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Widths of Finite Posets under the Majorization Ordering
Full text linkThis dissertation focuses on the structural properties of two types of posets, and , both of which are ordered by the majorization ordering. Specifically, we consider those cases where . The poset consists of sequences of non-negative integers of length that sum to , more formally defined as . The second poset, , is a subposet of where we restrict the sequences to be decreasing, i.e., .
We define the majorization ordering to be: for any two sequences we say that is majorized by if the following conditions hold:
We demonstrate that these posets exhibit Sperner-like properties. In particular, we show that the largest antichain in and for is realized by a ``middle'' ``level'', similar to that of the classical Sperner theorem. However since is not a graded poset, it does not have true levels, which is why we refer to these properties as ``Sperner-like''. We also use the term ``middle'' loosely here, as there may be many levels or induced levels which are maximal, and they all generally occur in the middle section of these posets. Despite this, many of the structural properties of are inherited by .
In the case of , we provide explicit chain decompositions, while for we give explicit chain decompositions for . For when , we give an inductive proof of the existence of a minimal chain decomposition on the outer layer(s), with induction handling the smaller poset
Advancing Secondary Mathematics Co-Teachers’ Culturally Sustaining and Collaborative Teaching Practices to Support Linguistically Diverse Students
No full textResearch on teacher learning in collaborative partnerships, job-embedded professional learning for teachers, and language diversity in secondary mathematics classrooms is limited (Barwell et al., 2017; Giles & Yazan, 2020). I investigated the impact of job-embedded, or situated, online professional learning on the instructional practices of high school mathematics co-teachers of linguistically diverse students. The professional learning was focused on culturally sustaining pedagogy, which advances cultural, linguistic, and literate pluralism (Paris, 2012). Culturally sustaining pedagogy demands that educators uplift their students’ unique cultural identities and actively resist assimilating practices. A single case study approach was used, which included semi-structured interviews, online discussion group meetings, classroom observations, and the evaluation of instructional artifacts, such as handouts. The impact of the professional learning experience was observed through interactions within each co-teaching pair and between co-teaching pairs across online and in person contexts. The participants were secondary mathematics co-teachers with varying years of teaching and professional learning experience around linguistically responsive practices. The participants’ diverse backgrounds and contributions were vital to their collaboration within the professional learning community. The findings suggest the participants’ engagement in an online situated professional learning experience focused on culturally sustaining pedagogy and co-teaching strategies led them to use new co-instructional and co-assessment approaches in their mathematics classrooms. The participants also discussed how the professional learning experience increased their desire to have a common co-planning time with other co-teachers. The collaboration and reflection within the participants’ co-teaching pairs and between co-teaching pairs in the professional learning community guided the implementation of culturally sustaining mathematics instructional practices
From Producer to Consumer: Sustainability in the U.S. Beef Industry
Full text linkSustainability in the livestock industry has been a significant focus in recent years, specifically in areas of environmental impact and animal welfare. Research into consumer perceptions of food systems is important so the industry has more information to make production and marketing decisions. It is also important to consider the beef producers’ perspectives regarding on-farm sustainable applications and management practices. Two unique studies were conducted to evaluate perceptions and opinions on sustainable beef production. The beef producer study included an IRB approved online survey with 36 questions that was distributed to Alabama beef producers from July to November 2024. Questions probed producer opinions on the importance of resources and their views about environmental impact and sustainability, knowledge of Climate-Smart Commodities programs, implementation of certain sustainable practices, and what resources are considered necessary for their operation to adopt and/or further improve sustainability practices. A total of 105 primarily cow-calf producers from 42 of the 67 counties in Alabama had varying implementation rates (~9-90%) of practices that can increase sustainability and resource management, specifically grazing management plans, growth-promoting technologies, and animal handling and welfare training. A recurring theme was the need for further information before producers made decisions regarding investing in certain sustainable practices. Providing producers with financial information or counseling on decision making could increase the adoption of sustainability practices. Extension educators may use results from this research to guide development of financial advisory programming and sustainability resource management information for producers. The consumer study used infographics as a mode to deliver information about the beef industry. These communication devices are effective in visually informing audiences and simplifying the messages; however, there is not a large body of literature on infographic use in agricultural education. An IRB approved Qualtrics survey gathered participants’ beef purchasing and consumption habits, their subjective and objective knowledge about resource usage, and their prioritization of sustainability issues to address. Participants then rated their agreement with statements about sustainability, grass-fed and conventional cattle, and hormone use. After viewing three infographics, they were reassessed on the same questions to determine any changes in opinions or knowledge. Results showed a significant increase in self-reported knowledge (p < .001) and positive increases in opinions and agreement on statements about sustainability in the beef industry (p < .001). Those who do not eat beef had smaller but still significant increases in both metrics. Participants expressed lingering doubt about the hormone information and the possible over- or underinflation of statistics represented. Further research could include more specific infographics focusing on fewer topics to decrease information load and integrating more interactive elements into the infographics themselves to increase participation and interaction. Overall, results from these studies provide more insight into the beef producer and consumer opinions on sustainability and data to encourage further communication and research initiatives to bridge the knowledge gap between these two segments in the beef industry
Improving Watershed-Scale Understanding of Land Use/Cover Impacts on Hydrologic and Biogeochemical Dynamics through Process-based Modeling
No full textUnderstanding the impacts of land use and land cover (LULC) changes on hydrologic and biogeochemical processes is essential for sustainable watershed management, particularly in ecologically sensitive and climatically dynamic regions like the eastern United States (U.S.). Different LULC types, such as forests, urban areas, wetlands, and croplands, exhibit distinct hydrologic and biogeochemical behaviors, making it imperative to improve process-based models to capture their influence accurately. This dissertation advances watershed-scale hydrologic and biogeochemical modeling by enhancing the representation of intra-watershed processes in the Soil and Water Assessment Tool (SWAT), with a focus on improving model accuracy across diverse LULC systems through targeted modifications in process representation, calibration techniques, and spatial data integration. The research comprises four interrelated studies.
The first study evaluates the applicability of the SWAT-Carbon (SWAT-C) model in simulating both terrestrial and aquatic carbon fluxes in a forested watershed that serves as a drinking water source for the City of Mobile City in the Southeast U.S. Using remote sensing and in-situ datasets, the model was calibrated to capture dominant pathways of dissolved organic carbon (DOC) transport. The results showed that extensive forest areas could be a major source of DOC, posing a significant risk to drinking water quality. Additionally, the study evaluated three management scenarios, including forest conversion, forest litter raking, and increased crop residue removal, for their potential to reduce DOC exports. This chapter highlighted the strong influence of forests and their management strategies on DOC dynamics and demonstrated the capability of the SWAT-C model in simulating vertical and lateral carbon fluxes within forested watersheds.
The second study introduces National Land Cover Dataset-Imperviousness (NLCD-Imp), a Quantum Geographical Information System (QGIS)-based plugin developed to enhance LULC maps by integrating detailed impervious fractions, directly connected impervious areas (DCIAs), and tree canopy cover (TCC). Applied to the Noonday Creek watershed in metropolitan Atlanta, Georgia, this tool demonstrated that default SWAT urban classifications in SWAT may introduce uncertainty in representing urban characteristics, and in simulating hydrology, and water quality predictions. The SWAT simulations using NLCD-Imp showed increased surface runoff, decreased evapotranspiration, and up to 2 to 4 times higher nitrogen and phosphorus loads in highly urbanized areas. By improving urban LULC representation in SWAT, NLCD-Imp reduces uncertainties in hydrological and water quality simulations, facilitating more precise urban water resource management. The freely available NLCD-Imp plugin, with slight modifications, can also be utilized with any watershed-scale model that utilizes the NLCD LULC map.
The third study developed and evaluated SWAT-WetQual, a coupled modeling framework that integrates SWAT with the process-based Wetland Watet Quality Model (WetQual) model to simulate detailed wetland biogeochemistry processes. The SWAT-WetQual model, validated in the Greensboro watershed, a wetland-rich basin in the mid-Atlantic U.S. in the states of Maryland, captured complex sediment, nutrient, and carbon cycling processes beyond the capabilities of SWAT’s default wetland module. Comparative scenario analyses revealed that wetlands reduced sediment (12%), nitrate (68%), total nitrogen (54%), and total organic carbon (24%) loads. Seasonal analyses further underscored the critical role of wetlands in mitigating pollutant exports during high-flow and agricultural activity periods. The newly developed SWAT-WetQual model offers a valuable tool for researchers, watershed planners, and decision-makers to better understand the cumulative effects of wetlands on watershed-scale water quality.
The fourth study applies the SWAT-WetQual framework alongside NLCD-Imp enhanced LULC maps to assess the long-term impacts of LULC change on hydrology and water quality trends in the St. Andrew Bay watershed, Florida. A shift toward wetter conditions and increased water quality loads over time were observed, particularly in subbasins experiencing forest-to-rangeland conversions. The model demonstrated that wetlands consistently mitigated pollutant exports, reducing nitrogen and total organic carbon (TOC) loads by 13–18% compared to scenarios without wetlands. These findings emphasize the importance of wetlands in buffering the effects of LULC change despite notable hydrologic biogeochemical responses to such changes.
Collectively, this dissertation demonstrates that improving intra-watershed process representation, particularly forest carbon cycling, urban impervious surface dynamics, and wetland biogeochemistry, enhances SWAT's predictive capacity across complex landscapes. Beyond methodological advancements, the research provides actionable insights for reducing nutrient and organic carbon loading and informs targeted watershed management strategies, underscoring the importance of spatially nuanced modeling for resilient water resource planning
Rainbow Connectivity and Proper Rainbow Connectivity
No full textA connected graph G is rainbow connected with respect to an edge coloring of G if each pair of distinct vertices of G are joined by a rainbow path--a path with no color appearing on more than one edge of the path. G is strongly rainbow connected if each pair of distinct vertices of G are joined by a rainbow geodesic, a shortest path in G between the vertices. The (strong) rainbow connection number of G, denoted (s)rc(G), is the smallest number of colors in an edge coloring of G with respect to which G is (strongly) rainbow connected.
Two more recently introduced parameters, prc and psrc, are defined as rc and src were, with the additional requirement that the edge colorings be proper. Some relations among the four parameters are mentioned and they are evaluated for some classes of graphs, including some of the theta graphs and some graphs constructed by joining arbitrarily many cycles at a cut vertex. The impact of several types of graph modifications on the values of parameters is also considered
Forest Structure, Composition, Basal Growth, Hydrology, and Salinity in the Lower Mobile-Tensaw Delta
No full textCoastal wetlands, particularly tidal freshwater forested wetlands (TFFWs), are among the most vulnerable ecosystems to climate change. They face direct impacts from global sea level rise and extreme weather events, compounded by indirect anthropogenic disturbances like urban development and hydrologic alterations. This research investigates the ecological responses of TFFWs to tidal influence and salinity intrusion within the Mobile-Tensaw River Delta (MTRD), an internationally significant deltaic region along the northern Gulf of Mexico. This work is intended to serve as a baseline for current forest conditions and an initial indication of resilience within the study area. This study consisted of vegetation surveys (n = 47) conducted in forested wetland stands across a tidal gradient. Results revealed five distinct canopy communities that corresponded with river distance to Mobile Bay and plot elevation. Multivariate analyses highlighted a strong response of tidal influence on forest composition and structure, indicating community-level sensitivity to estuarine influences. Forested areas located near Mobile Bay exhibited lower basal area, species richness, higher shrub stem density, and a higher proportion of visually stressed canopy trees. To assess species-level responses, over 50 Taxodium distichum (bald cypress) trees were monitored over two growing seasons using low-cost dendrometer bands and continuous hydrologic measurements. Results showed that inundation was the best determiner of tree basal growth, and that, surprisingly, floods with low salinity levels also acted as a subsidy for basal growth across the tidal gradient. However, tidal influence did not account for differences in growth among our long-term forest transects (n = 8). In addition, during the monitoring period, a major saltwater intrusion event following Hurricane Francene in September 2024 was documented near the end of the study. Although this event was near the end of the growing season, it further emphasized the vulnerability of these forests to extreme climatic events. Together, these findings demonstrate how tidal hydrology and salinity gradients influence forest structure, composition, and productivity in TFFWs. This research underscores the importance of site-specific monitoring to inform adaptive management and conservation strategies in the face of accelerating climate change. As sea levels continue to rise and saltwater intrusion events become more frequent and intense, understanding the nuanced responses of coastal forest communities will be critical for land managers looking to predict ecosystem trajectories and mitigate coastal forest loss
Advancing Water Cycle Prediction and Projections: An Investigation of the Effects of Model Resolution, Meteorological Forcing Uncertainty, and Land-Use Change Feedback
No full textAccurate predictions of water cycle components, including evapotranspiration, runoff, and soil moisture, are vital for sustainable water resource management, risk mitigation, and ecological preservation, particularly in light of ongoing climate change and anthropogenic land-use modifications. Despite substantial advances in climate and hydrological modeling, significant challenges persist due to inherent uncertainties associated with model resolution, meteorological forcing data, and complex feedback mechanisms between land surface processes and atmospheric dynamics. This dissertation systematically investigates key factors influencing hydrological cycle predictions and projections by analyzing the impacts of model resolution, meteorological forcing uncertainties, and land-use feedback mechanisms.
The first part of the research focuses on evaluating the role of spatial resolution in hydrological modeling. High-resolution simulations (12.5 km) using the Community Land Model version 5 (CLM5) and Noah land surface model with multi-parameterization options (Noah-MP) were conducted and compared against traditional low-resolution simulations (100 km) across the diverse continental United States. Model performance was rigorously assessed utilizing observational datasets from the National Ecological Observatory Network (NEON). The analyses emphasized critical hydrological variables, such as evapotranspiration, sensible heat flux, runoff, and soil moisture. Findings revealed that high-resolution models exhibited moderate but meaningful improvements in simulation accuracy, evident in higher correlation coefficients and lower normalized root mean square errors (NRMSE). Specifically, evapotranspiration and runoff predictions benefited significantly from increased resolution, though soil moisture improvements were spatially heterogeneous. These findings highlighted that increased resolution alone does not universally enhance model performance, underscoring the necessity of integrating detailed surface representations and accurate forcing data to realize the full potential of high-resolution hydrological models.
The second segment of this dissertation addresses uncertainties related to meteorological forcing and their influence on soil moisture dynamics, particularly Soil Moisture Memory (SMM). CLM5 simulations were driven by two distinct meteorological datasets: the Climate Forecast System Reanalysis version 2 (CFSR) and the Global Soil Wetness Project Phase 3 (GSWP3). Comparative analyses indicated substantial sensitivity of SMM to the choice of forcing data, with notable disparities between the two datasets. Simulations utilizing CFSR data demonstrated significantly higher soil moisture memory in tropical and subtropical regions, reflecting pronounced soil moisture-precipitation feedback. Randomizing atmospheric forcing from the CFSR dataset resulted in decreased SMM, aligning results more closely with GSWP3-driven simulations and indicating the crucial role atmospheric persistence plays in shaping soil moisture dynamics. These results underscore the complexity of land-atmosphere interactions and highlight the importance of accurately characterizing atmospheric forcing data in hydrological models to improve predictions of soil moisture and associated feedback processes.
In the third part, this dissertation explores the implications of land-use and land-cover changes (LULCC) on regional hydrology and climate, utilizing fully coupled simulations with the Community Earth System Model version 2 (CESM2). Simulations compared two contrasting scenarios: one including historical and projected land-use changes (CESM2-LU) and the other maintaining static land-use conditions (CESM2-noLU). Analysis identified strong regional disparities in hydrological responses to LULCC. In tropical regions such as South America and Africa, deforestation resulted in substantial reductions in evapotranspiration and precipitation, while simultaneously increasing surface runoff and altering soil moisture patterns. Conversely, agricultural expansion and afforestation efforts in mid-latitude regions, particularly North America and Eurasia, were associated with increased local precipitation and evapotranspiration, thus significantly affecting soil moisture dynamics and reducing runoff. These divergent hydrological outcomes further correlated with notable temperature anomalies: deforestation intensified surface warming due to reduced evapotranspiration and enhanced sensible heat flux, whereas mid-latitude agricultural zones exhibited localized cooling driven by moisture availability. These findings emphasize the profound influence of land-use practices on regional climate and hydrology.
Collectively, the research presented in this dissertation advances our understanding of hydrological predictability and highlights critical areas for improving model accuracy. Enhanced model resolution, accurate meteorological forcing datasets, and land-use impacts emerge as essential elements for robust hydrological forecasting and water cycle projections. By systematically addressing these factors, the research contributes to refining existing hydrological modeling frameworks and informs better water resource management strategies. This dissertation thus underscores the importance of comprehensive, integrated modeling approaches to predict and manage water resources sustainably under evolving climatic and anthropogenic changes, providing valuable insights for policymakers, resource managers, and climate scientists
Fatigue Behavior and Modeling of Additively Manufactured and Wrought Ti-6Al-4V Parts Under Realistic Loading Conditions
No full textThe study is a comprehensive dive into the fatigue behavior and related failure mechanisms of additively manufactured (AM) and commercially available wrought Ti-6Al-4V under realistic loading conditions, including mean stress, random, and multiaxial loading. Wrought titanium alloy has been broadly used in the biomedical and aerospace fields, specifically for implants and structural components. AM titanium parts aim to become a suitable alternative that may eventually be incorporated into fatigue critical applications. Additive Manufacturing (AM) technologies, specifically laser powder bed fusion (L-PBF), have made progress towards their full fledge adoption in aerospace, medical and several other applications. Although L-PBF Ti-6Al-4V has been heavily researched, there are fatigue performance aspects under realistic loadings that are not well explored. The detrimental effect and high fatigue life scatter, induced by volumetric defects generated from the AM processes and metal powder recycling, have proven challenging to address. In addition to the conventional challenges of fatigue characterization under realistic loading, AM components could encounter multiaxial stress states due to their inherently complex design; these stress states are also accompanied by residual stresses and/or fluctuating external loading. Moreover, it is known that the resultant fatigue performance can be affected by the metal powder condition used during L-PBF; therefore, it has been always preferred to use new (virgin) powder. The virgin powder use practice is not desirable due to its high cost and wastefulness. Hence, part of the research hinges on the effects of powder recycling on the fatigue performance of L-PBF Ti-6AL-4V parts. As a result, powder characteristics and mechanical performance of unmachined and machined specimens fabricated from new and heavily used Ti-6Al-4V powder are compared. For realistic loading conditions, mean stress effects are investigated under strain-controlled constant amplitude loading at different strain ratios, Rε. The generated data is used to compare several mean stress fatigue life prediction models such as Morrow, Smith-Watson-Topper, and Walker. Variable amplitude loading conditions include high-low (H-L), low-high (L-H), periodic overload (PO), and a randomly generated variable amplitude (VA) loading. Furthermore, effects of surface roughness are also investigated by comparing the fatigue performance of unmachined and machined specimens. Lastly, the effects of layer orientation on the multiaxial fatigue behavior are studied. Specimens are tested under axial, torsional, in-phase axial/torsional, and 90° out-of-phase axial-torsional cyclic loadings. Upon failure, fracture surface (of uniaxial specimens) and the crack orientation of vertical and diagonal (multiaxial) specimens is investigated to find a correlation between type of loading and the failure mechanisms. Understanding the effects of intrinsic AM properties (e.g., geometry, surface roughness, porosity, build orientation) on the fatigue behavior of AM metals under realistic loadings is one of the most important steps to facilitate the adoption of this technology in fatigue critical applications
Factors That Affect Completion of Employer-Driven Competency-Based Education and Skills-Based Learning Programs
No full textIn manufacturing, industry leaders increasingly value skills over traditional educational degree programs. Employers are more interested in what a candidate can do rather than what they know, which aligns with the foundation of competency-based education (Perea, 2020). The shift toward automation in the workplace requires workers to acquire advanced technology skills. Abelianski et al. (2020) projected that 37.9 million jobs will be replaced worldwide by 2030. Approximately 305 million jobs will need to be created from 2020-2030. Due to automation and robots replacing low skilled jobs, workers will need advanced technological skills. Additionally, industry technicians are now performing tasks once reserved for engineers. As technological advancements continue, technician roles are expected to require complex skills traditionally associated with college graduates (Cormier et al., 2022). The purpose of this study was to determine the impact of an industry-led, competency-based manufacturing curriculum in the Manufacturing Mobilizing Alabama Pathways (MAPs) program (Alabama Community College System, 2023). This study analyzed variables such as age, gender, ethnicity, education level, and employment status in relation to whether participants earned a Manufacturing MAPs credential. Understanding these associations may provide insight into innovative strategies for designing noncredit skills training programs that could close or significantly reduce Alabama’s skills gap through competency-based education (Beverley et al., 2024)
Aeromonas spp. challenge model development and immune response characterization in largemouth bass (Micropterus nigricans)
No full textLargemouth bass, Micropterus nigricans, is a popular sportfish in the United States and
commonly sought after recreationally in freshwater systems. The culture of LMB supports and
maintains large economic and traditional stocking practices in the United States. Recently, the
use of intensive aquaculture has led LMB to become a major food fish in areas outside of the
United States. Global production of LMB peaked at 0.458 million tons in 2017, predominantly in
China. As the need for LMB increases, the production and handling of these organisms must
increase. The influx of LMB density in intensive aquaculture systems generates various bacterial
and viral diseases, leading to economic losses and production inefficiencies. One specific
bacterial pathogen responsible for disease outbreaks is Aeromonas spp., which are abundant and
commonly found in freshwater ecosystems and aquaculture systems. Aeromonas spp. are
responsible for motile aeromonad septicemia (MAS), which is identified by skin lesions,
exophthalmia, and abdominal swelling. To effectively assess the impacts of MAS on largemouth
bass, a standardized immersion-based challenge model was developed for Aeromonas spp. and
was then applied to a long-term study of growth performance and disease susceptibility.
Challenge results from these studies show the viability of an immersion-based challenge model,
and the relationship between disease susceptibility and age/size of the largemouth bass. These
disease and growth assessments will allow for better rearing and disease management practices
for commercial largemouth bass production, as well as the future production of therapeutants and
new disease management strategies