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

We study the end behavior of three different discrete-time processes on a variety of graphs. The first is the cyclic particle system (CPS) on 3 colors with discordant voting, (Xt). Given a connected finite graph G = (V, E), start by randomly coloring each vertex with any of the 3 colors, labeled 0, 1, or 2. At every time-step, the color X(v) at vertex v randomly chooses an adjacent vertex u with the property X(v)−X(u) = 1 mod 3 and paints u with its color. This Markovian process is using the push update rule. In addition to push updates, we also consider pull updates in which v randomly chooses an adjacent vertex u with the property X(u) − X(v) = 1 mod 3 and paints itself with the color of v. In this way, v pulls the color of its discordant neighbor. Since G is a connected, finite graph and all colors interact, eventually there will be a consensus in color among all the vertices. Hence, we study the time until consensus with respect to n = |V | for the star graph and the complete graph. The second process we analyzed is the cyclic cellular automaton (CCA) on κ colors with threshold θ, (ξt). We study this on the infinite, (d + 1)-regular tree, Td, and on the random Galton-Watson tree with offspring distribution ζ, Tζ. So for a given tree, T, (ξt) is defined on the state space {0, 1, 2, . . . , κ − 1}T . Given a uniformly distributed random initial configuration, at each time-step t every vertex considers its neighbors. If v ∈ T has at least θ neighbors u, such that ξt(u)=ξt(v)+1 mod κ, then ξt+1(v)=ξt(v)+1 modκ. Otherwise, ξt+1(v) = ξt(v) mod κ. On Td, with these deterministic dynamics, we present sufficient conditions on κ and θ so that, for sufficiently large d, (ξt) either fixates or fluctuates almost surely i.e. all vertices in Td eventually do not change state or there exist vertices that will always change state. Furthermore on Tζ, we present sufficient conditions so that (ξt) fixates or fluctuates almost surely. The last process we studied was the Greenb (open full item for complete abstract)

Committee: David Sivakoff (Advisor); Matthew Kahle (Committee Member); Hoi Nguyen (Committee Member) Subjects: Mathematics

Doctor of Philosophy (PhD), Ohio University, 2021, Plant Biology (Arts and Sciences)

Carbon-mediated hydraulic failure is the current leading hypothesis for natural tree mortality. However, the physiological mechanisms of this process vary among species and environment. The way in which a tree responds to drought is defined as its hydraulic behavior, which is described using the isohydric/anisohydric continuum. Theoretically, diffuse-porous and ring-porous trees should fall at opposite ends of this continuum due to their contrasting xylem anatomy and associated carbon requirements. While previous studies have documented this trend, the relationship between wood type and hydraulic behavior is still unresolved, particularly in temperate forests. The overall goal of my research was to describe hydraulic behavior in ring- and diffuse-porous species in a temperate, deciduous forest. I included small and mature trees to understand the influence of size class on hydraulic behavior. My results indicate a distinct dichotomy between isohydric, diffuse-porous Acer saccharum and anisohydric, ring-porous Carya ovata; however, other species exemplify a spectrum of hydraulic behaviors, falling along a gradient between wood types. This pattern was consistent among size classes, validating comparisons of hydraulic behavior between small saplings and mature trees. Overall, this work provides new insights into the physiological mechanisms responsible for carbon-water trade-offs in ring- and diffuse-porous trees in temperate forests.

Committee: David Rosenthal (Advisor); Brian McCarthy (Committee Member); Rebecca Snell (Committee Member); James Dyer (Committee Chair) Subjects: Climate Change; Ecology; Environmental Science; Forestry; Physiology; Plant Sciences; Wood

Master of Science in Computer Engineering (MSCE), Wright State University, 2018, Computer Engineering

Mindfulness is the state of retaining awareness of what is happening at the current point in time. It has been used in multiple forms to reduce stress, anxiety, and even depression. Promoting Mindfulness can be done in various ways, but current research shows a trend towards preferential usage of breathing exercises over other methods to reach a mindful state. Studies have showcased that breathing can be used as a tool to promote brain control, specifically in the auditory cortex region. Research pertaining to disorders such as Tinnitus, the phantom awareness of sound, could potentially benefit from using these brain control strategies as the auditory cortex is suspected of being the region in the brain responsible for the production of symptoms associated with Tinnitus. Mobile Applications have become an increasingly popular tool, due to their accessibility, that can be used to promote mindfulness, and as a result help patients cope better with Tinnitus. Using applications to guide patient's breathing patterns could be a more desirable and effective method to attaining a more mindful state. This study explores the effectiveness of such an application, and how the application can modified to be adaptive towards each individual user. Two questionnaires, Attentional Control Scale (ACS) and Mindful Attention Awareness Scale (MAAS), are used to measure self-reported attentional control and mindfulness. The results obtained from the questionnaires along with number of times the application was used, were used to determine which features, and whether using the application more times, had an effect on a participant's mindful score. Machine learning regression trees and ANOVA was used as part of the analysis, but due to lack of data, concrete conclusions on whether using the application more times has a better affect on a participant's mindfulness could not be established. That said future work will include a larger more diverse dataset which could allo (open full item for complete abstract)

Committee: Subhashini Ganapathy Ph.D. (Advisor); Mateen Rizki Ph.D. (Committee Member); Michael Raymer Ph.D. (Committee Member) Subjects: Computer Engineering; Computer Science; Design; Industrial Engineering; Mental Health; Neurosciences

Master of Science (MS), Bowling Green State University, 2018, Applied Statistics (Math)

In 2014 Ohio began the Sexual Assault Kit Testing Initiative with the goal of analyzing all previously untested sexual assault kits (SAKs). Approximately 13,900 previously untested SAKs were sent for forensic analysis. Of these SAKs, a sample of 2,500 was drawn for statistical analysis. The goal was to gain some general information about the SAKs as well as to answer a variety of specific questions in the hopes of producing cost-saving measures in the future. Questions considered were those such as: which forensic samples most consistently produce Combined DNA Index System (CODIS)-eligible DNA profiles, what factors predict whether or not a kit will contain a DNA profile foreign to the victim, as well as others. The results of the initiative were published in Kerka, Heckman, Maddox, Sprague, & Albert (2018). This thesis expands upon the work in the aforementioned article. In the article, a logistic regression model was constructed to predict whether or not an SAK would contain a CODISeligible DNA profile. It was estimated to have a misclassification rate of 34.2%. This thesis compares three other models to the logistic regression model to determine if any improvements in performance can be made. The models tested were decision trees, bagged trees and random forests. The decision tree had an estimated misclassification rate of 29.7%, thus offering a moderate improvement over the logistic regression model. In addition, the same models were compared for their ability to predict which SAKs would contain duplicate DNA profiles across multiple forensic samples (vaginal sample, anal sample, etc). No model was able to do a satisfactory job of predicting this response.

Committee: Jim Albert Ph.D. (Advisor); Arkajyoti Roy Ph.D. (Committee Member); Jon Sprague Ph.D. (Committee Member) Subjects: Criminology; Mathematics; Statistics

Doctor of Philosophy, The Ohio State University, 1982, Graduate School

Committee: Not Provided (Other) Subjects: Agriculture

Doctor of Philosophy (Ph.D.), Bowling Green State University, 2016, Mathematics

In this dissertation, we study groups that act on twin trees. A twin tree consists of a pair of (infinite) simplicial trees (X+, X-) that are ``twinned" by means of a co-distance function δ*, which assigns a non-negative integer to pairs of vertices from each tree. If n=δ*(x+, y-) for vertices x+ in X+ and y- in X-, then we think of x+ and y- as having distance ∞ - n. An example of a twin tree is Τ=(Τ+, Τ-, δ*), where Τ+ and Τ- are the associated Bruhat-Tits trees arising from two different discrete valuations on the field k(t). A group G acts on a twin tree X=(X+, X-, δ*) if it acts on each tree X+, X- and preserves the co-distance function. For the twin tree Τ arising from discrete valuations on k(t), the group GL(2,k[t,t^-1]) naturally acts on the twinning. The subgroup GL(2,k[t]) stabilizes a vertex of the the tree Τ+. The action of GL(2,k[t]) on Τ- yields a fundamental domain an infinite ray, and from this action one obtains Nagao's Theorem. In this work, we investigate the fundamental domains for subgroups G < GL(2,k[t,t^-1]) that stabilize subtrees of the tree Τ+. For a general group G acting on a twin-tree, we consider its space of closed subgroups C(G), called the Chabauty space. By constructing a left-invariant metric on the underlying automorphism group of the twin-tree, one can endow C(G) with a metric as well. Using this, we study the distance between vertex stabilizer subgroups in G. This will hopeful lead to future work generalizing the special case of Τ and GL(2,k[t,t^-1]).

Committee: Rieuwert Blok (Advisor); Lee Nickoson (Other); Mihai Staic (Committee Member); Xiangdong Xie (Committee Member) Subjects: Mathematics

Master of Arts, The Ohio State University, 2006, Graduate School

Committee: Not Provided (Other) Subjects:

Master of Science, The Ohio State University, 2007, Graduate School

Committee: Not Provided (Other) Subjects:

Doctor of Philosophy, The Ohio State University, 2024, Statistics

Modern computer experiment applications may model a physical system using multiple physics-based simulators. The fidelity of each simulator may vary across the input domain. Rather than selecting a single simulator for inference and prediction, one strategy is to combine the set of simulators under consideration. The most common strategy is to estimate the underlying system by combining, or "mixing", the predictions from K different simulators using a linear combination. The primary objective is to then obtain a better global prediction of the system and gain some insight regarding the fidelity of each simulator. Classical approaches combine the K models using scalar weights. In some cases, these weights may indicate each individual model's overall, or global, predictive performance. More recent work combines the predictions from K models using input-dependent weights. This strategy allows for a more localized prediction and interpretation, as the weight functions may reflect each individual simulator's local fidelity. Local weighting schemes introduce a new challenge in that one must define a relationship between the inputs and the weights. A common choice is to define the weight functions using linear bases, however selecting the appropriate bases is a non-trivial task. This work proposes a Bayesian Additive Regression Tree (BART) model for the weight functions. The weight functions are then defined using tree bases that are adaptively learned based on the information in the data and the model set. Our approach is designed to not only improve global prediction of the system, but also allow for reliable inference regarding where each model is accurate or inaccurate, relative to the others in the model set. Using the additive tree bases, the weight functions are modeled as piecewise constant functions. In some cases, it may be desirable to estimate the weights and resulting mixed prediction as continuous functions. Motivated by this, we propose a ran (open full item for complete abstract)

Committee: Matthew Pratola (Advisor); Christopher Hans (Committee Member); Thomas Santner (Committee Member) Subjects: Statistics

Doctor of Philosophy (PhD), Ohio University, 2024, Physics and Astronomy (Arts and Sciences)

Synchronization is ubiquitous in natural and engineered systems and can be (un)favorable in the brain. For example, reduced coherent oscillations in the gamma band characterize Alzheimer's disease, while strong synchronization in the basal ganglia is a hallmark of Parkinson's disease. Even a single sensory neuron may possess a complex dendritic network with many interacting active elements, resulting in collective synchronous activity. This work studies the effect of network structure and its variability on steady states of coupled nonlinear excitable and oscillatory elements and the collective network response to external stimulation. First, we study the determinants of information processing in sensory neurons with myelinated dendrites, e.g., touch receptors and muscle spindles, using a tree network model of sensory neurons. In particular, we show that in the strong coupling limit, the statistics of the number of nodes and leaf nodes fully determine the network response, quantified by mutual information, regardless of the stimulus distribution among leaf nodes. However, the mutual information may strongly depend on the stimulus distribution among leaf nodes for intermediate coupling. Second, we study plastic networks of oscillatory neurons to address how synchronized and incoherent activities can spontaneously emerge and be controlled by stimulation. We develop models of neuronal networks with synaptic weight and structural plasticity to study the co-evolution of network activity and structure. We show that structural plasticity may enable the networks to optimize their structure for enhanced synchrony with reduced connectivity, rendering networks more robust against desynchronizing stimuli. The rewiring reduces the network randomness, leading to specific correlations in the number of incoming and outgoing synaptic contacts of neurons.

Committee: Alexander Neiman (Advisor); David Tees (Committee Member); Mitchell Day (Committee Member); Horacio Castillo (Committee Member) Subjects: Biophysics; Physics

Master of Science in Mechanical Engineering, Cleveland State University, 2023, Washkewicz College of Engineering

In structural design, the distribution of wind-induced pressure exerted on structures is crucial. The pressure distribution for a particular building is often determined by scale model tests in boundary layer wind tunnels (BLWTs). For all combinations of interesting building shapes and wind factors, experiments with BLWTs must be done. Resource or physical testing restrictions may limit the acquisition of needed data because this procedure might be time- and resource-intensive. Finding a trustworthy method to cyber-enhance data-collecting operations in BLWTs is therefore sought. This research analyzes how machine learning approaches may improve traditional BLWT modeling to increase the information obtained from tests while proportionally lowering the work needed to complete them. The more general question centers on how a machine learning-enhanced method ultimately leads to approaches that learn as data are collected and subsequently optimize the execution of experiments to shorten the time needed to complete user-specified objectives. 3 Different Machine Learning models, namely, Support vector regressors, Gradient Boosting regressors, and Feed Forward Neural networks were used to predict the surface Averaged Mean pressure coefficients cp on Isolated high-rise buildings. The models were trained to predict average cp for missing angles and also used to train for varying dimensions. Both global and local approaches to training the models were used and compared. The Tokyo Polytechnic University's Aerodynamic Database for Isolated High-rise buildings was used to train all the models in this study. Local and global prediction approaches were used for the DNN and GBRT models and no considerable difference has been found between them. The DNN model showed the best accuracy with (R2 > 99%, MSE < 1.5%) among the used models for both missing angles and missing dimensions, and the other two models also showed high accuracy with (R2 > 97%, MSE < 4%).

Committee: Navid Goudarzi (Committee Chair); Prabaha Sikder (Committee Member); Mustafa Usta (Committee Member) Subjects: Artificial Intelligence; Design; Engineering; Urban Planning

Master of Science (MS), Wright State University, 2023, Human Factors and Industrial/Organizational Psychology MS

Item Response Trees are a type of item response model that incorporates information about conditional responding to items using a rooted tree graph structure. Researchers have used item response trees for common measurement tasks and for testing novel hypotheses. Previous simulation studies investigating item response trees either lack generalizability to the broad domain of their use or lack thorough investigation and reporting of the results. I conducted a simulation study to explore how sample size, test length, item characteristics, and tree structure affect both item and person parameter recovery for 1PL and 2PL models. The results suggested that, as with any item response model, item response tree models are unbiased. However, large samples and long test lengths are needed to minimize estimate uncertainty. Issues of sample size and test length are compounded by the conditional structure incorporated in item response tree models. In particular, the depth of the tree and low item endorsement can pose severe estimation issues when sample sizes are not large and test lengths are not long. I used posterior predictive simulations to provide the reader with a practical understanding of the limitations of item response trees in the context of item and personnel selection and prediction of external variables.

Committee: David LaHuis Ph.D. (Committee Chair); Debra Steele-Johnson Ph.D. (Committee Member); Joseph Houpt Ph.D. (Committee Member) Subjects: Cognitive Psychology; Personality; Psychological Tests; Psychology; Quantitative Psychology; Statistics

PhD, University of Cincinnati, 2023, Engineering and Applied Science: Biomedical Engineering

Epilepsy is a neurological disease that causes recurrent, spontaneous seizures, which can lead people to experience ephemeral neurological and physiological impairments and disrupt day-to-day living. One of the most enervating facets of epilepsy is the unpredictability of seizures. Most people reside in fear, stress, and anxiety of not knowing when a seizure might occur, which in turn can serve as a major disability and cause people to encounter difficulties engaging in daily activities. For decades, many seizure prediction studies have concentrated on utilizing long term electroencephalography (EEG) data from continuous scalp or intracranial EEG electrode monitoring. While these studies have shown positive results for seizure predictive capabilities, continuous EEG electrode monitoring can be invasive, uncomfortable, and pose some potential risk for patient with epilepsy. Thus, seizure prediction remains a significant challenge within epilepsy-based research. In efforts to advance seizure prediction, this dissertation work applies both quantitative and machine learning methods to overcome these challenges. In examining patient-specific seizure diaries that consist of possible seizure predictive factors (e.g., measurements of mood, stress, and circadian patterns), the first method focuses on using generalized linear modeling, specifically logistic regression, to predict subsequent seizures within a 24-hour timeframe. Following, predictive factors were used to generate quantitative biomarkers that associated with seizure occurrences and were analyzed via diagnostic tests. The second method focused on using a machine learning technique, specifically decision trees, to showcase how possible predictive factors are associated with seizure outcome. Additionally, certain factors were categorized into groups based on frequently they appeared in patients' decision trees. The significance of these seizure predictive factors was also identified. This dissertation (open full item for complete abstract)

Committee: Marepalli Rao Ph.D. (Committee Chair); Ishita Basu Ph.D. (Committee Member); Michael Privitera M.D. (Committee Member); Matthew McCullough Ph.D. (Committee Member); Jason Heikenfeld Ph.D. (Committee Member) Subjects: Biomedical Engineering

Doctor of Philosophy, Case Western Reserve University, 2023, Biology

The urban forest is a patchwork of trees growing in natural forests and parks, private yards, street plantings and vacant lots. Urban trees provide numerous societal environmental, and health benefits, vastly improving the lives of people who reside in urban areas. Urban trees are subject to a unique set of pressures, however, which differ from those of nearby rural areas. These include human preferences and particularly abiotic factors such as elevated CO2 and higher temperatures. Because the urban forest is a heterogeneous conglomeration of trees across various types of land-use, it has been difficult to describe, quantify, and predict the ecological and functional patterns of the urban forest. In my dissertation, we explore urban trees by investigating if the coordination between physiological and morphological characteristics of urban trees differs compared to trees in other environmental contexts; exploring whether the patterns of diversity and community structure differ between urban and rural locations, and examining if drought response differs between saplings sourced from urban and rural locations. In chapter 2, we measured leaf level water relations including the leaf hydraulic conductance (Kleaf) and turgor loss point (πTLP). We found coordination between the change in Kleaf (ΔKleaf) and turgor loss point depression (ΔπTLP) across seasons, but this relationship was not the same between locations with different environmental conditions. Under cool, wet conditions we did not find this relationship; however, this relationship was significant under warmer, drier conditions suggesting that a lowered turgor loss point (i.e. more drought tolerant) buffered the potential negative effects of a decline in hydraulic capacity. We did not find expected relationships between leaf morphology and water relations, suggesting that further work is needed to assess the suitability of morphological traits to determine the services of urban trees. In chapter 3, we describe t (open full item for complete abstract)

Committee: Juliana Medeiros (Advisor); Jean Burns (Committee Member); Ryan Martin (Committee Member); Kevin Mueller (Committee Member); Katharine Stuble (Committee Member) Subjects: Biology; Physiology; Plant Biology; Plant Sciences; Urban Forestry

PHD, Kent State University, 2022, College of Arts and Sciences / Department of Biological Sciences

The eastern redcedar Juniperus virginiana is the most widespread conifer in the eastern United States, and can be found in every state east of the 100th meridian. This tree is encroaching into new habitats and old fields in the western states, as far as Nebraska and South Dakota. J. virginiana can survive and thrive in adverse conditions and extreme environments. We were interested in testing the effects of biotic and abiotic conditions on J. virginiana ecophysiology. We investigated the role of competition and soil substrates in a greenhouse experiment, and in a series of field experiments, we tested a stress-gradient approach on abiotic stress and intraspecific competition, the role of different soil types on local adaptation of two J. virginiana varieties, and the effects of tree size and season on J. virginiana performance and ecophysiology. We found that there was a strong effect of competition with grass (Bromus inermis) but not with post oak (Quercus stellata). In addition, fertilizer had a greater effect than lime on J. virginiana performance, indicating that J. virginiana tolerates rather than prefers limestone soil to avoid competition with other tree competitors. We also found support for Walter's two-layer hypothesis in which there was root partitioning between the J. virginiana and smooth brome grass. Similarly, we also found root partitioning and differentiation between the J. virginiana and post oak, due to root length differences. In our stress-gradient experiment, we found that the population at the site furthest from Lake Erie and with the highest soil nutrients had greater physiological activity and total biomass, which supported our predictions. Intraspecific competition was not an important factor affecting J. virginiana performance. Surprisingly, the intermediate site had the lowest overall performance and lowest water stress, due to poor drainage, indicating that more parameters need to be considered when setting up a stress-gradient experime (open full item for complete abstract)

Committee: David Ward (Advisor); Emily Rauschert (Committee Member); Oscar Rocha (Committee Member); Juliana Medeiros (Advisor) Subjects: Biology; Climate Change; Ecology; Plant Biology; Plant Sciences

Doctor of Philosophy, The Ohio State University, 2022, Statistics

In recent decades, Bayesian researchers have often utilized continuous latent variable formulations in problems involving discrete spaces. While powerful, viable implementations of a continuous latent variable mechanism are not always straightforward in certain types of discrete problems. One notable example may be found in the regression tree framework, wherein the posterior tree space is discrete, complex, and large. In this document I propose two novel approaches to address the problem of modeling discrete data using a tree-based Bayesian framework. First, I propose a novel Markov Chain Monte Carlo search algorithm: the taxicab sampler. I describe the construction of this sampler and discuss how its interpretation and usage differs from that of standard Metropolis-Hastings as well as the related Hamming ball sampler. The proposed taxicab sampling algorithm is then shown to demonstrate substantial improvement in computation time relative to a naive Metropolis-Hastings search in a motivating Bayesian regression tree count model, in which I leverage the discrete state space assumption to construct a novel likelihood function that allows for flexibly describing different mean-variance relationships while preserving parameter interpretability compared to existing likelihood functions for count data. Second, I propose a novel framework for modeling count data via regression trees using a decomposition approach. A common statistical modeling strategy lies in leveraging advantageous model factorizations in order to fit a collection of simpler submodels. Such a strategy is employed in Bayesian Additive Regression Tree (BART) models, which use collections of individual tree models to estimate functions of interest via an additive representation. While the BART framework has enjoyed success as a method for modeling continuous, binary, and polychotomous data, there are relatively few Bayesian regression tree methodologies designed to handle count data. I propose a nove (open full item for complete abstract)

Committee: Matthew Pratola (Advisor); Radu Herbei (Advisor); Laura Kubatko (Committee Member) Subjects: Statistics

MS, University of Cincinnati, 2021, Education, Criminal Justice, and Human Services: Information Technology-Distance Learning

STEM remains one of the fastest-growing and most segregated professions in the United States. Predominately white and male, opportunities in STEM continue to grow exponentially. For example, areas such as the Internet of Things (IoT) and Artificial Intelligence (AI) are expected to become $11 trillion industries by 2025. As companies struggle to find enough skilled candidates, we face the reality that African Americans are too often left behind. If we, for example, examine technology as a subset of STEM, we see that African Americans make up less than 5% of the IT workforce and a small percentage of IT graduates. Although there is a general acknowledgment and some investment by both industry and educational institutions, there has been minimal success in changing the demographic landscape. This study focuses on the advent of bias-conscious AI and how it can be used to better understand barriers to success, personalize student experiences, and provide pathways of attainment for an increasingly diverse student body.

Committee: Annu Prabhakar Ph.D. (Committee Chair); Michelle Chyatte Dr.P.H. M.P.H. (Committee Member); M. Murat Ozer Ph.D. (Committee Member) Subjects: Artificial Intelligence

Doctor of Philosophy, The Ohio State University, 2021, Industrial and Systems Engineering

This research explores the reinforcement learning methods, machine learning methods, and discrete event simulation models with applications in the field of cybersecurity. In cybersecurity, virtually all types of devices that contain computers have so-called “cyber vulnerabilities” which offer ways for attackers to gain access or at least limit performance. A race then follows between hackers' finding and applying “exploits”, and vendors offering patches that are discovered to be needed by scans and implemented by end users. If the hackers win, they cause losses. In this dissertation, we propose a discrete event simulation model in which the mechanism of vulnerabilities and hosts has been studied. A concept of a nested “birth and death” process is introduced in the context of vulnerability lifetime and its interaction with a host. Also, we investigate the benefits and drawbacks of the current scanning policy and maintenance policy with a case study of a major university. We also propose cost-effective alternatives and investigate the significance of celebrity vulnerabilities. Next, we explore the optimal control policies to schedule cyber maintenance actions in a partially observable environment caused by incomplete inspections. Incomplete inspection, resulting mainly from computers being turned off during the scan, leads to a challenge for scheduling maintenance actions. We propose the application of Partially Observable Markov Decision Processes (POMDPs) to derive cost-effective cyber-maintenance actions that minimize total costs. To assess the benefits of optimal policies obtained from POMDPs, we use real-world data from a major university. Compared with alternative policies using simulations, the optimal control policies can significantly (2x ~ 10x) reduce expected maintenance expenditures per host and relatively quickly mitigate the most important vulnerabilities. Further, we investigate the main disadvantages of the widely used Common Vulnerability Scoring S (open full item for complete abstract)

Committee: Theodore Allen (Advisor); Cathy Xia (Committee Member); Guzin Bayraksan (Committee Member) Subjects: Industrial Engineering

Bachelor of Science, Wittenberg University, 2020, Biology

In the Huron-Manistee National Forest, standing dead trees (snags) have great ecological value because they have cavities, which provide critical habitat for many animals. Snags are created in red pine timber plantations to simulate the number of snags typically found in naturally growing forests. This study compares the value of snags created by topping in 2011 to snags created during a prescribed burn in 2010. Creating snags via topping appears to be worth the investment as wildlife appears to use topped snags as much as snags created in a prescribed burn (topped = 49 cavities; burned = 59 cavities). GIS/GPS was used to locate and mark snag clumps. Height, DBH, decay class (1-5), and cavity presence was recorded for each clump (group of snags) and compared between and across snag creation type. The burned snags were planted in 1936 or 1938 and the topped snags were planted in 1936 or 1965 but the average DBH of each was similar (burned x = 10.8in; topped x = 10.5in). The presence of cavities below 20ft was compared between burned and topped snags. The average height for burned snags was 42.5ft and topped snags were cut at 20ft, but cavities appeared to be located near the tops of snags regardless of their height. The majority of cavities (83.7%) in topped snags were in decay classes one (59.2%) and two (24.5%). In burned snags, the majority of cavities (87.0%) were in decay classes one (22.2%), two (35.2%) and three (29.6%) with decay classes two and three containing the majority of the cavities (64.8%). Below 20ft, topped snags had a greater percentage of cavities (14.9%) than burned snags (6.7%), although there was a greater percentage of cavities in burned snags overall (burned = 22.7%). In the future, studies will also compare snags created during the Meridian wildfire of 2010.

Committee: Richard Phillips (Advisor); Matthew Collier (Committee Member); Doug Andrews (Committee Member) Subjects: Biology; Ecology; Environmental Science; Forestry; Natural Resource Management; Wildlife Management; Wood; Wood Sciences

Doctor of Philosophy, The Ohio State University, 2020, Statistics

As computing power grows, computer experiments have become an increasingly popular approach to study the relationship between the inputs and resulting outputs of a computational model. The most popular statistical model in computer experiments is the Gaussian Process model. However, the Bayesian Additive Regression Trees (BART) model can better handle the explosive increase in the quantity of available data. This thesis considers two problems in the design and analysis of computer experiments. The first problem is computing sensitivity indices for BART. The second problem is estimating the Pareto Front and Set of a multiobjective computer simulator using BART. To solve the first problem, we derive closed-form expressions of sensitivity indices for BART and establish a relationship between these indices and the count heuristic commonly used to measure input variable activity in BART. These expressions are exact and do not require integral approximation methods. We then empirically assess the performance of these BART-based sensitivity indices in capturing a function's sensitivity indices on several test functions. We compare this performance to that of the count heuristic and of the Treed Gaussian Process model whose sensitivity indices can be approximated. For the comparison to counts, we propose a novel ranking method suited for this input variable activity setting. To solve the second problem, we introduce a BART model with multidimensional outputs and provide an algorithm to find the exact Pareto Front and Set of the function that results from a trained multiple-output BART model. We also introduce two approaches of quantifying the uncertainty of these estimates. We then empirically compare these two uncertainty quantification approaches to each other on several test functions. For this comparison, we propose two metrics that capture certain desirable properties of a Pareto Front or Set estimate.

Committee: Matthew Pratola (Advisor); Thomas Santner (Advisor); Radu Herbei (Committee Member); Roshan Joseph (Committee Member); Mark Pitt (Other) Subjects: Statistics