Mathematics Commons^™

Behind The Screen: A Comprehensive Framework For Digital Work Metrics And Data Integration, F. Demaria, A. Papana Dagiasis, M. Cavicchioli, T. Fabbri

Mathematics and Statistics Faculty Publications

The digital transformation and the subsequent datafication of work generate rich electronic traces that can be transformed into actionable insights through modern analytics. In this context, this study proposes a data-driven framework that leverages sidClustering and unsupervised Random Forest (RF) for clustering and feature selection, constructs composite indicators via multiple aggregation strategies, and employs visual tools to enhance the interpretability of results. A key feature of the framework is the integration of two data sources: click metadata from Microsoft 365 and employee attitudes measured through a questionnaire. This integration enables the analysis of digital work behavior (DWB) in relation to …

Site Specific Reliability-Targeted Snow Loads And Winter Wind Parameters Across The World, Brennan Bean, Nicholas Brimhall, Bikram Bhusal, Marc Maguire, Maha Moussa

Mathematics and Statistics Faculty Publications

This report presents a framework for estimating Reliability Targeted Snow Loads (RTSLs) and Winter Wind Parameters (WWPs) at locations outside the Conterminous United States (OCONUS). The methodology integrates ground-based in-situmeasurements with gridded global climate products to generate spatially continuous RTSL estimates for nearly any location in OCONUS. RTSLs are computed at qualifying in-situ stations, and predictive models relating gridded climate products to in-situRTSLs enable estimation at locations lacking direct measurements. This report describes the development of the in-situ annual maximum snow load database, the construction of global gridded climate summaries, the estimation of site-specific RTSLs and Service Targeted …

An Algebraic-Combinatorial Proof Of A Bézout-Type Inequality For Mixed Volumes Of Three-Dimensional Zonoids, Gennadiy Averkov, Ivan Soprunov

Mathematics and Statistics Faculty Publications

We present a new algebraic-combinatorial approach to proving a Bézout-type inequality for zonoids in dimension three, which has recently been established by Fradelizi, Madiman, Meyer, and Zvavitch. Our approach hints at connections between inequalities for mixed volumes of zonoids and real algebra and matroid theory.

Line Graphs Of Directed Graphs I, Vaidy Sivaraman, Daniel Slilaty

Mathematics and Statistics Faculty Publications

We determine the forbidden induced subgraphs for the intersection of the classes of chordal bipartite graphs and line graphs of acyclic directed graphs. This is a first step towards finding the forbidden induced subgraphs for the class of line graphs of directed graphs.

Quantifying The Impact Of Rain-On-Snow Induced Flooding In The Western United States, Brennan Lynn Bean, Emma Watts

Mathematics and Statistics Faculty Publications

The potentially destructive flooding resulting from rain-on-snow (ROS) events motivates efforts to better incorporate these events and their residual effects into flood-related infrastructure design. This paper examines relationships between measured streamflow surges at streamgages across the Western United States and the meteorological conditions preceding them at SNOTEL stations within the same water catchment. Relevant stream surges are identified using a peak detection algorithm via time series analysis, which are then labeled ROS- or non-ROS-induced based on the preceding meteorological conditions. Both empirical and model-derived differences between ROS- and non-ROS-induced stream surges are then explored, which suggest that ROS-induced stream surges …

A Preliminary Fuzzy Inference System For Predicting Atmospheric Ozone In An Intermountain Basin, John R. Lawson, Seth N. Lyman

Mathematics and Statistics Faculty Publications

High concentrations of ozone in the Uinta Basin, Utah, can occur after sufficient snowfall and a strong atmospheric anticyclone creates a persistent cold pool that traps emissions from oil and gas operations, where sustained photolysis of the precursors builds ozone to unhealthy concentrations. The basin's winter-ozone system is well understood by domain experts and supported by archives of atmospheric observations. Rules of the system can be formulated in natural language ("sufficient snowfall and high pressure leads to high ozone"), lending itself to analysis with a fuzzy-logic inference system. This method encodes human expertise as machine intelligence in a more prescribed …

Landscape Influences On Thermal Sensitivity And Predicted Spatial Variability Among Brook Trout Streams In The Southeastern Usa, George P. Valentine, Xinyi Lu, C. Andrew Dolloff, Craig N. Roghair, Jacob M. Rash, Mevin B. Hooten, Yoichiro Kanno

Mathematics and Statistics Faculty Publications

Warming water temperatures as a result of climate change pose a major threat to coldwater organisms. However, the rate of warming is not spatially uniform due to surface-ground-water interactions and stream and watershed characteristics. Coldwater habitats that are most resistant to warming serve as thermal refugia and identifying their locations is critical to regional aquatic conservation planning. We quantified the thermal sensitivity of 203 streams providing current and potential habitat for brook trout (Salvelinus fontinalis) across nearly 1000 linear km of their native range in the southern and central Appalachian Mountains region, USA, and characterized their spatial variability …

Using Multi-Scale Spatial Models Of Dendritic Ecosystems To Infer Abundance Of A Stream Salmonid, Xinyi Lu, Yoichiro Kanno, George P. Valentine, Jacob M. Rash, Mevin B. Hooten

Mathematics and Statistics Faculty Publications

1. Understanding patterns of species abundance is essential for planning landscape-level conservation. The complex hierarchies of dendritic ecosystems result in different levels of heterogeneity at distinct geographic scales. Species responses to dynamic environmental drivers may also vary spatially depending on their interactions with landscape features. Monitoring abundance by explicitly quantifying their spatial and temporal variation is important for strategic management.

2. We analysed brook trout (Salvelinus fontinalis) count data collected from 173 sites in western North Carolina between 1989 and 2015. We developed a Bayesian hierarchical model that used single- and multi-pass electro-fishing data and characterized their respective …

Mediating Effect Of Bmi On The Association Of Economic Status And Coexistence Of Hypertension And Diabetes In Bangladesh: A Counterfactual Framework-Based Weighting Approach, Foyez , Md. Jamal Hossain Ahmmed, Md. Jamal Hossain, Md Tareq Ferdous Khan, Muhammad Mahabub Rahaman Manik, Saimon Shahriar, Dulal Chandra Nandi, Md Parvej Hussain

Mathematics and Statistics Faculty Publications

Background and Aims

Non-communicable diseases such as hypertension and diabetes are matters of huge concern worldwide, with an increasing trend in prevalence over the previous decade. First of all, this study aimed to evaluate the association between economic status (ES) and body mass index (BMI), ES and comorbidity of hypertension and diabetes, and BMI and comorbidity independently. Second, it explored the mediating role of BMI in the association between ES and comorbidity of hypertension and diabetes. Finally, it investigated whether the mediating effect differs with the place of residence, gender, and education levels.

Methods

A total of 11,291 complete cases …

Structure Identification For High-Dimensional Data In The Vicinity Of Bear Lake, Ben Shaw, Haley Burger, Brennan L. Bean, Kevin R. Moon

Mathematics and Statistics Faculty Publications

This report focuses on seven water quality measurements taken at 43 different depths on the Bear Lake, Utah-Idaho for the months of June - November in the years 2018 - 2023. These measurements create a high-dimensional dataset on which we apply state-of-the-art machine learning (ML) techniques to look for low-dimensional structure in the data. A similar effort was made for weather measurements taken near the lake. Our analysis reveals that water quality measurements tend to cluster (i.e., group together) by year, while weather measurements tend to cluster by time of the year. This in mind, we explore potential drivers of …

Random Forests Regression For Soft Interval Data, Paul Gaona-Partida, Chih-Ching Yeh, Yan Sun, Adele Cutler

Mathematics and Statistics Faculty Publications

Analyzing soft interval data for uncertainty quantification has attracted much attention recently. Within this context, regression methods for interval data have been extensively studied. As most existing works focus on linear models, it is important to note that many problems in practice are nonlinear in nature and the development of nonlinear regression tools for interval data is crucial. This paper proposes an interval-valued random forests model that defines the splitting criterion of variance reduction based on an L₂ type metric in the space of compact intervals. The model simultaneously considers the centers and ranges of the interval data as …

Using Assessments To Promote Growth Mindset In College Algebra, Hannah M. Lewis, Kady Schneiter, David Lane Tait

Mathematics and Statistics Faculty Publications

Scientific evidence highlights the positive impact of a growth mindset on student achievement. Students with a growth mindset view errors and obstacles as opportunities for growth and welcome challenges and the opportunity to learn from their mistakes. Much has been written about promoting growth mindset through lectures and attitudes, however, assessments can also be an important avenue for encouraging a growth mindset in students. In this paper, we describe how we used assessments to promote growth mindset in a college algebra class. In the sections that follow, we discuss the need for these assessments and the principles that underly their …

On Colorings And Orientations Of Signed Graphs, Daniel Slilaty

Mathematics and Statistics Faculty Publications

A classical theorem independently due to Gallai and Roy states that a graph G has a proper k-coloring if and only if G has an orientation without coherent paths of length k. An analogue of this result for signed graphs is proved in this article.

I-Optimal Or G-Optimal: Do We Have To Choose?, Stephen J. Walsh, Lu Lu, Christine M. Anderson-Cook

Mathematics and Statistics Faculty Publications

When optimizing an experimental design for good prediction performance based on an assumed second order response surface model, it is common to focus on a single optimality criterion, either G-optimality, for best worst-case prediction precision, or I-optimality, for best average prediction precision. In this article, we illustrate how using particle swarm optimization to construct a Pareto front of non-dominated designs that balance these two criteria yields some highly desirable results. In most scenarios, there are designs that simultaneously perform well for both criteria. Seeing alternative designs that vary how they balance the performance of G- and I …

Epidemic Highs And Lows: A Stochastic Diffusion Model For Active Cases, Luis F. Gordillo, Priscilla E. Greenwood, Dana Strong

Mathematics and Statistics Faculty Publications

We derive a stochastic epidemic model for the evolving density of infective individuals in a large population. Data shows main features of a typical epidemic consist of low periods interspersed without breaks of various intensities and duration. In our stochastic differential model, a novel reproductive term combines a factor expressing the recent notion of ‘attenuated Allee effect’ and a capacity factor is controlling the size of the process. Simulation of this model produces sample paths of the stochastic density of infectives, which behave much like long-time Covid-19 case data of recent years. Writing the process as a stochastic diffusion allows …

Graphs Without A 2c3-Minor And Bicircular Matroids Without A U3,6-Minor, Daniel Slilaty

Mathematics and Statistics Faculty Publications

In this note we characterize all graphs without a 2C3-minor. A consequence of this result is a characterization of the bicircular matroids with no U3,6-minor.

Odd Solutions To Systems Of Inequalities Coming From Regular Chain Groups, Daniel Slilaty

Mathematics and Statistics Faculty Publications

Hoffman’s theorem on feasible circulations and Ghouila-Houry’s theorem on feasible tensions are classical results of graph theory. Camion generalized these results to systems of inequalities over regular chain groups. An analogue of Camion’s result is proved in which solutions can be forced to be odd valued. The obtained result also generalizes the results of Pretzel and Youngs as well as Slilaty. It is also shown how Ghouila-Houry’s result can be used to give a new proof of the graph- coloring theorem of Minty and Vitaver.

Hamilton Cycles In Bidirected Complete Graphs, Arthur Busch, Mohammed A. Mutar, Daniel Slilaty

Mathematics and Statistics Faculty Publications

Zaslavsky observed that the topics of directed cycles in directed graphs and alternating cycles in edge 2-colored graphs have a common generalization in the study of coherent cycles in bidirected graphs. There are classical theorems by Camion, Harary and Moser, Häggkvist and Manoussakis, and Saad which relate strong connectivity and Hamiltonicity in directed "complete" graphs and edge 2-colored "complete" graphs. We prove two analogues to these theorems for bidirected "complete" signed graphs.

Fluid-Structure Interaction Modelling Of Neighboring Tubes With Primary Cilium Analysis, Nerion Zekaj, Shawn D. Ryan, Andrew Resnick

Mathematics and Statistics Faculty Publications

We have developed a numerical model of two osculating cylindrical elastic renal tubules to investigate the impact of neighboring tubules on the stress applied to a primary cilium. We hypothesize that the stress at the base of the primary cilium will depend on the mechanical coupling of the tubules due to local constrained motion of the tubule wall. The objective of this work was to determine the in-plane stresses of a primary cilium attached to the inner wall of one renal tubule subject to the applied pulsatile flow, with a neighboring renal tube filled with stagnant fluid in close proximity …

Symplectic Reduction Along A Submanifold, Peter Crooks, Maxence Mayrand

Mathematics and Statistics Faculty Publications

We introduce the process of symplectic reduction along a submanifold as a uniform approach to taking quotients in symplectic geometry. This construction holds in the categories of smooth manifolds, complex analytic spaces, and complex algebraic varieties, and has an interpretation in terms of derived stacks in shifted symplectic geometry. It also encompasses Marsden-Weinstein-Meyer reduction, Mikami-Weinstein reduction, the pre-images of Poisson transversals under moment maps, symplectic cutting, symplectic implosion, and the Ginzburg-Kazhdan construction of Moore-Tachikawa varieties in topological quantum field theory. A key feature of our construction is a concrete and systematic association of a Hamiltonian G-space 𝔐_𝐺,𝑆 to …

Leveraging The "Large" In Large Lecture Statistics Classes, Kady Schneiter, Kimberleigh Felix Hadfield, Jenny Lee Clements

Mathematics and Statistics Faculty Publications

Being a teacher or a student in a class with a large enrollment can be intimidating. Often, teachers view comforts that are common to small classes as unattainable in a larger class, including knowing students’ names, using active learning, employing group work, and creating group discussion. Students in large classes may find that the class size leads to isolation. At Utah State University, we offer introductory statistics classes for various audiences using a large lecture format. The authors have collectively led these large lectures dozens of times and found that, despite its shortcomings, the large lecture format can be an …

Interrogation Of Social Justice Contexts In Mathematical Modeling: The Use Of Simulations Of Practice In The Mathematical Preparation Of Teachers, Cynthia Oropesa Anhalt, Ricardo Cortez, Brynja Kohler, Will Tidwell

Mathematics and Statistics Faculty Publications

Research in prospective teachers’ development of mathematical modeling knowledge for teaching is gaining momentum. The Mathematics of Doing, Understanding, Learning, and Educating for Secondary Students [MODULE(S2)]* project developed a curriculum in modeling for teacher education that includes simulations of practice, in which prospective teachers reflect on and plan a discussion around student thinking, their models, and the contextualization of their results. We present an analysis of prospective teachers’ modeling work on the decreasing area of Indigenous reservation land in the U.S., and a simulation of practice which explores different methods for finding the area of land in connection to …

Numerical Solutions To The Robin Inverse Problem With Nonnegativity Constraints, Weifu Fang, Fu-Rong Lin

Mathematics and Statistics Faculty Publications

We present iterative numerical methods for solving the inverse problem of recovering the nonnegative Robin coefficient from partial boundary measurement of the solution to the Laplace equation. Based on the boundary integral equation formulation of the problem, nonnegativity constraints in the form of a penalty term are incorporated conveniently into least-squares iteration schemes for solving the inverse problem. Numerical implementation and examples are presented to illustrate the effectiveness of this strategy in improving recovery results.

Characterization Of A Family Of Rotationally Symmetric Spherical Quadrangulations, Lowell Abrams, Daniel Slilaty

Mathematics and Statistics Faculty Publications

A spherical quadrangulation is an embedding of a graph G in the sphere in which each facial boundary walk has length four. Vertices that are not of degree four in G are called curvature vertices. In this paper we classify all spherical quadrangulations with n-fold rotational symmetry (n ≥ 3) that have minimum degree 3 and the least possible number of curvature vertices, and describe all such spherical quadrangulations in terms of nets of quadrilaterals. The description reveals that such rotationally symmetric quadrangulations necessarily also have a pole-exchanging symmetry.

Heterogeneous Bacterial Swarms With Mixed Lengths, Shlomit Peled, Shawn D. Ryan, Sebastian Heidenreich, Markus Baer, Gil Ariel, Avraham Be'er

Mathematics and Statistics Faculty Publications

Heterogeneous systems of active matter exhibit a range of complex emergent dynamical patterns. In particular, it is difficult to predict the properties of the mixed system based on its constituents. These considerations are particularly significant for understanding realistic bacterial swarms, which typically develop heterogeneities even when grown from a single cell. Here, mixed swarms of cells with different aspect ratios are studied both experimentally and in simulations. In contrast with previous theory, there is no macroscopic phase segregation. However, locally, long cells act as nucleation cites, around which aggregates of short, rapidly moving cells can form, resulting in enhanced swarming …

Ground Snow Loads For Asce 7-22 – What Has Changed And Why?, Marc Maguire, Brennan L. Bean, James Harris, Abbie Liel, Scott Russell

Mathematics and Statistics Faculty Publications

The changes to the ASCE 7 ground snow load maps proposed for the 2022 edition target a uniform reliability rather than a uniform hazard – an important distinction – and are the first of their kind in ASCE 7. Previously, the ASCE 7 snow loads used a uniform-hazard 50-year mean recurrence interval (MRI) with a 1.6 load factor. The newly proposed loads directly target the safety levels stipulated in Chapter 1 of ASCE 7, resulting in a strength design level load that is to be used with a load factor of 1.0. This paper describes changes in design provisions that …

The 2020 National Snow Load Study, Brennan L. Bean, Marc Maguire, Yan Sun, Jadon Wagstaff, Salam Al-Rubaye, Jesse Wheeler, Scout Jarman, Miranda Rogers

Mathematics and Statistics Faculty Publications

The United States has a rich history of snow load studies at the state and national level. The current ASCE 7 snow loads are based on studies performed at the Cold Regions Research and Engineering Laboratory (CRREL) ca. 1980 and updated ca. 1993. The map includes large regions where a site-specific case study is required to establish the load. Many state reports attempt to address the "case-study regions" designated in the current ASCE 7 design snow load requirements. The independently developed state-specific requirements vary in approach, which can lead to discrepancies in requirements at state boundaries. In addition, there has …

A Unified Approach For Constructing Confidence Intervals And Hypothesis Tests Using H-Function, Weizhen Wang

Mathematics and Statistics Faculty Publications

We introduce a general method, named the h-function method, to unify the constructions of level-a exact test and 1-a exact confidence interval. Using this method, any confidence interval is improved as follows: i) an approximate interval, including a point estimator, is modified to an exact interval; ii) an exact interval is refined to be an interval that is a subset of the previous one. Two real datasets are used to illustrate the method.

Coloring Permutation-Gain Graphs, Daniel Slilaty

Mathematics and Statistics Faculty Publications

Correspondence colorings of graphs were introduced in 2018by Dvoˇr ́ak and Postle as a generalization of list colorings of graphswhich generalizes ordinary graph coloring. Kim and Ozeki observed thatcorrespondence colorings generalize various notions of signed-graph col-orings which again generalizes ordinary graph colorings. In this notewe state how correspondence colorings generalize Zaslavsky’s notionof gain-graph colorings and then formulate a new coloring theory ofpermutation-gain graphs that sits between gain-graph coloring and cor-respondence colorings. Like Zaslavsky’s gain-graph coloring, our newnotion of coloring permutation-gain graphs has well defined chromaticpolynomials and lifts to colorings of the regular covering graph of apermutation-gain graph

Dynamically Weighted Balanced Loss: Class Imbalanced Learning And Confidence Calibration Of Deep Neural Networks, K. Ruwani M. Fernando, Chris P. Tsokos

Mathematics and Statistics Faculty Publications

Imbalanced class distribution is an inherent problem in many real-world classification tasks where the minority class is the class of interest. Many conventional statistical and machine learning classification algorithms are subject to frequency bias, and learning discriminating boundaries between the minority and majority classes could be challenging. To address the class distribution imbalance in deep learning, we propose a class rebalancing strategy based on a class-balanced dynamically weighted loss function where weights are assigned based on the class frequency and predicted probability of ground-truth class. The ability of dynamic weighting scheme to self-adapt its weights depending on the prediction scores …