studied, research linking trait-level to behavioral mechanisms is more limited. Furthermore, most existing research uses standard inferential approaches, which are not well suited for modeling complex relations among causal influences at different levels of analysis. In this dissertation, I describe how both (1) the methods used to make inference on individual difference correlations across levels of analysis, and (2) the statistical models used to infer how data within levels of analysis arise often fail to fully embody the substantive theories that researchers aim to test. I use my prior work on the “Reliability Paradox” (Haines et al., 2020a) to demonstrate (1), and my work on the Iowa Gambling Task (Haines, Vassileva, & Ahn, 2018) to demonstrate (2). I then discuss a third study (Haines et al., 2020b) that shows how joint generative models across levels of analysis (between behavioral and trait mechanisms, behavioral and neural mechanisms, etc.) can be used to better capture individual differences of theoretical interest.

Committee: Theodore Beauchaine (Advisor); Brandon Turner (Advisor); Patricia Van Zandt (Committee Member); Mona Makhija (Other) Subjects: Clinical Psychology; Cognitive Psychology; Developmental Psychology; Psychology

Master of Science, University of Akron, 2018, Applied Mathematics

A mathematical model is developed to describe the light field in vertical line seaweed cultivation to determine the degree to which the seaweed shades itself and limits the amount of light available for photosynthesis. A probabilistic description of the spatial distribution of kelp is formulated using simplifying assumptions about frond geometry and orientation. An integro-partial differential equation called the radiative transfer equation is used to describe the light field as a function of position and angle. A finite difference solution is implemented, providing robustness and accuracy at the cost of large CPU and memory requirements, and a less computationally intensive asymptotic approximation is explored for the case of low scattering. Conditions for applicability of the asymptotic approximation are discussed, and depth-dependent light availability is compared to the predictions of simpler light models. The 3D model of this thesis is found to predict significantly lower light levels than the simpler 1D models, especially in regions of high kelp density where a precise description of self-shading is most important.

Committee: Kevin Kreider Ph.D (Advisor); Curtis Clemons Ph.D (Advisor); Gerald Young Ph.D (Advisor) Subjects: Applied Mathematics; Aquaculture; Aquatic Sciences; Ocean Engineering; Optics

Doctor of Philosophy (PhD), Ohio University, 2018, Curriculum and Instruction Mathematics Education (Education)

When students engage in mathematical modeling, they use mathematics to solve open-ended, real- world problems. This process helps students to make connections and fosters their learning of mathematics itself. Engaging students in mathematical modeling, however, is not an easy task for teachers due to their lack of experience in such teaching. Hence, professional development is needed to advance mathematics teachers' capacity to enact mathematical modeling. This study examined the Mathematical Modeling and Spatial Reasoning (Modspar) professional development program, designed for high school mathematics teachers in Ohio. Two research questions were asked: (a) What is the nature of the professional development program? and (b) What did the participants learn as a result of participating in the program, and how did the program affect their teaching of modeling? To provide data sources for the research questions, (a) I interviewed each of 5 of the 28 participating teachers three times (once before the summer 2016 Modspar program and twice during the 2016–2017 school year), (b) I observed all of the activities enacted during the summer program and collected daily reflections from the 5 selected participants, and (c) I observed 4 of these participants enacting modeling in their classrooms twice during the 2016–2017 school year. For the first question, I examined the level of engagement and the type of modeling enacted during the summer program as all of the participating teachers completed the 20 institute activities: 8 involving modeling with algebra and 12 related to modeling with geometry. For the second question, I examined how the Modspar program advanced the 5 selected participants' knowledge and instruction of modeling. I coded the data thematically and constructed case reports. Results for the first question suggest that the algebra activities focused on mathematical modeling (i.e., using mathematics to solve real-world problems); whereas, the geometry a (open full item for complete abstract)

Committee: Gregory D. Foley Ph.D. (Advisor) Subjects: Mathematics Education

Doctor of Philosophy (PhD), Wright State University, 2016, Human Factors and Industrial/Organizational Psychology PhD

When people look through the environment their eyes are guided in part by what they have recently seen. This phenomenon, referred to as visual priming, is studied in the laboratory through manipulations of stimulus repetition. Typically, in search tasks, response times are speeded when the same target is repeated relative to when it is changed (e.g., Maljkovic & Nakayama, 1994). Although priming is thought to be based on a memory mechanism in the visual system, there is a debate in the literature as to whether such a mechanism is driven by relatively early (e.g., feature-based accounts) or later (e.g., episodic memory accounts) processing. Across three experiments, this dissertation utilized a computational modeling framework (Systems Factorial Technology; Townsend & Nozawa, 1995) to directly compare early and later accounts of priming and determine when visual priming is processed within the visual system in both feature and conjunctive search tasks. Specifically, priming was assessed in terms of its temporal relation (i.e., parallel or serial) to a relatively early process (the processing of conspicuity) and a relatively later process (the processing of Rewards, Experiment 1a; the processing of Word Cues, Experiments 1b and 2) in the visual system. The results suggest that the priming manipulation is processed in parallel with the conspicuity and word cue manipulations within both singleton (Experiments 1a and 1b) and conjunctive (Experiment 2) search. This supports accounts of priming as an early process and suggest that models of priming as a later process within feature or conjunctive search should be rejected. Further, these results also provide evidence to suggest word cues are processed at early stages of visual processing. This supports models of visual processing that suggest high-level representations can modulate the earliest levels of the visual system. Together, these findings provide some of the strongest evidence about the temporal process (open full item for complete abstract)

Committee: Joseph Houpt Ph.D. (Committee Chair); Assaf Harel Ph.D. (Committee Member); Scott Watamaniuk Ph.D. (Committee Member); Alan Pinkus Ph.D. (Committee Member) Subjects: Cognitive Psychology; Experimental Psychology; Psychology

Doctor of Philosophy, University of Toledo, 2016, Industrial Engineering

The main goal of this research is to present new efficient methods and optimization models to enhance the Green Supply Chain Planning (GSCP). As a first objective, we focus on developing a novel optimization planning model in a green supply chain network consisting of suppliers, assemblers, distribution centers, and retailers. This model is subjected to various constraints which are related to the inventory and forward logistics management. We applied the proposed model for a vacuum and floor machines manufacturer case study located in the Midwestern, U.S. The main objective functions include: minimizing the costs of assembling, transporting, holding inventory at assembling sites and distribution centers, and shortage at retailers under carbon dioxide (CO2) emissions constraints throughout the logistic network; maximizing service levels and determining the acceptable service levels to meet final customers' demands. We applied three different solution methods including a gradient-based algorithm in MATLAB “Find Minimum of Constrained nonlinear multivariable function (FminCon)”, a novel metaheuristic algorithm “Grey Wolf”, and the “Branch and Bound (B&B)” algorithm in Lingo to find optimal solutions for the proposed optimization model, which has a specific complexity. We compared the achieved optimal solutions by these methods. The case study and expanded numerical example verify whenever the parameter of the minimum service level at retailers' sites increases or decreases, the amount of produced CO2 emissions and the total costs of the supply chain will directly correlate. It also demonstrates the trade-offs among the total costs of the supply chain network, CO2 emissions, and service levels. The achieved results reflect the efficiency of the proposed model for GSCP. As a second objective, we concentrate on revealing more information about optimal points in which performance measures of various adaptive (X ) ¯quality control charts hold their optimal minimum values. (open full item for complete abstract)

Committee: Matthew Franchetti Dr. (Committee Chair); Efstratios Nikolaidis Dr. (Committee Member); Kumar Ashok Dr. (Committee Member); Zhang Yue Dr. (Committee Member); Spivak Alex Dr. (Committee Member) Subjects: Applied Mathematics; Artificial Intelligence; Automotive Engineering; Business Costs; Computer Science; Engineering; Environmental Engineering; Environmental Management; Health Care; Health Care Management; Operations Research; Sustainability; Systems Design; Transportation Planning

Doctor of Philosophy (PhD), Ohio University, 2016, Curriculum and Instruction Mathematics Education (Education)

Mathematical modeling as an educational endeavor is growing in importance. Associated with this development is the increasing inclusion of mathematical modeling in school curriculum in the United States. Because teachers' content knowledge and attitude influence what and how they teach, and because modeling is a relatively new topic in the curriculum, instruments are needed to assess teachers' knowledge and attitude related to mathematical modeling. To meet this need, the author developed two scales for K–12 teachers of mathematics to assess teachers' knowledge of the nature of mathematical modeling and their attitude toward such modeling. The researcher employed survey research design in this study. The research comprised five phases: item writing, experts' reviews, cognitive interviews, a pilot study, and a field test. The researcher wrote an initial set of items. Then, 10 experts provided qualitative and quantitative data to inform item revision. The appropriateness of the items were judged by cognitive interviewees. Items were omitted and others revised based on the experts' reviews, feedback from the cognitive interviewees, and results from the pilot study. This provided content validity for the study. Teachers in nine school districts from a large Midwestern state participated in the Web-based survey during the field test. The Mathematical Modeling Knowledge Scale (MMKS) was designed to measure teachers' knowledge of the nature of mathematical modeling, and the Mathematical Modeling Attitude Scale (MMAS), to assess their attitude toward such modeling. The field test average MMKS score of 9.51 on a scale of 0–12 indicated satisfactory teacher knowledge of the nature of mathematical modeling. The teachers' average MMAS score of 4.82, on a 1–6 Likert scale, showed a slightly positive attitude toward mathematical modeling. There was a statistically significant positive correlation between the two scores. Psychometric analyses provided reliability and constru (open full item for complete abstract)

Committee: Gregory Foley PhD (Committee Chair); Brooks Gordon PhD (Committee Member); Eugene Geist PhD (Committee Member); Vardges Melkonian PhD (Committee Member) Subjects: Education; Educational Tests and Measurements; Mathematics; Mathematics Education; Teacher Education; Teaching

Master of Science in Engineering, University of Akron, 2009, Biomedical Engineering

Impedance cardiography is a non-invasive measurement method to determine cardiac output and stroke volume. The reason behind this method's lack of popularity for clinical purposes is a dearth of understanding about the factors contributing to the origin of impedance cardiogram. Variations in instantaneous volumes form the thoracic cavity contribute to the change in impedance curve, and in the past several simulations were performed based on this concept. In the present study, a lumped parameter model of a multi-loop circulatory system was developed using Simulink®. The model outputs were flow/pressure waveforms, which exhibit a similarity with physiological curves. The impedance cardiogram was determined by a first-order derivative of a weighted sum of instantaneous thoracic volumes. With correctly adjusted lumped volumes, it was assumed that the signal obtained from the model would be analogous to the dz/dt curve. The volumes were adjusted through variable gain amplifiers incorporated in the model and adjusted by the Simulink Response Optimization Toolbox ® routine of Matlab®. The optimization process tuned the gains to minimize the differences between the simulated and reference waveform. This process was carried out for different combinations of the volumes to obtain the most morphologically similar waveform. The results suggest that the impedance cardiogram waveform is related to volume changes in the thoracic vena cava, abdominal vena cava and ascending aorta.

Committee: Bruce C. Taylor PhD (Advisor) Subjects: Biomedical Research

PHD, Kent State University, 2024, College of Arts and Sciences / Department of Mathematical Sciences

We focus on problems in reaction-diffusion equations with applications to combustion. We specifically consider a special class of solutions called traveling front solutions. Moreover, we study problems where the reaction rates have stepwise ignition temperature kinetics. Three separate problems are contained in this dissertation. The first of which we consider a reaction-diffusion system describing the propagation of flames under the assumption of ignition-temperature kinetics and fractional reaction order. It was shown previously that this system admits a traveling front solution. We show that this traveling front is unique up to translations. We also study some qualitative properties of this solution using the combination of formal asymptotics and numerics. Our findings allow conjecture that the velocity of the propagation of the flame front is a decreasing function of all of the parameters of the problem: ignition temperature, reaction order and an inverse of the Lewis number. Secondly, we consider a classical model of gasless combustion in a one dimensional formulation under the assumption of ignition temperature kinetics. We study the propagation of flame fronts in this model when the initial distribution of the solid fuel is a spatially periodic function that varies on a large scale. It is shown that in certain parametric regimes the model supports periodic traveling fronts. An accurate asymptotic formula for the velocity of the flame front is derived and studied. The stability of periodic fronts is also explored, and a critical condition in terms of parameters of the problem is derived. It is also shown that the instability of periodic fronts, in certain parametric regimes, results in a propagation-extinction-diffusion-reignition pattern which is studied numerically. Finally, we formulate and analyze an elementary model for the propagation of advancing autoignition fronts in reactive co-flow fuel/oxidizer jets injected into an aqueous environment (open full item for complete abstract)

Committee: Peter Gordon (Advisor); Fedor Dragan (Committee Member); Maxim Dzero (Committee Member); Michael Hicks (Committee Member); Xiaoyu Zheng (Committee Member) Subjects: Applied Mathematics; Mathematics

MS, University of Cincinnati, 2024, Engineering and Applied Science: Mechanical Engineering

Within this thesis document we focus on the application of Nonlinear Model Predictive Control (NMPC) onto an epidemic compartmental model. The compartmental model is a partial differential equation (PDE) based Susceptible Latent Infected Recovered (SLIR) epidemic model. This model serves as the basis of the NMPC. In order to generate the necessary parameters for initializing and training the use of constrained optimization, a single-objective Genetic Algorithm (GA), and LSTM (Long-Short-Term-Memory) deep learning were explored. The spatial domains considered for the SLIR epidemic model includes Hamilton County, Ohio as well as the entire state of Ohio, USA. With respect to Hamilton County, Ohio three different time periods were evaluated in which varied levels of infection relating to COVID-19 were observed. At the state wide level only one time period was consider. The NMPC considers two control schemes. The first being control applied uniformly across the spatial domain of interest. While the second focuses on applying the control in a spatially targeted manner to specific geographical areas based on observed higher levels of infection. The NMPC also employs a cost function comprising the infection spread density and the associated cost of applied control measures. The latter of which in turn representing socioeconomic effects. Overall, the NMPC framework developed here is intended to aid in the evaluation of optimal Non-Pharmaceutical Interventions (NPI) towards spread mitigation of infectious diseases.

Committee: Manish Kumar Ph.D. (Committee Chair); Shelley Ehrlich M.D. (Committee Member); Subramanian Ramakrishnan Ph.D. (Committee Member); David Thompson Ph.D. (Committee Member) Subjects: Mechanical Engineering

PhD, University of Cincinnati, 2024, Medicine: Systems Biology and Physiology

This dissertation investigates the dynamic behavior of the hypothalamic-pituitary-adrenal (HPA) axis in response to stress and its implications for Major Depressive Disorder (MDD). The primary aim is to determine whether HPA axis activity can serve as an objective biomarker for MDD diagnosis by combining mechanistic and data-driven modeling approaches. Chapter 1 introduces MDD and the HPA axis, emphasizing the need for accurate and objective diagnostic tools beyond subjective patient reporting. The HPA axis, a critical regulator of the stress response, is highlighted as a potential source of biomarkers. Statistical analyses of our Trier Social Stress Test (TSST) data and background related to mathematical modeling methods are provided. Chapter 2 details the development of VeVaPy, a Python platform designed to facilitate the verification and validation (V&V) of systems biology models. VeVaPy addresses current V&V process shortfalls for HPA axis models, ensuring they meet systems biology and pharmacology community standards. The framework includes four functional modules and is publicly available on GitHub, demonstrating its utility through the V&V of five selected HPA axis models. This chapter underscores the importance of robust V&V for credible model contributions and proposes best practices for model publication and usage. Chapter 3 explores Neural Ordinary Differential Equations (NODEs) for analyzing hormone dynamics during TSST. The NODE models replicated hormone changes in healthy individuals and MDD patients without prior knowledge of the stressor. Dynamic analysis revealed that stress effects are embedded in non-autonomous vector fields derived from the NODE model. These learned vector fields were then used as inputs to Convolutional Neural Networks (CNNs) for classification. The results show the potential of combining NODEs and CNNs to classify patients based on disease state, offering a preliminary step toward clinical applications using HPA axi (open full item for complete abstract)

Committee: Tongli Zhang Ph.D. (Committee Chair); James Herman Ph.D. (Committee Member); Renu Sah Ph.D. (Committee Member); Eric Wohleb Ph.D. (Committee Member); Erik Nelson (Committee Member) Subjects: Physiology

Doctor of Philosophy, University of Akron, 2024, Chemical Engineering

This research aims to enhance the value and sustainability of soybean processing using carbohydrate-degrading enzymes. Soybeans consist mainly of protein (about 40%), carbohydrates (30%), and oil (20%). Oil and protein have significant market value, while the oligomeric and polymeric carbohydrates have indigestive/antinutritional concerns and complicate the protein enrichment and use. Monomerizing these carbohydrates by carbohydrases can simplify soybean processing and convert large quantities of waste carbohydrates to useful sugar-rich fermentation feedstock. Studies done here included enzyme production, optimization of pH and temperature of enzymatic reactions, and enzymatic processing of soybean particles and molasses. Hydrolyzing complex soybean carbohydrates requires cellulase, pectinase, xylanase, α-galactosidase, and invertase activities. These enzymes were produced in submerged and solid-state fermentations of Aspergillus niger NRRL 322 using soybean hull as substrate. Solid-state fermentation yielded higher productivity and enzyme activities with the adjustment of nitrogen and other macronutrients. For optimizing processing temperature, the short-term and long-term temperature effects on enzyme activity and degradation were measured and modeled. For 72-hour processing, the optimal temperature was found at 54°C for α-galactosidase, 48-54°C for invertase, 45°C for cellulase, and <45°C for xylanase and pectinase. Similarly, the pH effect on enzyme activity was measured. The optimal pH was found to be 4.5-4.8 for invertase, 4.5-5.0 for α-galactosidase, 4.5-6.0 for cellulase, and 4.5 for pectinase and xylanase. For the enzymatic processing of soybean particles, the goal was to fractionate oil, protein, and carbohydrate by enzymatically solubilizing the cell-wall polysaccharides to release the membrane-enclosed oil bodies and protein bodies, which are easily separable by centrifugation. Preliminary results confirmed the feasibility of achieving over 90% carbohydr (open full item for complete abstract)

Committee: Lu-Kwang Ju (Advisor); Edward A Evans (Committee Member); Christopher M Miller (Committee Member); Steven S Chuang (Committee Member); Zhenmeng Peng (Committee Member) Subjects: Biochemistry; Chemical Engineering

Bachelor of Science (BS), Ohio University, 2023, Mathematics

Infectious disease has been an issue since the beginnings of humankind. Though highly controversial, vaccination has been a solution for this ongoing struggle between science and disease. In this paper, we view vaccination through the eyes of game theory. We illustrate the importance of the addition of human behavioral aspects to the mathematics behind vaccination games. In order to show the significance, this paper covers two foundational models that set the precedent for the future of vaccination modeling. The goal of this project is to produce results that show the importance of vaccination, and how with enough of the population vaccinated, we are able to completely eradicate a disease from the population.

Committee: Winfried Just (Advisor); David Gerberry (Advisor) Subjects: Mathematics

Doctor of Philosophy, Case Western Reserve University, 2023, Applied Mathematics

Two of the many functions supporting life, pH regulations and gas exchange, appear to be related and many studies have been conducted on the gas exchange across cell membrane. After decades where the passage of gas through a cell membrane was modeled by Fick's law, recently there has been a body of work aiming to test the hypothesis that gas can enter a cell also utilizing gas channels present on the membrane, namely aquaporins (AQPs) and Rhesus (Rh) proteins. In the case of CO2 solutions, the gas exchange is also facilitated by the presence of carbonic anhydrase (CA), an enzyme that accelerates the reaction rates of association and dissociation of H2CO3 in water, increasing the gradient between the intracellular and the external solution. Many studies used Xenopus laevis as a biological model. A standard experiment consists of placing an oocyte of X. laevis inside an aqueous solution of CO2, and measuring the pH changes on the cell membrane by means of a micro-electrode. The hypothesis that pH change are greatly influenced by the presence of AQPs, Rh and CA on the membrane surface can be tested by injecting the oocyte with RNA encoding the different proteins of interest, then comparing the response of the wild type and modified membrane to exposure to a high-concentration CO2 aqueous solution. Several mathematical models have been proposed in the literature to describe this experiment, however simpler models do not fully match the data, only providing qualitative validation, while the more detailed ones require such a large computational effort to make them unsuited to solve the inverse problem of estimating the properties of the cell membrane, in particular its permeability. Estimating the permeability from pH measurements is a powerful tool to analyse the effects of AQPs, Rh proteins and CA on the gas transport, and could be used to confirm or reject the hypothesis of gas exchanges through preferential channels. In this thesis, a com (open full item for complete abstract)

Committee: Daniela Calvetti (Committee Chair); Wanda Strychalski (Committee Member); Bryan Schmidt (Committee Member); Erkki Somersalo (Advisor) Subjects: Applied Mathematics

Doctor of Philosophy, University of Toledo, 2022, Engineering

Autonomous Systems are soon expected to integrate into our lives as home assistants, delivery drones, and driverless cars. The level of automation in these systems, from being manually controlled to fully autonomous, would depend upon the autonomy approach chosen to design these systems. This selection would also affect other operational as well as essential aspects such as cybersecurity and trust. Consequently, the dawn of the areas of human-machine teams (HMT) and cyber-physical human systems (CPHS) have attempted to address the human trust in autonomy while traditional domains of security, along with these new domains, continue to attempt to address the security concerns. This dissertation revolves around these general ideas and attempts to answer many open questions. How did we get here? Where is the future? How do we ensure that the autonomous systems are secure enough so that we may trust their autonomous operation? Can we model the attacker and defender behavior based on the strategies for defense or attack? Given the importance of cybersecurity of these systems, we propose that simulation and modeling of these interactions to predict or select appropriate behavior is expected to lead to a greater trust in autonomous systems through explainable cause and action sequences. This first phase of this research reviews the historical evolution of autonomy, its approaches, and the current trends in related fields to build robust autonomous systems. Towards such a goal and with the increased number of cyberattacks, the security of these systems needs special attention from the research community. To gauge the extent of stat-of-the-art in this area, we study the works that attempt to improve the cybersecurity of these systems. We also found that it is essential to model the system architecture from a security perspective, identify the threats and vulnerabilities and then model the cyberattacks. A survey in this direction explores the various attack models that have (open full item for complete abstract)

Committee: Weiqing Sun (Advisor); Devinder Kaur (Committee Member); Junghwan Kim (Committee Member); Quamar Niyaz (Committee Member); Mohammed Niamat (Committee Member) Subjects: Computer Engineering

Master of Science (MS), Wright State University, 2021, Computer Science

A great percentage of documents in scientific and engineering disciplines include mathematical formulas and/or algorithms. Exploring the mathematical formulas in the technical documents, we focused on the mathematical operations associations, their syntactical correctness, and the association of these components into attributed graphs and Stochastic Petri Nets (SPN). We also introduce a formal language to generate mathematical formulas and evaluate their syntactical correctness. The main contribution of this work focuses on the automatic segmentation of mathematical documents for the parsing and analysis of detected algorithmic components. To achieve this, we present a synergy of methods, such as string parsing according to mathematical rules, Formal Language Modeling, optical analysis of technical documents in forms of images, structural analysis of text in images, and graph and Stochastic Petri Net mapping. Finally, for the recognition of the algorithms, we enriched our rule based model with machine learning techniques to acquire better results.

Committee: Nikolaos G. Bourbakis Ph.D. (Advisor); Euripides G.M. Petrakis Ph.D. (Committee Member); Soon M. Chung Ph.D. (Committee Member) Subjects: Computer Science

Doctor of Philosophy (PhD), Ohio University, 2021, Curriculum and Instruction Mathematics Education (Education)

In school mathematics, students' opportunity to learn varies according to the nature of instruction. Mathematical tasks––that is, problems or activities for student engagement––are critical instructional tools that shape students' mathematical thinking and reasoning. The cognitive demand of a task––the amount, types, and levels of thinking required to solve it––often changes as a teacher modifies the task during planning, setup, and implementation with students. Therefore, school mathematics teachers are instrumental in determining what and how much students learn through their selection and implementation of instructional tasks. This study explored the perspectives of 9 high school mathematics teachers on their selection, planning, setup, and implementation of mathematical tasks and identified the teachers' reasons for instructional decisions at each of these four phases. Using a thematic analysis approach, the researcher interviewed teachers before and after observing the enactment of a high cognitive demand task. Interviews also focused on teachers' perspectives of how their task unfolded and the cognitive demand associated with each phase of the task. The researcher and a co-observer analyzed each teacher's instructional task as it was (a) selected from curricular source materials, (b) adjusted during the teacher's planning, (c) set up prior to student engagement, and (d) implemented with students, using the Instructional Quality Assessment rubrics (Boston, 2012) at each phase. Interview data yielded 18 themes for teachers' task use: 5 for task selection, 5 for task planning, 3 for task setup, and 5 for task implementation. When selecting tasks, teachers frequently considered their learning environment (face-to-face, remote, or hybrid), potential student engagement, real-world contexts, mathematical content, and previous success with the task. During planning, teachers were flexible, adjusted their plan based on the (open full item for complete abstract)

Committee: Gregory Foley (Committee Chair); Allyson Hallman-Thrasher (Committee Member); Mathew Felton-Koestler (Committee Member); Gordon Brooks (Committee Member); Melissa Boston (Committee Member) Subjects: Education; Mathematics; Mathematics Education; Teacher Education; Teaching

Doctor of Philosophy, University of Toledo, 2021, Manufacturing and Technology Management

Commercial drones are among the technologies that are capable of changing business drastically. This dissertation aims to study the adoption and operations of commercial drones to provide methodologies and insights for scholars and practitioners into different stages of the commercial drones' lifecycle. The first essay reviews the current body of knowledge towards a broader scope. It provides a comprehensive literature review targeting published articles in top business journals. By using the Technology-Organization-Environment (TOE) framework and Diffusion Innovation theory and synthesizing the reviewed literature, the first essay identifies the influential factors on the rate of commercial drones' adoption. The second essay focuses on the post-adoption operational issues of commercial drones in a deterministic environment in which the customers' locations are known and fixed. It analytically studies the logistics planning of hybrid commercial drones and aims to maximize the sustainability of the logistics by evaluating social, environmental, economic costs. Two mathematical models are proposed to maximize the sustainability of logistics planning in a deterministic environment. The third essay incorporates the uncertainty in the customers' locations and proposes a two-step methodology to address such an uncertainty. The proposed methodology consists of scenario-based mathematical modeling to help with strategic decision-making, and a simulation-optimization approach to aid in tactical and operational decision-making. Overall, this dissertation studies the rapid adoption and sustainable operations of commercial drones in deterministic and stochastic environments. It identifies influential factors in the rate of adoption of commercial drones, develops two mathematical models to aid in sustainable logistics planning of commercial drones considering the deterministic customer locations, and proposes a two-step analytical method to assist in strategic, tactical, (open full item for complete abstract)

Committee: Yue Zhang PhD (Committee Co-Chair); Marcelo Alvarado-Vargas PhD (Committee Co-Chair); Xinghao Yan PhD (Committee Member); Matthew Franchetti PhD (Committee Member) Subjects: Management; Operations Research; Sustainability; Technology

Master of Science in Mathematics, Youngstown State University, 2021, Department of Mathematics and Statistics

Ectomycorrhizal fungi engage in nutrient exchanges outside the cells of plants [16]. This symbiotic relationship is important in healthy forest ecosystems, and also serves to help reduce atmospheric carbon dioxide levels by providing long lasting carbon storage [9]. Current models of mycelial growth focus mostly on the dynamics of hyphal tip growth from a central or uniform nutrient source. These models lack a "seeking" behavior observed in the mycelium as it grows through areas of low nutrient density to find pockets of higher nutrient densities. They also lack the flexability to adapt to new research about mycelial networks. A new agent-based model is proposed to investigate nutrient seeking as a catalyst for growth.

Committee: Alicia Prieto-Langaricia PhD (Advisor); Padraic Taylor PhD (Committee Member); Jozsi Jalics PhD (Committee Member) Subjects: Biology; Ecology; Mathematics

Master of Science (MS), Ohio University, 2021, Industrial and Systems Engineering (Engineering and Technology)

In the manufacturing industry, varying forms of assembly can be used based on the needs and requirements of the facility. Typically, an assembly line is used to assemble a part serially though stations on a line. Seru manufacturing is a method for assembly that involves one or a few workers who complete the entire product. In order to meet demand, some worker training is typically necessary. This thesis considers on the job (OTJ) training where no formal training is conducted, augmented reality (AR) training where advanced technology is used to guide the worker, and Non-AR training where paper manuals or slideshows are used. This thesis aims to investigate the application of Seru versus assembly line in terms of training cost when worker skill level and training method is considered. A two-phase model is used to determine required skill levels and worker assignments for assembly line. A single non-linear model was used to determine required skill levels for Seru. Based on a known demand, optimal assembly method and training method was determined for a variety of environments. Results show that under normal conditions, assembly line with Non-AR or AR training yields the lowest training cost. Additionally, when skills are tightly clustered, the same results were presented, but when skills are largely varied, Seru with Non-AR training is best. In all cases, some method of formal training performed better than just OTJ training.

Committee: Gursel Suer (Advisor) Subjects: Engineering

Bachelor of Science (BS), Ohio University, 2021, Mathematics

Historically, redistricting has been a process ridden with political manipulation in which politicians “gerrymander” districts to achieve a competitive advantage in future elections. However, the process of redistricting can be aided significantly by mathematical models that prioritize key characteristics of a “fair” district. This paper details one such integer linear programming model implemented in AMPL that ensures just that—a fair district. To ensure fairness, the model produces districts that reflect the political distribution of the state, with no party favored to win more districts than their share of the statewide vote. At the same time, the model prioritizes even population distribution while constraining for contiguous and compact districts. This model is tested and evaluated on data from the state of Ohio and details some possible variations and future directions that allow the model to adapt to other states and goals.

Committee: Vardges Melkonian (Advisor) Subjects: Computer Science; Mathematics; Operations Research; Political Science