TY - JOUR
TI - Sparse Approximation using $\ell_1-\ell_2$ Minimization and Its Application to Stochastic Collocation
AU - Yan, Liang
AU - Shin, Yeonjong
AU - Xiu, Dongbin
T2 - SIAM Journal on Scientific Computing
AB - We discuss the properties of sparse approximation using $\ell_1-\ell_2$ minimization. We present several theoretical estimates regarding its recoverability for both sparse and nonsparse signals. We then apply the method to sparse orthogonal polynomial approximations for stochastic collocation, with a focus on the use of Legendre polynomials. We study the recoverability of both the standard $\ell_1-\ell_2$ minimization and Chebyshev weighted $\ell_1-\ell_2$ minimization. It is noted that the Chebyshev weighted version is advantageous only at low dimensions, whereas the standard nonweighted version is preferred in high dimensions. Various numerical examples are presented to verify the theoretical findings.
DA - 2017/1//
PY - 2017/1//
DO - 10.1137/15m103947x
VL - 39
IS - 1
SP - A229-A254
UR - http://dx.doi.org/10.1137/15m103947x
ER -
TY - JOUR
TI - A Randomized Tensor Quadrature Method for High Dimensional Polynomial Approximation
AU - Wu, Kailiang
AU - Shin, Yeonjong
AU - Xiu, Dongbin
T2 - SIAM Journal on Scientific Computing
AB - We present a numerical method for polynomial approximation of multivariate functions. The method utilizes Gauss quadrature in tensor product form, which is known to be inefficient in high dimensions. Here we demonstrate that by using a new randomized algorithm and taking advantage of the tensor structure of the grids, a highly efficient algorithm can be constructed. The new method does not require prior knowledge/storage of the entire data set at all the tensor grid points, whose total number of points is excessively large in high dimensions. Instead the method utilizes one data point at a time and iteratively conducts the approximation. This feature allows the use of the method irrespective of the size of the data set. We establish the rate of convergence of this iterative algorithm and show that its operational counts can be lower than the standard methods, when applicable, such as least squares. Numerical examples in up to hundreds of dimensions are presented to verify the theoretical analysis and demonstrate the effectiveness of the method.
DA - 2017/1//
PY - 2017/1//
DO - 10.1137/16m1081695
VL - 39
IS - 5
SP - A1811-A1833
UR - http://dx.doi.org/10.1137/16m1081695
ER -
TY - JOUR
TI - A Randomized Algorithm for Multivariate Function Approximation
AU - Shin, Yeonjong
AU - Xiu, Dongbin
T2 - SIAM Journal on Scientific Computing
AB - The randomized Kaczmarz (RK) method is a randomized iterative algorithm for solving (overdetermined) linear systems of equations. In this paper, we extend the RK method to function approximation in a bounded domain. We demonstrate that by conducting the approximation randomly one sample at a time the method converges. Convergence analysis is conducted in terms of expectation, where we establish sharp upper and lower bounds for both the convergence rate of the algorithm and the error of the resulting approximation. The analysis also establishes the optimal sampling probability measure to achieve the optimal rate of convergence. Various numerical examples are provided to validate the theoretical results.
DA - 2017/1//
PY - 2017/1//
DO - 10.1137/16m1075193
VL - 39
IS - 3
SP - A983-A1002
UR - http://dx.doi.org/10.1137/16m1075193
ER -
TY - RPRT
TI - Hierarchical Matrices and Low-Rank Methods for Extreme-Scale Solvers.
AU - Boman, Erik G
AU - Chen, Chao
AU - Darve, Eric
AU - Rajamanickam, Sivasankaran
AU - Tuminaro, Raymond S
A3 - Sandia National Lab.(SNL-NM), Albuquerque, NM (United States); Sandia …
DA - 2017///
PY - 2017///
PB - Sandia National Lab.(SNL-NM), Albuquerque, NM (United States); Sandia …
ER -
TY - RPRT
TI - A Parallel Hierarchical Low-Rank Solver for General Sparse Matrices.
AU - Boman, Erik G
AU - Chen, Chao
AU - Darve, Eric
AU - Rajamanickam, Sivasankaran
AU - Tuminaro, Raymond S
A3 - Sandia National Lab.(SNL-NM), Albuquerque, NM (United States)
DA - 2017///
PY - 2017///
PB - Sandia National Lab.(SNL-NM), Albuquerque, NM (United States)
ER -
TY - RPRT
TI - A Hierarchical Low-Rank Solver for Large Sparse Linear Systems.
AU - Boman, Erik G
AU - Chen, Chao
AU - Darve, Eric
AU - Rajamanickam, Sivasankaran
AU - Tuminaro, Raymond S
A3 - Sandia National Lab.(SNL-NM), Albuquerque, NM (United States)
DA - 2017///
PY - 2017///
PB - Sandia National Lab.(SNL-NM), Albuquerque, NM (United States)
ER -
TY - JOUR
TI - Numerical Modeling of the Hydrodynamic Loads Applied on the «BREST-300» Reactor Steam Generator Tubes during a Primary-to-Secondary Leak Accident
T2 - Vestnik MEI
AB - The article considers the flashing of water in liquid lead and the hydrodynamic processes caused by this phenomenon initially in the emergency mode involving primary-to-secondary leak in the steam generator used as part of the «BREST-OD-300» fast-neutron lead-cooled nuclear reactor plant. The analysis was carried out using an integral equilibrium thermodynamic model for water describing the flashing of a single droplet. In the analysis, uniform distributions of the physical parameters (pressure, void fraction, etc.) inside the droplet are assumed. The liquid lead hydrodynamics is described by a system of nonsteady equations of continuity and motion for ideal incompressible fluid in a spherical system of coordinates. Mathematical descriptions of the “equilibrium” model and semi-implicit numerical method for solving the differential equations used in the model are given. Time dependences of the droplet expansion radius and droplet pressure are obtained. Spatial distributions of lead velocity and pressure for different moments of time are calculated and presented. Transitions of one kind of energy to another are analyzed. The numerical results obtained from the equilibrium model are compared with similar results calculated from an “explosion” model, the main assumption of which is that the initial excess energy of the droplet instantaneously transforms into the liquid lead mechanical energy. The article presents a short description of the explosion model developed proceeding from generalization of the model of instantaneous point energy release (explosion) in ideal incompressible liquid for the case of instantaneous energy release in a finite volume. The liquid lead velocity field is calculated, based on which the hydrodynamic force applied to the steam generator tube located in close vicinity of the rupture place is estimated. The calculation results have shown that this force is insufficient for causing damage to the nearest steam generator tubes. It has been shown that the hydrodynamic impact force calculated taking into account a finite rate of energy transfer from the droplet to the lead (the equilibrium model) is lower than that obtained from using the explosion model.
DA - 2017///
PY - 2017///
DO - 10.24160/1993-6982-2017-3-33-40
IS - 3
SP - 33-40
UR - http://dx.doi.org/10.24160/1993-6982-2017-3-33-40
ER -
TY - JOUR
TI - Effective $l^2$ decoupling for the parabola
DA - 2017/11/3/
PY - 2017/11/3/
ER -
TY - THES
TI - Thin films with non-conservative effects
AU - Ji, H.
DA - 2017///
PY - 2017///
M3 - PhD Dissertation
PB - Duke University
ER -
TY - JOUR
TI - Global existence of solutions to a tear film model with locally elevated evaporation rates
AU - Gao, Y.
AU - Ji, H.
AU - Liu, J.-G.
AU - Witelski, T.P.
T2 - Physica D: Nonlinear Phenomena
AB - Motivated by a model proposed by Peng et al. [Advances in Coll. and Interf. Sci. 206 (2014)] for break-up of tear films on human eyes, we study the dynamics of a generalized thin film model. The governing equations form a fourth-order coupled system of nonlinear parabolic PDE for the film thickness and salt concentration subject to non-conservative effects representing evaporation. We analytically prove the global existence of solutions to this model with mobility exponents in several different ranges and the results are then validated against PDE simulations. We also numerically capture other interesting dynamics of the model, including finite-time rupture-shock phenomenon due to the instabilities caused by locally elevated evaporation rates, convergence to equilibrium and infinite-time thinning.
DA - 2017///
PY - 2017///
DO - 10.1016/j.physd.2017.03.005
VL - 350
SP - 13-25
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-85017370200&partnerID=MN8TOARS
ER -
TY - JOUR
TI - Finite-time thin film rupture driven by modified evaporative loss
AU - Ji, H.
AU - Witelski, T.P.
T2 - Physica D: Nonlinear Phenomena
AB - Rupture is a nonlinear instability resulting in a finite-time singularity as a fluid layer approaches zero thickness at a point. We study the dynamics of rupture in a generalized mathematical model of thin films of viscous fluids with evaporative effects. The governing lubrication model is a fourth-order nonlinear parabolic partial differential equation with a non-conservative loss term due to evaporation. Several different types of finite-time singularities are observed due to balances between evaporation and surface tension or intermolecular forces. Non-self-similar behavior and two classes of self-similar rupture solutions are analyzed and validated against high resolution PDE simulations.
DA - 2017///
PY - 2017///
DO - 10.1016/j.physd.2016.10.002
VL - 342
SP - 1-15
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-85006445289&partnerID=MN8TOARS
ER -
TY - JOUR
TI - Virtualization Map for the Littelmann Path Model
AU - Pan, Jianping
AU - Scrimshaw, Travis
T2 - Transformation Groups
AB - We show the natural embedding of weight lattices from a diagram folding is a virtualization map for the Littelmann path model, which recovers a result of Kashiwara. As an application, we give a type-independent proof that certain Kirillov-Reshetikhin crystals respect diagram foldings, which is a known result on a special case of a conjecture given by Okado, Schilling, and Shimozono.
DA - 2017/11/10/
PY - 2017/11/10/
DO - 10.1007/s00031-017-9456-3
VL - 23
IS - 4
SP - 1045–1061
SN - 1083-4362 1531-586X
UR - http://dx.doi.org/10.1007/s00031-017-9456-3
ER -
TY - JOUR
TI - Perturbation Analysis for Investment Portfolios Under Partial Information with Expert Opinions
AU - Fouque, J.-P.
AU - Papanicolaou, A.
AU - Sircar, R.
T2 - SIAM Journal on Control and Optimization
AB - We analyze the Merton portfolio optimization problem when the growth rate is an unobserved Gaussian process whose level is estimated by filtering from observations of the stock price. We use the Kalman filter to track the hidden state(s) of expected returns given the history of asset prices, and then use this filter as input to a portfolio problem with an objective to maximize expected terminal utility. Our results apply for general concave utility functions. We incorporate time-scale separation in the fluctuations of the returns process, and utilize singular and regular perturbation analysis on the associated partial-information HJB equation, which leads to an intuitive interpretation of the additional risk caused by uncertainty in expected returns. The results are an extension of the partially informed investment strategies obtained by the Black--Litterman model, wherein investors' views on upcoming performance are incorporated into the optimization along with any degree of uncertainty that the investor may have in these views.
DA - 2017/1//
PY - 2017/1//
DO - 10.1137/15m1006854
VL - 55
IS - 3
SP - 1534-1566
J2 - SIAM J. Control Optim.
LA - en
OP -
SN - 0363-0129 1095-7138
UR - http://dx.doi.org/10.1137/15M1006854
DB - Crossref
KW - filtering
KW - control
KW - Hamilton-Jacobi-Bellman equation
KW - portfolio optimization
KW - partial information
KW - expert opinions
ER -
TY - JOUR
TI - Dimension Reduction in Statistical Estimation of Partially Observed Multiscale Processes
AU - Papanicolaou, Andrew
AU - Spiliopoulos, Konstantinos
T2 - SIAM/ASA Journal on Uncertainty Quantification
AB - We consider partially observed multiscale diffusion models that are specified up to an unknown vector parameter. We establish for a very general class of test functions that the filter of the original model converges to a filter of reduced dimension. Then, this result is used to justify statistical estimation for the unknown parameters of interest based on the model of reduced dimension but using the original available data. This allows us to learn the unknown parameters of interest while working in lower dimensions, as opposed to working with the original high dimensional system. Simulation studies support and illustrate the theoretical results.
DA - 2017/1//
PY - 2017/1//
DO - 10.1137/16m1085930
VL - 5
IS - 1
SP - 1220-1247
J2 - SIAM/ASA J. Uncertainty Quantification
LA - en
OP -
SN - 2166-2525
UR - http://dx.doi.org/10.1137/16M1085930
DB - Crossref
KW - data assimilation
KW - filtering
KW - parameter estimation
KW - homogenization
KW - multiscale diffusions,dimension reduction
ER -
TY - BOOK
TI - Convex Analysis and Monotone Operator Theory in Hilbert Spaces
AU - Bauschke, Heinz H.
AU - Combettes, Patrick L.
AB - This book provides a largely self-contained account of the main results of convex analysis and optimization in Hilbert space. A concise exposition of related constructive fixed point theory is present
DA - 2017///
PY - 2017///
DO - 10.1007/978-1-4419-9467-7
PB - Springer New York
UR - https://link.springer.com/book/10.1007%2F978-3-319-48311-5
ER -
TY - JOUR
TI - Analysis and prediction of protein folding energy changes upon mutation by element specific persistent homology
AU - Cang, Zixuan
AU - Wei, Guowei
T2 - Bioinformatics
AB - Site directed mutagenesis is widely used to understand the structure and function of biomolecules. Computational prediction of mutation impacts on protein stability offers a fast, economical and potentially accurate alternative to laboratory mutagenesis. Most existing methods rely on geometric descriptions, this work introduces a topology based approach to provide an entirely new representation of mutation induced protein stability changes that could not be obtained from conventional techniques. Topology based mutation predictor (T-MP) is introduced to dramatically reduce the geometric complexity and number of degrees of freedom of proteins, while element specific persistent homology is proposed to retain essential biological information. The present approach is found to outperform other existing methods in the predictions of globular protein stability changes upon mutation. A Pearson correlation coefficient of 0.82 with an RMSE of 0.92 kcal/mol is obtained on a test set of 350 mutation samples. For the prediction of membrane protein stability changes upon mutation, the proposed topological approach has a 84% higher Pearson correlation coefficient than the current state-of-the-art empirical methods, achieving a Pearson correlation of 0.57 and an RMSE of 1.09 kcal/mol in a 5-fold cross validation on a set of 223 membrane protein mutation samples. http://weilab.math.msu.edu/TML/TML-MP/ Supplementary data are available at Bioinformatics online.
DA - 2017/7/14/
PY - 2017/7/14/
DO - 10.1093/bioinformatics/btx460
VL - 7
UR - http://dx.doi.org/10.1093/bioinformatics/btx460
ER -
TY - JOUR
TI - TopologyNet: Topology based deep convolutional and multi-task neural networks for biomolecular property predictions
AU - Cang, Zixuan
AU - Wei, Guo-Wei
T2 - PLOS Computational Biology
AB - Although deep learning approaches have had tremendous success in image, video and audio processing, computer vision, and speech recognition, their applications to three-dimensional (3D) biomolecular structural data sets have been hindered by the geometric and biological complexity. To address this problem we introduce the element-specific persistent homology (ESPH) method. ESPH represents 3D complex geometry by one-dimensional (1D) topological invariants and retains important biological information via a multichannel image-like representation. This representation reveals hidden structure-function relationships in biomolecules. We further integrate ESPH and deep convolutional neural networks to construct a multichannel topological neural network (TopologyNet) for the predictions of protein-ligand binding affinities and protein stability changes upon mutation. To overcome the deep learning limitations from small and noisy training sets, we propose a multi-task multichannel topological convolutional neural network (MM-TCNN). We demonstrate that TopologyNet outperforms the latest methods in the prediction of protein-ligand binding affinities, mutation induced globular protein folding free energy changes, and mutation induced membrane protein folding free energy changes.weilab.math.msu.edu/TDL/.
DA - 2017/7/27/
PY - 2017/7/27/
DO - 10.1371/journal.pcbi.1005690
VL - 13
IS - 7
SP - e1005690
ER -
TY - BOOK
TI - Numerical Solution of Differential Equations
AU - Li, Zhilin
AU - Qiao, Zhonghua
AU - Tang, Tao
AB - This introduction to finite difference and finite element methods is aimed at graduate students who need to solve differential equations. The prerequisites are few (basic calculus, linear algebra, and ODEs) and so the book will be accessible and useful to readers from a range of disciplines across science and engineering. Part I begins with finite difference methods. Finite element methods are then introduced in Part II. In each part, the authors begin with a comprehensive discussion of one-dimensional problems, before proceeding to consider two or higher dimensions. An emphasis is placed on numerical algorithms, related mathematical theory, and essential details in the implementation, while some useful packages are also introduced. The authors also provide well-tested MATLAB® codes, all available online.
DA - 2017/11/30/
PY - 2017/11/30/
DO - 10.1017/9781316678725
PB - Cambridge University Press
UR - http://dx.doi.org/10.1017/9781316678725
ER -
TY - CONF
TI - Real-Time Implementation of a LQR-Based Controller for the Stabilization of a Double Inverted Pendulum
AU - Tran, H.
AU - Bernstein, A.
T2 - International MultiConference of Engineers and Computer Scientists
A2 - Ao, Sio-long
A2 - Castillo, Oscar
A2 - Douglas, Craig
A2 - Feng, David Dagan
A2 - Korunsky, Alexander
T3 - Lecture notes in engineering and computer science
C2 - 2017///
C3 - International MultiConference of Engineers and Computer Scientists : IMECS 2017: 15-17 March, 2017, the Royal Garden Hotel, Kowloon, Hong Kong
DA - 2017///
PY - 2017/3/15/
VL - I
SP - 245–250
PB - Newswood Limited
SN - 978-988-14047-3-2
ER -
TY - JOUR
TI - Degree-optimal moving frames for rational curves
DA - 2017/3/8/
PY - 2017/3/8/
ER -
TY - JOUR
TI - On Two Theorems of Darboux
DA - 2017/9/21/
PY - 2017/9/21/
ER -
TY - JOUR
TI - Subresultants in multiple roots: An extremal case
AU - Bostan, A.
AU - D'Andrea, C.
AU - Krick, T.
AU - Szanto, A.
AU - Valdettaro, M.
T2 - Linear Algebra and its Applications
AB - We provide explicit formulae for the coefficients of the order-d polynomial subresultant of (x−α)m and (x−β)n with respect to the set of Bernstein polynomials {(x−α)j(x−β)d−j,0≤j≤d}. They are given by hypergeometric expressions arising from determinants of binomial Hankel matrices.
DA - 2017/9//
PY - 2017/9//
DO - 10.1016/J.LAA.2017.04.019
VL - 529
SP - 185-198
J2 - Linear Algebra and its Applications
LA - en
OP -
SN - 0024-3795
UR - http://dx.doi.org/10.1016/J.LAA.2017.04.019
DB - Crossref
KW - Subresultants
KW - Hankel matrices
KW - Ostrowski's determinant
KW - Pfaff-Saalschiltz identity
ER -
TY - JOUR
TI - Inverse problems and techniques with applications in the biological sciences
AU - Banks, H. T.
AU - Burns, J. A.
T2 - Inverse Problems in Science and Engineering
DA - 2017/11/21/
PY - 2017/11/21/
DO - 10.1080/17415977.2017.1318490
VL - 26
IS - 2
SP - 151-151
J2 - Inverse Problems in Science and Engineering
LA - en
OP -
SN - 1741-5977 1741-5985
UR - http://dx.doi.org/10.1080/17415977.2017.1318490
DB - Crossref
ER -
TY - JOUR
TI - The Basic Reproductive Number for Disease Systems with Multiple Coupled Heterogeneities
AU - Lloyd, Alun
AU - Kitron, Uriel
AU - Perkins, Alex
AU - Prokopec, Gonzalo Vazquez
AU - Waller, Lance
T2 - bioRxiv
AB - In mathematical epidemiology, a well-known formula describes the impact of heterogeneity on the basic reproductive number, R0, for situations in which transmission is separable and for which there is one source of variation in susceptibility and one source of variation in infectiousness. This formula is written in terms of the magnitudes of the heterogeneities, as quantified by their coefficients of variation, and the correlation between them. A natural question to ask is whether analogous results apply when there are multiple sources of variation in susceptibility and/or infectiousness. In this paper we demonstrate that with three or more coupled heterogeneities, R0 under separable transmission depends on details of the distribution of the heterogeneities in a way that is not seen in the well-known simpler situation. We provide explicit formulae for the cases of multivariate normal and multivariate log-normal distributions, showing that R0 can again be expressed in terms of the magnitudes of the heterogeneities and the pairwise correlations between them. The formulae, however, differ between the two multivariate distributions, demonstrating that no formula of this type applies generally when there are three or more coupled heterogeneities. We see that the results of the formulae are approximately equal when heterogeneities are relatively small and show that an earlier result in the literature (Koella, 1991) should be viewed in this light. We provide numerical illustrations of our results and discuss a setting in which coupled heterogeneities are likely to have a major impact on the value of R0. We also describe a rather surprising result: in a system with three heterogeneities, R0 can exhibit non-monotonic behavior with increasing levels of heterogeneity, in marked contrast to the familiar two heterogeneity setting in which R0 either increases or decreases with increasing heterogeneity.
DA - 2017///
PY - 2017///
DO - 10.1016/j.mbs.2019.108294
SP - 220004
KW - Disease transmission model
KW - Heterogeneity
KW - Basic reproductive number
KW - Coupled heterogeneities
ER -
TY - JOUR
TI - Evaluating strategies for reversing CRISPR-Cas9 gene drives
AU - Vella, Michael R.
AU - Gunning, Christian E.
AU - Lloyd, Alun L.
AU - Gould, Fred
T2 - Scientific Reports
AB - Abstract A gene drive biases inheritance of a gene so that it increases in frequency within a population even when the gene confers no fitness benefit. There has been renewed interest in environmental releases of engineered gene drives due to recent proof of principle experiments with the CRISPR-Cas9 system as a drive mechanism. Release of modified organisms, however, is controversial, especially when the drive mechanism could theoretically alter all individuals of a species. Thus, it is desirable to have countermeasures to reverse a drive if a problem arises. Several genetic mechanisms for limiting or eliminating gene drives have been proposed and/or developed, including synthetic resistance, reversal drives, and immunizing reversal drives. While predictions about efficacy of these mechanisms have been optimistic, we lack detailed analyses of their expected dynamics. We develop a discrete time model for population genetics of a drive and proposed genetic countermeasures. Efficacy of drive reversal varies between countermeasures. For some parameter values, the model predicts unexpected behavior including polymorphic equilibria and oscillatory dynamics. The timing and number of released individuals containing a genetic countermeasure can substantially impact outcomes. The choice among countermeasures by researchers and regulators will depend on specific goals and population parameters of target populations.
DA - 2017/5/30/
PY - 2017/5/30/
DO - 10.1101/144097
VL - 5
SP - 11038
UR - https://doi.org/10.1101/144097
ER -
TY - JOUR
TI - On an New Algorithm for Function Approximation with Full Accuracy in the Presence of Discontinuities Based on the Immersed Interface Method
AU - Amat, Sergio
AU - Li, Zhilin
AU - Ruiz, Juan
T2 - Journal of Scientific Computing
DA - 2017/11/8/
PY - 2017/11/8/
DO - 10.1007/S10915-017-0596-3
VL - 75
IS - 3
SP - 1500-1534
J2 - J Sci Comput
LA - en
OP -
SN - 0885-7474 1573-7691
UR - http://dx.doi.org/10.1007/S10915-017-0596-3
DB - Crossref
KW - IIM
KW - Finite difference methods
KW - Correction terms
KW - Multiresolution schemes
KW - Improved adaption to discontinuities
KW - Signal processing
ER -
TY - JOUR
TI - Using Multi-Class Classification Methods to Predict Baseball Pitch Types
AU - Sidle, G.
AU - Tran, H.
T2 - Journal of Sports Analytics
DA - 2017///
PY - 2017///
DO - 10.3233/JSA-170171
VL - 4
IS - 1
SP - 85-93
ER -
TY - CHAP
TI - Implicit filtering and hidden constraints, in Advances and Trends in Optimization with Engineering Applications
AU - Kelley, C.T.
T2 - MOS-SIAM Series on Optimization
A2 - Terlaky, T.
A2 - Anjos, M.
A2 - Ahmed, S.
PY - 2017///
VL - 24
SP - 507–518
PB - SIAM
ER -
TY - JOUR
TI - A new analytical approach to consistency and overfitting in regularized empirical risk minimization
AU - TRILLOS, NICOLÁS GARCÍA
AU - MURRAY, RYAN
T2 - European Journal of Applied Mathematics
AB - This work considers the problem of binary classification: given training data x 1 , . . ., x n from a certain population, together with associated labels y 1 ,. . ., y n ∈ {0,1}, determine the best label for an element x not among the training data. More specifically, this work considers a variant of the regularized empirical risk functional which is defined intrinsically to the observed data and does not depend on the underlying population. Tools from modern analysis are used to obtain a concise proof of asymptotic consistency as regularization parameters are taken to zero at rates related to the size of the sample. These analytical tools give a new framework for understanding overfitting and underfitting, and rigorously connect the notion of overfitting with a loss of compactness.
DA - 2017/7//
PY - 2017/7//
DO - 10.1017/s0956792517000201
VL - 28
IS - 6
SP - 886-921
KW - Overfitting
KW - empirical risk minimization
KW - graph total variation
KW - discrete to continuum
KW - classification
ER -
TY - JOUR
TI - Cutoff estimates for the linearized Becker–Döring equations
AU - Murray, Ryan W.
AU - Pego, Robert L.
T2 - Communications in Mathematical Sciences
DA - 2017///
PY - 2017///
DO - 10.4310/cms.2017.v15.n6.a10
VL - 15
IS - 6
SP - 1685-1702
KW - coagulation-fragmentation equations
KW - spectrum
KW - cutoff estimates
ER -
TY - JOUR
TI - Coxeter-biCatalan combinatorics
AU - Barnard, Emily
AU - Reading, Nathan
T2 - Journal of Algebraic Combinatorics
AB - We pose counting problems related to the various settings for Coxeter-Catalan combinatorics (noncrossing, nonnesting, clusters, Cambrian). Each problem is to count “twin” pairs of objects from a corresponding problem in Coxeter-Catalan combinatorics. We show that the problems all have the same answer, and, for a given finite Coxeter group W, we call the common solution to these problems the W-biCatalan number. We compute the W-biCatalan number for all W and take the first steps in the study of Coxeter-biCatalan combinatorics.
DA - 2017///
PY - 2017///
DO - 10.1007/s10801-017-0775-1
VL - 8
IS - 2
SP - 241–300
KW - Alternating arc diagram
KW - Coxeter-Catalan combinatorics
KW - Doubled root poset
KW - Twin clusters
KW - Twin noncrossing partitions
KW - Twin nonnesting partitions
KW - Twin sortable elements
ER -
TY - JOUR
TI - Reduced-order description of transient instabilities and computation of finite-time Lyapunov exponents
T2 - Chaos: An Interdisciplinary Journal of Nonlinear Science
AB - High-dimensional chaotic dynamical systems can exhibit strongly transient features. These are often associated with instabilities that have a finite-time duration. Because of the finite-time character of these transient events, their detection through infinite-time methods, e.g., long term averages, Lyapunov exponents or information about the statistical steady-state, is not possible. Here, we utilize a recently developed framework, the Optimally Time-Dependent (OTD) modes, to extract a time-dependent subspace that spans the modes associated with transient features associated with finite-time instabilities. As the main result, we prove that the OTD modes, under appropriate conditions, converge exponentially fast to the eigendirections of the Cauchy–Green tensor associated with the most intense finite-time instabilities. Based on this observation, we develop a reduced-order method for the computation of finite-time Lyapunov exponents (FTLE) and vectors. In high-dimensional systems, the computational cost of the reduced-order method is orders of magnitude lower than the full FTLE computation. We demonstrate the validity of the theoretical findings on two numerical examples.
DA - 2017/6//
PY - 2017/6//
DO - 10.1063/1.4984627
UR - http://dx.doi.org/10.1063/1.4984627
ER -
TY - JOUR
TI - A critical comparison of Lagrangian methods for coherent structure detection
T2 - Chaos: An Interdisciplinary Journal of Nonlinear Science
AB - We review and test twelve different approaches to the detection of finite-time coherent material structures in two-dimensional, temporally aperiodic flows. We consider both mathematical methods and diagnostic scalar fields, comparing their performance on three benchmark examples: the quasiperiodically forced Bickley jet, a two-dimensional turbulence simulation, and an observational wind velocity field from Jupiter's atmosphere. A close inspection of the results reveals that the various methods often produce very different predictions for coherent structures, once they are evaluated beyond heuristic visual assessment. As we find by passive advection of the coherent set candidates, false positives and negatives can be produced even by some of the mathematically justified methods due to the ineffectiveness of their underlying coherence principles in certain flow configurations. We summarize the inferred strengths and weaknesses of each method, and make general recommendations for minimal self-consistency requirements that any Lagrangian coherence detection technique should satisfy.
DA - 2017/5//
PY - 2017/5//
DO - 10.1063/1.4982720
UR - http://dx.doi.org/10.1063/1.4982720
ER -
TY - JOUR
TI - Reduced-order prediction of rogue waves in two-dimensional deep-water waves
T2 - Journal of Computational Physics
AB - We consider the problem of large wave prediction in two-dimensional water waves. Such waves form due to the synergistic effect of dispersive mixing of smaller wave groups and the action of localized nonlinear wave interactions that leads to focusing. Instead of a direct simulation approach, we rely on the decomposition of the wave field into a discrete set of localized wave groups with optimal length scales and amplitudes. Due to the short-term character of the prediction, these wave groups do not interact and therefore their dynamics can be characterized individually. Using direct numerical simulations of the governing envelope equations we precompute the expected maximum elevation for each of those wave groups. The combination of the wave field decomposition algorithm, which provides information about the statistics of the system, and the precomputed map for the expected wave group elevation, which encodes dynamical information, allows (i) for understanding of how the probability of occurrence of rogue waves changes as the spectrum parameters vary, (ii) the computation of a critical length scale characterizing wave groups with high probability of evolving to rogue waves, and (iii) the formulation of a robust and parsimonious reduced-order prediction scheme for large waves. We assess the validity of this scheme in several cases of ocean wave spectra.
DA - 2017/7//
PY - 2017/7//
DO - 10.1016/j.jcp.2017.03.054
UR - http://dx.doi.org/10.1016/j.jcp.2017.03.054
KW - Prediction of rogue waves
KW - Extreme rare events
KW - Modulation instability and focusing
KW - Random waves
KW - Reduced-order stochastic prediction
ER -
TY - JOUR
TI - Optimal initial condition of passive tracers for their maximal mixing in finite time
T2 - Physical Review Fluids
AB - The efficiency of a fluid mixing device is often limited by fundamental laws and/or design constraints, such that a perfectly homogeneous mixture cannot be obtained in finite time. Here, we address the natural corollary question: Given the best available mixer, what is the optimal initial tracer pattern that leads to the most homogeneous mixture after a prescribed finite time? For ideal passive tracers, we show that this optimal initial condition coincides with the right singular vector (corresponding to the smallest singular value) of a suitably truncated Perron-Frobenius (PF) operator. The truncation of the PF operator is made under the assumption that there is a small length-scale threshold $\ell_\nu$ under which the tracer blobs are considered, for all practical purposes, completely mixed. We demonstrate our results on two examples: a prototypical model known as the sine flow and a direct numerical simulation of two-dimensional turbulence. Evaluating the optimal initial condition through this framework only requires the position of a dense grid of fluid particles at the final instance and their preimages at the initial instance of the prescribed time interval. As such, our framework can be readily applied to flows where such data is available through numerical simulations or experimental measurements.
DA - 2017/5/1/
PY - 2017/5/1/
DO - 10.1103/physrevfluids.2.054601
UR - http://dx.doi.org/10.1103/physrevfluids.2.054601
ER -
TY - JOUR
TI - A variational approach to probing extreme events in turbulent dynamical systems
AU - Farazmand, M.
AU - Sapsis, T. P.
T2 - Science Advances
AB - Extreme events are ubiquitous in a wide range of dynamical systems, including turbulent fluid flows, nonlinear waves, large-scale networks, and biological systems. We propose a variational framework for probing conditions that trigger intermittent extreme events in high-dimensional nonlinear dynamical systems. We seek the triggers as the probabilistically feasible solutions of an appropriately constrained optimization problem, where the function to be maximized is a system observable exhibiting intermittent extreme bursts. The constraints are imposed to ensure the physical admissibility of the optimal solutions, that is, significant probability for their occurrence under the natural flow of the dynamical system. We apply the method to a body-forced incompressible Navier-Stokes equation, known as the Kolmogorov flow. We find that the intermittent bursts of the energy dissipation are independent of the external forcing and are instead caused by the spontaneous transfer of energy from large scales to the mean flow via nonlinear triad interactions. The global maximizer of the corresponding variational problem identifies the responsible triad, hence providing a precursor for the occurrence of extreme dissipation events. Specifically, monitoring the energy transfers within this triad allows us to develop a data-driven short-term predictor for the intermittent bursts of energy dissipation. We assess the performance of this predictor through direct numerical simulations.
DA - 2017///
PY - 2017///
DO - 10.1126/sciadv.1701533
VL - 3
IS - 9
SP - e1701533
ER -
TY - JOUR
TI - Relative periodic orbits form the backbone of turbulent pipe flow
T2 - Journal of Fluid Mechanics
AB - Chaotic dynamics of low-dimensional systems, such as Lorenz or R\"ossler flows, is guided by the infinity of periodic orbits embedded in their strange attractors. Whether this also be the case for the infinite-dimensional dynamics of Navier--Stokes equations has long been speculated, and is a topic of ongoing study. Periodic and relative periodic solutions have been shown to be involved in transitions to turbulence. Their relevance to turbulent dynamics---specifically, whether periodic orbits play the same role in high-dimensional nonlinear systems like the Navier--Stokes equations as they do in lower-dimensional systems---is the focus of the present investigation. We perform here a detailed study of pipe flow relative periodic orbits with energies and mean dissipations close to turbulent values. We outline several approaches to reduction of the translational symmetry of the system. We study pipe flow in a minimal computational cell, and report a library of invariant solutions found with the aid of the method of slices. Detailed study of the unstable manifolds of a sample of these solutions is consistent with the picture that relative periodic orbits are embedded in the chaotic saddle and that they guide the turbulent dynamics.
DA - 2017/12/25/
PY - 2017/12/25/
DO - 10.1017/jfm.2017.699
UR - http://dx.doi.org/10.1017/jfm.2017.699
KW - nonlinear dynamical systems
KW - turbulence modelling
KW - turbulent flows
ER -
TY - JOUR
TI - Mathematical and Statistical Model Misspecifications in Modeling Immune Response in Renal Transplant Recipients
AU - Tran, Hien
AU - Everett, R.A.
AU - Banks, H.T.
AU - Hu, S.
AU - Murad, N.
T2 - Inverse Problems in Science and Engineering
DA - 2017///
PY - 2017///
DO - 10.1080/ 17415977.2017.1312363
VL - 26
IS - 2
SP - 1–18
ER -
TY - JOUR
TI - Mathematical and statistical model misspecifications in modelling immune response in renal transplant recipients
AU - Banks, H. T.
AU - Everett, R. A.
AU - Hu, Shuhua
AU - Murad, Neha
AU - Tran, H. T.
T2 - Inverse Problems in Science and Engineering
AB - We examine uncertainty in clinical data from a kidney transplant recipient infected with BK virus and investigate mathematical model and statistical model misspecifications in the context of least squares methodology. A difference-based method is directly applied to data to determine the correct statistical model that represents the uncertainty in data. We then carry out an inverse problem with the corresponding iterative weighted least squares technique and use the resulting modified residual plots to detect mathematical model discrepancy. This process is implemented using both clinical and simulated data. Our results demonstrate mathematical model misspecification when both simpler and more complex models are assumed compared to data dynamics.
DA - 2017/4/9/
PY - 2017/4/9/
DO - 10.1080/17415977.2017.1312363
VL - 26
IS - 2
SP - 203-222
J2 - Inverse Problems in Science and Engineering
LA - en
OP -
SN - 1741-5977 1741-5985
UR - http://dx.doi.org/10.1080/17415977.2017.1312363
DB - Crossref
KW - Renal transplant
KW - BK virus
KW - polyomavirus nephropathy
KW - inverse problems
KW - pseudo measurement errors
KW - difference-based methods
KW - model misspecification
KW - statistical error model
KW - 62P10
KW - 92B99
KW - 62G99
KW - 37N15
ER -
TY - CONF
TI - War-gaming application for future space systems acquisition: MATLAB implementation of war-gaming acquisition models and simulation results
AU - Vienhage, Paul
AU - Barcomb, Heather
AU - Marshall, Karel
AU - Black, William A.
AU - Coons, Amanda
AU - Tran, Hien T.
AU - Nguyen, Tien M.
AU - Guillen, Andy T.
AU - Yoh, James
AU - Kizer, Justin
AU - Rogers, Blake A.
T2 - SPIE Defense + Security
A2 - Pham, Khanh D.
A2 - Chen, Genshe
AB - The paper describes the MATLAB (MathWorks) programs that were developed during the REU workshop^{1} to implement The Aerospace Corporation developed Unified Game-based Acquisition Framework and Advanced Game - based Mathematical Framework (UGAF-AGMF) and its associated War-Gaming Engine (WGE) models. Each game can be played from the perspectives of the Department of Defense Acquisition Authority (DAA) or of an individual contractor (KTR). The programs also implement Aerospace’s optimum “Program and Technical Baseline (PTB) and associated acquisition” strategy that combines low Total Ownership Cost (TOC) with innovative designs while still meeting warfighter needs. The paper also describes the Bayesian Acquisition War-Gaming approach using Monte Carlo simulations, a numerical analysis technique to account for uncertainty in decision making, which simulate the PTB development and acquisition processes and will detail the procedure of the implementation and the interactions between the games.
C2 - 2017/5/5/
C3 - Sensors and Systems for Space Applications X
DA - 2017/5/5/
DO - 10.1117/12.2263247
PB - SPIE
UR - http://dx.doi.org/10.1117/12.2263247
DB - Crossref
KW - Unified Game-based Acquisition Framework
KW - Advanced Game-based Mathematical Framework
KW - Bayesian games
KW - Program and Technical Baseline
KW - Warfighter Capability
KW - MATLAB
KW - Nash equilibrium
KW - Monte Carlo simulations
KW - Fixed Price Seal Bid
KW - Firm Fixed Price
KW - Fixed Price Incentive Firm
ER -
TY - JOUR
TI - A physiologically based pharmacokinetic model of vitamin D
AU - Sawyer, Megan E.
AU - Tran, Hien T.
AU - Evans, Marina V.
T2 - Journal of Applied Toxicology
AB - Despite the plethora of studies discussing the benefits of vitamin D on physiological functioning, few mathematical models of vitamin D predict the response of the body on low-concentration supplementation of vitamin D under sunlight-restricted conditions. This study developed a physiologically based pharmacokinetic (PBPK) model utilizing published human data on the metabolic cascade of orally derived, low-concentration (placebo, 5 μg and 10 μg) supplementation of vitamin D over the course of 28 days in the absence of sunlight. Vitamin D and its metabolites are highly lipophilic and binding assays of these compounds in serum may not account for binding by lipids and additional proteins. To compensate for the additional bound amounts, this study allowed the effective adipose-plasma partition coefficient to vary dynamically with the concentration of each compound in serum utilizing the Hill equation for binding. Through incorporating the optimized parameters with the adipose partition coefficient adaptation to the PBPK model, this study was able to fit serum concentration data for circulating vitamin D at all three supplementation concentrations within confidence intervals of the data. Copyright © 2017 John Wiley & Sons, Ltd.
DA - 2017/6/6/
PY - 2017/6/6/
DO - 10.1002/jat.3489
VL - 37
IS - 12
SP - 1448-1454
J2 - J Appl Toxicol
LA - en
OP -
SN - 0260-437X
UR - http://dx.doi.org/10.1002/jat.3489
DB - Crossref
KW - vitamin D
KW - PBPK
KW - dynamic adipose partition coefficient
KW - Hill equation
KW - absorption
KW - distribution
KW - metabolism and excretion
ER -
TY - JOUR
TI - An Optimal Control Approach to Structured Treatment Interruptions for HIV Patients: A Personalized Medicine Perspective
AU - Attarian, Adam
AU - Tran, Hien
T2 - Applied Mathematics
AB - Highly Active Antiretroviral Therapy (HAART) has changed the course of human immunodeficiency virus (HIV) treatments since its introduction. However, for many patients, long term continuous HAART is expensive and can include problems with drug toxicity and side effects, as well as increased drug resistance. Because of these reasons, some HIV infected patients will voluntarily terminate HAART. Some of these patients will also interrupt the continuous prescribed therapies for short or long periods. After discontinuing HAART, patients will usually experience a rapid increase in viral load coupled with an immediate decline in CD4+ counts. The canonical example of a patient undergoing unsupervised breaks in HAART is that of the “Berlin patient”. In this case, the patient was able to control viral load in the absence of treatment by cycling HAART on and off due to non-related infections. Due to this patient, interest in the use of structured treatment interruptions (STI) as a mechanism to regulate an HIV infection piqued. This paper describes an optimal control approach to determine STI regimen for HIV patients. The optimal STI was implemented in the context of the receding horizon control (RHC) using a mathematical model for the in-vivo dynamics of an HIV type 1 infection. Using available clinical data, we calibrate the model by estimating on a patient specific basis, a best estimable set of parameters using sensitivity analysis and subset selection. We demonstrate how customized STI protocols can be designed through the variation of control parameters on a patient specific basis.
DA - 2017///
PY - 2017///
DO - 10.4236/am.2017.87074
VL - 08
IS - 07
SP - 934-955
J2 - AM
OP -
SN - 2152-7385 2152-7393
UR - http://dx.doi.org/10.4236/am.2017.87074
DB - Crossref
ER -
TY - CHAP
TI - Implicit Filtering and Hidden Constraints
T2 - Advances and Trends in Optimization with Engineering Applications
A2 - Terlaky, Tamas
A2 - Anjos, Miguel
A2 - Ahmed, Shabbir
AB - 38.1 ▪ IntroductionA hidden constraint, a yes-no constraint [409], or a virtual constraint [498] in an optimization problem is one without an explicit representation as an equality or inequality. In many cases, one detects constraint violation if the objective function fails to return a value. At other times, the constraint is tested by a separate computation but only returns a flag for failure or success. Our view is that if one cannot quantify the degree of infeasibility, then the constraints are hidden from the optimization.
PY - 2017///
DO - 10.1137/1.9781611974683.ch38
SP - 507–508
PB - SIAM
ER -
TY - CONF
TI - The Doppler Effect for SAR
AU - Gilman, Mikhail
AU - Tsynkov, Semyon
C2 - 2017///
C3 - Mathematical
and Numerical Aspects of Wave Propagation WAVES 2017,
The 13th International Conference, Minneapolis, MN, USA, May 15--19, 2017.
Book of Abstracts
DA - 2017///
VL -
SP - 369-370
UR - https://stsynkov.math.ncsu.edu/publications/waves_2017_Doppler_v3.pdf
ER -
TY - CONF
TI - High order numerical solution of the Helmholtz
equation for domains with reentrant corners
AU - Magura, S.
AU - Petropavlovsky, S.
AU - Tsynkov, S.
AU - Turkel, E.
C2 - 2017///
C3 - Mathematical
and Numerical Aspects of Wave Propagation WAVES 2017,
The 13th International Conference, Minneapolis, MN, USA, May 15--19, 2017.
Book of Abstracts
DA - 2017///
VL -
SP - 367-368
UR - https://stsynkov.math.ncsu.edu/publications/waves2017_Steven_v4.pdf
ER -
TY - CONF
TI - High order accurate solution of the wave equation by
compact finite differences and difference potentials
AU - Britt, Steven
AU - Tsynkov, Semyon
AU - Turkel, Eli
C2 - 2017///
C3 - Mathematical
and Numerical Aspects of Wave Propagation WAVES 2017,
The 13th International Conference, Minneapolis, MN, USA, May 15--19, 2017.
Book of Abstracts
DA - 2017///
VL -
SP - 63-64
UR - https://stsynkov.math.ncsu.edu/publications/waves2017_Steven_v4.pdf
ER -
TY - CONF
TI - Computational complexity of artificial boundary conditions
for Maxwell's equations in the FDTD method
AU - Osintcev, Mikhail
AU - Tsynkov, Semyon
C2 - 2017///
C3 - Mathematical
and Numerical Aspects of Wave Propagation WAVES 2017,
The 13th International Conference, Minneapolis, MN, USA, May 15--19, 2017.
Book of Abstracts
DA - 2017///
VL -
SP - 275-276
UR - https://stsynkov.math.ncsu.edu/publications/OsTsy_4.pdf
ER -
TY - CONF
TI - An efficient numerical algorithm for the 3D wave equation in domains
of complex shape
AU - Petropavlovsky, S.
AU - Tsynkov, S.
AU - Turkel, E.
C2 - 2017///
C3 - Mathematical
and Numerical Aspects of Wave Propagation WAVES 2017,
The 13th International Conference, Minneapolis, MN, USA, May 15--19, 2017.
Book of Abstracts
DA - 2017///
VL -
SP - 365-366
UR - https://stsynkov.math.ncsu.edu/publications/wavesPetropTsynkov_v3.pdf
ER -
TY - JOUR
TI - Eigenvector continuation with subspace learning
T2 - Phys. Rev. Lett. 121, 032501 (2018)
AB - A common challenge faced in quantum physics is finding the extremal eigenvalues and eigenvectors of a Hamiltonian matrix in a vector space so large that linear algebra operations on general vectors are not possible. There are numerous efficient methods developed for this task, but they generally fail when some control parameter in the Hamiltonian matrix exceeds some threshold value. In this work we present a new technique called eigenvector continuation that can extend the reach of these methods. The key insight is that while an eigenvector resides in a linear space with enormous dimensions, the eigenvector trajectory generated by smooth changes of the Hamiltonian matrix is well approximated by a very low-dimensional manifold. We prove this statement using analytic function theory and propose an algorithm to solve for the extremal eigenvectors. We benchmark the method using several examples from quantum many-body theory.
DA - 2017/11/19/
PY - 2017/11/19/
DO - 10.1103/physrevlett.121.032501
ER -
TY - CONF
TI - Univariate polynomial optimization with sum-of-squares interpolants
AU - Papp, D.
AB - One of the most common tools in polynomial optimization is the approximation of the cone of nonnegative polynomials with the cone of sum-of-squares polynomials. This leads to polynomial-time solvable approximations for many NP-hard optimization problems using semidefinite programming (SDP). While theoretically satisfactory, the translation of optimization problems involving sum-of-squares polynomials to SDPs is not always practical. First, in the common SDP formulation, the dual variables are semidefinite matrices whose condition numbers grow exponentially with the degree of the polynomials involved, which is detrimental for a floating-point implementation. Second, the SDP representation of sum-of-squares polynomials roughly squares the number of optimization variables, increasing the time and memory complexity of the solution algorithms by several orders of magnitude. In this paper we focus on the first, numerical, issue. We show that a reformulation of the sum-of-squares SDP using polynomial interpolants yields a substantial improvement over the standard formulation, and problems involving sum-of-squares interpolants of hundreds of degrees can be handled without difficulty by commonly used semidefinite programming solvers. Preliminary numerical results using semi-infinite optimization problems align with the theoretical predictions. In all problems considered, available memory is the only factor limiting the degrees of polynomials.
C2 - 2017///
C3 - Springer Proceedings in Mathematics and Statistics
DA - 2017///
DO - 10.1007/978-3-319-66616-7_9
VL - 213
SP - 143-162
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-85033453631&partnerID=MN8TOARS
ER -
TY - JOUR
TI - Plasmodium knowlesi invasion following spread by infected mosquitoes, macaques and humans
AU - Yakob, Laith
AU - Lloyd, Alun L.
AU - Kao, Rowland R.
AU - Ferguson, Heather M.
AU - Brock, Patrick M.
AU - Drakeley, Chris
AU - Bonsall, Michael B.
T2 - Parasitology
AB - SUMMARY Plasmodium knowlesi is increasingly recognized as a major cause of malaria in Southeast Asia. Anopheles leucosphyrous group mosquitoes transmit the parasite and natural hosts include long-tailed and pig-tailed macaques. Despite early laboratory experiments demonstrating successful passage of infection between humans, the true role that humans play in P. knowlesi epidemiology remains unclear. The threat posed by its introduction into immunologically naïve populations is unknown despite being a public health priority for this region. A two-host species mathematical model was constructed to analyse this threat. Global sensitivity analysis using Monte Carlo methods highlighted the biological processes of greatest influence to transmission. These included parameters known to be influential in classic mosquito-borne disease models (e.g. vector longevity); however, interesting ecological components that are specific to this system were also highlighted: while local vectors likely have intrinsic preferences for certain host species, how plastic these preferences are, and how this is shaped by local conditions, are key determinants of parasite transmission potential. Invasion analysis demonstrates that this behavioural plasticity can qualitatively impact the probability of an epidemic sparked by imported infection. Identifying key vector sub/species and studying their biting behaviours constitute important next steps before models can better assist in strategizing disease control.
DA - 2017/3/27/
PY - 2017/3/27/
DO - 10.1017/S0031182016002456
VL - 145
IS - 1
SP - 101-110
J2 - Parasitology
LA - en
OP -
SN - 0031-1820 1469-8161
UR - http://dx.doi.org/10.1017/S0031182016002456
DB - Crossref
KW - invasion analysis
KW - Plasmodium knowlesi
KW - vector-borne disease
KW - mathematical model
KW - vector behaviour
ER -
TY - BOOK
TI - Transionospheric Synthetic Aperture Imaging
AU - Gilman, M.
AU - Smith, E.
AU - Tsynkov, S.
DA - 2017///
PY - 2017///
VL - xxiii
SP - 458
ER -
TY - JOUR
TI - A simplified Kronecker rule for one hook shape
AU - Liu, Ricky Ini
T2 - Proceedings of the American Mathematical Society
AB - Recently Blasiak has given a combinatorial rule for the Kronecker coefficient g λ μ ν g_{\lambda \mu \nu } when μ \mu is a hook shape by defining a set of colored Yamanouchi tableaux with cardinality g λ μ ν g_{\lambda \mu \nu } in terms of a process called conversion. We give a characterization of colored Yamanouchi tableaux that does not rely on conversion, which leads to a simpler formulation and proof of the Kronecker rule for one hook shape.
DA - 2017/5/24/
PY - 2017/5/24/
DO - 10.1090/proc/13692
VL - 145
IS - 9
SP - 3657-3664
J2 - Proc. Amer. Math. Soc.
LA - en
OP -
SN - 0002-9939 1088-6826
UR - http://dx.doi.org/10.1090/proc/13692
DB - Crossref
ER -
TY - CONF
TI - Polynomial Time Interactive Proofs for Linear Algebra with Exponential Matrix Dimensions and Scalars Given by Polynomial Time Circuits
AU - Dumas, Jean-Guillaume
AU - Kaltofen, Erich L.
AU - Villard, Gilles
AU - Zhi, Lihong
T2 - the 2017 ACM
AB - We present an interactive probabilistic proof protocol that certifies in (log N)O(1) arithmetic and Boolean operations for the verifier the determinant, for example, of an N x N matrix over a field whose entries a(i,j) are given by a single (log NO(1)-depth arithmetic circuit, which contains (log NO(1) field constants and which is polynomial time uniform, for example, which has size (log NO(1). The prover can produce the interactive certificate within a (log NO(1) factor of the cost of computing the determinant. Our protocol is a version of the proofs for muggles protocol by Goldwasser, Kalai and Rothblum [STOC 2008, J. ACM 2015]. An application is the following: suppose in a system of k homogeneous polynomials of total degree ≤ d in the k variables y1,...,yk the coefficient of the term y1e1 ... ykek in the i-th polynomial is the (hypergeometric) value ((i+e1 + ... + ek)!)/((i!)(e1!)...(ek!)), where e! is the factorial of e. Then we have a probabilistic protocol that certifies (projective) solvability or inconsistency of such a system in (k log(d))O(1) bit complexity for the verifier, that is, in polynomial time in the number of variables k and the logarithm of the total degree, log(d).
C2 - 2017///
C3 - Proceedings of the 2017 ACM on International Symposium on Symbolic and Algebraic Computation - ISSAC '17
DA - 2017///
DO - 10.1145/3087604.3087640
PB - ACM Press
SN - 9781450350648
UR - http://dx.doi.org/10.1145/3087604.3087640
DB - Crossref
ER -
TY - CONF
TI - Early Termination in Parametric Linear System Solving and Rational Function Vector Recovery with Error Correction
AU - Kaltofen, Erich L.
AU - Pernet, Clément
AU - Storjohann, Arne
AU - Waddell, Cleveland
T2 - the 2017 ACM
AB - Consider solving a black box linear system, A(u) x = b(u), where the entries are polynomials in u over a field K, and A(u) is full rank. The solution, x = 1/g(u) f(u), where g is always the least common monic denominator, can be found by evaluating the system at distinct points ξl in K. The solution can be recovered even if some evaluations are erroneous. In [Boyer and Kaltofen, Proc. SNC 2014] the problem is solved with an algorithm that generalizes Welch/Berlekamp decoding of an algebraic Reed-Solomon code. Their algorithm requires the sum of a degree bound for the numerators plus a degree bound for the denominator of the solution. It is possible that the degree bounds input to their algorithm grossly overestimate the actual degrees. We describe an algorithm that given the same inputs uses possibly fewer evaluations to compute the solution. We introduce a second count for the number of evaluations required to recover the solution based on work by Stanley Cabay. The Cabay count includes bounds for the highest degree polynomial in the coefficient matrix and right side vector, but does not require solution degree bounds. Instead our algorithm iterates until the Cabay termination criterion is reached. At this point our algorithm returns the solution. Assuming we have the actual degrees for all necessary input parameters, we give the criterion that determines when the Cabay count is fewer than the generalized Welch/Berlekamp count.
C2 - 2017///
C3 - Proceedings of the 2017 ACM on International Symposium on Symbolic and Algebraic Computation - ISSAC '17
DA - 2017///
DO - 10.1145/3087604.3087645
PB - ACM Press
SN - 9781450350648
UR - http://dx.doi.org/10.1145/3087604.3087645
DB - Crossref
ER -
TY - BOOK
TI - Convex Analysis and Monotone Operator Theory in Hilbert Spaces
AU - Bauschke, Heinz H.
AU - Combettes, Patrick L.
T2 - CMS Books in Mathematics
AB - This reference text, now in its second edition, offers a modern unifying presentation of three basic areas of nonlinear analysis: convex analysis, monotone operator theory, and the fixed point theory
DA - 2017///
PY - 2017///
DO - 10.1007/978-3-319-48311-5
ET - 2nd
PB - Springer International Publishing
SN - 9783319483108 9783319483115
UR - http://dx.doi.org/10.1007/978-3-319-48311-5
ER -
TY - JOUR
TI - Uncertainty Quantification in a Patient-Specific One-Dimensional Arterial Network Model: EnKF-Based Inflow Estimator
AU - Arnold, Andrea
AU - Battista, Christina
AU - Bia, Daniel
AU - German, Yanina Zócalo
AU - Armentano, Ricardo L.
AU - Tran, Hien
AU - Olufsen, Mette S.
T2 - Journal of Verification, Validation and Uncertainty Quantification
AB - Successful clinical use of patient-specific models for cardiovascular dynamics depends on the reliability of the model output in the presence of input uncertainties. For 1D fluid dynamics models of arterial networks, input uncertainties associated with the model output are related to the specification of vessel and network geometry, parameters within the fluid and wall equations, and parameters used to specify inlet and outlet boundary conditions. This study investigates how uncertainty in the flow profile applied at the inlet boundary of a 1D model affects area and pressure predictions at the center of a single vessel. More specifically, this study develops an iterative scheme based on the ensemble Kalman filter (EnKF) to estimate the temporal inflow profile from a prior distribution of curves. The EnKF-based inflow estimator provides a measure of uncertainty in the size and shape of the estimated inflow, which is propagated through the model to determine the corresponding uncertainty in model predictions of area and pressure. Model predictions are compared to ex vivo area and blood pressure measurements in the ascending aorta, the carotid artery, and the femoral artery of a healthy male Merino sheep. Results discuss dynamics obtained using a linear and a nonlinear viscoelastic wall model.
DA - 2017/2/22/
PY - 2017/2/22/
DO - 10.1115/1.4035918
VL - 2
IS - 1
SP - 011002
J2 - J. Verif. Valid. Uncert
LA - en
OP -
SN - 2377-2158
UR - http://dx.doi.org/10.1115/1.4035918
DB - Crossref
ER -
TY - JOUR
TI - Spatiotemporal fractionation schemes for liver stereotactic body radiotherapy
AU - Unkelbach, Jan
AU - Papp, Dávid
AU - Gaddy, Melissa R.
AU - Andratschke, Nicolaus
AU - Hong, Theodore
AU - Guckenberger, Matthias
T2 - Radiotherapy and Oncology
AB - Dose prescription in stereotactic body radiotherapy (SBRT) for liver tumors is often limited by the mean liver dose. We explore the concept of spatiotemporal fractionation as an approach to facilitate further dose escalation in liver SBRT.Spatiotemporal fractionation schemes aim at partial hypofractionation in the tumor along with near-uniform fractionation in normal tissues. This is achieved by delivering distinct dose distributions in different fractions, which are designed such that each fraction delivers a high single fraction dose to complementary parts of the tumor while creating a similar dose bath in the surrounding noninvolved liver. Thereby, higher biologically effective doses (BED) can be delivered to the tumor without increasing the mean BED in the liver. Planning of such treatments is performed by simultaneously optimizing multiple dose distributions based on their cumulative BED. We study this concept for five liver cancer patients with different tumor geometries.Spatiotemporal fractionation presents a method of increasing the ratio of prescribed tumor BED to mean BED in the noninvolved liver by approximately 10-20%, compared to conventional SBRT using identical fractions.Spatiotemporal fractionation may reduce the risk of liver toxicity or facilitate dose escalation in liver SBRT in circumstances where the mean dose to the non-involved liver is the prescription-limiting factor.
DA - 2017/11//
PY - 2017/11//
DO - 10.1016/j.radonc.2017.09.003
VL - 125
IS - 2
SP - 357-364
J2 - Radiotherapy and Oncology
LA - en
OP -
SN - 0167-8140
UR - http://dx.doi.org/10.1016/j.radonc.2017.09.003
DB - Crossref
KW - Liver SBRT
KW - Dose escalation
KW - Fractionation
KW - Treatment plan optimization
ER -
TY - JOUR
TI - Hybrid Finite-Volume-Particle Method for Dusty Gas Flows
AU - Chertock, Alina
AU - Cui, Shumo
AU - Kurganov, Alexander
T2 - SMAI Journal of Computational Mathematics
AB - We first study the one-dimensional dusty gas flow modeled by the two-phase system composed of a gaseous carrier (gas phase) and a particulate suspended phase (dust phase). The gas phase is modeled by the compressible Euler equations of gas dynamics and the dust phase is modeled by the pressureless gas dynamics equations. These two sets of conservation laws are coupled through source terms that model momentum and heat transfers between the phases. When an Eulerian method is adopted for this model, one can notice the obtained numerical results are typically significantly affected by numerical diffusion. This phenomenon occurs since the pressureless gas equations are nonstrictly hyperbolic and have degenerate structure in which singular delta shocks are formed, and these strong singularities are vulnerable to the numerical diffusion.
DA - 2017///
PY - 2017///
DO - 10.5802/smai-jcm.23
VL - 3
SP - 139-180
J2 - SMAI-JCM
OP -
SN - 2426-8399
UR - http://dx.doi.org/10.5802/smai-jcm.23
DB - Crossref
ER -
TY - JOUR
TI - Continuous Structured Population Models for Daphnia magna
AU - Rutter, Erica M.
AU - Banks, H. T.
AU - LeBlanc, Gerald A.
AU - Flores, Kevin B.
T2 - Bulletin of Mathematical Biology
AB - We continue our efforts in modeling Daphnia magna, a species of water flea, by proposing a continuously structured population model incorporating density-dependent and density-independent fecundity and mortality rates. We collected new individual-level data to parameterize the individual demographics relating food availability and individual daphnid growth. Our model is fit to experimental data using the generalized least-squares framework, and we use cross-validation and Akaike Information Criteria to select hyper-parameters. We present our confidence intervals on parameter estimates.
DA - 2017/9/15/
PY - 2017/9/15/
DO - 10.1007/S11538-017-0344-8
VL - 79
IS - 11
SP - 2627-2648
J2 - Bull Math Biol
LA - en
OP -
SN - 0092-8240 1522-9602
UR - http://dx.doi.org/10.1007/S11538-017-0344-8
DB - Crossref
KW - Continuous structured population models
KW - Inverse problems
KW - Generalized least squares
KW - Model selection
KW - Information content
KW - Residual plots
ER -
TY - JOUR
TI - Estimating the rate of prion aggregate amplification in yeast with a generation and structured population model
AU - Banks, H. T.
AU - Flores, Kevin B.
AU - Langlois, Christine R.
AU - Serio, Tricia R.
AU - Sindi, Suzanne S.
T2 - Inverse Problems in Science and Engineering
AB - Prions are a special class of proteins capable of adopting multiple (misfolded) conformations, some of which have been associated with fatal diseases in mammals such as bovine spongiform encephalopathy or Creutzfeldt–Jakob Disease. Prion diseases, like protein misfolding diseases in general, are caused by the formation and amplification of ordered aggregates of proteins called amyloids. While such diseases in mammals can take decades to form, yeast have a variety of prion phenotypes that occur over a few hours, making this system an ideal model for protein misfolding disease in general. Most experimental assays of colonies with yeast prions provide steady-state population observations which complicate the inference of biochemical parameters both by the inability to directly measure aggregate amplification and by obscuring heterogeneity between cells. We develop a mathematical and inverse problem formulation to determine the amplification rate with prion aggregates from single-cell measurements observed in propagon amplification experiments. We demonstrate the ability of our formulation to determine heterogeneous amplification rates on simulated and experimental data. Our results show that aggregate amplification rates for two prion variants are strongly bimodal, suggesting that the generational structure in the yeast population impacts the ability of prion aggregates to amplify.
DA - 2017/4/18/
PY - 2017/4/18/
DO - 10.1080/17415977.2017.1316498
VL - 26
IS - 2
SP - 257-279
J2 - Inverse Problems in Science and Engineering
LA - en
OP -
SN - 1741-5977 1741-5985
UR - http://dx.doi.org/10.1080/17415977.2017.1316498
DB - Crossref
KW - Structured population model
KW - aggregate data
KW - inverse problem
KW - PDEs
KW - prion
KW - General biology and biomathematics
ER -
TY - JOUR
TI - Uniqueness of solutions to singular p-Laplacian equations with subcritical nonlinearity
AU - Maultsby, Bevin
T2 - Advances in Nonlinear Analysis
AB - Abstract We present a geometric approach to the study of quasilinear elliptic p -Laplacian problems on a ball in ℝ n ${\mathbb{R}^{n}}$ using techniques from dynamical systems. These techniques include a study of the invariant manifolds that arise from the union of the solutions to the elliptic PDE in phase space, as well as variational computations on two vector fields tangent to the invariant manifolds. We show that for a certain class of nonlinearities f with subcritical growth relative to the Sobolev critical exponent p * ${p^{*}}$ , there can be at most one such solution satisfying Δ p u + f ( u ) = 0 ${\Delta_{p}u+f(u)=0}$ on a ball with Dirichlet boundary conditions.
DA - 2017/1/1/
PY - 2017/1/1/
DO - 10.1515/anona-2015-0161
VL - 6
IS - 1
OP -
SN - 2191-9496 2191-950X
UR - http://dx.doi.org/10.1515/anona-2015-0161
DB - Crossref
KW - Singular p-Laplacian
KW - uniqueness
KW - quasilinear elliptic equations
KW - Emden-Fowler transformation
KW - invariant manifold
ER -
TY - JOUR
TI - Stationary Expansion Shocks for a Regularized Boussinesq System
AU - Shearer, Michael
AU - El, Gennady A.
AU - Hoefer, Mark A.
T2 - Studies in Applied Mathematics
AB - Abstract Stationary expansion shocks have been identified recently as a new type of solution to hyperbolic conservation laws regularized by nonlocal dispersive terms that naturally arise in shallow‐water theory. These expansion shocks were studied previously for the Benjamin‐Bona‐Mahony (BBM) equation using matched asymptotic expansions. In this paper, we extend the BBM analysis to the regularized Boussinesq system by using Riemann invariants of the underlying dispersionless shallow‐water equations. The extension for a system is nontrivial, requiring a combination of small amplitude, long‐wave expansions with high order matched asymptotics. The constructed asymptotic solution is shown to be in excellent agreement with accurate numerical simulations of the Boussinesq system for a range of appropriately smoothed Riemann data.
DA - 2017/9/14/
PY - 2017/9/14/
DO - 10.1111/sapm.12191
VL - 139
IS - 4
SP - 1–22
J2 - Studies in Applied Mathematics
LA - en
OP -
SN - 0022-2526
UR - http://dx.doi.org/10.1111/sapm.12191
DB - Crossref
ER -
TY - JOUR
TI - Cambrian frameworks for cluster algebras of affine type
AU - Reading, Nathan
AU - Speyer, David E.
T2 - Transactions of the American Mathematical Society
AB - We give a combinatorial model for the exchange graph and $\mathbf {g}$-vector fan associated to any acyclic exchange matrix $B$ of affine type. More specifically, we construct a reflection framework for $B$ in the sense of [N. Reading and D. E. Speyer, âCombinatorial frameworks for cluster algebrasâ] and establish good properties of this framework. The framework (and in particular the $\mathbf {g}$-vector fan) is constructed by combining a copy of the Cambrian fan for $B$ with an antipodal copy of the Cambrian fan for $-B$.
DA - 2017/9/15/
PY - 2017/9/15/
DO - 10.1090/tran/7193
VL - 370
IS - 2
SP - 1429-1468
J2 - Trans. Amer. Math. Soc.
LA - en
OP -
SN - 0002-9947 1088-6850
UR - http://dx.doi.org/10.1090/tran/7193
DB - Crossref
ER -
TY - JOUR
TI - Validation and uncertainty quantification of detector response functions for a 1″×2″ NaI collimated detector intended for inverse radioisotope source mapping applications
AU - Nelson, N.
AU - Azmy, Y.
AU - Gardner, R.P.
AU - Mattingly, J.
AU - Smith, R.
AU - Worrall, L.G.
AU - Dewji, S.
T2 - Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms
AB - Detector response functions (DRFs) are often used for inverse analysis. We compute the DRF of a sodium iodide (NaI) nuclear material holdup field detector using the code named g03 developed by the Center for Engineering Applications of Radioisotopes (CEAR) at NC State University. Three measurement campaigns were performed in order to validate the DRF’s constructed by g03: on-axis detection of calibration sources, off-axis measurements of a highly enriched uranium (HEU) disk, and on-axis measurements of the HEU disk with steel plates inserted between the source and the detector to provide attenuation. Furthermore, this work quantifies the uncertainty of the Monte Carlo simulations used in and with g03, as well as the uncertainties associated with each semi-empirical model employed in the full DRF representation. Overall, for the calibration source measurements, the response computed by the DRF for the prediction of the full-energy peak region of responses was good, i.e. within two standard deviations of the experimental response. In contrast, the DRF tended to overestimate the Compton continuum by about 45–65% due to inadequate tuning of the electron range multiplier fit variable that empirically represents physics associated with electron transport that is not modeled explicitly in g03. For the HEU disk measurements, computed DRF responses tended to significantly underestimate (more than 20%) the secondary full-energy peaks (any peak of lower energy than the highest-energy peak computed) due to scattering in the detector collimator and aluminum can, which is not included in the g03 model. We ran a sufficiently large number of histories to ensure for all of the Monte Carlo simulations that the statistical uncertainties were lower than their experimental counterpart’s Poisson uncertainties. The uncertainties associated with least-squares fits to the experimental data tended to have parameter relative standard deviations lower than the peak channel relative standard deviation in most cases and good reduced chi-square values. The highest sources of uncertainty were identified as the energy calibration polynomial factor (due to limited source availability and NaI resolution) and the Ba-133 peak fit (only a very weak source was available), which were 20% and 10%, respectively.
DA - 2017/11//
PY - 2017/11//
DO - 10.1016/j.nimb.2017.07.015
VL - 410
SP - 1-15
J2 - Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms
LA - en
OP -
SN - 0168-583X
UR - http://dx.doi.org/10.1016/j.nimb.2017.07.015
DB - Crossref
KW - Nal collimated detector
KW - Response function
KW - Validation
KW - Uncertainty quantification
KW - Holdup measurements
ER -
TY - JOUR
TI - A Linear Regression Framework for the Verification of Bayesian Model Calibration Algorithms
AU - McMahan, Jerry A., Jr.
AU - Williams, Brian J.
AU - Smith, Ralph C.
AU - Malaya, Nicholas
T2 - Journal of Verification, Validation and Uncertainty Quantification
AB - We describe a framework for the verification of Bayesian model calibration routines. The framework is based on linear regression and can be configured to verify calibration to data with a range of observation error characteristics. The framework is designed for efficient implementation and is suitable for verifying code intended for large-scale problems. We propose an approach for using the framework to verify Markov chain Monte Carlo (MCMC) software by combining it with a nonparametric test for distribution equality based on the energy statistic. Our matlab-based reference implementation of the framework is shown to correctly distinguish between output obtained from correctly and incorrectly implemented MCMC routines. Since correctness of output from an MCMC software depends on choosing settings appropriate for the problem-of-interest, our framework can potentially be used for verifying such settings.
DA - 2017/9/12/
PY - 2017/9/12/
DO - 10.1115/1.4037705
VL - 2
IS - 2
SP - 021006
J2 - J. Verif. Valid. Uncert
LA - en
OP -
SN - 2377-2158
UR - http://dx.doi.org/10.1115/1.4037705
DB - Crossref
ER -
TY - JOUR
TI - Bayesian model calibration and uncertainty quantification for an HIV model using adaptive Metropolis algorithms
AU - Wentworth, Mami T.
AU - Smith, Ralph C.
AU - Williams, Brian
T2 - Inverse Problems in Science and Engineering
AB - In this paper, we discuss Bayesian model calibration and use adaptive Metropolis algorithms to construct densities for input parameters in a previously developed HIV model. To quantify the uncertainty in the parameters, we employ two MCMC algorithms: Delayed Rejection Adaptive Metropolis (DRAM) and Differential Evolution Adaptive Metropolis (DREAM). The densities obtained using these methods are compared to those obtained through direct evaluation of Bayes formula. We also employ uncertainties in input parameters and observation errors to construct prediction intervals for a model response. We verify the accuracy of the Metropolis algorithms by comparing chains, densities and correlations obtained using DRAM, DREAM and direct numerical evaluation of Bayes’ formula. We also perform similar analysis for credible and prediction intervals for responses.
DA - 2017/4/6/
PY - 2017/4/6/
DO - 10.1080/17415977.2017.1312365
VL - 26
IS - 2
SP - 233-256
J2 - Inverse Problems in Science and Engineering
LA - en
OP -
SN - 1741-5977 1741-5985
UR - http://dx.doi.org/10.1080/17415977.2017.1312365
DB - Crossref
KW - Bayesian model calibration
KW - uncertainty quantification
KW - HIV model
ER -
TY - JOUR
TI - Deformation of an elastic substrate due to a resting sessile droplet
AU - Bardall, Aaron
AU - Daniels, Karen E.
AU - Shearer, Michael
T2 - European Journal of Applied Mathematics
AB - On a sufficiently soft substrate, a resting fluid droplet will cause significant deformation of the substrate. This deformation is driven by a combination of capillary forces at the contact line and the fluid pressure at the solid surface. These forces are balanced at the surface by the solid traction stress induced by the substrate deformation. Young's Law, which predicts the equilibrium contact angle of the droplet, also indicates an a priori radial force balance for rigid substrates, but not necessarily for soft substrates that deform under loading. It remains an open question whether the contact line transmits a non-zero force tangent to the substrate surface in addition to the conventional normal (vertical) force. We present an analytic Fourier transform solution technique that includes general interfacial energy conditions, which govern the contact angle of a 2D droplet. This includes evaluating the effect of gravity on the droplet shape in order to determine the correct fluid pressure at the substrate surface for larger droplets. Importantly, we find that in order to avoid a strain singularity at the contact line under a non-zero tangential contact line force, it is necessary to include a previously neglected horizontal traction boundary condition. To quantify the effects of the contact line and identify key quantities that will be experimentally accessible for testing the model, we evaluate solutions for the substrate surface displacement field as a function of Poisson's ratio and zero/non-zero tangential contact line forces.
DA - 2017/6/22/
PY - 2017/6/22/
DO - 10.1017/S0956792517000134
VL - 29
IS - 2
SP - 281-300
J2 - Eur. J. Appl. Math
LA - en
OP -
SN - 0956-7925 1469-4425
UR - http://dx.doi.org/10.1017/S0956792517000134
DB - Crossref
KW - PDEs in Connection with Mechanics of Deformable Solids
KW - Transform Methods
KW - Classical Linear Elasticity
KW - Numerical Approximation of Solutions
KW - Fluid-Solid Interactions
ER -
TY - JOUR
TI - Knot contact homology detects cabled, composite, and torus knots
AU - Gordon, Cameron
AU - Lidman, Tye
T2 - Proceedings of the American Mathematical Society
AB - Knot contact homology is an invariant of knots derived from Legendrian contact homology which has numerous connections to the knot group. We use basic properties of knot groups to prove that knot contact homology detects every torus knot. Further, if the knot contact homology of a knot is isomorphic to that of a cable (respectively composite) knot, then the knot is a cable (respectively composite).
DA - 2017/6/16/
PY - 2017/6/16/
DO - 10.1090/proc/13643
VL - 145
IS - 12
SP - 5405-5412
J2 - Proc. Amer. Math. Soc.
LA - en
OP -
SN - 0002-9939 1088-6826
UR - http://dx.doi.org/10.1090/proc/13643
DB - Crossref
ER -
TY - JOUR
TI - Corrigendum to “Taut Foliations, Left-Orderability, and Cyclic Branched Covers”
AU - Gordon, Cameron
AU - Lidman, Tye
T2 - Acta Mathematica Vietnamica
DA - 2017/6/28/
PY - 2017/6/28/
DO - 10.1007/s40306-017-0216-1
VL - 42
IS - 4
SP - 775-776
J2 - Acta Math Vietnam
LA - en
OP -
SN - 0251-4184 2315-4144
UR - http://dx.doi.org/10.1007/s40306-017-0216-1
DB - Crossref
ER -
TY - JOUR
TI - Generalized Control Systems in the Space of Probability Measures
AU - Cavagnari, Giulia
AU - Marigonda, Antonio
AU - Nguyen, Khai T.
AU - Priuli, Fabio S.
T2 - Set-Valued and Variational Analysis
DA - 2017/5/16/
PY - 2017/5/16/
DO - 10.1007/s11228-017-0414-y
VL - 26
IS - 3
SP - 663-691
J2 - Set-Valued Var. Anal
LA - en
OP -
SN - 1877-0533 1877-0541
UR - http://dx.doi.org/10.1007/s11228-017-0414-y
DB - Crossref
KW - Optimal transport
KW - Differential inclusions
KW - Time-optimal control
KW - Set-valued analysis
ER -
TY - JOUR
TI - The start-stop approximation
AU - Gilman, Mikhail
AU - Smith, Erick
AU - Tsynkov, Semyon
AU - Gilman, M
AU - Smith, E
AU - Tsynkov, S
T2 - TRANSIONOSPHERIC SYNTHETIC APERTURE IMAGING
AB - For the analysis of the SAR data inversion algorithm in Chapters 2 through 5, we have employed the start-stop approximation, which is considered standard in the literature, see, e.g., [25, 40, 76, 79] and also [86]. It assumes that the radar antenna is at standstill while it sends the interrogating pulse toward the target and receives the scattered response, after which the antenna moves down the flight track to the position where the next pulse is emitted and received.
DA - 2017///
PY - 2017///
DO - 10.1007/978-3-319-52127-5_6
SP - 265-309
ER -
TY - JOUR
TI - The effect of ionospheric anisotropy
AU - Gilman, Mikhail
AU - Smith, Erick
AU - Tsynkov, Semyon
AU - Gilman, M
AU - Smith, E
AU - Tsynkov, S
T2 - TRANSIONOSPHERIC SYNTHETIC APERTURE IMAGING
AB - In Chapter 3, we have shown that the Earth’s ionosphere exerts an adverse effect on SAR imaging. It is due to the mismatch between the actual radar signal affected by the dispersion of radio waves in the ionosphere and the matched filter used for signal processing. Accordingly, to improve the image one should correct the filter. This requires knowledge of the total electron content in the ionosphere, as well as of another parameter that characterizes the azimuthal variation of the electron number density (see Section 3.9). These quantities can be reconstructed by probing the ionosphere on two distinct carrier frequencies and exploiting the resulting redundancy in the data (see Section 3.10).
DA - 2017///
PY - 2017///
DO - 10.1007/978-3-319-52127-5_5
SP - 217-264
ER -
TY - JOUR
TI - SAR imaging through the Earth's ionosphere
AU - Gilman, Mikhail
AU - Smith, Erick
AU - Tsynkov, Semyon
AU - Gilman, M
AU - Smith, E
AU - Tsynkov, S
T2 - TRANSIONOSPHERIC SYNTHETIC APERTURE IMAGING
AB - When the signal of a spaceborne radar travels between the satellite and the ground, it becomes subject to the temporal dispersion of radio waves in the Earth’s ionosphere [18]. dispersion temporal The dispersion distorts the signal, and if the matched filter does not properly account for that, a mismatch occurs and the quality of the image deteriorates. The extent of deterioration becomes smaller as the ratio of the Langmuir frequency of the ionospheric plasma to the carrier frequency of the radar decreases. This is a part of the reason why many modern spaceborne SAR instruments operate in higher frequency bands. For example, TerraSAR-X operates in the X-band, on the frequency of 9.6GHz. X-band
DA - 2017///
PY - 2017///
DO - 10.1007/978-3-319-52127-5_3
SP - 59-161
ER -
TY - JOUR
TI - Conventional SAR imaging
AU - Gilman, Mikhail
AU - Smith, Erick
AU - Tsynkov, Semyon
AU - Gilman, M
AU - Smith, E
AU - Tsynkov, S
T2 - TRANSIONOSPHERIC SYNTHETIC APERTURE IMAGING
AB - In this chapter, we explain the fundamental principles of SAR data collection and image formation, i.e., inversion of the received data. Synthetic aperture radar uses microwaves for imaging the surface of the Earth from airplanes or satellites. Unlike photography which generates the picture by essentially recoding the intensity of the light reflected off the different parts of the target, SAR imaging exploits the phase information of the interrogating signals and as such can be categorized as a coherent imaging technology.
DA - 2017///
PY - 2017///
DO - 10.1007/978-3-319-52127-5_2
SP - 19-57
ER -
TY - CHAP
TI - A Simple Finite-Volume Method on a Cartesian Mesh for Pedestrian Flows with Obstacles
AU - Cheng, Yuanzhen
AU - Chertock, Alina
AU - Kurganov, Alexander
T2 - Springer Proceedings in Mathematics & Statistics
AB - We considerCheng, Yuanzhen a two-dimensionalChertock, Alina pedestrianKurganov, Alexander flow model with obstacles governed by scalar hyperbolic conservation laws, in which the flux is implicitly dependent on the density through the Eikonal equation. We propose a simple second-order finite-volume method, which is applicable to the case of obstacles of arbitrary shapes. Though the method is only first-order accurate near the obstacles, it is robust and provides sharp resolution of discontinuities as illustrated in a number of numerical experiments.
PY - 2017///
DO - 10.1007/978-3-319-57397-7_4
VL - 199
SP - 43-55
OP -
PB - Springer International Publishing
SN - 9783319573960 9783319573977
UR - http://dx.doi.org/10.1007/978-3-319-57397-7_4
DB - Crossref
KW - Pedestrian flow model
KW - Hyperbolic conservation laws
KW - Finite-volume method
KW - Interface tracking method
KW - Eikonal equation
KW - Fast sweeping method
ER -
TY - JOUR
TI - Transionospheric synthetic aperture imaging Introduction
AU - Gilman, M.
AU - Smith, E.
AU - Tsynkov, S.
T2 - Transionospheric synthetic aperture imaging
DA - 2017///
PY - 2017///
SP - 1-17
ER -
TY - JOUR
TI - Transionospheric Synthetic Aperture Imaging Discussion and outstanding questions
AU - Gilman, M.
AU - Smith, E.
AU - Tsynkov, S.
T2 - Transionospheric synthetic aperture imaging
DA - 2017///
PY - 2017///
SP - 417-431
ER -
TY - BOOK
TI - Transionospheric Synthetic Aperture Imaging
AU - Gilman, M.
AU - Smith, E.
AU - Tsynkov, S.
AU - Gilman, M
AU - Smith, E
AU - Tsynkov, S
AB - This landmark monograph presents the most recent mathematical developments in the analysis of ionospheric distortions of SAR images and offers innovative new strategies for their mitigation. As a prer
DA - 2017///
PY - 2017///
DO - 10.1007/978-3-319-52127-5
OP -
PB - Springer International Publishing
SE - 1-1
SN - 9783319521251 9783319521275
UR - http://dx.doi.org/10.1007/978-3-319-52127-5
DB - Crossref
ER -
TY - JOUR
TI - The effect of ionospheric turbulence
AU - Gilman, Mikhail
AU - Smith, Erick
AU - Tsynkov, Semyon
AU - Gilman, M
AU - Smith, E
AU - Tsynkov, S
T2 - TRANSIONOSPHERIC SYNTHETIC APERTURE IMAGING
AB - In Chapter 3, we have shown that temporal dispersion of the propagation medium (Earth’s ionosphere) causes distortions of SAR images (see Section 3.8). Moreover, we have identified the key integral characteristics of the ionospheric plasma that allow one to quantify those distortions. They are the zeroth moment of the electron number density N e, i.e., the TEC N H given by (3.66), as well the first moment $$\mathcal{Q}$$ of the azimuthal derivative of N e defined by ( 3.182 ). We have also demonstrated that one can obtain the unknown quantities N H and $$\mathcal{Q}$$ with the help of dual carrier probing (see Section 3.10 ) and subsequently incorporate them into the SAR matched filter matched filter in order to effectively eliminate the distortions (see Section 3.11 ). This correction of the filter is possible because one and the same pair of values $$(N_{H},\mathcal{Q})$$ “serves” all antenna signals used for the construction of the image, i.e., all the terms in the azimuthal sum. Once the values of N H and $$\mathcal{Q}$$ have been derived, the corrected filter will match the received signals for all antenna positions along the synthetic array.
DA - 2017///
PY - 2017///
DO - 10.1007/978-3-319-52127-5_4
SP - 163-215
ER -
TY - JOUR
TI - Modeling radar targets beyond the first Born approximation
AU - Gilman, Mikhail
AU - Smith, Erick
AU - Tsynkov, Semyon
AU - Gilman, M
AU - Smith, E
AU - Tsynkov, S
T2 - TRANSIONOSPHERIC SYNTHETIC APERTURE IMAGING
AB - In this chapter, we return to the foundations of the SAR ambiguity theory SAR ambiguity theory that we presented in Chapter 2 , and address the inconsistencies of the conventional approach outlined in Section 2.7 A standard representation of the image in the SAR ambiguity theory is SAR image by the convolution integral convolution ( 2.1 ) [see also ( 2.31 )]:
DA - 2017///
PY - 2017///
DO - 10.1007/978-3-319-52127-5_7
SP - 311-371
ER -
TY - JOUR
TI - Inverse scattering off anisotropic targets
AU - Gilman, M.
AU - Smith, E.
AU - Tsynkov, S.
T2 - Transionospheric synthetic aperture imaging
DA - 2017///
PY - 2017///
SP - 373-415
ER -
TY - JOUR
TI - Generating bipartite networks with a prescribed joint degree distribution
AU - Boroojeni, A. A.
AU - Dewar, J.
AU - Wu, T.
AU - Hyman, J. M.
T2 - Journal of Complex Networks
DA - 2017///
PY - 2017///
VL - 5
IS - 6
SP - 839-857
ER -
TY - JOUR
TI - Deriving Useful Information from Bimonthly Global-Scale Climate Analysis for Climate Change Adaptation Over East Africa
AU - Tetteh, Isaac K.
AU - Appiah-Badu, Nana K. A.
AU - Semazzi, Fredrick H. M.
AU - Olayide, Olawale E.
T2 - CLIMATE CHANGE ADAPTATION IN AFRICA: FOSTERING RESILIENCE AND CAPACITY TO ADAPT
AB - Implementation of appropriate climate change adaptation strategies is contingent on a good understanding of climate variability. Efforts to adapt to climate change impacts in East African societies have flourished. However, an area of research which has been neglected and could enhance adaptive capacity is bimonthly global-scale climate analysis in relationship to the long rains, during the climatologically prominent phase of El Niño Southern Oscillation (ENSO). Empirical analyses were carried out using nearly 60 years of standardized gridded rainfall, horizontal wind and sea surface temperature (SST) data, to gain predictive understanding of the region’s climate. This study has delineated SST and divergent circulation features related to three of the four rainfall modes. The modes responded differently to the Pacific ENSO, Atlantic and Indian Oceans. However, there was no clear relationship between the second mode and the global SST distributions. Having substantiated this with monthly and seasonal-scale SST analyses, it suggested that this atypical pattern warranted numerical modeling studies or should be verified using other high resolution datasets. The SST predictor features identified may be used to enhance operational seasonal climate prediction scheme. In this way, end users would be better prepared to select appropriate climate change adaption options.
DA - 2017///
PY - 2017///
DO - 10.1007/978-3-319-49520-0_8
SP - 125-140
SN - 1610-2010
ER -
TY - JOUR
TI - Characterizing Sources of Uncertainty from Global Climate Models and Downscaling Techniques
AU - Wootten, A.
AU - Terando, A.
AU - Reich, B. J.
AU - Boyles, R. P.
AU - Semazzi, F.
T2 - JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY
AB - Abstract In recent years, climate model experiments have been increasingly oriented toward providing information that can support local and regional adaptation to the expected impacts of anthropogenic climate change. This shift has magnified the importance of downscaling as a means to translate coarse-scale global climate model (GCM) output to a finer scale that more closely matches the scale of interest. Applying this technique, however, introduces a new source of uncertainty into any resulting climate model ensemble. Here a method is presented, on the basis of a previously established variance decomposition method, to partition and quantify the uncertainty in climate model ensembles that is attributable to downscaling. The method is applied to the southeastern United States using five downscaled datasets that represent both statistical and dynamical downscaling techniques. The combined ensemble is highly fragmented, in that only a small portion of the complete set of downscaled GCMs and emission scenarios is typically available. The results indicate that the uncertainty attributable to downscaling approaches ~20% for large areas of the Southeast for precipitation and ~30% for extreme heat days (>35°C) in the Appalachian Mountains. However, attributable quantities are significantly lower for time periods when the full ensemble is considered but only a subsample of all models is available, suggesting that overconfidence could be a serious problem in studies that employ a single set of downscaled GCMs. This article concludes with recommendations to advance the design of climate model experiments so that the uncertainty that accrues when downscaling is employed is more fully and systematically considered.
DA - 2017/12//
PY - 2017/12//
DO - 10.1175/jamc-d-17-0087.1
VL - 56
IS - 12
SP - 3245-3262
SN - 1558-8432
ER -
TY - JOUR
TI - Unimodular hierarchical model sand their Graver bases
AU - Bernstein, D. I.
AU - O'Neill, C.
T2 - Journal of Algebraic Statistics
AB - Given a simplicial complex whose vertices are labeled with positive integers, one can associate a vector configuration whose corresponding toric variety is the Zariski closure of a hierarchical model. We classify all the vertex-weighted simplicial complexes that give rise to unimodular vector configurations. We also provide a combinatorial characterization of their Graver bases.
DA - 2017///
PY - 2017///
DO - 10.18409/jas.v8i2.66
VL - 8
IS - 2
SP - 29-43
ER -
TY - JOUR
TI - Mean-Variance Risk-Averse Optimal Control of Systems Governed by PDEs with Random Parameter Fields Using Quadratic Approximations
AU - Alexanderian, Alen
AU - Petra, Noemi
AU - Stadler, Georg
AU - Ghattas, Omar
T2 - SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION
AB - We present a method for optimal control of systems governed by partial differential equations (PDEs) with uncertain parameter fields. We consider an objective function that involves the mean and variance of the control objective, leading to a risk-averse optimal control problem. Conventional numerical methods for optimization under uncertainty are prohibitive when applied to this problem. To make the optimal control problem tractable, we invoke a quadratic Taylor series approximation of the control objective with respect to the uncertain parameter field. This enables deriving explicit expressions for the mean and variance of the control objective in terms of its gradients and Hessians with respect to the uncertain parameter. The risk-averse optimal control problem is then formulated as a PDE-constrained optimization problem with constraints given by the forward and adjoint PDEs defining these gradients and Hessians. The expressions for the mean and variance of the control objective under the quadratic approximation involve the trace of the (preconditioned) Hessian and are thus prohibitive to evaluate. To overcome this difficulty, we employ trace estimators, which only require a modest number of Hessian-vector products. We illustrate our approach with two specific problems: the control of a semilinear elliptic PDE with an uncertain boundary source term, and the control of a linear elliptic PDE with an uncertain coefficient field. For the latter problem, we derive adjoint-based expressions for efficient computation of the gradient of the risk-averse objective with respect to the controls. Along with the quadratic approximation and trace estimation, this ensures that the cost of computing the risk-averse objective and its gradient with respect to the control---measured in the number of PDE solves---is independent of the (discretized) parameter and control dimensions, and depends only on the number of random vectors employed in the trace estimation, leading to an efficient quasi-Newton method for solving the optimal control problem. Finally, we present a comprehensive numerical study of an optimal control problem for fluid flow in a porous medium with an uncertain permeability field.
DA - 2017///
PY - 2017///
DO - 10.1137/16m106306x
VL - 5
IS - 1
SP - 1166-1192
SN - 2166-2525
KW - optimization under uncertainty
KW - PDE-constrained optimization
KW - optimal control
KW - risk-aversion
KW - PDEs with random coefficients
KW - Gaussian measure
KW - Hessian
KW - trace estimators
ER -
TY - CONF
TI - Mathematical analysis of SAR imaging through a turbulent ionosphere
AU - Gilman, M.
AU - Tsynkov, S.
T2 - APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 9th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’17
A2 - Todorov, Michail D.
AB - Synthetic aperture radar (SAR) imaging though the Earth ionosphere is subject to distortions due to ionospheric turbulence. We consider the limiting cases of small-scale and large-scale turbulence and characterize the distortions in terms of image blurring and azimuthal shift. It is shown that in the large-scale case, a high level of eikonal fluctuations can coexist with the low degree of image distortions, and that blurring becomes significant at much higher levels of fluctuations than the shift. In the small-scale case, a low level of eikonal fluctuations is a precondition for imaging, while the magnitude of distortions depends on the ratio between the eikonal correlation radius and the length of the synthetic aperture.
C2 - 2017///
C3 -
DA - 2017///
DO - 10.1063/1.5007357
VL - 1895
SP -
PB - Author(s)
UR - http://dx.doi.org/10.1063/1.5007357
DB - Crossref
ER -
TY - CHAP
TI - A Practical Guide to Deterministic Particle Methods
AU - Chertock, A.
T2 - Handbook of Numerical Analysis
AB - Abstract The past several decades have seen significant development in the design and numerical analysis of particle methods for approximating solutions of PDEs. In these methods, a numerical solution is sought as a linear combination of Dirac delta-functions located at certain points. The locations and coefficients (weights) of the delta-functions are first chosen to accurately approximate the initial data and then are evolved in time according to the system of ODEs obtained from a weak formulation of the considered problem. The main advantage of the particle methods is their low numerical diffusion that allows them to capture a variety of nonlinear waves with a high resolution. Even though the most “natural” application of the particle methods is linear transport equations, over the years, the range of these methods has been extended for approximating solutions of convection–diffusion and dispersive equations and general nonlinear problems. In this chapter, we provide a mathematical introduction to deterministic particle methods and review different aspects of their practical implementation such as recovering an approximate solution from its particle distribution and an investigation of various particle redistribution algorithms.
PY - 2017///
DO - 10.1016/bs.hna.2016.11.004
VL - 18
SP - 177-202
OP -
PB - Elsevier
SN - 9780444639103
UR - http://dx.doi.org/10.1016/bs.hna.2016.11.004
DB - Crossref
KW - Deterministic particle methods
KW - Particle function approximations
KW - Remising techniques
KW - Linear transport equations
KW - Convection-diffusion equation
KW - Dispersion equations
ER -
TY - JOUR
TI - Uncertainty Analysis of Continuum Phase Field Modeling in 180 degrees Domain Wall Structures
AU - Miles, Paul
AU - Leon, Lider
AU - Smith, Ralph
AU - Oates, William
T2 - BEHAVIOR AND MECHANICS OF MULTIFUNCTIONAL MATERIALS AND COMPOSITES 2017
AB - The evolution and formation of domain structures in ferroelectric materials is modeled using a continuum phase field approach and compared with density functional theory (DFT) using Bayesian uncertainty analysis. These simulations are carried out on the ferroelectric, lead titanate. Self-consistency between DFT and the continuum approach is advantageous when computing polydomain structures and domain wall dynamics. There is uncertainty in the phenomenological parameters related to the Landau energy, electrostriction, and twinned domain wall energy in single and polydomain ferroelectric crystals. To quantify the model parameter uncertainty associated with the phase field model, Bayesian statistics were used. Specifically, we will focus on estimating the value of the exchange parameters associated with polarization gradients. The phase field model predictions for the 180° domain wall energy are calibrated based upon DFT calculations. Model predictions of domain wall size are found to be on the same order as DFT calculations.
DA - 2017///
PY - 2017///
DO - 10.1117/12.2260130
VL - 10165
SP -
SN - 1996-756X
KW - Ferroelectrics
KW - Domain Wall Structures
KW - Uncertainty
KW - Parameter Estimation
ER -
TY - JOUR
TI - Taut foliations, left-orderability, and cyclic branched covers (vol 39, pg 599, 2014)
AU - Gordon, C.
AU - Lidman, T.
T2 - Acta Mathematica Vietnamica
DA - 2017///
PY - 2017///
VL - 42
IS - 4
SP - 775-776
ER -
TY - JOUR
TI - Surrogate Model Development and Feedforward Control Implementation for PZT Bimorph Actuators Employed for Robobee
AU - Bravo, Nikolas
AU - Smith, Ralph C.
AU - Crews, John
T2 - BEHAVIOR AND MECHANICS OF MULTIFUNCTIONAL MATERIALS AND COMPOSITES 2017
AB - In this paper, we discuss the development of models for PZT bimorph actuators used to power micro-air vehicles including Robobee. Due to the highly dynamic drive regimes required for the actuators, models must quantify the nonlinear, hysteretic, and rate-dependent behavior inherent to PZT. We first employ the homogenized energy model (HEM) framework to model the actuator dynamics. This provides a comprehensive model, which can be inverted and implemented for certain control regimes. We additionally discuss the development of data-driven models and focus on the implementation of a model based on a dynamic mode decomposition (DMD). Finally, we detail attributes of both approaches for uncertainty quantification and real-time control implementation.
DA - 2017///
PY - 2017///
DO - 10.1117/12.2259948
VL - 10165
SP -
SN - 1996-756X
KW - Modeling
KW - Control
KW - Dynamic Mode Decomposition
KW - Homogenized Energy Model
ER -
TY - JOUR
TI - QUASI-NONEXPANSIVE ITERATIONS ON THE AFFINE HULL OF ORBITS: FROM MANN'S MEAN VALUE ALGORITHM TO INERTIAL METHODS
AU - Combettes, Patrick L.
AU - Glaudin, Lilian E.
T2 - SIAM JOURNAL ON OPTIMIZATION
AB - Fixed point iterations play a central role in the design and the analysis of a large number of optimization algorithms. We study a new iterative scheme in which the update is obtained by applying a composition of quasi-nonexpansive operators to a point in the affine hull of the orbit generated up to the current iterate. This investigation unifies several algorithmic constructs, including Mann's mean value method, inertial methods, and multilayer memoryless methods. It also provides a framework for the development of new algorithms, such as those we propose for solving monotone inclusion and minimization problems.
DA - 2017///
PY - 2017///
DO - 10.1137/17m112806x
VL - 27
IS - 4
SP - 2356-2380
SN - 1095-7189
KW - averaged operator
KW - fixed point iteration
KW - forward-backward algorithm
KW - inertial algorithm
KW - mean value iterations
KW - monotone operator splitting
KW - nonsmooth minimization
KW - Peaceman-Rachford algorithm
KW - proximal algorithm
ER -
TY - JOUR
TI - Global Sensitivity Analysis for a Quantum Informed Ferroelectric Phase Field Model
AU - Leon, Lider S.
AU - Smith, Ralph C.
AU - Oates, William S.
AU - Miles, Paul
T2 - BEHAVIOR AND MECHANICS OF MULTIFUNCTIONAL MATERIALS AND COMPOSITES 2017
AB - We consider global sensitivity analysis (GSA) for correlated parameters in a continuum phase-field model for ferroelectric materials. The model was previously calibrated using density functional theory (DFT) simulations. For single domain ferroelectric lead titanate crystals, GSA is employed to rank the sensitivity of phenomenological parameters governing the Landau energy surface. The sensitivity analysis is based on Sobol’s variance-based decomposition in which the component functions of the high-dimensional representation (HDMR) of the model are computed analytically. For the subset of parameters that are most correlated, high-order component functions and sensitivity indices are found to be significant.
DA - 2017///
PY - 2017///
DO - 10.1117/12.2259945
VL - 10165
SP -
SN - 1996-756X
KW - Density functional theory (DFT)
KW - ferroelectricity
KW - global sensitivity analysis
KW - HDMR
KW - lead titanate
ER -
TY - JOUR
TI - Comment on solution of differential-algebraic equations through gradient flow embedding
AU - Campbell, Stephen L.
T2 - Computers & Chemical Engineering
AB - The paper “On the solution of differential-algebraic equations through gradient flow embedding,” Computers and Chemical Engineering, 103 (2017), 165–173, presents an algorithm that is designed to integrate some index one DAEs. This letter reviews index one DAEs, and clarifies how the assumptions of the algorithm fit within a more general framework. The types of index one DAEs for which the new algorithm are not appropriate are discussed.
DA - 2017/11//
PY - 2017/11//
DO - 10.1016/j.compchemeng.2017.07.008
VL - 106
SP - 529-531
J2 - Computers & Chemical Engineering
LA - en
OP -
SN - 0098-1354
UR - http://dx.doi.org/10.1016/j.compchemeng.2017.07.008
DB - Crossref
KW - Differential-algebraic equations
KW - Gradient flows
KW - Index
KW - Ordinary differential equations
ER -
TY - JOUR
TI - CPDE special section
AU - Smith, Ralph C.
AU - Zwart, Hans
T2 - ANNUAL REVIEWS IN CONTROL
AB - The world surrounding us has become increasingly technological. Nowadays, the influence of automation is perceived in each aspect of everyday life. If automation makes some aspects of life easier, faster and safer, empirical data also suggests that it could have negative performance and safety consequences regarding human operators, a set of difficulties called the “out-of-the-loop” (OOTL) performance problem. However, after decades of research, this phenomenon remains difficult to grasp and counter. In this paper, we propose a neuroergonomics approach to treat this phenomenon. We first describe how automation impacts human operators. Then, we present the current knowledge relative to this OOTL phenomenon. Finally, we describe how recent insights in neurosciences can help characterize, quantify and compensate this phenomenon.
DA - 2017///
PY - 2017///
DO - 10.1016/j.arcontrol.2017.09.007
VL - 44
SP - 183-183
SN - 1367-5788
ER -
TY - JOUR
TI - Unextendible Maximally Entangled Bases and Mutually Unbiased Bases in Multipartite Systems
AU - Zhang, Ya-Jing
AU - Zhao, Hui
AU - Jing, Naihuan
AU - Fei, Shao-Ming
T2 - INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
AB - We generalize the notion of unextendible maximally entangled basis from bipartite systems to multipartite quantum systems. It is proved that there do not exist unextendible maximally entangled bases in three-qubit systems. Moreover, two types of unextendible maximally entangled bases are constructed in tripartite quantum systems and proved to be not mutually unbiased.
DA - 2017/11//
PY - 2017/11//
DO - 10.1007/s10773-017-3505-5
VL - 56
IS - 11
SP - 3425-3430
SN - 1572-9575
KW - Unextendible maximally entangled bases
KW - Mutually unbiased bases
KW - Multipartite quantum systems
ER -
TY - CONF
TI - Uncertainty analysis of ferroelectric polydomain structures
AU - Miles, P.
AU - Oates, W.
AU - Leon, L.
AU - Smith, Ralph
AB - Ferroelectric materials exhibit strong electromechanical behavior which has led to the production of a wide variety of adaptive structures and intelligent systems, ranging from structural health monitoring sensors, energy harvesting circuits, and flow control actuators. Given the large number of applications, accurate prediction of ferroelectric materials constitutive behavior is critical. This presents many challenges, including the need to predict behavior from electronic structures up to macroscropic continuum. Many of the structure-property relations in these materials can be accurately calculated using density functional theory (DFT). However, DFT is not necessarily conducive to the large scale computations required to solve these problems on a continuum scale. Introducing a phase field polarization order parameter is an alternative approach, which provides a means to simulate the length scale gap between nano- and microscale domain structure evolution. The introduction of the phase field approximation results in uncertainty. Bayesian statistical analysis is an ideal tool for quantifying the uncertainty associated with the continuum phase field model parameters. Analyses of monodomain structures allows for identification of Landau energy and electrostrictive stress parameters. Identifying the exchange parameters, which are proportional to the polarization gradients, requires consideration of polydomain structures. This is a nontrivial problem as domain wall structures are fully coupled between the Landau energy, electrostrictive, and exchange parameters. Accurately quantifying the uncertainty in the phase field parameters will provide insight into the nonlinear constitutive behavior.
C2 - 2017///
C3 - Proceedings of the asme conference on smart materials adaptive
DA - 2017///
DO - 10.1115/smasis2017-3916
ER -
TY - JOUR
TI - Transcriptional Reprogramming during Effector-to-Memory Transition Renders CD4(+) T Cells Permissive for Latent HIV-1 Infection
AU - Shan, Liang
AU - Deng, Kai
AU - Gao, Hongbo
AU - Xing, Sifei
AU - Capoferri, Adam A.
AU - Durand, Christine M.
AU - Rabi, S. Alireza
AU - Laird, Gregory M.
AU - Kim, Michelle
AU - Hosmane, Nina N.
AU - Yang, Hung-Chih
AU - Zhang, Hao
AU - Margolick, Joseph B.
AU - Li, Linghua
AU - Cai, Weiping
AU - Ke, Ruian
AU - Flavell, Richard A.
AU - Siliciano, Janet D.
AU - Siliciano, Robert F.
T2 - IMMUNITY
AB - The latent reservoir for HIV-1 in resting memory CD4+ T cells is the major barrier to curing HIV-1 infection. Studies of HIV-1 latency have focused on regulation of viral gene expression in cells in which latent infection is established. However, it remains unclear how infection initially becomes latent. Here we described a unique set of properties of CD4+ T cells undergoing effector-to-memory transition including temporary upregulation of CCR5 expression and rapid downregulation of cellular gene transcription. These cells allowed completion of steps in the HIV-1 life cycle through integration but suppressed HIV-1 gene transcription, thus allowing the establishment of latency. CD4+ T cells in this stage were substantially more permissive for HIV-1 latent infection than other CD4+ T cells. Establishment of latent HIV-1 infection in CD4+ T could be inhibited by viral-specific CD8+ T cells, a result with implications for elimination of latent HIV-1 infection by T cell-based vaccines.
DA - 2017/10/17/
PY - 2017/10/17/
DO - 10.1016/j.immuni.2017.09.014
VL - 47
IS - 4
SP - 766-+
SN - 1097-4180
ER -
TY - JOUR
TI - SEMI-INFINITE PROGRAMMING USING HIGH-DEGREE POLYNOMIAL INTERPOLANTS AND SEMIDEFINITE PROGRAMMING
AU - Papp, David
T2 - SIAM JOURNAL ON OPTIMIZATION
AB - In a common formulation of semi-infinite programs, the infinite constraint set is a requirement that a function parametrized by the decision variables is nonnegative over an interval. If this function is sufficiently closely approximable by a polynomial or a rational function, then the semi-infinite program can be reformulated as an equivalent semidefinite program, which in turn can be solved with interior point methods very efficiently to high accuracy. On the other hand, solving this semidefinite program is challenging if the polynomials involved are of high degree, due to numerical difficulties and bad scaling arising both from the polynomial approximations and from the fact that the semidefinite programming constraints coming from the sum-of-squares representation of nonnegative polynomials are badly scaled. We combine polynomial function approximation techniques and polynomial programming to overcome these numerical difficulties, using sum-of-squares interpolants. Specifically, it is shown that the conditioning of the reformulations using sum-of-squares interpolants does not deteriorate with increasing degrees, and problems involving sum-of-squares interpolants of hundreds of degrees can be handled without difficulty. The proposed reformulations are sufficiently well scaled that they can be solved easily with every commonly used semidefinite programming solver, such as SeDuMi, SDPT3, and CSDP. Motivating applications include convex optimization problems with semi-infinite constraints and semidefinite conic inequalities, such as those arising in the optimal design of experiments. Numerical results align with the theoretical predictions; in the problems considered, available memory was the only factor limiting the degrees of polynomials to approximately 1000.
DA - 2017///
PY - 2017///
DO - 10.1137/15m1053578
VL - 27
IS - 3
SP - 1858-1879
SN - 1095-7189
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-85032876902&partnerID=MN8TOARS
KW - sum-of-squares
KW - interpolation
KW - polynomial optimization
KW - semi-infinite programming
KW - design of experiments
KW - semidefinite optimization
ER -
TY - JOUR
TI - On the correlation and parametric approaches to calculation of credit value adjustment
AU - Pang, Tao
AU - Chen, Wei
AU - Li, Le
T2 - JOURNAL OF RISK MODEL VALIDATION
AB - Credit value adjustment (CVA) is an adjustment added to the fair value of an over-the-counter trade due to the risk of counterparty defaults. When the exposure to the counterparty and the counterparty default risk tend to change in the same direction, so-called wrong-way risk (WWR) must be taken into account. Right-way risk takes place when the two factors move in opposite directions. These two comovement effects are also called directional-way risk (DWR). Many efforts have been made to reduce the computational burden of calculating CVA with DWR. The two most popular approaches are the parametric approach and the correlation approach. In this paper, we develop a connection between these two approaches. In particular, by decomposing the DWR into a robust correlation coefficient and a profile multiplier, we bring the parametric approach into the correlation approach framework. This allows us to explain the parameters in the parametric approach. Our results suggest that the parametric approach can become sensitive when calculating the WWR in certain scenarios. For risk model governance and validation purposes, caution should be exercised when using the parametric approach for CVA calculation.
DA - 2017/9//
PY - 2017/9//
DO - 10.21314/jrmv.2017.177
VL - 11
IS - 3
SP - 49-67
SN - 1753-9587
KW - credit value adjustment (CVA)
KW - wrong-way risk (WWR)
KW - right-way risk
KW - correlation approach
KW - parametric approach
ER -
TY - CONF
TI - Identifiability and active subspace analysis for a polydomain ferroelectric phase field model
AU - Leon, L. S.
AU - Smith, Ralph
AU - Oates, W. S.
AU - Miles, P.
AB - We consider subset selection and active subspace techniques for parameters in a continuum phase-field polydomain model for ferroelectric materials. This analysis is necessary to mathematically determine the parameter subset or subspace critically affecting the response, prior to model calibration using either experimental or synthetic data constructed using density functional theory (DFT) simulations. For the 180° domain wall model, we employ identifiability analysis using a Fisher information matrix methodology, and subspace selection to determine the active subspace. We demonstrate the implementation and interpretation of techniques that accommodate the model structure and discuss results in the context of identifiable parameter subsets and active subspaces quantifying the strongest influence on the model output. Our results indicate that the governing domain wall gradient energy exchange parameter is most identifiable.
C2 - 2017///
C3 - Proceedings of the asme conference on smart materials adaptive
DA - 2017///
DO - 10.1115/smasis2017-3845
ER -
TY - JOUR
TI - Dynamics of degenerate quasilinear reaction diffusion systems with nonnegative initial functions
AU - Pao, C. V.
AU - Ruan, W. H.
T2 - JOURNAL OF DIFFERENTIAL EQUATIONS
AB - This paper is concerned with a system of quasilinear reaction–diffusion equations with density dependent diffusion coefficients and mixed quasimonotone reaction functions. The equations are allowed to be degenerate and the boundary conditions are of the nonlinear type. The main goals are to prove the existence and uniqueness of the weak solution between a pair of coupled upper and lower solutions; show that the weak solution evolves into the classical solution, and analyze the asymptotic behavior of the solution using quasi-solutions of the steady-state system. The general results are applied to a degenerate Lotka–Volterra competition model. Conditions are given for the solution to exist globally, to evolve into the classical solution, and to be attracted into a sector formed by quasi-solutions of the elliptic system. Especially for the Neumann problem we give a simple condition for the solution to converge to a unique constant steady-state solution which is a global attractor.
DA - 2017/12/5/
PY - 2017/12/5/
DO - 10.1016/j.jde.2017.08.024
VL - 263
IS - 11
SP - 7709-7752
SN - 1090-2732
KW - Quasilinear reaction diffusion systems
KW - Upper and lower solutions
KW - Weak and classical solutions
KW - Asymptotic behavior
KW - Lotka-Volterra models
ER -
TY - CONF
TI - Data-driven model development and feedback control design for PZT bimorph actuators
AU - Bravo, N.
AU - Smith, Ralph
AU - Crews, J.
AB - In the paper, we discuss the development of a high-fidelity and surrogate model for a PZT bimorph used as an actuator for micro-air vehicles including Robobee. The models must quantify the nonlinear, hysteretic, and rate-dependent behavior inherent to PZT in dynamic operating regimes. The actuator dynamics are initially modeled using the homogenized energy model (HEM) framework. This provides a comprehensive high-fidelity model, which can be inverted and implemented in real time for certain control regimes. To improve efficiency, we additionally discuss the development of data-driven models and focus on the implementation of a surrogate model based on a dynamic mode decomposition (DMD). Finally, we detail the design and implementation of a PI controller on the surrogate and high-fidelity models.
C2 - 2017///
C3 - Proceedings of the asme conference on smart materials adaptive
DA - 2017///
DO - 10.1115/smasis2017-3847
ER -
TY - JOUR
TI - Completion of tree metrics and rank 2 matrices
AU - Bernstein, Daniel Irving
T2 - LINEAR ALGEBRA AND ITS APPLICATIONS
AB - Motivated by applications to low-rank matrix completion, we give a combinatorial characterization of the independent sets in the algebraic matroid associated to the collection of m×n rank-2 matrices and n×n skew-symmetric rank-2 matrices. Our approach is to use tropical geometry to reduce this to a problem about phylogenetic trees which we then solve. In particular, we give a combinatorial description of the collections of pairwise distances between several taxa that may be arbitrarily prescribed while still allowing the resulting dissimilarity map to be completed to a tree metric.
DA - 2017/11/15/
PY - 2017/11/15/
DO - 10.1016/j.laa.2017.07.016
VL - 533
SP - 1-13
SN - 1873-1856
KW - Low-rank matrix completion
KW - Algebraic matroids
KW - Tropical geometry
KW - Tree-metric completion
ER -
TY - CONF
TI - A multi-axial electromechanically-coupled homogenized energy model for ferroelectric materials
AU - Oates, W. S.
AU - Smith, Ralph
AB - In this paper, we discuss the development and implementation of a 3-D electromechanically coupled homogenized energy model (HEM) for ferroelectric materials. A stochastic-based methodology is introduced and applied to problems involving large scale switching of ferroelectric and ferroelastic materials. Switching criteria for polarization variants are developed using density distributions in three dimensions to accommodate both electrical and mechanical loading and their coupled response. The theory accommodates non-proportional loading and major/minor loop hysteresis. Such formulations are known to accelerate computations for real-time control of nonlinear and hysteretic actuators. The proposed formulation maintains superior computational efficiency in the three dimensional case through the application of density formulations that are based on internal distributions of stress and electric field to produce a distribution of polarization switching events over a range of applied fields and stresses.
C2 - 2017///
C3 - Proceedings of the asme conference on smart materials adaptive
DA - 2017///
DO - 10.1115/smasis2017-3848
ER -
TY - CONF
TI - A maximum entropy approach for uncertainty quantification and analysis of multifunctional materials
AU - Gao, W.
AU - Oates, W. S.
AU - Smith, Ralph
AB - The Maximum Entropy (ME) method is shown to provide a new approach for quantifying model uncertainty in the presence of complex, heterogeneous data. This is important in model validation of a variety of multifunctional constitutive relations. For example, multifunctional materials contain field-coupled material parameters that should be self-consistent regardless of the measurement. A classical example is piezoelectricity which may be quantified from charge induced by stress or strain induced by an electric field. The proposed tools provide new statistical information to address measurement discrepancies, guide model development, and catalyze materials discovery for data fusion problems. The error between the model outputs and heterogeneous data is quantified and used to formulate a second moment constraint within the entropy functional. This leads to an augmented likelihood function that weights each individual set of data by its respective variance and covariance between each data set. As a first step, the method is evaluated on a piezoelectric ceramic to illustrate how the covariance matrix influences piezoelectric parameter estimation from heterogeneous electric displacement and strain data.
C2 - 2017///
C3 - Proceedings of the asme conference on smart materials adaptive
DA - 2017///
DO - 10.1115/smasis2017-3919
ER -
TY - JOUR
TI - A Stochastic Model of Optimal Debt Management and Bankruptcy
AU - Bressan, Alberto
AU - Marigonda, Antonio
AU - Nguyen, Khai T.
AU - Palladino, Michele
T2 - SIAM JOURNAL ON FINANCIAL MATHEMATICS
AB - A problem of optimal debt management is modeled as a noncooperative interaction between a borrower and a pool of lenders, in an infinite time horizon with exponential discount. The yearly income of the borrower is governed by a stochastic process. When the debt-to-income ratio $x(t)$ reaches a given size $x^*$, bankruptcy instantly occurs. The interest rate charged by the risk-neutral lenders is precisely determined in order to compensate for this possible loss of their investment. For a given bankruptcy threshold $x^*$, existence and properties of optimal feedback strategies for the borrower are studied, in a stochastic framework as well as in a limit deterministic setting. The paper also analyzes how the expected total cost to the borrower changes, depending on different values of $x^*$.
DA - 2017///
PY - 2017///
DO - 10.1137/16m1095019
VL - 8
IS - 1
SP - 841-873
SN - 1945-497X
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-85041586490&partnerID=MN8TOARS
KW - debt management and bankruptcy
KW - infinite time horizon
KW - optimal feedback solution
ER -
TY - JOUR
TI - MULTIPRECONDITIONED GMRES FOR SHIFTED SYSTEMS
AU - Bakhos, Tania
AU - Kitanidis, Peter K.
AU - Ladenheim, Scott
AU - Saibaba, Arvind K.
AU - Szyld, Daniel B.
T2 - SIAM JOURNAL ON SCIENTIFIC COMPUTING
AB - An implementation of GMRES with multiple preconditioners is proposed for solving shifted linear systems with shift-and-invert preconditioners. With this type of preconditioner, the Krylov subspace can be built without requiring the matrix-vector product with the shifted matrix. Furthermore, the multipreconditioned search space is shown to grow only linearly with the number of preconditioners. This allows for a more efficient implementation of the algorithm. The proposed implementation is tested on shifted systems that arise in computational hydrology and the evaluation of different matrix functions. The numerical results indicate the effectiveness of the proposed approach.
DA - 2017///
PY - 2017///
DO - 10.1137/16m1068694
VL - 39
IS - 5
SP - S222-S247
SN - 1095-7197
KW - shifted systems
KW - Krylov solvers
KW - GMRES
ER -
TY - JOUR
TI - Local Improvement Results for Anderson Acceleration with Inaccurate Function Evaluations
AU - Toth, Alex
AU - Ellis, J. Austin
AU - Evans, Tom
AU - Hamilton, Steven
AU - Kelley, C. T.
AU - Pawlowski, Roger
AU - Slattery, Stuart
T2 - SIAM Journal on Scientific Computing
AB - We analyze the convergence of Anderson acceleration when the fixed point map is corrupted with errors. We consider uniformly bounded errors and stochastic errors with infinite tails. We prove local improvement results which describe the performance of the iteration up to the point where the accuracy of the function evaluation causes the iteration to stagnate. We illustrate the results with examples from neutronics.
DA - 2017/1//
PY - 2017/1//
DO - 10.1137/16m1080677
VL - 39
IS - 5
SP - S47-S65
J2 - SIAM J. Sci. Comput.
LA - en
OP -
SN - 1064-8275 1095-7197
UR - http://dx.doi.org/10.1137/16M1080677
DB - Crossref
KW - nonlinear equations
KW - Anderson acceleration
KW - local improvement
ER -
TY - JOUR
TI - GENERALIZED HYBRID ITERATIVE METHODS FOR LARGE-SCALE BAYESIAN INVERSE PROBLEMS
AU - Chung, Julianne
AU - Saibaba, Arvind K.
T2 - SIAM JOURNAL ON SCIENTIFIC COMPUTING
AB - We develop a generalized hybrid iterative approach for computing solutions to large-scale Bayesian inverse problems. We consider a hybrid algorithm based on the generalized Golub--Kahan bidiagonalization for computing Tikhonov regularized solutions to problems where explicit computation of the square root and inverse of the covariance kernel for the prior covariance matrix is not feasible. This is useful for large-scale problems where covariance kernels are defined on irregular grids or are available only via matrix-vector multiplication, e.g., those from the Matérn class. We show that iterates are equivalent to LSQR iterates applied to a directly regularized Tikhonov problem, after a transformation of variables, and we provide connections to a generalized singular value decomposition filtered solution. Our approach shares many benefits of standard hybrid methods such as avoiding semiconvergence and automatically estimating the regularization parameter. Numerical examples from image processing demonstrate the effectiveness of the described approaches.
DA - 2017///
PY - 2017///
DO - 10.1137/16m1081968
VL - 39
IS - 5
SP - S24-S46
SN - 1095-7197
KW - inverse problems
KW - Bayesian methods
KW - hybrid iterative methods
KW - Tikhonov regularization
KW - Golub-Kahan bidiagonalization
KW - Matern covariance kernels
ER -
TY - JOUR
TI - ACCURATE GRADIENT COMPUTATIONS AT INTERFACES USING FINITE ELEMENT METHODS
AU - Qin, Fangfang
AU - Wang, Zhaohui
AU - Ma, Zhijie
AU - Li, Zhilin
T2 - INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS AND COMPUTER SCIENCE
AB - Abstract New finite element methods are proposed for elliptic interface problems in one and two dimensions. The main motivation is to get not only an accurate solution, but also an accurate first order derivative at the interface (from each side). The key in 1D is to use the idea of Wheeler (1974). For 2D interface problems, the point is to introduce a small tube near the interface and propose the gradient as part of unknowns, which is similar to a mixed finite element method, but only at the interface. Thus the computational cost is just slightly higher than in the standard finite element method. We present a rigorous one dimensional analysis, which shows a second order convergence order for both the solution and the gradient in 1D. For two dimensional problems, we present numerical results and observe second order convergence for the solution, and super-convergence for the gradient at the interface.
DA - 2017/9//
PY - 2017/9//
DO - 10.1515/amcs-2017-0037
VL - 27
IS - 3
SP - 527-537
SN - 2083-8492
KW - elliptic interface problems
KW - gradient/flux computation
KW - IFEM
KW - mixed FE formulation
KW - computational tube
ER -
TY - JOUR
TI - Quantum hyperdeterminants and hyper-Pfaffians
AU - Jing, Naihuan
AU - Zhang, Jian
T2 - MATHEMATISCHE ZEITSCHRIFT
AB - The irreducible spin character values of the wreath products of the hyperoctahedral groups with an arbitrary finite group are determined.
DA - 2017/12//
PY - 2017/12//
DO - 10.1007/s00209-017-1850-y
VL - 287
IS - 3-4
SP - 897-914
SN - 1432-1823
KW - Quantum hyperdeterminants
KW - Cayley's hyperdeterminant
KW - Quantum hyper-Pfaffians
KW - q-Forms
KW - Quantum monoids
ER -
TY - JOUR
TI - Idempotent conjugacy in monoids
AU - Putcha, Mohan S.
T2 - SEMIGROUP FORUM
DA - 2017/10//
PY - 2017/10//
DO - 10.1007/s00233-016-9818-5
VL - 95
IS - 2
SP - 366-378
SN - 1432-2137
KW - Idemotent conjugacy
KW - Parabolic subgroups
KW - Graham blocks
ER -
TY - JOUR
TI - An Augmented Method for 4th Order PDEs with Discontinuous Coefficients
AU - Li, Zhilin
AU - Qin, Fangfang
T2 - JOURNAL OF SCIENTIFIC COMPUTING
DA - 2017/12//
PY - 2017/12//
DO - 10.1007/s10915-017-0487-7
VL - 73
IS - 2-3
SP - 968-979
SN - 1573-7691
KW - 4th order PDE
KW - Discontinuous coefficient
KW - Fast Poisson solver
KW - Augmented immersed interface method
KW - Schur complement
KW - Natural jump conditions
ER -
TY - JOUR
TI - Well-posed continuum equations for granular flow with compressibility and
μ
(
I
)-rheology
AU - Barker, T.
AU - Schaeffer, D. G.
AU - Shearer, M.
AU - Gray, J. M. N. T.
T2 - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
AB - Continuum modelling of granular flow has been plagued with the issue of ill-posed dynamic equations for a long time. Equations for incompressible, two-dimensional flow based on the Coulomb friction law are ill-posed regardless of the deformation, whereas the rate-dependent μ ( I )-rheology is ill-posed when the non-dimensional inertial number I is too high or too low. Here, incorporating ideas from critical-state soil mechanics, we derive conditions for well-posedness of partial differential equations that combine compressibility with I -dependent rheology. When the I -dependence comes from a specific friction coefficient μ ( I ), our results show that, with compressibility, the equations are well-posed for all deformation rates provided that μ ( I ) satisfies certain minimal, physically natural, inequalities.
DA - 2017/5/3/
PY - 2017/5/3/
DO - 10.1098/rspa.2016.0846
VL - 473
IS - 2201
SP - 20160846
J2 - Proc. R. Soc. A
LA - en
OP -
SN - 1364-5021 1471-2946
UR - http://dx.doi.org/10.1098/rspa.2016.0846
DB - Crossref
KW - granular flow
KW - continuum modelling
KW - rheology
ER -
TY - JOUR
TI - SENSITIVITY ANALYSIS IN PORO-ELASTIC AND PORO-VISCO-ELASTIC MODELS WITH RESPECT TO BOUNDARY DATA
AU - Banks, H. T.
AU - Bekele-Maxwell, K.
AU - Bociu, L.
AU - Noorman, M.
AU - Guidoboni, G.
T2 - QUARTERLY OF APPLIED MATHEMATICS
AB - In this article we consider poro-elastic and poro-visco-elastic models inspired by problems in medicine and biology, and we perform sensitivity analysis on the solutions of these fluid-solid mixture problems with respect to the imposed boundary data, which are the main drivers of the system. Moreover, we compare the results obtained in the elastic case vs. visco-elastic case, as it is known that structural viscosity of biological tissues decreases with age and disease. Sensitivity analysis is the first step towards optimization and control problems associated with these models, which is our ultimate goal.
DA - 2017/12//
PY - 2017/12//
DO - 10.1090/qam/1475
VL - 75
IS - 4
SP - 697-735
SN - 1552-4485
KW - Sensitivity
KW - poro-elastic
KW - poro-visco-elastic
KW - biological tissues
KW - complex-step method
ER -
TY - JOUR
TI - SB-labelings and posets with each interval homotopy equivalent to a sphere or a ball
AU - Hersh, Patricia
AU - Meszaros, Karola
T2 - JOURNAL OF COMBINATORIAL THEORY SERIES A
AB - We introduce a new class of edge labelings for locally finite lattices which we call SB-labelings. We prove for finite lattices which admit an SB-labeling that each open interval has the homotopy type of a ball or of a sphere of some dimension. Natural examples include the weak order, the Tamari lattice, and the finite distributive lattices.
DA - 2017/11//
PY - 2017/11//
DO - 10.1016/j.jcta.2017.06.001
VL - 152
SP - 104-120
SN - 1096-0899
KW - Poset topology
KW - Mobius function
KW - Crosscut complex
KW - Tamari lattice
KW - Weak order
ER -
TY - JOUR
TI - Randomized matrix-free trace and log-determinant estimators
AU - Saibaba, Arvind K.
AU - Alexanderian, Alen
AU - Ipsen, Ilse C. F.
T2 - NUMERISCHE MATHEMATIK
AB - We present randomized algorithms for estimating the trace and determinant of Hermitian positive semi-definite matrices. The algorithms are based on subspace iteration, and access the matrix only through matrix vector products. We analyse the error due to randomization, for starting guesses whose elements are Gaussian or Rademacher random variables. The analysis is cleanly separated into a structural (deterministic) part followed by a probabilistic part. Our absolute bounds for the expectation and concentration of the estimators are non-asymptotic and informative even for matrices of low dimension. For the trace estimators, we also present asymptotic bounds on the number of samples (columns of the starting guess) required to achieve a user-specified relative error. Numerical experiments illustrate the performance of the estimators and the tightness of the bounds on low-dimensional matrices, and on a challenging application in uncertainty quantification arising from Bayesian optimal experimental design.
DA - 2017/10//
PY - 2017/10//
DO - 10.1007/s00211-017-0880-z
VL - 137
IS - 2
SP - 353-395
SN - 0945-3245
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-85017115710&partnerID=MN8TOARS
ER -
TY - JOUR
TI - Paul Frederick Zweifel
AU - McCormick, Norman J.
AU - Siewert, Charles E.
AU - Ganapol, Barry D.
AU - Prinja, Anil K.
T2 - PHYSICS TODAY
AB - Paul Frederick Zweifel died on 12 February 2017 in Blacksburg, Virginia. He was a prominent leader in the mathematical theory of nuclear reactors and the mathematical development of transport theory. Paul Frederick Zweifel PPT|High resolutionBorn in New York City on 21 June 1929, Paul later moved with his family to Spartanburg, South Carolina. At age 15 he was awarded a Pepsi-Cola scholarship to attend the college of his choice, Carnegie Institute of Technology (now Carnegie Mellon University). There he shared living quarters with John Nash Jr, the US mathematician who received the 1994 Nobel Memorial Prize in Economic Sciences. After graduating from Carnegie Tech in three years, he attended Duke University, where he received his PhD in physics in 1954 under the guidance of Eugene Greuling. The title of his dissertation was “Capture-positron branching ratios.” During his years of graduate study, he was a sports journalist at the Durham Sun newspaper, where he interviewed Willie Mays and other athletes.After completing his PhD, Paul worked at the General Electric Knolls Atomic Power Laboratory. For his contributions to the theory of the slowing down and thermalization of neutrons, which are important in the design and development of water-moderated nuclear reactors, he received an Ernest Orlando Lawrence Memorial Award from the Department of Energy in 1972.From 1958 to 1968, Paul was a professor of nuclear engineering at the University of Michigan. There he began working with physicist Kenneth Case, who made groundbreaking contributions to neutron transport theory at Los Alamos during the Manhattan Project. In 1967 they published their widely cited monograph Linear Transport Theory (Addison-Wesley) on the linear Boltzmann equation. That equation is used, for example, to analyze energy transport by neutrons in a nuclear reactor or photons in an absorbing and scattering medium. Paul and Case’s mathematical approach enables a more direct solution to many problems of the type analyzed by Boris Davison in Neutron Transport Theory (Clarendon Press, 1957) and Subrahmanyan Chandrasekhar in Radiative Transfer (Dover, 1960).During a sabbatical year at the Middle East Technical University in 1965, Paul and physicist Erdal İnönü organized a NATO Advanced Study Institute on transport theory in Ankara, Turkey.In 1968 Paul moved to Blacksburg, Virginia, where he became a professor of physics at Virginia Tech and was soon appointed as University Distinguished Professor. In 1969 he founded a series of conferences now known as the International Conferences on Transport Theory (ICTT). The biennial meetings continue to bring together experts in mathematical and applied transport theory in multifarious science and engineering disciplines from around the world. Because of his leadership and the force of his personality, the conferences, which are not affiliated with any professional society, have been held in the US 14 times, Italy 3 times, and once each in China, Brazil, Sweden, Russia, England, and Hungary; Paul hosted six of the conferences in Blacksburg.The journal Transport Theory and Statistical Physics (TTSP), with Paul as its founding editor from 1971 until 1983, has published the proceedings of nearly every ICTT meeting. The journal was retitled in 2014 as the Journal of Computational and Theoretical Transport in recognition of the growing popularity of numerical techniques in transport theory.Perhaps Paul’s most notable work in transport theory was pioneering the use of rigorous mathematics to bring order to the chaos of mathematical approaches for solving the linear transport equation. He developed existence and uniqueness theorems for the neutron transport equation and investigated the spectrum of the linear transport operator under general conditions.Paul retired from Virginia Tech in 1996. He was an opera lover, a musician, and a vocalist. He also was fluent in Italian; with his wife, Kathy, they provided supertitles for opera companies across the US, and they advertised their services with “Have Projector, Will Travel” business cards. He published articles on the mathematical theory of ancient and modern music. Paul loved to travel, and one of his most memorable trips, which he took with his family, was his 1983–84 sabbatical in Florence, Italy, where he also served as choir director of St James Episcopal Church. Throughout his life, Paul continued his passions for Gilbert and Sullivan musical theater, sports, and bridge.To those who study particle transport theory, Paul was a special figure. He was as comfortable with practical applications of the transport equation, particularly to nuclear reactors, as he was with the underlying mathematics. He had a flare for the unusual, and he often provided readers of TTSP with book reviews on esoteric subjects and entertained audiences with presentations on topics such as why Albert Einstein should have received five Nobel Prizes. Intellectually, Paul cast a large shadow on our community. Although sometimes contentious and seldom politically correct, with his witty sense of humor he could flatter with ridicule, critique with praise, and encourage with affection. He was an inspiration to us and a delightful colleague who will be greatly missed.© 2017 American Institute of Physics.
DA - 2017/8//
PY - 2017/8//
DO - 10.1063/pt.3.3671
VL - 70
IS - 8
SP - 73-73
SN - 1945-0699
ER -
TY - JOUR
TI - On the Death Rate of Abortively Infected Cells: Estimation from Simian-Human Immunodeficiency Virus Infection
AU - Ke, Ruian
AU - Cong, Mian-er
AU - Li, David
AU - Garcia-Lerma, J. Gerardo
AU - Perelson, Alan S.
T2 - JOURNAL OF VIROLOGY
AB - Progressive T cell depletion during chronic human immunodeficiency virus type 1 (HIV) infection is a key mechanism that leads to the development of AIDS. Recent studies have suggested that most T cells in the tissue die through pyroptosis triggered by abortive infection, i.e., infection of resting T cells in which HIV failed to complete reverse transcription. However, the contribution of abortive infection to T cell loss and how quickly abortively infected cells die in vivo, key parameters for a quantitative understanding of T cell population dynamics, are not clear. Here, we infected rhesus macaques with simian-human immunodeficiency viruses (SHIV) and followed the dynamics of both plasma SHIV RNA and total cell-associated SHIV DNA. Fitting mathematical models to the data, we estimate that upon infection a majority of CD4+ T cells (approximately 65%, on average) become abortively infected and die at a relatively high rate of 0.27 day-1 (half-life, 2.6 days). This confirms the importance of abortive infection in driving T cell depletion. Further, we find evidence suggesting that an immune response may be restricting viral infection 1 to 3 weeks after infection. Our study serves as a step forward toward a quantitative understanding of the mechanisms driving T cell depletion during HIV infection.IMPORTANCE In HIV-infected patients, progressive CD4+ T cell loss ultimately leads to the development of AIDS. The mechanisms underlying this T cell loss are not clear. Recent experimental data suggest that the majority of CD4+ T cells in tissue die through abortive infection, where the accumulation of incomplete HIV transcripts triggers cell death. To investigate the role of abortive infection in driving CD4+ T cell loss in vivo, we infected macaques with simian-human immunodeficiency viruses (SHIV) and followed the viral kinetics of both plasma RNA and cell-associated DNA during infection. Fitting mathematical models, we estimated that a large fraction of infected cells dies through abortive infection and has a half-life of approximately 2.6 days. Our results provide the first in vivo quantitative estimates of parameters characterizing abortive infection and support the notion that abortive infection represents an important mechanism underlying progressive CD4+ T cell depletion in vivo.
DA - 2017/9//
PY - 2017/9//
DO - 10.1128/jvi.00352-17
VL - 91
IS - 18
SP -
SN - 1098-5514
KW - abortive infection
KW - SHIV
KW - mathematical modeling
KW - viral kinetics
ER -
TY - JOUR
TI - Investigation of Biotransport in a Tumor With Uncertain Material Properties Using a Nonintrusive Spectral Uncertainty Quantification Method
AU - Alexanderian, Alen
AU - Zhu, Liang
AU - Salloum, Maher
AU - Ma, Ronghui
AU - Yu, Meilin
T2 - JOURNAL OF BIOMECHANICAL ENGINEERING-TRANSACTIONS OF THE ASME
AB - In this study, statistical models are developed for modeling uncertain heterogeneous permeability and porosity in tumors, and the resulting uncertainties in pressure and velocity fields during an intratumoral injection are quantified using a nonintrusive spectral uncertainty quantification (UQ) method. Specifically, the uncertain permeability is modeled as a log-Gaussian random field, represented using a truncated Karhunen–Lòeve (KL) expansion, and the uncertain porosity is modeled as a log-normal random variable. The efficacy of the developed statistical models is validated by simulating the concentration fields with permeability and porosity of different uncertainty levels. The irregularity in the concentration field bears reasonable visual agreement with that in MicroCT images from experiments. The pressure and velocity fields are represented using polynomial chaos (PC) expansions to enable efficient computation of their statistical properties. The coefficients in the PC expansion are computed using a nonintrusive spectral projection method with the Smolyak sparse quadrature. The developed UQ approach is then used to quantify the uncertainties in the random pressure and velocity fields. A global sensitivity analysis is also performed to assess the contribution of individual KL modes of the log-permeability field to the total variance of the pressure field. It is demonstrated that the developed UQ approach can effectively quantify the flow uncertainties induced by uncertain material properties of the tumor.
DA - 2017/9//
PY - 2017/9//
DO - 10.1115/1.4037102
VL - 139
IS - 9
SP -
SN - 1528-8951
KW - uncertain permeability and porosity
KW - statistical modeling
KW - mass transportation
KW - uncertainty quantification
KW - Karhunen-Loeve expansion
KW - polynomial chaos
KW - nonintrusive spectral projection
KW - sparse quadrature
ER -
TY - JOUR
TI - Evaluating strategies for reversing CRISPR-Cas9 gene drives
AU - Vella, Michael R.
AU - Gunning, Christian E.
AU - Lloyd, Alun L.
AU - Gould, Fred
T2 - Scientific Reports
AB - A gene drive biases inheritance of a gene so that it increases in frequency within a population even when the gene confers no fitness benefit. There has been renewed interest in environmental releases of engineered gene drives due to recent proof of principle experiments with the CRISPR-Cas9 system as a drive mechanism. Release of modified organisms, however, is controversial, especially when the drive mechanism could theoretically alter all individuals of a species. Thus, it is desirable to have countermeasures to reverse a drive if a problem arises. Several genetic mechanisms for limiting or eliminating gene drives have been proposed and/or developed, including synthetic resistance, reversal drives, and immunizing reversal drives. While predictions about efficacy of these mechanisms have been optimistic, we lack detailed analyses of their expected dynamics. We develop a discrete time model for population genetics of a drive and proposed genetic countermeasures. Efficacy of drive reversal varies between countermeasures. For some parameter values, the model predicts unexpected behavior including polymorphic equilibria and oscillatory dynamics. The timing and number of released individuals containing a genetic countermeasure can substantially impact outcomes. The choice among countermeasures by researchers and regulators will depend on specific goals and population parameters of target populations.
DA - 2017/9/8/
PY - 2017/9/8/
DO - 10.1038/s41598-017-10633-2
VL - 7
IS - 1
SP -
J2 - Sci Rep
LA - en
OP -
SN - 2045-2322
UR - http://dx.doi.org/10.1038/s41598-017-10633-2
DB - Crossref
ER -
TY - JOUR
TI - An augmented IIM & preconditioning technique for jump embedded boundary conditions
AU - Angot, P.
AU - Li, Z. L.
T2 - International Journal of Numerical Analysis and Modeling
DA - 2017///
PY - 2017///
VL - 14
IS - 4-5
SP - 712-729
ER -
TY - JOUR
TI - R-matrix realization of two-parameter quantum affine algebra U-r,U-s(<(gl(n))over cap>)
AU - Jing, Naihuan
AU - Liu, Ming
T2 - JOURNAL OF ALGEBRA
AB - We introduce the two-parameter quantum affine algebra U r , s ( gl ˆ n ) via the RTT realization. The Drinfeld realization is given and the type A quantum affine algebra is proved to be a special subalgebra of our extended algebra.
DA - 2017/10/15/
PY - 2017/10/15/
DO - 10.1016/j.jalgebra.2017.05.028
VL - 488
SP - 1-28
SN - 1090-266X
KW - Drinfeld realization
KW - RTT formulation
KW - Quantum affine algebras
KW - Gauss decomposition
ER -
TY - JOUR
TI - Hybrid optimization and Bayesian inference techniques for a non-smooth radiation detection problem
AU - Ştefănescu, Răzvan
AU - Schmidt, Kathleen
AU - Hite, Jason
AU - Smith, Ralph C.
AU - Mattingly, John
T2 - International Journal for Numerical Methods in Engineering
AB - We propose several algorithms to recover the location and intensity of a radiation source located in a simulated 250 × 180 m block of an urban center based on synthetic measurements. Radioactive decay and detection are Poisson random processes, so we employ likelihood functions based on this distribution. Owing to the domain geometry and the proposed response model, the negative logarithm of the likelihood is only piecewise continuous differentiable, and it has multiple local minima. To address these difficulties, we investigate three hybrid algorithms composed of mixed optimization techniques. For global optimization, we consider simulated annealing, particle swarm, and genetic algorithm, which rely solely on objective function evaluations; that is, they do not evaluate the gradient in the objective function. By employing early stopping criteria for the global optimization methods, a pseudo-optimum point is obtained. This is subsequently utilized as the initial value by the deterministic implicit filtering method, which is able to find local extrema in non-smooth functions, to finish the search in a narrow domain. These new hybrid techniques, combining global optimization and implicit filtering address, difficulties associated with the non-smooth response, and their performances, are shown to significantly decrease the computational time over the global optimization methods. To quantify uncertainties associated with the source location and intensity, we employ the delayed rejection adaptive Metropolis and DiffeRential Evolution Adaptive Metropolis algorithms. Marginal densities of the source properties are obtained, and the means of the chains compare accurately with the estimates produced by the hybrid algorithms. Copyright © 2016 John Wiley & Sons, Ltd.
DA - 2017/2/6/
PY - 2017/2/6/
DO - 10.1002/nme.5491
VL - 111
IS - 10
SP - 955-982
J2 - Int. J. Numer. Meth. Engng
LA - en
OP -
SN - 0029-5981
UR - http://dx.doi.org/10.1002/nme.5491
DB - Crossref
KW - inverse problems
KW - simulated annealing
KW - particle swarm
KW - genetic algorithm
KW - implicit filtering
KW - DiffeRential Evolution Adaptive Metropolis
KW - delayed rejection adaptive Metropolis
ER -
TY - JOUR
TI - From the weak Bruhat order to crystal posets
AU - Hersh, Patricia
AU - Lenart, Cristian
T2 - MATHEMATISCHE ZEITSCHRIFT
AB - We investigate the ways in which fundamental properties of the weak Bruhat order on a Weyl group can be lifted (or not) to a corresponding highest weight crystal graph, viewed as a partially ordered set; the latter projects to the weak order via the key map. First, a crystal theoretic analogue of the statement that any two reduced expressions for the same Coxeter group element are related by Coxeter moves is proven for all lower intervals $$[\hat{0},v]$$ in a simply or doubly laced crystal. On the other hand, it is shown that no finite set of moves exists, even in type A, for arbitrary crystal graph intervals. In fact, it is shown that there are relations of arbitrarily high degree amongst crystal operators that are not implied by lower degree relations. Second, for crystals associated to Kac–Moody algebras it is shown for lower intervals that the Möbius function is always 0 or ±1, and in finite type this is also proven for upper intervals, with a precise formula given in each case. Moreover, the order complex for each of these intervals is proven to be homotopy equivalent to a ball or to a sphere of some dimension, despite often not being shellable. For general intervals, examples are constructed with arbitrarily large Möbius function, again even in type A. Any interval having Möbius function other than 0 or ±1 is shown to contain within it a relation amongst crystal operators that is not implied by the relations giving rise to the local structure of the crystal, making precise a tight relationship between the Möbius function and these somewhat unexpected relations appearing in crystals. New properties of the key map are also derived. The key is shown to be determined entirely by the edge-colored poset-theoretic structure of the crystal, and a recursive algorithm is given for calculating it. In finite types, the fiber of the longest element of any parabolic subgroup of the Weyl group is also proven to have a unique minimal and a unique maximal element; this property fails for more general elements of the Weyl group.
DA - 2017/8//
PY - 2017/8//
DO - 10.1007/s00209-016-1808-5
VL - 286
IS - 3-4
SP - 1435-1464
SN - 1432-1823
KW - Crystal graph
KW - Weak Bruhat order
KW - Key map
KW - Stembridge moves
KW - Order complex
ER -
TY - JOUR
TI - AIC under the framework of least squares estimation
AU - Banks, H. T.
AU - Joyner, Michele L.
T2 - APPLIED MATHEMATICS LETTERS
AB - In this note we explain the use of the Akiake Information Criterion and its related model comparison indices (usually derived for maximum likelihood estimator inverse problem formulations) in the context of least squares (ordinary, weighted, iterative weighted or “generalized”, etc.) based inverse problem formulations. The ideas are illustrated with several examples of interest in biology.
DA - 2017/12//
PY - 2017/12//
DO - 10.1016/j.aml.2017.05.005
VL - 74
SP - 33-45
SN - 0893-9659
KW - Inverse problems
KW - Akiake information content
KW - Least squares estimation
KW - Biological applications
ER -
TY - JOUR
TI - Valuation of a hypothetical mining project under commodity price and exchange rate uncertainties by using numerical methods
AU - Aminrostamkolaee, Behnam
AU - Scroggs, Jeffrey S.
AU - Borghei, Matin Sadat
AU - Safdari-Vaighani, Ali
AU - Mohammadi, Teymour
AU - Pourkazemi, Mohammad Hossein
T2 - RESOURCES POLICY
AB - One of the goals presented here is the use of a radial basis function (RBF) method to approximate the numerical values of a gold mining project. RBFs have many attractive features compared to implicit finite differences method (FDM) and explicit FDM. They are mesh-free, computationally more efficient in high dimensions, and very accurate. In other words, the model is more comprehensive, and results are more accurate compared to the previous works. This paper compares accuracy of the RBF method with that of the implicit method (FDM) in this case study. The results indicate that convergence order of the RBF is higher than that of the implicit method. Also, this paper compares the results of the RBF method with those of implicit method for various scenarios. The most important goal presented here is combining exchange rate uncertainty together with commodity price (spot price) uncertainty. In fact, this paper tries to address this question: how can we model the exchange rate volatility and the correlation coefficient between returns of commodity price and exchange rate in assessing a gold mining project. Considering the disadvantages of the Discounted Cash Flow (DCF) method which does not use uncertainties, the approach presented here makes use of real options valuation for a gold mine project valuation. This paper uses an explicit method (FDM) for these calculations. The results indicate increasing volatilities for either or both commodity price or exchange rate results in decreasing the maximum project value. Also, the correlation coefficients between returns of commodity price and exchange rate in different years are negative and statistically significant. The final result indicates that with an increase in the correlation coefficient, the volatility of gold price in terms of Canadian dollar decreases and therefore the maximum project value increases too. In summary, the exchange rate volatility and the correlation coefficient between returns of commodity price and exchange rate have a significant impact on mining project values.
DA - 2017/6//
PY - 2017/6//
DO - 10.1016/j.resourpol.2017.04.004
VL - 52
SP - 296-307
SN - 1873-7641
KW - Discounted cash flow
KW - Real options valuation
KW - Geometric Brownian Motion
KW - Commodity price
KW - Volatility
KW - Implicit FDM and explicit FDM
KW - Radial basis function
KW - Exchange rate
ER -
TY - JOUR
TI - Solving an inverse eigenvalue problem with triple constraints on eigenvalues, singular values, and diagonal elements
AU - Wu, Sheng-Jhih
AU - Chu, Moody T.
T2 - INVERSE PROBLEMS
DA - 2017/8//
PY - 2017/8//
DO - 10.1088/1361-6420/aa76c4
VL - 33
IS - 8
SP -
SN - 1361-6420
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-85026767399&partnerID=MN8TOARS
KW - inverse eigenvalue problem
KW - majorization relationships
KW - projected gradient
KW - projected Hessian
KW - analytic gradient dynamics
ER -
TY - JOUR
TI - NS5A inhibitors unmask differences in functional replicase complex half-life between different hepatitis C virus strains
AU - Benzine, Tiffany
AU - Brandt, Ryan
AU - Lovell, William C.
AU - Yamane, Daisuke
AU - Neddermann, Petra
AU - De Francesco, Raffaele
AU - Lemon, Stanley M.
AU - Perelson, Alan S.
AU - Ke, Ruian
AU - McGivern, David R.
T2 - PLOS PATHOGENS
AB - Hepatitis C virus (HCV) RNA is synthesized by the replicase complex (RC), a macromolecular assembly composed of viral non-structural proteins and cellular co-factors. Inhibitors of the HCV NS5A protein block formation of new RCs but do not affect RNA synthesis by pre-formed RCs. Without new RC formation, existing RCs turn over and are eventually lost from the cell. We aimed to use NS5A inhibitors to estimate the half-life of the functional RC of HCV. We compared different cell culture-infectious strains of HCV that may be grouped based on their sensitivity to lipid peroxidation: robustly replicating, lipid peroxidation resistant (LPOR) viruses (e.g. JFH-1 or H77D) and more slowly replicating, lipid peroxidation sensitive (LPOS) viruses (e.g. H77S.3 and N.2). In luciferase assays, LPOS HCV strains declined under NS5A inhibitor therapy with much slower kinetics compared to LPOR HCV strains. This difference in rate of decline was not observed for inhibitors of the NS5B RNA-dependent RNA polymerase suggesting that the difference was not simply a consequence of differences in RNA stability. In further analyses, we compared two isoclonal HCV variants: the LPOS H77S.3 and the LPOR H77D that differ only by 12 amino acids. Differences in rate of decline between H77S.3 and H77D following NS5A inhibitor addition were not due to amino acid sequences in NS5A but rather due to a combination of amino acid differences in the non-structural proteins that make up the HCV RC. Mathematical modeling of intracellular HCV RNA dynamics suggested that differences in RC stability (half-lives of 3.5 and 9.9 hours, for H77D and H77S.3, respectively) are responsible for the different kinetics of antiviral suppression between LPOS and LPOR viruses. In nascent RNA capture assays, the rate of RNA synthesis decline following NS5A inhibitor addition was significantly faster for H77D compared to H77S.3 indicating different half-lives of functional RCs.
DA - 2017/6//
PY - 2017/6//
DO - 10.1371/journal.ppat.1006343
VL - 13
IS - 6
SP -
SN - 1553-7374
ER -
TY - JOUR
TI - L-INFINITY OPTIMIZATION TO LINEAR SPACES AND PHYLOGENETIC TREES
AU - Bernstein, Daniel Irving
AU - Long, Colby
T2 - SIAM JOURNAL ON DISCRETE MATHEMATICS
AB - Given a distance matrix consisting of pairwise distances between species, a distance-based phylogenetic reconstruction method returns a tree metric or equidistant tree metric (ultrametric) that best fits the data. We investigate distance-based phylogenetic reconstruction using the $l^\infty$-metric. In particular, we analyze the set of ultrametrics and tree metrics $l^\infty$-closest to an arbitrary dissimilarity map to determine its dimension and the tree topologies it represents. In the case of ultrametrics, we decompose the space of dissimilarity maps on three elements and on four elements relative to the tree topologies represented. Our approach is to first address uniqueness issues arising in $l^\infty$-optimization to linear spaces. We show that the $l^\infty$-closest point in a linear space is unique if and only if the underlying matroid of the linear space is uniform. We also give a polyhedral decomposition of $\mathbb{R}^m$ based on the dimension of the set of $l^\infty$-closest points in a linear space.
DA - 2017///
PY - 2017///
DO - 10.1137/16m1101027
VL - 31
IS - 2
SP - 875-889
SN - 1095-7146
KW - distance-based methods
KW - tree metric
KW - ultrametric
KW - subdominant ultrametric
KW - oriented matroid
KW - zonotope
ER -
TY - JOUR
TI - Increased blood pressure variability upon standing up improves reproducibility of cerebral autoregulation indices
AU - Mandi, Adam
AU - Nikolic, Dragana
AU - Birch, Anthony A.
AU - Olufsen, Mette S.
AU - Panerai, Ronney B.
AU - Simpson, David M.
AU - Payne, Stephen J.
T2 - MEDICAL ENGINEERING & PHYSICS
AB - Dynamic cerebral autoregulation, that is the transient response of cerebral blood flow to changes in arterial blood pressure, is currently assessed using a variety of different time series methods and data collection protocols. In the continuing absence of a gold standard for the study of cerebral autoregulation it is unclear to what extent does the assessment depend on the choice of a computational method and protocol. We use continuous measurements of blood pressure and cerebral blood flow velocity in the middle cerebral artery from the cohorts of 18 normotensive subjects performing sit-to-stand manoeuvre. We estimate cerebral autoregulation using a wide variety of black-box approaches (including the following six autoregulation indices ARI, Mx, Sx, Dx, FIR and ARX) and compare them in the context of reproducibility and variability. For all autoregulation indices, considered here, the intra-class correlation was greater during the standing protocol, however, it was significantly greater (Fisher’s Z-test) for Mx (p < 0.03), Sx (p < 0.003) and Dx (p < 0.03). In the specific case of the sit-to-stand manoeuvre, measurements taken immediately after standing up greatly improve the reproducibility of the autoregulation coefficients. This is generally coupled with an increase of the within-group spread of the estimates.
DA - 2017/9//
PY - 2017/9//
DO - 10.1016/j.medengphy.2017.06.006
VL - 47
SP - 151-158
SN - 1873-4030
KW - Cerebral autoregulation
KW - Cerebral blood flow
KW - Reproducibility
KW - Variability
ER -
TY - JOUR
TI - Hybrid modeling and prediction of dynamical systems
AU - Hamilton, Franz
AU - Lloyd, Alun L.
AU - Flores, Kevin B.
T2 - PLOS Computational Biology
AB - Scientific analysis often relies on the ability to make accurate predictions of a system’s dynamics. Mechanistic models, parameterized by a number of unknown parameters, are often used for this purpose. Accurate estimation of the model state and parameters prior to prediction is necessary, but may be complicated by issues such as noisy data and uncertainty in parameters and initial conditions. At the other end of the spectrum exist nonparametric methods, which rely solely on data to build their predictions. While these nonparametric methods do not require a model of the system, their performance is strongly influenced by the amount and noisiness of the data. In this article, we consider a hybrid approach to modeling and prediction which merges recent advancements in nonparametric analysis with standard parametric methods. The general idea is to replace a subset of a mechanistic model’s equations with their corresponding nonparametric representations, resulting in a hybrid modeling and prediction scheme. Overall, we find that this hybrid approach allows for more robust parameter estimation and improved short-term prediction in situations where there is a large uncertainty in model parameters. We demonstrate these advantages in the classical Lorenz-63 chaotic system and in networks of Hindmarsh-Rose neurons before application to experimentally collected structured population data.
DA - 2017/7/10/
PY - 2017/7/10/
DO - 10.1371/journal.pcbi.1005655
VL - 13
IS - 7
SP - e1005655
J2 - PLoS Comput Biol
LA - en
OP -
SN - 1553-7358
UR - http://dx.doi.org/10.1371/journal.pcbi.1005655
DB - Crossref
ER -
TY - JOUR
TI - High-order numerical solution of the Helmholtz equation for domains with reentrant corners
AU - Magura, S.
AU - Petropavlovsky, S.
AU - Tsynkov, S.
AU - Turkel, E.
T2 - Applied Numerical Mathematics
AB - Standard numerical methods often fail to solve the Helmholtz equation accurately near reentrant corners, since the solution may become singular. The singularity has an inhomogeneous contribution from the boundary data near the corner and a homogeneous contribution that is determined by boundary conditions far from the corner. We present a regularization algorithm that uses a combination of analytical and numerical tools to distinguish between these two contributions and ultimately subtract the singularity. We then employ the method of difference potentials to numerically solve the regularized problem with high-order accuracy over a domain with a curvilinear boundary. Our numerical experiments show that the regularization successfully restores the design rate of convergence.
DA - 2017/8//
PY - 2017/8//
DO - 10.1016/j.apnum.2017.02.013
VL - 118
SP - 87-116
J2 - Applied Numerical Mathematics
LA - en
OP -
SN - 0168-9274
UR - http://dx.doi.org/10.1016/j.apnum.2017.02.013
DB - Crossref
KW - Singularity subtraction
KW - Regularization
KW - Asymptotic expansion near singularity
KW - Difference potentials
KW - Curvilinear boundaries
KW - Compact differencing
ER -
TY - JOUR
TI - Early warnings of hazardous thunderstorms over Lake Victoria
AU - Thiery, Wim
AU - Gudmundsson, Lukas
AU - Bedka, Kristopher
AU - Semazzi, Fredrick H. M.
AU - Lhermitte, Stef
AU - Willems, Patrick
AU - Lipzig, Nicole P. M.
AU - Seneviratne, Sonia I.
T2 - ENVIRONMENTAL RESEARCH LETTERS
AB - Weather extremes have harmful impacts on communities around Lake Victoria in East Africa. Every year, intense nighttime thunderstorms cause numerous boating accidents on the lake, resulting in thousands of deaths among fishermen. Operational storm warning systems are therefore crucial. Here we complement ongoing early warning efforts based on numerical weather prediction, by presenting a new satellite data-driven storm prediction system, the prototype Lake Victoria Intense storm Early Warning System (VIEWS). VIEWS derives predictability from the correlation between afternoon land storm activity and nighttime storm intensity on Lake Victoria, and relies on logistic regression techniques to forecast extreme thunderstorms from satellite observations. Evaluation of the statistical model reveals that predictive power is high and independent of the type of input dataset. We then optimise the configuration and show that false alarms also contain valuable information. Our results suggest that regression-based models that are motivated through process understanding have the potential to reduce the vulnerability of local fishing communities around Lake Victoria. The experimental prediction system is publicly available under the MIT licence at http://github.com/wthiery/VIEWS.
DA - 2017/7//
PY - 2017/7//
DO - 10.1088/1748-9326/aa7521
VL - 12
IS - 7
SP -
SN - 1748-9326
KW - Lake Victoria
KW - early warning systems
KW - extreme weather
KW - vulnerability
ER -
TY - JOUR
TI - EFFICIENT COMPUTATION OF SOBOL' INDICES FOR STOCHASTIC MODELS
AU - Hart, J. L.
AU - Alexanderian, A.
AU - Gremaud, P. A.
T2 - SIAM JOURNAL ON SCIENTIFIC COMPUTING
AB - Stochastic models are necessary for the realistic description of an increasing number of applications. The ability to identify influential parameters and variables is critical to a thorough analysis and understanding of the underlying phenomena. We present a new global sensitivity analysis approach for stochastic models, i.e., models with both uncertain parameters and intrinsic stochasticity. Our method relies on an analysis of variance through a generalization of Sobol' indices and on the use of surrogate models. We show how to efficiently compute the statistical properties of the resulting indices and illustrate the effectiveness of our approach by computing first order Sobol' indices for two stochastic models.
DA - 2017///
PY - 2017///
DO - 10.1137/16m106193x
VL - 39
IS - 4
SP - A1514-A1530
SN - 1095-7197
KW - global sensitivity
KW - Sobol' indices
KW - stochastic models
KW - surrogate models
KW - MARS
KW - high dimensions
ER -
TY - JOUR
TI - Computation of the difference-differential Galois group and differential relations among solutions for a second-order linear difference equation
AU - Arreche, Carlos E.
T2 - COMMUNICATIONS IN CONTEMPORARY MATHEMATICS
AB - We apply the difference-differential Galois theory developed by Hardouin and Singer to compute the differential-algebraic relations among the solutions to a second-order homogeneous linear difference equation [Formula: see text] where the coefficients [Formula: see text] are rational functions in [Formula: see text] with coefficients in [Formula: see text]. We develop algorithms to compute the difference-differential Galois group associated to such an equation, and show how to deduce the differential-algebraic relations among the solutions from the defining equations of the Galois group.
DA - 2017/12//
PY - 2017/12//
DO - 10.1142/s0219199716500565
VL - 19
IS - 6
SP -
SN - 1793-6683
KW - Difference equations
KW - differential equations
KW - difference Galois theory
KW - difference-differential Galois theory
ER -
TY - JOUR
TI - Classification and Regression Using an Outer Approximation Projection-Gradient Method
AU - Barlaud, Michel
AU - Belhajali, Wafa
AU - Combettes, Patrick L.
AU - Fillatre, Lionel
T2 - IEEE TRANSACTIONS ON SIGNAL PROCESSING
AB - This paper deals with sparse feature selection and grouping for classification and regression. The classification or regression problems under consideration consists of minimizing a convex empirical risk function subject to an ℓ ^{1} constraint, a pairwise ℓ ^{∞} constraint, or a pairwise ℓ ^{1} constraint. Existing work, such as the Lasso formulation, has focused mainly on Lagrangian penalty approximations, which often require ad hoc or computationally expensive procedures to determine the penalization parameter. We depart from this approach and address the constrained problem directly via a splitting method. The structure of the method is that of the classical gradient-projection algorithm, which alternates a gradient step on the objective and a projection step onto the lower level set modeling the constraint. The novelty of our approach is that the projection step is implemented via an outer approximation scheme in which the constraint set is approximated by a sequence of simple convex sets consisting of the intersection of two half-spaces. Convergence of the iterates generated by the algorithm is established for a general smooth convex minimization problem with inequality constraints. Experiments on both synthetic and biological data show that our method outperforms penalty methods.
DA - 2017/9/1/
PY - 2017/9/1/
DO - 10.1109/tsp.2017.2709262
VL - 65
IS - 17
SP - 4635-4644
SN - 1941-0476
KW - Convex optimization
KW - outer approximation
KW - projection-gradient algorithm
ER -
TY - JOUR
TI - Adaptive filtering for hidden node detection and tracking in networks
AU - Hamilton, Franz
AU - Setzer, Beverly
AU - Chavez, Sergio
AU - Tran, Hien
AU - Lloyd, Alun L.
T2 - Chaos: An Interdisciplinary Journal of Nonlinear Science
AB - The identification of network connectivity from noisy time series is of great interest in the study of network dynamics. This connectivity estimation problem becomes more complicated when we consider the possibility of hidden nodes within the network. These hidden nodes act as unknown drivers on our network and their presence can lead to the identification of false connections, resulting in incorrect network inference. Detecting the parts of the network they are acting on is thus critical. Here, we propose a novel method for hidden node detection based on an adaptive filtering framework with specific application to neuronal networks. We consider the hidden node as a problem of missing variables when model fitting and show that the estimated system noise covariance provided by the adaptive filter can be used to localize the influence of the hidden nodes and distinguish the effects of different hidden nodes. Additionally, we show that the sequential nature of our algorithm allows for tracking changes in the hidden node influence over time.
DA - 2017/7//
PY - 2017/7//
DO - 10.1063/1.4990985
VL - 27
IS - 7
SP - 073106
J2 - Chaos
LA - en
OP -
SN - 1054-1500 1089-7682
UR - http://dx.doi.org/10.1063/1.4990985
DB - Crossref
ER -
TY - JOUR
TI - A-optimal encoding weights for nonlinear inverse problems, with application to the Helmholtz inverse problem
AU - Crestel, Benjamin
AU - Alexanderian, Alen
AU - Stadler, Georg
AU - Ghattas, Omar
T2 - INVERSE PROBLEMS
AB - The computational cost of solving an inverse problem governed by PDEs, using multiple experiments, increases linearly with the number of experiments. A recently proposed method to decrease this cost uses only a small number of random linear combinations of all experiments for solving the inverse problem. This approach applies to inverse problems where the PDE solution depends linearly on the right-hand side function that models the experiment. As this method is stochastic in essence, the quality of the obtained reconstructions can vary, in particular when only a small number of combinations are used. We develop a Bayesian formulation for the definition and computation of encoding weights that lead to a parameter reconstruction with the least uncertainty. We call these weights A-optimal encoding weights. Our framework applies to inverse problems where the governing PDE is nonlinear with respect to the inversion parameter field. We formulate the problem in infinite dimensions and follow the optimize-then-discretize approach, devoting special attention to the discretization and the choice of numerical methods in order to achieve a computational cost that is independent of the parameter discretization. We elaborate our method for a Helmholtz inverse problem, and derive the adjoint-based expressions for the gradient of the objective function of the optimization problem for finding the A-optimal encoding weights. The proposed method is potentially attractive for real-time monitoring applications, where one can invest the effort to compute optimal weights offline, to later solve an inverse problem repeatedly, over time, at a fraction of the initial cost.
DA - 2017/7//
PY - 2017/7//
DO - 10.1088/1361-6420/aa6d8e
VL - 33
IS - 7
SP -
SN - 1361-6420
KW - source encoding
KW - Bayesian nonlinear inverse problem
KW - A-optimal experimental design
KW - randomized trace estimator
KW - Helmholtz equation
ER -
TY - JOUR
TI - Uncertainty under quantum measures and quantum memory
AU - Xiao, Yunlong
AU - Jing, Naihuan
AU - Li-Jost, Xianqing
T2 - QUANTUM INFORMATION PROCESSING
AB - The uncertainty principle restricts potential information one gains about physical properties of the measured particle. However, if the particle is prepared in entanglement with a quantum memory, the corresponding entropic uncertainty relation will vary. Based on the knowledge of correlations between the measured particle and quantum memory, we have investigated the entropic uncertainty relations for two and multiple measurements, and generalized the lower bounds on the sum of Shannon entropies without quantum side information to those that allow quantum memory. In particular, we have obtained generalization of Kaniewski-Tomamichel-Wehner's bound for effective measures and majorization bounds for noneffective measures to allow quantum side information. Furthermore, we have derived several strong bounds for the entropic uncertainty relations in the presence of quantum memory for two and multiple measurements. Finally, potential applications of our results to entanglement witnesses are discussed via the entropic uncertainty relation in the absence of quantum memory.
DA - 2017/4//
PY - 2017/4//
DO - 10.1007/s11128-017-1554-6
VL - 16
IS - 4
SP -
SN - 1573-1332
KW - Entropic uncertainty relations
KW - Quantum memory
KW - Quantum side information
ER -
TY - JOUR
TI - Super quantum discord for general two qubit X states
AU - Jing, Naihuan
AU - Yu, Bing
T2 - QUANTUM INFORMATION PROCESSING
AB - The exact solutions of the super quantum discord are derived for general two qubit X states in terms of a one-variable function. Several exact solutions of the super quantum discord are given for the general X state over nontrivial regions of a seven-dimensional manifold.
DA - 2017/4//
PY - 2017/4//
DO - 10.1007/s11128-017-1547-5
VL - 16
IS - 4
SP -
SN - 1573-1332
KW - Super quantum discord
KW - Quantum correlation
KW - General X states
KW - Weak measurement
ER -
TY - JOUR
TI - SECOND-ORDER FULLY DISCRETE CENTRAL-UPWIND SCHEME FOR TWO-DIMENSIONAL HYPERBOLIC SYSTEMS OF CONSERVATION LAWS
AU - Kurganov, Alexander
AU - Prugger, Martina
AU - Wu, Tong
T2 - SIAM JOURNAL ON SCIENTIFIC COMPUTING
AB - In this paper, we derive a new second-order fully discrete Godunov-type central-upwind scheme for two-dimensional hyperbolic systems of conservation laws. The scheme is derived in three steps: reconstruction, evolution, and projection. The novelty of our approach is in the evolution step, which is performed using the nonuniform quadrilateral control volumes obtained based on the one-sided local speeds of propagation, and in the projection step, in which the evolved solution is projected back onto the uniform grid with the help of a new sharp piecewise polynomial reconstruction. The scheme is tested on a number of numerical examples for the Euler equations of gas dynamics. We have demonstrated that the new scheme is nonoscillatory and at the same time it achieves higher resolution than the second-order semidiscrete central-upwind scheme. The latter suggests that the fully discrete scheme has a smaller amount of numerical dissipation.
DA - 2017///
PY - 2017///
DO - 10.1137/15m1038670
VL - 39
IS - 3
SP - A947-A965
SN - 1095-7197
KW - two-dimensional hyperbolic systems of conservation laws
KW - Godunov-type finite-volume schemes
KW - central-upwind schemes
KW - Euler equations of gas dynamics
ER -
TY - JOUR
TI - Quasi-alternating links with small determinant
AU - Lidman, Tye
AU - Sivek, Steven
T2 - MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY
AB - Abstract Quasi-alternating links of determinant 1, 2, 3 and 5 were previously classified by Greene and Teragaito, who showed that the only such links are two-bridge. In this paper, we extend this result by showing that all quasi-alternating links of determinant at most 7 are connected sums of two-bridge links, which is optimal since there are quasi-alternating links not of this form for all larger determinants. We achieve this by studying their branched double covers and characterising distance-one surgeries between lens spaces of small order, leading to a classification of formal L-spaces with order at most 7.
DA - 2017/3//
PY - 2017/3//
DO - 10.1017/s0305004116000578
VL - 162
IS - 2
SP - 319-336
SN - 1469-8064
ER -
TY - JOUR
TI - Modelling populations of Lygus hesperus on cotton fields in the San Joaquin Valley of California: the importance of statistical and mathematical model choice
AU - Banks, H. T.
AU - Banks, J. E.
AU - Rosenheim, Jay
AU - Tillman, Kristen
T2 - JOURNAL OF BIOLOGICAL DYNAMICS
AB - Understanding the population dynamics of herbivorous insects is critical to developing and implementing effective pest control protocols. In the context of inverse problems, we explore the dynamic effects of pesticide treatments on Lygus hesperus, a common pest of cotton in the western United States. Fitting models to field data, we explore the topic of model selection for an appropriate mathematical model and corresponding statistical models, and use techniques including ANOVA-based model comparison tests and residual plot analysis to make the best selections. In addition we explore the topic of data information content: in this example, we are testing the question of whether data, as it is currently collected, can support time-dependent parameter estimation. Furthermore, we investigate the statistical assumptions often haphazardly made in the process of parameter estimation and consider the implications of unfounded assumptions.
DA - 2017/3//
PY - 2017/3//
DO - 10.1080/17513758.2016.1143533
VL - 11
IS - 1
SP - 25-39
SN - 1751-3766
KW - Inverse problem
KW - ordinary least squares
KW - generalized least squares
KW - model selection
KW - information content
KW - bootstrapping
KW - residual plots
KW - linear splines
KW - hemiptera
KW - herbivory
KW - pest suppression
KW - pesticide
ER -
TY - JOUR
TI - Modeling bumble bee population dynamics with delay differential equations
AU - Banks, H. T.
AU - Banks, J. E.
AU - Bommarco, Riccardo
AU - Laubmeier, A. N.
AU - Myers, N. J.
AU - Rundlof, Maj
AU - Tillman, Kristen
T2 - ECOLOGICAL MODELLING
AB - Bumble bees are ubiquitous creatures and crucial pollinators to a vast assortment of crops worldwide. Bumble bee populations have been decreasing in recent decades, with demise of flower resources and pesticide exposure being two of several suggested pressures causing declines. Many empirical investigations have been performed on bumble bees and their natural history is well documented, but the understanding of their population dynamics over time, causes for observed declines, and potential benefits of management actions is poor. To provide a tool for projecting and testing sensitivity of growth of populations under contrasting and combined pressures, we propose a delay differential equation model that describes multi-colony bumble bee population dynamics. We explain the usefulness of delay equations as a natural modeling formulation, particularly for bumble bee modeling. We then introduce a particular numerical method that approximates the solution of the delay model. Next, we provide simulations of seasonal population dynamics in the absence of pressures. We conclude by describing ways in which resource limitation, pesticide exposure and other pressures can be reflected in the model.
DA - 2017/5/10/
PY - 2017/5/10/
DO - 10.1016/j.ecolmodel.2017.02.011
VL - 351
SP - 14-23
SN - 1872-7026
KW - Population models
KW - Delay differential equations
KW - Non-linear
KW - Non-autonomous
KW - Spline approximations
KW - Bombus terrestris
KW - Reproduction
ER -
TY - JOUR
TI - Markov chains with memory, tensor formulation, and the dynamics of power iteration
AU - Wu, Sheng-Jhih
AU - Chu, Moody T.
T2 - APPLIED MATHEMATICS AND COMPUTATION
AB - A Markov chain with memory is no different from the conventional Markov chain on the product state space. Such a Markovianization, however, increases the dimensionality exponentially. Instead, Markov chain with memory can naturally be represented as a tensor, whence the transitions of the state distribution and the memory distribution can be characterized by specially defined tensor products. In this context, the progression of a Markov chain can be interpreted as variants of power-like iterations moving toward the limiting probability distributions. What is not clear is the makeup of the “second dominant eigenvalue” that affects the convergence rate of the iteration, if the method converges at all. Casting the power method as a fixed-point iteration, this paper examines the local behavior of the nonlinear map and identifies the cause of convergence or divergence. As an application, it is found that there exists an open set of irreducible and aperiodic transition probability tensors where the Z-eigenvector type power iteration fails to converge.
DA - 2017/6/15/
PY - 2017/6/15/
DO - 10.1016/j.amc.2017.01.030
VL - 303
SP - 226-239
SN - 1873-5649
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-85012267381&partnerID=MN8TOARS
KW - Markov chain with memory
KW - Transition probability tensor
KW - Stationary distribution
KW - Power method
KW - Rate of convergence
KW - Second dominant eigenvalue
ER -
TY - JOUR
TI - Integrated Inflammatory Stress (ITIS) Model
AU - Bangsgaard, Elisabeth O.
AU - Hjorth, Poul G.
AU - Olufsen, Mette S.
AU - Mehlsen, Jesper
AU - Ottesen, Johnny T.
T2 - BULLETIN OF MATHEMATICAL BIOLOGY
AB - During the last decade, there has been an increasing interest in the coupling between the acute inflammatory response and the Hypothalamic-Pituitary-Adrenal (HPA) axis. The inflammatory response is activated acutely by pathogen- or damage-related molecular patterns, whereas the HPA axis maintains a long-term level of the stress hormone cortisol which is also anti-inflammatory. A new integrated model of the interaction between these two subsystems of the inflammatory system is proposed and coined the integrated inflammatory stress (ITIS) model. The coupling mechanisms describing the interactions between the subsystems in the ITIS model are formulated based on biological reasoning and its ability to describe clinical data. The ITIS model is calibrated and validated by simulating various scenarios related to endotoxin (LPS) exposure. The model is capable of reproducing human data of tumor necrosis factor alpha, adrenocorticotropic hormone (ACTH) and cortisol and suggests that repeated LPS injections lead to a deficient response. The ITIS model predicts that the most extensive response to an LPS injection in ACTH and cortisol concentrations is observed in the early hours of the day. A constant activation results in elevated levels of the variables in the model while a prolonged change of the oscillations in ACTH and cortisol concentrations is the most pronounced result of different LPS doses predicted by the model.
DA - 2017/7//
PY - 2017/7//
DO - 10.1007/s11538-017-0293-2
VL - 79
IS - 7
SP - 1487-1509
SN - 1522-9602
KW - Mathematical modeling
KW - Nonlinear ODE model
KW - HPA axis
KW - Acute inflammatory system
KW - Immune system
KW - Response to endotoxin (LPS)
ER -
TY - JOUR
TI - Dynamic Modeling of Problem Drinkers Undergoing Behavioral Treatment
AU - Banks, H. T.
AU - Bekele-Maxwell, Kidist
AU - Everett, R. A.
AU - Stephenson, Lyric
AU - Shao, Sijing
AU - Morgenstern, Jon
T2 - BULLETIN OF MATHEMATICAL BIOLOGY
AB - We use dynamical systems modeling to help understand how selected intra-personal factors interact to form mechanisms of behavior change in problem drinkers. Our modeling effort illustrates the iterative process of modeling using an individual's clinical data. Due to the lack of previous work in modeling behavior change in individual patients, we build our preliminary model relying on our understandings of the psychological relationships among the variables. This model is refined and the psychological understanding is then enhanced through the iterative modeling process. Our results suggest that this is a promising direction in research in alcohol use disorders as well as other behavioral sciences.
DA - 2017/6//
PY - 2017/6//
DO - 10.1007/s11538-017-0282-5
VL - 79
IS - 6
SP - 1254-1273
SN - 1522-9602
KW - Mathematical psychology
KW - Inverse problems
KW - Iterative weighted least squares
KW - Behavior change
KW - Personalized medicine
ER -
TY - JOUR
TI - Chromatic homology, Khovanov homology, and torsion
AU - Lowrance, Adam M.
AU - Sazdanovic, Radmila
T2 - TOPOLOGY AND ITS APPLICATIONS
AB - In the first few homological gradings, there is an isomorphism between the Khovanov homology of a link and the categorification of the chromatic polynomial of a graph related to the link. In this article, we show that all torsion in the categorification of the chromatic polynomial is of order two, and hence all torsion in Khovanov homology in the gradings where the isomorphism is defined is of order two. We also prove that odd Khovanov homology is torsion-free in its first few homological gradings.
DA - 2017/5/15/
PY - 2017/5/15/
DO - 10.1016/j.topol.2017.02.078
VL - 222
SP - 77-99
SN - 1879-3207
KW - Knots
KW - Spectral sequence
KW - Khovanov homology
KW - Chromatic polynomial
KW - Categorification
KW - Torsion
ER -
TY - JOUR
TI - An epidemiological model of internet worms with hierarchical dispersal and spatial clustering of hosts
AU - Hiebeler, David E.
AU - Audibert, Andrew
AU - Strubell, Emma
AU - Michaud, Isaac J.
T2 - JOURNAL OF THEORETICAL BIOLOGY
AB - Beginning in 2001, many instances of malicious software known as Internet worms have been using biological strategies such as hierarchical dispersal to seek out and spread to new susceptible hosts more efficiently. We measured the distribution of potentially susceptible hosts in the space of Internet addresses to determine their clustering. We have used the results to construct a full-size simulated Internet with 232 hosts with mean and variance of susceptible hosts chosen to match our measurements at multiple spatial scales. Epidemiological simulations of outbreaks among the roughly 2.8×106 susceptible hosts on this full-sized network show that local preference scanning greatly increases the chances for an infected host to locate and infect other susceptible hosts by a factor of as much as several hundred. However, once deploying this strategy, the overall success of a worm is relatively insensitive to the details of its dispersal strategy over a wide range of parameters. In addition, although using localized interactions may allow malicious software to spread more rapidly or to more hosts on average, it can also lead to increased variability in infection levels among replicate simulations. Using such dispersal strategies may therefore be a high risk, high reward strategy for the authors of such software.
DA - 2017/4/7/
PY - 2017/4/7/
DO - 10.1016/j.jtbi.2017.01.035
VL - 418
SP - 8-15
SN - 1095-8541
KW - Network models
KW - Malicious software
ER -
TY - JOUR
TI - SENSITIVITY VIA THE COMPLEX-STEP METHOD FOR DELAY DIFFERENTIAL EQUATIONS WITH NON-SMOOTH INITIAL DATA
AU - Banks, H. T.
AU - Bekele-Maxwell, Kidist
AU - Bociu, Lorena
AU - Wang, Chuyue
T2 - QUARTERLY OF APPLIED MATHEMATICS
AB - In this report, we use the complex-step derivative approximation technique to compute sensitivities for delay differential equations (DDEs) with non-smooth (discontinuous and even distributional) history functions. We compare the results with exact derivatives and with those computed using the classical sensitivity equations whenever possible. Our results demonstrate that the implementation of the complex-step method using the method of steps and the Matlab solver dde23 provides a very good approximation of sensitivities as long as discontinuities in the initial data do not cause loss of smoothness in the solution: that is, even when the underlying smoothness with respect to the initial data for the Cauchy-Riemann derivation of the method does not hold. We conclude with remarks on our findings regarding the complex-step method for computing sensitivities for simpler ordinary differential equation systems in the event of lack of smoothness with respect to parameters.
DA - 2017/6//
PY - 2017/6//
DO - 10.1090/qam/1458
VL - 75
IS - 2
SP - 231-248
SN - 1552-4485
KW - Inverse problems
KW - sensitivity with respect to parameters
KW - complex-step method
KW - delay differential equations
ER -
TY - JOUR
TI - SADDLE-NODE BIFURCATIONS OF MULTIPLE HOMOCLINIC SOLUTIONS IN ODES
AU - Lin, Xiao-Bin
AU - Zhu, Changrong
T2 - DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
AB - We study codimension 3 degenerate homoclinic bifurcations under periodic perturbations. Assume that among the 3 bifurcation equations, one is due to the homoclinic tangecy along the orbital direction. To the lowest order, the bifurcation equations become 3 quadratic equations. Under generic conditions on perturbations of the normal and tangential directions of the homoclinic orbit, up to 8 homoclinic orbits can be created through saddle-node bifurcations. Our results generate the homoclinic tangency bifurcation in Guckenheimer and Holmes [8].
DA - 2017/6//
PY - 2017/6//
DO - 10.3934/dcdsb.2017069
VL - 22
IS - 4
SP - 1435-1460
SN - 1553-524X
KW - Degenerate homoclinic bifurcation
KW - Lyapunov-Schmidt reduction
KW - exponential dichotomy
KW - codiagonalization of quadratic forms
ER -
TY - JOUR
TI - On deflation and multiplicity structure
AU - Hauenstein, Jonathan D.
AU - Mourrain, Bernard
AU - Szanto, Agnes
T2 - JOURNAL OF SYMBOLIC COMPUTATION
AB - This paper presents two new constructions related to singular solutions of polynomial systems. The first is a new deflation method for an isolated singular root. This construction uses a single linear differential form defined from the Jacobian matrix of the input, and defines the deflated system by applying this differential form to the original system. The advantages of this new deflation is that it does not introduce new variables and the increase in the number of equations is linear in each iteration instead of the quadratic increase of previous methods. The second construction gives the coefficients of the so-called inverse system or dual basis, which defines the multiplicity structure at the singular root. We present a system of equations in the original variables plus a relatively small number of new variables that completely deflates the root in one step. We show that the isolated simple solutions of this new system correspond to roots of the original system with given multiplicity structure up to a given order. Both constructions are “exact” in that they permit one to treat all conjugate roots simultaneously and can be used in certification procedures for singular roots and their multiplicity structure with respect to an exact rational polynomial system.
DA - 2017///
PY - 2017///
DO - 10.1016/j.jsc.2016.11.013
VL - 83
SP - 228-253
SN - 0747-7171
UR - http://dx.doi.org/10.1016/j.jsc.2016.11.013
KW - Deflation
KW - Multiplicity structure
KW - Newton's method
KW - Inverse system
KW - Multiplication matrix
ER -
TY - JOUR
TI - Non-deteriorating time domain numerical algorithms for Maxwell's electrodynamics
AU - Petropavlovsky, S.
AU - Tsynkov, S.
T2 - Journal of Computational Physics
AB - The Huygens' principle and lacunae can help construct efficient far-field closures for the numerical simulation of unsteady waves propagating over unbounded regions. Those closures can be either standalone or combined with other techniques for the treatment of artificial outer boundaries. A standalone lacunae-based closure can be thought of as a special artificial boundary condition (ABC) that is provably free from any error associated with the domain truncation. If combined with a different type of ABC or a perfectly matched layer (PML), a lacunae-based approach can help remove any long-time deterioration (e.g., instability) that arises at the outer boundary regardless of why it occurs in the first place. A specific difficulty associated with Maxwell's equations of electromagnetism is that in general their solutions do not have classical lacunae and rather have quasi-lacunae. Unlike in the classical case, the field inside the quasi-lacunae is not zero; instead, there is an electrostatic solution driven by the electric charges that accumulate over time. In our previous work [23], we have shown that quasi-lacunae can also be used for building the far-field closures. However, for achieving a provably non-deteriorating performance over arbitrarily long time intervals, the accumulated charges need to be known ahead of time. The main contribution of the current paper is that we remove this limitation and modify the algorithm in such a way that one can rather avoid the accumulation of charge all together. Accordingly, the field inside the quasi-lacunae becomes equal to zero, which facilitates obtaining the temporally uniform error estimates as in the case of classical lacunae. The performance of the modified algorithm is corroborated by a series of numerical simulations. The range of problems that the new method can address includes important combined formulations, for which the interior subproblem may be non-Huygens', and only the exterior subproblem, i.e., the far field, is Huygens'.
DA - 2017/5//
PY - 2017/5//
DO - 10.1016/j.jcp.2017.01.068
VL - 336
SP - 1-35
J2 - Journal of Computational Physics
LA - en
OP -
SN - 0021-9991
UR - http://dx.doi.org/10.1016/j.jcp.2017.01.068
DB - Crossref
KW - Unsteady electromagnetic waves
KW - Maxwell's equations
KW - Unbounded regions
KW - Grid truncation
KW - Artificial outer boundaries
KW - Artificial boundary conditions (ABCs)
KW - Non-reflecting boundaries
KW - Perfectly matched layer (PML)
KW - Long time deterioration
KW - Loss of accuracy, loss of stability, error build-up
KW - The Huygens' principle
KW - Aft fronts of the waves
KW - Lacunae of the solutions
KW - Quasi-lacunae
KW - Accumulation of charge
KW - Guaranteed accuracy
KW - Temporally uniform error bounds
ER -
TY - JOUR
TI - An asymptotic-preserving method for a relaxation of the Navier-Stokes-Korteweg equations
AU - Chertock, Alina
AU - Degond, Pierre
AU - Neusser, Jochen
T2 - JOURNAL OF COMPUTATIONAL PHYSICS
AB - The Navier–Stokes–Korteweg (NSK) equations are a classical diffuse-interface model for compressible two-phase flows. As direct numerical simulations based on the NSK system are quite expensive and in some cases even impossible, we consider a relaxation of the NSK system, for which robust numerical methods can be designed. However, time steps for explicit numerical schemes depend on the relaxation parameter and therefore numerical simulations in the relaxation limit are very inefficient. To overcome this restriction, we propose an implicit–explicit asymptotic-preserving finite volume method. We prove that the new scheme provides a consistent discretization of the NSK system in the relaxation limit and demonstrate that it is capable of accurately and efficiently computing numerical solutions of problems with realistic density ratios and small interfacial widths.
DA - 2017/4/15/
PY - 2017/4/15/
DO - 10.1016/j.jcp.2017.01.030
VL - 335
SP - 387-403
SN - 1090-2716
UR - https://doi-org.prox.lib.ncsu.edu/10.1016/j.jcp.2017.01.030
KW - Asymptotic-preserving scheme
KW - Diffuse-interface model
KW - Compressible flow with phase transition
ER -
TY - JOUR
TI - A new elusive otodontid shark (Lamniformes: Otodontidae) from the lower Miocene, and comments on the taxonomy of otodontid genera, including the 'megatoothed' clade
AU - Shimada, Kenshu
AU - Chandler, Richard E.
AU - Lam, Otto Lok Tao
AU - Tanaka, Takeshi
AU - Ward, David J.
T2 - HISTORICAL BIOLOGY
AB - We describe a new large otodontid lamniform shark, Megalolamna paradoxodon gen. nov. et sp. nov., chronostratigraphically restricted to the early Miocene (Aquitanian–Burdigalian). This new species is based on isolated teeth found from five globally distributed localities: the Jewett Sand in southern California, USA; the Pungo River Formation of North Carolina, USA; the Chilcatay Formation of Peru; the Oi Formation in Mie Prefecture, Japan; and the O’oshimojo Formation in Nagano Prefecture, Japan. Extrapolations based on available published data on modern macrophagous lamniforms suggest that the largest specimen of M. paradoxodon gen. nov. et sp. nov. possibly came from an individual that measured at least 3.7 m in total length. All specimens came from deposits in the mid-latitudinal zones representing shallow-water, shelf-type, coastal environments. Its dentition likely exhibited monognathic heterodonty suited for capturing and cutting relatively large prey (e.g. medium-sized fishes). We recommend the genus Otodus to include sharks of the ‘megatoothed’ (e.g. megalodon) lineage in order to avoid Otodus paraphyly. We also propose the following phylogenetic hypothesis: [Kenolamna + [Cretalamna + [Megalolamna + Otodus]]].ZooBank LSID for the genus Megalolamna is: urn: lsid:zoobank.org:act:B4791DEF-4D96-4FEB-9B7B-0EF816B96079ZooBank LSID for the species Megalolamna paradoxodon is: urn:lsid:zoobank.org:act:7D3D7442-53C6-43A2-9E8D-6339729565B6
DA - 2017///
PY - 2017///
DO - 10.1080/08912963.2016.1236795
VL - 29
IS - 5
SP - 704-714
SN - 1029-2381
KW - Elasmobranchii
KW - evolution
KW - fossil
KW - taxonomy
KW - phylogeny
ER -
TY - JOUR
TI - A Uniformly Stable Nonconforming FEM Based on Weighted Interior Penalties for Darcy-Stokes-Brinkman Equations
AU - Huang, Peiqi
AU - Li, Zhilin
T2 - NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS
AB - Abstract A nonconforming rectangular finite element method is proposed to solve a fluid structure interaction problem characterized by the Darcy-Stokes-Brinkman Equation with discontinuous coefficients across the interface of different structures. A uniformly stable mixed finite element together with Nitsche-type matching conditions that automatically adapt to the coupling of different sub-problem combinations are utilized in the discrete algorithm. Compared with other finite element methods in the literature, the new method has some distinguished advantages and features. The Boland-Nicolaides trick is used in proving the inf-sup condition for the multidomain discrete problem. Optimal error estimates are derived for the coupled problem by analyzing the approximation errors and the consistency errors. Numerical examples are also provided to confirm the theoretical results.
DA - 2017/2//
PY - 2017/2//
DO - 10.4208/nmtma.2017.m1610
VL - 10
IS - 1
SP - 22-43
SN - 2079-7338
KW - Fluid structure interactions
KW - Darcy-Stokes-Brinkman equations
KW - Stokes equations
KW - Darcy flow
KW - discontinuous coefficient
KW - nonconforming rectangular element
KW - interior penalty
KW - infsup condition
KW - error estimates
ER -
TY - JOUR
TI - The Alexander module, Seifert forms, and categorification
AU - Hom, Jennifer
AU - Lidman, Tye
AU - Watson, Liam
T2 - JOURNAL OF TOPOLOGY
AB - We show that bordered Floer homology provides a categorification of a topological quantum field theory (TQFT) described by Donaldson [Proceedings of the Kirbyfest, Berkeley, CA, 1998, Geometry & Topology Monographs 2 (Geometry & Topology Publications, Coventry, 1999) 87–102]. This, in turn, leads to a proof that both the Alexander module of a knot and the Seifert form are completely determined by Heegaard Floer theory.
DA - 2017///
PY - 2017///
DO - 10.1112/topo.12001
VL - 10
IS - 1
SP - 22-100
SN - 1753-8424
ER -
TY - JOUR
TI - ON PRINCIPAL REALIZATION OF MODULES FOR THE AFFINE LIE ALGEBRA A(1)((1)) AT THE CRITICAL LEVEL
AU - Adamovic, Drazen
AU - Jing, Naihuan
AU - Misra, Kailash C.
T2 - TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
DA - 2017/7//
PY - 2017/7//
DO - 10.1090/tran/7009
VL - 369
IS - 7
SP - 5113-5136
SN - 1088-6850
KW - Vertex superalgebras
KW - affine Lie algebras
KW - Clifford algebras
KW - Weyl algebra
KW - lattice vertex operator algebras
KW - critical level
KW - Z-algebras
ER -
TY - JOUR
TI - Modeling the distribution of distance data in Euclidean space
AU - Davidson, Ruth
AU - Rusinko, Joseph
AU - Vernon, Zoe
AU - Xi, Jing
T2 - ALGEBRAIC AND GEOMETRIC METHODS IN DISCRETE MATHEMATICS
AB - Phylogenetic inference-the derivation of a hypothesis for the common evolutionary history of a group of species- is an active area of research at the intersection of biology, computer science, mathematics, and statistics. One assumes the data contains a phylogenetic signal that will be recovered with varying accuracy due to the quality of the method used, and the quality of the data. The input for distance-based inference methods is an element of a Euclidean space with coordinates indexed by the pairs of organisms. For several algorithms there exists a subdivision of this space into polyhedral cones such that inputs in the same cone return the same tree topology. The geometry of these cones has been used to analyze the inference algorithms. In this chapter, we model how input data points drawn from DNA sequences are distributed throughout Euclidean space in relation to the space of tree metrics, which in turn can also be described as a collection of polyhedral cones.
DA - 2017///
PY - 2017///
DO - 10.1090/conm/685/13750
VL - 685
SP - 117-135
SN - 1098-3627
ER -
TY - JOUR
TI - Impulsive control problem governed by fractional differential equations and applications
AU - Medhin, N. G.
AU - Sambandham, M.
T2 - Dynamic Systems and Applications
DA - 2017///
PY - 2017///
VL - 26
IS - 1
SP - 37-63
ER -
TY - JOUR
TI - Automated assay and differential model of western honey bee (Apis mellifera) autogrooming using digital image processing
AU - Giuffre, Carl
AU - Lubkin, Sharon R.
AU - Tarpy, David R.
T2 - COMPUTERS AND ELECTRONICS IN AGRICULTURE
AB - In animals, self-grooming is an important component of their overall hygiene because it reduces the risk of disease and parasites. The European honey bee (Apis mellifera) exhibits hygienic behavior, which refers to the ability of the members of a colony to remove diseased or dead brood from the hive. Individual grooming behavior, however, is when a bee grooms itself to remove parasites. While both behaviors are critical for the mitigation of disease, hygienic behavior is overwhelmingly more studied because, unlike grooming behavior, it has a simple bioassay to measure its phenotype. Here, we develop a novel bioassay to expedite data collection of grooming behavior by testing different honey bee genotypes (stocks). Individual worker bees from different commercial stocks were coated in baking flour, placed in an observation arena, and digitally recorded to automatically measure grooming rates. The videos were analyzed in MATLAB, and an exponential function was fit to the pixel data to calculate individual grooming rates. While bees from the different commercial stocks were not significantly different in their grooming rates, the automation of grooming measurements may facilitate future research and stock selection for this important mechanism of social immunity.
DA - 2017/4/1/
PY - 2017/4/1/
DO - 10.1016/j.compag.2017.02.003
VL - 135
SP - 338-344
SN - 1872-7107
KW - Grooming behavior
KW - Honey bees
KW - Social insects
KW - Image processing
ER -
TY - JOUR
TI - ACCURATE SOLUTION AND GRADIENT COMPUTATION FOR ELLIPTIC INTERFACE PROBLEMS WITH VARIABLE COEFFICIENTS
AU - Li, Zhilin
AU - Ji, Haifeng
AU - Chen, Xiaohong
T2 - SIAM JOURNAL ON NUMERICAL ANALYSIS
AB - A new augmented method is proposed for elliptic interface problems with a piecewise variable coefficient that has a finite jump across a smooth interface. The main motivation is to get not only a second order accurate solution but also a second order accurate gradient from each side of the interface. Key to the new method is introducing the jump in the normal derivative of the solution as an augmented variable and rewriting the interface problem as a new PDE that consists of a leading Laplacian operator plus lower order derivative terms near the interface. In this way, the leading second order derivative jump relations are independent of the jump in the coefficient that appears only in the lower order terms after the scaling. An upwind type discretization is used for the finite difference discretization at the irregular grid points on or near the interface so that the resulting coefficient matrix is an M-matrix. A multigrid solver is used to solve the linear system of equations, and the GMRES iterative method is used to solve the augmented variable. Second order convergence for the solution and the gradient from each side of the interface is proved in this paper. Numerical examples for general elliptic interface problems confirm the theoretical analysis and efficiency of the new method.
DA - 2017///
PY - 2017///
DO - 10.1137/15m1040244
VL - 55
IS - 2
SP - 570-597
SN - 1095-7170
KW - elliptic interface problem
KW - accurate gradient computation
KW - variable coefficient with discontinuity
KW - interface
KW - M-matrix
KW - convergence proof
KW - discrete Green function
ER -
TY - JOUR
TI - A stochastic portfolio optimization model with complete memory
AU - Pang, Tao
AU - Hussain, Azmat
T2 - STOCHASTIC ANALYSIS AND APPLICATIONS
AB - In this article, we consider a portfolio optimization problem of the Merton’s type with complete memory over a finite time horizon. The problem is formulated as a stochastic control problem on a finite time horizon and the state evolves according to a process governed by a stochastic process with memory. The goal is to choose investment and consumption controls such that the total expected discounted utility is maximized. Under certain conditions, we derive the explicit solutions for the associated Hamilton–Jacobi–Bellman (HJB) equations in a finite-dimensional space for exponential, logarithmic, and power utility functions. For those utility functions, verification results are established to ensure that the solutions are equal to the value functions, and the optimal controls are also derived.
DA - 2017///
PY - 2017///
DO - 10.1080/07362994.2017.1299629
VL - 35
IS - 4
SP - 742-766
SN - 1532-9356
KW - Portfolio optimization
KW - Hamilton-Jacobi-Bellman equation
KW - dynamic programming
KW - stochastic delay equation
ER -
TY - JOUR
TI - A Computationally Viable Version of the PN Method for Spheres
AU - Garcia, R. D. M.
AU - Siewert, C. E.
AU - Thomas, J. R., Jr.
T2 - NUCLEAR SCIENCE AND ENGINEERING
AB - The long-standing problem of implementing the method effectively for spherical geometry is revisited in this work. It is shown that a least-squares approach to the method resolves to a great extent the numerical instability reported for the first time by Aronson in 1984. In the proposed version of the method, a small loss of accuracy is still observed for intermediate orders of the approximation, but in high order (typically ), full accuracy is recovered, and the method can be used with confidence even for extremely high orders of the approximation. Numerical results of benchmark quality are tabulated for the quantities of interest for two basic transport problems in spherical geometry: the albedo problem for a sphere and the critical-sphere problem, both including cases that show the effects of scattering anisotropy described by the binomial law.
DA - 2017/5//
PY - 2017/5//
DO - 10.1080/00295639.2016.1273627
VL - 186
IS - 2
SP - 103-119
SN - 1943-748X
KW - Neutron transport
KW - spherical geometry
KW - spherical harmonics method
ER -
TY - JOUR
TI - Stability of Nonlinear Convection-Diffusion-Reaction Systems in Discontinuous Galerkin Methods
AU - Michoski, C.
AU - Alexanderian, A.
AU - Paillet, C.
AU - Kubatko, E. J.
AU - Dawson, C.
T2 - JOURNAL OF SCIENTIFIC COMPUTING
DA - 2017/2//
PY - 2017/2//
DO - 10.1007/s10915-016-0256-z
VL - 70
IS - 2
SP - 516-550
SN - 1573-7691
KW - Stability analysis
KW - Nonlinear
KW - von Neumann
KW - Discontinuous Galerkin
KW - Runge-Kutta methods
KW - RKSSP
KW - RKC
KW - Convection-Reaction-Diffusion
ER -
TY - JOUR
TI - Spin characters of hyperoctahedral wreath products
AU - Hu, Xiaoli
AU - Jing, Naihuan
T2 - JOURNAL OF PURE AND APPLIED ALGEBRA
AB - The irreducible spin character values of the wreath products of the hyperoctahedral groups with an arbitrary finite group are determined.
DA - 2017/9//
PY - 2017/9//
DO - 10.1016/j.jpaa.2016.12.004
VL - 221
IS - 9
SP - 2220-2235
SN - 1873-1376
ER -
TY - JOUR
TI - On the n-symplectic structure of faithful irreducible representations
AU - Norris, L. K.
T2 - JOURNAL OF MATHEMATICAL PHYSICS
AB - Each faithful irreducible representation of an N-dimensional vector space V1 on an n-dimensional vector space V2 is shown to define a unique irreducible n-symplectic structure on the product manifold V1×V2. The basic details of the associated Poisson algebra are developed for the special case N = n2, and 2n-dimensional symplectic submanifolds are shown to exist.
DA - 2017/4//
PY - 2017/4//
DO - 10.1063/1.4979625
VL - 58
IS - 4
SP -
SN - 1089-7658
ER -
TY - JOUR
TI - Imaginary Verma modules for U-q<((sl(2)))over cap> and crystal-like bases
AU - Cox, Ben
AU - Futorny, Vyacheslav
AU - Misra, Kailash C.
T2 - JOURNAL OF ALGEBRA
AB - We consider imaginary Verma modules for quantum affine algebra Uq(sl(2)ˆ) and define a crystal-like base which we call an imaginary crystal basis using the Kashiwara algebra Kq constructed in earlier work of the authors. In particular, we prove the existence of imaginary crystal-like bases for a suitable category of reduced imaginary Verma modules for Uq(sl(2)ˆ).
DA - 2017/7/1/
PY - 2017/7/1/
DO - 10.1016/j.jalgebra.2017.02.017
VL - 481
SP - 12-35
SN - 1090-266X
KW - Quantum affine algebras
KW - Imaginary Verma modules
KW - Kashiwara algebras
KW - Crystal bases
ER -
TY - JOUR
TI - Hamel's Formalism for Infinite-Dimensional Mechanical Systems
AU - Shi, Donghua
AU - Berchenko-Kogan, Yakov
AU - Zenkov, Dmitry V.
AU - Bloch, Anthony M.
T2 - JOURNAL OF NONLINEAR SCIENCE
DA - 2017/2//
PY - 2017/2//
DO - 10.1007/s00332-016-9332-7
VL - 27
IS - 1
SP - 241-283
SN - 1432-1467
KW - Hamel equations
KW - Nonholonomic constraints
KW - Momentum
KW - Symmetry
ER -
TY - JOUR
TI - Galois groups for integrable and projectively integrable linear difference equations
AU - Arreche, Carlos K.
AU - Singer, Michael F.
T2 - JOURNAL OF ALGEBRA
AB - We consider first-order linear difference systems over $\mathbb{C}(x)$, with respect to a difference operator $\sigma$ that is either a shift $\sigma:x\mapsto x+1$, $q$-dilation $\sigma:x\mapsto qx$ with $q\in{\mathbb{C}^\times}$ not a root of unity, or Mahler operator $\sigma:x\mapsto x^q$ with $q\in\mathbb{Z}_{\geq 2}$. Such a system is integrable if its solutions also satisfy a linear differential system; it is projectively integrable if it becomes integrable "after moding out by scalars." We apply recent results of Sch\"{a}fke and Singer to characterize which groups can occur as Galois groups of integrable or projectively integrable linear difference systems. In particular, such groups must be solvable. Finally, we give hypertranscendence criteria.
DA - 2017/6/15/
PY - 2017/6/15/
DO - 10.1016/j.jalgebra.2017.02.032
VL - 480
SP - 423-449
SN - 1090-266X
KW - Differential Galois theory of difference equations
KW - Linear differential algebraic groups
KW - Hypertranscendence
KW - Difference algebra
KW - Differential algebra
ER -
TY - JOUR
TI - Distributions of topological tree metrics between a species tree and a gene tree
AU - Xi, Jing
AU - Xie, Jin
AU - Yoshida, Ruriko
T2 - ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS
AB - In order to conduct a statistical analysis on a given set of phylogenetic gene trees, we often use a distance measure between two trees. In a statistical distance-based method to analyze discordance between gene trees, it is a key to decide “biologically meaningful” and “statistically well-distributed” distance between trees. Thus, in this paper, we study the distributions of the three tree distance metrics: the edge difference, the path difference, and the precise K interval cospeciation distance, between two trees: First, we focus on distributions of the three tree distances between two random unrooted trees with n leaves ( $$n \ge 4$$ ); and then we focus on the distributions the three tree distances between a fixed rooted species tree with n leaves and a random gene tree with n leaves generated under the coalescent process with the given species tree. We show some theoretical results as well as simulation study on these distributions.
DA - 2017/6//
PY - 2017/6//
DO - 10.1007/s10463-016-0557-x
VL - 69
IS - 3
SP - 647-671
SN - 1572-9052
KW - Coalescent
KW - Phylogenetics
KW - Tree metrics
KW - Tree topologies
ER -
TY - JOUR
TI - COSMETIC SURGERY IN L-SPACES AND NUGATORY CROSSINGS
AU - Lidman, Tye
AU - Moore, Allison H.
T2 - TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
AB - The cosmetic crossing conjecture (also known as the ânugatory crossing conjectureâ) asserts that the only crossing changes that preserve the oriented isotopy class of a knot in the 3-sphere are nugatory. We use the Dehn surgery characterization of the unknot to prove this conjecture for knots in integer homology spheres whose branched double covers are L-spaces satisfying a homological condition. This includes as a special case all alternating and quasi-alternating knots with square-free determinant. As an application, we prove the cosmetic crossing conjecture holds for all knots with at most nine crossings and provide new examples of knots, including pretzel knots, non-arborescent knots and symmetric unions for which the conjecture holds.
DA - 2017/5//
PY - 2017/5//
DO - 10.1090/tran/6839
VL - 369
IS - 5
SP - 3639-3654
SN - 1088-6850
ER -
TY - JOUR
TI - A model of ovulatory regulation examining the effects of insulin-mediated testosterone production on ovulatory function
AU - Graham, Erica J.
AU - Selgrade, James F.
T2 - JOURNAL OF THEORETICAL BIOLOGY
AB - Polycystic ovary syndrome (PCOS), a common cause of infertility in women, is often accompanied by abnormal reproductive and metabolic hormone levels. Specifically, androgens such as testosterone are elevated in many PCOS women, and the syndrome itself is frequently associated with insulin resistance, which leads to hyperinsulinemia, i.e., elevated insulin. Although the precise role of insulin in ovulatory function is unclear, its role in ovulatory dysfunction is often linked to the effects of increased ovarian androgen production. We present a mathematical model of the menstrual cycle that incorporates regulation by the pituitary-ovarian axis and mechanisms of ovarian testosterone production. We determine a physiological role for testosterone in the normal ovulatory cycle and study the role of hyperinsulinemia in pathological regulation of the cycle. Model results indicate increased ovulatory disruption with elevated insulin-mediated testosterone production and suggest that variations in the response of ovarian follicles to essential signals can alter the degree to which hyperinsulinemia disrupts the ovulatory cycle. The model also provides insight into the various PCOS phenotypes and the severity of ovulatory dysfunction.
DA - 2017/3/7/
PY - 2017/3/7/
DO - 10.1016/j.jtbi.2017.01.007
VL - 416
SP - 149-160
SN - 1095-8541
KW - Polycystic ovary syndrome
KW - Steroidogenesis
ER -
TY - JOUR
TI - A Bayesian approach to modeling diffraction profiles and application to ferroelectric materials
AU - Iamsasri, Thanakorn
AU - Guerrier, Jonathon
AU - Esteves, Giovanni
AU - Fancher, Chris M.
AU - Wilson, Alyson G.
AU - Smith, Ralph C.
AU - Paisley, Elizabeth A.
AU - Johnson-Wilke, Raegan
AU - Ihlefeld, Jon F.
AU - Bassiri-Gharb, Nazanin
AU - Jones, Jacob L.
T2 - Journal of Applied Crystallography
AB - A new statistical approach for modeling diffraction profiles is introduced, using Bayesian inference and a Markov chain Monte Carlo (MCMC) algorithm. This method is demonstrated by modeling the degenerate reflections during application of an electric field to two different ferroelectric materials: thin-film lead zirconate titanate (PZT) of composition PbZr 0.3 Ti 0.7 O 3 and a bulk commercial PZT polycrystalline ferroelectric. The new method offers a unique uncertainty quantification of the model parameters that can be readily propagated into new calculated parameters.
DA - 2017/2/1/
PY - 2017/2/1/
DO - 10.1107/S1600576716020057
VL - 50
IS - 1
SP - 211-220
J2 - J Appl Cryst
OP -
SN - 1600-5767
UR - http://dx.doi.org/10.1107/S1600576716020057
DB - Crossref
KW - ferroelectric materials
KW - Bayesian inference
KW - domain switching fraction
KW - modeling diffraction profiles
ER -
TY - JOUR
TI - Statistically Consistent k-mer Methods for Phylogenetic Tree Reconstruction
AU - Allman, Elizabeth S.
AU - Rhodes, John A.
AU - Sullivant, Seth
T2 - JOURNAL OF COMPUTATIONAL BIOLOGY
AB - Frequencies of k-mers in sequences are sometimes used as a basis for inferring phylogenetic trees without first obtaining a multiple sequence alignment. We show that a standard approach of using the squared Euclidean distance between k-mer vectors to approximate a tree metric can be statistically inconsistent. To remedy this, we derive model-based distance corrections for orthologous sequences without gaps, which lead to consistent tree inference. The identifiability of model parameters from k-mer frequencies is also studied. Finally, we report simulations showing that the corrected distance outperforms many other k-mer methods, even when sequences are generated with an insertion and deletion process. These results have implications for multiple sequence alignment as well since k-mer methods are usually the first step in constructing a guide tree for such algorithms.
DA - 2017/2//
PY - 2017/2//
DO - 10.1089/cmb.2015.0216
VL - 24
IS - 2
SP - 153-171
SN - 1557-8666
KW - phylogenetic trees
KW - alignment-free methods
KW - k-mer
ER -
TY - JOUR
TI - Representation Stability for Cohomology of Configuration Spaces in R-d
AU - Hersh, Patricia
AU - Reiner, Victor
T2 - INTERNATIONAL MATHEMATICS RESEARCH NOTICES
AB - This paper studies representation stability in the sense of Church and Farb for representations of the symmetric group |$S_n$| on the cohomology of the configuration space of |$n$| ordered points in |${\mathbb{R}}^d$|. This cohomology is known to vanish outside of dimensions divisible by |$d-1$|; it is shown here that the |$S_n$|-representation on the |$i(d-1){\rm st}$| cohomology stabilizes sharply at |$n=3i$| (resp. |$n=3i+1$|) when |$d$| is odd (resp. even). The result comes from analyzing |$S_n$|-representations known to control the cohomology: the Whitney homology of set partition lattices for |$d$| even, and the higher Lie representations for |$d$| odd. A similar analysis shows that the homology of any rank-selected subposet in the partition lattice stabilizes by |$n\geq 4i$|, where |$i$| is the maximum rank selected. Further properties of the Whitney homology and more refined stability statements for |$S_n$|-isotypic components are also proven, including conjectures of J. Wiltshire-Gordon.
DA - 2017/3//
PY - 2017/3//
DO - 10.1093/imrn/rnw060
VL - 2017
IS - 5
SP - 1433-1486
SN - 1687-0247
ER -
TY - JOUR
TI - Dispersive and Diffusive-Dispersive ShockWaves for Nonconvex Conservation Laws
AU - El, G. A.
AU - Hoefer, M. A.
AU - Shearer, M.
T2 - SIAM REVIEW
AB - We consider two physically and mathematically distinct regularization mechanisms of scalar hyperbolic conservation laws. When the flux is convex, the combination of diffusion and dispersion is known to give rise to monotonic and oscillatory traveling waves that approximate shock waves. The zero-diffusion limits of these traveling waves are dynamically expanding dispersive shock waves (DSWs). A richer set of wave solutions can be found when the flux is nonconvex. This review compares the structure of solutions of Riemann problems for a conservation law with nonconvex, cubic flux regularized by two different mechanisms: (1) dispersion in the modified Korteweg--de Vries (mKdV) equation; and (2) a combination of diffusion and dispersion in the mKdV--Burgers equation. In the first case, the possible dynamics involve two qualitatively different types of DSWs, rarefaction waves (RWs), and kinks (monotonic fronts). In the second case, in addition to RWs, there are traveling wave solutions approximating both classical (Lax) and nonclassical (undercompressive) shock waves. Despite the singular nature of the zero-diffusion limit and rather differing analytical approaches employed in the descriptions of dispersive and diffusive-dispersive regularization, the resulting comparison of the two cases reveals a number of striking parallels. In contrast to the case of convex flux, the mKdVB to mKdV mapping of Riemann problem solutions is not one-to-one. The mKdV kink solution is identified as an undercompressive DSW. Other prominent features, such as shock-rarefactions, also find their purely dispersive counterparts involving special contact DSWs, which exhibit features analogous to contact discontinuities. This review describes an important link between two major areas of applied mathematics: hyperbolic conservation laws and nonlinear dispersive waves.
DA - 2017///
PY - 2017///
DO - 10.1137/15m1015650
VL - 59
IS - 1
SP - 3-61
SN - 1095-7200
KW - shock waves
KW - conservation laws
KW - partial differential equations
KW - dispersive equations
KW - traveling waves
ER -
TY - JOUR
TI - Wetting dynamics of a collapsing fluid hole
AU - Bostwick, J. B.
AU - Dijksman, J. A.
AU - Shearer, M.
T2 - PHYSICAL REVIEW FLUIDS
AB - The collapse dynamics of an axisymmetric fluid cavity that wets the bottom of a rotating bucket bound by vertical sidewalls are studied. Lubrication theory is applied to the governing field equations for the thin film to yield an evolution equation that captures the effect of capillary, gravitational and centrifugal forces on this converging flow. The focus is on the quasi-static spreading regime, whereby contact-line motion is governed by a constitutive law relating the contact-angle to the contact-line speed. The collapse time, as it depends upon the initial hole size, is reported showing that gravity accelerates the collapse process. Surface tension forces dominate the collapse dynamics for small holes leading to a universal power law whose exponent compares favorably to experiments in the literature. Volume dependence is predicted and compared with experiment. Centrifugal forces slow the collapse process and lead to complex dynamics characterized by stalled spreading behavior that separates the large and small hole asymptotic regimes.
DA - 2017/1/26/
PY - 2017/1/26/
DO - 10.1103/physrevfluids.2.014006
VL - 2
IS - 1
SP -
SN - 2469-990X
ER -
TY - JOUR
TI - Unimodular binary hierarchical models
AU - Bernstein, Daniel Irving
AU - Sullivant, Seth
T2 - JOURNAL OF COMBINATORIAL THEORY SERIES B
AB - Associated to each simplicial complex is a binary hierarchical model. We classify the simplicial complexes that yield unimodular binary hierarchical models. Our main theorem provides both a construction of all unimodular binary hierarchical models, together with a characterization in terms of excluded minors, where our definition of a minor allows the taking of links and induced complexes. A key tool in the proof is the lemma that the class of unimodular binary hierarchical models is closed under the Alexander duality operation on simplicial complexes.
DA - 2017/3//
PY - 2017/3//
DO - 10.1016/j.jctb.2016.11.003
VL - 123
SP - 97-125
SN - 1096-0902
KW - Graver basis
KW - Algebraic statistics
KW - Log-linear models
KW - Hierarchical models
KW - Toric ideal
ER -
TY - JOUR
TI - Symmetric interpolation, Exchange Lemma and Sylvester sums
AU - Krick, Teresa
AU - Szanto, Agnes
AU - Valdettaro, Marcelo
T2 - COMMUNICATIONS IN ALGEBRA
AB - The theory of symmetric multivariate Lagrange interpolation is a beautiful but rather unknown tool that has many applications. Here we derive from it an Exchange Lemma that allows to explain in a simple and natural way the full description of the double sum expressions introduced by Sylvester in 1853 in terms of subresultants and their Bézout coeﬃcients.
DA - 2017///
PY - 2017///
DO - 10.1080/00927872.2016.1236121
VL - 45
IS - 8
SP - 3231-3250
SN - 1532-4125
UR - http://dx.doi.org/10.1080/00927872.2016.1236121
KW - Subresultants
KW - Sylvester double sums
KW - symmetric Lagrange interpolation
ER -
TY - JOUR
TI - A Cartesian grid nonconforming immersed finite element method for planar elasticity interface problems
AU - Qin, Fangfang
AU - Chen, Jinru
AU - Li, Zhilin
AU - Cai, Mingchao
T2 - COMPUTERS & MATHEMATICS WITH APPLICATIONS
AB - In this paper, a new nonconforming immersed finite element (IFE) method on triangular Cartesian meshes is developed for solving planar elasticity interface problems. The proposed IFE method possesses optimal approximation property for both compressible and nearly incompressible problems. Its degree of freedom is much less than those of existing finite element methods for the same problem. Moreover, the method is robust with respect to the shape of the interface and its location relative to the domain and the underlying mesh. Both theory and numerical experiments are presented to demonstrate the effectiveness of the new method. Theoretically, the unisolvent property and the consistency of the IFE space are proved. Experimentally, extensive numerical examples are given to show that the approximation orders in L2 norm and semi-H1 norm are optimal under various Lamé parameters settings and different interface geometry configurations.
DA - 2017/2/1/
PY - 2017/2/1/
DO - 10.1016/j.camwa.2016.11.033
VL - 73
IS - 3
SP - 404-418
SN - 1873-7668
KW - Nonconforming immersed finite element
KW - Elasticity interface problems
KW - Cartesian grid
ER -
TY - JOUR
TI - Spin groups of super metrics and a theorem of Rogers
AU - Fulp, Ronald
T2 - JOURNAL OF GEOMETRY AND PHYSICS
AB - We derive the canonical forms of super Riemannian metrics and the local isometry groups of such metrics. For certain super metrics we also compute the simply connected covering groups of the local isometry groups and interpret these as local spin groups of the super metric. Super metrics define reductions OSg of the relevant frame bundle. When principal bundles S˜g exist with structure group the simply connected covering group G̃ of the structure group of OSg, representations of G̃ define vector bundles associated to S˜g whose sections are “spinor fields” associated with the super metric g. Using a generalization of a Theorem of Rogers, which is itself one of the main results of this paper, we show that for super metrics we call body reducible, each such simply connected covering group G̃ is a super Lie group with a conventional super Lie algebra as its corresponding super Lie algebra. Some of our results were known to DeWitt (1984) using formal Grassmann series and others were known by Rogers using finitely many Grassmann generators and passing to a direct limit. We work exclusively in the category of G∞ supermanifolds with G∞ mappings. Our supernumbers are infinite series of products of Grassmann generators subject to convergence in the ℓ1 norm introduced by Rogers (1980, 2007).
DA - 2017/1//
PY - 2017/1//
DO - 10.1016/j.geomphys.2016.10.009
VL - 111
SP - 40-53
SN - 1879-1662
KW - G(infinity)-supermanifolds
KW - Super Riemannian metrics
KW - Canonical forms
KW - Local isometry groups
KW - Super Lie groups
KW - Conventional super Lie algebras
ER -
TY - JOUR
TI - Open weak CAD and its applications
AU - Han, Jingjun
AU - Dai, Liyun
AU - Hong, Hoon
AU - Xia, Bican
T2 - JOURNAL OF SYMBOLIC COMPUTATION
AB - The concept of open weak CAD is introduced. Every open CAD is an open weak CAD. On the contrary, an open weak CAD is not necessarily an open CAD. An algorithm for computing projection polynomials of open weak CADs is proposed. The key idea is to compute the intersection of projection factor sets produced by different projection orders. The resulting open weak CAD often has smaller number of sample points than open CADs. The algorithm can be used for computing sample points for all open connected components of f≠0 for a given polynomial f. It can also be used for many other applications, such as testing semi-definiteness of polynomials and copositive problems. In fact, we solved several difficult semi-definiteness problems efficiently by using the algorithm. Furthermore, applying the algorithm to copositive problems, we find an explicit expression of the polynomials producing open weak CADs under some conditions, which significantly improves the efficiency of solving copositive problems.
DA - 2017///
PY - 2017///
DO - 10.1016/j.jsc.2016.07.032
VL - 80
SP - 785-816
SN - 0747-7171
UR - http://dx.doi.org/10.1016/j.jsc.2016.07.032
KW - Open weak CAD
KW - Open weak delineable
KW - CAD projection
KW - Semi-definiteness
KW - Copositivity
ER -
TY - JOUR
TI - Normal Binary Hierarchical Models
AU - Bernstein, Daniel Irving
AU - Sullivant, Seth
T2 - EXPERIMENTAL MATHEMATICS
AB - Each simplicial complex and integer vector yields a vector configuration whose combinatorial properties are important for the analysis of contingency tables. We study the normality of these vector configurations including a description of operations on simplicial complexes that preserve normality, constructions of families of minimally nonnormal complexes, and computations classifying all of the normal complexes on up to six vertices. We repeat this analysis for compressed vector configurations, classifying all of the compressed complexes on up to six vertices.
DA - 2017///
PY - 2017///
DO - 10.1080/10586458.2016.1142911
VL - 26
IS - 2
SP - 153-164
SN - 1944-950X
KW - algebraic statistics
KW - contingency tables
KW - Hilbert basis
KW - Groebner basis
KW - combinatorics
ER -
TY - JOUR
TI - Dynamical behavior of an epidemiological model with a demographic Allee effect
AU - Usaini, Salisu
AU - Lloyd, Alun L.
AU - Anguelov, Roumen
AU - Garba, Salisu M.
T2 - Mathematics and Computers in Simulation
AB - As the Allee effect refers to small density or population size, it cannot be deduced whether or not the Allee mechanisms responsible for an Allee effect at low population density or size will affect the dynamics of a population at high density or size as well. We show using susceptible–exposed–infectious (SEI) model that such mechanisms combined with disease pathogenicity have a detrimental impact on the dynamics of a population at high population level. In fact, the eventual outcome could be an inevitable population crash to extinction. The tipping point marking the unanticipated population collapse at high population level is mathematically associated with a saddle–node bifurcation. The essential mechanism of this scenario is the simultaneous population size depression and the increase of the extinction threshold owing to disease virulence and the Allee effect. Using numerical continuation software MatCont another saddle–node bifurcation is detected, which results in the re-emergence of two non-trivial equilibria since highly pathogenic species cause their own extinction but not that of their host.
DA - 2017/3//
PY - 2017/3//
DO - 10.1016/j.matcom.2016.04.010
VL - 133
SP - 311-325
J2 - Mathematics and Computers in Simulation
LA - en
OP -
SN - 0378-4754
UR - http://dx.doi.org/10.1016/j.matcom.2016.04.010
DB - Crossref
KW - Allee effect
KW - Threshold
KW - Extinction
KW - Saddle-node bifurcation
ER -
TY - JOUR
TI - Algorithm for computing mu-bases of univariate polynomials
AU - Hong, Hoon
AU - Hough, Zachary
AU - Kogan, Irina A.
T2 - JOURNAL OF SYMBOLIC COMPUTATION
AB - We present a new algorithm for computing a μ-basis of the syzygy module of n polynomials in one variable over an arbitrary field K. The algorithm is conceptually different from the previously-developed algorithms by Cox, Sederberg, Chen, Zheng, and Wang for n=3, and by Song and Goldman for an arbitrary n. The algorithm involves computing a “partial” reduced row-echelon form of a (2d+1)×n(d+1) matrix over K, where d is the maximum degree of the input polynomials. The proof of the algorithm is based on standard linear algebra and is completely self-contained. The proof includes a proof of the existence of the μ-basis and as a consequence provides an alternative proof of the freeness of the syzygy module. The theoretical (worst case asymptotic) computational complexity of the algorithm is O(d2n+d3+n2). We have implemented this algorithm (HHK) and the one developed by Song and Goldman (SG). Experiments on random inputs indicate that SG is faster than HHK when d is sufficiently large for a fixed n, and that HHK is faster than SG when n is sufficiently large for a fixed d.
DA - 2017///
PY - 2017///
DO - 10.1016/j.jsc.2016.08.013
VL - 80
SP - 844-874
SN - 0747-7171
UR - http://dx.doi.org/10.1016/j.jsc.2016.08.013
KW - mu-basis
KW - Syzygy module
KW - Polynomial vectors
KW - Rational curves
ER -
TY - JOUR
TI - A DYNAMICAL APPROACH TO PHYTOPLANKTON BLOOMS
AU - Jones, Christopher K. R. T.
AU - Maultsby, Bevin
T2 - DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
AB - Algae in the ocean absorb carbon dioxide from the atmosphere and thus play an important role in the carbon cycle. An algal bloom occurs when there is a rapid increase in an algae population. We consider a reaction-advection-diffusion model for algal bloom density and present new proofs of existence and uniqueness results for the steady state solutions using techniques from dynamical systems. On the question of stability of the bloom profiles, we show that the only possible bifurcation would be due to an oscillatory instability.
DA - 2017/2//
PY - 2017/2//
DO - 10.3934/dcds.2017035
VL - 37
IS - 2
SP - 859-878
SN - 1553-5231
KW - Non-local
KW - phytoplankton
KW - reaction-diffusion-advection
KW - phase space
KW - existence and uniqueness
ER -
TY - JOUR
TI - New Conservative Finite Volume Element Schemes for the Modified Regularized Long Wave Equation
AU - Yan, Jinliang
AU - Lai, Ming-Chih
AU - Li, Zhilin
AU - Zhang, Zhiyue
T2 - ADVANCES IN APPLIED MATHEMATICS AND MECHANICS
AB - Abstract In this paper, we propose a new energy-preserving scheme and a new momentum-preserving scheme for the modified regularized long wave equation. The proposed schemes are designed by using the discrete variational derivative method and the finite volume element method. For comparison, we also propose a finite volume element scheme. The conservation properties of the proposed schemes are analyzed and we find that the energy-preserving scheme can precisely conserve the discrete total mass and total energy, the momentum-preserving scheme can precisely conserve the discrete total mass and total momentum, while the finite volume element scheme merely conserve the discrete total mass. We also analyze their linear stability property using the Von Neumann theory and find that the proposed schemes are unconditionally linear stable. Finally, we present some numerical examples to illustrate the effectiveness of the proposed schemes.
DA - 2017/4//
PY - 2017/4//
DO - 10.4208/aamm.2014.m888
VL - 9
IS - 2
SP - 250-271
SN - 2075-1354
KW - Energy
KW - momentum
KW - mass
KW - finite volume element method
KW - MRLW equation
ER -
TY - JOUR
TI - Modeling the differentiation of A- and C-type baroreceptor firing patterns
AU - Sturdy, Jacob
AU - Ottesen, Johnny T.
AU - Olufsen, Mette S.
T2 - JOURNAL OF COMPUTATIONAL NEUROSCIENCE
AB - The baroreceptor neurons serve as the primary transducers of blood pressure for the autonomic nervous system and are thus critical in enabling the body to respond effectively to changes in blood pressure. These neurons can be separated into two types (A and C) based on the myelination of their axons and their distinct firing patterns elicited in response to specific pressure stimuli. This study has developed a comprehensive model of the afferent baroreceptor discharge built on physiological knowledge of arterial wall mechanics, firing rate responses to controlled pressure stimuli, and ion channel dynamics within the baroreceptor neurons. With this model, we were able to predict firing rates observed in previously published experiments in both A- and C-type neurons. These results were obtained by adjusting model parameters determining the maximal ion-channel conductances. The observed variation in the model parameters are hypothesized to correspond to physiological differences between A- and C-type neurons. In agreement with published experimental observations, our simulations suggest that a twofold lower potassium conductance in C-type neurons is responsible for the observed sustained basal firing, where as a tenfold higher mechanosensitive conductance is responsible for the greater firing rate observed in A-type neurons. A better understanding of the difference between the two neuron types can potentially be used to gain more insight about pathophysiology and treatment of diseases related to baroreflex function, e.g. in patients with autonomic failure, a syndrome that is difficult to diagnose in terms of its pathophysiology.
DA - 2017/2//
PY - 2017/2//
DO - 10.1007/s10827-016-0624-6
VL - 42
IS - 1
SP - 11-30
SN - 1573-6873
KW - Baroreflex model
KW - Mechanosensitivity
KW - A- and C-type afferent baroreceptors
KW - Biophysical model
KW - Computational model
ER -
TY - JOUR
TI - Feasibility of parameter estimation in hepatitis C viral dynamics models
AU - Arthur, Joseph G.
AU - Tran, Hien T.
AU - Aston, Philip
T2 - JOURNAL OF INVERSE AND ILL-POSED PROBLEMS
AB - Abstract Methodologies are presented for assessing the feasibility of parameter estimation in nonlinear ordinary differential equation (ODE) models. These methods are applied to a recent model for hepatitis C viral dynamics. Subset selection is performed on the model parameters, and maximum likelihood estimation is conducted using available data from the literature.
DA - 2017/2//
PY - 2017/2//
DO - 10.1515/jiip-2014-0048
VL - 25
IS - 1
SP - 69-80
SN - 1569-3945
KW - Parameter estimation
KW - expectation maximization
KW - identifiability
KW - sensitivity analysis
ER -
TY - JOUR
TI - A numerical scheme for the early steps of nucleation-aggregation models
AU - Banks, Harvey Thomas
AU - Doumic, Marie
AU - Kruse, Carola
T2 - JOURNAL OF MATHEMATICAL BIOLOGY
AB - In the formation of large clusters out of small particles, the initializing step is called the nucleation, and consists in the spontaneous reaction of agents which aggregate into small and stable polymers called nuclei. After this early step, the polymers are involved in a number of reactions such as polymerization, fragmentation and coalescence. Since there may be several orders of magnitude between the size of a particle and the size of an aggregate, building efficient numerical schemes to capture accurately the kinetics of the reaction is a delicate step of key importance. In this article, we propose a conservative scheme, based on finite volume methods on an adaptive grid, which is capable of simulating well the early steps of the reaction as well as the later chain reactions.
DA - 2017/1//
PY - 2017/1//
DO - 10.1007/s00285-016-1026-0
VL - 74
IS - 1-2
SP - 259-287
SN - 1432-1416
KW - Polymerization
KW - Aggregation-fragmentation models
KW - Finite volume schemes
KW - Adaptive grid
ER -
TY - JOUR
TI - On classification of four-dimensional nilpotent Leibniz algebras
AU - Demir, Ismail
AU - Misra, Kailash C.
AU - Stitzinger, Ernie
T2 - COMMUNICATIONS IN ALGEBRA
AB - Leibniz algebras are certain generalization of Lie algebras. In this paper, we give the classification of four-dimensional non-Lie nilpotent Leibniz algebras. We use the canonical forms for the congruence classes of matrices of bilinear forms and some other techniques to obtain our result.
DA - 2017///
PY - 2017///
DO - 10.1080/00927872.2016.1172626
VL - 45
IS - 3
SP - 1012-1018
SN - 1532-4125
KW - Classification
KW - Leibniz algebra
KW - nilpotency
KW - solvability
ER -
TY - JOUR
TI - High-order numerical schemes based on difference potentials for 2D elliptic problems with material interfaces
AU - Albright, Jason
AU - Epshteyn, Yekaterina
AU - Medvinsky, Michael
AU - Xia, Qing
T2 - APPLIED NUMERICAL MATHEMATICS
AB - Numerical approximations and computational modeling of problems from Biology and Materials Science often deal with partial differential equations with varying coefficients and domains with irregular geometry. The challenge here is to design an efficient and accurate numerical method that can resolve properties of solutions in different domains/subdomains, while handling the arbitrary geometries of the domains. In this work, we consider 2D elliptic models with material interfaces and develop efficient high-order accurate methods based on Difference Potentials for such problems.
DA - 2017/1//
PY - 2017/1//
DO - 10.1016/j.apnum.2016.08.017
VL - 111
SP - 64-91
SN - 1873-5460
UR - https://doi.org/10.1016/j.apnum.2016.08.017
KW - Boundary value problems
KW - Piecewise-constant coefficients
KW - High-order accuracy
KW - Difference potentials
KW - Boundary projections
KW - Interface problems
KW - Non-matching grids
KW - Mixed-order
KW - Parallel algorithms
KW - Application to the simulation of the biological cell electropermeabilization model
ER -
TY - JOUR
TI - A dynamical modeling approach for analysis of longitudinal clinical trials in the presence of missing endpoints
AU - Banks, H. T.
AU - Hu, Shuhua
AU - Rosenberg, Eric
T2 - APPLIED MATHEMATICS LETTERS
AB - Randomized longitudinal clinical trials are the gold standard to evaluate the effectiveness of interventions among different patient treatment groups. However, analysis of such clinical trials becomes difficult in the presence of missing data, especially in the case where the study endpoints become difficult to measure because of subject dropout rates or/and the time to discontinue the assigned interventions are different among the patient groups. Here we report on using a validated mathematical model combined with an inverse problem approach to predict the values for the missing endpoints. A small randomized HIV clinical trial where endpoints for most of patients are missing is used to demonstrate this approach.
DA - 2017/1//
PY - 2017/1//
DO - 10.1016/j.aml.2016.07.002
VL - 63
SP - 109-117
SN - 0893-9659
KW - HIV
KW - Hypothesis testing
KW - Ordinary differential equation
KW - Inverse problems
ER -
TY - JOUR
TI - Codiagonalization of matrices and existence of multiple homoclinic solutions
AU - Lin, X. B.
AU - Zhu, C. R.
T2 - Journal of Applied Analysis and Computation
DA - 2017///
PY - 2017///
VL - 7
IS - 1
SP - 172-188
ER -
TY - JOUR
TI - Statistical error model comparison for logistic growth of green algae (Raphidocelis subcapitata)
AU - Banks, H.T.
AU - Collins, Elizabeth
AU - Flores, Kevin
AU - Pershad, Prayag
AU - Stemkovski, Michael
AU - Stephenson, Lyric
T2 - Applied Mathematics Letters
AB - We validate a model for the population dynamics, as they occur in a chemostat environment, of the green algae Raphidocelis subcapitata, a species that is often used as a primary food source in toxicity experiments for the fresh water crustacean Daphnia magna. We collected longitudinal data from 4 replicate population experiments with R. subcapitata. This data was fit to a logistic growth model to reveal patterns of the algae growth in a continuous culture. Overall, our results suggest that a proportional error statistical model is the most appropriate for logistic growth modeling of R. subcapitata continuous population growth.
DA - 2017/2//
PY - 2017/2//
DO - 10.1016/j.aml.2016.09.006
VL - 64
SP - 213-222
J2 - Applied Mathematics Letters
LA - en
OP -
SN - 0893-9659
UR - http://dx.doi.org/10.1016/J.AML.2016.09.006
DB - Crossref
KW - Algae growth models
KW - Parameter estimation
KW - Uncertainty quantification
KW - Asymptotic theory
ER -
TY - JOUR
TI - Resultants over commutative idempotent semirings I: Algebraic aspect
AU - Hong, Hoon
AU - Kim, Yonggu
AU - Scholten, Georgy
AU - Sendra, J. Rafael
T2 - JOURNAL OF SYMBOLIC COMPUTATION
AB - The resultant theory plays a crucial role in computational algebra and algebraic geometry. The theory has two aspects: algebraic and geometric. In this paper, we focus on the algebraic aspect. One of the most important and well known algebraic properties of the resultant is that it is equal to the determinant of the Sylvester matrix. In 2008, Odagiri proved that a similar property holds over the tropical semiring if one replaces subtraction with addition. The tropical semiring belongs to a large family of algebraic structures called commutative idempotent semiring. In this paper, we prove that the same property (with subtraction replaced with addition) holds over an arbitrary commutative idempotent semiring.
DA - 2017///
PY - 2017///
DO - 10.1016/j.jsc.2016.02.009
VL - 79
SP - 285-308
SN - 1095-855X
UR - http://dx.doi.org/10.1016/j.jsc.2016.02.009
KW - Resultant
KW - Commutative idempotent semiring
KW - Tropical algebra
KW - Sylvester matrix
KW - Permanent
ER -