Mathematics Commons^™

Forecasting The Effect Of The Amethyst Initiative On College Drinking, Ben G. Fitzpatrick, Richard Scribner, Azmy S. Ackleh, Jawaid Rasul, Geoffrey Jacquez, Neal Simonsen, Robert Rommel

Mathematics Faculty Works

Background

A number of college presidents have endorsed the Amethyst Initiative, a call to consider lowering the minimum legal drinking age (MLDA). Our objective is to forecast the effect of the Amethyst Initiative on college drinking.

Methods

A system model of college drinking siumlates MLDA changes through (1) a decrease in heavy episodic drinking (HED) due to the lower likelihood of students drinking in unsupervised settings where they model irresponsible drinking (misperception), and (2) an increase in overall drinking among currently underage students due to increased social availability of alcohol (wetness).

Results

For the proportion of HEDs on campus, effects …

Computational Modeling And Numerical Methods For Spaciotemporal Calcium Cycling In Ventricular Myocytes, Robert Rovetti

Mathematics Faculty Works

Intracellular calcium (Ca) cycling dynamics in cardiac myocytes is regulated by a complex network of spatially distributed organelles, such as sarcoplasmic reticulum (SR), mitochondria, and myofibrils. In this study, we present a mathematical model of intracellular Ca cycling and numerical and computational methods for computer simulations. The model consists of a coupled Ca release unit (CRU) network, which includes a SR domain and a myoplasm domain. Each CRU contains 10 L-type Ca channels and 100 ryanodine receptor channels, with individual channels simulated stochastically using a variant of Gillespie’s method, modified here to handle time-dependent transition rates. Both the SR domain …

Computational Modeling And Numerical Methods For Spatiotemporal Calcium Cycling In Ventricular Myocytes, Michael Nivala, Enno De Lange, Robert J. Rovetti, Zhilin Qu

Mathematics Faculty Works

Intracellular calcium (Ca) cycling dynamics in cardiac myocytes is regulated by a complex network of spatially distributed organelles, such as sarcoplasmic reticulum (SR), mitochondria, and myofibrils. In this study, we present a mathematical model of intracellular Ca cycling and numerical and computational methods for computer simulations. The model consists of a coupled Ca release unit (CRU) network, which includes a SR domain and a myoplasm domain. Each CRU contains 10 L-type Ca channels and 100 ryanodine receptor channels, with individual channels simulated stochastically using a variant of Gillespie’s method, modified here to handle time-dependent transition rates. Both the SR domain …

Effects Of Visual, Auditory, And Kinesthetic Imagery Interventions On Dancers’ Plié Arabesques, Teresa Heiland, Robert Rovetti

Mathematics Faculty Works

The goal of this study was to examine the influence of visual, auditory, and kinesthetic delivery modes of Franklin Method images (anatomical bone rhythms, metaphorical image, and tactile aid, respectively) on the performance of college dancers’ Plié Arabesques by assessing its influence on three measures: plié depth; maintenance of rotation; and simultaneous use of hip, knee, and ankle (Tri-fold). Eighteen participants performed a series of Plié Arabesques during three visits over a period of two months; at each visit, pliés were performed before and after an image intervention, and the change in mean Likert scale rating was calculated for each …

Enhancements Of Rack Counting Invariants Via Dynamical Cocycles, Alissa S. Crans, Sam Nelson, Aparna Sarkar

Mathematics Faculty Works

We introduce the notion of N-reduced dynamical cocycles and use these objects to define enhancements of the rack counting invariant for classical and virtual knots and links. We provide examples to show that the new invariants are not determined by the rack counting invariant, the Jones polynomial or the generalized Alexander polynomial.

Upper Bounds In The Ohtsuki-Riley-Sakuma Partial Order On 2-Bridge Knots, Scott M. Garrabrant, Jim Hoste, Patrick D. Shanahan

Mathematics Faculty Works

In this paper we use continued fractions to study a partial order on the set of 2-bridge knots derived from the work of Ohtsuki, Riley, and Sakuma. We establish necessary and sufficient conditions for any set of 2-bridge knots to have an upper bound with respect to the partial order. Moreover, given any 2-bridge knot K we characterize all other 2-bridge knots J such that {K, J} has an upper bound. As an application we answer a question of Suzuki, showing that there is no upper bound for the set consisting of the trefoil and figure-eight knots.

How Well Do The Nsf Funded Elementary Mathematics Curricula Align With The Gaise Report Recommendations?, Anna E. Bargagliotti

Mathematics Faculty Works

Statistics and probability have become an integral part of mathematics education. Therefore it is important to understand whether curricular materials adequately represent statistical ideas. The Guidelines for Assessment and Instruction in Statistics Education (GAISE) report (Franklin, Kader, Mewborn, Moreno, Peck, Perry, & Scheaffer, 2007), endorsed by the American Statistical Association, provides a two-dimensional (process and level) framework for statistical learning. This paper examines whether the statistics content contained in the NSF funded elementary curricula Investigations in Number, Data, and Space, Math Trailblazers, and Everyday Mathematics aligns with the GAISE recommendations. Results indicate that there are differences in the approaches used …

Characterization Of Radially Symmetric Finite Time Blowup In Multidimensional Aggregation Equations, Andrea L. Bertozzi, John B. Garnett, Thomas Laurent

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This paper studies the transport of a mass $\mu$ in $\mathbb{R}^d, d \geq 2,$ by a flow field $v= -\nabla K*\mu$. We focus on kernels $K=|x|^\alpha/ \alpha$ for $2-d\leq \alpha<2$ for which the smooth densities are known to develop singularities in finite time. For this range we prove the existence for all time of radially symmetric measure solutions that are monotone decreasing as a function of the radius, thus allowing for continuation of the solution past the blowup time. The monotone constraint on the data is consistent with the typical blowup profiles observed in recent numerical studies of these singularities. We prove monotonicity is preserved for all time, even after blowup, in contrast to the case $\alpha >2$ where radially symmetric solutions are known to lose monotonicity. In the case of the Newtonian potential ($\alpha=2-d$), under the assumption of radial symmetry the equation can be transformed into the inviscid Burgers equation on a half line. This enables us to prove preservation of monotonicity using the classical theory of conservation laws. In the case $2 -d < \alpha < 2$ and at the critical exponent p we exhibit initial data in $L^p$ for which the solution immediately develops a Dirac mass singularity. This extends recent work on the local ill-posedness of solutions at the critical exponent.

Spatial Graphs With Local Knots, Erica Flapan, Blake Mellor, Ramin Naimi

Mathematics Faculty Works

It is shown that for any locally knotted edge of a 3-connected graph in S³, there is a ball that contains all of the local knots of that edge and is unique up to an isotopy setwise fixing the graph. This result is applied to the study of topological symmetry groups of graphs embedded in S³.

On Levi-Civita’S Alternating Symbol, Schouten’S Alternating Unit Tensors, Cpt, And Quantization, Evert Jan Post, Stan Sholar, Hooman Rahimizadeh, Michael Berg

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The purpose of the present article is to demonstrate that by adopting a unifying differential geometric perspective on certain themes in physics one reaps remarkable new dividends in both microscopic and macroscopic domains. By replacing algebraic objects by tensor-transforming objects and introducing methods from the theory of differentiable manifolds at a very fundamental level we obtain a Kottler-Cartan metric-independent general invariance of the Maxwell field, which in turn makes for a global quantum superstructure for Gauss-Amp`ere and Aharonov-Bohm “quantum integrals.” Beyond this, our approach shows that postulating a Riemannian metric at the quantum level is an unnecessary concept and our …

Convergence Of A Steepest Descent Algorithm For Ratio Cut Clustering, Xavier Bresson, Thomas Laurent, David Uminsky, James H. Von Brecht

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Unsupervised clustering of scattered, noisy and high-dimensional data points is an important and difficult problem. Tight continuous relaxations of balanced cut problems have recently been shown to provide excellent clustering results. In this paper, we present an explicit-implicit gradient flow scheme for the relaxed ratio cut problem, and prove that the algorithm converges to a critical point of the energy. We also show the efficiency of the proposed algorithm on the two moons dataset.

Congrats You’Re Abd! Now What?, Alissa Crans

Mathematics Faculty Works

No abstract provided.