Applied Mathematics Commons^™

On The Relationship Between Two Notions Of Compatibility For Bi-Hamiltonian Systems, Manuele Santoprete

Mathematics Faculty Publications

Bi-Hamiltonian structures are of great importance in the theory of integrable Hamiltonian systems. The notion of compatibility of symplectic structures is a key aspect of bi-Hamiltonian systems. Because of this, a few different notions of compatibility have been introduced. In this paper we show that, under some additional assumptions, compatibility in the sense of Magri implies a notion of compatibility due to Fass`o and Ratiu, that we dub bi-affine compatibility. We present two proofs of this fact. The first one uses the uniqueness of the connection parallelizing all the Hamiltonian vector fields tangent to the leaves of a Lagrangian foliation. …

Stochastic Models For Plant Microtubule Self-Organization And Structure, Ezgi Can Eren, Ram Dixit, Natarajan Gautam

Biology Faculty Research

One of the key enablers of shape and growth in plant cells is the cortical microtubule (CMT) system, which is a polymer array that forms an appropriately-structured scaffolding in each cell. Plant biologists have shown that stochastic dynamics and simple rules of interactions between CMTs can lead to a coaligned CMT array structure. However, the mechanisms and conditions that cause CMT arrays to become organized are not well understood. It is prohibitively time-consuming to use actual plants to study the effect of various genetic mutations and environmental conditions on CMT self-organization. In fact, even computer simulations with multiple replications are …

Existence Of Homoclinic Solutions For Second Order Difference Equations With P-Laplacian, John R. Graef, Lingju Kong, Min Wang

College of Science & Mathematics Departmental Research

Using the variational method and critical point theory, the authors study the existence of infinitely many homoclinic solutions to the difference equation described in the paper.

Filters And Matrix Factorization, Myung-Sin Song, Palle E. T. Jorgensen

SIUE Faculty Research, Scholarship, and Creative Activity

We give a number of explicit matrix-algorithms for analysis/synthesis

in multi-phase filtering; i.e., the operation on discrete-time signals which

allow a separation into frequency-band components, one for each of the

ranges of bands, say N , starting with low-pass, and then corresponding

filtering in the other band-ranges. If there are N bands, the individual

filters will be combined into a single matrix action; so a representation of

the combined operation on all N bands by an N x N matrix, where the

corresponding matrix-entries are periodic functions; or their extensions to

functions of a complex variable. Hence our setting entails …

From Subcompact To Domain Representable, William Fleissner, Lynne Yengulalp

Mathematics Faculty Publications

No abstract provided.

Partial Covariance Based Functional Connectivity Computation Using Ledoit-Wolf Covariance Regularization, Matthew R. Brier, Anish Mitra, John E. Mccarthy, Beau M. Ances, Abraham Z. Snyder

Mathematics Faculty Research

Highlights •We use the well characterized matrix regularization technique described by Ledoit and Wolf to calculate high dimensional partial correlations in fMRI data. •Using this approach we demonstrate that partial correlations reveal RSN structure suggesting that RSNs are defined by widely and uniquely shared variance. •Partial correlation functional connectivity is sensitive to changes in brain state indicating that they contain functional information. Functional connectivity refers to shared signals among brain regions and is typically assessed in a task free state. Functional connectivity commonly is quantified between signal pairs using Pearson correlation. However, resting-state fMRI is a multivariate process exhibiting a …

Local And Distributed Pib Accumulation Associated With Development Of Preclinical Alzheimer's Disease, Matthew R. Brier, John E. Mccarthy, Tammie L.S. Benzinger, Ari Stern, Yi Su, Karl A. Friedrichsen, John C. Morris, Beau M. Ances, Andrei G. Vlassenko

Mathematics Faculty Research

Amyloid-beta plaques are a hallmark of Alzheimer's disease (AD) that can be assessed by amyloid imaging (e.g., Pittsburgh B compound [PiB]) and summarized as a scalar value. Summary values may have clinical utility but are an average over many regions of interest, potentially obscuring important topography. This study investigates the longitudinal evolution of amyloid topographies in cognitively normal older adults who had normal (N = 131) or abnormal (N = 26) PiB scans at baseline. At 3 years follow-up, 16 participants with a previously normal PiB scan had conversion to PiB scans consistent with preclinical AD. We investigated the multivariate …

Algebraic Complexity Theory, Jerzy Weyman

Dalrymple Lecture Series

I will discuss the basic notions related to the complexity theory. The classes of P and NP problems will be defined, with examples given. Besides discussing the statements of the problems, I will talk about the effectiveness of algorithms used in linear algebra (multiplying matrices and solving the systems of linear equations). No previous knowledge of complexity theory will be assumed, however some knowledge of linear algebra (matrices and their multiplication) will be needed.

A Nonlinear Splitting Algorithm For Systems Of Partial Differential Equations With Self-Diffusion, Matthew Beauregard, Joshua L. Padgett, Rana D. Parshad

Faculty Publications

Systems of reaction-diffusion equations are commonly used in biological models of food chains. The populations and their complicated interactions present numerous challenges in theory and in numerical approximation. In particular, self-diffusion is a nonlinear term that models overcrowding of a particular species. The nonlinearity complicates attempts to construct efficient and accurate numerical approximations of the underlying systems of equations. In this paper, a new nonlinear splitting algorithm is designed for a partial differential equation that incorporates self diffusion. We present a general model that incorporates self-diffusion and develop a numerical approximation. The numerical analysis of the approximation provides criteria for …

Geometric Approach To Convex Subdifferential Calculus, Boris S. Mordukhovich, Nguyen Mau Nam

Mathematics and Statistics Faculty Publications and Presentations

In this paper, we develop a geometric approach to convex subdifferential calculus in finite dimensions with employing some ideas of modern variational analysis. This approach allows us to obtain natural and rather easy proofs of basic results of convex subdifferential calculus in full generality and also derive new results of convex analysis concerning optimal value/marginal functions, normals to inverse images of sets under set-valued mappings, calculus rules for coderivatives of single-valued and set-valued mappings, and calculating coderivatives of solution maps to parameterized generalized equations governed by set-valued mappings with convex graphs.

Using An Agent-Based Model To Study The Effect Of Reproductive Skew On Mongoose Populations, Stacy Lee Mowry

Theses and Dissertations

Reproductive skew is the name given to the unequal partitioning of breeding

within social groups. Within these groups a mating hierarchy emerges wherein one dominant mating pair holds an unproportional majority of the group's reproductive benefit, while other members mate infrequently, yet allocate energy and resources toward the offspring of the dominant group members. In this paper, we use an agent-based model, which mimics dwarf and banded mongoose populations, to investigate how reproductive skew aftects the speed natural selection, and thus how reproductive skew affects fitness. The results of the model show that due to the geometric structure of skewed …

Comparison Of Fecal Microbiota In Children With Autism Spectrum Disorders And Neurotypical Siblings In The Simons Simplex Collection, Joshua S. Son, Ling J. Zheng, Leahana M. Rowehl, Ellen Li, Xinyu Tian, Yuanhao Zhang, Wei Zhu, Leighann Litcher-Kelly, Kenneth D. Gadow, Grace Gathungu, Charles E. Robertson, Diana Ir, Daniel N. Frank

Department of Applied Mathematics & Statistics Faculty Publications

In order to assess potential associations between autism spectrum disorder (ASD) phenotype, functional GI disorders and fecal microbiota, we recruited simplex families, which had only a single ASD proband and neurotypical (NT) siblings, through the Simons Simplex Community at the Interactive Autism Network (SSC@IAN). Fecal samples and metadata related to functional GI disorders and diet were collected from ASD probands and NT siblings of ASD probands (age 7–14). Functional gastrointestinal disorders (FGID) were assessed using the parent-completed ROME III questionnaire for pediatric FGIDs, and problem behaviors were assessed using the Child Behavior Check List (CBCL). Targeted quantitative polymerase chain reaction …

Congruent Visual Speech Enhances Entrainment To Continuous Auditory Speech In Noise-Free Conditions, Michael Crosse, John S. Butler, Edmumd Lalor

Articles

Congruent audiovisual speech enhances our ability to comprehend a speaker, even in noise-free conditions. When incongruent auditory and visual information is presented concurrently, it can hinder a listener’s perception and even cause him or her to perceive information that was not presented in either modality. Efforts to investigate the neural basis of these effects have often focused on the special case of discrete audiovisual syllables that are spatially and temporally congruent, with less work done on the case of natural, continuous speech. Recent electrophysiological studies have demonstrated that cortical response measures to continuous auditory speech can be easily obtained using …

Local Characterization Of A Class Of Ruled Hypersurfaces In C2, Michael Bolt

University Faculty Publications and Creative Works

Let M3⊂C2 be a three times differentiable real hypersurface. The Levi form of M transforms under biholomorphism, and when restricted to the complex tangent space, the skew-hermitian part of the second fundamental form transforms under fractional linear transformation. The surfaces for which these forms are constant multiples of each other were identified in previous work, but when the constant had unit modulus there was a global requirement. Here we give a local characterization of hypersurfaces for which the constant has unit modulus.

Pattern Formation Of Elastic Waves And Energy Localization Due To Elastic Gratings, A. Berezovski, J. Engelbrecht, Mihhail Berezovski

Publications

Elastic wave propagation through diffraction gratings is studied numerically in the plane strain setting. The interaction of the waves with periodically ordered elastic inclusions leads to a self-imaging Talbot effect for the wavelength equal or close to the grating size. The energy localization is observed at the vicinity of inclusions in the case of elastic gratings. Such a localization is absent in the case of rigid gratings.

Wright State University Math And Statistics Department History, Joanne Dombrowski, David Miller

Mathematics and Statistics Faculty Publications

No abstract provided.

A Nonlinear Filter For Markov Chains And Its Effect On Diffusion Maps, Stefan Steinerberger

Yale Day of Data

Diffusion maps are a modern mathematical tool that helps to find structure in large data sets - we present a new filtering technique that is based on the assumption that errors in the data are intrinsically random to isolate and filter errors and thus boost the efficiency of diffusion maps. Applications include data sets from medicine (the Cleveland Heart Disease Data set and the Wisconsin Breast Cancer Data set) and engineering (the Ionosphere data set).

A Machine Learning Approach To Post-Market Surveillance Of Medical Devices, Jonathan Bates, Shu-Xia Li, Craig Parzynski, Ronald Coifman, Harlan Krumholz, Joseph Ross

Yale Day of Data

Post-market surveillance is a collection of processes and activities used by product manufacturers and regulators, such as the U.S. Food and Drug Administration (FDA) to monitor the safety and effectiveness of medical devices once they are available for use “on the market”. These activities are designed to generate information to identify poorly performing devices and other safety problems, accurately characterize real-world device performance and clinical outcomes, and facilitate the development of new devices, or new uses for existing devices. Typically, a device is monitored by comparing adverse events in the exposed population to a matched unexposed population. This research considers …

Factors Affecting Dimensional Precision Of Consumer 3d Printing, David D. Hernandez

International Journal of Aviation, Aeronautics, and Aerospace

This paper investigates the factors affecting dimensional precision of consumer-grade 3D printing, attempting to isolate and mitigate sources of error. The focus is on creating engineering prototypes of, tooling for, or finalized instances of mechanical devices. A specific fused deposition modeling printer – the Ultimaker 2 – is analyzed in terms of meeting precise physical dimensions, consistent shapes, and predictable surface finish. Extensive trial and error resulted in removal of several sources of bias, with square test articles exhibiting a lower-than-anticipated mean percentage error of -0.387% (SD = 0.559), a value comparable to other modern manufacturing techniques. A full …

Testing The Adequacy Of A Semi-Markov Process, Richard S. Seymour

Theses and Dissertations

Due to the versatility of its structure, the semi-Markov process is a powerful modeling tool used to describe complex systems. Though similar in structure to continuous time Markov chains, semi-Markov processes allow for any transition time distribution which enables these processes to t a wider range of problems than the continuous time Markov chain. While semi-Markov processes have been applied in fields as varied as biostatistics and finance, there does not exist a theoretically-based, systematic method to determine if a semi-Markov process accurately fits the underlying data used to create the model. In fields such as regression and analysis of …

Modeling Radiation Effectiveness For Inactivation Of Bacillus Spores, Emily A. Knight

Theses and Dissertations

This research models and analyzes the inactivation of Bacillus spores following a radiation exposure and the process enacted by the Bacillus spore to repair the resulting damage. Irradiation of a spore and the medium surrounding the spore induces chemical reactions that produce reactive oxygen species (ROS). This research will consider the reaction- diffusion of these ROS throughout the spore. These ROS can react with the spore's DNA and enzymes to degrade them to such an extent that the DNA cannot be repaired or replicated, thus causing spore death. In order to survive a dose of radiation, a spore must repair …

Art, Math, And Physics; All About For, Chris Brownell, Steve Pauls

The Transdisciplinary STEAM+ Journal

Anish Kapoor’s public sculpture “Cloud Gate” and Frame of Reference.

Wall Mechanical Properties And Hemodynamics Of Unruptured Intracranial Aneurysms, J. R. Cebral, X. Duan, Bong Jae Chung, C. Putman, Khaled Aziz, A. M. Robertson

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

BACKGROUND AND PURPOSE: Aneurysm progression and rupture is thought to be governed by progressive degradation and weakening of the wall in response to abnormal hemodynamics. Our goal was to investigate the relationship between the intra-aneurysmal hemodynamic conditions and wall mechanical properties in human aneurysms. MATERIALS AND METHODS: A total of 8 unruptured aneurysms were analyzed. Computational fluid dynamics models were constructed from preoperative 3D rotational angiography images. The aneurysms were clipped, and the domes were resected and mechanically tested to failure with a uniaxial testing system under multiphoton microscopy. Linear regression analysis was performed to explore possible correlations between hemodynamic …

Construction Of Nonlinear Expression For Recursive Number Sequences, Tian-Xiao He

Scholarship

A type of nonlinear expressions of Lucas sequences are established inspired by Hsu [9]. Using the relationships between the Lucas sequence and other linear recurring sequences satisfying the same recurrence relation of order 2, we may transfer the identities of Lucas sequences to the latter.

Per-Contact Infectivity Of Hcv Associated With Injection Exposures In A Prospective Cohort Of Young Injection Drug Users In San Francisco, Ca (Ufo Study), Yuridia Leyva

Mathematics & Statistics ETDs

Sharing needles and ancillary injection drug equipment places injection drug users (IDU) at risk for Hepatitis C Virus (HCV), a highly infectious blood-borne virus. A limited number of studies have analyzed the per-contact infectivity of HCV associated with the use of previously-used needles, but per-contact infectivity of ancillary injecting equipment has not been previously investigated. Our goal is to estimate the per-contact infectivity of HCV associated with (1) injecting with another person's previously-used needle, classified as receptive needle sharing (RNS), and (2) using another person's previously-used ancillary injecting equipment, such as cookers to melt drugs and cottons to strain impurities …

Transients Of Platoons With Asymmetric And Different Laplacians, Ivo Herman, Dan Martinec, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

We consider an asymmetric control of platoons of identical vehicles with nearest-neighbor interaction. Recent results show that if the vehicle uses different asymmetries for position and velocity errors, the platoon has a short transient and low overshoots. In this paper we investigate the properties of vehicles with friction. To achieve consensus, an integral part is added to the controller, making the vehicle a third-order system. We show that the parameters can be chosen so that the platoon behaves as a wave equation with different wave velocities. Simulations suggest that our system has a better performance than other nearest-neighbor scenarios. Moreover, …

Numerical Solutions Of Generalized Burgers' Equations For Some Incompressible Non-Newtonian Fluids, Yupeng Shu

LSU New Orleans Theses and Dissertations

The author presents some generalized Burgers' equations for incompressible and isothermal flow of viscous non-Newtonian fluids based on the Cross model, the Carreau model, and the Power-Law model and some simple assumptions on the flows. The author numerically solves the traveling wave equations for the Cross model, the Carreau model, the Power-Law model by using industrial data. The author proves existence and uniqueness of solutions to the traveling wave equations of each of the three models. The author also provides numerical estimates of the shock thickness as well as maximum strain $\varepsilon_{11}$ for each of the fluids.

A Framework For Inferring Unobserved Multistrain Epidemic Subpopulations Using Synchronization Dynamics, Eric Forgoston, Leah B. Shaw, Ira B. Schwartz

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

A new method is proposed to infer unobserved epidemic subpopulations by exploiting the synchronization properties of multistrain epidemic models. A model for dengue fever is driven by simulated data from secondary infective populations. Primary infective populations in the driven system synchronize to the correct values from the driver system. Most hospital cases of dengue are secondary infections, so this method provides a way to deduce unobserved primary infection levels. We derive center manifold equations that relate the driven system to the driver system and thus motivate the use of synchronization to predict unobserved primary infectives. Synchronization stability between primary and …

Simulating And Animating The Spatial Dynamics Of Interacting Species Living On A Torus, Boyan Kostadinov

Publications and Research

The goal of this talk is to present a student research project in computational population biology, which aims at creating a computer simulation and animation of the spatial dynamics of interactions between two kinds of species living on a torus-shaped universe. The habitat for spatial interactions is modeled by a 2D lattice with periodic boundary conditions, which wrap the rectangular grid into a torus. The spatial interactions between the species have two components: 1. Population dynamics modeled by the classical Nicholson-Bailey two-parameter family of models for coupled interactions between species, extended to incorporate space and 2. Two-parameter migration dynamics, modeled …

Spontaneous Synchrony On Graphs And The Emergence Of Order From Disorder, Dylan Linville, Daniel Trugillo Martins Fontes

Mathematical Sciences Technical Reports (MSTR)

From pulsars to pedestrians and bacteria to brain cells, objects that exhibit cyclical behavior, called oscillators, are found in a variety of different settings. When oscillators adjust their behavior in response to nearby oscillators, they often achieve a state of synchrony, in which they all have the same phase and frequency. Here, we explore the Kuramoto model, a simple and general model which describes oscillators as dynamical systems on a graph and has been used to study synchronization in systems ranging from firefly swarms to the power grid. We discuss analytical and numerical methods used to investigate the governing system …