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Articles 1 - 30 of 37
Full-Text Articles in Mathematics
Diet And Lifetyle Factors Associated With Mirna Expression In Colorectal Tissue, Martha L. Slattery, Jennifer S. Herrick, Lila E. Mullany, John R. Stevens, Roger K. Wolff
Diet And Lifetyle Factors Associated With Mirna Expression In Colorectal Tissue, Martha L. Slattery, Jennifer S. Herrick, Lila E. Mullany, John R. Stevens, Roger K. Wolff
Mathematics and Statistics Faculty Publications
MicroRNAs (miRNAs) are small non-protein-coding RNA molecules that regulate gene expression. Diet and lifestyle factors have been hypothesized to be involved in the regulation of miRNA expression. In this study it was hypothesized that diet and lifestyle factors are associated with miRNA expression. Data from 1,447 cases of colorectal cancer to evaluate 34 diet and lifestyle variables using miRNA expression in normal colorectal mucosa as well as for differential expression between paired carcinoma and normal tissue were used. miRNA data were obtained using an Agilent platform. Multiple comparisons were adjusted for using the false discovery rate q-value. There were 250 …
Projective-Planar Graphs With No K3,4-Minor. Ii., John Maharry, Dan Slilaty
Projective-Planar Graphs With No K3,4-Minor. Ii., John Maharry, Dan Slilaty
Mathematics and Statistics Faculty Publications
The authors previously published an iterative process to generate a class of projectiveplanar K3,4-free graphs called ‘patch graphs’. They also showed that any simple, almost 4-connected, nonplanar, and projective-planar graph that is K3,4-free is a subgraph of a patch graph. In this paper, we describe a simpler and more natural class of cubic K3,4- free projective-planar graphs which we call M¨obius hyperladders. Furthermore, every simple, almost 4-connected, nonplanar, and projective-planar graph that is K3,4-free is a minor of a M¨obius hyperladder. As applications of these structures we determine the page number of patch graphs and of M¨obius hyperladders.
Managing The Spread Of Alfalfa Stem Nematodes (Ditylenchus Dipsaci): The Relationship Between Crop Rotation Periods And Pest Re-Emergence, S. Jordan, Claudia Nischwitz, R. Ramirez, Luis F. Gordillo
Managing The Spread Of Alfalfa Stem Nematodes (Ditylenchus Dipsaci): The Relationship Between Crop Rotation Periods And Pest Re-Emergence, S. Jordan, Claudia Nischwitz, R. Ramirez, Luis F. Gordillo
Mathematics and Statistics Faculty Publications
Alfalfa is a critical cash/rotation crop in the western region of the United States, where it is common to find crops affected by the alfalfa stem nematode (Ditylenchus dipsaci). Understanding the spread dynamics associated with this pest would allow growers to design better management programs and farming practices. This understanding is of particular importance given that there are no nematicides available against alfalfa stem nematodes and control strategies largely rely on crop rotation to non-host crops or by planting resistant varieties of alfalfa. In this paper we present a basic host-parasite model that describes the spread of the …
Bezout Inequality For Mixed Volumes, Ivan Soprunov, Artem Zvavitch
Bezout Inequality For Mixed Volumes, Ivan Soprunov, Artem Zvavitch
Mathematics and Statistics Faculty Publications
In this paper we consider the following analog of Bezout inequality for mixed volumes: V(P1,…,Pr,Δn−r)Vn(Δ)r−1≤∏i=1rV(Pi,Δn−1) for 2≤r≤n. We show that the above inequality is true when Δ is an n-dimensional simplex and P1,…,Pr are convex bodies in Rn. We conjecture that if the above inequality is true for all convex bodies P1,…,Pr, then Δ must be an n-dimensional simplex. We prove that if the above inequality is true for all convex bodies P1,…,Pr, then Δ must be indecomposable (i.e. cannot be written as the Minkowski sum of two convex bodies which are not homothetic to Δ), which confirms the conjecture …
Random Walks In A Sparse Random Environment, Anastasios Matzavinos, Alexander Roitershtein, Youngsoo Seol
Random Walks In A Sparse Random Environment, Anastasios Matzavinos, Alexander Roitershtein, Youngsoo Seol
Mathematics and Statistics Faculty Publications
We introduce random walks in a sparse random environment on ℤ and investigate basic asymptotic properties of this model, such as recurrence-transience, asymptotic speed, and limit theorems in both the transient and recurrent regimes. The new model combines features of several existing models of random motion in random media and admits a transparent physical interpretation. More specifically, a random walk in a sparse random environment can be characterized as a “locally strong” perturbation of a simple random walk by a random potential induced by “rare impurities,” which are randomly distributed over the integer lattice. Interestingly, in the critical (recurrent) regime, …
Eventual Quasi-Linearity Of The Minkowski Length, Ivan Soprunov, Jenya Soprunova
Eventual Quasi-Linearity Of The Minkowski Length, Ivan Soprunov, Jenya Soprunova
Mathematics and Statistics Faculty Publications
The Minkowski length of a lattice polytope PP is a natural generalization of the lattice diameter of PP. It can be defined as the largest number of lattice segments whose Minkowski sum is contained in PP. The famous Ehrhart theorem states that the number of lattice points in the positive integer dilates tPtP of a lattice polytope PP behaves polynomially in t∈Nt∈N. In this paper we prove that for any lattice polytope PP, the Minkowski length of tPtP for t∈Nt∈N is eventually a quasi-polynomial with linear constituents. We also give a formula for the Minkowski length of coordinates boxes, degree …
Trimethylamine N-Oxide And Mortality Risk In Patients With Peripheral Artery Disease, Vichai Senthong, Zeneng Wang, Yiying Fan, Yuping Wu, Stanley L. Hazen, W.H. Wilson Tang
Trimethylamine N-Oxide And Mortality Risk In Patients With Peripheral Artery Disease, Vichai Senthong, Zeneng Wang, Yiying Fan, Yuping Wu, Stanley L. Hazen, W.H. Wilson Tang
Mathematics and Statistics Faculty Publications
Background: Production of the proatherogenic metabolite, trimethylamine N-oxide (TMAO), from dietary nutrients by intestinal microbiota enhances atherosclerosis development in animal models and is associated with atherosclerotic coronary artery disease in humans. The utility of studying plasma levels of TMAO to risk stratify in patients with peripheral artery disease (PAD) has not been reported. Methods and Results: We examined the relationship between fasting plasma TMAO and all-cause mortality (5-year), stratified by subtypes of PAD and presence of coronary artery disease in 935 patients with PAD who underwent elective angiography for cardiac evaluation at a tertiary care hospital. Median plasma TMAO was …
On The Geometry Of The Rotating Liquid Drop, Ivailo M. Mladenov, John Oprea
On The Geometry Of The Rotating Liquid Drop, Ivailo M. Mladenov, John Oprea
Mathematics and Statistics Faculty Publications
Here we consider the problem of a fluid body rotating with a constant angular velocity and subjected to surface tension. Determining the equilibrium configuration of this system turns out to be equivalent to the geometrical problem of determining the surface of revolution with a prescribed mean curvature. In the simply connected case, the equilibrium surface can be parameterized explicitly via elliptic integrals of the first and second kind. Here, we present two such parameterizations of the drops and we use the second of them to study finer details of the drop surfaces such as the existence of closed geodesics.
Modeling Zombie Outbreaks: A Problem-Based Approach To Improving Mathematics One Brain At A Time, Matthew Lewis, James A. Powell
Modeling Zombie Outbreaks: A Problem-Based Approach To Improving Mathematics One Brain At A Time, Matthew Lewis, James A. Powell
Mathematics and Statistics Faculty Publications
A great deal of educational literature has focused on problem-based learning (PBL) in mathematics at the primary and secondary level, but arguably there is an even greater need for PBL in college math courses. We present a project centered around the Humans vs. Zombies moderated tag game played on the USU campus. We discuss the project in the context of an undergraduate differential equations course and discuss how the project is launched. We highlight examples of students mathematical models along with their verbal and written responses as well as discussing assessment and student learning. Results are discussed in the context …
Realizing Spaces As Classifying Spaces, Gregory Lupton, Samuel Bruce Smith
Realizing Spaces As Classifying Spaces, Gregory Lupton, Samuel Bruce Smith
Mathematics and Statistics Faculty Publications
Which spaces occur as a classifying space for fibrations with a given fibre? We address this question in the context of rational homotopy theory. We construct an infinite family of finite complexes realized (up to rational homotopy) as classifying spaces. We also give several non-realization results, including the following: the rational homotopy types of and are not realized as the classifying space of any simply connected, rational space with finite-dimensional homotopy groups.
Anomalous Fluctuations In The Orientation And Velocity Of Swarming Bacteria, Shawn D. Ryan, Gil Ariel, Avraham Be’Er
Anomalous Fluctuations In The Orientation And Velocity Of Swarming Bacteria, Shawn D. Ryan, Gil Ariel, Avraham Be’Er
Mathematics and Statistics Faculty Publications
Simultaneous acquisition of phase-contrast light microscopy and fluorescently labeled bacteria, moving within a dense swarm, reveals the intricate interactions between cells and the collective flow around them. By comparing wild-type and immotile cells embedded in a dense wild-type swarm, the effect of the active thrust generated by the flagella can be singled out. It is shown that while the distribution of angles among cell velocity, cell orientation, and the local flow around it is Gaussian-like for immotile bacteria, wild-type cells exhibit anomalous non-Gaussian deviations and are able to move in trajectories perpendicular to the collective flow. Thus, cells can maneuver …
How The Magnitude Of Prey Genetic Variation Alters Predator-Prey Eco-Evolutionary Dynamics, Michael H. Cortez
How The Magnitude Of Prey Genetic Variation Alters Predator-Prey Eco-Evolutionary Dynamics, Michael H. Cortez
Mathematics and Statistics Faculty Publications
Evolution can alter the stability and dynamics of ecological communities; for example, prey evolution can drive cyclic dynamics in predator-prey systems that are not possible in the absence of evolution. However, it is unclear how the magnitude of additive genetic variation in the evolving species mediates those effects. In this study, I explore how the magnitude of prey additive genetic variation determines what effects prey evolution has on the dynamics and stability of predator-prey systems. I use linear stability analysis to decompose the stability of a general eco-evolutionary predator-prey model into components representing the stabilities of the ecological and evolutionary …
Intestinal Microbiota-Generated Metabolite Trimethylamine-N-Oxide And 5-Year Mortality Risk In Stable Coronary Artery Disease: The Contributory Role Of Intestinal Microbiota In A Courage-Like Patient Cohort, Vichai Senthong, Zeneng Wang, Xinmin S. Li, Yiying Fan, Yuping Wu, W. H. Wilson Tang, Stanley L. Hazen
Intestinal Microbiota-Generated Metabolite Trimethylamine-N-Oxide And 5-Year Mortality Risk In Stable Coronary Artery Disease: The Contributory Role Of Intestinal Microbiota In A Courage-Like Patient Cohort, Vichai Senthong, Zeneng Wang, Xinmin S. Li, Yiying Fan, Yuping Wu, W. H. Wilson Tang, Stanley L. Hazen
Mathematics and Statistics Faculty Publications
Background: Trimethylamine-N-oxide (TMAO), a metabolite derived from gut microbes and dietary phosphatidylcholine, is linked to both coronary artery disease pathogenesis and increased cardiovascular risks. The ability of plasma TMAO to predict 5-year mortality risk in patients with stable coronary artery disease has not been reported. This study examined the clinical prognostic value of TMAO in patients with stable coronary artery disease who met eligibility criteria for a patient cohort similar to that of the Clinical Outcomes Utilizing Revascularization and Aggressive Drug Evaluation (COURAGE) trial. Methods and Results: We examined the relationship between fasting plasma TMAO and all-cause mortality over 5-year …
Characterization Of Simplices Via The Bezout Inequality For Mixed Volumes, Christos Saroglou, Ivan Soprunov, Arten Zvavitch
Characterization Of Simplices Via The Bezout Inequality For Mixed Volumes, Christos Saroglou, Ivan Soprunov, Arten Zvavitch
Mathematics and Statistics Faculty Publications
We consider the following Bezout inequality for mixed volumes: V (K1, . . . ,Kr, Δ[n − r])Vn(Δ)r−1 ≤ r i=1 V (Ki, Δ[n − 1]) for 2 ≤ r ≤ n. It was shown previously that the inequality is true for any -dimensional simplex and any convex bodies in . It was conjectured that simplices are the only convex bodies for which the inequality holds for arbitrary bodies in . In this paper we prove that this is indeed the case if we assume that is a convex polytope. Thus the Bezout inequality characterizes simplices in the class of …
Plasma Trimethylamine N-Oxide, A Gut Microbe–Generated Phosphatidylcholine Metabolite, Is Associated With Atherosclerotic Burden, Vichai Senthong, Xinmin S. Li, Timothy Hudec, John Coughlin, Yuping Wu, Bruce Levison, Zeneng Wang, Stanley L. Hazen, W.H. Wilson Tang
Plasma Trimethylamine N-Oxide, A Gut Microbe–Generated Phosphatidylcholine Metabolite, Is Associated With Atherosclerotic Burden, Vichai Senthong, Xinmin S. Li, Timothy Hudec, John Coughlin, Yuping Wu, Bruce Levison, Zeneng Wang, Stanley L. Hazen, W.H. Wilson Tang
Mathematics and Statistics Faculty Publications
Background: Trimethylamine N-oxide (TMAO), a gut microbiota metabolite from dietary phosphatidylcholine, has mechanistic links to atherosclerotic coronary artery disease (CAD) pathogenesis and is associated with adverse outcomes. Objectives: This study sought to examine the relationship between plasma TMAO levels and the complexity and burden of CAD and degree of subclinical myonecrosis. Methods: We studied 353 consecutive stable patients with evidence of atherosclerotic CAD detected by elective coronary angiography between 2012 and 2014. Their high-sensitivity cardiac troponin T (hs-cTnT) levels were measured. SYNTAX (Synergy Between Percutaneous Coronary Intervention With Taxus and Cardiac Surgery) scores and lesion characteristics were used to quantify …
A Proof Of Concept Study Of Function-Based Statistical Analysis Of Fnirs Data: Syntax Comprehension In Children With Specific Language Impairment Compared To Typically-Developing Controls, Matthew D. Meng, Nicholas J. Wan, Joseph M. Baker, James Montgomery, Julia L. Evans, Ronald Gillam
A Proof Of Concept Study Of Function-Based Statistical Analysis Of Fnirs Data: Syntax Comprehension In Children With Specific Language Impairment Compared To Typically-Developing Controls, Matthew D. Meng, Nicholas J. Wan, Joseph M. Baker, James Montgomery, Julia L. Evans, Ronald Gillam
Mathematics and Statistics Faculty Publications
Functional near infrared spectroscopy (fNIRS) is a neuroimaging techonology that enables investigators to indirectly monitor brain activity in vivo through relative changes in the concentration of oxygenated and deoxygenated hemoglobin. One of the key features of fNIRS is its superior temporal resolution, with dense measurements over very short periods of time (100ms increments). Unfortunately, most statistical analysis approaches in the existing literature have not fully utilized the high temporal resolution of fNIRS. For example, many analysis procedures are based on linearity assumptions that only extract partial information, thereby neglecting the overall dynamic trends in fNIRS trajectories. The main goal of …
Hydra Effects In Stable Communities And Their Implications For System Dynamics, Michael H. Cortez, Peter A. Abrams
Hydra Effects In Stable Communities And Their Implications For System Dynamics, Michael H. Cortez, Peter A. Abrams
Mathematics and Statistics Faculty Publications
A hydra effect occurs when the mean density of a species increases in response to greater mortality. We show that, in a stable multispecies system, a species exhibits a hydra effect only if maintaining that species at its equilibrium density destabilizes the system. The stability of the original system is due to the responses of the hydra-effect species to changes in the other species’ densities. If that dynamical feedback is removed by fixing the density of the hydra-effect species, large changes in the community make-up (including the possibility of species extinction) can occur. This general result has several implications: (1) …
A Model For Collective Dynamics In Ant Raids, Shawn D. Ryan
A Model For Collective Dynamics In Ant Raids, Shawn D. Ryan
Mathematics and Statistics Faculty Publications
Ant raiding, the process of identifying and returning food to the nest or bivouac, is a fascinating example of collective motion in nature. During such raids ants lay pheromones to form trails for others to find a food source. In this work a coupled PDE/ODE model is introduced to study ant dynamics and pheromone concentration. The key idea is the introduction of two forms of ant dynamics: foraging and returning, each governed by different environmental and social cues. The model accounts for all aspects of the raiding cycle including local collisional interactions, the laying of pheromone along a trail, and …
Usefulness Of Relative Hypochromia In Risk Stratification For Nonanemic Patients With Chronic Heart Failure, Muhammad Hammadah, Marie Luise Brennan, Yuping Wu, Stanley L. Hazen, W.H. Wilson Tang
Usefulness Of Relative Hypochromia In Risk Stratification For Nonanemic Patients With Chronic Heart Failure, Muhammad Hammadah, Marie Luise Brennan, Yuping Wu, Stanley L. Hazen, W.H. Wilson Tang
Mathematics and Statistics Faculty Publications
The purpose of this study is to investigate the impact of a reduction of hemoglobin (Hb) content in the erythrocytes as estimated by mean corpuscular hemoglobin concentration (MCHC) on long-term clinical outcomes in nonanemic patients with heart failure (HF). We prospectively enrolled 1,579 subjects with HF who underwent coronary angiography enrolled in the GeneBank study with 5-year follow-up of all-cause mortality. Levels of Hb and MCHC were assessed at enrollment and after 6 months of follow-up. Anemia was defined as Hb levels <13 g/dl in men and <12 g/dl in women. In our nonanemic cohort (n = 785, 49.7%), mean Hb and median MCHC were 13.8 ± 1.1 g/dl and 34.3 g/dL (interquartile range 33.6 to 35), respectively. Nonanemic patients with heart failure with lower MCHC had higher mortality risk (quartiles 1 vs 4, hazard ratio = 2.1, 95% confidence interval 1.4 to 3.3, p = 0.001). In a subset of nonanemic patients with persistent normal Hb on follow-up (n = 206), the mean time between baseline and follow-up MCHC levels was 169.3 ± 41.6 days. In comparison with patients with levels of MCHC more than the first quartile (≥33.6 g/dl) on baseline and follow-up, patients with persistently low MCHC (<33.6 g/dl) had a significantly increased mortality risk (log rank <0.001). All models remained significant even after adjusting for traditional cardiac risk factors, left ventricular ejection fraction, baseline Hb levels, and mean corpuscular volume. In conclusion, relative hypochromia is an independent predictor of increased mortality risk in patients with HF, even in the setting of normal Hb levels.
Yeast For Mathematicians - A Ferment Of Discovery, Matthew Lewis, James A. Powell
Yeast For Mathematicians - A Ferment Of Discovery, Matthew Lewis, James A. Powell
Mathematics and Statistics Faculty Publications
In addition to the memorization, algorithmic skills and vocabulary which are the default focus in many mathematics classrooms, professional mathematicians are expected to creatively apply known techniques, construct new mathematical approaches and communicate with and about mathematics. We propose that students can learn these professional, higher-level skills through Laboratory Experiences in Mathematical Biology which put students in the role of mathematics researcher creating mathematics to describe and understand biological data. Here we introduce a laboratory experience centered on yeast (Saccharomyces cerevisiae) growing in a small capped flask with a jar to collect carbon dioxide created during yeast growth …
Quandle Coloring And Cocycle Invariants Of Composite Knots And Abelian Extensions, W Edwin Clark, Masahico Saito, Leandro Vendramin
Quandle Coloring And Cocycle Invariants Of Composite Knots And Abelian Extensions, W Edwin Clark, Masahico Saito, Leandro Vendramin
Mathematics and Statistics Faculty Publications
Quandle colorings and cocycle invariants are studied for composite knots, and applied to chirality and abelian extensions. The square and granny knots, for example, can be distinguished by quandle colorings, so that a trefoil and its mirror can be distinguished by quandle coloring of composite knots. We investigate this and related phenomena. Quandle cocycle invariants are studied in relation to quandle coloring of the connected sum, and formulas are given for computing the cocycle invariant from the number of colorings of composite knots. Relations to corresponding abelian extensions of quandles are studied, and extensions are examined for the table of …
Gut Microbial Metabolite Tmao Enhances Platelet Hyperreactivity And Thrombosis Risk, Weifei Zhu, Jill C. Gregory, Elin Org, Jennifer A. Buffa, Nilaksh Gupta, Zeneng Wang, Lin Li, Xiaoming Fu, Yuping Wu, Margarete Mehrabian, R. Balfour Sartor, Thomas M. Mcintyre, Roy L. Silverstein, W.H. Wilson Tang, Joseph A. Didonato, J. Mark Brown, Aldons J. Lusis, Stanley L. Hazen
Gut Microbial Metabolite Tmao Enhances Platelet Hyperreactivity And Thrombosis Risk, Weifei Zhu, Jill C. Gregory, Elin Org, Jennifer A. Buffa, Nilaksh Gupta, Zeneng Wang, Lin Li, Xiaoming Fu, Yuping Wu, Margarete Mehrabian, R. Balfour Sartor, Thomas M. Mcintyre, Roy L. Silverstein, W.H. Wilson Tang, Joseph A. Didonato, J. Mark Brown, Aldons J. Lusis, Stanley L. Hazen
Mathematics and Statistics Faculty Publications
Normal platelet function is critical to blood hemostasis and maintenance of a closed circulatory system. Heightened platelet reactivity, however, is associated with cardiometabolic diseases and enhanced potential for thrombotic events. We now show gut microbes, through generation of trimethylamine N-oxide (TMAO), directly contribute to platelet hyperreactivity and enhanced thrombosis potential. Plasma TMAO levels in subjects (n > 4,000) independently predicted incident (3 years) thrombosis (heart attack, stroke) risk. Direct exposure of platelets to TMAO enhanced sub-maximal stimulus-dependent platelet activation from multiple agonists through augmented Ca2+ release from intracellular stores. Animal model studies employing dietary choline or TMAO, germ-free mice, and microbial …
Expression Profiles Of Mirna Subsets Distinguish Human Colorectal Carcinoma And Normal Colonic Mucosa, Daniel F. Pellatt, John R. Stevens, Roger K. Wolff, Lila E. Mullany, Jennifer S. Herrick, Wade Samowitz, Martha L. Slattery
Expression Profiles Of Mirna Subsets Distinguish Human Colorectal Carcinoma And Normal Colonic Mucosa, Daniel F. Pellatt, John R. Stevens, Roger K. Wolff, Lila E. Mullany, Jennifer S. Herrick, Wade Samowitz, Martha L. Slattery
Mathematics and Statistics Faculty Publications
OBJECTIVES: MicroRNAs (miRNAs) are small, non-protein-coding RNA molecules that are commonly dysregulated in colorectal tumors. The objective of this study was to identify smaller subsets of highly predictive miRNAs.
METHODS: Data come from population-based studies of colorectal cancer conducted in Utah and the Kaiser Permanente Medical Care Program. Tissue samples were available for 1,953 individuals, of which 1,894 had carcinoma tissue and 1,599 had normal mucosa available for statistical analysis. Agilent Human miRNA Microarray V.19.0 was used to generate miRNA expression profiles; validation of expression levels was carried out using quantitative PCR. We used random forest analysis and verified findings …
Increased Mortality With Elevated Plasma Endothelin-1 In Acute Heart Failure: An Ascend-Hf Biomarker Substudy, Antonio L. Perez, Justin L. Grodin, Yuping Wu, Adrian F. Hernandez, Javed Butler, Marco Metra, Michael G. Felker, Adriaan A. Voors, John J. Mcmurray, Paul W. Armstrong, Randall C. Starling, Christopher M. O'Connor, W. H. Wilson Tang
Increased Mortality With Elevated Plasma Endothelin-1 In Acute Heart Failure: An Ascend-Hf Biomarker Substudy, Antonio L. Perez, Justin L. Grodin, Yuping Wu, Adrian F. Hernandez, Javed Butler, Marco Metra, Michael G. Felker, Adriaan A. Voors, John J. Mcmurray, Paul W. Armstrong, Randall C. Starling, Christopher M. O'Connor, W. H. Wilson Tang
Mathematics and Statistics Faculty Publications
Aims: Endothelin-1 (ET-1) is an endogenous vasoconstrictor implicated in pulmonary and systemic hypertension, as well as ventricular dysfunction, through effects on vascular smooth muscle, the kidneys, and cardiomyocytes. We aimed to determine the association between serial ET-1 levels and acute heart failure patient outcomes. Methods and results: We measured plasma ET-1 at baseline, 48–72 h, and 30 days in a cohort of 872 patients hospitalized with acute heart failure from the ASCEND-HF trial (randomized to nesiritide vs. placebo), and its association with 30-day mortality, 180-day mortality, in-hospital death or worsening heart failure, and 30-day mortality or rehospitalization. Median ET-1 was …
A Remark On The Global Dynamics Of Competitive Systems On Ordered Banach Spaces, King Yeung Lam, Daniel Munther
A Remark On The Global Dynamics Of Competitive Systems On Ordered Banach Spaces, King Yeung Lam, Daniel Munther
Mathematics and Statistics Faculty Publications
A well-known result in [Hsu-Smith-Waltman, Trans. Amer. Math. Soc. (1996)] states that in a competitive semiflow defined on , the product of two cones in respective Banach spaces, if and are the global attractors in and respectively, then one of the following three outcomes is possible for the two competitors: either there is at least one coexistence steady state, or one of attracts all trajectories initiating in the order interval . However, it was demonstrated by an example that in some cases neither nor is globally asymptotically stable if we broaden our scope to all of . In this paper, …
Effective Rheological Properties In Semi-Dilute Bacterial Suspensions, Mykhailo Potomkin, Shawn D. Ryan, Leonid Berlyand
Effective Rheological Properties In Semi-Dilute Bacterial Suspensions, Mykhailo Potomkin, Shawn D. Ryan, Leonid Berlyand
Mathematics and Statistics Faculty Publications
Interactions between swimming bacteria have led to remarkable experimentally observable macroscopic properties such as the reduction in the effective viscosity, enhanced mixing, and diffusion. In this work, we study an individual-based model for a suspension of interacting point dipoles representing bacteria in order to gain greater insight into the physical mechanisms responsible for the drastic reduction in the effective viscosity. In particular, asymptotic analysis is carried out on the corresponding kinetic equation governing the distribution of bacteria orientations. This allows one to derive an explicit asymptotic formula for the effective viscosity of the bacterial suspension in the limit of bacterium …
An Efficient Scheme For Numerical Solution Of Burgers’ Equation Using Quintic Hermite Interpolating Polynomials, Shelly Arora, Inderpreet Kaur
An Efficient Scheme For Numerical Solution Of Burgers’ Equation Using Quintic Hermite Interpolating Polynomials, Shelly Arora, Inderpreet Kaur
Mathematics and Statistics Faculty Publications
A numerical scheme combining the features of quintic Hermite interpolating polynomials and orthogonal collocation method has been presented to solve the well-known non-linear Burgers’ equation. The quintic Hermite collocation method (QHCM) solves the non-linear Burgers’ equation directly without converting it into linear form using Hopf–Cole transformation. Stability of the QHCM has been checked using Eucledian and Supremum norms. Numerical values obtained from QHCM are compared with the values obtained from other techniques such as orthogonal collocation method, orthogonal collocation on finite elements and pdepe solver. Numerical values have been plotted using plane and surface plots to demonstrate the results graphically. …
Counter Machines And Crystallographic Structures, Natasha Jonoska, Mile Krajcevski, Gregory Mccolm
Counter Machines And Crystallographic Structures, Natasha Jonoska, Mile Krajcevski, Gregory Mccolm
Mathematics and Statistics Faculty Publications
One way to depict a crystallographic structure is by a periodic (di)graph, i.e., a graph whose group of automorphisms has a translational subgroup of finite index acting freely on the structure. We establish a relationship between periodic graphs representing crystallographic structures and an infinite hierarchy of intersection languages DCLd,d=0,1,2,…, within the intersection classes of deterministic context-free languages. We introduce a class of counter machines that accept these languages, where the machines with d counters recognize the class DCLd. An intersection of d languages in DCL1 defines DCLd. We prove that there is …
Approximating Optimal Release In A Deterministic Model For The Sterile Insect Technique, Sergio Ramirez, Luis F. Gordillo
Approximating Optimal Release In A Deterministic Model For The Sterile Insect Technique, Sergio Ramirez, Luis F. Gordillo
Mathematics and Statistics Faculty Publications
Cost/benefit analyses are essential to support management planning and decisions before launching any pest control program. In particular, applications of the sterile insect technique (SIT) are often prevented by the projected economic burden associated with rearing processes. This has had a deep impact on the technique development and its use on insects with long larval periods, as often seen in beetles. Under the assumptions of long adult timespan and multiple mating, we show how to find approximate optimal sterile release policies that minimize costs. The theoretical framework proposed considers the release of insects by pulses and finds approximate optimal release …
A Transformation Class For Spatio-Temporal Survival Data With A Cure Fraction, Sandra M. Hurtado Rua, Dipak K. Dey
A Transformation Class For Spatio-Temporal Survival Data With A Cure Fraction, Sandra M. Hurtado Rua, Dipak K. Dey
Mathematics and Statistics Faculty Publications
We propose a hierarchical Bayesian methodology to model spatially or spatio-temporal clustered survival data with possibility of cure. A flexible continuous transformation class of survival curves indexed by a single parameter is used. This transformation model is a larger class of models containing two special cases of the well-known existing models: the proportional hazard and the proportional odds models. The survival curve is modeled as a function of a baseline cumulative distribution function, cure rates, and spatio-temporal frailties. The cure rates are modeled through a covariate link specification and the spatial frailties are specified using a conditionally autoregressive model with …