Mathematics Commons^™

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 …

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 …

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.

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 …

Upper Bounds For The Isolation Number Of A Matrix Over Semirings, Leroy B. Beasley, Seok-Zun Song

Mathematics and Statistics Faculty Publications

Let S be an antinegative semiring. The rank of an m×n matrix B over S is the minimal integer r such that B is a product of an m×r matrix and an r×n matrix. The isolation number of B is the maximal number of nonzero entries in the matrix such that no two entries are in the same column, in the same row, and in a submatrix of B of the form [b_i,j b_k,j

b_i,l b_k,l] with nonzero entries. We know that the isolation number of B is …

Charged Nanoparticles Quench The Propulsion Of Active Janus Colloids, Marola W. Issa, Nicky R. Baumgartner, Mohammed A. Kalil, Shawn D. Ryan, Christopher L. Wirth

Mathematics and Statistics Faculty Publications

Active colloidal particles regularly interact with surfaces in applications ranging from microfluidics to sensing. Recent work has revealed the complex nature of these surface interactions for active particles. Herein, we summarize experiments and simulations that show the impact of charged nanoparticles on the propulsion of an active colloid near a boundary. Adding charged nanoparticles not only decreased the average separation distance of a passive colloid because of depletion attraction as expected but also decreased the apparent propulsion of a Janus colloid to near zero. Complementary agentbased simulations considering the impact of hydrodynamics for active Janus colloids were conducted in the …

English Translation Of Einige Gesetze Ueber Die Theilung Der Ebene Und Des Raumes, Justin Heavilin

Mathematics and Statistics Faculty Publications

The article “Einige Gesetze ueber die Theilung der Ebene und des Raumes.” was published by J. Steiner in the very first volumn of the Journal fuer die reine und angewandte Mathematik in 1826. Journal fuer die reine und angewandte Mathematik is the oldest mathematics periodical in existence.† . My translation is meant to convey the ideas published by Steiner, and when presented with the choice between translating faithfully to the original text or clarity of his ideas, I admit to choosing the later. There are two footnotes original to the text, which appear with asterisks. Where helpful I included additional …

Power In Pairs: Assessing The Statistical Value Of Paired Samples In Tests For Differential Expression, John R. Stevens, Jennifer S. Herrick, Roger K. Wolff, Martha L. Slattery

Mathematics and Statistics Faculty Publications

Background: When genomics researchers design a high-throughput study to test for differential expression, some biological systems and research questions provide opportunities to use paired samples from subjects, and researchers can plan for a certain proportion of subjects to have paired samples. We consider the effect of this paired samples proportion on the statistical power of the study, using characteristics of both count (RNA-Seq) and continuous (microarray) expression data from a colorectal cancer study.

Results: We demonstrate that a higher proportion of subjects with paired samples yields higher statistical power, for various total numbers of samples, and for various strengths of …

Logarithmic Hennings Invariants For Restricted Quantum Sl (2), Anna Beliakova, Christian Blanchet, Alexandra Tebbs

Mathematics and Statistics Faculty Publications

We construct a Hennings-type logarithmic invariant for restricted quantum sl (2) at a 2p^th root of unity. This quantum group U is not quasitriangular and hence not ribbon, but factorizable. The invariant is defined for a pair: a 3–manifold M and a colored link L inside M. The link L is split into two parts colored by central elements and by trace classes, or elements in the 0^th Hochschild homology of U, respectively. The two main ingredients of our construction are the universal invariant of a string link with values in tensor powers of U, and the modified …

Developmental Parameters Of A Southern Mountain Pine Beetle (Coleoptera: Curculionidae) Population Reveal Potential Source Of Latitudinal Differences In Generation Time, Anne E. Mcmanis, James A. Powell, Barbara J. Bentz

Mathematics and Statistics Faculty Publications

Mountain pine beetle (Dendroctonus ponderosae, Hopkins) is a major disturbance agent in pine ecosystems of western North America. Adaptation to local climates has resulted in primarily univoltine generation time across a thermally diverse latitudinal gradient. We hypothesized that voltinism patterns have been shaped by selection for slower developmental rates in southern populations inhabiting warmer climates. To investigate traits responsible for latitudinal differences we measured lifestage-specific development of southern mountain pine beetle eggs, larvae and pupae across a range of temperatures. Developmental rate curves were fit using maximum posterior likelihood estimation with a Bayesian prior to improve fit stability. …

With-In Host Dynamics Of L. Monocytogenes And Thresholds For Distinct Infection Scenarios, Ashrafur Rahman, Daniel Munther, Aamir Fazil, Ben Smith, Jianhong Wu

Mathematics and Statistics Faculty Publications

The case fatality and illness rates associated with L. monocytogenes continue to pose a serious public health burden despite the significant efforts and control protocol administered by private and public sectors. Due to the advance in surveillance and improvement in detection methodology, the knowledge of sources, transmission routes, growth potential in food process units and storage, effect of pH and temperature are well understood. However, the with-in host growth and transmission mechanisms of L. monocytogenes, particularly within the human host, remain unclear, largely due to the limited access to scientific experimentation on the human population. In order to provide insight …

Collective Dynamics Of Two-Dimensional Swimming Bacteria: Experiments And Models, Gil Ariel, Marina Sidortsov, Shawn D. Ryan, Sebastian Heidenreich, Markus Baer, Avraham Be'er

Mathematics and Statistics Faculty Publications

The physical properties of collectively swimming bacteria have been thoroughly investigated both experimentally and theoretically using simulations. While models successfully predict some aspects of the dynamics observed in experiments, both models and experiments vary in their underlying assumptions and physical conditions. Hence, it is not clear which models are appropriate for which experimental setups. Here, we study, both experimentally and using two types of models (agent-based and continuous), the statistics of two strains of Serratia marcescens, wild-type and a nontumbling strain, swimming on a two-dimensional monolayer at varying concentrations. The experimental setup allows for a direct comparison with simulation results. …

Genome-Wide Association Study For Variants That Modulate Relationships Between Cerebrospinal Fluid Amyloid-Beta 42, Tau, And P-Tau Levels, Taylor J. Maxwell, Chris Corcoran, Jorge L. Del-Aguila, John P. Budde, Yuetiva Deming, Carlos Cruchaga, Alison M. Goate, John S. K. Kauwe, Alzheimer's Disease Neuroimaging Initiative

Mathematics and Statistics Faculty Publications

Background: A relationship quantitative trait locus exists when the correlation between multiple traits varies by genotype for that locus. Relationship quantitative trait loci (rQTL) are often involved in gene-by-gene (G×G) interactions or gene-by-environmental interactions, making them a powerful tool for detecting G×G.

Methods: We performed genome-wide association studies to identify rQTL between tau and Aβ42 and ptau and Aβ42 with over 3000 individuals using age, gender, series, APOE ε2, APOE ε4, and two principal components for population structure as covariates. Each significant rQTL was separately screened for interactions with other loci for each trait in the rQTL model. Parametric bootstrapping …

Remarks On Legendrian Self-Linking, Chris Beasley, Brendan Mclellan, Ruoran Zhang

Mathematics and Statistics Faculty Publications

The Thurston-Bennequin invariant provides one notion of self-linking for any homologically-trivial Legendrian curve in a contact three-manifold. Here we discuss related analytic notions of self-linking for Legendrian knots in R³. Our definition is based upon reformulation of the elementary Gauss linking integral and is motivated by ideas from supersymmetric gauge theory. We recover the Thurston-Bennequin invariant as a special case.

Advancing Risk Assessment: Mechanistic Dose-Response Modelling Of Listeria Monocytogenes Infection In Human Populations, Ashrafur Rahman, Daniel Munther, Aamir Fazil, Ben Smith, Jianhong Wu

Mathematics and Statistics Faculty Publications

Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited. The utility of characterizing the effects of strain variation and individual/subgroup susceptibility on dose-response outcomes has motivated the search for new approaches beyond the popular use of the exponential dose-response model for listeriosis. While descriptive models can account for such variation, they have limited power to extrapolate beyond the details of particular outbreaks. By contrast, this study exhibits dose-response relationships from a mechanistic basis, quantifying key biological factors involved in pathogen-host dynamics. An …

Ensemble Estimation Of Information Divergence, Kevin R. Moon, Kumar Sricharan, Kristjan Greenewald, Alfred O. Hero Iii

Mathematics and Statistics Faculty Publications

Recent work has focused on the problem of nonparametric estimation of information divergence functionals between two continuous random variables. Many existing approaches require either restrictive assumptions about the density support set or difficult calculations at the support set boundary which must be known a priori. The mean squared error (MSE) convergence rate of a leave-one-out kernel density plug-in divergence functional estimator for general bounded density support sets is derived where knowledge of the support boundary, and therefore, the boundary correction is not required. The theory of optimally weighted ensemble estimation is generalized to derive a divergence estimator that achieves the …

Limit Behavior Of Mass Critical Hartree Minimization Problems With Steep Potential Wells, Yujin Guo, Yong Luo, Zhi-Qiang Wang

Mathematics and Statistics Faculty Publications

We consider minimizers of the following mass critical Hartree minimization problem: e_λ(N) ≔ inf{u∈H¹(ℝ^d),‖u‖²₂=N} E_λ(u), where d ≥ 3, λ > 0, and the Hartree energy functional E_λ(u) is defined by E_λ(u)≔∫_R^d|∇u(x)|²dx + λ∫_R^d g(x)u²(x)dx − 1/2∫_R^d∫_R^d {u²(x)u²(y)/|x−y|²} dxdy. Here the steep potential g(x) satisfies 0 = g(0) = inf_ℝ^dg(x) ≤ g(x) ≤ 1 and 1 …

The Effect Of Warmer Winters On The Demography Of An Outbreak Insect Is Hidden By Intraspecific Competition, Devin W. Goodsman, Guenchik Grosklos, Brian H. Aukema, Caroline Whitehouse, Katherine P. Bleiker, Nate G. Mcdowell, Richard S. Middleton, Chonggang Xu

Mathematics and Statistics Faculty Publications

Warmer climates are predicted to increase bark beetle outbreak frequency, severity, and range. Even in favorable climates, however, outbreaks can decelerate due to resource limitation, which necessitates the inclusion of competition for limited resources in analyses of climatic effects on populations. We evaluated several hypotheses of how climate impacts mountain pine beetle reproduction using an extensive 9‐year dataset, in which nearly 10,000 trees were sampled across a region of approximately 90,000 km², that was recently invaded by the mountain pine beetle in Alberta, Canada. Our analysis supports the hypothesis of a positive effect of warmer winter temperatures on …

Full Dyon Excitation Spectrum In Extended Levin-Wen Models, Yuting Hu, Alexandra Tebbs, Yong-Shi Wu

Mathematics and Statistics Faculty Publications

In Levin-Wen (LW) models, a wide class of exactly solvable discrete models, for two-dimensional topological phases, it is relatively easy to describe only single-fluxon excitations, but not the charge and dyonic as well as many-fluxon excitations. To incorporate charged and dyonic excitations in (doubled) topological phases, an extension of the LW models is proposed in this paper. We first enlarge the Hilbert space with adding a tail on one of the edges of each trivalent vertex to describe the internal charge degrees of freedom at the vertex. Then, we study the full dyon spectrum of the extended LW models, including …

Gaps In The Saturation Spectrum Of Trees, Ronald J. Gould, Paul Horn, Michael S. Jacobson, Brent J. Thomas

Mathematics and Statistics Faculty Publications

A graph G is H-saturated if H is not a subgraph of G but the addition of any edge from the complement of G to G results in a copy of H. The minimum number of edges (the size) of an H-saturated graph on n vertices is denoted sat(n, H), while the maximum size is the well studied extremal number, ex(n, H). The saturation spectrum for a graph H is the set of sizes of H-saturated graphs between sat(n, H) and ex(n, H). In …

Feasibility Of Predicting Vietnam’S Autumn Rainfall Regime Based On The Tree-Ring Record And Decadal Variability, Yan Sun, Shih-Yu (Simon) Wang, Rong Li, Brendan M. Buckley, Robert R. Gilies, Kyle G. Hansen

Mathematics and Statistics Faculty Publications

We investigate the feasibility of developing decadal prediction models for autumn rainfall ( R_A ) over Central Vietnam by utilizing a published tree-ring reconstruction of October–November (ON) rainfall derived from the earlywood width measurements from a type of Douglas-fir (Pseudotsuga sinensis). Autumn rainfall for this region accounts for a large percentage of the annual total, and is often the source of extreme flooding. Central Vietnam’s R_A along with its notable autocorrelation and significant cross-correlation with basin-wide Pacific sea surface temperature (SST) variability, to develop four discrete time-series models. The sparse autoregressive model, with Pacific SST as …

Possible Isolation Number Of A Matrix Over Nonnegative Integers, Leroy B. Beasley, Young Bae Jun, Seok-Zun Song

Mathematics and Statistics Faculty Publications

Let ℤ₊ be the semiring of all nonnegative integers and A an m × n matrix over ℤ₊. The rank of A is the smallest k such that A can be factored as an m × k matrix times a k×n matrix. The isolation number of A is the maximum number of nonzero entries in A such that no two are in any row or any column, and no two are in a 2 × 2 submatrix of all nonzero entries. We have that the isolation number of A is a lower bound of the rank of …

Generalized Multiplicities Of Edge Ideals, Alie Alilooee, Ivan Soprunov, Javid Validashti

Mathematics and Statistics Faculty Publications

We explore connections between the generalized multiplicities of square-free monomial ideals and the combinatorial structure of the underlying hypergraphs using methods of commutative algebra and polyhedral geometry. For instance, we show that the j-multiplicity is multiplicative over the connected components of a hypergraph, and we explicitly relate the j-multiplicity of the edge ideal of a properly connected uniform hypergraph to the Hilbert–Samuel multiplicity of its special fiber ring. In addition, we provide general bounds for the generalized multiplicities of the edge ideals and compute these invariants for classes of uniform hypergraphs.

Jacobian Elliptic Kummer Surfaces And Special Function Identities, Elise Griffin, Andreas Malmendier

Mathematics and Statistics Faculty Publications

We derive formulas for the construction of all inequivalent Jacobian elliptic fibrations on the Kummer surface of two non-isogeneous elliptic curves from extremal rational elliptic surfaces by rational base transformations and quadratic twists. We then show that each such decomposition yields a description of the Picard-Fuchs system satisfied by the periods of the holomorphic two-form as either a tensor product of two Gauss' hypergeometric differential equations, an Appell hypergeometric system, or a GKZ differential system. As the answer must be independent of the fibration used, identities relating differential systems are obtained. They include a new identity relating Appell's hypergeometric system …

Genetic Variation Determines Which Feedbacks Drive And Alter Predator–Prey Eco-Evolutionary Cycles, Michael H. Cortez

Mathematics and Statistics Faculty Publications

Evolution can alter the ecological dynamics of communities, but the effects depend on the magnitudes of standing genetic variation in the evolving species. Using an eco‐coevolutionary predator–prey model, I identify how the magnitudes of prey and predator standing genetic variation determine when ecological, evolutionary, and eco‐evolutionary feedbacks influence system stability and the phase lags in predator–prey cycles. Here, feedbacks are defined by subsystems, i.e., the dynamics of a subset of the components of the whole system when the other components are held fixed; ecological (evolutionary) feedbacks involve the direct and indirect effects between population densities (species traits) and eco‐evolutionary feedbacks …

Second Order Fully Discrete Energy Stable Methods On Staggered Grids For Hydrodynamic Phase Field Models Of Binary Viscous Fluids, Yuezheng Gong, Jia Zhao, Qi Wang

Mathematics and Statistics Faculty Publications

We present second order, fully discrete, energy stable methods on spatially staggered grids for a hydrodynamic phase field model of binary viscous fluid mixtures in a confined geometry subject to both physical and periodic boundary conditions. We apply the energy quadratization strategy to develop a linear-implicit scheme. We then extend it to a decoupled, linear scheme by introducing an intermediate velocity term so that the phase variable, velocity field, and pressure can be solved sequentially. The two new, fully discrete linear schemes are then shown to be unconditionally energy stable, and the linear systems resulting from the schemes are proved …

Partitioning The Effects Of Eco-Evolutionary Feedbacks On Community Stability, Swati Patel, Michael H. Cortez, Sebastian J. Schreiber

Mathematics and Statistics Faculty Publications

A fundamental challenge in ecology continues to be identifying mechanisms that stabilize community dynamics. By altering the interactions within a community, eco-evolutionary feedbacks may play a role in community stability. Indeed, recent empirical and theoretical studies demonstrate that these feedbacks can stabilize or destabilize communities and, moreover, that this sometimes depends on the relative rate of ecological to evolutionary processes. So far, theory on how eco-evolutionary feedbacks impact stability exists only for a few special cases. In our work, we develop a general theory for determining the effects of eco-evolutionary feedbacks on stability in communities with an arbitrary number of …