Physical Sciences and Mathematics Commons^™

The Constructions Of Almost Binary Sequence Pairs And Binary Sequence Pairs With Three-Level Autocorrelation, Xiuping Peng, Chengqian Xu, Guang Li, Krishnasamy T. Arasu

Mathematics and Statistics Faculty Publications

In this letter, a new class of almost binary sequence pairs with a single zero element and three autocorrelation values is presented. The new almost binary sequence pairs are based on cyclic difference sets and difference set pairs. By applying the method to the binary sequence pairs, new binary sequence pairs with three-level autocorrelation are constructed. It is shown that new sequence pairs from our constructions are balanced or almost balanced and have optimal three-level autocorrelation when the characteristic sequences or sequence pairs of difference sets or difference set pairs are balanced or almost balanced and have optimal autocorrelations.

Viscosity Of Bacterial Suspensions: Hydrodynamic Interactions And Self-Induced Noise, Shawn D. Ryan, Brian M. Haines, Leonid Berlyand, Falko Ziebert, Igor S. Aranson

Mathematics and Statistics Faculty Publications

The viscosity of a suspension of swimming bacteria is investigated analytically and numerically. We propose a simple model that allows for efficient computation for a large number of bacteria. Our calculations show that long-range hydrodynamic interactions, intrinsic to self-locomoting objects in a viscous fluid, result in a dramatic reduction of the effective viscosity. In agreement with experiments on suspensions of Bacillus subtilis, we show that the viscosity reduction is related to the onset of large-scale collective motion due to interactions between the swimmers. The simulations reveal that the viscosity reduction occurs only for relatively low concentrations of swimmers: Further …

Multiple Solutions For An Elliptic Problem Related To Vortex Pairs, Yi Li, Shuangjie Peng

Mathematics and Statistics Faculty Publications

Let Ω be a bounded domain in RN (N⩾2), φ a harmonic function in Ω¯. In this paper we study the existence of solutions to the following problem arising in the study of vortex pairs(Pλ){−Δu=λ(u−φ)+p−1,x∈Ω,u=0,x∈∂Ω. The set Ωp={x∈Ω,u(x)>φ} is called “vortex core”. Existence of solutions whose “vortex core” consists of one component and asymptotic behavior of “vortex core” were studied by many authors for large λ recently. Under the condition that φ has k strictly local minimum points on the boundary ∂Ω, we obtain in this paper that for λ large enough, (Pλ) has a solution with “vortex core” …

Gut Flora Metabolism Of Phosphatidylcholine Promotes Cardiovascular Disease, Zeneng Wang, Elizabeth Klipfell, Brian J. Bennett, Robert Koeth, Bruce S. Levison, Brandon Dugar, Ariel E. Feldstein, Earl B. Britt, Xiaoming Fu, Yoo Mi Chung, Yuping Wu, Phil Schauer, Jonathan D. Smith, Hooman Allayee, W.H. Wilson Tang, Joseph A. Didonato, Aldons J. Lusis, Stanley L. Hazen

Mathematics and Statistics Faculty Publications

Metabolomics studies hold promise for the discovery of pathways linked to disease processes. Cardiovascular disease (CVD) represents the leading cause of death and morbidity worldwide. Here we used a metabolomics approach to generate unbiased small-molecule metabolic profiles in plasma that predict risk for CVD. Three metabolites of the dietary lipid phosphatidylcholine—choline, trimethylamine N-oxide (TMAO) and betaine—were identified and then shown to predict risk for CVD in an independent large clinical cohort. Dietary supplementation of mice with choline, TMAO or betaine promoted upregulation of multiple macrophage scavenger receptors linked to atherosclerosis, and supplementation with choline or TMAO promoted atherosclerosis. Studies using …

Quantitative Interpretation Of A Genetic Model Of Carcinogenesis Using Computer Simulations, Donghai Dai, Brandon Beck, Xiaofang Wang, Cory Howk, Yi Li

Mathematics and Statistics Faculty Publications

The genetic model of tumorigenesis by Vogelstein et al. (V theory) and the molecular definition of cancer hallmarks by Hanahan and Weinberg (W theory) represent two of the most comprehensive and systemic understandings of cancer. Here, we develop a mathematical model that quantitatively interprets these seminal cancer theories, starting from a set of equations describing the short life cycle of an individual cell in uterine epithelium during tissue regeneration. The process of malignant transformation of an individual cell is followed and the tissue (or tumor) is described as a composite of individual cells in order to quantitatively account for intra-tumor …

Projective-Planar Graphs With No K3,4-Minor, John Maharry, Dan Slilaty

Mathematics and Statistics Faculty Publications

An exact structure is described to classify the projective‐planar graphs that do not contain a K3, 4‐minor.

Rank 2 Distributions Of Monge Equations: Symmetries, Equivalences, Ex-Tensions, Ian M. Anderson, B. Kruglikov

Mathematics and Statistics Faculty Publications

By developing the Tanaka theory for rank 2 distributions, we completely classify classical Monge equations having maximal finite-dimensional symmetry algebras with fixed (albeit arbitrary) pair of its orders. Investigation of the corresponding Tanaka algebras leads to a new Lie-Backlund theorem. We prove that all flat Monge equations are successive integrable extensions of the Hilbert-Cartan equation. Many new examples are provided.

Additive And Multiplicative Hazards Modeling For Recurrent Event Data Analysis, Hyun J. Lim, Xu Zhang

Mathematics and Statistics Faculty Publications

Background: Sequentially ordered multivariate failure time or recurrent event duration data are commonly observed in biomedical longitudinal studies. In general, standard hazard regression methods cannot be applied because of correlation between recurrent failure times within a subject and induced dependent censoring. Multiplicative and additive hazards models provide the two principal frameworks for studying the association between risk factors and recurrent event durations for the analysis of multivariate failure time data.

Methods: Using emergency department visits data, we illustrated and compared the additive and multiplicative hazards models for analysis of recurrent event durations under (i) a varying baseline with a common …

Discrete-Time Recurrent Neural Network And Its Application To Compression Of Infra-Red Spectrum, Leong-Kwan Li, Sally S. L. Shao

Mathematics and Statistics Faculty Publications

We study the discrete-time recurrent neural network that derived from the Leaky-integrator model and its application to compression of infra-red spec- trum. Our results show that the discrete-time Leaky-integrator recurrent neural network (RNN) model can be used to approximate the continuous-time model and inherit its dynamical characters if a proper step size is chosen. Moreover, the discrete-time Leaky-integrator RNN model is absolutely stable. By developing the double discrete integral method and employing the state space search algorithm for the discrete-time recurrent neural network model, we demonstrate with quality spectra regenerated from the compressed data how to compress the infra-red spectrum …

Plasma Myeloperoxidase Predicts Incident Cardiovascular Risks In Stable Patients Undergoing Medical Management For Coronary Artery Disease, W.H. Wilson Tang, Yuping Wu, Stephen J. Nicholls, Stanley L. Hazen

Mathematics and Statistics Faculty Publications

BACKGROUND: Myeloperoxidase (MPO) concentrations predict adverse clinical outcomes in the setting of acute coronary syndromes and heart failure, but the prognostic role of MPO in stable patients with known atherosclerotic burden is unclear. METHODS: We examined plasma MPO concentrations and their relationship with prevalent significant coronary artery disease (defined as >50% stenosis in any coronary vessel) and incident major adverse cardiovascular events (MACEs), including death, myocardial infarction, and stroke, in a 3-year prospective follow-up study of 1895 patients undergoing elective coronary angiography. RESULTS: The median plasma MPO concentration was 101 pmol/L (interquartile range 68–187 pmol/L). Patients with plasma MPO concentrations …

Diminished Antioxidant Activity Of High-Density Lipoprotein–Associated Proteins In Systolic Heart Failure, W.H. Wilson Tang, Yuping Wu, Shirley Mann, Michael Pepoy, Kevin Shrestha, Allen G. Borowski, Stanley L. Hazen

Mathematics and Statistics Faculty Publications

Background— Diminished serum arylesterase activity, catalyzed by the high-density lipoprotein–associated paraoxonase-1, is associated with heightened systemic oxidative stress and atherosclerosis risk. In the present study, we sought to determine the prognostic role of serum arylesterase activity in subjects with systolic heart failure, particularly in relation to established cardiac biomarkers. Methods and Results— We measured serum arylesterase activity in 760 subjects with impaired left ventricular systolic function (left ventricular ejection fraction <50%), and prospectively followed major adverse cardiac events (including death, nonfatal myocardial infarction, and stroke) for 3 years. In our study cohort (mean age, 64±11 years; 74% men; median left ventricular ejection fraction, 35%; median creatinine clearance, 96 mg/dL), mean serum arylesterase activity (98±25 μmol/L/min/mL) was lower compared with that in healthy control subjects (mean, 115±26 μmol/L/min/mL, P<0.01) but higher compared with advanced decompensated heart failure subjects (mean, 69±22 μmol/L/min/mL, P<0.01). Within our cohort, there was modest correlation between serum arylesterase activity and high-density lipoprotein cholesterol (r=0.33, P<0.01) as well as B-type natriuretic peptide (r=−0.23, P<0.01). Lower serum arylesterase activity was a strong predictor of poorer outcomes (hazard ratio, 2.94; 95% confidence interval, 1.54, 5.62; P<0.001). After adjusting for traditional risk factors, medication use, B-type natriuretic peptide, and creatinine clearance, lower serum arylesterase still conferred an increased risk of major adverse cardiac events at 3 years (hazard ratio, 2.69; 95% confidence interval, 1.37 to 5.28; P=0.004). Conclusions— In patients with systolic heart failure, decreased serum arylesterase activity, a measure of diminished antioxidant properties of high-density lipoprotein, predicts higher risk of incident long-term adverse cardiac event independent of established clinical and biochemical risk factors.