Mathematics Commons^™

"Beyond Bio2010: Celebration And Opportunities" At The Intersection Of Mathematics And Biology, John R. Jungck, Holly D. Gaff, Adam P. Fagen, Jay B. Labov

Biological Sciences Faculty Publications

With this special edition of CBE-LSE, which focuses on connections between and integration of the biological and mathematical sciences, it is especially fitting that we report on an important symposium, Beyond BIO2010: Celebration and Opportunities,1 which was held at the National Acad- emy of Sciences (NAS) in Washington, D.C. on May 21–22, 2010. This symposium was organized to assess what progress has been made in addressing the challenges and recommendations in the National Research Council’s (NRC) report: BIO2010: Transforming Undergraduate Education for Future Research Biologists (NRC, 2003a). Most of the presen- tations and posters at this event emphasized the increasing …

Mathematical Manipulative Models: In Defense Of "Beanbag Biology", John R. Jungck, Holly Gaff, Anton E. Weisstein

Biological Sciences Faculty Publications

Mathematical manipulative models have had a long history of influence in biological research and in secondary school education, but they are frequently neglected in undergraduate biology education. By linking mathematical manipulative models in a four-step process-1) use of physical manipulatives, 2) interactive exploration of computer simulations, 3) derivation of mathematical relationships from core principles, and 4) analysis of real data sets-we demonstrate a process that we have shared in biological faculty development workshops led by staff from the BioQUEST Curriculum Consortium over the past 24 yr. We built this approach based upon a broad survey of literature in mathematical educational …

Estimation Of Quality Adjusted Lifetime (Qal) Distribution., Biswabrata Pradhan Dr.

Doctoral Theses

Quality Adjusted Lifetime (QAL)Normally, overall survival time is considered as the end point for many clinical trials to study the effectiveness of different treatments. If the survival time passes through different health states, which differ in their quality of life, then other endpoints are also considered for treatment comparison, which incorporates both quality and duration of life. It is, therefore, necessary to provide a composite measure for comparison of different treatment choices, specially in the context of clinical trials, after taking into account both quality and duration of life. This issue has been first addressed by Gelber and coauthors in …

Teaching Calculus With Wolfram Alpha, Andrew Lang

College of Science and Engineering Faculty Research and Scholarship

This article describes the benefits and drawbacks of using Wolfram|Alpha as the platform for teaching calculus concepts in the lab setting. It is a result of our experiences designing and creating an entirely new set of labs using Wolfram|Alpha. We present the reasoning behind our transition from using a standard computer algebra system (CAS) to Wolfram|Alpha in our differential and integral calculus labs, together with the positive results from our experience. We also discuss the current limitations of Wolfram|Alpha, including a discussion on why we still use a CAS for our multivariate calculus labs.

Consistency Properties For Growth Model Parameters Under An Infill Asymptotics Domain, David T. Mills

Theses and Dissertations

Growth curves are used to model various processes, and are often seen in biological and agricultural studies. Underlying assumptions of many studies are that the process may be sampled forever, and that samples are statistically independent. We instead consider the case where sampling occurs in a finite domain, so that increased sampling forces samples closer together, and also assume a distance-based covariance function. We first prove that, under certain conditions, the mean parameter of a fixed-mean model cannot be estimated within a finite domain. We then numerically consider more complex growth curves, examining sample sizes, sample spacing, and quality of …

Roger Temam On The Occasion Of His 70th Birthday, Claude Michel Brauner, Danielle Hilhorst, Alain Miranville, Shouhong Wang, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

An Explicit Super‐Time‐Stepping Scheme For Non‐Symmetric Parabolic Problems, Stephen O'Sullivan, Katharine Gurski

Conference papers

Explicit numerical methods for the solution of a system of differential equations may suffer from a time step size that approaches zero in order to satisfy stability conditions. When the differential equations are dominated by a skew-symmetric component, the problem is that the real eigenvalues are dominated by imaginary eigenvalues. We compare results for stable time step limits for the super-time-stepping method of Alexiades, Amiez, and Gremaud (super-time-stepping methods belong to the Runge-Kutta-Chebyshev class) and a new method modeled on a predictor-corrector scheme with multiplicative operator splitting. This new explicit method increases stability of the original super-time-stepping whenever the skew-symmetric …

Diffeomorphic Approximation Of Sobolev Homeomorphisms, Tadeusz Iwaniec, Leonid V. Kovalev, Jani Onninen

Mathematics - All Scholarship

Every homeomorphism h: X -> Y between planar open sets that belongs to the Sobolev class W^1;p(X;Y), 1 < p < 1, can be approximated in the Sobolev norm by C^infinity -smooth dieomorphisms.

Schrödinger Dispersive Dstimates For A Dcaling-Critical Class Of Potentials, Marius Beceanu, Michael Goldberg

Mathematics and Statistics Faculty Scholarship

Consider the focussing cubic nonlinear Schr\"odinger equation in R 3 :

iψ t +Δψ=−|ψ| 2 ψ.

It admits special solutions of the form e itα ϕ , whereϕ is a Schwartz function and a positive (ϕ>0 ) solution of

−Δϕ+αϕ=ϕ 3 .

The space of all such solutions, together with those obtained from them by rescaling and applying phase and Galilean coordinate changes, called standing waves, is the eight-dimensional manifold that consists of functions of the form e i(v⋅+Γ) ϕ(⋅−y,α) . We prove that any solution starting sufficiently close to a standing wave in the Σ=W 1,2 (R 3 …

Bioinformatics Across The Sciences, Nigel Yarlett

Cornerstone 3 Reports : Interdisciplinary Informatics

No abstract provided.

Zeons, Lattices Of Partitions, And Free Probability, René Schott, G Stacey Staples

Communications on Stochastic Analysis

No abstract provided.

A Finite Element Method For Martingale-Driven Stochastic Partial Differential Equations, Andrea Barth

Communications on Stochastic Analysis

No abstract provided.

Solutions Of Semilinear Wave Equation Via Stochastic Cascades, Yuri Bakhtin, Carl Mueller

Communications on Stochastic Analysis

No abstract provided.

Sample Properties Of Random Fields Iii: Differentiability, Jürgen Potthoff

Communications on Stochastic Analysis

No abstract provided.

Upper Bounds On Rubinstein Distances On Configuration Spaces And Applications, Laurent Decreusefond, Aldéric Joulin, Nicolas Savy

Communications on Stochastic Analysis

No abstract provided.

Convergence Of Particle Filtering Method For Nonlinear Estimation Of Vortex Dynamics, Sivaguru S Sritharan, Meng Xu

Communications on Stochastic Analysis

No abstract provided.

Covariance Identities And Mixing Of Random Transformations On The Wiener Space, Nicolas Privault

Communications on Stochastic Analysis

No abstract provided.

The Itô Integral For A Certain Class Of Lévy Processes And Its Application To Stochastic Partial Differential Equations, Erika Hausenblas

Communications on Stochastic Analysis

No abstract provided.

Surface Measures On The Dual Space Of The Schwartz Space, S Chaari, F Cipriano, H.-H. Kuo, H Ouerdiane

Communications on Stochastic Analysis

No abstract provided.

Sufficient Conditions Of Optimality For Backward Stochastic Evolution Equations, Abdulrahman Al-Hussein

Communications on Stochastic Analysis

No abstract provided.

Coarser Connected Metrizable Topologies, Lynne Yengulalp

Mathematics Faculty Publications

We show that every metric space, X, with w(⩾) c has a coarser connected metrizable topology.

Quantitative Analysis Of Arterial Spin Labeling Fmri Data Using A General Linear Model, Luis Hernandez-Garcia, Hesamoddin Jahanian, Daniel B. Rowe

Mathematics, Statistics and Computer Science Faculty Research and Publications

Arterial spin labeling techniques can yield quantitative measures of perfusion by fitting a kinetic model to difference images (tagged-control). Because of the noisy nature of the difference images investigators typically average a large number of tagged versus control difference measurements over long periods of time. This averaging requires that the perfusion signal be at a steady state and not at the transitions between active and baseline states in order to quantitatively estimate activation induced perfusion. This can be an impediment for functional magnetic resonance imaging task experiments. In this work, we introduce a general linear model (GLM) that specifies Blood …

A Methodology For Engineering Collaborative And Ad-Hoc Mobile Applications Using Syd Middleware, Praveen Madiraju, Srilaxmi Malladi, Janaka Balasooriya, Arthi Hariharan, Sushil K. Prasad, Anu Bourgeois

Mathematics, Statistics and Computer Science Faculty Research and Publications

Today’s web applications are more collaborative and utilize standard and ubiquitous Internet protocols. We have earlier developed System on Mobile Devices (SyD) middleware to rapidly develop and deploy collaborative applications over heterogeneous and possibly mobile devices hosting web objects. In this paper, we present the software engineering methodology for developing SyD-enabled web applications and illustrate it through a case study on two representative applications: (i) a calendar of meeting application, which is a collaborative application and (ii) a travel application which is an ad-hoc collaborative application. SyD-enabled web objects allow us to create a collaborative application rapidly with limited coding …

A Class Of Models For Uncorrelated Random Variables, Nader Ebrahimi, Gholamhossein Hamedani, Ehsan S. Soofi, Hans Volkmer

Mathematics, Statistics and Computer Science Faculty Research and Publications

We consider the class of multivariate distributions that gives the distribution of the sum of uncorrelated random variables by the product of their marginal distributions. This class is defined by a representation of the assumption of sub-independence, formulated previously in terms of the characteristic function and convolution, as a weaker assumption than independence for derivation of the distribution of the sum of random variables. The new representation is in terms of stochastic equivalence and the class of distributions is referred to as the summable uncorrelated marginals (SUM) distributions. The SUM distributions can be used as models for the joint distribution …

Processing Induced Voxel Correlation In Sense Fmri Via The Ammust Framework, Daniel B. Rowe, Iain P. Bruce

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

A Numerical Study On The Propagation And Interaction Of Strongly Nonlinear Solitary Waves, Qiyi Zhou

Dissertations

We study numerically a strongly nonlinear long wave model for surface gravity waves propagating in both one and two horizontal dimensions. This model often referred to as the Su-Gardner or Green-Naghdi equations can be derived from the Euler equations under the assumption that the ratio between the characteristic wavelength and water depth is small, but no assumption on the wave amplitude is required. We first generalize the model to describe large amplitude one-dimensional solitary waves in the presence of background shear of constant vorticity. After computing the solitary wave solution of the strongly nonlinear model, the interaction between two solitary …

Computational Methods For Two-Phase Flow With Soluble Surfactant, Kuan Xu

Dissertations

A mathematical model is formulated and solved for the two-phase flow of a viscous drop or inviscid bubble in an immiscible, viscous surrounding fluid in the zero Reynold's number or Stokes flow limit. A surfactant that is present on the interface is also soluble in the exterior fluid, and the drop is deformed by an imposed linear flow. The geometry is two-dimensional and Cartesian.

The dissolved surfactant is considered in the physically realistic limit of large bulk Péclet number. That is, it convects and diffuses as a passive scalar in the bulk flow where the ratio of its convection to …

Cannon-Thurston Maps And Relative Hyperbolicity., Abhijit Pal Dr.

Doctoral Theses

Let P : Y → T be a tree of strongly relatively hyperbolic spaces such that Y is also a strongly relatively hyperbolic space. Let X be a vertex space and i : X ֒→ Y denote the inclusion. The main aim of this thesis is to extend i to a continuous map i : X → Y , where X and Y are the Gromov compactifications of X and Y respectively. Such continuous extensions are called Cannon-Thurston maps. This is a generalization of [Mit98b] which proves the existence of Cannon-Thurston maps for X and Y hyperbolic. By generalizing a …

Single And Multiobjective Approaches To Clustering With Point Symmetry., Sriparna Saha Dr.

Doctoral Theses

In our every day life, we make decisions consciously or unconsciously. This decision can be very simple such as selecting the color of dress or deciding the menu for lunch, or may be as difficult as those involved in designing a missile or in selecting a career. The former decision is easy to take, while the latter one might take several years due to the level of complexity involved in it. The main goal of most kinds of decision-making is to optimize one or more criteria in order to achieve the desired result. In other words, problems related to optimization …

Hamilton Decompositions Of 6-Regular Abelian Cayley Graphs, Erik E. Westlund

Dissertations, Master's Theses and Master's Reports - Open

In 1969, Lovasz asked whether every connected, vertex-transitive graph has a Hamilton path. This question has generated a considerable amount of interest, yet remains vastly open. To date, there exist no known connected, vertex-transitive graph that does not possess a Hamilton path. For the Cayley graphs, a subclass of vertex-transitive graphs, the following conjecture was made:

Weak Lovász Conjecture: Every nontrivial, finite, connected Cayley graph is hamiltonian.

The Chen-Quimpo Theorem proves that Cayley graphs on abelian groups flourish with Hamilton cycles, thus prompting Alspach to make the following conjecture:

Alspach Conjecture: Every 2k-regular, connected Cayley graph on a …