A Regime Switching Model For The Term Structure Of Credit Risk Spreads,
2015
University of Nevada, Las Vegas
A Regime Switching Model For The Term Structure Of Credit Risk Spreads, Seungmook Choi, Michael D. Marcozzi
Mathematical Sciences Faculty Research
We consider a rating-based model for the term structure of credit risk spreads wherein the credit worthiness of the issuer is represented as a finite-state continuous time Markov process. This approach entails a progressive drift in creditquality towards default. A model of the economy is presented featuring stochastic transition probabilities; credit instruments are valued via an ultraparabolic Hamilton-Jacobi system of equations discretized utilizing the method-of-lines finite difference method. Computations for a callable bond are presented demonstrating the efficiency of the method.
Biological Control Via "Ecological" Damping: An Approach That Attenuates Non-Target Effects,
2015
Stephen F. Austin State University
Biological Control Via "Ecological" Damping: An Approach That Attenuates Non-Target Effects, Rana D. Parshad, Kelly Black, Emmanuel Quansah, Matthew Beauregard
Faculty Publications
In this work we develop and analyze a mathematical model of biological control to prevent or attenuate the explosive increase of an invasive species population in a three-species food chain. We allow for finite time blowup in the model as a mathematical construct to mimic the explosive increase in population, enabling the species to reach “disastrous” levels, in a finite time. We next propose various controls to drive down the invasive population growth and, in certain cases, eliminate blow-up. The controls avoid chemical treatments and/or natural enemy introduction, thus eliminating various non-target effects associated with such classical methods. We refer …
Modeling Neurovascular Coupling From Clustered Parameter Sets For Multimodal Eeg-Nirs,
2015
Dartmouth College
Modeling Neurovascular Coupling From Clustered Parameter Sets For Multimodal Eeg-Nirs, M. Tanveer Talukdar, H. Robert Frost, Solomon G. G. Diamond
Dartmouth Scholarship
Despite significant improvements in neuroimaging technologies and analysis methods, the fundamental relationship between local changes in cerebral hemodynamics and the underlying neural activity remains largely unknown. In this study, a data driven approach is proposed for modeling this neurovascular coupling relationship from simultaneously acquired electroencephalographic (EEG) and near-infrared spectroscopic (NIRS) data. The approach uses gamma transfer functions to map EEG spectral envelopes that reflect time-varying power variations in neural rhythms to hemodynamics measured with NIRS during median nerve stimulation. The approach is evaluated first with simulated EEG-NIRS data and then by applying the method to experimental EEG-NIRS data measured from …
Best Practice Recommendations For Data Screening,
2015
University of Nebraska—Lincoln,
Best Practice Recommendations For Data Screening, Justin A. Desimone, Peter D. Harms, Alice J. Desimone
Department of Management: Faculty Publications
Survey respondents differ in their levels of attention and effort when responding to items. There are a number of methods researchers may use to identify respondents who fail to exert sufficient effort in order to increase the rigor of analysis and enhance the trustworthiness of study results. Screening techniques are organized into three general categories, which differ in impact on survey design and potential respondent awareness. Assumptions and considerations regarding appropriate use of screening techniques are discussed along with descriptions of each technique. The utility of each screening technique is a function of survey design and administration. Each technique has …
Preconditioning For Matrix Computation,
2015
CUNY Graduate Center
Preconditioning For Matrix Computation, Xiaodong Yan
Dissertations, Theses, and Capstone Projects
Preconditioning is a classical subject of numerical solution of linear systems of equations. The goal is to turn a linear system into another one which is easier to solve. The two central subjects of numerical matrix computations are LIN-SOLVE, that is, the solution of linear systems of equations and EIGEN-SOLVE, that is, the approximation of the eigenvalues and eigenvectors of a matrix. We focus on the former subject of LIN-SOLVE and show an application to EIGEN-SOLVE. We achieve our goal by applying randomized additive and multiplicative preconditioning. We facilitate the numerical solution by decreasing the condition of the coefficient matrix …
Four Tails Problems For Dynamical Collapse Theories,
2015
Chapman University
Four Tails Problems For Dynamical Collapse Theories, Kelvin J. Mcqueen
Philosophy Faculty Articles and Research
The primary quantum mechanical equation of motion entails that measurements typically do not have determinate outcomes, but result in superpositions of all possible outcomes. Dynamical collapse theories (e.g. GRW) supplement this equation with a stochastic Gaussian collapse function, intended to collapse the superposition of outcomes into one outcome. But the Gaussian collapses are imperfect in a way that leaves the superpositions intact. This is the tails problem. There are several ways of making this problem more precise. But many authors dismiss the problem without considering the more severe formulations. Here I distinguish four distinct tails problems. The first (bare tails …
Monomials And Basin Cylinders For Network Dynamics,
2015
Oregon Health & Science University
Monomials And Basin Cylinders For Network Dynamics, Daniel Austin, Ian H. Dinwoodie
Mathematics and Statistics Faculty Publications and Presentations
We describe methods to identify cylinder sets inside a basin of attraction for Boolean dynamics of biological networks. Such sets are used for designing regulatory interventions that make the system evolve towards a chosen attractor, for example initiating apoptosis in a cancer cell. We describe two algebraic methods for identifying cylinders inside a basin of attraction, one based on the Groebner fan that finds monomials that define cylinders and the other on primary decomposition. Both methods are applied to current examples of gene networks.
A Rank 7 Pfaffian System On A 15-Dimensional Manifold With F4 Symmetry Algebra,
2015
Utah State University
A Rank 7 Pfaffian System On A 15-Dimensional Manifold With F4 Symmetry Algebra, Ian M. Anderson
Tutorials on... in 1 hour or less
Let I be a differential system on a manifold M. The infinitesimal symmetry algebra of I is the set of all vectors fields X on M such that preserve I. In this worksheet we present an example, due to E. Cartan of a rank 7 Pfaffian system on a 15-dimensional manifold whose infinitesimal symmetry algebra is the split real form of the exceptional Lie algebra f4 .
And Or Not – The System, The Body And Time,
2015
Technological University Dublin
And Or Not – The System, The Body And Time, Brian Fay
Articles
This catalogue text discusses artists and artworks featured in the exhibition BOOLEAN EXPRESSIONS: Contemporary Art and Mathematical Data, presented at The Lewis Glucksman Gallery, University College Cork, Ireland, 23 July – 8 November 2015. For an overview of the exhibition see the link https://vimeo.com/137620854
Dynamics Of Planar Systems That Model Stage-Structured Populations,
2015
Virginia Commonwealth University
Dynamics Of Planar Systems That Model Stage-Structured Populations, N. Lazaryan, Hassan Sedaghat
Mathematics and Applied Mathematics Publications
We study a general discrete planar system for modeling stage-structured populations. Our results include conditions for the global convergence of orbits to zero (extinction) when the parameters (vital rates) are time and density dependent. When the parameters are periodic we obtain weaker conditions for extinction. We also study a rational special case of the system for Beverton-Holt type interactions and show that the persistence equilibrium (in the positive quadrant) may be globally attracting even in the presence of interstage competition. However, we determine that with a sufficiently high level of competition, the persistence equilibrium becomes unstable (a saddle point) and …
Periodic And Chaotic Orbits Of A Discrete Rational System,
2015
Virginia Commonwealth University
Periodic And Chaotic Orbits Of A Discrete Rational System, N. Lazaryan, Hassan Sedaghat
Mathematics and Applied Mathematics Publications
We study a rational planar system consisting of one linear-affine and one linear-fractional difference equation. If all of the system’s parameters are positive (so that the positive quadrant is invariant and the system is continuous), then we show that the unique fixed point of the system in the positive quadrant cannot be repelling and the system does not have a snap-back repeller. By folding the system into a second-order equation, we find special cases of the system with some negative parameter values that do exhibit chaos in the sense of Li and Yorke within the positive quadrant of the plane.
Qualitative Theory Of Functional Differential And Integral Equations,
2015
University of Dayton
Qualitative Theory Of Functional Differential And Integral Equations, Muhammad Islam, Cemil Tunc, Mouffak Benchohra, Bingwen Lui, Samir H. Saker
Mathematics Faculty Publications
Functional differential equations arise in many areas of science and technology: whenever a deterministic relationship involving some varying quantities and their rates of change in space and/or time (expressed as derivatives or differences) is known or postulated. This is illustrated in classical mechanics, where the motion of a body is described by its position and velocity as the time varies. In some cases, this differential equation (called an equation of motion) may be solved explicitly. In fact, differential equations play an important role in modelling virtually every physical, technical, biological, ecological, and epidemiological process, from celestial motion, to bridge design, …
A Look At Vanilla Options And Greeks,
2015
Augustana College - Rock Island
A Look At Vanilla Options And Greeks, Kevin Barbian
Mathematics: Student Scholarship & Creative Works
No abstract provided.
Spin Glass Reflection Of The Decoding Transition For Quantum Error Correcting Codes,
2015
University of Nebraska - Lncoln
Spin Glass Reflection Of The Decoding Transition For Quantum Error Correcting Codes, Alexey Kovalev, Leonid P. Pryadko
Department of Physics and Astronomy: Faculty Publications
We study the decoding transition for quantum error correcting codes with the help of a mapping to random-bond Wegner spin models. Families of quantum low density parity-check (LDPC) codes with a finite decoding threshold lead to both known models (e.g., random bond Ising and random plaquette Z2 gauge models) as well as unexplored earlier generally non-local disordered spin models with non-trivial phase diagrams. The decoding transition corresponds to a transition from the ordered phase by proliferation of "post-topological" extended defects which generalize the notion of domain walls to non-local spin models. In recently discovered quantum LDPC code families with …
Bounded, Asymptotically Stable, And L^1 Solutions Of Caputo Fractional Differential Equations,
2015
University of Dayton
Bounded, Asymptotically Stable, And L^1 Solutions Of Caputo Fractional Differential Equations, Muhammad Islam
Mathematics Faculty Publications
The existence of bounded solutions, asymptotically stable solutions, and L1 solutions of a Caputo fractional differential equation has been studied in this paper. The results are obtained from an equivalent Volterra integral equation which is derived by inverting the fractional differential equation. The kernel function of this integral equation is weakly singular and hence the standard techniques that are normally applied on Volterra integral equations do not apply here. This hurdle is overcomed using a resolvent equation and then applying some known properties of the resolvent. In the analysis Schauder's fixed point theorem and Liapunov's method have been employed. …
Why Lattice-Valued Fuzzy Values? A Mathematical Justification,
2015
Chiang Mai University
Why Lattice-Valued Fuzzy Values? A Mathematical Justification, Rujira Ouncharoen, Vladik Kreinovich, Hung T. Nguyen
Departmental Technical Reports (CS)
To take into account that expert's degrees of certainty are not always comparable, researchers have used partially ordered set of degrees instead of the more traditional linearly (totally) ordered interval [0,1]. In most cases, it is assumed that this partially ordered set is a lattice, i.e., every two elements have the greatest lower bound and the least upper bound. In this paper, we prove a theorem explaining why it is reasonable to require that the set of degrees is a lattice.
Solutions Of A Logistic Equation On Varying Time Scales: A Quantitative And Qualitative Analysis,
2015
Marshall University
Solutions Of A Logistic Equation On Varying Time Scales: A Quantitative And Qualitative Analysis, Alexandria Amity Amorim
Theses, Dissertations and Capstones
Time Scale Calculus, introduced by Dr. Stefan Hilger in 1988, combines the study of differential and difference equations into a single topic. We begin with an introduction of sets used in this field, time scales, and build up to the definition of the exponential function on a time scale. The main focus of this work is a study of the solutions of a particular logistic dynamic equation on varying time scales. We study both the analytical and graphical solutions of this equation. Analytical solutions are worked out using theorems from Time Scale Calculus, including properties of the exponential function. Graphical …
Firing Rate Dynamics In Recurrent Spiking Neural Networks With Intrinsic And Network Heterogeneity,
2015
Virginia Commonwealth University
Firing Rate Dynamics In Recurrent Spiking Neural Networks With Intrinsic And Network Heterogeneity, Cheng Ly
Statistical Sciences and Operations Research Publications
Heterogeneity of neural attributes has recently gained a lot of attention and is increasing recognized as a crucial feature in neural processing. Despite its importance, this physiological feature has traditionally been neglected in theoretical studies of cortical neural networks. Thus, there is still a lot unknown about the consequences of cellular and circuit heterogeneity in spiking neural networks. In particular, combining network or synaptic heterogeneity and intrinsic heterogeneity has yet to be considered systematically despite the fact that both are known to exist and likely have significant roles in neural network dynamics. In a canonical recurrent spiking neural network model, …
Algae Population Self-Replenishment,
2015
George Fox University
Algae Population Self-Replenishment, R. Corban Harwood
Faculty Publications - Department of Mathematics
This modeling scenario investigates the massive algal blooms that struck Lake Chapala, Mexico, in 1994. After reading a summary of news articles on the incident, students create an ODE system model from a verbal description of the factors, visualize this system using an executable Java applet (PPLANE) to predict overall behavior, and then analyze the nonlinear system using the Jacobian matrix, eigenvalues, phase plane, and feasibility conditions on parameters to fully describe the system behavior. Students are expected to be familiar with systems of differential equations, equilibria, jacobian matrices, and eigenvalues. Students will learn modeling from qualitative descriptions, nondimensionalization, applying …
Minimax Portfolio Optimization Under Interval Uncertainty,
2015
Waseda University
Minimax Portfolio Optimization Under Interval Uncertainty, Meng Yuan, Xu Lin, Junzo Watada, Vladik Kreinovich
Departmental Technical Reports (CS)
In the 1950s, Markowitz proposed to combine different investment instruments to design a portfolio that either maximizes the expected return under constraints on volatility (risk) or minimizes the risk under given expected return. Markowitz's formulas are still widely used in financial practice. However, these formulas assume that we know the exact values of expected return and variance for each instrument, and that we know the exact covariance of every two instruments. In practice, we only know these values with some uncertainty. Often, we only know the bounds of these values -- i.e., in other words, we only know the intervals …
