Dark–Bright Ring Solitons In Bose–Einstein Condensates, 2011 UMASS, Amherst

#### Dark–Bright Ring Solitons In Bose–Einstein Condensates, J. Stockhofe, Panos Kevrekidis, D. J. Frantzeskakis, P. Schmelcher

*Panos Kevrekidis*

We study dark–bright (DB) ring solitons in two-component Bose–Einstein condensates. In the limit of large densities of the dark component, we describe the soliton dynamics by means of an equation of motion for the ring radius. The presence of the bright, 'filling' species is demonstrated to have a stabilizing effect on the ring dark soliton. Near the linear limit, we discuss the symmetry-breaking bifurcations of DB soliton stripes and vortex-bright soliton clusters from the DB ring and relate the stabilizing effect of filling to changes in the bifurcation diagram. Finally, we show that the stabilization by means of ...

Gm-Csf Production Allows The Identification Of Immunoprevalent Antigens Recognized By Human Cd4+ T Cells Following Smallpox Vaccination, 2011 Torrey Pines Institute for Molecular Studies (TPIMS)

#### Gm-Csf Production Allows The Identification Of Immunoprevalent Antigens Recognized By Human Cd4+ T Cells Following Smallpox Vaccination, Valeria A. Judkowski, Alcinette Bunying, Feng Ge, Jon R. Appel, Kingyee Law, Atima Sharma, Claudia Raja-Gabaglia, Patricia Norori, Radleigh Santos, Marc Giulianotti, Mark K. Slifka, Daniel C. Douek, Barney S. Graham, Clemencia Pinilla

*Mathematics Faculty Articles*

The threat of bioterrorism with smallpox and the broad use of vaccinia vectors for other vaccines have led to the resurgence in the study of vaccinia immunological memory. The importance of the role of CD4+ T cells in the control of vaccinia infection is well known. However, more CD8+ than CD4+ T cell epitopes recognized by human subjects immunized with vaccinia virus have been reported. This could be, in part, due to the fact that most of the studies that have identified human CD4+ specific protein-derived fragments or peptides have used IFN-γ production to evaluate vaccinia specific T cell responses ...

Are Symbolic Powers Highly Evolved?, 2011 University of Nebraska - Lincoln

#### Are Symbolic Powers Highly Evolved?, Brian Harbourne, Craig Hunkeke

*Faculty Publications, Department of Mathematics*

Searching for structural reasons behind old results and conjectures of Chudnovksy regarding the least degree of a nonzero form in an ideal of fat points in PN, we make conjectures which explain them, and we prove the conjectures in certain cases, including the case of general points in P2. Our conjectures were also partly motivated by the Eisenbud-Mazur Conjecture on evolutions, which concerns symbolic squares of prime ideals in local rings, but in contrast we consider higher symbolic powers of homogeneous ideals in polynomial rings.

Modeling Of The Gastric Mucus Gel On The Gastric Epithelium, 2011 Occidental College

#### Modeling Of The Gastric Mucus Gel On The Gastric Epithelium, Frank Lynch, J.P. Keener

*Frank Lynch*

The mucus lining of the mammalian stomach has a thickness on the order of hundreds of microns. Across this mucus layer there is a large change in pH, from pH ∼ 2 inside the stomach to pH ∼ 7 at the intersection of the mucus lining with the stomach wall. The gel layer is thought to simultaneously protect the stomach lining from the acidity of the lumen while transporting gastric acid and other important digestive enzymes toward the lumen. The mechanisms by which these phenomena occur are not well understood. We use partial differential equations to model the protective features of the ...

Stationary States Of A Nonlinear Schrödinger Lattice With A Harmonic Trap, 2011 UMass, Amherst

#### Stationary States Of A Nonlinear Schrödinger Lattice With A Harmonic Trap, V. Achilleos, G. Theocharis, Panos Kevrekidis, N. I. Karachalios, F. K. Diakonos, D. J. Frantzeskakis

*Panos Kevrekidis*

We study a discrete nonlinear Schrödinger lattice with a parabolic trapping potential. The model, describing, e.g., an array of repulsive Bose-Einstein condensate droplets confined in the wells of an optical lattice, is analytically and numerically investigated. Starting from the linear limit of the problem, we use global bifurcation theory to rigorously prove that – in the discrete regime – all linear states lead to nonlinear generalizations thereof, which assume the form of a chain of discrete dark solitons (as the density increases). The stability of the ensuing nonlinear states is studied and it is found that the ground state is stable ...

Lipschitz Regularity For Inner-Variational Equations, 2011 Syracuse University and University of Helsinki

#### Lipschitz Regularity For Inner-Variational Equations, Tadeusz Iwaniec, Leonid V. Kovalev, Jani Onninen

*Mathematics - Faculty Scholarship*

We obtain Lipschitz regularity results for a fairly general class of nonlinear first-order PDEs. These equations arise from the inner variation of certain energy integrals. Even in the simplest model case of the Dirichlet energy the inner-stationary solutions need not be differentiable everywhere; the Lipschitz continuity is the best possible. But the proofs, even in the Dirichlet case, turn out to relay on topological arguments. The appeal to the inner-stationary solutions in this context is motivated by the classical problems of existence and regularity of the energy-minimal deformations in the theory of harmonic mappings and certain mathematical models of nonlinear ...

Wavelet Thresholding In Partially Linear Models: A Computation And Simulation, 2011 Boise State University

#### Wavelet Thresholding In Partially Linear Models: A Computation And Simulation, Leming Qu

*Leming Qu*

Partially linear models have a linear part as in the linear regression and a non-linear part similar to that in the non-parametric regression. The estimates in Partially Linear Models have been studied previously using traditional smoothing methods such as smoothing spline, kernel and piecewise polynomial smoothers. In this paper, a wavelet thresholding method for estimating the corresponding parameters in Partially Linear Models is presented. Extensive simulation results shows that wavelet smoothing approach is comparable to traditional smoothing methods when their assumptions are satisfied. But wavelet smoothing is often superior when assumptions about the smoothness of the underlying function of non-parametric ...

Change Point Estimation Of Bilevel Functions, 2011 Boise State University

#### Change Point Estimation Of Bilevel Functions, Leming Qu, Yi-Cheng Tu

*Leming Qu*

Reconstruction of a bilevel function such as a bar code signal in a partially blind deconvolution problem is an important task in industrial processes. Existing methods are based on either the local approach or the regularization approach with a total variation penalty. This article reformulated the problem explicitly in terms of change points of the 0-1 step function. The bilevel function is then reconstructed by solving the nonlinear least squares problem subject to linear inequality constraints, with starting values provided by the local extremas of the derivative of the convolved signal from discrete noisy data. Simulation results show a considerable ...

Inversion For Non-Smooth Models With Physical Bounds, 2011 ConocoPhillips

#### Inversion For Non-Smooth Models With Physical Bounds, Partha S. Routh, Leming Qu, Mrinal K. Sen, Phil D. Anno

*Leming Qu*

Geological processes produce structures at multiple scales. A discontinuity in the subsurface can occur due to layering, tectonic activities such as faulting, folding and fractures. Traditional approaches to invert geophysical data employ smoothness constraints. Such methods produce smooth models and thefore sharp contrasts in the medium such as lithological boundaries are not easily discernible. The methods that are able to produce non-smooth models, can help interpret the geological discontinuity. In this paper we examine various approaches to obtain non-smooth models from a finite set of noisy data. Broadly they can be categorized into approaches: (1) imposing non-smooth regularization in the ...

Rayleigh Wave Dispersion Curve Inversion: Occam Versus The L1-Norm, 2011 Boise State University

#### Rayleigh Wave Dispersion Curve Inversion: Occam Versus The L1-Norm, Matthew M. Haney, Leming Qu

*Leming Qu*

We compare inversions of Rayleigh wave dispersion curves for shear wave velocity depth profiles based on the L2-norm (Occam's Inversion) and L1-norm (TV Regularization). We forward model Rayleigh waves using a finite-element method instead of the conventional technique based on a recursion formula and root-finding. The forward modeling naturally leads to an inverse problem that is overparameterized in depth. Solving the inverse problem with Occam's Inversion gives the smoothest subsurface model that satisfies the data. However, the subsurface need not be smooth and we therefore also solve the inverse problem with TV Regularization, a procedure that does not ...

Bayesian Wavelet Estimation Of Long Memory Parameter, 2011 Boise State University

#### Bayesian Wavelet Estimation Of Long Memory Parameter, Leming Qu

*Leming Qu*

A Bayesian wavelet estimation method for estimating parameters of a stationary I(d) process is represented as an useful alternative to the existing frequentist wavelet estimation methods. The effectiveness of the proposed method is demonstrated through Monte Carlo simulations. The sampling from the posterior distribution is through the Markov Chain Monte Carlo (MCMC) easily implemented in the WinBUGS software package.

Copula Density Estimation By Total Variation Penalized Likelihood With Linear Equality Constraints, 2011 Boise State University

#### Copula Density Estimation By Total Variation Penalized Likelihood With Linear Equality Constraints, Leming Qu, Wotao Yin

*Leming Qu*

A copula density is the joint probability density function (PDF) of a random vector with uniform marginals. An approach to bivariate copula density estimation is introduced that is based on a maximum penalized likelihood estimation (MPLE) with a total variation (TV) penalty term. The marginal unity and symmetry constraints for copula density are enforced by linear equality constraints. The TV-MPLE subject to linear equality constraints is solved by an augmented Lagrangian and operator-splitting algorithm. It offers an order of magnitude improvement in computational efficiency over another TV-MPLE method without constraints solved by log-barrier method for second order cone program. A ...

Wavelet Image Restoration And Regularization Parameters Selection, 2011 Boise State University

#### Wavelet Image Restoration And Regularization Parameters Selection, Leming Qu

*Leming Qu*

For the restoration of an image based on its noisy distorted observations, we propose wavelet domain restoration by scale-dependent ∫1 penalized regularization method (WaveRSL1). The data adaptive choice of the regularization parameters is based on the Akaike Information Criterion (AIC) and the degrees of freedom (df) is estimated by the number of nonzero elements in the solution. Experiments on some commonly used testing images illustrate that the proposed method possesses good empirical properties.

Wavelet Reconstruction Of Nonuniformly Sampled Signals, 2011 Boise State University

#### Wavelet Reconstruction Of Nonuniformly Sampled Signals, Leming Qu, Partha S. Routh, Phil D. Anno

*Leming Qu*

For the reconstruction of a nonuniformly sampled signal based on its noisy observations, we propose a level dependent l1 penalized wavelet reconstruction method. The LARS/Lasso algorithm is applied to solve the Lasso problem. The data adaptive choice of the regularization parameters is based on the AIC and the degrees of freedom is estimated by the number of nonzero elements in the Lasso solution. Simulation results conducted on some commonly used 1_D test signals illustrate that the proposed method possesses good empirical properties.

Wavelet Deconvolution In A Periodic Setting Using Cross-Validation, 2011 Boise State University

#### Wavelet Deconvolution In A Periodic Setting Using Cross-Validation, Leming Qu, Partha S. Routh, Kyungduk Ko

*Leming Qu*

The wavelet deconvolution method WaveD using band-limited wavelets offers both theoretical and computational advantages over traditional compactly supported wavelets. The translation-invariant WaveD with a fast algorithm improves further. The twofold cross-validation method for choosing the threshold parameter and the finest resolution level in WaveD is introduced. The algorithm’s performance is compared with the fixed constant tuning and the default tuning in WaveD.

Wavelet-Based Bayesian Estimation Of Partially Linear Regression Models With Long Memory Errors, 2011 Boise State University

#### Wavelet-Based Bayesian Estimation Of Partially Linear Regression Models With Long Memory Errors, Kyungduk Ko, Leming Qu, Marina Vannucci

*Leming Qu*

In this paper we focus on partially linear regression models with long memory errors, and propose a wavelet-based Bayesian procedure that allows the simultaneous estimation of the model parameters and the nonparametric part of the model. Employing discrete wavelet transforms is crucial in order to simplify the dense variance-covariance matrix of the long memory error. We achieve a fully Bayesian inference by adopting a Metropolis algorithm within a Gibbs sampler. We evaluate the performances of the proposed method on simulated data. In addition, we present an application to Northern hemisphere temperature data, a benchmark in the long memory literature.

On Semiparametric Regression Via Wavelets, 2011 Purdue University

#### On Semiparametric Regression Via Wavelets, Leming Qu

*Leming Qu*

Semiparametric regression models have a linear part as in the linear regression and a nonlinear part similar to that in the nonparametric regression. The estimates in semiparametric regression models have been studied previously in traditional smoothing methods such as smoothing spline, kernel and piecewise polynomial smoothers. In this thesis, we apply the regularized wavelet estimators by penalizing the l1 norm of the wavelet coefficients of the nonparametric function. The regularization parameter is chosen by universal threshold or cross-validation. When there is only one explanatory variable in the linear part, we directly solve the linear coefficient. When the linear part has ...

Numerical Solutions For A Model Of Tissue Invasion And Migration Of Tumour Cells, 2011 University of Warmia and Mazury

#### Numerical Solutions For A Model Of Tissue Invasion And Migration Of Tumour Cells, Mikhail Kolev, Barbara Zubik-Kowal

*Barbara Zubik-Kowal*

The goal of this paper is to construct a new algorithm for the numerical simulations of the evolution of tumour invasion and metastasis. By means of mathematical model equations and their numerical solutions we investigate how cancer cells can produce and secrete matrix degradative enzymes, degrade extracellular matrix, and invade due to diffusion and haptotactic migration. For the numerical simulations of the interactions between the tumour cells and the surrounding tissue, we apply numerical approximations, which are spectrally accurate and based on small amounts of grid-points. Our numerical experiments illustrate the metastatic ability of tumour cells.

Several Approaches For The Derivation Of Stationary Conditions For Elliptic Mpecs With Upper-Level Control Constraints, 2011 University of Berlin, Germany

#### Several Approaches For The Derivation Of Stationary Conditions For Elliptic Mpecs With Upper-Level Control Constraints, M Hintermüller, Boris S. Mordukhovich, T Surowiec

*Mathematics Research Reports*

The derivation of multiplier-based optimality conditions for elliptic mathematical programs with equilibrium constraints (MPEC) is essential for the characterization of solutions and development of numerical methods. Though much can be said for broad classes of elliptic MPECs in both polyhedric and non-polyhedric settings, the calculation becomes significantly more complicated when additional constraints are imposed on the control. In this paper we develop three derivation methods for constrained MPEC problems: via concepts from variational analysis, via penalization of the control constraints, and via penalization of the lower-level problem with the subsequent regularization of the resulting nonsmoothness. The developed methods and obtained ...

Some New Exact Solutions Of The (3+1)-Dimensional Breaking Soliton Equation By The Exp-Function Method, 2011 University of Kermanshah, Razi

#### Some New Exact Solutions Of The (3+1)-Dimensional Breaking Soliton Equation By The Exp-Function Method, Mohammad Najafi M.Najafi, Mohammad Taghi Darvishi, Maliheh Najafi

*mohammad najafi*

This paper applies the Exp-function method to search for new exact traveling wave solutions of the (3+1)-dimensional breaking soliton equation, their physical expantions are given graphically.