Physical Sciences and Mathematics Commons^™

When Cp(X) Is Domain Representable, William Fleissner, Lynne Yengulalp

Lynne Yengulalp

Let M be a metrizable group. Let G be a dense subgroup of M^X . If G is domain representable, then G = MX . The following corollaries answer open questions. If X is completely regular and C_p(X) is domain representable, then X is discrete. If X is zero-dimensional, T₂ , and C_p(X;D) is subcompact, then X is discrete.

Sphere Representations, Stacked Polytopes, And The Colin De Verdière Number Of A Graph, Lon Mitchell, Lynne Yengulalp

Lynne Yengulalp

We prove that a k-tree can be viewed as a subgraph of a special type of (k + 1)- tree that corresponds to a stacked polytope and that these “stacked” (k + 1)-trees admit representations by orthogonal spheres in R k+1. As a result, we derive lower bounds for Colin de Verdi`ere’s µ of complements of partial k-trees and prove that µ(G) + µ(G) > |G| − 2 for all chordal G.

Coarser Connected Topologies And Non-Normality Points, Lynne Yengulalp

Lynne Yengulalp

We investigate two topics, coarser connected topologies and non-normality points. The motivating question in the first topic is:

Question 0.0.1. When does a space have a coarser connected topology with a nice topological property? We will discuss some results when the property is Hausdorff and prove that if X is a non-compact metric space that has weight at least c, then it has a coarser connected metrizable topology. The second topic is concerned with the following question:

Question 0.0.2. When is a point y ∈ β X\X a non-normality point of β X\X? We will discuss the question in the …

Non-Normality Points Of Β X\X, William Fleissner, Lynne Yengulalp

Lynne Yengulalp

We seek conditions implying that (β X\X) \ {y} is not normal. Our main theorem: Assume GCH and all uniform ultrafilters are regular. If X is a locally compact metrizable space without isolated points, then (β X\X) \ {y} is not normal for all y ∈ β X\X. In preparing to prove this theorem, we generalize the notions “uniform”, “regular”, and “good” from set ultrafilters to z-ultrafilters. We discuss non-normality points of the product of a discrete space and the real line. We topologically embed a nonstandard real line into the remainder of this product space.

Differences In Hemodynamics And Rupture Rate Of Aneurysms At The Bifurcation Of The Basilar And Internal Carotid Arteries, Ravi Doddasomayajula, Bong Jae Chung, Farid Hamzei-Sichani, Christopher M. Putman, Juan Cebral

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

BACKGROUND AND PURPOSE: Cerebral aneurysms in the posterior circulation are known to have a higher rupture risk than those in the anterior circulation. We sought to test the hypothesis that differences in hemodynamics can explain the difference in rupture rates.

MATERIALS AND METHODS: A total of 117 aneurysms, 63 at the tip of the basilar artery (27 ruptured, 36 unruptured, rupture rate = 43%) and 54 at the bifurcation of the internal carotid artery (11 ruptured, 43 unruptured, rupture rate = 20%) were analyzed with image-based computational fluid dynamics. Several hemodynamic variables were compared among aneurysms at each location and …

A Discontinuous Galerkin Method For Unsteady Two-Dimensional Convective Flows, Andreas C. Aristotelous, N. C. Papanicolaou

Andreas Aristotelous

We develop a High-Order Symmetric Interior Penalty (SIP) Discontinuous Galerkin (DG) Finite Element Method (FEM) to investigate two-dimensional in space natural convective flows in a vertical cavity. The physical problem is modeled by a coupled nonlinear system of partial differential equations and admits various solutions including stable and unstable modes in the form of traveling and/or standing waves, depending on the governing parameters. These flows are characterized by steep boundary and internal layers which evolve with time and can be well-resolved by high-order methods that also are adept to adaptive meshing. The standard no-slip boundary conditions which apply on the …

The Subject Librarian Newsletter, Mathematics, Spring 2017, Sandy Avila

Libraries' Newsletters

No abstract provided.

Utilizing Social Network Analysis To Study Communities Of Women In Conflict Zones, James R. Gatewood, Candice R. Price

Journal of Humanistic Mathematics

This article proposes to study the plight of women in conflict zones through the lens of social network analysis. We endorse the novel idea of building a social network within troubled regions to assist in understanding the structure of women's communities and identifying key individuals and groups that will help rebuild and empower the lives of women. Our main argument is that we can better understand the complexity of a society with quantitative measures using a network analysis approach. Given the foundation of this paper, one can develop a model that will represent the connections between women in these communities. …

Metastable States In Terminal Orientation Of Hinged Symmetric Bodies In A Flow, Doralia Castillo, Bong Jae Chung, Klaus Schnitzer, Karina Soriano, Haiyan Su, Ashuwin Vaidya

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Symmetric bodies such as cylinders and spheroidal bodies, in their terminal stable states, are long known to have their long axis align themselves perpendicular to the direction of the flow. This property has been confirmed in primarily sedimentation based theoretical, experimental and numerical techniques and the transition to a terminal stable state is believed to coincide with the onset of significant inertial effects in the flow. However, the threshold at which this transition occurs is yet unknown. We conduct modified experiments with hinged bodies and a CFD study to examine the nature of the transition of prolate spheroids and cylinders …

Application Of An Rbf Blending Interpolation Method To Problems With Shocks, Michael Harris, Eduardo Divo, Alain J. Kassab

Publications

Radial basis functions (RBF) have become an area of research in recent years, especially in the use of solving partial differential equations (PDE). Radial basis functions have an impressive capability in interpolating scattered data, even for data with discontinuities. Although, for infinitely smooth radial basis functions such as the multi-quadrics and inverse multi-quadrics, the shape parameter must be chosen properly to obtain accurate approximations while avoiding ill-conditioning of the interpolating matrices. The optimum shape parameter can vary depending on the field, such as in locations of sharp gradients or shocks. Typically, the shape parameter is chosen to maintain a high …

Global Stability Of Nonlinear Stochastic Sei Epidemic Model With Fluctuations In Transmission Rate Of Disease, Olusegun M. Otunuga

Olusegun Michael Otunuga

On The Three Dimensional Interaction Between Flexible Fibers And Fluid Flow, Bogdan Nita, Ryan Allaire

Department of Mathematics Facuty Scholarship and Creative Works

In this paper we discuss the deformation of a flexible fiber clamped to a spherical body and immersed in a flow of fluid moving with a speed ranging between 0 and 50 cm/s by means of three dimensional numerical simulation developed in COMSOL . The effects of flow speed and initial configuration angle of the fiber relative to the flow are analyzed. A rigorous analysis of the numerical procedure is performed and our code is benchmarked against well established cases. The flow velocity and pressure are used to compute drag forces upon the fiber. Of particular interest is the behavior …

Extracting Geography From Datasets In Social Sciences, Yuke Li, Tianhao Wu, Nicholas Marshall, Stefan Steinerberger

Yale Day of Data

No abstract provided.

Steady State Probabilities In Relation To Eigenvalues, Pellegrino Christopher

The Kabod

By using the methods of Hamdy Taha, eigenvectors can be used in solving problems to compute steady state probabilities, and they work every time.

Modified Error In Constitutive Equations (Mece) Approach For Ultrasound Elastography

Susanta Ghosh

No abstract provided.

Numerical Simulation Of Acoustic Emission During Crack Growth In 3-Point Bending Test, Mihhail Berezovski, Arkadi Berezovski

Publications

Numerical simulation of acoustic emission by crack propagation in 3-point bending tests is performed to investigate how the interaction of elastic waves generates a detectable signal. It is shown that the use of a kinetic relation for the crack tip velocity combined with a simple crack growth criterion provides the formation of waveforms similar to those observed in experiments.

Eigenvalue Dependence Of Numerical Oscillations In Parabolic Partial Differential Equations, R. Corban Harwood

Faculty Publications - Department of Mathematics

This paper investigates oscillation-free stability conditions of numerical methods for linear parabolic partial differential equations with some example extrapolations to nonlinear equations. Not clearly understood, numerical oscillations can create infeasible results. Since oscillation-free behavior is not ensured by stability conditions, a more precise condition would be useful for accurate solutions. Using Von Neumann and spectral analyses, we find and explore oscillation-free conditions for several finite difference schemes. Further relationships between oscillatory behavior and eigenvalues is supported with numerical evidence and proof. Also, evidence suggests that the oscillation-free stability condition for a consistent linearization may be sufficient to provide oscillation-free stability …

Steady And Stable: Numerical Investigations Of Nonlinear Partial Differential Equations, R. Corban Harwood

Faculty Publications - Department of Mathematics

Excerpt: "Mathematics is a language which can describe patterns in everyday life as well as abstract concepts existing only in our minds. Patterns exist in data, functions, and sets constructed around a common theme, but the most tangible patterns are visual. Visual demonstrations can help undergraduate students connect to abstract concepts in advanced mathematical courses. The study of partial differential equations, in particular, benefits from numerical analysis and simulation."

Joint Hierarchical Models For Sparsely Sampled High-Dimensional Lidar And Forest Variables, Andrew O. Finley, Sudipto Banerjee, Yuzhen Zhou, Bruce D. Cook, Chad Babcock

United States National Aeronautics and Space Administration: Publications

Recent advancements in remote sensing technology, specifically Light Detection and Ranging (LiDAR) sensors, provide the data needed to quantify forest characteristics at a fine spatial resolution over large geographic domains. From an inferential standpoint, there is interest in prediction and interpolation of the often sparsely sampled and spatially misaligned LiDAR signals and forest variables. We propose a fully process-based Bayesian hierarchical model for above ground biomass (AGB) and LiDAR signals. The processbased framework offers richness in inferential capabilities, e.g., inference on the entire underlying processes instead of estimates only at pre-specified points. Key challenges we obviate include misalignment between the …

A Two-Species Stage-Structured Model For West Nile Virus Transmission, Taylor A. Beebe, Suzanne L. Robertson

Mathematics and Applied Mathematics Publications

We develop a host–vector model of West Nile virus (WNV) transmission that incorporates multiple avian host species as well as host stage-structure (juvenile and adult stages), allowing for both species-specific and stage-specific biting rates of vectors on hosts. We use this ordinary differential equation model to explore WNV transmission dynamics that occur between vectors and multiple structured host populations as a result of heterogeneous biting rates on species and/or life stages. Our analysis shows that increased exposure of juvenile hosts generally results in larger outbreaks of WNV infectious vectors when compared to differential host species exposure. We also find that …

A Theoretical Framework For Analyzing Coupled Neuronal Networks: Application To The Olfactory System, Andrea K. Barreiro, Shree Hari Gautam, Woodrow L. Shew, Cheng Ly

Mathematics and Applied Mathematics Publications

Determining how synaptic coupling within and between regions is modulated during sensory processing is an important topic in neuroscience. Electrophysiological recordings provide detailed information about neural spiking but have traditionally been confined to a particular region or layer of cortex. Here we develop new theoretical methods to study interactions between and within two brain regions, based on experimental measurements of spiking activity simultaneously recorded from the two regions. By systematically comparing experimentally-obtained spiking statistics to (efficiently computed) model spike rate statistics, we identify regions in model parameter space that are consistent with the experimental data. We apply our new technique …

On Some Impulse Control Problems With Constraint, Jose L. Menaldi, Maurice Robin

Mathematics Faculty Research Publications

The impulse control of a Markov–Feller process is considered when the impulses are allowed only when a signal arrives. This is referred to as an impulse control problem with constraint. A detailed setting is described, a characterization of the optimal cost is obtained using previous results of the authors on optimal stopping problems with constraint, and an optimal impulse control is identified.

C.V. - Wojciech Budzianowski, Wojciech M. Budzianowski

Wojciech Budzianowski

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Renewable Energy And Sustainable Development (Resd) Group, Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.

Solitary Wave Solution Of Flat Surface Internal Geophysical Waves With Vorticity, Alan Compelli

Conference papers

A fluid system bounded by a flat bottom and a flat surface with an internal wave and depth-dependent current is con-sidered. The Hamiltonian of the system is presented and the dynamics of the system are discussed. A long-wave regime is then considered and extended to produce a KdV approximation. Finally, a solitary wave solution is obtained.

Weihrauch Reducibility And Finite-Dimensional Subspaces, Sean Sovine

Theses, Dissertations and Capstones

In this thesis we study several principles involving subspaces and decompositions of vector spaces, matroids, and graphs from the perspective of Weihrauch reducibility. We study the problem of decomposing a countable vector space or countable matroid into 1-dimensional subspaces. We also study the problem of producing a finite-dimensional or 1-dimensional subspace of a countable vector space, and related problems for producing finite-dimensional subspaces of a countable matroid. This extends work in the reverse mathematics setting by Downey, Hirschfeldt, Kach, Lempp, Mileti, and Montalb´an (2007) and recent work of Hirst and Mummert (2017). Finally, we study the problem of producing a …

Eigenvector Centrality: Illustrations Supporting The Utility Of Extracting More Than One Eigenvector To Obtain Additional Insights Into Networks And Interdependent Structures, Dawn Iacobucci, Rebecca Mcbride, Deidre L. Popovich

University Faculty Publications and Creative Works

Among the many centrality indices used to detect structures of actors’ positions in networks is the use of the first eigenvector of an adjacency matrix that captures the connections among the actors. This research considers the seeming pervasive current practice of using only the first eigenvector. It is shows that, as in other statistical applications of eigenvectors, subsequent vectors can also contain illuminating information. Several small examples, and Freeman’s EIES network, are used to illustrate that while the first eigenvector is certainly informative, the second (and subsequent) eigenvector(s) can also be equally tractable and informative.

Gene Expression Noise Enhances Robust Organization Of The Early Mammalian Blastocyst, William R. Holmes, Nabora Soledad Reyes De Mochel, Qixuan Wang, Huijing Du, Tao Peng, Michael Chiang, Olivier Cinquin, Ken Cho, Qing Nie

Department of Mathematics: Faculty Publications

A critical event in mammalian embryo development is construction of an inner cell mass surrounded by a trophoectoderm (a shell of cells that later form extraembryonic structures). We utilize multi-scale, stochastic modeling to investigate the design principles responsible for robust establishment of these structures. This investigation makes three predictions, each supported by our quantitative imaging. First, stochasticity in the expression of critical genes promotes cell plasticity and has a critical role in accurately organizing the developing mouse blastocyst. Second, asymmetry in the levels of noise variation (expression fluctuation) of Cdx2 and Oct4 provides a means to gain the benefits of …

A Wasserstein Gradient Flow Approach To Poisson-Nernst-Planck Equations, David Kinderlehrer, Leinard Monsaingeon, Xiang Xu

Mathematics & Statistics Faculty Publications

The Poisson-Nernst-Planck system of equations used to model ionic transport is interpreted as a gradient flow for the Wasserstein distance and a free energy in the space of probability measures with finite second moment. A variational scheme is then set up and is the starting point of the construction of global weak solutions in a unified framework for the cases of both linear and non-linear diffusion. The proof of the main results relies on the derivation of additional estimates based on the flow interchange technique developed by Matthes et al. in [D. Matthes, R.J. McCann and G. Savare, Commun. Partial …

On A Time Domain Boundary Integral Equation Formulation For Acoustic Scattering By Rigid Bodies In Uniform Mean Flow, Fang Q. Hu, Michelle E. Pizzo, Douglas M. Nark

Mathematics & Statistics Faculty Publications

It has been well-known that under the assumption of a uniform mean flow, the acoustic wave propagation equation can be formulated as a boundary integral equation. However, the constant mean flow assumption, while convenient for formulating the integral equation, does not satisfy the solid wall boundary condition wherever the body surface is not aligned with the assumed uniform flow. A customary boundary condition for rigid surfaces is that the normal acoustic velocity be zero. In this paper, a careful study of the acoustic energy conservation equation is presented that shows such a boundary condition would in fact lead to source …