Physical Sciences and Mathematics Commons^™

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 …

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 con- structions of level- exact test and 1− 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 …

The Family Of Bicircular Matroids Closed Under Duality, Vaidy Sivaraman, Daniel Slilaty

Mathematics and Statistics Faculty Publications

We characterize the 3-connected members of the intersection of the class of bicircular and cobi- circular matroids. Aside from some exceptional matroids with rank and corank at most 5, this class consists of just the free swirls and their minors.

An Agent-Based Simulator For The Gastrointestinal Pathway Of Listeria Monocytogenes, Ashrafur Rahman, Ali Asgary, Daniel Munther, Aamir Fazil, Ben A. Smith, Jianhong Wu

Mathematics and Statistics Faculty Publications

We developed an agent-based gastric simulator for a human host to illustrate the within host survival mechanisms of Listeria monocytogenes. The simulator incorporates the gastric physiology and digestion processes that are critical for pathogen survival in the stomach. Mathematical formulations for the pH dynamics, stomach emptying time, and survival probability in the presence of gastric acid are integrated in the simulator to evaluate the portion of ingested bacteria that survives in the stomach and reaches the small intestine. The parameters are estimated using in vitro data relevant to the human stomach and L. monocytogenes. The simulator predicts that 5%–29% of …

Classification Of Triples Of Lattice Polytopes With A Given Mixed Volume, Gennadiy Averkov, Christopher Borger, Ivan Soprunov

Mathematics and Statistics Faculty Publications

We present an algorithm for the classification of triples of lattice polytopes with a given mixed volumemin dimension 3. It is known that the classification can be reduced to the enumeration of so-called irreducible triples, the number of which is finite for fixed m. Following this algorithm, we enumerate all irreducible triples of normalized mixed volume up to 4 that are inclusion-maximal. This produces a classification of generic trivariate sparse polynomial systems with up to 4 solutions in the complex torus, up to monomial changes of variables. By a recent result of Esterov, this leads to a description of all …

Inequalities Between Mixed Volumes Of Convex Bodies: Volume Bounds For The Minkowski Sum, Gennadiy Averkov, Christopher Borger, Ivan Soprunov

Mathematics and Statistics Faculty Publications

n the course of classifying generic sparse polynomial systems which are solvable in radicals, Esterov recently showed that the volume of the Minkowski sum P1++Pd of d-dimensional lattice polytopes is bounded from above by a function of order O(m2d), where m is the mixed volume of the tuple (P1,,Pd). This is a consequence of the well-known Aleksandrov-Fenchel inequality. Esterov also posed the problem of determining a sharper bound. We show how additional relations between mixed volumes can be employed to improve the bound to O(md), which is asymptotically sharp. We furthermore prove a sharp exact upper bound in dimensions 2 …

Active Disturbance Rejection Control Of Torsional Plant With Unknown Frequency Harmonic Disturbance, Rafal Madonski, Momir Stanković, Sally Shao, Zhiqiang Gao, Jun Yang, Shihua Li

Mathematics and Statistics Faculty Publications

In this work, a new robust control algorithm is introduced for uncertain systems with harmonic disturbances of unknown frequencies. The proposed solution works under the active disturbance rejection control (ADRC) framework and utilizes a specialized observer for sinusoidal uncertainties, aided with an on-line harmonic disturbance frequency estimator. The entire governing structure is derived in a convenient error-based domain, easily deployable in various industrial control software. The idea behind the introduced approach is general, but is conveyed here using solely a three degrees-of-freedom torsional system, which is considered a benchmark for vibration phenomenon in many mechanical systems. The efficacy of the …

Bipartite Dot Product Graphs, Sean Bailey, David E. Brown

Mathematics and Statistics Faculty Publications

Given a bipartite graph G = (X, Y, E), the bipartite dot product representation of G is a function f : X ∪Y → ℝ^k and a positive threshold t such that for any x ∈ X and y ∈ Y , xy ∈ E if and only if f(x) · f(y) ≥ t. The minimum k such that a bipartite dot product representation exists for G is the bipartite dot product dimension of G, denoted bdp(G). We will show that such representations exist for all bipartite graphs as well as give an upper bound for the bipartite dot …

Linear Operators That Preserve Two Genera Of A Graph, Leroy B. Beasley, Kyung-Tae Kang, Seok-Zun Song

Mathematics and Statistics Faculty Publications

If a graph can be embedded in a smooth orientable surface of genus g without edge crossings and can not be embedded on one of genus g − 1 without edge crossings, then we say that the graph has genus g. We consider a mapping on the set of graphs with m vertices into itself. The mapping is called a linear operator if it preserves a union of graphs and it also preserves the empty graph. On the set of graphs with m vertices, we consider and investigate those linear operators which map graphs of genus g to graphs of …

Describing Quasi-Graphic Matroids, Nathan Bowler, Daryl Funk, Dan Slilaty

Mathematics and Statistics Faculty Publications

The class of quasi-graphic matroids recently introduced by Geelen, Gerards, and Whittle generalises each of the classes of frame matroids and liftedgraphic matroids introduced earlier by Zaslavsky. For each biased graph (G, B) Zaslavsky defined a unique lift matroid L(G, B) and a unique frame matroid F(G, B), each on ground set E(G). We show that in general there may be many quasi-graphic matroids on E(G) and describe them all: for each graph G and partition (B, L, F) of its cycles such that B satisfies the theta property and each cycle in L meets each cycle in F, there …

Towards Enhanced Chlorine Control: Mathematical Modeling For Free Chlorine Kinetics During Fresh-Cut Carrot, Cabbage And Lettuce Washing, Parthasarathy Srinivasan, Mohammadreza Dehghan Abnavi, Anthony Sulak, Chandrasekhar R. Kothapalli, Daniel Munther

Mathematics and Statistics Faculty Publications

In this study, we developed a novel produce-specific mechanistic model to predict free chlorine (FC) dynamics during washing of disk-cut carrots, cut cabbage, and cut iceberg lettuce, in 3 L and 50–100 L tanks, and of shredded iceberg lettuce in 3200 L pilot-plant trials. Ranges for two key parameters: β (L mg−1 min−1) the apparent reaction rate constant of FC with produce constituents, and γ, the fraction of the increase of chemical oxygen demand (COD) contributing to the reaction, were determined at the 3 L scale. For disk carrots β∈[0.05,0.09] and γ∈[0.054,0.078], for cut cabbage β∈[0.05,0.10] and γ∈[0.09,0.12], and for …

Explicit Ambient Metrics And Holonomy, Ian M. Anderson, Thomas Leistner, Pawel Nurowski

Mathematics and Statistics Faculty Publications

We present three large classes of examples of conformal structures whose Fefferman-Graham ambient metrics can be found explicitly. Our method for constructing these examples rests upon a set of sufficiency conditions under which the Fefferman-Graham equations are assured to reduce to a system of inhomogeneous linear partial differential equations. Our examples include conformal pp-waves and, more importantly, conformal structures that are defined by generic co-rank 3 distributions in dimensions 5 and 6.Our examples illustrate various aspects of the ambient metric construction.

The holonomy algebras of our ambient metrics are studied in detail. In particular, we exhibit a large class of …

Enhancing Produce Safety: State Estimation-Based Robust Adaptive Control Of A Produce Wash System, Vahid Azimi, Daniel Munther, Mojtaba Sharifi, Patricio A. Vela

Mathematics and Statistics Faculty Publications

The rapid introduction of fresh-cut produce into a produce wash system can dramatically decrease the free chlorine (FC) concentration level in the wash water, resulting in potential widespread cross-contamination throughout the entire wash system. To minimize such contamination, a sufficient level of FC must be maintained in the wash water. This paper presents a state estimation-based robust adaptive sliding mode (RASM) control strategy for the wash system to stabilize the FC concentration level during fresh-cut iceberg lettuce washing. This feedback control law for FC dosing is suggested to provide a sufficient FC injection rate (FCIR) to the wash system in …

Arbitrarily High-Order Unconditionally Energy Stable Schemes For Thermodynamically Consistent Gradient Flow Models, Yuezheng Gong, Jia Zhao, Qi Wang

Mathematics and Statistics Faculty Publications

We present a systematic approach to developing arbitrarily high-order, unconditionally energy stable numerical schemes for thermodynamically consistent gradient flow models that satisfy energy dissipation laws. Utilizing the energy quadratization method, we formulate the gradient flow model into an equivalent form with a corresponding quadratic free energy functional. Based on the equivalent form with a quadratic energy, we propose two classes of energy stable numerical approximations. In the first approach, we use a prediction-correction strategy to improve the accuracy of linear numerical schemes. In the second approach, we adopt the Gaussian collocation method to discretize the equivalent form with a quadratic …

Formation Of Escherichia Coli O157: H7 Persister Cells In The Lettuce Phyllosphere And Application Of Differential Equation Models To Predict Their Prevalence On Lettuce Plants In The Field, Daniel S. Munther, Michelle Q. Carter, Claude V. Aldric, Renata Ivanek, Maria T. Brandl

Mathematics and Statistics Faculty Publications

American Society for Microbiology. Escherichia coli O157:H7 (EcO157) infections have been recurrently associated with produce. The physiological state of EcO157 cells surviving the many stresses encountered on plants is poorly understood. EcO157 populations on plants in the field generally follow a biphasic decay in which small subpopulations survive over longer periods of time. We hypothesized that these subpopulations include persister cells, known as cells in a transient dormant state that arise through phenotypic variation in a clonal population. Using three experimental regimes (with growing, stationary at carrying capacity, and decaying populations), we measured the persister cell fractions in culturable EcO157 …