2017

  • - 3:30pm - Allen 14
    CAM seminar
    Multiscale discontinuous Galerkin method for schrodinger equations
    Dr. Wei Wang, Mathematics and Statistics, Florida International University,

    Title:  Multiscale discontinuous Galerkin method for schrodinger equations
    Abstract:  In this talk we will introduce the multiscale discontinuous Galerkin (DG) method for one-dimensional stationary Schrodinger equations. Because of the oscillatory behavior of the solutions, traditional numerical methods require extremely refined meshes to resolve the small scale structure of solutions, thus the computational cost is huge. The main ingredient of our method is to incorporate the small scales into finite element basis functions so that the method can capture the multiscale solution on coarse meshes.
    Link: http://cam.math.msstate.edu/sem20171109WW.html

  • - 3:00pm - Allen 14
    ACT seminar
    Detecting Local Properties of Fundamental Groups
    Dr. Jeremy Brazas, Mathematics, West Chester University,

    Title:  Detecting Local Properties of Fundamental Groups
    Abstract:  The algebraic structure of the fundamental group of a path-connected metric space X often depends heavily on the local structure of X. Roughly speaking, to verify local properties that characterize this kind of dependence, it is necessary to detect the existence of a specific homotopy given a certain, possibly infinite, arrangement of paths. In this talk I'll discuss joint work with Hanspeter Fischer that introduces a unified approach to characterizing and comparing a number of these properties by constructing closure operators on the π1-subgroup lattice in terms of maps from a fixed “test" domain.

    Biography: Dr. Brazas received his Ph.D. in Mathematics from the University of New Hampshire in 2011 under the advisement of Dr. Maria Basterra. His primary research focus is in the area of algebraic topology. He is currently an Assistant Professor at West Chester University in West Chester, Pennsylvania.

  • - 3:30pm - Allen 14
    CAM seminar
    Dual-Mesh characteristics for particle-mesh methods for the simulation of convection-dominated flow
    Dr. Byungjoon Lee, Mathematics, Seoul National University, ,

    Title:  Dual-Mesh characteristics for particle-mesh methods for the simulation of convection-dominated flow
    Abstract:  The particle-mesh method (PMM) is a powerful computational tool for the simulation of convection-dominated diffusion flows. The method introduces computational particles each of which is given a finite size and represents a large number of physical particles with the same properties. The convection part of the flow can be solved by moving the computational particles along the characteristics, while the diffusion part is carried out by utilizing a heat solver on a regular mesh. However, the method in practical applications shows the so-called ringing instability, an amplitude fluctuation in the computed solution. In this talk, we suggest a new numerical technique of particle movement, called the dual-mesh characteristics (DMC) of which the second mesh is formed by tracking back the cells along the characteristics.The particle movement is carried out by interpreting the particle positions (in the previous time level) in terms of the multi-linear coordinates of the second mesh. Strategies for the average velocity and interpolations are also suggested to move the computational particles accurately with a minimum numerical dissipation. The resulting algorithm, PMM-DMC, turns out to be mass-conservative, non-oscillatory, of negligible dissipation, and more efficient than the conventional schemes. Numerical results are shown to demonstrate its accuracy and efficiency.
    Link: http://cam.math.msstate.edu/sem20171026BL.html

  • - 3:30pm - Allen 14
    CAM seminar
    Optimization and Monitoring of Laser-Based Additive Manufacturing: Framework, Challenges, and Solutions.
    Dr. Linkan Bian, Industrial System Engineering,Msstate,

    Title:  Optimization and Monitoring of Laser-Based Additive Manufacturing: Framework, Challenges, and Some Solutions.
    Abstract:  The additive manufacturing (AM) process has the potential to propel the United States to a position of world-wide leadership in the production and repair of complex/precious part which will impact automotive, aerospace, biomedical, and other major industries. However, the highly dynamic thermo-physical transitions during the fabrication making it difficult to identify the operational conditions that result in targeted physical and mechanical properties. This variability and the associated uncertainty associated with AM processes leads to inadvertent and inevitable process anomalies (e.g., defects and porosity), causing fabricated parts lack of satisfactory quality to meet the requirements of industrial applications. We propose a theoretical framework to characterize the parameter-process-property relationships of AM, using a combined experimental and analytical approach. By optimizing the process parameters and characterizing in-situ process signals, we have demonstrated that our approach allows for the efficient fabrication full-dense parts with desired geometric accuracy and mechanical properties. Future work aims at transforming the AM procedure to a 'hands-off' operation governed by in-situ diagnostics and control which provides for customized parts for targeted applications.

    Biography: Linkan Bian is an assistant professor in Industrial and Systems Engineering Department at Mississippi State University. He received his Ph.D. in Industrial and Systems Engineering from Georgia Institute of Technology in 2013 and a B.S. degree in Applied Mathematics from Beijing University. Dr. Bian research interests focus on the development of advanced data analytic methods for modeling and optimization of complex engineering systems. Applications of his research include additive manufacturing and supply chains. He has received federal funding from NSF, DoD, and DoE, as well as industrial companies. Dr. Bian's publications have appeared in journals such as IISE Transactions, Additive Manufacturing, Rapid Prototyping, IEEE Transactions, and other journals. Dr. Bian also received the Outstanding Young Investigator Award from IISE Manufacturing and Design subdivision.
    Link: http://cam.math.msstate.edu/sem20171019LB.html

  • - 3:30pm - Allen 411
    ACT seminar
    Categorical Isomorphisms, Initial and Terminal objects, Illustrations and Applications
    Dr. Paul Fabel, Mathematics, Msstate,

    Title: Categorical Isomorphisms, Initial and Terminal objects, Illustrations and Applications
    Abstract:   Recall a category is a `universe' comprised of objects (dots) and morphisms (you can think of a morphism as an arrow with a unique initial object and a unique target object), obeying very simple rules:

    1) Composition of morphisms is defined when two arrows meet tip to tail.
    2) Composition of morphisms is associative.
    3) Each object partners with an identity morphism, comprising the left and right identities of the all the morphisms.

    You may have noticed in group theory that there is a unique homomorphism from an arbitrary group G to a trivial group, and also a unique homomorphism from a trivial group to G. Can you think of another group with these mentioned properties? What can you say about two `different' trivial groups? Why in practice can we say `the trivial group' rather than `a trivial group', and rarely cause confusion? The previous questions motivate the categorical notions of `terminal object' `initial object', `isomorphism' and `unique up to unique isomorphism.'

  • - 3:30pm - Allen 14
    Statistics seminar
    Using empirical likelihood estimation of density functionals to test location and scale parameters
    Dr. Ningning Wang, Math&Stat,Jackson State University
    ,

    Title:  Using empirical likelihood estimation of density functionals to test location and scale parameters
    Abstract:  A novel class of empirical likelihood nonparametric estimates of density functionals (ELKDFE) is constructed based on kernel density function (KDF) and the concepts of empirical likelihood. These estimates have smaller bias and mean square error than the standard estimates based on KDF. Applications of this to location and scale parameters testing simulation results show that the empirical likelihood estimates are significantly better than the standard ones for small and moderate sample sizes.

  • - 3:30pm - Allen 411
    Math Club seminar
    The p-adic number system and their strange properties
    Dr. Matt McBride, Mathematics, Msstate,

    Title:   The p-adic number system and their strange properties
    Abstract:  The p-adic numbers are a different extension of the rational numbers from the usual extension to get the real and complex numbers. This is achieved by defining "closeness" in a different way. With this new idea, some very "strange" things occur. I will discuss the geometry, topology, and calculus on this new number system as well as give an application in how they are used.

  • - 3:30pm - Allen 411
    ACT seminar
    Shackled and Freed by (Cat)egories
    Dr. Paul Fabel, Mathematics, Msstate,

    Title:  Shackled and Freed by (Cat)egories
    Abstract:  The speaker's mild obsession with categories is plausibly linked to toxoplasmosis, and the goal of the talk is to infect the audience with the former. Teaser: Geometrically the two dimensional unit square is the product of two 1 dimensional line segments. Moreover, a line segment naturally can be understood as a graph. Is there a reasonable/useful way to multiply two graphs so that the product is a graph?

  • - 3:30pm - Allen 14
    CAM seminar
    A new hydrostatic reconstruction scheme for shallow water equations based on subcell reconstructions
    Dr. Guoxian Chen, Mathematics, Wuhan University,

    Title:  A new hydrostatic reconstruction scheme for shallow water equations based on subcell reconstructions
    Abstract:  A key difficulty in the analysis and numerical approximation of the shallow water equations is the non-conservative product of measures due to the gravitational force acting on a sloped bottom. Solutions may be non-unique, and numerical schemes are not only consistent discretizations of the shallow water equations, but they also make a decision how to model the physics. Our derivation is based on a subcell reconstruction using infinitesimal singular layers at the cell boundaries, as inspired by [Noelle, Xing, Shu, JCP 2007]. One key step is to separate the singular measures. Another aspect is the reconstruction of the solution variables in the singular layers. We study three reconstructions. The first leads to the well-known scheme of [Audusse, Bristeau, Bouchut, Klein, Perthame, SISC 2004], which introduces the hydrostatic reconstruction. The second is a modification proposed in [Morales, Castro, Pares, AMC 2013], which analyzes if a wave has enough energy to overcome a step. The third is our new scheme, and borrows its structure from the wet-dry front. For a number of cases discussed in recent years, where water runs down a hill, Audusse's scheme converges slowly or fails. Morales' scheme gives a visible improvement. Both schemes are clearly outperformed by our new scheme.
    Link: http://cam.math.msstate.edu/sem20170907GC.html

  • - 3:30pm - Allen 14
    CAM seminar
    Robust a posterior error estimations for nonconforming finite element methods on interface problems
    Dr. Cuiyu He, Mathematics, Purdue University,

    Title:  Robust a posterior error estimations for nonconforming finite element methods on interface problems
    Abstract:  Robust a posteriori error estimation for problems with discontinuous parameters has been extensively studied in the last two decades. Robustness here means that both the global reliability and the local efficiency constants are independent of the jump of the parameters. In this talk, I will introduce both the residual-based and equilibrated-type a posteriori error estimations for the nonconforming finite element method applied to interface problems with diffusion coefficients that might undergo large jumps across interfaces. Theoretically, we are able to prove both the robust global reliability and local efficiency regardless of the distribution of the coefficient.
    Link: http://cam.math.msstate.edu/sem20170831CH.html

  • - 3:30pm - Allen 14
    CAM seminar
    A two-level Stochastic collocation method for quasilinear elliptic equation with random input data
    Dr. Luoping Chen, Mathematics, Southwest Jiaotong University,

    Title:  A two-level Stochastic collocation method for quasilinear elliptic equation with random input data
    Abstract:  In this talk, we will study a novel two-level discretization for solving semi-linear elliptic equations with random coecients. Motivated by the two-grid method for deterministic partial differential equations introduced by Jinchao Xu, our two-level stochastic collocation method utilizes a two-grid finite element discretization in the physical space and a two-level collocation method in the random domain. We prove that the approximated solution obtained from this method achieves the same order of accuracy as that from solving the original semilinear problem directly by stochastic collocation method. The two-level method is computationally more efficient, especially for nonlinear problems with high random dimensions. Numerical experiments are also provided to verify the theoretical results.
    Link: http://cam.math.msstate.edu/sem20170824LC.html

  • - 3:30pm - Allen 14
    CAM seminar
    A unified analysis of quasi-optimal convergence for adaptive mixed finite element methods
    Dr. Guozhu Yu, Mathematics, Southwest Jiaotong University, China,

    Title:  A unified analysis of quasi-optimal convergence for adaptive mixed finite element methods
    Abstract:  In this talk, we present a unified analysis of both convergence and optimality of adaptive mixed finite element methods for a class of problems when the finite element spaces and corresponding a posteriori error estimates under consideration satisfy five hypotheses. The main ingredient for the analysis is a new method to analyze both discrete reliability and quasi-orthogonality. This new method arises from an appropriate and natural choice of the norms for both the discrete displacement and stress spaces, and a newly defined projection operator from the discrete stress space on the coarser mesh onto the discrete divergence free space on the finer mesh. As applications, we prove these five hypotheses for the Raviart--Thomas and Brezzi--Douglas--Marini elements of the Poisson and Stokes problems in both 2D and 3D.
    Link: http://cam.math.msstate.edu/sem20170817GY.html

  • - 3:30pm - Allen 14
    CAM seminar
    On developing stable finite element methods for pseudo-time simulation of biomolecular electrostatics
    Dr. Shan Zhao, Mathematics, University of Alabama,

    Title:  On developing stable finite element methods for pseudo-time simulation of biomolecular electrostatics
    Abstract:  The Poisson-Boltzmann Equation (PBE) is a widely used implicit solvent model for the electrostatic analysis of solvated biomolecules. To address the exponential nonlinearity of the PBE, a pseudo-time approach has been developed in the literature, which completely suppresses the nonlinear instability through an analytic integration in a time splitting framework. This work aims to develop novel Finite Element Methods (FEMs) in this pseudo-time framework for solving the PBE. Two treatments to the singular charge sources are investigated, one directly applies the definition of the delta function in the variational formulation and the other avoids numerical approximation of the delta function by using a regularization formulation. To apply the proposed FEMs for both PBE and regularized PBE in real protein systems, a new tetrahedral mesh generator based on the minimal molecular surface definition is developed. Numerical experiments of several benchmark examples and free energy calculations of protein systems are conducted to demonstrate the stability, accuracy, and robustness of the proposed PBE solvers. This is a joint work with Weishan Deng and Jin Xu (Institute of Software, CAS, China).
    Link: http://cam.math.msstate.edu/sem20170427SZ.html

  • - 3:00pm - Allen 411
    ACT seminar
    Arrangements and the independence polynomial
    Dr. Russ Woodroofe, Mathematics, Msstate,

    Title:  Arrangements and the independence polynomial
    Abstract:  I'll show how to construct a subspace arrangement which encodes the independence polynomial of a graph G. I'll discuss possible applications to unimodality questions.

  • - 3:30pm - Allen 14
    Statistics seminar
    Distribution-free test based on runs and pattern and their application to quality control
    Dr. Tung-Lung Wu, Statistics, Msstate,

    Title:  Distribution-free test based on runs and pattern and their application to quality control
    Abstract: A simple method based on random permutations and the finite Markov chain imbedding technique is developed to determine the exact conditional distributions of runs and patterns in a sequence of Bernoulli trials given the total number of successes. We also extend the result to multi-state trials. The conditional distributions studied here leads to distribution-frees test based on runs and patterns whose applications are widespread. Applications to runs and scans rules control charts are studied. The conditional probability that the charting statistic exceeds the control limit at present given that there is no alarm before the current time point can be control at a desired rate.

  • - 3:30pm - Allen 14
    Statistics seminar
    A statistical analysis of snow depth trends in North America
    Dr. Jon Woody, Statistics, Msstate,

    Title:  A statistical analysis of snow depth trends in North America
    Abstract: Several attempts to assess regional snow depth trends across various portions of North America have been made. Previous studies estimated trends by applying various statistical approaches to snow depth data, snow fall data, or their climatological proxies such as snow water equivalents. In most of these studies, inhomogeneities (changepoints) have not been taken into account on a region-wide basis.
    This talk begins with considerations of how changepoints effect statistical inference in environmental data, with particular consideration applied towards snow observations. A detailed statistical methodology to estimate trends in daily snow depths from a given data set that accounts for changepoints is considered. Changepoint times are estimated by applying a genetic algorithm to a minimum description length penalized likelihood score. A storage model balance equation with periodic features that allows for changepoints is used to extract standard errors of the estimated trends. The methods are demonstrated on a scientifically accepted gridded data set covering parts of United States and Canada. Results indicate that over half of the grid cells are estimated to contain at least one changepoint and that the average daily snow depth is increasing without changepoints and decreasing with changepoints included in the model.

  • - 3:00pm - Allen 411
    ACT seminar
    Stumbling into categories
    Dr. Paul Fabel, Mathematics, Msstate,

    Title:  Stumbling into categories
    Abstract: Categories are hiding in plain sight all around us. We will gently/accidently discover a bit about them.

  • - 3:30pm - Allen 14
    CAM seminar
    Hamiltonian HDG methods for wave propagation phenomena
    Dr. Manuel Sanchez Uribe, Mathematics, University of Minnesota,

    Title:  Hamiltonian HDG methods for wave propagation phenomena
    Abstract:  We devise the first symplectic Hamiltonian Hybridizable Discontinuous Galerkin (HDG) methods for the acoustic wave equation. We discretize in space by using a Hamiltonian HDG scheme and in time by using symplectic, diagonally implicit and explicit partitioned Runge-Kutta methods. The fundamental characteristic of the semi-discrete scheme is it preserves the Hamiltonian structure of the wave equation, which combined with symplectic time integrators guarantees the conservation of the energy. We obtain optimal approximations of order $k+1$ in the $L^{2}$-norm when polynomials of degree $k\geq0$ and Runge-Kutta formulae of order $k+1$ are used. In addition, by means of post-processing techniques and augmenting the order of the Runge-Kutta method to $k+2$, we obtain superconvergent approximations of order $k+2$ in the $L^2$ norm for the displacement and velocity. We provide numerical examples corroborating these convergence properties as well as depicting the conservative features of the methods.
    Link: http://cam.math.msstate.edu/sem20170323MS.html

  • - 2:30pm - Allen 411
    Statistics Seminar
    A nonparametric goodness-of-fit test
    Dr. Prakash Patil, Statistics, Msstate,

    Title:  A nonparametric goodness-of-fit test

    (This talk was rescheduled from its original date of Feb 28th. Note the changed time!)

    Abstract:  We propose a smoothing-based goodness-of-fit test for a probability density function. The most important aspect of the test is its power against any departure from the null hypothesis. That is, the test has power against the large class of alternatives and can detect alternatives converging to null at a rate n-η where η < 1/2 and n is the sample size.

  • - 3:30pm - Allen 14
    Statistics seminar
    Assessing incremental value of biomarkers with multi-phase nested case-control studies
    Dr. Qian (Michelle) Zhou, Statistics, Msstate,

    Title:  Assessing incremental value of biomarkers with multi-phase nested case-control studies
    Abstract:  Accurate risk prediction models are needed to identify different risk groups for individualized prevention and treatment strategies. In the Nurses’ Health Study, to examine the effects of several biomarkers and genetic markers on the risk of rheumatoid arthritis (RA), a three-phase nested case-control (NCC) design was conducted, in which two sequential NCC subcohorts were formed with one nested within the other, and one set of new markers measured on each of the subcohorts. One objective of the study is to evaluate clinical values of novel biomarkers in improving upon existing risk models because of potential cost associated with assaying biomarkers. In this paper, we develop robust statistical procedures for constructing risk prediction models for RA and estimating the incremental value of new markers based on three-phase NCC studies. Our method also takes into account possible time-varying effects of biomarkers in risk modeling, which allows us to more robustly assess the biomarker utility and address the question of whether a marker is better suited for short-term or long-term risk prediction. 

  • - 3:00pm - Allen 411
    ACT seminar
    On automorphism groups of deleted wreath products
    Dr. Ted Dobson, Mathematics, Msstate,

    Title:  On automorphism groups of deleted wreath products
      (2nd part of a 2 part talk; abstract from last week's 1st part is below.)

    Abstract:  Let Γ1 and Γ2 be digraphs. The deleted wreath product of Γ1 and Γ2, denoted Γ1d Γ2, is the digraph with vertex set V(Γ1) × V(Γ2) and arc set {((x1y1)(x2y2)) : (x1x2) ∈ A(Γ1) and y1y2 or x1 = x2 and (y1y2) ∈ A(Γ2)}. We study the automorphism group of Γ1d Γ2, and amongst other things, show that if Γ is a vertex-transitive digraph and n a positive integer such that n  > |V(Γ)|, then Aut(Γd Kn) = Aut(Γ) × Sn with an explicit list of exceptions (here Kn is the complement of the complete graph). As a corollary, we show that if in addition Γ is 1/2-transitive, then Γd Kn is also 1/2-transitive. This is joint work with Stefko Miklavič and Primož Šparl.

  • - 3:00pm - Allen 411
    ACT seminar
    On automorphism groups of deleted wreath products
    Dr. Ted Dobson, Mathematics, Msstate
    ,

    Title:  On automorphism groups of deleted wreath products
    Abstract:  Let Γ1 and Γ2 be digraphs. The deleted wreath product of Γ1 and Γ2, denoted Γ1d Γ2, is the digraph with vertex set V(Γ1) × V(Γ2) and arc set {((x1y1)(x2y2)) : (x1x2) ∈ A(Γ1) and y1y2 or x1 = x2 and (y1y2) ∈ A(Γ2)}. We study the automorphism group of Γ1d Γ2, and amongst other things, show that if Γ is a vertex-transitive digraph and n a positive integer such that n  > |V(Γ)|, then Aut(Γd Kn) = Aut(Γ) × Sn with an explicit list of exceptions (here Kn is the complement of the complete graph). As a corollary, we show that if in addition Γ is 1/2-transitive, then Γd Kn is also 1/2-transitive. This is joint work with Stefko Miklavič and Primož Šparl.

  • - 3:30pm - Allen 14
    Finite element analysis of THM model for strain localization, rapid catastrophic landslide and hydraulic fracturing.
    Dr. Cao Duc Toan, Civil&Environmental Engineering,Msstate,

    Title:  Finite element analysis of Thermo-Hydro-Mechanical (THM) model for strain localization, rapid catastrophic landslide and hydraulic fracturing.
    Abstract:  This research aims to develop a physical, mathematical and computational model for the virtual simulation of non-isothermal multiphase porous materials under dynamic responses, suitable for environmental engineering and geophysical applications, and the better understanding of some yet unexplained types of geology, e.g. slow earthquakes, the behaviour of faults during earthquakes, hydraulic fracturing in earth-rock (impermeable rock and permeable rock) of pavement problems and dams, etc. These events occur in materials which are porous, of multiphase nature, involve multi-physics aspects and are fully coupled. A fully coupled general mathematical model for the analysis of the thermo-hydro-mechanical behavior of multiphase geomaterials is reduced to a computationally efficient formulation within the u-p-T approach [Cao et al. 2016]. The modified effective stress state is limited by the Drucker-Prager yield surface for simplicity. The standard Galerkin finite element method is applied to discretize the governing equations in space, while the generalized Newmark scheme is used for the time discretization. The final non-linear set of equations is solved by the Newton-Raphson method with a monolithic. Dynamic analysis of a plain strain test for strain localization, rapid catastrophic landslide and hydraulic fracturing is presented.
    Link: http://cam.math.msstate.edu/sem20170209CD.html

  • - 3:00pm - Allen 411
    ACT seminar
    Unimodal and log-concave sequences in combinatorics
    Dr. Russ Woodroofe, Mathematics, Msstate,

    Title:  Unimodal and log-concave sequences in combinatorics
    Abstract:  A sequence of numbers is unimodal if the numbers go up, then go down, so that they have a single 'peak'. Many natural sequences in combinatorics are unimodal. Since unimodality is not preserved by a number of natural operations, it is often more convenient to deal with the more technical definition of log-concavity.

    I'll give a general overview of this interesting topic. If time allows, I will present Major's recent proof that the f-vector of a cyclic polytope is log-concave.

  • - 3:30pm - Allen 14
    CAM seminar
    Efficient iterative one-shot methods for PDE-constrained optimation problems.
    Dr. Jun Liu, Mathematics & Statistical Sciences, Jackson State University,

    Title:  Efficient iterative one-shot methods for PDE-constrained optimation problems.
    Abstract:  PDE-Constrained optimization problems arise in many different scientific and engineering applications, such as computational fluid dynamics, inverse problems of PDE, and medical imaging. In this talk, I will present some efficient iterative methods for solving the discretized first-order optimality KKT system of PDE-Constrained optimization problems. I first briefly introduce finite difference discretization and multigrid method. Then, semismooth Newton (SSN) method is motivated to handle non-smooth and non-linear PDE constraints.

    Putting all components together, we obtained several efficient iterative methods: 

    1. For elliptic and parabolic PDE cases, we employed SSN method as the outer iterations and multigrid method (one V cycle) as inner solvers for the Jacobian systems. The obtained solver delivers competitive performance compared with the currently available solvers.

    2. For hyperbolic wave PDE cases, the multigrid method fails to work. Instead, we proposed a new scheme in time and a robust preconditioner to accelerate the convergence of the Krylov subspace method (e.g., GMRES).

    3. More recently, we proposed several domain decomposition algorithms in time to address the difficulty of huge system size from the KKT system of parabolic PDE-constrained optimization, which allows one-shot methods to be used on parallel computing platforms.

    Numerical results will be shown to illustrate the effectiveness of our proposed algorithms.
    Link: http://cam.math.msstate.edu/sem20170202JL.html
  • - 3:30pm - Allen 14
    CAM seminar
    An adaptive algorithm for solving stochastic boundary value problem
    Davood Damircheli, Mathematics, Msstate,

    Title:  An adaptive algorithm for solving stochastic boundary value problem
    Abstract:  Numerical methods to solve initial value problems in stochastic differential equations (SDE-IVPs) have been extensively researched in the last two decades. This is not the case for stochastic boundary value problems (SBVPs), because of complications both in theoretical as well as computational aspects. These equations appear naturally in a variety of fields such as smoothing, maximum a posteriori estimation of trajectories of diffusions, wave motion in random media, stochastic optimal control, valuation of boundary-linked assets, and in the study of reciprocal processes. They also arise from the semi-discretization of stochastic partial differential equations by the method of lines or Rothe's method. Taking into account the fact that the exact solution of these equations is rarely available in analytic form, trying to find efficient approximation schemes for the trajectories of the solution process or its moments, seems to be a natural candidate. I present an adaptive multiple-shooting method to solve stochastic multi-point boundary value problems.We first analyze the strong order of convergence of the underlying multiple shooting method. We then proceed to describe the proposed strategy to adaptively choose the location of shooting points. We analyze the effect of method parameters on the performance of the overall scheme using a benchmark linear two-point stochastic boundary value problem.
    Link: http://cam.math.msstate.edu/sem20170126DD.html

  • - 3:00pm - Allen 411
    ACT seminar
    Some easy to state open problems related to R-trees
    Dr. Paul Fabel, Mathematics, Msstate,

    Title:  Some easy to state open problems related to R-trees

    Abstract: "All trains lead to Paris" is the abstract of Evelyn Lamb's recent article in Roots of Unity, her math blog for Scientific American. The idea is that to get from anywhere to anywhere in France, traveling by train you will likely go to Paris, even if (as the crow flies) there's a much shorter route.
    The content of the article is a mathematical version of this idea, in which (thinking of the origin (0, 0) as Paris) the distance between planar points (xy) and (zw) is no longer the usual one, but rather the following. If (xy) and (zw) and (0, 0) are not collinear, instead of the usual distance we use sqrt(x2+y2) + sqrt(z2+w2).
    The resulting metric space is an example of an R-tree, a metric space so that there is a unique arc between any two points, and moreover the arc length is the distance between the endpoints.
    We will discuss some fundamental open questions related to R-trees.

  • - 3:30pm - Allen 14
    CAM seminar
    High-order and adaptive finite element simulation of fluid-structure interaction instabilities.
    Dr. Manav Bhatia, Department of Aerospace Engineering, Msstate,

    Title:  High-order and adaptive finite element simulation of fluid-structure interaction instabilities.
    Abstract:  Static and dynamic instabilities arising from fluid-structure interactions (FSI), such as aeroelastic divergence and flutter phenomena, are important metrics for flight vehicle performance. Conventionally, time-accurate simulations have been used to estimate the damping and frequency characteristics of the multi-physics response. This talk discusses the challenges inherent to such an approach and then focuses on methods to improve the robustness and computational efficiency of procedures to predict FSI instabilities. The concept of small-disturbances is used to linearize the nonlinear dynamic system of equations and pose the problem as a linear stability eigensolution. Both fluid and structural models are discretized with high-order schemes and convergence rates are established for the simulation. Finally, preliminary results are discussed on error-estimation and h-adaptive simulation for the class of problems studied here.
    Link: http://cam.math.msstate.edu/sem20170119MB.html

2016

  • - 3:30pm - Allen 14
    CAM seminar
    Analytical analysis and computer simulations of a thermohaline circulation model
    Dr. Zhenbu Zhang, Mathematics & Statistics, Jackson State University,

    Title:  Analytical analysis and computer simulations of a thermohaline circulation model
    Abstract:  Thermohaline circulation (THC) is a part of the large-scale ocean circulation that is driven by global density gradients created by surface heat and freshwater fluxes. The THC plays a major role in maintaining the Earth's overall energy balance, so a change of the circulation pattern will have a dramatic impact on the global climate. In this talk, we will go over a conceptual thermohaline circulation model which is used to study the overturning circulation in the North Atlantic Ocean. We will cover the background of the model, the statement of the model, the reduction of the model, the qualitative analysis including equilibrium points and their stability, bifurcation analysis and computer simulations of the model. Since there are several parameters in the model, we will have a look at the different values of the parameters to investigate the long time behavior of the solutions of the model analytically and numerically.
    Link: http://cam.math.msstate.edu/sem20161202ZZ.html

  • - 2:00pm - Allen 411
    CAM seminar
    On a class of functional inequalities and their applications to fourth-order nonlinear parabolic equations
    Dr. Xiangsheng Xu, Mathematics, Msstate,

    Title:  On a class of functional inequalities and their applications to fourth-order nonlinear parabolic equations
    Abstract:  This is a joint work with Jian-Guo Liu of Duke University. We study a class of fourth order nonlinear parabolic equations which include the thin-film equation and the quantum drift-diffusion model as special cases. We investigate these equations by first developing functional inequalities of the type
    which seem to be of interest on their own right.
    Link: http://cam.math.msstate.edu/sem20161118XX.html

  • - 3:30pm - Allen 411
    CAM seminar
    Error analysis of an HDG method for a distributed optimal control problem
    Dr. Huiqing Zhu, Mathematics, University of Southern Mississippi,

    Title:  Error analysis of an HDG method for a distributed optimal control problem
    Abstract:  The first part of this talk will introduce the implementation of an HDG method for solving a distributed optimal control problem governed by diffusion equations and convection-diffusion equations. It then proceeds to the a priori error estimates for the HDG approximations to both fluxes and scalar functions. We showed that, when piecewise polynomials of degree k are used, the convergence rates of HDG approximations to fluxes and scalar functions are of order k+1
    Link: http://cam.math.msstate.edu/sem20161111HZ.html

  • - 3:30pm - Allen 14
    Statistics seminar
    A Pearson chi-square hypothesis testing for hazard rate
    Ralph Vital, Statistics, Msstate,

    Title:  A Pearson chi-square hypothesis testing for hazard rate
    Abstract:  In the literature there exists, many hypothesis testing to conclude whether or not a sample data is from a parametric hazard rate function, say : h0. The log-rank, the Herrington and Fleming, and the Tarone-Ware test divide the range of the hazard function into class intervals, and lead to hazard function estimates that are constant over each interval. However, we know that a better measurement for the discrepancy between the estimated and the true function is the integrated square error (ISE). Our work is to develop a non parametric (smoothing-based) test lack-of-fit for the hazard rate function based on the Integrated Square Error. To begin with, we are investigating the conditions for a Pearson chi-square test for hazard rate function.

  • - 2:00pm - Allen 14
    CAM seminar
    Particular Solutions for Solving Elliptic Partial Differential Equations
    Dr. C.S. Chen, Mathematics, University of Southern Mississippi,

    Title:  Particular Solutions for Solving Elliptic Partial Differential Equations
    Abstract:  In the past, polynomial particular solutions have been obtained for certain types of partial differential operators without convection terms. In this talk, a closed-form particular solution for more general partial differential operators with constant coefficients has been derived for polynomial basis functions. The newly derived particular solution is further coupled with the method of particular solutions (MPS) for numerically solving a large class of elliptic partial differential equations. In contrast to the use of Chebyshev polynomial basis functions, the proposed approach is more flexible in selecting the collocation points inside the domain. The polynomial basis functions are well-known for yielding ill-conditioned systems when their order becomes large. The multiple scale technique is applied to circumvent the difficulty of ill-conditioning problem. Five numerical examples are presented to demonstrate the effectiveness of the proposed algorithm. This is a joint work with Thir Dangal.
    Link: http://cam.math.msstate.edu/sem20161104CC.html

  • - 2:00pm - Allen 14
    CAM seminar
    Minimum curvature method for surface reconstruction
    Dr. Hyeona Lim, Mathematics, Msstate,

    Title:  Minimum curvature method for surface reconstruction
    Abstract:  Surface reconstruction is a challenging problem when no constraint is imposed on data locations. The problem is ill-posed and most computational algorithms become overly expensive as the number of sample points increases. This talk will present a generalization of a popular integral method called minimum curvature (MC) method, which is based on the numerical solution of a modified biharmonic partial differential equation (PDE). Surface reconstruction through the PDE solution for scattered data can be considered as an interior value problem. A new model is suggested to construct image surface that satisfies data constraints accurately and conveniently. In order to improve efficiency of the MC method, an effective initialization scheme is suggested. The resulting algorithm is applied for image zooming, synthetic scattered data, and agricultural data acquired by light detection and ranging (LiDAR) technology.
    Link: http://cam.math.msstate.edu/sem20161028HL.html

  • - 2:00pm - Allen 14
    CAM seminar
    Entropy, maximum entropy, and the maximum entropy method
    Dr. Jiu Ding, Mathematics, University of Southern Mississippi,

    Title:  Entropy, maximum entropy, and the maximum entropy method
    Abstract:  The maximum entropy method has been used for the recovery of density functions in physical science and engineering. We introduce the concept of entropy and describe Jaynes’ maximum entropy principle. Then we incorporate the principle with finite elements to develop a maximum entropy method for the statistical and computational study of chaos.
    Link: http://cam.math.msstate.edu/sem20161020JD.html

  • - 2:00pm - Allen 411
    CAM seminar
    A nonlinear electrochemical phase-field model and its applications to Li-ion batteries
    Dr. Lei Chen, Mechanical Engineering, Msstate,

    Title:  A nonlinear electrochemical phase-field model and its applications to Li-ion batteries
    Abstract:  The success of electric vehicles (EVs) requires a significant increase in the energy storage density of lithium (Li)-ion batteries. Remarkable efforts have been recently devoted to high-capacity electrode materials such as Li metal, silicon (Si) and germanium (Ge) as anodes, and Sulphur (S) and oxygen (O2) as cathodes. However, such high-capacity anodes form dendritic and mossy deposits, leading to serious safety concerns and degraded efficiency over recharging cycles. These high-capacity anodes also inherently suffer from their large volume change (e.g., ~300% for Si) when alloyed with Li, which induces plastic flow, fracture and pulverization in the electrodes. Although intensive experimental attempts have helped shed light on understanding the degradation processes, effective strategies to improve the cycling of alloy or metal anodes remain elusive. In this talk, I will present an innovative nonlinear phase-field model to fundamentally understand these degradation mechanisms. To accomplish this, the proposed model, for the first time, accounts for both nonlinear Butler-Volmer electrochemical reaction kinetics and large elasto-plastic deformation for modelling the co-evolution of microstructure and stress. The model is further validated utilizing both theoretical solutions and experimental observations. In particular, the retardation effect of elasto-plasticity on the lithiation kinetics is identified and discussed. A design map is proposed to tailor cell parameters and operating conditions to avoid undesired dendritic degradation. Finally, our recent attempts on phase-field model of microstructure evolution for additive manufacturing alloys, e.g., Ti-6Al-4V and IN718 are presented.
    Link: http://cam.math.msstate.edu/

  • - 2:00pm - Allen 411
    CAM seminar
    A simple bound-preserving sweeping technique for conservative numerical approximations
    Dr. Yuan Liu, Mathematics, Msstate,

    Title:  A simple bound-preserving sweeping technique for conservative numerical approximations
    Abstract:  In this talk, we introduce a simple bound-preserving sweeping procedure for conservative numerical approximations. Conservative schemes are of importance in many applications, yet for high order methods, the numerical solutions do not necessarily satisfy maximum principle. This paper constructs a simple sweeping algorithm to enforce the bound of the solutions. It has a very general framework acting as a postprocessing step accommodating many point-based or cell average-based discretizations. The method is proven to preserve the bounds of the numerical solution while conserving a prescribed quantity designated as a weighted average of values from all points. The technique is demonstrated to work well with a spectral method, high order finite difference and finite volume methods for scalar conservation laws and incompressible flows. Extensive numerical tests in 1D and 2D are provided to verify the accuracy of the sweeping procedure.
    Link: http://cam.math.msstate.edu/sem20160916YL.html

  • - 1:00pm - Allen 411
    CAM seminar
    An introduction of 1D immersed finite element methods for differential equations with discontinuous coefficients
    Dr. Xu Zhang, Mathematics, Msstate,

    Title:  An introduction of 1D immersed finite element methods for differential equations with discontinuous coefficients
    Abstract:  This talk is an introduction of immersed finite element methods. we will first recall the standard finite element methods (FEM) for solving one-dimensional differential equations. Then we will introduce the immersed finite element (IFE) methods for differential equations with discontinuous coefficients (so-called interface problems). The advantage of IFE methods is that the mesh is independent of coefficient jump, thus a uniform mesh can be used for such interface problems. We will demonstrate how to construct IFE basis functions that can accommodate interface jump conditions. We will also present the approximation capability, the error estimation, and the superconvergence behavior of IFE methods. If time permits, we will talk about how to extend this immersed idea to two-dimensional interface problems.

    This talk is accessible to mathematician, graduate students and senior undergraduates in math major with some numerical analysis background.
    Link: http://cam.math.msstate.edu/

  • - 3:30pm - Allen 14
    Statistics seminar
    Determining the optimum number of topics in a latent Dirichlet allocation topic model
    Dr. Dale Bowman, Mathematical Statistics, University of Memphis,

    Title:  Determining the optimum number of topics in a latent Dirichlet allocation topic model
    Abstract:  Topic modeling is a useful tool for examining latent structures in a corpus of documents. Latent Dirichlet allocation (LDA) is a popular topic modeling method that assumes a Bayesian generative model for collections of exchangeable binary observations such as the presence or absence of words within a document. The degree to which an LDA model is useful for modeling a corpus depends, in part, on the number of topics selected. Too few topics can result in an LDA model that does not provide sufficient separation of topics and too many topics can result in a model that is overly complex and difficult to interpret. Several ad hoc, heuristic methods for selecting the proper number of topics have been proposed. These typically require that the LDA model be fit over a varying number of topics and the performance of the resulting model be measured by some criteria such as perplexity, rate of perplexity change, and goodness of fit statistics. We propose a new method based on a goodness of fit test and compare to existing methods.

    Refreshment will be provided in the faculty lounge at 3:00 pm. Everyone is welcome.

  • - TALK CANCELLED
    Positive periodic solutions of first order functional differential equations and applications to population dynamics
    Dr. Seshadev Padhi, Math., Birla Institute
    ,

    Title:  Positive periodic solutions of first order functional differential equations and applications to population dynamics

  • - 3:30pm - Allen 14
    Statistics seminar
    Jackknife empirical likelihood methods for the Gini index
    Dr. Yichuan Zhao, Statistics, Georgia State University,

    Title: Jackknife empirical likelihood methods for the Gini index
    Abstract: A variety of statistical methods have been developed to the interval estimation of a Gini index, one of the most widely used measures of economic inequality. However there is still plenty of room for improvement in terms of coverage accuracy and interval length. In this paper, we propose interval estimators for the index and the difference of two Gini indices via jackknife empirical likelihood. Via expressing the estimating equations in the form of U-statistics, our method can be simply applied as the standard empirical likelihood for an univariate mean and avoid maximizing the profile empirical likelihood for the difference of two Gini indices. Simulation studies show that our method is comparable to existing empirical likelihood methods in terms of coverage accuracy, but yields shorter intervals. The proposed methods are illustrated using a real data set.

  • - 3:30pm - Allen 14
    Statistics seminar
    Option pricing: Modification of Black-Scholes model through fat-tailed distributions
    Dr. Xing Yang, Jackson State University,

    Title:  Option pricing: Modification of Black-Scholes model through fat-tailed distributions

  • - 3:30pm - Allen 14
    Statistics seminar
    Selecting the optimum number of topics in an LDA model
    Dr. Dale Bowman, Mathematical Sciences, University of Memphis,

    Title:  Selecting the optimum number of topics in an LDA model
    Abstract: The Latent Dirichlet Allocation (LDA) model is one of the most used topic models in text analytics. LDA assumes that documents in a corpus are generated using a hierarchical Bayesian model in which each document is modeled as a finite mixture over a set of latent topics. Modeling these topics in order to reduce dimensionality and to cluster documents are the goals of analysis using the LDA model. Gibb’s sampling and variational EM algorithms are often used to estimate the parameters of the underlying Bayesian model. Both algorithms assume that the number of latent topics is a fixed and known quantity. Of interest is criteria that may be used to select the optimum number of topics for a corpus of documents. In this presentation several methods which have been proposed to determine the best number of topics will be discussed and a new method based on goodness of fit of the LDA model is proposed.

  • - 3:30pm - Allen 14
    Statistics seminar
    Merging mixture components for clustering
    Dr. Volodymyr Melnykov, Statistics, University of Alabama,

    Title:  Merging mixture components for clustering
    Abstract:  Finite mixture models are well-known for their flexibility in modeling heterogeneity in data. Model-based clustering is an important application of mixture models that assumes that each mixture component distribution can adequately model a particular group of data. Unfortunately, when more than one component is needed for each group, the appealing one-to-one correspondence between mixture components and groups of data is ruined and model-based clustering loses its attractive interpretation. Several remedies have been considered in literature. We discuss the most promising recent results obtained in this area and propose a new algorithm that finds partitionings through merging mixture components relying on their pairwise overlap. Extensions of the developed technique are considered in the context of clustering large datasets.

2015

  • - 3:30pm - Allen 411
    ACT seminar
    Edge-disjoint (u,v)-trails
    Dr. Hehui Wu, Mathematics, University of Mississippi,

    Title:  Edge-disjoint (u,v)-trails
    Abstract:  For a graph G and vertices u,vV(G), let packing(u,v) be the maximum number of edge-disjoint (u,v)-trails of odd length, and let transversal(u,v) be the minimum number of edges that intersect every odd (u,v)-trail in G. It is proved that packing(u,v) ≤ transversal(u,v) ≤ 8packing(u,v).
    This is joint work with Ross Churchley and Bojan Mohar in Simon Fraser University.

  • - 3:30pm - Allen 14
    Statistics seminar
    Asymptotic independence of sample means and extremes in regenerative processes
    Dr. Peter Kiessler, Mathematical Sciences, Clemson University,

    Title:  Asymptotic independence of sample means and extremes in regenerative processes
    Abstract:  In this paper, the asymptotic independence between sample means and maxima for regenerative processes is derived. Using regenerative process framework, the process is partitioned into IID cycles. Here, point process techniques are used to quantify the distribution of the maximums and the Découpage de Lévy Theorem gives the asymptotic independence between maximums and partial sums.

  • - 2:00pm - Allen 14
    Statistics seminar
    High dimension low sample size asymptotics
    Dr. J S Marron, Statistics and Operations Research, University of North Carolina at Chapel Hill,

    Title:  High dimension low sample size asymptotics

    Abstract: The asymptotics of growing sample size are the foundation of classical mathematical statistics. But modern big data challenges suggest consideration of growing dimension as well. A perhaps extreme case of this has fixed sample size. That context is seen to have some counter-intuitive mathematical structure. These non-standard ways of thinking about data are seen to be the key to understanding important aspects of real genomic data.

  • - 12:00pm - Allen 14
    Statistics seminar
    A new way of modeling integer count time series
    Dr. Robert Lund, Mathematical Sciences, Clemson University,

    Title:  A new way of modeling integer count time series
    Abstract:  This talk proposes a new but simple method of modeling stationary time series of integer counts. Previous work has focused on thinning methods and classical time series autoregressive moving-average (ARMA) difference equations; in contrast, our methods bypass ARMA tactics altogether by using a stationary renewal process to generate a correlated sequence of Bernoulli trials. By superpositioning independent copies of such processes, stationary series with binomial, Poisson, geometric, or any other discrete marginal distribution are easily constructed. Excursions into multivariate count series and models with periodic features are considered. The models are naturally parsimonious, can have negative autocorrelations, and can be fitted via one- step-ahead linear prediction techniques for stationary series. As examples, count models with binomial marginal distributions are fitted to observed counts of rainy days in consecutive weeks at Key West, Florida.

  • - 3:30pm - Allen 14
    Statistics seminar
    Statistical considerations in clinical research studies
    Dr. Karan P. Singh, Medicine, University of Alabama at Birmingham,

    Title:  Statistical considerations in clinical research studies
    Abstract:  Investigators conducting research at clinical research centers often ask statisticians, “Does new intervention work? Or can we get something equivalent to the existing one just as effective and more economical?"

    Statisticians help clinical researchers design studies, help to choose what data to collect, analyze data from experiments, help interpret the results of the study, and collaborate in writing manuscripts to describe the results. Nearly all clinical research studies involve statistician from beginning to end. Statisticians help researchers make sense of the data collected to decide whether an intervention is working or to find factors that may contribute significantly to outcomes.

    In this presentation we present statistical considerations for a research study from beginning to end using practical examples. We hope that it will enhance the understanding of the role a statistician in an investigation conducted at a research center.

  • - 3:30pm - Allen 14
    Statistics seminar
    Robust model-based learning via Spatial-EM Algorithm
    Dr. Xin Dang, Mathematics, University of Mississippi,

    Title:  Robust model-based learning via Spatial-EM Algorithm
    Abstract:  This talk presents a new robust EM algorithm for the finite mixture learning procedures. The proposed Spatial-EM algorithm utilizes median-based location and rank- based scatter estimators to replace sample mean and sample covariance matrix in each M step, hence enhancing stability and robustness of the algorithm. It is robust to outliers and initial values. Compared with many robust mixture learning methods, the Spatial- EM has the advantages of simplicity in implementation and statistical efficiency. We apply Spatial-EM to supervised and unsupervised learning scenarios. More specifically, robust clustering and outlier detection methods based on Spatial-EM have been proposed. We apply the outlier detection to taxonomic research on fish species novelty discovery. Two real datasets are used for clustering analysis. Compared with the regular EM and many other existing methods such as K-median, X-EM and SVM, our method demonstrates superior performance and high robustness.

  • - 3:30pm - Allen 411
    ACT seminar
    Are homotopy groups only groups? (Part II)
    Dr. Paul Fabel, Mathematics, Msstate,

    Title:  Are homotopy groups only groups? (Part II of a 2 part talk)
    Abstract:  Are homotopy groups only groups? The question appears on Qiaochu Yuan's blog
    https://qchu.wordpress.com/2013/09/08/the-homotopy-groups-are-only-groups/.
    Yuan and Ronnie Brown seem to favor a ``no'' answer. However Jeremy Brazas and Omar Antolin Camarena suggest a useful/natural ``yes'' answer is perhaps possible provided one works within a particular category such as CGWH the compactly generated weakly Hausdorff spaces.
    In further support of ``yes'', starting with a totally path disconnected space X in CGWH, we indicate how categorically in CGWH to construct a space X+ whose fundamental group is the free topological group in CGWH generated by X.
    By way of application we have the following. Suppose Z is connected, locally path connected and metrizable. Then there exist metrizable spaces X and X+ so X+Z is a quotient, and the induced F(X) → π1(Z) is a topological quotient.

  • - 3:30pm - Allen 14
    Statistics seminar
    Estimating the sperm whale population density in the gulf of mexico to study the effect of british petroleum oil spill
    Dr. Nabendu Pal, UL Lafayette,

    Title:  Estimating the sperm whale population density in the gulf of mexico to study the effect of british petroleum oil spill
    Abstract:  There has been a lot of interest in the Gulf of Mexico (USA) marine biology due to the disastrous British Petroleum (BP)'s Deep Horizon Oil Rig explosion on April 20, 2010, and subsequent oil spill for nearly five months. Attention has been focused on studying marine creatures to see how the oil spill has affected the surrounding ecosystem. As a part of this investigation we looked into the passive acoustic data obtained by submerged sensors to estimate certain marine mammal populations, particularly sperm whales and beaked whales. The acoustic data obtained after the oil spill is used to estimate the population density of each species, and then compared with those available from the historical data. In this talk we will discuss the estimation method along with the model assumptions.

    Everyone is welcome. Graduate students in statistics are especially encouraged to attend the seminar. Refreshment will be provided at 3:00 pm in the faculty lounge.

  • - 11:00am - Allen 15
    Analysis seminar
    Topics in functional analysis
    Matt McBride, Mathematics, Msstate,

    Title:  Topics in functional analysis

  • - 3:30pm - Allen 411
    ACT seminar
    Are homotopy groups only groups?
    Dr. Paul Fabel, Mathematics, Msstate,

    Title:  Are homotopy groups only groups?
    Abstract:  Are homotopy groups only groups? The question appears on Qiaochu Yuan's blog
    https://qchu.wordpress.com/2013/09/08/the-homotopy-groups-are-only-groups/.
    Yuan and Ronnie Brown seem to favor a ``no'' answer. However Jeremy Brazas and Omar Antolin Camarena suggest a useful/natural ``yes'' answer is perhaps possible provided one works within a particular category such as CGWH the compactly generated weakly Hausdorff spaces.
    In further support of ``yes'', starting with a totally path disconnected space X in CGWH, we indicate how categorically in CGWH to construct a space X+ whose fundamental group is the free topological group in CGWH generated by X.
    By way of application we have the following. Suppose Z is connected, locally path connected and metrizable. Then there exist metrizable spaces X and X+ so X+Z is a quotient, and the induced F(X) → π1(Z) is a topological quotient.

  • - 11:00am - Allen 15
    Analysis seminar
    Topics in functional analysis
    Matt McBride, Mathematics, Msstate,

    Title:  Topics in functional analysis

  • - 3:30pm - Allen 411
    Top Combo Fun seminar
    The cocycle equation on commutative semigroups II
    Dr. Bruce Ebanks, Mathematics, Msstate,

    Title:  The cocycle equation on commutative semigroups
    Abstract:  Let (S, ⋅) be a commutative semigroup and (G, +) be an abelian group. Any solution F : S × SG of the functional equation

    F(x, y) + F(xy, z) = F(x, yz) + F(y, z),    for all    x,y,zS,

    is called a cocycle, and the equation is called the cocycle equation. It is easy to check that any F of the form

    F(x, y) := f(x) + f(y) - f(xy),     x,yS,

    is a cocycle. The question is whether all symmetric cocycles are of this form. The answer is "yes" if S is an abelian group (known for about 50 years), but the general theory on commutative semigroups is far from complete. We introduce a framework which allows a significant advance in the development of this theory.

    This is Part II of a 2-part talk. Part I is linked here.

  • - 3:30pm - Allen 411
    Top Combo Fun seminar
    The cocycle equation on commutative semigroups
    Dr. Bruce Ebanks, Mathematics, Msstate,

    Title:  The cocycle equation on commutative semigroups
    Abstract:  Let (S, ⋅) be a commutative semigroup and (G, +) be an abelian group. Any solution F : S × SG of the functional equation

    F(x, y) + F(xy, z) = F(x, yz) + F(y, z),    for all    x,y,zS,

    is called a cocycle, and the equation is called the cocycle equation. It is easy to check that any F of the form

    F(x, y) := f(x) + f(y) - f(xy),     x,yS,

    is a cocycle. The question is whether all symmetric cocycles are of this form. The answer is "yes" if S is an abelian group (known for about 50 years), but the general theory on commutative semigroups is far from complete. We introduce a framework which allows a significant advance in the development of this theory.

  • - 3:30pm - Allen 14
    Statistics seminar
    Self-exciting hurdle models for terrorist activity
    Dr. Michael Porter, Statistics, University of Alabama,

    Title:  Self-exciting hurdle models for terrorist activity
    Abstract:  A predictive model of terrorist activity is developed by examining the daily number of terrorist attacks in Indonesia from 1994 through 2007. The dynamic model employs a shot noise process to explain the self-exciting nature of the terrorist activities. This estimates the probability of future attacks as a function of the times since the past attacks. In addition, the excess of non-attack days coupled with the presence of multiple coordinated attacks on the same day compelled the use of hurdle models to jointly model the probability of an attack day and corresponding number of attacks. A power law distribution with a shot noise driven parameter best modeled the number of attacks on an attack day. Interpretation of the model parameters is discussed and predictive performance of the models is evaluated.

  • - 3:30pm - Allen 14
    Statistics seminar
    Signal discrimination without denoising
    Dr. Ferebee Tunno, Statistics, Arkansas State University,

    Title:  Signal discrimination without denoising
    Abstract:  This talk reveals that a certain class of tests for autocovariance equality between stationary autoregressive moving average (ARMA) processes can also be used to discriminate between harmonic signals embedded in noise without the need for any reconstruction or modeling. An application involving functional magnetic resonance imaging (fMRI) is presented.

  • - 3:30pm - Allen 411
    Top Combo Fun seminar
    Automorphism groups of codes II
    Dr. Ted Dobson, Mathematics, Msstate,

    Title:  Automorphism groups of codes
         (See part I here.)
    Abstract:  In a recent arXiv posting, Mikhail Muzychuk noticed a relationship between the isomorphism problem for Cayley digraphs of a group G and the isomorphism problem for codes permutation invariant under G. For cyclic groups, he showed that in fact the permutation isomorphism problem for cyclic codes reduces to the isomorphism problem for circulant digraphs. This latter problem has been completely solved, and so Muzychuk produced a solution to the permutation isomorphism problem for cyclic codes. We consider the problem of computing the automorphism group of cyclic codes (and codes invariant under other groups as well). We first give a sufficient condition to decompose a code C into two subcodes C1 and C2, both invariant under the permutation automorphism group of C, and which are determined by codes of smaller length. Additionally, we show that PAut(C) = PAut(C1) ∩ PAut(C2). This sufficient condition corresponds to an existing sufficient condition that gives a similar decomposition of a vertex-transitive digraph. I will give two seminars, with the first discussing the background of the Cayley isomorphism problem for graphs and discussing the proof of the decomposition theorem for a vertex-transitive digraph. The second will give basic information about codes, and then discuss the decomposition theorem for codes. This is joint work with Mikhail Muzychuk of Netanya Academic College.

  • - 3:30pm - Allen 19
    Top Combo Fun seminar
    Automorphism groups of codes I
    Dr. Ted Dobson, Mathematics, Msstate,

    Title:  Automorphism groups of codes
    Abstract:  In a recent arXiv posting, Mikhail Muzychuk noticed a relationship between the isomorphism problem for Cayley digraphs of a group G and the isomorphism problem for codes permutation invariant under G. For cyclic groups, he showed that in fact the permutation isomorphism problem for cyclic codes reduces to the isomorphism problem for circulant digraphs. This latter problem has been completely solved, and so Muzychuk produced a solution to the permutation isomorphism problem for cyclic codes. We consider the problem of computing the automorphism group of cyclic codes (and codes invariant under other groups as well). We first give a sufficient condition to decompose a code C into two subcodes C1 and C2, both invariant under the permutation automorphism group of C, and which are determined by codes of smaller length. Additionally, we show that PAut(C) = PAut(C1) ∩ PAut(C2). This sufficient condition corresponds to an existing sufficient condition that gives a similar decomposition of a vertex-transitive digraph. I will give two seminars, with the first discussing the background of the Cayley isomorphism problem for graphs and discussing the proof of the decomposition theorem for a vertex-transitive digraph. The second will give basic information about codes, and then discuss the decomposition theorem for codes. This is joint work with Mikhail Muzychuk of Netanya Academic College.

  • - 3:30pm - Allen 14
    Statistics seminar
    Copulas and Estimation problems with dependent observations
    Dr. Martial Longla, Statistics, University of Mississippi,

    Title:  Copulas and Estimation Problems with Dependent Observations
    Abstract:  When one lacks independence in a statistical problem, it is necessary to model the dependence structure of the data. Copulas have proven to be an exceptional tool for such studies. The use of copulas helps us establish the convergence properties of dependence coefficients that in their turn provide various central limit theorems. The central limit theorems that we obtain can then be used for inference on parameters or distributions of the data. This talk will take us through the described relationships and some conditions on the densities of the model copulas and their mixtures for various dependence coefficients for stationary Markov chains.

  • - 3:30pm - Allen 411
    Math Club
    Let's do launch with Mathematica: the good, the bad, and the ugly in the optimization of projectile motion
    Dr. Michael Neumann, Mathematics, Msstate,

    Title:  Let's do launch with Mathematica: the good, the bad, and the ugly in the optimization of projectile motion

    See our Facebook page for more information.

  • - 3:30pm - Allen 411
    Top Combo Fun seminar
    Does “topological infinite word reduction” yield unique results?
    Dr. Paul Fabel, Mathematics, Msstate,

    Title:  Does “topological infinite word reduction” yield unique results?
    Abstract:  A basic fact about free groups is each element has a unique irreducible representative as a finite word in finitely many generators.
    This talk explores an analagous phenomenon which can be viewed, at least metaphorically, as a kind of ‘ infinite word reduction’ in which words are allowed to have infinitely many letters, and it is permitted to collapse ‘infinite trivial subwords’.

    J. Dydak (2011) posed an open question to which Jeremy Brazas and I think we have a counterexample based on an orginal idea of Brazas.

    Suppose Y is the closed unit disk. Suppose Π : XY is a continuous surjection and suppose X is a path connected and locally path connected metric space. Suppose if Π(x) = y and if α is a path in Y with initial point y, there exists a unique path β in X with initial point x so that Πβ = α. Must Π be a homeomorphism? (i.e. must Π be continuous, 1-1, onto, and Π−1 is continuous)?

    We expect the answer is ‘no’. A potential counterexample is straightforward to describe but it is proving surprisingly difficult to verify it’s an authentic counterexample. The intent of this talk is to communicate a question, which if settled, would patch what appears to be the largest gap in understanding our construction.

  • - 3:30pm - Allen 14
    Statistics seminar
    Properties of nonlinear transformations of non-Gaussian linear processes
    Dr. Hailin Sang, Statistics, University of Mississippi,

    Title:  Properties of nonlinear transformations of non-Gaussian linear processes
    Abstract:  In this talk, we study the memory properties of nonlinear transformations of non-Gaussian linear processes. Dittmann and Granger (2002) studied the Hermite transformations of Gaussian I(d) processes by applying the orthonormality of the Hermite polynomials under the measure of the standard normal distribution. Nevertheless, the orthogonality does not hold for transformation of non-Gaussian linear processes. We apply the martingale decomposition method developed by Ho and Hsing (1996, 1997) to study the memory properties of nonlinear transformations of non-Gaussian linear processes and obtain consistent results as in the Gaussian case. In particular, the transformation of short-memory time series still has short-memory and the transformation of long-memory time series may have a different memory parameter. This study has application in financial market data analysis and econometrics when the time series observations have non-Gaussian heavy tails.

2014

  • - 3:30pm - Allen 14
    Statistics seminar
    On finite Markov chain imbedding and its applications
    Dr. Tung-Lung Wu, Statistics, Msstate,

    Title:  On finite Markov chain imbedding and its applications
    Abstract:  The method of Finite Markov Chain Imbedding proposed by Fu and Koutras (1994) has been successfully applied in various fields for finding the exact or approximate distributions of runs and patterns under i.i.d or Markov dependent trials and has potential applications in other areas. In this talk, we will talk about the central idea of the finite Markov chain imbedding technique and give several applications, including distributions of runs and patterns, scan statistics and boundary crossing probabilities of Brownian motion.

  • - 3:30pm - Allen 411
    Top Combo Fun seminar
    Additive functions and derivations on rings
    Shayea Aldossari, Mathematics, Msstate,

    Title:  Additive functions and derivations on rings
    Abstract:  We will give the solution of the functional equation
        A(xk+j) + xjB(xk) = 0,
    where R is an integral domain of characteristic 0, and A, B : RR are additive functions. Here k and j are positive integers.

  • - 2:00pm - Allen 411
    Analysis seminar
    Cesaro-like operators on the Hardy space and weighted Bergman spaces of the upper half plane (part II)
    Dr. Len Miller, Mathematics, Msstate,

    Title:  Cesaro-like operators on the Hardy space and weighted Bergman spaces of the upper half plane (part II)

  • - 3:30pm - Allen 14
    Statistics seminar
    Stochastic orders in reliability with hypothesis testing applications
    Dr. Mohammad Sepehrifar, Statistics, Msstate,

    Title:  Stochastic orders in reliability with hypothesis testing applications
    Abstract:  The concept of stochastic orders plays a major role in the theory and practice of statistics. It has been shown that they are very useful in applied probability, statistics, reliability, operation research, economics, and other related fields.It generally refers to a set of relations that may hold between a pair of distributions of random life variables. In reliability theory, stochastic orders are employed to compare lifetime of two systems. Various types of stochastic orders and associated properties have been developed rapidly over the years. In this curriculum talk, we review the recent studies on stochastic orders along with its hypothesis testing applications.

  • - 3:30pm - Allen 411
    Top Combo Fun seminar
    Characterizing ring derivations via functional equations, II
    Dr. Bruce Ebanks, Mathematics, Msstate,

    Title: Characterizing ring derivations via functional equations, Part II
       (a continuation of Dr. Ebanks' talk of Nov 3rd.)
    Abstract: A ring derivation (of order 1) is a map d from a ring R into itself that is additive,

    d( x + y) = d( x ) + d( y)

    and satisfies the product rule

    d( xy) = xd( y ) + d( x)y

    for all x, y in R. We will also define derivations of higher order.
    We will describe results using functional equations to characterize derivations on integral domains of characteristic 0. We provide a unifying framework for the treatment of equations of the form

    Σ xpk fk( xqk ) = 0

    for additive maps fk and integers pk, qk (1 ≤ kn ).

  • - 2:00pm - Allen 411
    Analysis seminar
    Cesaro-like operators on Hardy and weighted Bergman spaces of the upper half plane
    Job Bonyo, Mathematics, Msstate,

    Title: Cesaro-like operators on Hardy and weighted Bergman spaces of the upper half plane

  • - 3:30pm - Allen 411
    Top Combo Fun seminar
    Characterizing ring derivations via functional equations
    Dr. Bruce Ebanks, Mathematics, Msstate,

    Title: Characterizing ring derivations via functional equations
    Abstract: A ring derivation (of order 1) is a map d from a ring R into itself that is additive,

    d( x + y) = d( x ) + d( y)

    and satisfies the product rule

    d( xy) = xd( y ) + d( x)y

    for all x, y in R. We will also define derivations of higher order.
    We will describe results using functional equations to characterize derivations on integral domains of characteristic 0. We provide a unifying framework for the treatment of equations of the form

    Σ xpk fk( xqk ) = 0

    for additive maps fk and integers pk, qk (1 ≤ kn ).

  • - 3:30pm - Allen 411
    Statistics Seminar
    A Test of Independence for Bivariate Observations
    Dr. Prakash Patil, Statistics, Msstate,

    Title: A Test of Independence for Bivariate Observations
    Abstract: A new nonparametric test of independence between the components of bivariate random vectors (X, Y) is proposed. The test statistics is based on the fact that under independence, every quantile of Y given X = x is constant. This is in contrast to the most commonly used basis that the joint probability density or distribution function of X and Y, equals to the product of their marginal probability densities or distributions respectively. The asymptotic distribution of the proposed test under the null and alternative hypotheses are established as well as its consistency against all dependence alternatives. Moreover, a bandwidth selection rule which is based on balancing the trade-off between power and size is provided, so as to facilitate the test’s implementation in practice. Numerical evidence is given for the power of the proposed test statistic in comparison with standard independence tests, already existing in the literature.


  • - 3:30pm - Allen 411
    Top Combo Fun Seminar
    Largest intersecting set systems
    Dr. Russ Woodroofe, Mathematics, Msstate,

    Title: Largest intersecting set systems
    Abstract: The Erdős-Ko-Rado Theorem says that a largest system of pairwise intersecting k-subsets of [n] is obtained by taking all the k-subsets containing a fixed element if k <= n/2. There is a famous and elegant proof by Katona.
    An extension of the original statement of the theorem is that, if the inequality is strict and k < n/2, then every largest system takes the form of all the k-subsets containing a fixed element. I'll review Katona's proof of the EKR Theorem, and show how to extend it to a proof of the strict inequality statement.


  • - 3:00pm - Allen 14
    Statistics seminar
    A prediction interval estimator for the original response when using Box-Cox transformations
    Dr. Marcus Perry, University of Alabama,

    Title: A prediction interval estimator for the original response when using Box-Cox transformations
    Abstract: Motivated by electron microscopy experiments, we develop an approximate prediction interval on the response variable Y, where it is assumed that a normal-theory linear model is fit using a transformed version of Y, and the transformation type is contained in the Box-Cox family. We derive a closed-form approximation to the kth moment of the original response variable Y, which is then used to estimate the mean and variance of Y, given parameter estimates obtained from fitting the model in the transformed domain. Chebychev’s inequality is then used to construct a 100(1 − α)% prediction interval estimator on Y. Using Monte Carlo simulation, we assess the width performance of our proposed Chebychev prediction interval, relative to that obtained by employing a more common interval construction approach. General results suggest that, for a given level of expected coverage, the proposed interval estimator will achieve a smaller mean and variance of the interval width estimates, especially as the number of degrees of freedom beyond that required to estimate model terms is small. We apply our method to two real experimental data sets, one involving a standard 2k design, and the other involving a 2k design with a split-plot error structure.

  • - 3:30pm - Allen 411
    Top Combo Fun seminar
    Topological Characterizations of R-trees and complete R-trees
    Dr. Paul Fabel, Mathematics, Msstate,

    Title: Topological Characterizations of R-trees and complete R-trees.
    Abstract: An arc is a topological space homeomorphic to [0,1]. A topological R-tree P is a metrizable, locally path connected, uniquely arcwise connected topological space. It is only within the last 30 years discovered that each such P admits a metric d, so that each arc in (P, d) is isometric to a Euclidean line segment, i.e. P is a so-called R-tree. The proof is long (25 pages) and appears in TAMS.

    http://www.ams.org/journals/tran/1990-320-01/S0002-9947-1990-0961626-8/S0002-9947-1990-0961626-8.pdf

    Paul Fabel claims to have a new and short and elementary proof of the mentioned result, and moreover a by-product of the proof is the following apparently new and arguably major result: We can arrange that (P,d) is complete if and only if 1) P is topologically complete, and 2) if for each x in P, there exists a closed neighborhood B of x such that each maximal interval in B is compact.

  • Top Combo Fun seminar, irregular Mondays from 3:30-4:30pm, Allen 411, Fall 2014. Topics related to Topology, Combinatorics, or Functional Equations (broadly considered). Organizer: Dr. Russ Woodroofe.

2013

  • Statistics Seminar, Link: http://math.msstate.edu/pdf/StatisticsSeminar.pdf
  • Analysis Seminar: "Extensions of spaces of analytic functions via pointwise limits of bounded sequences and two integral operators on generalized Block spaces" by Len Miller, Analysis Seminar: "Extensions of spaces of analytic functions via pointwise limits of bounded sequences and two integral operators on generalized Block spaces." by Len Miller

2011

2007

  • Peter Takac, Institut fur Mathematik, Universitat Rostock of Rostock, Germany, 4:00 pm, Monday, November 5, 2007, Allen 14
  • Marek Ptak, Department of Mathematics, Agriculture University of Krakow, Poland, 4:00 pm, Tuesday, August 21, 2007, Allen 411
  • Abdellatif Bourhim, Department of Mathematics, University of Laval, Canada, 3:30 pm, March 6, 2007, Allen 411

2006

  • QiQi Lu, Department of Mathematics and Statistics, Mississippi State University, March 24 and March 31, 2006
  • Russell Stocker, Department of Mathematics and Statistics, Mississippi State University, February 24 and March 10, 2006
  • Patrick Gerard, Department of Mathematics and Statistics, Experimental Statistics Station, Mississippi State University, February 10, 2006
  • Jane Harvill, Department of Mathematics and Statistics, Mississippi State University, January 27, 2006

2005

  • Kevin Knudson, Department of Mathematics and Statistics, Mississippi State University - 411 Allen, 6:00 pm, Wednesday, September 21, 2005

2004

2003

2002