Applied Mathematics Commons^™

An Exploration Of Modeling Techniques For The Study Of The Dynamics Of E-Mail Viruses, Karin Weule

Theses, Dissertations and Culminating Projects

We analyze real data sets from two e-mail viruses, the Magistr.b and the Sircam.a to explore how we can use mathematical models to predict the behavior described by the data. Analysis of the data is conducted primarily with computer programming in MatLab. We focus mainly on the use of two continuous models commonly used in the study of biological diseases, the SIS and the SIR models. A discrete modeling approach using agent-based simulations is also explored and revealed to be potentially useful in developing a compartmentalized model that incorporates both SIS and SIR model behavior. The theory behind the continuous …

How Do Neurons Work Together? Lessons From Auditory Cortex, Kenneth D. Harris, Peter Bartho, Paul Chadderton, Carina Curto, Jaime De La Rocha, Liad Hollender, Vladimir Itskov, Artur Luczak, Stephan Marguet, Alfonso Renart, Shuzo Sakata

Department of Mathematics: Faculty Publications

Recordings of single neurons have yielded great insights into the way acoustic stimuli are represented in auditory cortex. However, any one neuron functions as part of a population whose combined activity underlies cortical information processing. Here we review some results obtained by recording simultaneously from auditory cortical populations and individual morphologically identified neurons, in urethane-anesthetized and unanesthetized passively listening rats. Auditory cortical populations produced structured activity patterns both in response to acoustic stimuli, and spontaneously without sensory input. Population spike time patterns were broadly conserved across multiple sensory stimuli and spontaneous events, exhibiting a generally conserved sequential organization lasting approximately …

Neural Spike Renormalization. Part I — Universal Number 1, Bo Deng

Department of Mathematics: Faculty Publications

For a class of circuit models for neurons, it has been shown that the transmembrane electrical potentials in spike bursts have an inverse correlation with the intra-cellular energy conversion: the fewer spikes per burst the more energetic each spike is. Here we demonstrate that as the per-spike energy goes down to zero, a universal constant to the bifurcation of spike-bursts emerges in a similar way as Feigenbaum’s constant does to the period-doubling bifurcation to chaos generation, and the new universal constant is the first natural number 1.

Asymptotic Expansions And Stability Of Hybrid Systems With Two-Time Scales, Dung Tien Nguyen

Wayne State University Dissertations

In this dissertation, we consider solutions of hybrid systems in which both continuous dynamics and discrete events coexists. One

of the main ingredients of our models is the two-time-scale formulation. Under broad conditions, asymptotic expansions are developed for the solutions of the systems of backward equations for switching diffusion in two classes of models, namely, fast switching systems and fast diffusion systems. To prove the validity of the asymptotic expansions, uniform error bounds are obtained.

In the second part of the dissertation, a singular linear system is considered. Again a two-time-scale formulation is used. Under suitable conditions, the system has …

Physical Process Models As Regularization Constraints On Geophysical Imaging Problems, Rachel Grotheer

All Theses

Obtaining accurate images of solute plumes in the subsurface is important to understand site-specific subsurface flow and transport processes. Since image reconstruction is an inverse problem, its ill-posed nature makes obtaining an accurate, high-resolution image difficult. Further, current geophysical methods for plume imaging do not take into account models of the specific process being targeted for imaging.
The main objective of the research is to find a suitable basis that gives a sparse representation of the plume. In future work, we seek to use this basis as a physical constraint during the inversion so as to increase accuracy in imaging. …

Problems In Gps Accuracy, Michael Thomas Vodhanel

CGU Theses & Dissertations

Improving and predicting the accuracy of positioning estimates derived from the global positioning system (GPS) continues to be a problem of great interest. Dependable and accurate positioning is especially important for navigation applications such as the landing of commercial aircraft. This subject gives rise to many interesting and challenging mathematical problems. This dissertation investigates two such problems. The first problem involves the study of the relationship between positioning accuracy and satellite geometry configurations relative to a user's position. In this work, accuracy is measured by so-called dilution of precision (DOP) terms. The DOP terms arise from the linear regression model …

Algebraic Structures Using Super Interval Matrices, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

The advantage of using super interval matrices is that one can build only one vector space using m × n interval matrices, but in case of super interval matrices we can have several such spaces depending on the partition on the interval matrix.

This book has seven chapters. Chapter one is introductory in nature, just introducing the super interval matrices or interval super matrices. In chapter two essential operations on super interval matrices are defined. Further in this chapter algebraic structures are defined on these super interval matrices using these operation. Using these super interval matrices semirings and semivector spaces …

Studies In Sampling Techniques And Time Series Analysis, Florentin Smarandache, Rajesh Singh

Branch Mathematics and Statistics Faculty and Staff Publications

This book has been designed for students and researchers who are working in the field of time series analysis and estimation in finite population. There are papers by Rajesh Singh, Florentin Smarandache, Shweta Maurya, Ashish K. Singh, Manoj Kr. Chaudhary, V. K. Singh, Mukesh Kumar and Sachin Malik. First chapter deals with the problem of time series analysis and the rest of four chapters deal with the problems of estimation in finite population. The book is divided in five chapters as follows: Chapter 1. Water pollution is a major global problem. In this chapter, time series analysis is carried out …

Algebraic Structures Using Natural Class Of Intervals, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

Authors in this book introduce a new class of intervals called the natural class of intervals, also known as the special class of intervals or as natural intervals. These intervals are built using increasing intervals, decreasing intervals and degenerate intervals. We say an interval [a, b] is an increasing interval if a < b for any a, b in the field of reals R. An interval [a, b] is a decreasing interval if a > b and the interval [a, b] is a degenerate interval if a = b for a, b in the field of reals R. The natural class of intervals consists of the collection of increasing intervals, decreasing intervals and the degenerate intervals. Clearly R is contained in the natural …

Study Of Natural Class Of Intervals Using (–∞,∞) And (∞, –∞), Florentin Smarandache, W.B. Vasantha Kandasamy, D. Datta, H.S. Kushwaha, P.A. Jadhav

Branch Mathematics and Statistics Faculty and Staff Publications

In this book the authors study the properties of natural class of intervals built using (–∞, ∞) and (∞, –∞). These natural class of intervals behave like the reals R, as far as the operations of addition, multiplication, subtraction and division are concerned. Using these natural class of intervals we build interval row matrices, interval column matrices and m × n interval matrices. Several properties about them are defined and studied. Also all arithmetic operations are performed on them in the usual way. The authors by defining so have made it easier for operations like multiplication, addition, finding determinant and …

Dsm Super Vector Space Of Refined Labels, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors for the first time introduce the notion of supermatrices of refined labels. Authors prove super row matrix of refined labels form a group under addition. However super row matrix of refined labels do not form a group under product; it only forms a semigroup under multiplication. In this book super column matrix of refined labels and m × n matrix of refined labels are introduced and studied. We mainly study this to introduce to super vector space of refined labels using matrices. We in this book introduce the notion of semifield of refined labels using which …

Dsm Vector Spaces Of Refined Labels, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

The study of DSm linear algebra of refined labels have been done by Florentin Smarandache, Jean Dezert, and Xinde Li.

In this book the authors introduce the notion of DSm vector spaces of refined labels. The reader is requested to refer the paper as the basic concepts are taken from that paper [35]. This book has six chapters. The first one is introductory in nature just giving only the needed concepts to make this book a self contained one. Chapter two introduces the notion of refined plane of labels, the three dimensional space of refined labels DSm vector spaces. Clearly …

Mesoscopic Methods In Engineering And Science, Chuguang Zheng, Jiding Lu, Zhaoli Guo, Li-Shi Luo, Manfred Krafczyk

Mathematics & Statistics Faculty Publications

Matter, conceptually classified into fluids and solids, can be completely described by the microscopic physics of its constituent atoms or molecules. However, for most engineering applications a macroscopic or continuum description has usually been sufficient, because of the large disparity between the spatial and temporal scales relevant to these applications and the scales of the underlying molecular dynamics. In this case, the microscopic physics merely determines material properties such as the viscosity of a fluid or the elastic constants of a solid. These material properties cannot be derived within the macroscopic framework, but the qualitative nature of the macroscopic dynamics …

Essays On Hedge Fund Replication: Methodological Assessment And Development Of The Factor Approach, Nonlinear Modeling And Policy Perspectives, Guillaume Weisang

2011

This dissertation is concerned with hedge fund replication, a subject of a practical and theoretical importance, both from an investment and a risk management point of view. One of our goals is to extend known methodologies in order to enhance our understanding of an industry that is known for its secrecy and its lack of transparency. A second goal is to contribute to the quantitative finance literature with improved techniques for hedge fund replication. Hedge fund replication (HFR) is approached from the methodological as well as from practical and regulatory perspectives. The first two chapters provide the motivation and the …

Fully Nonlinear Boundary Value Problems With Impulse, Paul Eloe, Muhammad Usman

Mathematics Faculty Publications

An impulsive boundary value problem with nonlinear boundary conditions for a second order ordinary differential equation is studied. In particular, sufficient conditions are provided so that a compression- expansion cone theoretic fixed point theorem can be applied to imply the existence of positive solutions. The nonlinear forcing term is assumed to satisfy usual sublinear or superlinear growth as t → ∞ or t → 0 +. The nonlinear impulse terms and the nonlinear boundary terms are assumed to satisfy the analogous asymptotic behavior.

Prospective Teachers' Use Of Representations In Solving Statistical Tasks With Dynamic Statistical Software, Hollylynne Lee, Shannon O. Driskell, Suzanne R. Harper, Keith R. Leatham, Gladis Kersaint, Robin L. Angotti

Mathematics Faculty Publications

This study examined a random stratified sample (n=62) of prospective teachers' work across eight institutions on three tasks that utilized dynamic statistical software. Our work was guided by considering how teachers may utilize their statistical knowledge and technological statistical knowledge to engage in cycles of investigation. Although teachers did not tend to take full advantage of dynamic linking capabilities, they utilized a large variety of graphical representations and often added statistical measures or other augmentations to graphs as part of their analysis.

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

Mathematics Faculty Publications

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.

Algorithms For Area Preserving Flows, Catherine Kublik, Selim Esedoglu, Jeffrey A. Fessler

Mathematics Faculty Publications

We propose efficient and accurate algorithms for computing certain area preserving geometric motions of curves in the plane, such as area preserving motion by curvature. These schemes are based on a new class of diffusion generated motion algorithms using signed distance functions. In particular, they alternate two very simple and fast operations, namely convolution with the Gaussian kernel and construction of the distance function, to generate the desired geometric flow in an unconditionally stable manner. We present applications of these area preserving flows to large scale simulations of coarsening.

On Constrained Optimization Schemes For Joint Inversion Of Geophysical Datasets, Uram Anibal Sosa Aguirre

Open Access Theses & Dissertations

In the area of geological sciences, there exist several experimental techniques used to advance in the understanding of the Earth. We implement a joint inversion least-squares (LSQ) algorithm to characterize one dimensional Earth's structure by using seismic shear wave velocities as a model parameter. We use two geophysical datasets sensitive to shear velocities, namely Receiver Function and Surface Wave dispersion velocity observations, with a choice of an optimization method: Truncated Singular Value Decomposition (TSVD) or Primal-Dual Interior-Point (PDIP). The TSVD and the PDIP methods solve a regularized unconstrained and a constrained minimization problem, respectively. Both techniques include bounds into the …

Commuting Smoothed Projectors In Weighted Norms With An Application To Axisymmetric Maxwell Equations, Jay Gopalakrishnan, Minah Oh

Mathematics and Statistics Faculty Publications and Presentations

We construct finite element projectors that can be applied to functions with low regularity. These projectors are continuous in a weighted norm arising naturally when modeling devices with axial symmetry. They have important commuting diagram properties needed for finite element analysis. As an application, we use the projectors to prove quasioptimal convergence for the edge finite element approximation of the axisymmetric time-harmonic Maxwell equations on nonsmooth domains. Supplementary numerical investigations on convergence deterioration at high wavenumbers and near Maxwell eigenvalues and are also reported.