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Articles 1 - 19 of 19
Full-Text Articles in Entire DC Network
The Effect Of Rare Variants In Trem2 And Pld3 On Longitudinal Cognitive Function In The Wisconsin Registry For Alzheimer's Prevention, Corinne D. Engelman, Burcu F. Darst, Murat Bilgel, Eva Vasiljevic, Rebecca L. Koscik, Bruno M. Jedynak, Sterling C. Johnson
The Effect Of Rare Variants In Trem2 And Pld3 On Longitudinal Cognitive Function In The Wisconsin Registry For Alzheimer's Prevention, Corinne D. Engelman, Burcu F. Darst, Murat Bilgel, Eva Vasiljevic, Rebecca L. Koscik, Bruno M. Jedynak, Sterling C. Johnson
Mathematics and Statistics Faculty Publications and Presentations
Recent studies have found an association between functional variants in TREM2 and PLD3 and Alzheimer's disease (AD), but their effect on cognitive function is unknown. We examined the effect of these variants on cognitive function in 1449 participants from the Wisconsin Registry for Alzheimer's Prevention, a longitudinal study of initially asymptomatic adults, aged 36–73 years at baseline, enriched for a parental history of AD. A comprehensive cognitive test battery was performed at up to 5 visits. A factor analysis resulted in 6 cognitive factors that were standardized into z scores (∼N [0, 1]); the mean of these z scores was …
Variational Geometric Approach To Generalized Differential And Conjugate Calculi In Convex Analysis, Boris S. Mordukhovich, Nguyen Mau Nam, R. Blake Rector, T. Tran
Variational Geometric Approach To Generalized Differential And Conjugate Calculi In Convex Analysis, Boris S. Mordukhovich, Nguyen Mau Nam, R. Blake Rector, T. Tran
Mathematics and Statistics Faculty Publications and Presentations
This paper develops a geometric approach of variational analysis for the case of convex objects considered in locally convex topological spaces and also in Banach space settings. Besides deriving in this way new results of convex calculus, we present an overview of some known achievements with their unified and simplified proofs based on the developed geometric variational schemes. Key words. Convex and variational analysis, Fenchel conjugates, normals and subgradients, coderivatives, convex calculus, optimal value functions.
Social Balance And The Bernoulli Equation, J. J. P. Veerman
Social Balance And The Bernoulli Equation, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
Since the 1940s there has been an interest in the question of why social networks often give rise to two antagonistic factions. Recently a dynamical model of how and why such a balance might occur was developed. This note provides an introduction to the notion of social balance and a new (and simplified) analysis of that model. This new analysis allows us to choose general initial conditions, as opposed to the symmetric ones previously considered. We show that for general initial conditions, four factions will evolve instead of two. We characterize the four factions, and give an idea of their …
Classification Of Minimal Separating Sets In Low Genus Surfaces, J. J. P. Veerman, William Maxwell, Victor Rielly, Austin K. Williams
Classification Of Minimal Separating Sets In Low Genus Surfaces, J. J. P. Veerman, William Maxwell, Victor Rielly, Austin K. Williams
Mathematics and Statistics Faculty Publications and Presentations
Consider a surface S and let M ⊂ S. If S \ M is not connected, then we say M separates S, and we refer to M as a separating set of S. If M separates S, and no proper subset of M separates S, then we say M is a minimal separating set of S. In this paper we use computational methods of combinatorial topology to classify the minimal separating sets of the orientable surfaces of genus g = 2 and g = 3. The classification for genus 0 and 1 was done …
Random Walks On Digraphs, J.J.P. Veerman
Random Walks On Digraphs, J.J.P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
Let V = {1, · · · n} be a vertex set and S a non-negative row-stochastic matrix (i.e. rows sum to 1). V and S define a digraph G = G(V, S) and a directed graph Laplacian L as follows. If (S)ij > 0 (in what follows we will leave out the parentheses) there is a directed edge j → i. Thus the ith row of S identifies the edges coming into vertex i and their weights. This set of vertices are collectively the neighbors of i, and is denoted by Ni . The diagonal elements Sii are chosen such …
A Weighted Möbius Function, Derek Garton
A Weighted Möbius Function, Derek Garton
Mathematics and Statistics Faculty Publications and Presentations
Fix an odd prime ℓ and let G be the poset of isomorphism classes of finite abelian ℓ-groups, ordered by inclusion. If ξ:G→R≥0 is a discrete probability distribution on G and A ∈ G, define the Ath moment of ξ to be . The question of determining conditions that ensure ξ is completely determined by its moments has been of recent interest in many problems of Cohen–Lenstra type. Furthermore, recovering ξ from its moments requires a new Möbius-type inversion formula on G. In this paper, we define this function, relate it to the classical Möbius …
A Finite Difference Method For Off-Fault Plasticity Throughout The Earthquake Cycle, Brittany A. Erickson, Eric M. Dunham, Arash Khosravifar
A Finite Difference Method For Off-Fault Plasticity Throughout The Earthquake Cycle, Brittany A. Erickson, Eric M. Dunham, Arash Khosravifar
Mathematics and Statistics Faculty Publications and Presentations
We have developed an efficient computational framework for simulating multiple earthquake cycles with off-fault plasticity. The method is developed for the classical antiplane problem of a vertical strike-slip fault governed by rate-and-state friction, with inertial effects captured through the radiationdamping approximation. Both rate-independent plasticity and viscoplasticity are considered, where stresses are constrained by a Drucker-Prager yield condition. The off-fault volume is discretized using finite differences and tectonic loading is imposed by displacing the remote side boundaries at a constant rate. Time-stepping combines an adaptive Runge-Kutta method with an incremental solution process which makes use of an elastoplastic tangent stiffness tensor …
Dynamically Distinguishing Polynomials, Andrew Bridy, Derek Garton
Dynamically Distinguishing Polynomials, Andrew Bridy, Derek Garton
Mathematics and Statistics Faculty Publications and Presentations
A polynomial with integer coefficients yields a family of dynamical systems indexed by primes as follows: For any prime p, reduce its coefficients mod p and consider its action on the field FpFp. We say a subset of Z[x]Z[x] is dynamically distinguishable mod p if the associated mod pdynamical systems are pairwise non-isomorphic. For any k,M∈Z>1k,M∈Z>1, we prove that there are infinitely many sets of integers MM of size M such that {xk+m∣m∈M}{xk+m∣m∈M} is dynamically distinguishable mod p for most p (in the sense of natural density). Our proof uses the Galois theory of dynatomic polynomials largely developed …
Subgradients Of Minimal Time Functions Without Calmness, Nguyen Mau Nam, Dang Van Cuong
Subgradients Of Minimal Time Functions Without Calmness, Nguyen Mau Nam, Dang Van Cuong
Mathematics and Statistics Faculty Publications and Presentations
In recent years there has been great interest in variational analysis of a class of nonsmooth functions called the minimal time function. In this paper we continue this line of research by providing new results on generalized differentiation of this class of functions, relaxing assumptions imposed on the functions and sets involved for the results. In particular, we focus on the singular subdifferential and the limiting subdifferential of this class of functions.
Shift-Symmetric Configurations In Two-Dimensional Cellular Automata: Irreversibility, Insolvability, And Enumeration, Peter Banda, John S. Caughman Iv, Martin Cenek, Christof Teuscher
Shift-Symmetric Configurations In Two-Dimensional Cellular Automata: Irreversibility, Insolvability, And Enumeration, Peter Banda, John S. Caughman Iv, Martin Cenek, Christof Teuscher
Mathematics and Statistics Faculty Publications and Presentations
The search for symmetry as an unusual yet profoundly appealing phenomenon, and the origin of regular, repeating configuration patterns have been for a long time a central focus of complexity science, and physics.
Here, we introduce group-theoretic concepts to identify and enumerate the symmetric inputs, which result in irreversible system behaviors with undesired effects on many computational tasks. The concept of so-called configuration shift-symmetry is applied on two-dimensional cellular automata as an ideal model of computation. The results show the universal insolvability of “non-symmetric” tasks regardless of the transition function. By using a compact enumeration formula and bounding the number …
Nesterov's Smoothing Technique And Minimizing Differences Of Convex Functions For Hierarchical Clustering, Mau Nam Nguyen, Wondi Geremew, Sam Raynolds, Tuyen Tran
Nesterov's Smoothing Technique And Minimizing Differences Of Convex Functions For Hierarchical Clustering, Mau Nam Nguyen, Wondi Geremew, Sam Raynolds, Tuyen Tran
Mathematics and Statistics Faculty Publications and Presentations
A bilevel hierarchical clustering model is commonly used in designing optimal multicast networks. In this paper we will consider two different formulations of the bilevel hierarchical clustering problem -- a discrete optimization problem which can be shown to be NP-hard. Our approach is to reformulate the problem as a continuous optimization problem by making some relaxations on the discreteness conditions. This approach was considered by other researchers earlier, but their proposed methods depend on the square of the Euclidian norm because of its differentiability. By applying the Nesterov smoothing technique and the DCA -- a numerical algorithm for minimizing differences …
Some Remarks On Interpolation And Best Approximation, Randolph E. Bank, Jeffrey S. Ovall
Some Remarks On Interpolation And Best Approximation, Randolph E. Bank, Jeffrey S. Ovall
Mathematics and Statistics Faculty Publications and Presentations
Sufficient conditions are provided for establishing equivalence between best approximation error and projection/interpolation error in finite-dimensional vector spaces for general (semi)norms. The results are applied to several standard finite element spaces, modes of interpolation and (semi)norms, and a numerical study of the dependence on polynomial degree of constants appearing in our estimates is provided.
Space-Time Cfosls Methods With Amge Upscaling, Martin Neumüller, Panayot Vassilevski, Umberto E. Villa
Space-Time Cfosls Methods With Amge Upscaling, Martin Neumüller, Panayot Vassilevski, Umberto E. Villa
Mathematics and Statistics Faculty Publications and Presentations
This work considers the combined space-time discretization of time-dependent partial differential equations by using first order least square methods. We also impose an explicit constraint representing space-time mass conservation. To alleviate the restrictive memory demand of the method, we use dimension reduction via accurate element agglomeration AMG coarsening, referred to as AMGe upscaling. Numerical experiments demonstrating the accuracy of the studied AMGe upscaling method are provided.
Reorganizing Algebraic Thinking: An Introduction To Dynamic System Modeling, Diana Fisher
Reorganizing Algebraic Thinking: An Introduction To Dynamic System Modeling, Diana Fisher
Mathematics and Statistics Faculty Publications and Presentations
System Dynamics (SD) modeling is a powerful analytical method used by professional scientists, academics, and governmental officials to study the behavior patterns of complex systems. Specifically through use of the Stella software, it is a method that I and others have used for over two decades with high school, and even middle school, math and science students. In this paper I describe an introduction to SD modeling intended for an algebra class (in either middle or high school). In the body of the paper, a nested sequence of simple bank account examples, increasing in complexity, is used to demonstrate a …
Increasing Student Cognitive Engagement In The Math Classroom Through Sustained Professional Development, Eva Thanheiser, Brenda Rosencrans, Kathleen Mary Melhuish, Joshua B. Fagan, Layla Guyot
Increasing Student Cognitive Engagement In The Math Classroom Through Sustained Professional Development, Eva Thanheiser, Brenda Rosencrans, Kathleen Mary Melhuish, Joshua B. Fagan, Layla Guyot
Mathematics and Statistics Faculty Publications and Presentations
We share the case of one teacher engaged in professional development (PD) designed to improve collective argumentation. We present an analysis of two lessons in her classroom, one before and one after her engagement with the professional development. Findings show that the classrooms differ across both teacher support for collective argumentation (requesting ideas and elaboration vs. requesting/acts and methods), and student contributions Oustifications vs. procedures and facts) .
Connecting Teachers’ Buy-Into Professional Development With Classroom Habits And Practices, Joshua B. Fagan, Kathleen Mary Melhuish, Eva Thanheiser, Brenda Rosencrans, Layla Guyot, Jodi I. Fasteen
Connecting Teachers’ Buy-Into Professional Development With Classroom Habits And Practices, Joshua B. Fagan, Kathleen Mary Melhuish, Eva Thanheiser, Brenda Rosencrans, Layla Guyot, Jodi I. Fasteen
Mathematics and Statistics Faculty Publications and Presentations
While professional development (PD) provides an opportunity for teachers to cultivate skills that are consistent with best practices in the field, it is their buy-into the PD that ultimately determines the effectiveness of the PD. We examined how teacher buy-in affected the classroom habits and practice of four elementary teachers who took part in a district wide PD. Using baseline and first-year implementation video recordings, in conjunction with frameworks for discourse analysis, cognitive demand, and tools built specifically to measure PD implementation, we found that varying combinations of teachers' beliefs served as a mitigating factor for PD implementation.
Equators Have At Most Countable Many Singularities With Bounded Total Angle, Pilar Herreros, Mario Ponce, J.J.P. Veerman
Equators Have At Most Countable Many Singularities With Bounded Total Angle, Pilar Herreros, Mario Ponce, J.J.P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
For distinct points p and q in a two-dimensional Riemannian manifold, one defines their mediatrix Lpq as the set of equidistant points to p and q. It is known that mediatrices have a cell decomposition consisting of a finite number of branch points connected by Lipschitz curves. In the case of a topological sphere, mediatrices are called equators and it can benoticed that there are no branching points, thus an equator is a topological circle with possibly many Lipschitz singularities. This paper establishes that mediatrices have the radial …
On The Uniformity Of (3/2)N Modulo 1, Paula Neeley, Daniel Taylor-Rodriguez, J.J.P. Veerman, Thomas Roth
On The Uniformity Of (3/2)N Modulo 1, Paula Neeley, Daniel Taylor-Rodriguez, J.J.P. Veerman, Thomas Roth
Mathematics and Statistics Faculty Publications and Presentations
It has been conjectured that the sequence (3/2)n modulo 1 is uniformly distributed. The distribution of this sequence is significant in relation to unsolved problems in number theory including the Collatz conjecture. In this paper, we describe an algorithm to compute (3/2)n modulo 1 to n = 108 . We then statistically analyze its distribution. Our results strongly agree with the hypothesis that (3/2)n modulo 1 is uniformly distributed.
Convergence Analysis Of A Proximal Point Algorithm For Minimizing Differences Of Functions, Thai An Nguyen, Mau Nam Nguyen
Convergence Analysis Of A Proximal Point Algorithm For Minimizing Differences Of Functions, Thai An Nguyen, Mau Nam Nguyen
Mathematics and Statistics Faculty Publications and Presentations
Several optimization schemes have been known for convex optimization problems. However, numerical algorithms for solving nonconvex optimization problems are still underdeveloped. A significant progress to go beyond convexity was made by considering the class of functions representable as differences of convex functions. In this paper, we introduce a generalized proximal point algorithm to minimize the difference of a nonconvex function and a convex function. We also study convergence results of this algorithm under the main assumption that the objective function satisfies the Kurdyka– ᴌojasiewicz property.