Physical Sciences and Mathematics Commons^™

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 …

Pulsatile Flow Through Idealized Renal Tubules: Fluid-Structure Interaction And Dynamic Pathologies, Niksa Praljak, Shawn D. Ryan, Andrew Resnick

Mathematics and Statistics Faculty Publications

Kidney tubules are lined with flow-sensing structures, yet information about the flow itself is not easily obtained. We aim to generate a multiscale biomechanical model for analyzing fluid flow and fluid-structure interactions within an elastic kidney tubule when the driving pressure is pulsatile. We developed a two-dimensional macroscopic mathematical model of a single fluid-filled tubule corresponding to a distal nephron segment and determined both flow dynamics and wall strains over a range of driving frequencies and wall compliances using finite-element analysis. The results presented here demonstrate good agreement with available analytical solutions and form a foundation for future inclusion of …

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 …

Role Of Hydrodynamic Interactions In Chemotaxis Of Bacterial Populations, Shawn D. Ryan

Mathematics and Statistics Faculty Publications

How bacteria sense local chemical gradients and decide to move has been a fascinating area of recent study. Chemotaxis of bacterial populations has been traditionally modeled using either individual-based models describing the motion of a single bacterium as a velocity jump process, or macroscopic PDE models that describe the evolution of the bacterial density. In these models, the hydrodynamic interaction between the bacteria is usually ignored. However, hydrodynamic interaction has been shown to induce collective bacterial motion and self-organization resulting in larger mesoscale structures. In this paper, the role of hydrodynamic interactions in bacterial chemotaxis is investigated by extending a …

Individual Based Modeling And Analysis Of Pathogen Levels In Poultry Chilling Process, Zachary Mccarthy, Ben Smith, Aamir Fazil, Jianhong Wu, Shawn D. Ryan, Daniel Munther

Mathematics and Statistics Faculty Publications

Pathogen control during poultry processing critically depends on more enhanced insight into contamination dynamics. In this study we build an individual based model (IBM) of the chilling process. Quantifying the relationships between typical Canadian processing specifications, water chemistry dynamics and pathogen levels both in the chiller water and on individual carcasses, the IBM is shown to provide a useful tool for risk management as it can inform risk assessment models. We apply the IBM to Campylobacter spp. contamination on broiler carcasses, illustrating how free chlorine (FC) sanitization, organic load in the water, and pre-chill carcass pathogen levels affect pathogen levels …

Normalized Multi-Bump Solutions For Saturable Schrödinger Equations, Xiaoming Wang, Zhi-Qiang Wang

Mathematics and Statistics Faculty Publications

In this paper, we are concerned with the existence of multi-bump solutions for a class of semiclassical saturable Schrödinger equations with an density function:

We prove that, with the density function being radially symmetric, for given integer k ≥ 2 there exist a family of non-radial, k-bump type normalized solutions (i.e., with the L² constraint) which concentrate at the global maximum points of density functions when ε → 0⁺. The proof is based on a variational method in particular on a convexity technique and the concentration-compactness method.

On Vibration Suppression And Trajectory Tracking In Largely Uncertain Torsional System: An Error-Based Adrc Approach, R. Madonski, M. Ramirez-Neria, M. Stankovic, Sally Shao, Zhiqiang Gao, J. Yang, S. Li

Mathematics and Statistics Faculty Publications

In this work, a practically relevant control problem of compensating harmonic uncertainties is tackled. The problem is formulated and solved here using an active disturbance rejection control (ADRC) methodology. A novel, custom ADRC structure is proposed that utilizes an innovative resonant extended state observer (RESO), dedicated to systems subjected to harmonic interferences. In order to make the introduced solution more industry-friendly, the entire observer-centered control topology is additionally restructured into one degree-of-freedom, compact, feedback error-based form (similar to ubiquitous in practice PID controller). Such reorganization enables a straightforward implementation and commission of the proposed technique in wide range of industrial …

An Individual-Carcass Model For Quantifying Bacterial Cross-Contamination In An Industrial Three-Stage Poultry Scalding Tank, Zachary Mccarthy, Ben Smith, Aamir Fazil, Shawn D. Ryan, Jianhong Wu, Daniel Munther

Mathematics and Statistics Faculty Publications

No abstract provided.

Convergence Rates For Empirical Estimation Of Binary Classification Bounds, Salimeh Yasaei Sekeh, Morteza Noshad, Kevin R. Moon, Alfred O. Hero

Mathematics and Statistics Faculty Publications

Bounding the best achievable error probability for binary classification problems is relevant to many applications including machine learning, signal processing, and information theory. Many bounds on the Bayes binary classification error rate depend on information divergences between the pair of class distributions. Recently, the Henze–Penrose (HP) divergence has been proposed for bounding classification error probability. We consider the problem of empirically estimating the HP-divergence from random samples. We derive a bound on the convergence rate for the Friedman–Rafsky (FR) estimator of the HP-divergence, which is related to a multivariate runs statistic for testing between two distributions. The FR estimator is …

Feasibility Of Multi-Year Forecast For The Colorado River Water Supply: Time Series Modeling, Brian Plucinski, Yan Sun, Shih-Yu (Simon) Wang, Robert R. Gilies, James Eklund, Chih-Chia Wang

Mathematics and Statistics Faculty Publications

The future of the Colorado River water supply (WS) affects millions of people and the US economy. A recent study suggested a cross-basin correlation between the Colorado River and its neighboring Great Salt Lake (GSL). Following that study, the feasibility of using the previously developed multi-year prediction of the GSL water level to forecast the Colorado River WS was tested. Time-series models were developed to predict the changes in WS out to 10 years. Regressive methods and the GSL water level data were used for the depiction of decadal variability of the Colorado River WS. Various time-series models suggest a …

Nonlinear Reaction–Diffusion Process Models Improve Inference For Population Dynamics, Xinyi Lu, Perry J. Williams, Mevin B. Hooten, James A. Powell, Jamie N. Womble, Michael R. Bower

Mathematics and Statistics Faculty Publications

Partial differential equations (PDEs) are a useful tool for modeling spatiotemporal dynamics of ecological processes. However, as an ecological process evolves, we need statistical models that can adapt to changing dynamics as new data are collected. We developed a model that combines an ecological diffusion equation and logistic growth to characterize colonization processes of a population that establishes long‐term equilibrium over a heterogeneous environment. We also developed a homogenization strategy to statistically upscale the PDE for faster computation and adopted a hierarchical framework to accommodate multiple data sources collected at different spatial scales. We highlighted the advantages of using a …

The Graphs That Have Antivoltages Using Groups Of Small Order, Vaidy Sivaraman, Dan Slilaty

Mathematics and Statistics Faculty Publications

Given a group Γ of order at most six, we characterize the graphs that have Γ-antivoltages and also determine the list of minor-minimal graphs that have no Γ-antivoltage. Our characterizations yield polynomial-time recognition algorithms for such graphs.

A Three-Dimensional Rna Motif Mediates Directional Trafficking Of Potato Spindle Tuber Viroid From Epidermal To Palisade Mesophyll Cells In Nicotiana Benthamiana, Jian Wu, Neocles B. Leontis, Craig L. Zirbel, David M. Bisaro, Biao Ding

Mathematics and Statistics Faculty Publications

Potato spindle tuber viroid (PSTVd) is a circular non-coding RNA of 359 nucleotides that replicates and spreads systemically in host plants, thus all functions required to establish an infection are mediated by sequence and structural elements in the genome. The PSTVd secondary structure contains 26 Watson-Crick base-paired stems and 27 loops. Most of the loops are believed to form three-dimensional (3D) structural motifs through non-Watson-Crick base pairing, base stacking, and other local interactions. Homology-based prediction using the JAR3D online program revealed that loop 27 (nucleotides 177-182) most likely forms a 3D structure similar to the loop of a conserved hairpin …

Modeling Of Free Chlorine Consumption And Escherichia Coli O157:H7 Cross-Contamination During Fresh-Cut Produce Wash Cycles, Mohammadreza Dehghan Abnavi, Ali Alradaan, Daniel Munther, Chandrasekhar R. Kothapalli, Partha Srinivasan

Mathematics and Statistics Faculty Publications

Controlling the free chlorine (FC) availability in wash water during sanitization of fresh produce enhances our ability to reduce microbial levels and prevent cross-contamination. However, maintaining an ideal concentration of FC that could prevent the risk of contamination within the wash system is still a technical challenge in the industry, indicating the need to better understand wash water chemistry dynamics. Using bench-scale experiments and modeling approaches, we developed a comprehensive mathematical model to predict the FC concentration during fresh-cut produce wash processes for different lettuce types (romaine, iceberg, green leaf, and red leaf), carrots, and green cabbage as well as …

(0,1)-Matrices, Discrepancy And Preservers, Leroy B. Beasley

Mathematics and Statistics Faculty Publications

Let m and n be positive integers, and let R = (r₁, . . . , r_m) and S = (s₁, . . . , s_n) be nonnegative integral vectors. Let A(R,S) be the set of all m × n (0, 1)-matrices with row sum vector R and column vector S. Let R and S be nonincreasing, and let F(R) be the m × n (0, 1)-matrix, where for each i, the ith row of F(R, …

From The Signature Theorem To Anomaly Cancellation, Andreas Malmendier, Michael T. Schultz

Mathematics and Statistics Faculty Publications

We survey the Hirzebruch signature theorem as a special case of the Atiyah–Singer index theorem. The family version of the Atiyah–Singer index theorem in the form of the Riemann–Roch–Grothendieck–Quillen (RRGQ) formula is then applied to the complexified signature operators varying along the universal family of elliptic curves. The RRGQ formula allows us to determine a generalized cohomology class on the base of the elliptic fibration that is known in physics as (a measure of) the local and global anomaly. Combining several anomalous operators allows us to cancel the local anomaly on a Jacobian elliptic surface, a construction that is based …

Comparing Design Ground Snow Load Prediction In Utah And Idaho, Brennan L. Bean, Marc Maguire, Yan Sun

Mathematics and Statistics Faculty Publications

Snow loads in the western United States are largely undefined due to complex geography and climates, leaving the individual states to publish detailed studies for their region, usually through the local Structural Engineers Association (SEAs). These associations are typically made up of engineers not formally trained to develop or evaluate spatial statistical methods for their regions and there is little guidance from ASCE 7. Furthermore, little has been written to compare the independently developed design ground snow load prediction methods used by various western states. This paper addresses this topic by comparing the accuracy of a variety of spatial methods …

Long-Dose Intensive Therapy Is Necessary For Strong, Clinically Significant, Upper Limb Functional Gains And Retained Gains In Severe/Moderate Chronic Stroke, Janis J. Daly, Jessica P. Mccabe, John P. Holcomb, Michelle Monkiewicz, Jennifer Gansen, Svetlana Pundik

Mathematics and Statistics Faculty Publications

Background. Effective treatment methods are needed for moderate/severely impairment chronic stroke. Objective. The questions were the following: (1) Is there need for long-dose therapy or is there a mid-treatment plateau? (2) Are the observed gains from the prior-studied protocol retained after treatment? Methods. Single-blind, stratified/randomized design, with 3 applied technology treatment groups, combined with motor learning, for long-duration treatment (300 hours of treatment). Measures were Arm Motor Ability Test time and coordination-function (AMAT-T, AMAT-F, respectively), acquired pre-/posttreatment and 3-month follow-up (3moF/U); Fugl-Meyer (FM), acquired similarly with addition of mid-treatment. Findings. There was no group difference in …

Noise-Induced Stabilization Of Perturbed Hamiltonian Systems, Tiffany N. Kolba, Anthony Coniglio, Sarah Sparks, Daniel Weithers

Mathematics and Statistics Faculty Publications

Noise-induced stabilization is the phenomenon in which the addition of randomness to an unstable system of ordinary differential equations results in a stable system of stochastic differential equations. With stability defined as global stochastic boundedness, Hamiltonian systems can never be stabilized by the addition of noise that is constant in space. In this article, we investigate how to deterministically perturb a class of unstable Hamiltonian systems in such a way that the qualitative behavior is preserved, but that enables the systems to exhibit noise-induced stabilization.

Formation Of Radial Patterns Via Mixed Attractive And Repulsive Interactions For Schrödinger Systems, Jaeyoung Byeon, Youngae Lee, Zhi-Qiang Wang

Mathematics and Statistics Faculty Publications

This paper is concerned with the asymptotic behavior of least energy vector solutions for nonlinear Schrödinger systems with mixed couplings of attractive and repulsive forces. We focus here on the radially symmetric case while the general studies were already conducted in our earlier work [J. Byeon, Y. Sato, and Z.-Q. Wang, J. Math. Pures Appl. (9), 106 (2016), pp. 477--511], [J. Byeon, Y. Sato, and Z.-Q. Wang, J. Fixed Point Theory Appl., 19 (2017), pp. 559--583]. Though there is still the general phenomenon of component-wise pattern formation with co-existence of partial synchronization and segregation for positive least energy …

Ph Dependent C-Jejuni Thermal Inactivation Models And Application To Poultry Scalding, Zachary Mccarthy, Ben Smith, Aamir Fazil, Jianhong Wu, Shawn D. Ryan, Daniel Munther

Mathematics and Statistics Faculty Publications

Campylobacter jejuni related outbreaks and prevalence on retail poultry products pose threats to public health and cause financial burden worldwide. To resolve these problems, it is imperative to take a closer look at poultry processing practices and standards. Using available data (D-values) on the thermal inactivation of C. jejuni we develop a comprehensive inactivation model, taking into account the variation of strain-specific heat resistance, experimental method, and suspension pH. Utilizing our C. jejuni thermal inactivation model, we study the poultry scalding process. We present a mechanistic model of bacteria transfer and inactivation during a typical immersion scald in a high-speed …

Association Of Rare Coding Mutations With Alzheimer Disease And Other Dementias Among Adults Of European Ancestry, Devanshi Patel, Jesse Mez, Badri N. Vardarajan, Lyndsay Staley, Jaeyoon Chung, Xiaoling Zhang, John J. Farrell, Michael J. Rynkiewicz, Lisa A. Cannon-Albright, Craig C. Teerlink, Jeffery Stevens, Chris Corcoran, Et Al.

Mathematics and Statistics Faculty Publications

IMPORTANCE Some of the unexplained heritability of Alzheimer disease (AD) may be due to rare variants whose effects are not captured in genome-wide association studies because very large samples are needed to observe statistically significant associations.

OBJECTIVE To identify genetic variants associated with AD risk using a nonstatistical approach.

DESIGN, SETTING, AND PARTICIPANTS Genetic association study in which rare variants were identified by whole-exome sequencing in unrelated individuals of European ancestry from the Alzheimer’s Disease Sequencing Project (ADSP). Data were analyzed between March 2017 and September 2018.

MAIN OUTCOMES AND MEASURES Minor alleles genome-wide and in 95 genes previously associated …

Linear Operators That Preserve The Genus Of A Graph, Leroy B. Beasley, Jeong Han Kim, Seok-Zun Song

Mathematics and Statistics Faculty Publications

A graph has genus k if it can be embedded without edge crossings on a smooth orientable surface of genus k and not on one of genus k−1. A mapping of the set of graphs on n vertices to itself is called a linear operator if the image of a union of graphs is the union of their images and if it maps the edgeless graph to the edgeless graph. We investigate linear operators on the set of graphs on n vertices that map graphs of genus k to graphs of genus k and graphs of genus k+1 to graphs …

Prediction Of Stress Increase At Ultimate In Unbonded Tendons Using Sparse Principal Component Analysis, Eric Mckinney, Minwoo Chang, Marc Maguire, Yan Sun

Mathematics and Statistics Faculty Publications

While internal and external unbonded tendons are widely utilized in concrete structures, an analytical solution for the increase in unbonded tendon stress at ultimate strength, Δ������, is challenging due to the lack of bond between strand and concrete. Moreover, most analysis methods do not provide high correlation due to the limited available test data. The aim of this paper is to use advanced statistical techniques to develop a solution to the unbonded strand stress increase problem, which phenomenological models by themselves have done poorly. In this paper, Principal Component Analysis (PCA), and Sparse Principal Component Analysis (SPCA) are employed on …

Gluing Semigroups And Strongly Indispensable Free Resolutions, Mesut Sahin, Leah Gold Stella

Mathematics and Statistics Faculty Publications

We study strong indispensability of minimal free resolutions of semigroup rings focusing on the operation of gluing used in literature to take examples with a special property and producenew ones. We give a naive condition to determine whether gluing of two semigroup rings has astrongly indispensable minimal free resolution. As applications, we determine simple gluings of 3-generated non-symmetric, 4-generated symmetric and pseudo symmetric numerical semigroups as well as obtain infinitely many new complete intersection semigroups of any embedding dimensions, having strongly indispensable minimal free resolutions.

General Error-Based Active Disturbance Rejection Control For Swift Industrial Implementations, R. Madonski, S. Shao, H. Zhang, Z. Gao, J. Yang, S. Li

Mathematics and Statistics Faculty Publications

In this article, a typical 2DOF active disturbance rejection control (ADRC) design is restructured into a 1DOF form, thus making it compatible with standard industrial control function blocks and enhancing its market competitiveness. This methodology integrates the previously separated components, such as the profile generator, state observer, feedback controller, feedforward terms, and disturbance rejection, into one unified structure. In doing so, certain ADRC components can be made simpler (or even obsolete) without sacrificing the nominal control performance, which further simplifies the control synthesis and tuning. A generalized version of the error-driven design is adopted and rigorously proved here using the …

Factors That Influence Mathematical Creativity, Joseph S. Kozlowski, Scott A. Chamberlin, Eric Mann

Mathematics and Statistics Faculty Publications

Creativity is a psychological construct that has gained research popularity (Akgul & Kaveci, 2016), however it remains a challenging one to define. The variety of definitions promulgated to understand creativity hints at the complexity of the mental process. Furthermore, as a subset of creativity, domain-specific mathematical creativity has also garnered a variety of definitions. The transdisciplinary research on creativity (Sriraman & Haavold, 2017) is seminal in this world of fast-paced innovation, invention, solution, and synthesis. Considering every human being with at least average cognitive abilities possesses the ability to think creatively (Baran, 2011), developing students’ creative talents and abilities must …

Exploring Mortality Rates For Major Causes Of Death In Korea, Hyo Jung Oh, Donng Min Yang, Chong Hyuck Kim, Jae Gyu Jeon, Nam Hyung Jung, Chan Young Kim, Jurgen Symanzik, Hyo Won Oh, Akugizibwe Edwin, Seong Ii Jo, Jeong Yong Ahn

Mathematics and Statistics Faculty Publications

Background: The trends and patterns of the mortality rates for causes of death are meaningful information. They can provide a basis for national demographic and health care policies by identifying the number, causes, and geographical distribution of deaths.

Objective: To explore and analyze the characteristics of the mortality rates for major causes of death in Korea.

Methods: Some common data analysis methods were used to describe the data. We also used some visualization techniques such as heat maps and line plots to present mortality rates by gender, age, and year.

Results: Our analysis shows the crude …