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Articles 1 - 11 of 11
Full-Text Articles in Physical Sciences and Mathematics
Augmenting The Immersed Boundary Method With Radial Basis Functions (Rbfs) For The Modeling Of Platelets In Hemodynamic Flows, Varun Shankar, Grady B. Wright, Robert M. Kirby, Aaron L. Fogelson
Augmenting The Immersed Boundary Method With Radial Basis Functions (Rbfs) For The Modeling Of Platelets In Hemodynamic Flows, Varun Shankar, Grady B. Wright, Robert M. Kirby, Aaron L. Fogelson
Mathematics Faculty Publications and Presentations
We present a new computational method by extending the Immersed Boundary (IB) method with a geometric model based on parametric Radial Basis Function (RBF) interpolation of the Lagrangian structures. Our specific motivation is the modeling of platelets in hemodynamic flows, though we anticipate that our method will be useful in other applications involving surface elasticity. The efficacy of our new RBF-IB method is shown through a series of numerical experiments. Specifically, we test the convergence of our method and compare our method with the traditional IB method in terms of computational cost, maximum stable time-step size and volume loss. We …
Lower Bound For Ranks Of Invariant Forms, Harm Derksen, Zach Teitler
Lower Bound For Ranks Of Invariant Forms, Harm Derksen, Zach Teitler
Mathematics Faculty Publications and Presentations
We give a lower bound for the Waring rank and cactus rank of forms that are invariant under an action of a connected algebraic group. We use this to improve the Ranestad-Schreyer-Shafiei lower bounds for the Waring ranks and cactus ranks of determinants of generic matrices, Pfaffians of generic skew-symmetric matrices, and determinants of generic symmetric matrices.
A Critical Proton Mr Spectroscopy Marker Of Alzheimer Early Neurodegenerative Change: Low Hippocampal Naa/Cr Ratio Impacts Apoe 4 Mexico City Children And Their Parents., Partha S. Mukherjee
A Critical Proton Mr Spectroscopy Marker Of Alzheimer Early Neurodegenerative Change: Low Hippocampal Naa/Cr Ratio Impacts Apoe 4 Mexico City Children And Their Parents., Partha S. Mukherjee
Mathematics Faculty Publications and Presentations
Severe air pollution exposures produce systemic, respiratory, myocardial, and brain inflammation and Alzheimer’s disease (AD) hallmarks in clinically healthy children. We tested whether hippocampal metabolite ratios are associated with contrasting levels of air pollution, APOE and BMI in paired healthy children and one parent sharing the same APOE alleles. We used (1) H-MRS to interrogate bilateral hippocampal single-voxel in 57 children (12.45± 3.4 years) and their 48 parents (37.5± 6.78 years) low pollution city v Mexico City (MC). NAA/Cr, Cho/Cr, and mI/Cr metabolite ratios were analysed. The right hippocampus N-acetylaspartate/creatine (NAA/Cr) was significantly different between cohorts (p=0.007). The NAA/Cr ratio …
How Do U.S. And Chinese Biology Students Compare In Explaining Energy Consumption Issues?, Hui Jin, Hayat Hokayem, Sasha Wang, Xin Wei
How Do U.S. And Chinese Biology Students Compare In Explaining Energy Consumption Issues?, Hui Jin, Hayat Hokayem, Sasha Wang, Xin Wei
Mathematics Faculty Publications and Presentations
This qualitative study investigates how biology majors explain energy consumption issues. In particular, we focus on two energy consumption activities that account for about two-thirds of global carbon dioxide emissions in 2011: burning fossil fuels for transportation and using electricity. We conducted in-depth clinical interviews with twenty U.S. students and twenty Chinese students. We compared these two groups of students in terms of two aspects of explanation: 1) naming scientific terms in the explanation, and 2) explaining an energy consumption issue. Regarding naming, we examined the frequency of naming different terms of scientific concepts and principles in students’ explanations. Regarding …
Mexico City Normal Weight Children Exposed To High Concentrations Of Ambient Pm2.5 Show High Blood Leptin And Endothelin-1, Vitamin D Deficiency, And Food Reward Hormone Dysregulation Versus Low Pollution Controls. Relevance For Obesity And Alzheimer Disease, Partha S. Mukherjee
Mathematics Faculty Publications and Presentations
Millions of Mexico, US and across the world children are overweight and obese. Exposure to fossil-fuel combustion sources increases the risk for obesity and diabetes, while long-term exposure to fine particulate matter (PM 2.5) and ozone (O3) above US EPA standards is associated with increased risk of Alzheimer’s disease (AD). Mexico City Metropolitan Area children are chronically exposed to PM2.5 and O3 concentrations above the standards and exhibit systemic, brain and intrathecal inflammation, cognitive deficits, and Alzheimer disease neuropathology. We investigated adipokines, food reward hormones, endothelial dysfunction, vitamin D and apolipoprotein E (APOE) relationships in …
Castelnuovo–Mumford Regularity And Arithmetic Cohen–Macaulayness Of Complete Bipartite Subspace Arrangements, Zach Teitler, Douglas A. Torrence
Castelnuovo–Mumford Regularity And Arithmetic Cohen–Macaulayness Of Complete Bipartite Subspace Arrangements, Zach Teitler, Douglas A. Torrence
Mathematics Faculty Publications and Presentations
We give the Castelnuovo–Mumford regularity of arrangements of (n−2)-planes in Pn whose incidence graph is a sufficiently large complete bipartite graph, and determine when such arrangements are arithmetically Cohen–Macaulay.
Order-Preserving Derivative Approximation With Periodic Radial Basis Functions, Edward Fuselier, Grady B. Wright
Order-Preserving Derivative Approximation With Periodic Radial Basis Functions, Edward Fuselier, Grady B. Wright
Mathematics Faculty Publications and Presentations
In this exploratory paper we study the convergence rates of an iterated method for approximating derivatives of periodic functions using radial basis function (RBF) interpolation. Given a target function sampled on some node set, an approximation of the m th derivative is obtained by m successive applications of the operator “interpolate, then differentiate”- this process is known in the spline community as successive splines or iterated splines. For uniformly spaced nodes on the circle, we give a sufficient condition on the RBF kernel to guarantee that, when the error is measured only at the nodes, this iterated method approximates …
A Refinement Of Michener’S Example Classification, Laurie O. Cavey, Margaret T. Kinzel
A Refinement Of Michener’S Example Classification, Laurie O. Cavey, Margaret T. Kinzel
Mathematics Faculty Publications and Presentations
In this paper we propose a refinement of Michener’s (1978) well-known example classification based on data from university mathematicians. The refinement takes into account the mathematician’s perspective on the role of examples in doing mathematics. More specifically, our work provides insight into the ways in which mathematicians talk about using examples in their scholarly work and their work with students. The proposed classification has the potential to inform our work as teachers as we strive to create opportunities to engage students in authentic mathematical work.
Image Denoising By A Local Clustering Framework, Partha Sarathi Mukherjee, Peihua Qiu
Image Denoising By A Local Clustering Framework, Partha Sarathi Mukherjee, Peihua Qiu
Mathematics Faculty Publications and Presentations
Images often contain noise due to imperfections in various image acquisition techniques. Noise should be removed from images so that the details of image objects (e.g., blood vessels, inner foldings, or tumors in the human brain) can be clearly seen, and the subsequent image analyses are reliable. With broad usage of images in many disciplines—for example, medical science—image denoising has become an important research area. In the literature, there are many different types of image denoising techniques, most of which aim to preserve image features, such as edges and edge structures, by estimating them explicitly or implicitly. Techniques based on …
Extension Of Chebfun To Periodic Functions, Grady B. Wright, Mohsin Javed, Hadrien Montanelli, Lloyd N. Trefethen
Extension Of Chebfun To Periodic Functions, Grady B. Wright, Mohsin Javed, Hadrien Montanelli, Lloyd N. Trefethen
Mathematics Faculty Publications and Presentations
Algorithms and underlying mathematics are presented for numerical computation with periodic functions via approximations to machine precision by trigonometric polynomials, including the solution of linear and nonlinear periodic ordinary differential equations. Differences from the nonperiodic Chebyshev case are highlighted.
Identifying Similar Polygons: Comparing Prospective Teachers’ Routines With A Mathematician’S, Sasha Wang
Identifying Similar Polygons: Comparing Prospective Teachers’ Routines With A Mathematician’S, Sasha Wang
Mathematics Faculty Publications and Presentations
This paper reports two prospective teachers' and a mathematician's ways of identifying similar triangle and hexagons through the analysis of routines, a characteristic of geometric discourse. The findings show that visual recognition was a common approach for the mathematician as wells as the two prospective teachers. However, when asked for justification, their routines of identifying similar polygons diverged. The paper also discusses the implication of classroom discourse practices to enhance prospective teachers' communication and reasoning skills while learning geometric concepts such as similarity.