Mathematics Commons^™

The Geometry Of Spacetime And Its Singular Nature, Filip Dul

Honors Scholar Theses

One hundred years ago, Albert Einstein revolutionized our understanding of gravity, and thus the large-scale structure of spacetime, by implementing differential geometry as the pri- mary medium of its description, thereby condensing the relationship between mass, energy and curvature of spacetime manifolds with the Einstein field equations (EFE), the primary compo- nent of his theory of General Relativity. In this paper, we use the language of Semi-Riemannian Geometry to examine the Schwarzschild and the Friedmann-Lemaˆıtre-Robertson-Walker met- rics, which represent some of the most well-known solutions to the EFE. Our investigation of these metrics will lead us to the problem of …

The Power Of Two: Two Tips For Mathematicians, Gizem Karaali

Pomona Faculty Publications and Research

This post is about two great tips involving the number 2 that I learned along the way. They will perhaps not double your happiness or fortune, but I promise you that you will not regret it if you do decide to take them along for the ride.

Cognitive And Behavioral Deficits Arising From Neurodegeneration And Traumatic Brain Injury: A Model For The Underlying Role Of Focal Axonal Swellings In Neuronal Networks With Plasticity, Samuel Rudy, Pedro D. Maia, J. Nathan Kutz

Mathematics Faculty Publications - Archive

Neurodegenerative diseases and traumatic brain injury, whose hallmark features are the presence of focal axonal swellings (FAS), are leading causes of cognitive dysfunction. By leveraging biophysical observations of FAS statistics, we develop a theoretical model of functional neural network activity driven by adaptive changes from plasticity. Based upon the FORCE model of Sussillo and Abbott [1], our innovations highlight the role of plasticity in overcoming injuries and degeneration of neurons in a network architecture. We provide a quantitative measure, on a network level, of cognitive deficits arising from injury. We demonstrate that plasticity is capable of overcoming mild injuries while …

Inference On Time-To-Event Distribution From Retrospective Data With Imperfect Recall., Sedigheh Salehabadi Dr.

Doctoral Theses

Time-to-event data arises from measurements of time till the occurrence of an event of interest. Such data are common in the fields of biology, epidemiology, pub- lic health, medical research, economics and industry. The event of interest can be the death of a human being (Klein and Moeschberger, 2003), failure of a machine (Zhiguo et al., 2007), onset of menarche in adolescent and young adult females (Bergsten-Brucefors, 1976; Chumlea et al., 2003; Mirzaei, Sengupta and Das, 2015), onset (or relapse) of a disease (Klein and Moeschberger, 2003), dental develop- ment (Demirjian, Goldstien and Tanner, 1973; Eveleth and Tanner, 1990), breast …

Introduction To The Early Development Of Mathematics (Book Review), Calvin Jongsma

Faculty Work Comprehensive List

Reviewed Title: An Introduction to the Early Development of Mathematics by Michael K. J. Goodman. Wiley, 2016. 233 pp. ISBN: 9781119104971.

Sources And Characteristics Of Medium-Scale Traveling Ionospheric Disturbances Observed By High-Frequency Radars In The North American Sector, N. A. Frissell, J. B. H. Baker, J. M. Ruohoniemi, R. A. Greenwald, A. J. Gerrard, E. S. Miller, M. L. West

Department of Mathematics Faculty Scholarship and Creative Works

Medium-scale traveling ionospheric disturbances (MSTIDs) are wave-like ionospheric perturbations routinely observed by high-frequency radars. We focus on a class of MSTIDs observed during the winter daytime at high latitudes and midlatitudes. The source of these MSTIDs remains uncertain, with the two primary candidates being space weather and lower atmospheric processes. We surveyed observations from four high-latitude and six midlatitude Super Dual Auroral Radar Network radars in the North American sector from November to May 2012 to 2015. The MSTIDs observed have horizontal wavelengths between ∼150 and 650 km and horizontal velocities between ∼75 and 325 m s−1. In local fall …

Gut Microbial Metabolite Tmao Enhances Platelet Hyperreactivity And Thrombosis Risk, Weifei Zhu, Jill C. Gregory, Elin Org, Jennifer A. Buffa, Nilaksh Gupta, Zeneng Wang, Lin Li, Xiaoming Fu, Yuping Wu, Margarete Mehrabian, R. Balfour Sartor, Thomas M. Mcintyre, Roy L. Silverstein, W.H. Wilson Tang, Joseph A. Didonato, J. Mark Brown, Aldons J. Lusis, Stanley L. Hazen

Mathematics and Statistics Faculty Publications

Normal platelet function is critical to blood hemostasis and maintenance of a closed circulatory system. Heightened platelet reactivity, however, is associated with cardiometabolic diseases and enhanced potential for thrombotic events. We now show gut microbes, through generation of trimethylamine N-oxide (TMAO), directly contribute to platelet hyperreactivity and enhanced thrombosis potential. Plasma TMAO levels in subjects (n > 4,000) independently predicted incident (3 years) thrombosis (heart attack, stroke) risk. Direct exposure of platelets to TMAO enhanced sub-maximal stimulus-dependent platelet activation from multiple agonists through augmented Ca2+ release from intracellular stores. Animal model studies employing dietary choline or TMAO, germ-free mice, and microbial …

Generalized Phase Retrieval: Isometries In Vector Spaces, Josiah Park

USF Tampa Graduate Theses and Dissertations

In this thesis we generalize the problem of phase retrieval of vector to that of multi-vector. The identification of the multi-vector is done up to some special classes of isometries in the space. We give some upper and lower estimates on the minimal number of multi-linear operators needed for the retrieval. The results are preliminary and far from sharp.

Asymptotically Periodic Solutions Of Volterra Integral Equations, Muhammad Islam

Mathematics Faculty Publications

We study the existence of asymptotically periodic solutions of a nonlinear Volterra integral equation. In the process, we obtain the existence of periodic solutions of an associated nonlinear integral equation with infinite delay. Schauder's fixed point theorem is used in the analysis.

Geometric Optimization, Analysis, And Design, Denise Halverson

Journal of Undergraduate Research

1. Evaluation of how well the academic objectives of the proposal were met

The goals for the mentoring environment were reached:

• Academic Development – Each student had the opportunity to work on a cutting edge research problem, as indicated below. Papers are in various stages of completion, a few submitted or accepted for publication, but all have drafted papers.
• Community Development – Several students were able to attend the MAA Math Fest in both 2014 and 2015. Most students gave presentations at the CPMS Student Research Conference. My students have been able to interact with engineering student working on similar …

Resonant Solutions To (3+1)-Dimensional Bilinear Differential Equations, Yue Sun

USF Tampa Graduate Theses and Dissertations

In this thesis, we attempt to obtain a class of generalized bilinear differential equations in (3+1)-dimensions by D_p-operators with p = 5, which have resonant solutions. We construct resonant solutions by using the linear superposition principle and parameterizations of wave numbers and frequencies. We test different values of p in Maple computations, and generate three classes of generalized bilinear differential equations and their resonant solutions when p = 5.

Smallest Eigenvalues For A Right Focal Boundary Value Problem, Paul W. Eloe, Jeffrey T. Neugebauer

Mathematics Faculty Publications

We establish the existence of smallest eigenvalues for the fractional linear boundary value problems D^α₀₊u+λ₁p(t)u = 0 and D^α₀₊u+λ₂q(t)u = 0, 0

Review Paper: The Shape Of Phylogenetic Treespace, Katherine St. John

Publications and Research

Trees are a canonical structure for representing evolutionary histories. Many popular criteria used to infer optimal trees are computationally hard, and the number of possible tree shapes grows super-exponentially in the number of taxa. The underlying structure of the spaces of trees yields rich insights that can improve the search for optimal trees, both in accuracy and in running time, and the analysis and visualization of results. We review the past work on analyzing and comparing trees by their shape as well as recent work that incorporates trees with weighted branch lengths.

On The Number Of Colors In Quandle Knot Colorings, Jeremy William Kerr

USF Tampa Graduate Theses and Dissertations

A major question in Knot Theory concerns the process of trying to determine when two knots are different. A knot invariant is a quantity (number, polynomial, group, etc.) that does not change by continuous deformation of the knot. One of the simplest invariant of knots is colorability. In this thesis, we study Fox colorings of knots and knots that are colored by linear Alexander quandles. In recent years, there has been an interest in reducing Fox colorings to a minimum number of colors. We prove that any Fox coloring of a 13-colorable knot has a diagram that uses exactly five …

Sticky Seeding In Discrete-Time Reversible-Threshold Networks, Gwen Spencer

Mathematics Sciences: Faculty Publications

When nodes can repeatedly update their behavior (as in agent-based models from computational social science or repeated-game play settings) the problem of optimal network seeding becomes very complex. For a popular spreading-phenomena model of binary-behavior updating based on thresholds of adoption among neighbors, we consider several planning problems in the design of Sticky Interventions: when adoption decisions are reversible, the planner aims to find a Seed Set where temporary intervention leads to long-term behavior change. We prove that completely converting a network at minimum cost is Ω(ln(OP T ))-hard to approximate and that maximizing conversion subject to a budget is …

Hawking Radiation Screening And Penrose Process Shielding In The Kerr Black Hole, Eamon Mccaughey

Articles

The radial motion of massive particles in the equatorial plane of aKerr black hole is considered. Screening of the Hawking radiation and shielding of the Penrose process are examined (both inside and outside the ergosphere) and their effect on the evaporation of the black hole is studied. In particular, the locus and width of a classically forbidden region and their dependence on the particle’s angular momentum and energy is analysed. Tunneling of particles between the boundaries of this region is considered and the transmission coefficient determined.

Applying Linear Controls To Chaotic Continuous Dynamical Systems, James P. Braselton, Yan Wu

Mathematical Sciences: Faculty Publications

In this case-study, we examine the effects of linear control on continuous dynamical systems that exhibit chaotic behavior using the symbolic computer algebra system Mathematica. Stabilizing (or controlling) higher-dimensional chaotic dynamical systems is generally a difficult problem, Musielak and Musielak, [1]. We numerically illustrate that sometimes elementary approaches can yield the desired numerical results with two different continuous higher order dynamical systems that exhibit chaotic behavior, the Lorenz equations and the Rössler attractor.

Periodicity In Quantum Calculus, Jeffrey T. Neugebauer

Mathematics Colloquium Series

After a brief introduction to time scales, we will explore periodic functions on time scales. We will discuss how periodicity is defined on time scales that are not periodic. In particular, we will look at periodicity in the quantum case. Two definitions of periodicity have recently been introduced. One definition is based on the equality of areas lying below the graph of the function at each period; the other regards a periodic function to be one that repeats its values after a certain number of steps. We will show a relation between these two definitions and then use this relation …

On The Dynamics Of Boolean Gene Regulatory Networks With Stochasticity, Yuezhe Li

Theses and Dissertations

Genes are responsible for producing proteins that are essential to the construction of complex biological systems. The mechanisms by which this production is regulated have long been the center of wide spread research efforts. Deterministic Boolean gene regulatory models have been a particularly effective avenue of research in this field. However these models fall short of accounting for variations in the gene functionality due to the uncertain internal or external environmental conditions. One of the recent attempts to overcome this weakness is by (Murrugarra, 2012), in which a probabilistic component is introduced as the fixed activation/degradation propensities at the cellular …

Oscillation Of Solution To Second-Order Half-Linear Delay Dynamic Equations On Time Scales, Hongwu Wu, Lynn Erbe, Allan Peterson

Department of Mathematics: Faculty Publications

This article concerns the oscillation of solutions to second-order half-linear dynamic equations with a variable delay. By using integral averaging techniques and generalized Riccati transformations, new oscillation criteria are obtained. Our results extend Kamenev-type, Philos-type and Li-type oscillation criteria. Several examples are given to illustrate our results.