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Articles 1 - 14 of 14
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Comparing Hecke Coefficients Of Automorphic Representations, Liubomir Chiriac, Andrei Jorza
Comparing Hecke Coefficients Of Automorphic Representations, Liubomir Chiriac, Andrei Jorza
Mathematics and Statistics Faculty Publications and Presentations
We prove a number of unconditional statistical results of the Hecke coefficients for unitary cuspidal representations of over number fields. Using partial bounds on the size of the Hecke coefficients, instances of Langlands functoriality, and properties of Rankin-Selberg -functions, we obtain bounds on the set of places where linear combinations of Hecke coefficients are negative. Under a mild functoriality assumption we extend these methods to . As an application, we obtain a result related to a question of Serre about the occurrence of large Hecke eigenvalues of Maass forms. Furthermore, in the cases where the Ramanujan conjecture is satisfied, we …
On The Equality Case Of The Ramanujan Conjecture For Hilbert Modular Forms, Liubomir Chiriac
On The Equality Case Of The Ramanujan Conjecture For Hilbert Modular Forms, Liubomir Chiriac
Mathematics and Statistics Faculty Publications and Presentations
The generalized Ramanujan Conjecture for cuspidal unitary automorphic representations π on GL(2) asserts that |av(π)| ≤ 2. We prove that this inequality is strict if π is generated by a CM Hilbert modular form of parallel weight two and v is a finite place of degree one. Equivalently, the Satake parameters of πv are necessarily distinct. We also give examples where the equality case does occur for primes of degree two.
Diffusion And Consensus On Weakly Connected Directed Graphs, J. J. P. Veerman, Ewan Kummel
Diffusion And Consensus On Weakly Connected Directed Graphs, J. J. P. Veerman, Ewan Kummel
Mathematics and Statistics Faculty Publications and Presentations
Let G be a weakly connected directed graph with asymmetric graph Laplacian L. Consensus and diffusion are dual dynamical processes defined on G by x˙=−Lx for consensus and p˙=−pL for diffusion. We consider both these processes as well their discrete time analogues. We define a basis of row vectors {γ¯i}ki=1 of the left null-space of L and a basis of column vectors {γi}ki=1 of the right null-space of L in terms of the partition of G into strongly connected components. This allows for complete characterization of the asymptotic behavior of both diffusion and consensus --- discrete and continuous --- in …
Trefftz Finite Elements On Curvilinear Polygons, Akash Anand, Jeffrey S. Ovall, Samuel E. Reynolds, Steffen Weisser
Trefftz Finite Elements On Curvilinear Polygons, Akash Anand, Jeffrey S. Ovall, Samuel E. Reynolds, Steffen Weisser
Mathematics and Statistics Faculty Publications and Presentations
We present a Trefftz-type finite element method on meshes consisting of curvilinear polygons. Local basis functions are computed using integral equation techniques that allow for the efficient and accurate evaluation of quantities needed in the formation of local stiffness matrices. To define our local finite element spaces in the presence of curved edges, we must also properly define what it means for a function defined on a curved edge to be "polynomial" of a given degree on that edge. We consider two natural choices, before settling on the one that yields the inclusion of complete polynomial spaces in our local …
Family Math Night: Increasing Engagement In University Mathematics Courses For Prospective Teachers, Eva Thanheiser
Family Math Night: Increasing Engagement In University Mathematics Courses For Prospective Teachers, Eva Thanheiser
Mathematics and Statistics Faculty Publications and Presentations
Prospective elementary school teachers (PSTs) often do not perceive mathematics activities as fun or engaging and perceive the mathematics tasks in their university content courses as inauthentic and irrelevant. Both these points were addressed by connecting the university classroom tasks to the K–5 environment via a Family Math Night (FMN). Survey results from 23 PSTs showed that PSTs were excited about the authenticity of the tasks, learned about children’s mathematical thinking, and reconceptualized mathematics learning as potentially enjoyable. In combination, these results may lead to PSTs’ increased engagement in the mathematics content course and, thus, result in their increased mathematics …
Navigating Around Convex Sets, J. J. P. Veerman
Navigating Around Convex Sets, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
We review some basic results of convex analysis and geometry in Rn in the context of formulating a differential equation to track the distance between an observer flying outside a convex set K and K itself.
Leveraging Variation Of Historical Number Systems To Build Understanding Of The Base-Ten Place-Value System, Eva Thanheiser, Kathleen Melhuish
Leveraging Variation Of Historical Number Systems To Build Understanding Of The Base-Ten Place-Value System, Eva Thanheiser, Kathleen Melhuish
Mathematics and Statistics Faculty Publications and Presentations
Prospective elementary school teachers (PTs) come to their mathematics courses fluent in using procedures for adding and subtracting multidigit whole numbers, but many are unaware of the essential features inherent in understanding the base-ten place-value system (i.e., grouping, place value, base). Understanding these features is crucial to understanding and teaching number and place value. The research aims of this paper are (1) to present a local instructional theory (LIT), designed to familiarize PTs with these features through comparison with historical number systems and (2) to present the effects of using the LIT in the PT classroom. A theory of learning …
Spectral Discretization Errors In Filtered Subspace Iteration, Jay Gopalakrishnan, Luka Grubišić, Jeffrey S. Ovall
Spectral Discretization Errors In Filtered Subspace Iteration, Jay Gopalakrishnan, Luka Grubišić, Jeffrey S. Ovall
Mathematics and Statistics Faculty Publications and Presentations
We consider filtered subspace iteration for approximating a cluster of eigenvalues (and its associated eigenspace) of a (possibly unbounded) selfadjoint operator in a Hilbert space. The algorithm is motivated by a quadrature approximation of an operator-valued contour integral of the resolvent. Resolvents on infinite dimensional spaces are discretized in computable finite-dimensional spaces before the algorithm is applied. This study focuses on how such discretizations result in errors in the eigenspace approximations computed by the algorithm. The computed eigenspace is then used to obtain approximations of the eigenvalue cluster. Bounds for the Hausdorff distance between the computed and exact eigenvalue clusters …
Analysis Of Feast Spectral Approximations Using The Dpg Discretization, Jay Gopalakrishnan, Luka Grubišić, Jeffrey S. Ovall, Benjamin Quanah Parker
Analysis Of Feast Spectral Approximations Using The Dpg Discretization, Jay Gopalakrishnan, Luka Grubišić, Jeffrey S. Ovall, Benjamin Quanah Parker
Mathematics and Statistics Faculty Publications and Presentations
A filtered subspace iteration for computing a cluster of eigenvalues and its accompanying eigenspace, known as “FEAST”, has gained considerable attention in recent years. This work studies issues that arise when FEAST is applied to compute part of the spectrum of an unbounded partial differential operator. Specifically, when the resolvent of the partial differential operator is approximated by the discontinuous Petrov Galerkin (DPG) method, it is shown that there is no spectral pollution. The theory also provides bounds on the discretization errors in the spectral approximations. Numerical experiments for simple operators illustrate the theory and also indicate the value of …
A Bayesian Nonparametric Multiple Testing Procedure For Comparing Several Treatments Against A Control, Luis Gutiérrez, Andrés Barrientos, Jorge González, Daniel Taylor-Rodríguez
A Bayesian Nonparametric Multiple Testing Procedure For Comparing Several Treatments Against A Control, Luis Gutiérrez, Andrés Barrientos, Jorge González, Daniel Taylor-Rodríguez
Mathematics and Statistics Faculty Publications and Presentations
We propose a Bayesian nonparametric strategy to test for differences between a control group and several treatment regimes. Most of the existing tests for this type of comparison are based on the differences between location parameters. In contrast, our approach identifies differences across the entire distribution, avoids strong modeling assumptions over the distributions for each treatment, and accounts for multiple testing through the prior distribution on the space of hypotheses. The proposal is compared to other commonly used hypothesis testing procedures under simulated scenarios. Two real applications are also analyzed with the proposed methodology.
Deep Learning Based Topology Guaranteed Surface And Mme Segmentation Of Multiple Sclerosis Subjects From Retinal Oct, Yufan He, Aaron Carass, Yihao Liu, Bruno Jedynak, Sharon D. Solomon, Shiv Saidha, Peter A. Calabresi, Jerry L. Prince
Deep Learning Based Topology Guaranteed Surface And Mme Segmentation Of Multiple Sclerosis Subjects From Retinal Oct, Yufan He, Aaron Carass, Yihao Liu, Bruno Jedynak, Sharon D. Solomon, Shiv Saidha, Peter A. Calabresi, Jerry L. Prince
Mathematics and Statistics Faculty Publications and Presentations
Optical coherence tomography (OCT) is a noninvasive imaging modality that can be used to obtain depth images of the retina. Patients with multiple sclerosis (MS) have thinning retinal nerve fiber and ganglion cell layers, and approximately 5% of MS patients will develop microcystic macular edema (MME) within the retina. Segmentation of both the retinal layers and MME can provide important information to help monitor MS progression. Graph-based segmentation with machine learning preprocessing is the leading method for retinal layer segmentation, providing accurate surface delineations with the correct topological ordering. However, graph methods are time-consuming and they do not optimally incorporate …
A Dc Programming Approach For Solving Multicast Network Design Problems Via The Nesterov Smoothing Technique, Wondi Geremew, Mau Nam Nguyen, A. Semenov, V. Boginski, E. Pasiliao
A Dc Programming Approach For Solving Multicast Network Design Problems Via The Nesterov Smoothing Technique, Wondi Geremew, Mau Nam Nguyen, A. Semenov, V. Boginski, E. Pasiliao
Mathematics and Statistics Faculty Publications and Presentations
This paper continues our effort initiated in [19] to study Multicast Communication Networks, modeled as bilevel hierarchical clustering problems, by using mathematical optimization techniques. Given a finite number of nodes, we consider two different models of multicast networks by identifying a certain number of nodes as cluster centers, and at the same time, locating a particular node that serves as a total center so as to minimize the total transportation cost through the network. The fact that the cluster centers and the total center have to be among the given nodes makes this problem a discrete optimization problem. Our approach …
Active Learning In Computer-Based College Algebra, Steven Boyce, Joyce O'Halloran
Active Learning In Computer-Based College Algebra, Steven Boyce, Joyce O'Halloran
Mathematics and Statistics Faculty Publications and Presentations
We describe the process of adjusting the balance between computerbased learning and peer interaction in a college algebra course. In our first experimental class, students used the adaptive-learning program ALEKS within an emporium-style format. Comparing student performance in the emporium format class with that in a traditional lecture format class, we found an improvement in procedural skills, but a weakness in the students’ conceptual understanding of mathematical ideas. Consequently, we shifted to a blended format, cutting back on the number of ALEKS (procedural) topics and integrating activities that fostered student discourse about mathematics concepts. In our third iteration using ALEKS, …
Stability Conditions For Coupled Oscillators In Linear Arrays, Pablo Enrique Baldivieso Blanco, J.J.P. Veerman
Stability Conditions For Coupled Oscillators In Linear Arrays, Pablo Enrique Baldivieso Blanco, J.J.P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
In this paper, we give necessary conditions for stability of flocks in R. We focus on linear arrays with decentralized agents, where each agent interacts with only a few its neighbors. We obtain explicit expressions for necessary conditions for asymptotic stability in the case that the systems consists of a periodic arrangement of two or three different types of agents, i.e. configurations as follows: ...2-1-2-1 or ...3-2-1-3-2-1. Previous literature indicated that the (necessary) condition for stability in the case of a single agent (...1-1-1) held that the first moment of certain coefficients governing the interactions between agents has to be …