Physical Sciences and Mathematics Commons^™

Expression Of Wnt-Signaling Pathway Genes And Their Associations With Mirnas In Colorectal Cancer, Martha L. Slattery, Lila E. Mullany, Lori C. Sakoda, Wade S. Samowitz, Roger K. Wolff, John R. Stevens, Jennifer S. Herrick

Mathematics and Statistics Faculty Publications

The Wnt-signaling pathway functions in regulating cell growth and thus is involved in the carcinogenic process of several cancers, including colorectal cancer. We tested the hypothesis that multiple genes in this signaling pathway are dysregulated and that miRNAs are associated with these dysregulated genes. We used data from 217 colorectal cancer (CRC) cases to evaluate differences in Wnt-signaling pathway gene expression between paired CRC and normal mucosa and identify miRNAs that are associated with these genes. Gene expression data from RNA-Seq and miRNA expression data from Agilent Human miRNA Microarray V19.0 were analyzed. We focused on genes most strongly associated …

A Universal Genus-Two Curve From Siegel Modular Forms, Andreas Malmendier, Tony Shaska

Mathematics and Statistics Faculty Publications

Let p be any point in the moduli space of genus-two curves M₂ and K its field of moduli. We provide a universal equation of a genus-two curve C_α,β defined over K(α, β), corresponding to p, where α and β satisfy a quadratic α² + bβ² = c such that b and c are given in terms of ratios of Siegel modular forms. The curve C_α,β is defined over the field of moduli K if and only if the quadratic has a K-rational point (α, β). We discover some interesting …

Stability Of Equilibria In Quantitative Genetic Models Based On Modified-Gradient Systems, Benjamin J. Ridenhour, Jerry R. Ridenhour

Mathematics and Statistics Faculty Publications

Motivated by questions in biology, we investigate the stability of equilibria of the dynamical system x′ = P(t)∇f(x) which arise as critical points of f, under the assumption that P(t) is positive semi-definite. It is shown that the condition ∫^∞λ₁(P(t)) dt = ∞, where λ₁(P(t)) is the smallest eigenvalue of P(t), plays a key role in guaranteeing uniform asymptotic stability and in providing information on the basis of attraction of those equilibria.

Biomarkers Of Cardiovascular Disease, Ying Huang, Kailash Gulshan, Truc Nguyen, Yuping Wu

Mathematics and Statistics Faculty Publications

No abstract provided.

Hybrid Extended Kalman Filtering And Noise Statistics Optimization For Produce Wash State Estimation, Vahid Azimi, Daniel Munther, Seyed Abolfazl Fakoorian, Thang Tien Nguyen, Daniel J. Simon

Mathematics and Statistics Faculty Publications

Food-borne diseases associated with fresh produce consistently cause serious public health issues. Although sanitization measures are utilized to enhance the safety of fresh produce, strategies that neglect the dynamic nature of commercial wash processes are limited, creating the potential for pathogen cross-contamination and major disease outbreaks. In light of this risk, there is an urgent need for new control approaches during produce washing to reduce the probability of outbreaks. As an important step in this direction, a hybrid extended Kalman filter (HEKF) and particle swarm optimization (PSO)-based noise statistics optimization are designed for a produce wash system. The HEKF uses …

A Bivariate Hypothesis Testing Approach For Mapping The Trait-Influential Gene, Garrett Saunders, Matthew D. Meng, John R. Stevens

Mathematics and Statistics Faculty Publications

The linkage disequilibrium (LD) based quantitative trait loci (QTL) model involves two indispensable hypothesis tests: the test of whether or not a QTL exists, and the test of the LD strength between the QTaL and the observed marker. The advantage of this two-test framework is to test whether there is an influential QTL around the observed marker instead of just having a QTL by random chance. There exist unsolved, open statistical questions about the inaccurate asymptotic distributions of the test statistics. We propose a bivariate null kernel (BNK) hypothesis testing method, which characterizes the joint distribution of the two test …

Minimal Noise-Induced Stabilization Of One-Dimensional Diffusions, Tony Allen, Emily Gebhardt, Adam Kluball, Tiffany N. Kolba

Mathematics and Statistics Faculty Publications

The phenomenon of noise-induced stabilization occurs when an unstable deterministic system of ordinary differential equations is stabilized by the addition of randomness into the system. In this paper, we investigate under what conditions one-dimensional, autonomous stochastic differential equations are stable, where we take the notion of stability to be that of global stochastic boundedness. Specifically, we find the minimum amount of noise necessary for noise-induced stabilization to occur when the drift and noise coefficients are power, polynomial, exponential, or logarithmic functions.

Physiological Health Parameters Among College Students To Promote Chronic Disease Prevention And Health Promotion, David R. Black, Daniel C. Coster, Samantha R. Paige

Mathematics and Statistics Faculty Publications

This study aimed to provide physiologic health risk parameters by gender and age among college students enrolled in a U.S. Midwestern University to promote chronic disease prevention and ameliorate health. A total of 2615 college students between 18 and 25 years old were recruited annually using a series of cross-sectional designs during the spring semester over an 8-year period. Physiologic parameters measured included body mass index (BMI), percentage body fat (%BF), blood serum cholesterol (BSC), and systolic (SBP) and diastolic (DBP) blood pressure. These measures were compared to data from NHANES to identify differences in physiologic parameters among 18-25 year …

Mri Analysis Of White Matter Myelin Water Content In Multiple Sclerosis: A Novel Approach Applied To Finding Correlates Of Cortical Thinning, Michael Dayan, Sandra M. Hurtado Rua, Elizabeth Monohan, Kyoko Fujimoto, Sneha Pandya, Eve M. Locastro, Tim Vartanian, Thanh D. Nguyen, Ashish Raj, Susan A. Gauthier

Mathematics and Statistics Faculty Publications

A novel lesion-mask free method based on a gamma mixture model was applied to myelin water fraction (MWF) maps to estimate the association between cortical thickness and myelin content, and how it differs between relapsing-remitting (RRMS) and secondary-progressive multiple sclerosis (SPMS) groups (135 and 23 patients, respectively). It was compared to an approach based on lesion masks. The gamma mixture distribution of whole brain, white matter (WM) MWF was characterized with three variables: the mode (most frequent value) m1 of the gamma component shown to relate to lesion, the mode m2 of the component shown to be associated with normal …

A Comparison Of Multiple Testing Adjustment Methods With Block-Correlation Positively-Dependent Tests, John R. Stevens, Abdullah Al Masud, Anvar Suyundikov

Mathematics and Statistics Faculty Publications

In high dimensional data analysis (such as gene expression, spatial epidemiology, or brain imaging studies), we often test thousands or more hypotheses simultaneously. As the number of tests increases, the chance of observing some statistically significant tests is very high even when all null hypotheses are true. Consequently, we could reach incorrect conclusions regarding the hypotheses. Researchers frequently use multiplicity adjustment methods to control type I error rates—primarily the family-wise error rate (FWER) or the false discovery rate (FDR)—while still desiring high statistical power. In practice, such studies may have dependent test statistics (or p-values) as tests can be dependent …

An Adaptive Threshold Determination Method Of Feature Screening For Genomic Selection, Matthew D. Meng, Gang Wang, Aaron R. Brough

Mathematics and Statistics Faculty Publications

Background
Although the dimension of the entire genome can be extremely large, only a parsimonious set of influential SNPs are correlated with a particular complex trait and are important to the prediction of the trait. Efficiently and accurately selecting these influential SNPs from millions of candidates is in high demand, but poses challenges. We propose a backward elimination iterative distance correlation (BE-IDC) procedure to select the smallest subset of SNPs that guarantees sufficient prediction accuracy, while also solving the unclear threshold issue for traditional feature screening approaches.

Results
Verified through six simulations, the adaptive threshold estimated by the BE-IDC performed …

Mass Action In Two-Sex Population Models: Encounters, Mating Encounters And The Associated Numerical Correction, Katherine Snyder, Brynja R. Kohler, Luis F. Gordillo

Mathematics and Statistics Faculty Publications

Ideal gas models are a paradigm used in Biology for the phenomenological modelling of encounters between individuals of different types. These models have been used to approximate encounter rates given densities, velocities and distance within which an encounter certainly occurs. When using mass action in two-sex populations, however, it is necessary to recognize the difference between encounters and mating encounters. While the former refers in general to the (possibly simultaneous) collisions between particles, the latter represents pair formation that will produce offspring. The classical formulation of the law of mass action does not account this difference. In this short paper, …

Criteria For Strict Monotonicity Of The Mixed Volume Of Convex Polytopes, Bihan Frederic, Ivan Soprunov

Mathematics and Statistics Faculty Publications

Let P₁,..., P_n and Q_1,...,Q_n be convex polytopes in Rⁿ such that P_i is a proper subset of Q_i . It is well-known that the mixed volume has the monotonicity property: V (P1,...,P_n) is less than or equal to V (Q_1,...,Q_n) . We give two criteria for when this inequality is strict in terms of essential collections of faces as well as mixed polyhedral subdivisions. This geometric result allows us to characterize sparse polynomial systems with Newton polytopes P₁,..., P_n whose number …

Analytic Approximation Of Invasion Wave Amplitude Predicts Severity Of Insect Outbreaks, Antje R. H. Graul, James A. Powell

Mathematics and Statistics Faculty Publications

Outbreaks of phytophagous forest insects are largely driven by host demographics and spatial effects of dispersal. We develop a structured integrodifference equation (IDE) outbreak model that tracks the demographics of sedentary hosts under insect infestation pressure. The model is appropriate for a spectrum of pests attacking the later age classes of long-lived hosts, including mountain pine beetle (MPB), spruce budworm, and spruce beetle, which, among them are responsible for more forest damage than fire. The model generates a train of periodic waves of infestation. We approximate the IDE with a partial differential equation and search for traveling wave solutions. The …

A Variant Of Clark's Theorem And Its Applications For Nonsmooth Functionals Without The Palais-Smale Condition, Shaowei Chen, Zhaoli Liu, Zhi-Qiang Wang

Mathematics and Statistics Faculty Publications

By introducing a new notion of the genus with respect to the weak topology in Banach spaces, we prove a variant of Clark's theorem for nonsmooth functionals without the Palais-Smale condition. In this new theorem, the Palais-Smale condition is replaced by a weaker assumption, and a sequence of critical points converging weakly to zero with nonpositive energy is obtained. As applications, we obtain infinitely many solutions for a quasi-linear elliptic equation which is very degenerate and lacks strict convexity, and we also prove the existence of infinitely many homoclinic orbits for a second-order Hamiltonian system for which the functional is …

Hereditary Properties Of Co-Kähler Manifolds, Giovanni Bazzoni, Gregory Lupton, John F. Oprea

Mathematics and Statistics Faculty Publications

We show how certain topological properties of co-Kähler manifolds derive from those of the Kähler manifolds which construct them. We go beyond Betti number results and describe the cohomology algebra structure of co-Kähler manifolds. As a consequence, we prove that co-Kähler manifolds satisfy the Toral Rank Conjecture: dim(H^∗(M; Q)) ≥2^r, for any r-torus T^r which acts almost freely on M.

Flexibility Of Projective-Planar Embeddings, John Maharry, Neil Robertson, Vaidy Sivaraman, Dan Slilaty

Mathematics and Statistics Faculty Publications

Given two embeddings σ1 and σ2 of a labeled nonplanar graph in the projective plane, we give a collection of maneuvers on projective-planar embeddings that can be used to take σ1 to σ2

Bounding And Stabilizing Realizations Of Biased Graphs With A Fixed Group, Nancy Ann Neudauer, Dan Slilaty

Mathematics and Statistics Faculty Publications

Given a group Γ and a biased graph (G, B), we define a what is meant by a Γ-realization of (G, B) and a notion of equivalence of Γ-realizations. We prove that for a finite group Γ and t ≥ 3, that there are numbers n(Γ) and n(Γ, t) such that the number of Γ-realizations of a vertically 3-connected biased graph is at most n(Γ) and that the number of Γ-realizations of a nonseparable biased graph without a (2Ct , ∅)-minor is at most n(Γ, t). Other results pertaining to contrabalanced biased graphs are presented as well as an analogue …

Predator-Prey Coevolution Drives Productivity-Richness Relationships In Planktonic Systems, Zhichao Pu, Michael H. Cortez, Lin Jiang

Mathematics and Statistics Faculty Publications

The relationship between environmental productivity and species richness often varies among empirical studies, and despite much research, simple explanations for this phenomenon remain elusive. We investigated how phytoplankton and zooplankton coevolution shapes productivity-richness relationships in both phytoplankton and zooplankton, using a simple nutrient-phytoplankton-zooplankton model that incorporates size-dependent metabolic rates summarized from empirical studies. The model allowed comparisons of evolved species richness across productivity levels and at different evolutionary times. Our results show that disruptive selection leads to evolutionary branching of phytoplankton and zooplankton. Both the time required for evolutionary branching and the number of evolved species in phytoplankton and zooplankton …

Use Of Sex-Specific Clinical And Exercise Risk Scores To Identify Patients At Increased Risk For All-Cause Mortality, Paul C. Cremer, Yuping Wu, Haitham M. Ahmed, Lee M. Pierson, Danielle M. Brennan, Mouaz H. Al-Mallah, Clinton A. Brawner, Jonathan K. Ehrman, Steven J. Keteyian, Roger S. Blumenthal, Michael J. Blaha, Leslie Cho

Mathematics and Statistics Faculty Publications

Importance Risk assessment tools for exercise treadmill testing may have limited external validity. Cardiovascular mortality has decreased in recent decades, and women have been underrepresented in prior cohorts.

Objectives To determine whether exercise and clinical variables are associated with differential mortality outcomes in men and women and to assess whether sex-specific risk scores better estimate all-cause mortality.

Design, Setting, and Participants This retrospective cohort study included 59 877 patients seen at the Cleveland Clinic Foundation (CCF cohort) from January 1, 2000, through December 31, 2010, and 49 278 patients seen at the Henry Ford Hospital (FIT cohort) from January 1, …