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- Mathematics and Statistics Faculty Publications (10)
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Articles 1 - 29 of 29
Full-Text Articles in Mathematics
Hopf Bifurcation In Models For Pertussis Epidemiology, Herbert W. Hethcote, Yi Li, Zhujun Jing
Hopf Bifurcation In Models For Pertussis Epidemiology, Herbert W. Hethcote, Yi Li, Zhujun Jing
Yi Li
Pertussis (whooping cough) incidence in the United States has oscillated with a period of about four years since data was first collected in 1922. An infection with pertussis confers immunity for several years, but then the immunity wanes, so that reinfection is possible. A pertussis reinfection is mild after partial loss of immunity, but the reinfection can be severe after complete loss of immunity. Three pertussis transmission models with waning of immunity are examined for periodic solutions. Equilibria and their stability are determined. Hopf bifurcation of periodic solutions around the endemic equilibrium can occur for some parameter values in two …
Hopf Bifurcation In Models For Pertussis Epidemiology, Herbert W. Hethcote, Yi Li, Zhujun Jing
Hopf Bifurcation In Models For Pertussis Epidemiology, Herbert W. Hethcote, Yi Li, Zhujun Jing
Mathematics and Statistics Faculty Publications
Pertussis (whooping cough) incidence in the United States has oscillated with a period of about four years since data was first collected in 1922. An infection with pertussis confers immunity for several years, but then the immunity wanes, so that reinfection is possible. A pertussis reinfection is mild after partial loss of immunity, but the reinfection can be severe after complete loss of immunity. Three pertussis transmission models with waning of immunity are examined for periodic solutions. Equilibria and their stability are determined. Hopf bifurcation of periodic solutions around the endemic equilibrium can occur for some parameter values in two …
Self-Consistency Algorithms, Thaddeus Tarpey
Self-Consistency Algorithms, Thaddeus Tarpey
Mathematics and Statistics Faculty Publications
The k-means algorithm and the principal curve algorithm are special cases of a self-consistency algorithm. A general self-consistency algorithm is described and results are provided describing the behavior of the algorithm for theoretical distributions, in particular elliptical distributions. The results are used to contrast the behavior of the algorithms when applied to a theoretical model and when applied to finite datasets from the model. The algorithm is also used to determine principal loops for the bivariate normal distribution.
A Hierarchy Of Maps Between Compacta, Paul Bankston
A Hierarchy Of Maps Between Compacta, Paul Bankston
Mathematics, Statistics and Computer Science Faculty Research and Publications
Let CH be the class of compacta (i.e., compact Hausdorff spaces), with BS the subclass of Boolean spaces. For each ordinal α and pair $\langle K,L\rangle$ of subclasses of CH, we define Lev≥α K,L), the class of maps of level at least α from spaces in K to spaces in L, in such a way that, for finite α, Lev≥α (BS,BS) consists of the Stone duals of Boolean lattice embeddings that preserve all prenex first-order formulas of quantifier rank α. Maps of level ≥ 0 are just the continuous surjections, and the maps of level ≥ 1 are …
Generalized Averages For Solutions Of Two-Point Dirichlet Problems, Philip Korman, Yi Li
Generalized Averages For Solutions Of Two-Point Dirichlet Problems, Philip Korman, Yi Li
Mathematics and Statistics Faculty Publications
For very general two-point boundary value problems we show that any positive solution satisfies a certain integral relation. As a consequence we obtain some new uniqueness and multiplicity results.
Evaluating Maximum Likelihood Estimation Methods To Determine The Hurst Coefficient, Christina Marie Kendziorski, J. B. Bassingthwaighte, Peter J. Tonellato
Evaluating Maximum Likelihood Estimation Methods To Determine The Hurst Coefficient, Christina Marie Kendziorski, J. B. Bassingthwaighte, Peter J. Tonellato
Mathematics, Statistics and Computer Science Faculty Research and Publications
A maximum likelihood estimation method implemented in S-PLUS (S-MLE) to estimate the Hurst coefficient (H) is evaluated. The Hurst coefficient, with 0.5<HS-MLE was developed to estimate H for fractionally differenced (fd) processes. However, in practice it is difficult to distinguish between fd processes and fractional Gaussian noise (fGn) processes. Thus, the method is evaluated for estimating H for both fd and fGn processes. S-MLE gave biased results of H for fGn processes of any length and for fd processes of lengths less than 210. A modified method is proposed to correct for …
Generalized Averages For Solutions Of Two-Point Dirichlet Problems, Philip Korman, Yi Li
Generalized Averages For Solutions Of Two-Point Dirichlet Problems, Philip Korman, Yi Li
Yi Li
For very general two-point boundary value problems we show that any positive solution satisfies a certain integral relation. As a consequence we obtain some new uniqueness and multiplicity results.
Axiomatic Approach For Quantification Of Image Resolution, Ge Wang, Yi Li
Axiomatic Approach For Quantification Of Image Resolution, Ge Wang, Yi Li
Yi Li
Image resolution is the primary parameter for performance characterization of any imaging system. In this work, we present an axiomatic approach for quantification of image resolution, and demonstrate that a good image resolution measure should be proportional to the standard deviation of the point spread function of an imaging system.
Axiomatic Approach For Quantification Of Image Resolution, Ge Wang, Yi Li
Axiomatic Approach For Quantification Of Image Resolution, Ge Wang, Yi Li
Mathematics and Statistics Faculty Publications
Image resolution is the primary parameter for performance characterization of any imaging system. In this work, we present an axiomatic approach for quantification of image resolution, and demonstrate that a good image resolution measure should be proportional to the standard deviation of the point spread function of an imaging system.
Random Fluctuations Of Convex Domains And Lattice Points, Alex Iosevich, Kimberly Kinateder
Random Fluctuations Of Convex Domains And Lattice Points, Alex Iosevich, Kimberly Kinateder
Mathematics and Statistics Faculty Publications
In this paper, we examine a random version of the lattice point problem.
Variational Principles For Average Exit Time Moments For Diffusions In Euclidean Space, Kimberly Kinateder, Patrick Mcdonald
Variational Principles For Average Exit Time Moments For Diffusions In Euclidean Space, Kimberly Kinateder, Patrick Mcdonald
Mathematics and Statistics Faculty Publications
Let D be a smoothly bounded domain in Euclidean space and let Xt be a diffusion in Euclidean space. For a class of diffusions, we develop variational principles which characterize the average of the moments of the exit time from D of a particle driven by Xt, where the average is taken overall starting points in D.
Openness And Monotoneity Of Induced Mappings, W. J. Charatonik
Openness And Monotoneity Of Induced Mappings, W. J. Charatonik
Mathematics and Statistics Faculty Research & Creative Works
It is shown that for locally connected continuum X if the induced mapping C(f) : C(X) ->C(Y) is open, then f is monotone. As a corollary it follows that if the continuum X is hereditarily locally connected and C(f) is open, then f is a homeomorphism. An example is given to show that local connectedness is essential in the result.
Positive Solutions To Semilinear Problems With Coefficient That Changes Sign, Nguyen Phuong Cac, Juan A. Gatica, Yi Li
Positive Solutions To Semilinear Problems With Coefficient That Changes Sign, Nguyen Phuong Cac, Juan A. Gatica, Yi Li
Yi Li
No abstract provided.
Positive Solutions To Semilinear Problems With Coefficient That Changes Sign, Nguyen Phuong Cac, Juan A. Gatica, Yi Li
Positive Solutions To Semilinear Problems With Coefficient That Changes Sign, Nguyen Phuong Cac, Juan A. Gatica, Yi Li
Mathematics and Statistics Faculty Publications
No abstract provided.
Why The Player Never Wins In The Long Run At La Blackjack, Arthur T. Benjamin, Michael Lauzon '00, Christopher Moore '00
Why The Player Never Wins In The Long Run At La Blackjack, Arthur T. Benjamin, Michael Lauzon '00, Christopher Moore '00
All HMC Faculty Publications and Research
No abstract provided in this article.
Anticommuting Derivations, Steen Pedersen
Anticommuting Derivations, Steen Pedersen
Mathematics and Statistics Faculty Publications
We show that the re are no non-trivial closable derivations of a C*-algebra anticommuting with an ergodic action of a compact group, supposing that the set of squares is dense in the group. We also show that the re are no non-trivial closable densely defined rank one derivations on any C*-algebra.
The Moral Significance Of Indetectable Effects, Sven Ove Hansson
The Moral Significance Of Indetectable Effects, Sven Ove Hansson
RISK: Health, Safety & Environment (1990-2002)
A reassessment of Parfit's fifth "mistake in moral mathematics."
Invariant Measure For Diffusions With Jumps, Jose-Luis Menaldi, Maurice Robin
Invariant Measure For Diffusions With Jumps, Jose-Luis Menaldi, Maurice Robin
Mathematics Faculty Research Publications
Our purpose is to study an ergodic linear equation associated to diffusion processes with jumps in the whole space. This integro-differential equation plays a fundamental role in ergodic control problems of second order Markov processes. The key result is to prove the existence and uniqueness of an invariant density function for a jump diffusion, whose lower order coefficients are only Borel measurable. Based on this invariant probability, existence and uniqueness (up to an additive constant) of solutions to the ergodic linear equation are established.
Structure-Function Relationships In The Pulmonary Arterial Tree, Christopher A. Dawson, Gary S. Krenz, Kelly Lynn Karau, Steven Thomas Haworth, Christopher C. Hanger, John H. Linehan
Structure-Function Relationships In The Pulmonary Arterial Tree, Christopher A. Dawson, Gary S. Krenz, Kelly Lynn Karau, Steven Thomas Haworth, Christopher C. Hanger, John H. Linehan
Mathematics, Statistics and Computer Science Faculty Research and Publications
Knowledge of the relationship between structure and function of the normal pulmonary arterial tree is necessary for understanding normal pulmonary hemodynamics and the functional consequences of the vascular remodeling that accompanies pulmonary vascular diseases. In an effort to provide a means for relating the measurable vascular geometry and vessel mechanics data to the mean pressure-flow relationship and longitudinal pressure profile, we present a mathematical model of the pulmonary arterial tree. The model is based on the observation that the normal pulmonary arterial tree is a bifurcating tree in which the parent-to-daughter diameter ratios at a bifurcation and vessel distensibility are …
03. Preface Of Design And Analysis Of Experiments - 1st Edition, Angela Dean, Dan Voss, Danel Draguljic
03. Preface Of Design And Analysis Of Experiments - 1st Edition, Angela Dean, Dan Voss, Danel Draguljic
Design and Analysis of Experiments
Preface of the first edition of Design and Analysis of Experiments.
Path Decompositions Of A Brownian Bridge Related To The Ratio Of Its Maximum And Amplitude, Jim Pitman, Marc Yor
Path Decompositions Of A Brownian Bridge Related To The Ratio Of Its Maximum And Amplitude, Jim Pitman, Marc Yor
Jim Pitman
We give two new proofs of Csaki's formula for the law of the ratio 1-Q of the maximum relative to the amplitude (i.e. the maximum minus minimum) for a standard Brownian bridge. The second of these proofs is based on an absolute continuity relation between the law of the Brownian bridge restricted to the event (Q < v) and the law of a process obtained by a Brownian scaling operation after back-to back joining of two independent three-dimensional Bessel processes, each started at v and run until it first hits 1. Variants of this construction and some properties of the joint law of Q and the amplitude are described.
Bayes Estimation Of A Distribution Function Using Ranked Set Samples, Paul H. Kvam, Ram C. Tiwari
Bayes Estimation Of A Distribution Function Using Ranked Set Samples, Paul H. Kvam, Ram C. Tiwari
Department of Math & Statistics Faculty Publications
Aranked set sample (RSS), if not balanced, is simply a sample of independent order statistics generated from the same underlying distribution F. Kvam and Samaniego (1994) derived maximum likelihood estimates of F for a general RSS. In many applications, including some in the environmental sciences, prior information about F is available to supplement the data-based inference. In such cases, Bayes estimators should be considered for improved estimation. Bayes estimation (using the squared error loss function) of the unknown distribution function F is investigated with such samples. Additionally, the Bayes generalized maximum likelihood estimator (GMLE) is derived. An iterative scheme based …
Fisher Information In Weighted Distributions, Satish Iyengar, Paul H. Kvam, Harshinder Singh
Fisher Information In Weighted Distributions, Satish Iyengar, Paul H. Kvam, Harshinder Singh
Department of Math & Statistics Faculty Publications
Standard inference procedures assume a random sample from a population with density fμ(x) for estimating the parameter μ. However, there are many applications in which the available data are a biased sample instead. Fisher modeled biased sampling using a weight function w(x) ¸ 0, and constructed a weighted distribution with a density fμw(x) that is proportional to w(x)fμ(x). In this paper, we assume that fμ(x) belongs to an exponential family, and study the Fisher information about μ in observations obtained from some commonly arising weighted distributions: (i) the kth order …
A Quantile‐Based Approach For Relative Efficiency Measurement, Paul M. Griffin, Paul H. Kvam
A Quantile‐Based Approach For Relative Efficiency Measurement, Paul M. Griffin, Paul H. Kvam
Department of Math & Statistics Faculty Publications
Two popular approaches for efficiency measurement are a non‐stochastic approach called data envelopment analysis (DEA) and a parametric approach called stochastic frontier analysis (SFA). Both approaches have modeling difficulty, particularly for ranking firm efficiencies. In this paper, a new parametric approach using quantile statistics is developed. The quantile statistic relies less on the stochastic model than SFA methods, and accounts for a firm's relationship to the other firms in the study by acknowledging the firm's influence on the empirical model, and its relationship, in terms of similarity of input levels, to the other firms.
On The Decomposition Of Order-Separable Posets Of Countable Width Into Chains, Gary Gruenhage, Joe Mashburn
On The Decomposition Of Order-Separable Posets Of Countable Width Into Chains, Gary Gruenhage, Joe Mashburn
Mathematics Faculty Publications
partially ordered set X has countable width if and only if every collection of pairwise incomparable elements of X is countable. It is order-separable if and only if there is a countable subset D of X such that whenever p, q ∈ X and p < q, there is r ∈ D such that p ≤ r ≤ q. Can every order-separable poset of countable width be written as the union of a countable number of chains? We show that the answer to this question is "no" if there is a 2-entangled subset of IR, and "yes" under the Open Coloring Axiom.
Stability Of A Semilinear Cauchy Problem, Yi Liu, Yi Li, Yinbin Deng
Stability Of A Semilinear Cauchy Problem, Yi Liu, Yi Li, Yinbin Deng
Mathematics and Statistics Faculty Publications
A report of progress in linear and nonlinear partial differential equations, microlocal analysis, singular partial differential operators, spectral analysis and hyperfunction theory. The papers aretaken from a conference on partial differential equations and their applications, held in Wuhan.
On The Exactness Of An S-Shaped Bifurcation Curve, Philip Korman, Yi Li
On The Exactness Of An S-Shaped Bifurcation Curve, Philip Korman, Yi Li
Mathematics and Statistics Faculty Publications
For a class of two-point boundary value problems we prove exactness of an S-shaped bifurcation curve. Our result applies to a problem from combustion theory, which involves nonlinearities like for .
The Stable Manifold Theorem For Stochastic Differential Equations, Salah-Eldin A. Mohammed, Michael K. R. Scheutzow
The Stable Manifold Theorem For Stochastic Differential Equations, Salah-Eldin A. Mohammed, Michael K. R. Scheutzow
Articles and Preprints
We formulate and prove a local stable manifold theorem for stochastic differential equations (SDEs) that are driven by spatial Kunita-type semimartingales with stationary ergodic increments. Both Stratonovich and Itô-type equations are treated. Starting with the existence of a stochastic flow for a SDE, we introduce the notion of a hyperbolic stationary trajectory. We prove the existence of invariant random stable and unstable manifolds in the neighborhood of the hyperbolic stationary solution. For Stratonovich SDEs, the stable and unstable manifolds are dynamically characterized using forward and backward solutions of the anticipating SDE. The proof of the stable manifold theorem is based …
On The Laws Of Homogeneous Functionals Of The Brownian Bridge, Philippe Carmona, Frédérique Petit, Jim Pitman, Marc Yor
On The Laws Of Homogeneous Functionals Of The Brownian Bridge, Philippe Carmona, Frédérique Petit, Jim Pitman, Marc Yor
Jim Pitman
No abstract provided.