TY - JOUR
TI - A normal form for cubic surfaces
AU - Li, Zane Kun
T2 - International Journal of Algebra
DA - 2010///
PY - 2010///
VL - 4
IS - 5
SP - 233–239
ER -
TY - JOUR
TI - On a special case of the intersection of quadric and cubic surfaces
AU - Li, Zane Kun
T2 - Journal of Pure and Applied Algebra
AB - The intersection curve between two surfaces in three-dimensional real projective space RP3 is important in the study of computer graphics and solid modelling. However, much of the past work has been directed towards the intersection of two quadric surfaces. In this paper we study the intersection curve between a quadric and a cubic surface and its projection onto the plane at infinity. Formulas for the plane and space curves are given for the intersection of a quadric and a cubic surface. A family of cubic surfaces that give the same space curve when we intersect them with a quadric surface is found. By generalizing the methods in Wang et al. (2002) [6] that are used to parametrize the space curve between two quadric surfaces, we give a parametrization for the intersection curve between a quadric and a cubic surface when the intersection has a singularity of order 3.
DA - 2010/11//
PY - 2010/11//
DO - 10.1016/j.jpaa.2010.02.013
VL - 214
IS - 11
SP - 2078-2086
J2 - Journal of Pure and Applied Algebra
LA - en
OP -
SN - 0022-4049
UR - http://dx.doi.org/10.1016/j.jpaa.2010.02.013
DB - Crossref
ER -
TY - JOUR
TI - A normal form for cubic surfaces
T2 - International Journal of Algebra
DA - 2010///
PY - 2010///
UR - http://www.m-hikari.com/ija/ija-2010/ija-5-8-2010/liIJA5-8-2010.pdf
ER -
TY - JOUR
TI - Filtering for fast mean-reverting processes
AU - Papanicolaou, Andrew
T2 - Asymptotic Analysis
AB - We consider nonlinear filtering applications to target tracking based on a vector of multi-scaled models where some of the processes are rapidly mean reverting to their local equilibria. We focus attention on target tracking problems because multiple scaled models with fast mean-reversion (FMR) are a simple way to model latency in the response of tracking systems. The main results of this paper show that nonlinear filtering algorithms for multi-scale models with FMR states can be simplified significantly by exploiting the FMR structures, which leads to a simplified Baum-Welch recursion that is of reduced dimension. We implement the simplified algorithms with numerical simulations and discuss their efficiency and robustness.
DA - 2010///
PY - 2010///
DO - 10.3233/ASY-2010-1011
VL - 70
IS - 3-4
SP - 155-176
OP -
SN - 0921-7134
UR - http://dx.doi.org/10.3233/ASY-2010-1011
DB - Crossref
KW - nonlinear filtering
KW - tracking
KW - fast mean reversion
KW - Kramers-Smoluchowski
ER -
TY - RPRT
TI - The Role of Symbolic, Numeric and Algebraic Computation in Cyber-Enabled Discovery and Innovation (CDI)
AU - Kaltofen, Erich L.
A3 - University of Rhode Island
DA - 2010///
PY - 2010///
PB - University of Rhode Island
ER -
TY - CONF
TI - Stabilized Completions of Differential Algebraic Equations and the Design of Observers
AU - Bobinyec, K.
AU - Campbell, S.L.
AU - Kunkel, P.
T2 - Fourth International Conference on Neural, Parallel and Scientific Computation
C2 - 2010///
C3 - Proceedings of Neural, Parallel, and Scientific Computation
CY - Atlanta, GA
DA - 2010///
PY - 2010///
ER -
TY - CONF
TI - Rank-deficient and ill-conditioned nonlinear least squares problems
AU - Kelley, C.T.
AU - Ipsen, I.C.F.
AU - Pope, S.R.
T2 - East Asian Society of Industrial and Applied Mathematics Conference
C2 - 2010///
C3 - Proceedings of the 2010 East Asian SIAM Conference
DA - 2010///
PY - 2010///
ER -
TY - THES
TI - Categorification of Knot and Graph Polynomials and the Polynomial Ring, Electronic dissertation published by ProQuest
AU - Sazdanović, R.
DA - 2010///
PY - 2010///
UR - http://surveyor.gelman.gwu.edu/.
ER -
TY - CHAP
TI - On splitting-based numerical methods for convection-diffusionequations
AU - Chertock, A.
AU - Kurganov, A.
T2 - Numerical Methods for Balance Laws
A2 - Puppo, G.
A2 - Russo, G.
T3 - Quaderni di Matematica
PY - 2010///
VL - 24
SP - 303
PB - Dipartimento di matematica della Seconda Universitá di Napoli
SV - 24
ER -
TY - JOUR
TI - Tutte and Jones polynomials of links, polyominoes and graphical recombination patterns
AU - Jablan, S.
AU - Radović, Lj.
AU - Sazdanović, R.
T2 - Journal of Mathematical Chemistry
DA - 2010/10/7/
PY - 2010/10/7/
DO - 10.1007/S10910-010-9731-1
VL - 49
IS - 1
SP - 79-94
J2 - J Math Chem
LA - en
OP -
SN - 0259-9791 1572-8897
UR - http://dx.doi.org/10.1007/S10910-010-9731-1
DB - Crossref
KW - Knot
KW - Link
KW - Tait graph
KW - Middle graph
KW - Polyiamond
KW - Polyomino
KW - Polyhex
KW - Tutte polynomial
KW - Jones polynomial
KW - Polymer
ER -
TY - JOUR
TI - Medea selfish genetic elements as tools for altering traits of wild populations: A theoretical analysis.
AU - Ward, Catherine M.
AU - Su, Jessica T.
AU - Huang, Yunxin
AU - Lloyd, Alun L.
AU - Gould, Fred
AU - Hay, Bruce A.
T2 - Evolution
AB - One strategy for controlling transmission of insect-borne disease involves replacing the native insect population with transgenic animals unable to transmit disease. Population replacement requires a drive mechanism to ensure the rapid spread of linked transgenes, the presence of which may result in a fitness cost to carriers. Medea selfish genetic elements have the feature that when present in a female, only offspring that inherit the element survive, a behavior that can lead to spread. Here, we derive equations that describe the conditions under which Medea elements with a fitness cost will spread, and the equilibrium allele frequencies are achieved. Of particular importance, we show that whenever Medea spreads, the non-Medea genotype is driven out of the population, and we estimate the number of generations required to achieve this goal for Medea elements with different fitness costs and male-only introduction frequencies. Finally, we characterize two contexts in which Medea elements with fitness costs drive the non-Medea allele from the population: an autosomal element in which not all Medea-bearing progeny of a Medea-bearing mother survive, and an X-linked element in species in which X/Y individuals are male. Our results suggest that Medea elements can drive population replacement under a wide range of conditions.
DA - 2010/12/22/
PY - 2010/12/22/
DO - 10.1111/j.1558-5646.2010.01186.x
VL - 65
IS - 4
SP - 1149-1162
SN - 0014-3820
UR - http://dx.doi.org/10.1111/j.1558-5646.2010.01186.x
KW - Dengue
KW - introgression
KW - malaria
KW - maternal effect
KW - mosquito
KW - population replacement
ER -
TY - CONF
TI - Connectivity in Semi-algebraic Sets
AU - Hong, Hoon
A2 - Ida, Tetsuo
A2 - Negru, Viorel
A2 - Jebelean, Tudor
A2 - Petcu, Dana
A2 - Watt, Stephen M.
A2 - Zaharie, Daniela
AB - We consider the problem of deciding whether two given points in a semialgebraic set can be connected, that is, whether the two points lie in a same connected component. In particular, we consider a semialgebraic set consisting of points where a given polynomial is non-zero. We will describe a method based on gradient fields, eigenvectors and interval analysis.
C2 - 2010/9//
C3 - 2010 12th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing
DA - 2010/9//
DO - 10.1109/synasc.2010.91
SP - 4-7
PB - IEEE
UR - http://dx.doi.org/10.1109/synasc.2010.91
KW - connectivity
KW - road map
KW - semi-algebraic sets
KW - gradient fields
KW - Morse-Smale complex
ER -
TY - BOOK
TI - Spectral Analysis of Large Dimensional Random Matrices
AU - Bai, Z.D.
AU - Silverstein, Jack
DA - 2010///
PY - 2010///
ET - 2
PB - Springer
ER -
TY - CONF
TI - Alternating proximal algorithm for blind image recovery
AU - Bolte, J.
AU - Combettes, P.L.
AU - Pesquet, J.-C.
T2 - Proceedings of the IEEE International Conference on Image Processing
AB - We consider a variational formulation of blind image recovery problems. A novel iterative proximal algorithm is proposed to solve the associated nonconvex minimization problem. Under suitable assumptions, this algorithm is shown to have better convergence properties than standard alternating minimization techniques. The objective function includes a smooth convex data fidelity term and nonsmooth convex regularization terms modeling prior information on the data and on the unknown linear degradation operator. A novelty of our approach is to bring into play recent nonsmooth analysis results. The pertinence of the proposed method is illustrated in an image restoration example.
C2 - 2010///
C3 - Proceedings of the IEEE International Conference on Image Processing
CY - Hong Kong
DA - 2010///
PY - 2010/9/26/
DO - 10.1109/ICIP.2010.5652173
SP - 1673–1676
KW - Blind restoration
KW - blind reconstruction
KW - proximal methods
KW - nonlinear optimization
KW - wavelets
ER -
TY - CONF
TI - Proximal method for geometry and texture image decomposition
AU - Briceño-Arias, L.M.
AU - Combettes, P.L.
AU - Pesquet, J.-C.
AU - Pustelnik, N.
T2 - Proceedings of the IEEE International Conference on Image Processing
AB - We propose a variational method for decomposing an image into a geometry and a texture component. Our model involves the sum of two functions promoting separately properties of each component, and of a coupling function modeling the interaction between the components. None of these functions is required to be differentiable, which significantly broadens the range of decompositions achievable through variational approaches. The convergence of the proposed proximal algorithm is guaranteed under suitable assumptions. Numerical examples are provided that show an application of the algorithm to image decomposition and restoration in the presence of Poisson noise.
C2 - 2010///
C3 - Proceedings of the IEEE International Conference on Image Processing
CY - Hong Kong
DA - 2010///
PY - 2010/9/26/
DO - 10.1109/ICIP.2010.5653670
SP - 2721–2724
KW - Convex optimization
KW - denoising
KW - image decomposition
KW - image restoration
KW - proximity operator
ER -
TY - JOUR
TI - Steady state and scaling limit for a traffic congestion model
AU - Grigorescu, Ilie
AU - Kang, Min
T2 - ESAIM: Probability and Statistics
AB - In a general model (AIMD) of transmission control protocol (TCP) used in internet traffic congestion management, the time dependent data flow vector x(t) > 0 undergoes a biased random walk on two distinct scales. The amount of data of each component xi(t) goes up to xi(t)+a with probability 1-ζi(x) on a unit scale or down to γxi(t), 0 < γ < 1 with probability ζi(x) on a logarithmic scale, where ζi depends on the joint state of the system x. We investigate the long time behavior, mean field limit, and the one particle case. According to c = lim inf|x|→∞ |x|ζi(x) , the process drifts to ∞ in the subcritical c < c+(n, γ) case and has an invariant probability measure in the supercritical case c > c+(n, γ). Additionally, a scaling limit is proved when ζi(x) and a are of order N–1 and t → Nt, in the form of a continuum model with jump rate α(x).
DA - 2010///
PY - 2010///
DO - 10.1051/ps:2008029
VL - 14
SP - 271-285
J2 - ESAIM: PS
OP -
SN - 1292-8100 1262-3318
UR - http://dx.doi.org/10.1051/ps:2008029
DB - Crossref
KW - TCP
KW - AIMD
KW - fluid limit
KW - mean field interaction
ER -
TY - CONF
TI - Eigen-inference for multi-source power estimation
AU - Couillet, Romain
AU - Silverstein, Jack W.
AU - Debbah, Merouane
T2 - 2010 IEEE International Symposium on Information Theory - ISIT
AB - This paper introduces a new method to estimate the power transmitted by multiple signal sources, when the number of sensing devices and the available samples are sufficiently large compared to the number of sources. This work makes use of recent advances in the field of random matrix theory that prove more efficient than previous “moment-based” approaches to the problem of multi-source power detection. Simulations are performed which corroborate the theoretical claims.
C2 - 2010/6//
C3 - 2010 IEEE International Symposium on Information Theory
DA - 2010/6//
DO - 10.1109/isit.2010.5513327
PB - IEEE
SN - 9781424478927 9781424478903 9781424478910
UR - http://dx.doi.org/10.1109/isit.2010.5513327
DB - Crossref
ER -
TY - BOOK
TI - Quantum affine algebras, extended affine Lie algebras, and their applications
DA - 2010///
PY - 2010///
ER -
TY - JOUR
TI - Quantum information and entanglement
AU - Fei, S.-M.
AU - Albeverio, S.
AU - Cabello, A.
AU - Jing, N.
AU - Goswami, D.
T2 - Advances in Mathematical Physics
AB - 1 School of Mathematical Sciences, Capital Normal University, Beijing 100048, China 2 Institute of Applied Mathematics, University of Bonn, 53115 Bonn, Germany 3 Departamento de Fisica Aplicada II, Universidad de Sevilla, 41012 Sevilla, Spain 4 Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA 5 Statistics and Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
DA - 2010///
PY - 2010///
DO - 10.1155/2010/657878
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84890161694&partnerID=MN8TOARS
ER -
TY - JOUR
TI - Expository research papers
AU - Ipsen, I.
T2 - SIAM Review
DA - 2010///
PY - 2010///
VL - 52
IS - 4
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-79952956707&partnerID=MN8TOARS
ER -
TY - JOUR
TI - Expository Research Papers
AU - Ipsen, Ilse
T2 - SIAM Review
AB - The two papers in this issue are concerned with analysis of differential equations: the first paper discusses the solution of partial differential equations that describe heat transfer, while the second one analyzes dynamical systems whose behavior alternates between continuous and discrete modes. The paper “Application of Standard and Refined Heat Balance Integral Methods to One-Dimensional Stefan Problems,” by Sarah Mitchell and Tim Myers, deals with a heat transfer problem, on a semi-infinite region. Consider an experiment on a long metal bar occupying the positive real-axis. The experiment starts by heating the origin, thereby raising the bar above the melting temperature. The bar melts near the origin, and as the heat diffuses, the solid-liquid interface propagates slowly but surely towards infinity. The temperature is modeled by heat equations across the two regions, and by a Stefan condition at their interface. The authors heat balance integral methods to solve for the temperature. These methods reduce a partial differential equation to an ordinary differential equation. The authors investigate different boundary conditions, and different approximating functions for the temperature. Readers interested in heat balance integral methods will find this to be a valuable survey with new results that preserve the simplicity of the method. The second paper is concerned with so-called hybrid dynamical systems. A bouncing ball, for instance, is a hybrid dynamical system. The movement of the ball above ground can be described by Newton's law. However, at the very moment the ball hits the ground and bounces, an instantaneous reversal of velocity occurs along with some dissipation of energy. After the bounce, the ball moves again according to Newton's law until the next bounce, and so on. Mathematically one can show that the time points at which the ball bounces represent a convergent sequence. The convergence of this sequence implies that infinitely many bounces occur in a finite amount of time. This is called “Zeno behavior”: infinitely many switches of mode in a finite amount of time. If Zeno behavior occurs in a control system, a numerical simulation of the system is extremely difficult, if not impossible. In the terminology of dynamical systems, the movement of the ball above ground is a “flow” and the bounce is a “jump.” Hybrid dynamical systems alternate between continuous (flow) and discrete (jump) modes. Rafal Goebel and Andrew Teel in their paper “Preasymptotic Stability and Homogeneous Approximations of Hybrid Dynamical Systems” model hybrid dynamical systems and approximate them by simpler systems obtained from linearization and tangent cones. The authors analyze preasymptotic stability, homogeneity, and convergence. A variety of well-chosen simple examples helps us to understand the general concepts and results.
DA - 2010/1//
PY - 2010/1//
DO - 10.1137/siread000052000001000055000001
VL - 52
IS - 1
SP - 55-55
ER -
TY - JOUR
TI - Sortable elements for quivers with cycles
AU - Reading, N.
AU - Speyert, D.E.
T2 - Electronic Journal of Combinatorics
DA - 2010///
PY - 2010///
VL - 17
IS - 1
SP - 1-19
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-77955640004&partnerID=MN8TOARS
ER -
TY - JOUR
TI - A comparison of nonlinear filtering approaches in the context of an HIV model
AU - Banks, H.
AU - Hu, Shuhua
AU - Kenz, Zackary
AU - Tran, Hien
T2 - Mathematical Biosciences and Engineering
AB - In this paper three different filtering methods, the Extended Kalman Filter (EKF), the Gauss-Hermite Filter (GHF), and the Unscented Kalman Filter (UKF), are compared for state-only and coupled state and parameter estimation when used with log state variables of a model of the immunologic response to the human immunodeficiency virus (HIV) in individuals. The filters are implemented to estimate model states as well as model parameters from simulated noisy data, and are compared in terms of estimation accuracy and computational time. Numerical experiments reveal that the GHF is the most computationally expensive algorithm, while the EKF is the least expensive one. In addition, computational experiments suggest that there is little difference in the estimation accuracy between the UKF and GHF. When measurements are taken as frequently as every week to two weeks, the EKF is the superior filter. When measurements are further apart, the UKF is the best choice in the problem under investigation.
DA - 2010/4//
PY - 2010/4//
DO - 10.3934/mbe.2010.7.213
VL - 7
IS - 2
SP - 213-236
J2 - MBE
LA - en
OP -
SN - 1551-0018
UR - http://dx.doi.org/10.3934/mbe.2010.7.213
DB - Crossref
KW - extended Kalman filter
KW - unscented Kalman filter
KW - Gauss-Hermite filter
KW - HIV
ER -
TY - JOUR
TI - On surface radiation conditions for an ellipse
DA - 2010/7/15/
PY - 2010/7/15/
UR - http://www.sciencedirect.com/science/article/pii/S0377042709004865
ER -
TY - JOUR
TI - Sortable elements for quivers with cycles
AU - Reading, Nathan
AU - Speyer, David
T2 - The Electronic Journal of Combinatorics
AB - Each Coxeter element $c$ of a Coxeter group $W$ defines a subset of $W$ called the $c$-sortable elements. The choice of a Coxeter element of $W$ is equivalent to the choice of an acyclic orientation of the Coxeter diagram of $W$. In this paper, we define a more general notion of $\Omega$-sortable elements, where $\Omega$ is an arbitrary orientation of the diagram, and show that the key properties of $c$-sortable elements carry over to the $\Omega$-sortable elements. The proofs of these properties rely on reduction to the acyclic case, but the reductions are nontrivial; in particular, the proofs rely on a subtle combinatorial property of the weak order, as it relates to orientations of the Coxeter diagram. The $c$-sortable elements are closely tied to the combinatorics of cluster algebras with an acyclic seed; the ultimate motivation behind this paper is to extend this connection beyond the acyclic case.
DA - 2010///
PY - 2010///
DO - 10.37236/362
VL - 17
IS - 1
SP - R90
UR - http://www.combinatorics.org/Volume_17/Abstracts/v17i1r90.html
ER -
TY - JOUR
TI - Noncrossing partitions, clusters and the Coxeter plane
AU - Reading, N.
T2 - Séminaire Lotharingien de Combinatoire
DA - 2010///
PY - 2010///
VL - 63
SP - B63b
SN - 1286-4889
UR - https://www.mat.univie.ac.at/~slc/wpapers/s63reading.html
ER -
TY - JOUR
TI - Rank-Deficient and Ill-Conditioned Nonlinear Least Squares Problems
AU - Kelley, C T
AU - Ipsen, I C F
AU - Pope, S R
DA - 2010///
PY - 2010///
ER -
TY - CONF
TI - Optimization of a Mathematical Model of Cerebral Autoregulation Using patient Data
AU - Aoi, M C
AU - Kelley, C T
AU - Novak, V
AU - Olufsen, M S
AB - This study presents an analysis of a cerebral autoregulation (CA) model developed by Ursino and Lodi Ursino and Lodi (1997). We have used this model to analyze non-invasive measurements of cerebral blood flow velocity (CBFV) and arterial blood pressure obtained during postural change from sitting to standing for a healthy young subject. This paper includes a sensitivity analysis, ranking model parameters from the most to the least sensitive, and an analysis (using a methodology called subset selection) that allows identification of correlations among model parameters. Finally, we estimated patient specific parameters using the Levenberg-Marquardt optimization method minimizing the least square errors between computed and measured values of CBFV.
C2 - 2010///
C3 - Proceedings of 7th IFAC Symposium on Modelling and Control in Biomedical Systems
DA - 2010///
DO - 10.3182/20090812-3-DK-2006.0088
SP - 6 pages
ER -
TY - CONF
TI - Parallel Computation of Surrogate Models for Potential Energy Surfaces
AU - Mokrauer, David
AU - Kelley, C T
AU - Bykhovski, Alexei
A2 - Qingping, Quo
A2 - Yucheng, Guo
C2 - 2010///
C3 - 2010 International Symposium on Distributed Computing and Applications to Business, Engineering and Science
CY - Los Alamitos, CA
DA - 2010///
SP - 1-4
PB - IEEE
ER -
TY - JOUR
TI - Expository Research Papers
AU - Ipsen, Ilse
T2 - SIAM Review
AB - The first paper in this issue is concerned with the numerical solution of an inverse problem, and the second one with detecting properties of networks. Alexander Graham Bell discovered the photoacoustic effect in the nineteenth century. He noticed that thin discs emit a sound when they are exposed to a light beam that is rapidly turned on and off. What happens is that the disks absorb the energy from the light, and convert it to heat. The heat then produces a momentary expansion, which in turn sets off a pressure wave or sound. The photoacoustic effect is exploited in biomedical applications, to help with the detection of lesions and cancer. The tissue is exposed to energy pulses and then expands. The expansion produces ultrasonic waves that propagate to the boundary and can be detected there. The objective of the paper “Mathematical Modeling in Photoacoustic Imaging of Small Absorbers” by Habib Ammari, Emmanuel Bossy, Vincent Jugnon, and Hyeonbae Kang is to identify energy absorbing regions from measurements taken at the boundary. This is an inverse problem, and the boundary conditions require special attention. The authors derive a reconstruction method, and present numerical experiments to illustrate its effectiveness. This is noteworthy paper, due to its potential contribution to medical imaging. Mathematicians like to gauge their position in the community via the so-called Erdös number, which represents the “collaborative distance” to Paul Erdös. Erdös (1913–1996) was a prolific Hungarian mathematician who worked in many areas, including combinatorics, graph theory, and number theory, and published by some accounts as many as 1400 papers. Erdös himself has an Erdös number of 0, while his coauthors have an Erdös number of 1. To compute your own Erdös number, take the lowest Erdös number among all of your coauthors, and then add one. If none of your coauthors has a finite Erdös number, neither do you, and your Erdös number is $\infty$. How can we express the influence of Paul Erdös in mathematical terms? There is his centrality, measured by the number of his coauthors and said to exceed 500. There is his communicability, which is the sum of all finite Erdös numbers, but with larger Erdös numbers given less weight (i.e., Erdös number k is divided by k!). And there is his betweenness, a measure of what would happen to the communicability of the other mathematicians had Erdös not existed. Concepts such as centrality, communicability, and betweenness quantify the connectivity and topology of general networks. Ernesto Estrada and Desmond Higham, in their paper “Network Properties Revealed through Matrix Functions,” express these concepts in terms of the exponential and resolvent of the adjacency matrix, and compare them on real test data from social science, ecology, and proteomics. This well-written paper gives us a glimpse into network science, a new area that studies patterns of interactions, and exposes the opportunities for contributions from linear algebra.
DA - 2010/1//
PY - 2010/1//
DO - 10.1137/siread000052000004000675000001
VL - 52
IS - 4
SP - 675-675
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-79952956707&partnerID=MN8TOARS
ER -
TY - JOUR
TI - Expository Research Papers
AU - Ipsen, Ilse
T2 - SIAM Review
AB - The two papers in this issue deal with differential equations, one with the numerical solution of partial differential equations, and the other one with analytic solutions for ordinary differential equations.
In his paper From Functional Analysis to Iterative Methods, Robert Kirby is concerned with linear systems arising from discretizations of partial differential equations (PDEs). Specifically, the PDEs are elliptic and describe boundary value problems; the discretizations are done via finite elements, and at issue is the convergence rate of iterative methods for solving the linear systems. The author's approach is to go back to the underlying variational problem in a Hilbert space, and to make ample use of the Riesz representation theorem. This point of view results in short and elegant proofs, as well as the construction of efficient preconditioners. The general theory is illustrated with two concrete model problems of PDEs for convection diffusion and planar elasticity. This paper will appeal to anybody who has an interest in the numerical solution of PDEs.
In 1963 the mathematician/meteorologist Edward Lorenz formulated a system of three coupled nonlinear ordinary differential equations, whose long-term behavior is described by an attractor with fractal structure. You can see a beautiful rendition of the thus named Lorenz attractor on the cover of this issue. Although it is easy to plot solutions of the Lorenz system, it is much harder to determine them mathematically. This is what motivated the paper Complex Singularities and the Lorenz Attractor by Divakar Viswanath and Sonmez Sahutoglu. Their idea is to allow the time variable to be complex, rather than real; to focus on singular solutions; and to express these singular solutions in terms of so-called psi series. After all is said and done, the authors end up with a two-parameter family of complex solutions to the Lorenz system. This a highly readable and very enjoyable paper, with concrete steps for future research, and connections to thunderstorms and analytic function theory.
DA - 2010/1//
PY - 2010/1//
DO - 10.1137/siread000052000002000267000001
VL - 52
IS - 2
SP - 267-267
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-77249161188&partnerID=MN8TOARS
ER -
TY - JOUR
TI - Expository Research Papers
AU - Ipsen, Ilse
T2 - SIAM Review
AB - The two papers in this issue have to do with matrices and sparsity—but from different points of view. Sparsity, in the first paper, means many zero elements in the matrix, while in the second paper it refers to many zero singular values, i.e., low rank. The context of the first paper, “On the Block Triangular Form of Symmetric Matrices” by Iain Duff and Bora Uçar, is the solution of linear systems of equations $Ax = b$ whose coefficient matrix A is sparse, i.e., has many zero elements. A direct method, such as Gaussian elimination, becomes more efficient if one can first permute the rows and columns of A into block triangular form. The classical method for permuting a matrix to block triangular form is due to Dulmage and Mendelsohn and dates back to 1963. The idea is to represent the matrix A as a bipartite graph whose nodes are columns and rows of A, and whose edges correspond to nonzero elements of A, and then to determine a matching of maximum cardinality in this graph. That means determining a maximal number of nonzero elements no two of which belong to the same row or column. Duff and Uçar analyze the block triangular form for a particular class of square matrices A: These matrices are structurally symmetric, i.e., their zero/nonzero structure is symmetric; and they can be structurally rank deficient, i.e., any rank deficiency is evident from the zero/nonzero structure of A. This paper illustrates nicely how graph theory can contribute to improving the efficiency of sparse matrix methods. The paper should appeal to those who need to solve large sparse linear systems, as well as those interested in graph theory. The second paper, “Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization” by Benjamin Recht, Maryam Fazel, and Pablo Parrilo, has applications to model reduction and system identification, machine learning, and image compression, just to name a few. Given a set of affine constraints for a matrix, the problem is to find a matrix of minimum rank that satisfies these constraints. The authors attack this hard nonconvex optimization problem by replacing it with a convex approximation: Instead of minimizing the rank, they minimize the sum of the singular values, the so-called nuclear norm. Nuclear norm minimization thus extends the compressed sensing framework from finding sparse vectors via $\ell_1$ minimization to finding low-rank matrices via $\ell_1$ minimization of the (vector of) singular values. The purpose of this paper is to justify mathematically why nuclear norm minimization does so well in practice. In addition to extending the restricted isometry property to matrices, the authors also discuss algorithms, computational performance, and numerical issues. This is a fascinating and well-written paper that combines results from compressed sensing, matrix theory, optimization, and probability.
DA - 2010/1//
PY - 2010/1//
DO - 10.1137/siread000052000003000453000001
VL - 52
IS - 3
SP - 453-453
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-77954340593&partnerID=MN8TOARS
ER -
TY - CONF
TI - Computing the radius of positive semidefiniteness of a multivariate real polynomial via a dual of Seidenberg's method
AU - Hutton, Sharon
AU - Kaltofen, Erich L.
AU - Zhi, Lihong
T2 - the 2010 International Symposium
AB - We give a stability criterion for real polynomial inequalities with floating point or inexact scalars by estimating from below or computing the radius of semidefiniteness. That radius is the maximum deformation of the polynomial coefficient vector measured in a weighted Euclidean vector norm within which the inequality remains true. A large radius means that the inequalities may be considered numerically valid.
C2 - 2010///
C3 - Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation - ISSAC '10
DA - 2010///
DO - 10.1145/1837934.1837979
PB - ACM Press
SN - 9781450301503
UR - http://dx.doi.org/10.1145/1837934.1837979
DB - Crossref
ER -
TY - CONF
TI - Fifteen years after DSC and WLSS2 what parallel computations I do today
AU - Kaltofen, Erich L.
T2 - the 4th International Workshop
AB - A second wave of parallel and distributed computing research is rolling in. Today's multicore/multiprocessor computers facilitate everyone's parallel execution. In the mid 1990s, manufactures of expensive main-frame parallel computers faltered and computer science focused on the Internet and the computing grid. After a ten year hiatus, the Parallel Symbolic Computation Conference (PASCO) is awakening with new vigor.
C2 - 2010///
C3 - Proceedings of the 4th International Workshop on Parallel and Symbolic Computation - PASCO '10
DA - 2010///
DO - 10.1145/1837210.1837213
PB - ACM Press
SN - 9781450300674
UR - http://dx.doi.org/10.1145/1837210.1837213
DB - Crossref
ER -
TY - BOOK
TI - Modeling and Simulation in Scilab/Scicos with ScicosLab 4.4
AU - Campbell, Stephen L.
AU - Chancelier, Jean-Philippe
AU - Nikoukhah, Ramine
AB - Scilab is a free open-source software package for scientific computation. It includes hundreds of general purpose and specialized functions for numerical computation, organized in libraries called too
DA - 2010///
PY - 2010///
DO - 10.1007/978-1-4419-5527-2
PB - Springer New York
ER -
TY - JOUR
TI - Understanding Uncertainties in Model-Based Predictions of Aedes aegypti Population Dynamics
AU - Xu, Chonggang
AU - Legros, Mathieu
AU - Gould, Fred
AU - Lloyd, Alun L.
T2 - PLoS Neglected Tropical Diseases
AB - Background Aedes aegypti is one of the most important mosquito vectors of human disease. The development of spatial models for Ae. aegypti provides a promising start toward model-guided vector control and risk assessment, but this will only be possible if models make reliable predictions. The reliability of model predictions is affected by specific sources of uncertainty in the model. Methodology/Principal Findings This study quantifies uncertainties in the predicted mosquito population dynamics at the community level (a cluster of 612 houses) and the individual-house level based on Skeeter Buster, a spatial model of Ae. aegypti, for the city of Iquitos, Peru. The study considers two types of uncertainty: 1) uncertainty in the estimates of 67 parameters that describe mosquito biology and life history, and 2) uncertainty due to environmental and demographic stochasticity. Our results show that for pupal density and for female adult density at the community level, respectively, the 95% prediction confidence interval ranges from 1000 to 3000 and from 700 to 5,000 individuals. The two parameters contributing most to the uncertainties in predicted population densities at both individual-house and community levels are the female adult survival rate and a coefficient determining weight loss due to energy used in metabolism at the larval stage (i.e. metabolic weight loss). Compared to parametric uncertainty, stochastic uncertainty is relatively low for population density predictions at the community level (less than 5% of the overall uncertainty) but is substantially higher for predictions at the individual-house level (larger than 40% of the overall uncertainty). Uncertainty in mosquito spatial dispersal has little effect on population density predictions at the community level but is important for the prediction of spatial clustering at the individual-house level. Conclusion/Significance This is the first systematic uncertainty analysis of a detailed Ae. aegypti population dynamics model and provides an approach for identifying those parameters for which more accurate estimates would improve model predictions.
DA - 2010/9/28/
PY - 2010/9/28/
DO - 10.1371/journal.pntd.0000830
VL - 4
IS - 9
SP - e830
J2 - PLoS Negl Trop Dis
LA - en
OP -
SN - 1935-2735
UR - http://dx.doi.org/10.1371/journal.pntd.0000830
DB - Crossref
ER -
TY - JOUR
TI - Gene-drive into insect populations with age and spatial structure: a theoretical assessment
AU - Huang, Yunxin
AU - Lloyd, Alun L.
AU - Legros, Mathieu
AU - Gould, Fred
T2 - Evolutionary Applications
AB - The potential benefits and risks of genetically engineered gene-drive systems for replacing wild pest strains with more benign strains must be assessed prior to any field releases. We develop a computer simulation model to assess the feasibility of using engineered underdominance constructs to drive transgenes into age- and spatially structured mosquito populations. Our practical criterion for success is the achievement of a transgene frequency of at least 0.80 within 3 years of release. The impacts of a number of parameters that may affect the success of gene-drive, such as the release area, release age, density-dependent larval survival, fitness cost of the engineered genes, and migration probability of adults, are examined. Results show that patchy release generally requires the release of fewer engineered insects to achieve success than central release. When the fitness cost is very low, central release covering 25% of the total area can be more effective than a completely uniform release over the whole area. This study demonstrates that to determine the best method of spatial release, and the total number of engineered insects that must be released, it is important to take into account the age and sex of the released insects and spatial structure of the population.
DA - 2010/9/14/
PY - 2010/9/14/
DO - 10.1111/j.1752-4571.2010.00153.x
VL - 4
IS - 3
SP - 415-428
LA - en
OP -
SN - 1752-4571
UR - http://dx.doi.org/10.1111/j.1752-4571.2010.00153.x
DB - Crossref
KW - age and spatial structure
KW - engineered underdominance
KW - gene drive
KW - release threshold
KW - theoretical assessment
ER -
TY - CHAP
TI - On splitting-based numerical methods for convection-diffusion equations
AU - Chertock, A.
AU - Kurganov, A.
T2 - Numerical Methods for Balance Laws, Quaderni di Matematica, Aracne editrice S.r.l
PY - 2010///
VL - 24
SP - 303
ER -
TY - JOUR
TI - A Parallel Splitting Method for Coupled Monotone Inclusions
AU - Attouch, Hédy
AU - Briceño-Arias, Luis M.
AU - Combettes, Patrick L.
T2 - SIAM Journal on Control and Optimization
AB - A parallel splitting method is proposed for solving systems of coupled monotone inclusions in Hilbert spaces, and its convergence is established under the assumption that solutions exist. Unlike existing alternating algorithms, which are limited to two variables and linear coupling, our parallel method can handle an arbitrary number of variables as well as nonlinear coupling schemes. The breadth and flexibility of the proposed framework is illustrated through applications in the areas of evolution inclusions, variational problems, best approximation, and network flows.
DA - 2010/1//
PY - 2010/1//
DO - 10.1137/090754297
VL - 48
IS - 5
SP - 3246-3270
J2 - SIAM J. Control Optim.
LA - en
OP -
SN - 0363-0129 1095-7138
UR - http://dx.doi.org/10.1137/090754297
DB - Crossref
KW - coupled systems
KW - demiregular operator
KW - evolution inclusion
KW - forward-backward algorithm
KW - maximal monotone operator
KW - operator splitting
KW - parallel algorithm
KW - weak convergence
ER -
TY - JOUR
TI - Functions with prescribed best linear approximations
AU - Combettes, Patrick L.
AU - Reyes, Noli N.
T2 - Journal of Approximation Theory
AB - A common problem in applied mathematics is that of finding a function in a Hilbert space with prescribed best approximations from a finite number of closed vector subspaces. In the present paper we study the question of the existence of solutions to such problems. A finite family of subspaces is said to satisfy the Inverse Best Approximation Property (IBAP) if there exists a point that admits any selection of points from these subspaces as best approximations. We provide various characterizations of the IBAP in terms of the geometry of the subspaces. Connections between the IBAP and the linear convergence rate of the periodic projection algorithm for solving the underlying affine feasibility problem are also established. The results are applied to investigate problems in harmonic analysis, integral equations, signal theory, and wavelet frames.
DA - 2010/5//
PY - 2010/5//
DO - 10.1016/j.jat.2009.12.007
VL - 162
IS - 5
SP - 1095-1116
J2 - Journal of Approximation Theory
LA - en
OP -
SN - 0021-9045
UR - http://dx.doi.org/10.1016/j.jat.2009.12.007
DB - Crossref
ER -
TY - JOUR
TI - Dualization of Signal Recovery Problems
AU - Combettes, Patrick L.
AU - Dũng, Đinh
AU - Vũ, Bằng Công
T2 - Set-Valued and Variational Analysis
AB - In convex optimization, duality theory can sometimes lead to simpler solution methods than those resulting from direct primal analysis. In this paper, this principle is applied to a class of composite variational problems arising in particular in signal recovery. These problems are not easily amenable to solution by current methods but they feature Fenchel–Moreau–Rockafellar dual problems that can be solved by forward-backward splitting. The proposed algorithm produces simultaneously a sequence converging weakly to a dual solution, and a sequence converging strongly to the primal solution. Our framework is shown to capture and extend several existing duality-based signal recovery methods and to be applicable to a variety of new problems beyond their scope.
DA - 2010/9/2/
PY - 2010/9/2/
DO - 10.1007/s11228-010-0147-7
VL - 18
IS - 3-4
SP - 373-404
J2 - Set-Valued Anal
LA - en
OP -
SN - 1877-0533 1877-0541
UR - http://dx.doi.org/10.1007/s11228-010-0147-7
DB - Crossref
KW - Convex optimization
KW - Denoising
KW - Dictionary
KW - Dykstra-like algorithm
KW - Duality
KW - Forward-backward splitting
KW - Image reconstruction
KW - Image restoration
KW - Inverse problem
KW - Signal recovery
KW - Primal-dual algorithm
KW - Proximity operator
KW - Total variation
ER -
TY - JOUR
TI - Proximal Algorithms for Multicomponent Image Recovery Problems
AU - Briceño-Arias, L. M.
AU - Combettes, P. L.
AU - Pesquet, J.-C.
AU - Pustelnik, N.
T2 - Journal of Mathematical Imaging and Vision
AB - In recent years, proximal splitting algorithms have been applied to various monocomponent signal and image recovery problems. In this paper, we address the case of multicomponent problems. We first provide closed form expressions for several important multicomponent proximity operators and then derive extensions of existing proximal algorithms to the multicomponent setting. These results are applied to stereoscopic image recovery, multispectral image denoising, and image decomposition into texture and geometry components.
DA - 2010/12/21/
PY - 2010/12/21/
DO - 10.1007/s10851-010-0243-1
VL - 41
IS - 1-2
SP - 3-22
J2 - J Math Imaging Vis
LA - en
OP -
SN - 0924-9907 1573-7683
UR - http://dx.doi.org/10.1007/s10851-010-0243-1
DB - Crossref
KW - Convex minimization
KW - Image recovery
KW - Inverse problems
KW - Multicomponent images
KW - Multichannel images
KW - Multispectral images
KW - Proximal algorithm
KW - Sparsity
KW - Stereoscopy
KW - Wavelets
ER -
TY - JOUR
TI - Acyclic, or totally tight, two-person game forms: Characterization and main properties
AU - Boros, Endre
AU - Gurvich, Vladimir
AU - Makino, Kazuhisa
AU - Papp, Dávid
T2 - Discrete Mathematics
AB - It is known that a two-person game form g is Nash-solvable if and only if it is tight. We strengthen the concept of tightness as follows: a game form is called totally tight if each of its 2×2 subforms is tight. (It is easy to show that in this case all, not only 2×2, subforms are tight.) We characterize totally tight game forms, and derive from this characterization that they are tight, Nash-solvable, dominance-solvable, acyclic, and assignable. In particular, total tightness and acyclicity are equivalent properties of two-person game forms.
DA - 2010/4//
PY - 2010/4//
DO - 10.1016/j.disc.2009.11.009
VL - 310
IS - 6-7
SP - 1135-1151
J2 - Discrete Mathematics
LA - en
OP -
SN - 0012-365X
UR - http://dx.doi.org/10.1016/j.disc.2009.11.009
DB - Crossref
KW - Game
KW - Game form
KW - Effectivity function
KW - Improvement cycle
KW - Acyclic
KW - Assignable
KW - Tight
KW - Totally tight
KW - Nash-solvable
KW - Dominance-solvable
ER -
TY - JOUR
TI - Sonar Measurements in Ship Wakes Simultaneous With TerraSAR-X Overpasses
AU - Soloviev, A.
AU - Gilman, M.
AU - Young, K.
AU - Brusch, S.
AU - Lehner, S.
T2 - IEEE Transactions on Geoscience and Remote Sensing
AB - A pilot experiment was conducted in the period from April to June 2008 in the Straits of Florida near Port Everglades, Florida, in order to study the dynamics of far wakes of ships. In this experiment, a small boat with downward-looking sonar made ¿snakelike¿ sections through wakes of ships of opportunity during the *TerraSAR-X* overpasses. The ship and its parameters (length, speed, course, etc.) were identified utilizing an automated identification system. The sonar responded to the clouds of microbubbles generated in the ship wake by the propulsion system and ship-hull turbulence. The ship wakes were traced in the sonar signal typically from 10 to 30 min after the ship's passage. A preliminary analysis of the measurements suggests that the visibility of the centerline ship wake in synthetic aperture radar (SAR) images is correlated with the presence of microbubbles in the wake. This supports the hypothesis that natural surfactants scavenged and brought to the surface by rising bubbles play an important role in the wake visibility in SAR. The influence of the wind-wave field on the ship wake, as well as the effect of screening of the wind-wave field by the ship's hull, adds another level of complexity to wake patterns observed in SAR images.
DA - 2010/2//
PY - 2010/2//
DO - 10.1109/tgrs.2009.2032053
VL - 48
IS - 2
SP - 841-851
J2 - IEEE Trans. Geosci. Remote Sensing
OP -
SN - 0196-2892 1558-0644
UR - http://dx.doi.org/10.1109/tgrs.2009.2032053
DB - Crossref
KW - Geophysical measurements
KW - remote sensing
KW - sonar imaging
KW - synthetic aperture radar (SAR)
ER -
TY - JOUR
TI - On surface radiation conditions for an ellipse
AU - Medvinsky, M.
AU - Turkel, E.
T2 - Journal of Computational and Applied Mathematics
AB - We compare several On Surface Radiation Boundary Conditions in two dimensions, for solving the Helmholtz equation exterior to an ellipse. We also introduce a new boundary condition for an ellipse based on a modal expansion in Mathieu functions. We compare the OSRC to a finite difference method.
DA - 2010/7//
PY - 2010/7//
DO - 10.1016/j.cam.2009.08.011
VL - 234
IS - 6
SP - 1647-1655
J2 - Journal of Computational and Applied Mathematics
LA - en
OP -
SN - 0377-0427
UR - http://dx.doi.org/10.1016/j.cam.2009.08.011
DB - Crossref
KW - Helmholtz equation
KW - OSRC
KW - Mathieu functions
ER -
TY - JOUR
TI - An algorithmic Littlewood-Richardson rule
AU - Liu, Ricky Ini
T2 - Journal of Algebraic Combinatorics
AB - We introduce a Littlewood-Richardson rule based on an algorithmic deformation of skew Young diagrams and present a bijection with the classical rule. The result is a direct combinatorial interpretation and proof of the geometric rule presented by Coskun (2000). We also present a corollary regarding the Specht modules of the intermediate diagrams.
DA - 2010/1/21/
PY - 2010/1/21/
DO - 10.1007/s10801-009-0184-1
VL - 31
IS - 2
SP - 253-266
J2 - J Algebr Comb
LA - en
OP -
SN - 0925-9899 1572-9192
UR - http://dx.doi.org/10.1007/s10801-009-0184-1
DB - Crossref
KW - Littlewood-Richardson rule
KW - Specht modules
KW - Grassmannian
ER -
TY - JOUR
TI - Teaching Introductory Differential Equations with ScicosLab
AU - Campbell, Stephen
AU - Nikoukhah, Ramine
T2 - CODEE Journal
AB - Perhaps the largest and most capable open source software for doing applied mathematics is the open source package Scicoslab. Widely used in Europe and Asia it is less well known in the United States. In this article we will explain how ScicosLab can be easily used to help teach differential equations and to also introduce students to a software package that they can take with them for the rest of their careers.
DA - 2010///
PY - 2010///
DO - 10.5642/codee.201007.01.02
VL - 7
IS - 1
SP - 1-12
J2 - CODEE
OP -
SN - 2160-5211
UR - http://dx.doi.org/10.5642/codee.201007.01.02
DB - Crossref
ER -
TY - JOUR
TI - Local Hadamard well-posedness for nonlinear wave equations with supercritical sources and damping
AU - Bociu, Lorena
AU - Lasiecka, Irena
T2 - Journal of Differential Equations
AB - We consider the wave equation with supercritical interior and boundary sources and damping terms. The main result of the paper is local Hadamard well-posedness of finite energy (weak) solutions. The results obtained: (1) extend the existence results previously obtained in the literature (by allowing more singular sources); (2) show that the corresponding solutions satisfy Hadamard well-posedness conditions during the time of existence. This result provides a positive answer to an open question in the area and it allows for the construction of a strongly continuous semigroup representing the dynamics governed by the wave equation with supercritical sources and damping.
DA - 2010/8//
PY - 2010/8//
DO - 10.1016/j.jde.2010.03.009
VL - 249
IS - 3
SP - 654-683
J2 - Journal of Differential Equations
LA - en
OP -
SN - 0022-0396
UR - http://dx.doi.org/10.1016/j.jde.2010.03.009
DB - Crossref
KW - Wave equation
KW - Local existence
KW - Nonlinear damping
KW - Boundary source
KW - Interior source
KW - Critical exponents
ER -
TY - CHAP
TI - The Eigenproblem and Invariant Subspaces: Perturbation Theory
AU - Ipsen, Ilse C. F.
T2 - G.W. Stewart
AB - In this collection of papers, Pete Stewart established the foundations for the perturbation theory of invariant subspaces. He introduced two crucial concepts that allow a systematic approach toward such a perturbation theory: subspace rotation and operator separation. These two concepts form the guiding principle in most of these papers.
PY - 2010///
DO - 10.1007/978-0-8176-4968-5_7
SP - 71-93
OP -
PB - Birkhäuser Boston
SN - 9780817649678 9780817649685
UR - http://dx.doi.org/10.1007/978-0-8176-4968-5_7
DB - Crossref
ER -
TY - JOUR
TI - The random walk of Azospirillum brasilense
AU - Flores, Kevin
AU - Hadeler, K. P.
T2 - Journal of Biological Dynamics
AB - The bacterium Azospirillum brasilense has been frequently studied in laboratory experiments. It performs movements in space where long forward and backward runs on a straight line occur simultaneously with slow changes of direction of the line. A model is presented in which a correlated random walk on a line is joined to diffusion on a sphere of directions. For this transport system, a hierarchy of moment approximations is derived, ranging from a hyperbolic system with four dependent variables to a scalar damped wave equation (telegraph equation) and then to a single diffusion equation for particle density. The original parameters are compounded in the diffusion quotient. The effects of these parameters, such as particle speed or turning rate, on the diffusion coefficient are discussed in detail.
DA - 2010/1//
PY - 2010/1//
DO - 10.1080/17513750902773914
VL - 4
IS - 1
SP - 71-85
SN - 1751-3758 1751-3766
UR - http://dx.doi.org/10.1080/17513750902773914
ER -
TY - JOUR
TI - Irreducibility of a Symmetry Group Implies Isotropy
AU - Alexanderian, Alen
AU - Rathinam, Muruhan
AU - Rostamian, Rouben
T2 - Journal of Elasticity
DA - 2010/8/31/
PY - 2010/8/31/
DO - 10.1007/s10659-010-9268-3
VL - 102
IS - 2
SP - 151-174
J2 - J Elast
LA - en
OP -
SN - 0374-3535 1573-2681
UR - http://dx.doi.org/10.1007/s10659-010-9268-3
DB - Crossref
KW - Linear elasticity
KW - Isotropy
KW - Symmetry groups
KW - Group representation
KW - Schur's Lemma
KW - Random media
ER -
TY - THES
TI - Specht modules and Schubert varieties for general diagrams
AU - Liu, Ricky Ini
T2 - Thesis
DA - 2010/5//
PY - 2010/5//
M3 - PhD Thesis
UR - http://hdl.handle.net/1721.1/60196.
ER -
TY - JOUR
TI - The Baillon-Haddad theorem revisited
AU - Bauschke, H.H.
AU - Combettes, P.L.
T2 - Journal of Convex Analysis
DA - 2010/12//
PY - 2010/12//
VL - 17
IS - 4
SP - 781–787
ER -
TY - JOUR
TI - Normal binary graph models.
AU - Sullivant, Seth
T2 - Annals of the Institute of Statistical Mathematics, Special Issue: Algebraic Methods in Computational Statistics
DA - 2010///
PY - 2010///
VL - 64
IS - 4
SP - 717–726
ER -
TY - CHAP
TI - Maximum likelihood estimation in latent class models for contingency table data
AU - Fienberg, S. E.
AU - Hersh, P.
AU - Rinaldo, A.
AU - Zhou, Y.
T2 - Algebraic and Geometric Methods in Statistics
A2 - Gibilisco, Paolo
A2 - Riccomagno, Eva
A2 - Rogantin, Maria Piera
A2 - Wynn, Henry P.
AB - Statistical models with latent structure have a history going back to the 1950s and have seen widespread use in the social sciences and, more recently, in computational biology and in machine learning. Here we study the basic latent class model proposed originally by the sociologist Paul F. Lazarfeld for categorical variables, and we explain its geometric structure. We draw parallels between the statistical and geometric properties of latent class models and we illustrate geometrically the causes of many problems associated with maximum likelihood estimation and related statistical inference. In particular, we focus on issues of non-identifiability and determination of the model dimension, of maximisation of the likelihood function and on the effect of symmetric data. We illustrate these phenomena with a variety of synthetic and real-life tables, of different dimension and complexity. Much of the motivation for this work stems from the ‘100 Swiss Francs’ problem, which we introduce and describe in detail.
PY - 2010/7/1/
DO - 10.1017/cbo9780511642401.003
SP - 27-62
OP -
PB - Cambridge University Press
SN - 9780511642401
UR - http://dx.doi.org/10.1017/cbo9780511642401.003
DB - Crossref
ER -
TY - JOUR
TI - Radial Spreading of a Surfactant on a Thin Liquid Film
AU - Peterson, E. R.
AU - Shearer, M.
T2 - Applied Mathematics Research eXpress
AB - When a surfactant is placed on a layer of fluid, it reduces surface tension locally, creating a surface stress imbalance that sets the fluid in motion. The lubrication approximation is applied to axisymmetric spreading, yielding a coupled system of nonlinear partial differential equation for the height of the fluid free surface and the distribution of the surfactant. For a simplified system ignoring the effects of gravity and capillarity, as well as diffusion of surfactant molecules, the location of the surfactant can be tracked numerically. The free surface height converges quickly to a similarity form [Jensen, “Self-similar, surfactant-driven flows.” Physics of Fluids 6 (1994): 1084–94] away from the origin. Near the origin, a self-similar solution is identified, but it differs qualitatively from long-time numerical solutions. Including nonself-similar terms in an expansion around the origin corrects this inconsistency.
DA - 2010/9/13/
PY - 2010/9/13/
DO - 10.1093/amrx/abq015
VL - 9
J2 - Applied Mathematics Research eXpress
LA - en
OP -
SN - 1687-1200 1687-1197
UR - http://dx.doi.org/10.1093/amrx/abq015
DB - Crossref
ER -
TY - JOUR
TI - Evolution of a Mixing Zone in Granular Avalanches
AU - McIntyre, M.
AU - Rowe, E. L.
AU - Shearer, M.
AU - Gray, J. M. N. T.
AU - Thornton, A. R.
T2 - Applied Mathematics Research eXpress
AB - A nonlinear first-order partial differential equation in two space variables and time describes the process of kinetic sieving in an avalanche, in which larger particles tend to rise to the surface while smaller particles descend, quickly leading to completely segregated layers. The interface between layers is a shock wave satisfying its own nonlinear equation. When the interface becomes vertical, it loses stability, and develops a mixing zone. The mixing zone is described explicitly under idealized initial conditions, and verified with numerical simulation. The problem and its solution are similar to twodimensional Riemann problems for scalar first-order conservation laws; the difference here is that the equation is not scale-invariant, due to shear in the avalanche, an essential ingredient of kinetic sieving.
DA - 2010/7/9/
PY - 2010/7/9/
DO - 10.1093/amrx/abm008
VL - 7
J2 - Applied Mathematics Research eXpress
LA - en
OP -
SN - 1687-1200 1687-1197
UR - http://dx.doi.org/10.1093/amrx/abm008
DB - Crossref
ER -
TY - CONF
TI - The Gray-Thornton Model of Granular Segregation
AU - Shearer, Michael
AU - May, Lindsay B. H.
AU - Giffen, Nicholas
AU - Daniels, Karen E.
AU - Goddard, Joe
AU - Giovine, Pasquale
AU - Jenkins, James T.
T2 - IUTAM-ISIMM SYMPOSIUM ON MATHEMATICAL MODELING AND PHYSICAL INSTANCES OF GRANULAR FLOWS
AB - Views Icon Views Article contents Figures & tables Video Audio Supplementary Data Peer Review Share Icon Share Twitter Facebook Reddit LinkedIn Tools Icon Tools Reprints and Permissions Cite Icon Cite Search Site Citation Michael Shearer, Lindsay B. H. May, Nicholas Giffen, Karen E. Daniels; The Gray‐Thornton Model of Granular Segregation. AIP Conference Proceedings 5 May 2010; 1227 (1): 371–378. https://doi.org/10.1063/1.3435407 Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentAIP Publishing PortfolioAIP Conference Proceedings Search Advanced Search |Citation Search
C2 - 2010///
C3 -
DA - 2010///
DO - 10.1063/1.3435407
PB - AIP
UR - http://dx.doi.org/10.1063/1.3435407
DB - Crossref
KW - Segregation
KW - granular materials
KW - shock waves
KW - hyperbolic conservation laws
ER -
TY - JOUR
TI - Hypographs satisfying an external sphere condition and the regularity of the minimum time function
AU - Nguyen, Khai T.
T2 - Journal of Mathematical Analysis and Applications
AB - We prove that if the hypograph of a continuous function f admits at every boundary point a supporting ball then it has “essentially” positive reach, i.e. the hypograph of the restriction of f outside a closed set of zero measure has (locally) positive reach. Hence such a function enjoys some properties of a concave function, in particular a.e. twice differentiability. We apply this result to a minimum time problem in the case of a nonlinear smooth dynamics and a target satisfying internal sphere condition.
DA - 2010/12//
PY - 2010/12//
DO - 10.1016/j.jmaa.2010.07.010
VL - 372
IS - 2
SP - 611-628
J2 - Journal of Mathematical Analysis and Applications
LA - en
OP -
SN - 0022-247X
UR - http://dx.doi.org/10.1016/j.jmaa.2010.07.010
DB - Crossref
KW - Normal vectors
KW - phi-convex (prox-regular, positive reach) sets
KW - Internal/external sphere condition
ER -
TY - JOUR
TI - On the Structure of the Minimum Time Function
AU - Colombo, Giovanni
AU - Nguyen, Khai T.
T2 - SIAM Journal on Control and Optimization
AB - A minimum time problem with a nonlinear smooth dynamics and a target satisfying an internal sphere condition is considered. Under the assumption that the minimum time T be continuous and the normal cone to the hypograph of T, $N_{hypo(T)}$, be pointed, we show that $hypo(T)$ is $\varphi$-convex, i.e., satisfies a strong external sphere condition. Consequently, T is a.e. twice differentiable and satisfies some further regularity properties. Our results are based on a representation of Clarke generalized gradient of T. An example is provided, showing that if $N_{hypo(T)}$ is not pointed, then the result may fail.
DA - 2010/1//
PY - 2010/1//
DO - 10.1137/090774549
VL - 48
IS - 7
SP - 4776-4814
J2 - SIAM J. Control Optim.
LA - en
OP -
SN - 0363-0129 1095-7138
UR - http://dx.doi.org/10.1137/090774549
DB - Crossref
KW - normal vectors
KW - phi-convex (prox-regular, positive reach) sets
KW - internal sphere condition
KW - small time controllability
KW - adjoint flow
ER -
TY - JOUR
TI - On Orbit Decompositions for Symmetric k-Varieties
AU - Helminck, A. G.
T2 - SYMMETRY AND SPACES
AB - Orbit decompositions play a fundamental role in the study of symmetric k-varieties and their applications to representation theory and many other areas of mathematics, such as geometry, the study of automorphic forms and character sheaves. Symmetric k-varieties generalize symmetric varieties and are defined as the homogeneous spaces G k /H k , where G is a connected reductive algebraic group defined over a field k of characteristic not 2, H the fixed point group of an involution σ and G k (resp., H k ) the set of k-rational points of G (resp., H). In this contribution we give a survey of results on the various orbit decompositions which are of importance in the study of these symmetric k-varieties and their applications with an emphasis on orbits of parabolic k-subgroups acting on symmetric k-varieties. We will also discuss a number of open problems.
DA - 2010///
PY - 2010///
DO - 10.1007/978-0-8176-4875-6_6
VL - 278
SP - 83-127
SN - 0743-1643
KW - Symmetric spaces
KW - symmetric varieties
KW - involutions of algebraic groups
ER -
TY - JOUR
TI - Linear and Nonlinear Viscoelastic Modeling of Ovine Aortic Biomechanical Properties under in vivo and ex vivo Conditions
AU - Valdez-Jasso, D.
AU - Bia, D.
AU - Haider, M. A.
AU - Zocalo, Y.
AU - Armentano, R. L.
AU - Olufsen, M. S.
T2 - 2010 ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY (EMBC)
AB - This study uses linear and nonlinear viscoelastic models to describe the dynamic distention of the aorta induced by time-varying arterial blood pressure. We employ an inverse mathematical modeling approach on a four-parameter (linear) Kelvin viscoelastic model and two five-parameter nonlinear viscoelastic models (arctangent and sigmoid) to infer vascular biomechanical properties under in vivo and ex vivo experimental conditions in ten and eleven male Merino sheep, respectively. We used the Akaike Information Criterion (AIC) as a goodness-of-fit measure. Results show that under both experimental conditions, the nonlinear models generally outperform the linear Kelvin model, as judged by the AIC. Furthermore, the sigmoid nonlinear viscoelastic model consistently achieves the lowest AIC and also matches the zero-stress vessel radii measured ex vivo. Based on these observations, we conclude that the sigmoid nonlinear viscoelastic model best describes the biomechanical properties of ovine large arteries under both experimental conditions considered in this study.
DA - 2010///
PY - 2010///
DO - 10.1109/iembs.2010.5626563
SP - 2634-2637
SN - 1557-170X
ER -
TY - JOUR
TI - Efficiently Certifying Non-Integer Powers
AU - Kaltofen, Erich
AU - Lavin, Mark
T2 - COMPUTATIONAL COMPLEXITY
DA - 2010/9//
PY - 2010/9//
DO - 10.1007/s00037-010-0297-x
VL - 19
IS - 3
SP - 355-366
SN - 1420-8954
KW - Integer roots
KW - integer powers
KW - linear-time algorithm
KW - bit complexity
KW - Chebotarev density theorem
ER -
TY - JOUR
TI - ADDENDUM TO "DRINFELD REALIZATION OF TWISTED QUANTUM AFFINE ALGEBRAS"
AU - Jing, Naihuan
AU - Zhang, Honglian
T2 - COMMUNICATIONS IN ALGEBRA
AB - We provide necessary details to several arguments that appeared in our previous paper “Drinfeld Realization of Twisted Quantum Affine Algebras,” Commun. Algebra 35 (2007) 3683–3698.
DA - 2010///
PY - 2010///
DO - 10.1080/00927870902933213
VL - 38
IS - 9
SP - 3484-3488
SN - 1532-4125
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-77957732758&partnerID=MN8TOARS
KW - Drinfield realization
KW - Quantum affine algebras
ER -
TY - JOUR
TI - Scalar Conservation Laws with Nonconstant Coefficients with Application to Particle Size Segregation in Granular Flow
AU - May, Lindsay B. H.
AU - Shearer, Michael
AU - Daniels, Karen E.
T2 - Journal of Nonlinear Science
AB - Granular materials will segregate by particle size when subjected to shear, as occurs, for example, in avalanches. The evolution of a bidisperse mixture of particles can be modeled by a nonlinear first order partial differential equation, provided the shear (or velocity) is a known function of position. While avalanche-driven shear is approximately uniform in depth, boundary-driven shear typically creates a shear band with a nonlinear velocity profile. In this paper, we measure a velocity profile from experimental data and solve initial value problems that mimic the segregation observed in the experiment, thereby verifying the value of the continuum model. To simplify the analysis, we consider only one-dimensional configurations, in which a layer of small particles is placed above a layer of large particles within an annular shear cell and is sheared for arbitrarily long times. We fit the measured velocity profile to both an exponential function of depth and a piecewise linear function which separates the shear band from the rest of the material. Each solution of the initial value problem is nonstandard, involving curved characteristics in the exponential case, and a material interface with a jump in characteristic speed in the piecewise linear case.
DA - 2010/5/5/
PY - 2010/5/5/
DO - 10.1007/s00332-010-9069-7
VL - 20
IS - 6
SP - 689-707
J2 - J Nonlinear Sci
LA - en
OP -
SN - 0938-8974 1432-1467
UR - http://dx.doi.org/10.1007/s00332-010-9069-7
DB - Crossref
KW - Conservation laws
KW - First order partial differential equations
KW - Granular flow
KW - Particle segregation
ER -
TY - JOUR
TI - THE RELATIVE FRAME BUNDLE OF AN INFINITE-DIMENSIONAL FLAG VARIETY AND SOLUTIONS OF INTEGRABLE HIERARCHIES
AU - Helminck, G. F.
AU - Helminck, A. G.
AU - Opimakh, A. V.
T2 - THEORETICAL AND MATHEMATICAL PHYSICS
DA - 2010/12//
PY - 2010/12//
DO - 10.1007/s11232-010-0133-0
VL - 165
IS - 3
SP - 1610-1636
SN - 0040-5779
KW - upper-triangular Z x Z matrices
KW - Lax equations
KW - zero curvature form
ER -
TY - JOUR
TI - STABILITY OF TRAVELING WAVES FOR A CLASS OF REACTION-DIFFUSION SYSTEMS THAT ARISE IN CHEMICAL REACTION MODELS
AU - Ghazaryan, Anna
AU - Latushkin, Yuri
AU - Schecter, Stephen
T2 - SIAM JOURNAL ON MATHEMATICAL ANALYSIS
AB - Stability results are proved for traveling waves in a class of reaction-diffusion systems that arise in chemical reaction models. The class includes systems in which there is no diffusion in some equations. A weight function that decays exponentially at one end is required to stabilize the essential spectrum. Perturbations of the wave in $H^1$ or $BUC$ that are small in both the weighted norm and the unweighted norm are shown to stay small in the unweighted norm and to decay exponentially to a shift of the traveling wave in the weighted norm. Perturbations that are in addition small in the $L^1$ norm decay algebraically to a shift of the wave in the $L^\infty$ norm. A decomposition of the variables that yields a triangular structure for the linearization at one end of the wave is exploited to prove the results. An application to exothermic-endothermic reactions is given.
DA - 2010///
PY - 2010///
DO - 10.1137/100786204
VL - 42
IS - 6
SP - 2434-2472
SN - 0036-1410
KW - traveling wave
KW - nonlinear stability
KW - reaction-diffusion system
KW - degenerate diffusion matrix
KW - weighted norm
KW - combustion
ER -
TY - JOUR
TI - Proper Orthogonal Decomposition with Updates for Efficient Control Design in Smart Material Systems
AU - May, Stephen F.
AU - Smith, Ralph C.
T2 - BEHAVIOR AND MECHANICS OF MULTIFUNCTIONAL MATERIALS AND COMPOSITES 2010
AB - Proper orthogonal decomposition (POD) is a basis reduction technique that allows simulations of complicated systems to be calculated at faster speeds with minimal loss of accuracy. The reduced order basis is created from a set of system data called snapshots. The speed and information retention of POD make it an attractive method to implement reduced-order models of smart material systems. This can allow for the modeling of larger systems and the implementation of real time control, which may be impossible when using the full-order system. There are times when the dynamics of a system can change during a simulation, and the addition of more information to the set of snapshots would be beneficial. The implementation of control on a system is a time when adding new snapshots to the collection can increase the accuracy of the model. Using updates allows more flexibility when trying to balance the accuracy and the speed of the simulation. By updating the POD basis at specific times throughout the interval, we can increase the accuracy of the model and control by using a greater amount of the information given by the snapshots, while we can increase the speed of the simulation during times when using less information will still result in sufficient accuracy.
DA - 2010///
PY - 2010///
DO - 10.1117/12.847579
VL - 7644
SP -
SN - 0277-786X
KW - Smart materials
KW - proper orthogonal decomposition
KW - control
ER -
TY - JOUR
TI - Inverse Model Construction for Control Implementation of Macro Fiber Composite Actuators Operating in Hysteretic Regimes
AU - Stuebner, Michael
AU - Smith, Ralph C.
T2 - BEHAVIOR AND MECHANICS OF MULTIFUNCTIONAL MATERIALS AND COMPOSITES 2010
AB - Macro Fiber Composite (MFC) actuators utilize PZT fibers embedded in an epoxy matrix for structural actuation.
Due to their construction, they are lightweight and provide broadband inputs. Significant advantages of
MFC actuators are their high performance, durability, and flexibility when compared to traditional piezoceramic
actuators. They are presently being considered for a range of applications including positioning of membrane
mirrors and structural control in the aerospace and automotive industry. However, they exhibit varying degrees of
hysteresis and constitutive nonlinearities throughout their operating range that must be incorporated in models
to achieve the full capabilities of the materials. In this paper, hysteresis is modeled using the homogenized energy
model. The inverse model is then used to construct an inverse compensator framework suitable for subsequent
control design. The performance of the inverse compensator is illustrated through a numerical example.
DA - 2010///
PY - 2010///
DO - 10.1117/12.848256
VL - 7644
SP -
SN - 0277-786X
KW - Hysteretic systems
KW - Inverse compensator
ER -
TY - JOUR
TI - Design of RF MEMS Switches without Pull-in Instability
AU - Proctor, W. Cyrus
AU - Richards, Gregory P.
AU - Shen, Chongyi
AU - Skorczewski, Tyler
AU - Wang, Min
AU - Zhang, Jingyan
AU - Zhong, Peng
AU - Massad, Jordan E.
AU - Smith, Ralph
T2 - BEHAVIOR AND MECHANICS OF MULTIFUNCTIONAL MATERIALS AND COMPOSITES 2010
AB - Micro-electro-mechanical systems (MEMS) switches for radio-frequency (RF) signals have certain advantages over solid-state switches, such as lower insertion loss, higher isolation, and lower static power dissipation. Mechanical dynamics can be a determining factor for the reliability of RF MEMS. The RF MEMS ohmic switch discussed in this paper consists of a plate suspended over an actuation pad by four double-cantilever springs. Closing the switch with a simple step actuation voltage typically causes the plate to rebound from its electrical contacts. The rebound interrupts the signal continuity and degrades the performance, reliability and durability of the switch. The switching dynamics are complicated by a nonlinear, electrostatic pull-in instability that causes high accelerations. Slow actuation and tailored voltage control signals can mitigate switch bouncing and effects of the pull-in instability; however, slow switching speed and overly-complex input signals can significantly penalize overall system-level performance. Examination of a balanced and optimized alternative switching solution is sought. A step toward one solution is to consider a pull-in-free switch design. In this paper, determine how simple RC-circuit drive signals and particular structural properties influence the mechanical dynamics of an RF MEMS switch designed without a pull-in instability. The approach is to develop a validated modeling capability and subsequently study switch behavior for variable drive signals and switch design parameters. In support of project development, specifiable design parameters and constraints will be provided. Moreover, transient data of RF MEMS switches from laser Doppler velocimetry will be provided for model validation tasks. Analysis showed that a RF MEMS switch could feasibly be designed with a single pulse waveform and no pull-in instability and achieve comparable results to previous waveform designs. The switch design could reliably close in a timely manner, with small contact velocity, usually with little to no rebound even when considering manufacturing variability.
DA - 2010///
PY - 2010///
DO - 10.1117/12.848045
VL - 7644
SP -
SN - 1996-756X
ER -
TY - JOUR
TI - A discrete events delay differential system model for transmission of Vancomycin-resistant enterococcus (VRE) in hospitals
AU - Ortiz, A.
AU - Banks, H. T.
AU - Castillo-Chavez, C.
AU - Chowell, G.
AU - Wang, X. H.
T2 - Journal of Inverse and Ill-Posed Problems
DA - 2010///
PY - 2010///
VL - 18
IS - 7
SP - 787-821
ER -
TY - JOUR
TI - THE LINK BETWEEN REGULARITY AND STRONG-PI-REGULARITY
AU - Patricio, Pedro
AU - Hartwig, R. E.
T2 - JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY
AB - Abstract It is shown that if all powers of a ring element a are regular, then a is strongly pi-regular exactly when a suitable word in the powers of a and their inner inverses is a unit.
DA - 2010/8//
PY - 2010/8//
DO - 10.1017/s1446788710001448
VL - 89
IS - 1
SP - 17-22
SN - 1446-8107
KW - Drazin inverse
KW - strongly pi-regular
KW - Drazin index
ER -
TY - JOUR
TI - SYSTEMS OF HYPERBOLIC CONSERVATION LAWS WITH PRESCRIBED EIGENCURVES
AU - Jenssen, Helge Kristian
AU - Kogan, Irina A.
T2 - JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS
AB - We study the problem of constructing systems of hyperbolic conservation laws in one space dimension with prescribed eigencurves, i.e. the eigenvector fields of the Jacobian of the flux are given. We formulate this as a typically overdetermined system of equations for the eigenvalues-to-be. Equivalent formulations in terms of differential and algebraic-differential equations are considered. The resulting equations are then analyzed using appropriate integrability theorems (Frobenius, Darboux and Cartan–Kähler). We give a complete analysis of the possible scenarios, including examples, for systems of three equations. As an application we characterize conservative systems with the same eigencurves as the Euler system for 1-dimensional compressible gas dynamics. The case of general rich systems of any size (i.e. when the given eigenvector fields are pairwise in involution; this includes all systems of two equations) is completely resolved and we consider various examples in this class.
DA - 2010/6//
PY - 2010/6//
DO - 10.1142/s021989161000213x
VL - 7
IS - 2
SP - 211-254
SN - 1793-6993
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-77954208923&partnerID=MN8TOARS
KW - Hyperbolic systems of conservation laws
KW - eigenvector fields
KW - eigenvalues
KW - rich systems
KW - Frobenius, Darboux and Cartan-Kahler integrability theorems
KW - connections on frame bundles
ER -
TY - JOUR
TI - Efficient Solution of the Wigner-Poisson Equation for Modeling Resonant Tunneling Diodes
AU - Costolanski, Anne S
AU - Kelley, C T
T2 - IEEE Transactions on Nanotechnology
AB - A more efficient and accurate discretization of the Wigner-Poisson model for double barrier resonant tunneling diodes is presented. This new implementation uses nonuniform grids and higher order numerical methods to improve the accuracy of the solutions at a significantly lower computational cost. Using the new implementation, devices with short and long contact regions are analyzed as well as the effect of a correlation length parameter that defines the degree of nonlocality effects. The results show that devices with longer contact regions reduce numerical inconsistencies present when modeling shorter devices, and that longer correlation lengths generally improve the correspondence of the numerical solutions with those typically expected from experimental measurement. These new numerical simulation tools will enable researchers to successfully apply the Wigner-Poisson model to describe electron transport in nanoscale semiconductor tunneling devices. More specifically, the computationally more efficient numerical algorithms presented will be shown to allow for the quantum-based studies of resonant tunneling devices useful as sources and detectors at very high frequencies (e.g., THz regime). These types of devices are very important for use in sensors and sensing systems where very long wavelength characterization capabilities are important (e.g., interrogation of chemical and biological systems) as well as an array of other electronics applications.
DA - 2010///
PY - 2010///
DO - 10.1109/tnano.2010.2053214
VL - 9
IS - 6
SP - 708-715
ER -
TY - JOUR
TI - Viscous-slip, thermal-slip, and temperature-jump coefficients based on the linearized Boltzmann equation (and five kinetic models) with the Cercignani-Lampis boundary condition
AU - Garcia, R. D. M.
AU - Siewert, C. E.
T2 - EUROPEAN JOURNAL OF MECHANICS B-FLUIDS
AB - A polynomial expansion procedure and the ADO (analytical discrete-ordinates) method are used to compute the viscous-slip coefficient, the thermal-slip coefficient, and the temperature-jump coefficient from the linearized Boltzmann equation (LBE) for rigid-sphere interactions and the Cercignani–Lampis (CL) boundary condition. These same quantities are also computed from five kinetic models, with the CL condition, and compared to the LBE result. Equivalent results for the LBE and the kinetic models, all based on the usual Maxwell boundary condition, are also reported.
DA - 2010///
PY - 2010///
DO - 10.1016/j.euromechflu.2010.01.005
VL - 29
IS - 3
SP - 181-191
SN - 1873-7390
KW - Rarefied gas dynamics
KW - Linearized Boltzmann equation
KW - Cercignani-Lampis boundary condition
KW - Viscous-slip coefficient
KW - Thermal-slip coefficient
KW - Temperature-jump coefficient
ER -
TY - JOUR
TI - Stability of Gasless Combustion Fronts in One-Dimensional Solids
AU - Ghazaryan, Anna
AU - Latushkin, Yuri
AU - Schecter, Stephen
AU - Souza, Aparecido J.
T2 - ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
DA - 2010/12//
PY - 2010/12//
DO - 10.1007/s00205-010-0358-y
VL - 198
IS - 3
SP - 981-1030
SN - 1432-0673
ER -
TY - JOUR
TI - SEMISMOOTH NEWTON METHODS FOR TIME-OPTIMAL CONTROL FOR A CLASS OF ODES
AU - Ito, Kazufumi
AU - Kunisch, Karl
T2 - SIAM JOURNAL ON CONTROL AND OPTIMIZATION
AB - Time-optimal control problems for a class of linear multi-input systems are considered. The problems are regularized and the asymptotic and monotone behavior of the regularization procedure is investigated. For the regularized problems the applicability of semismooth Newton methods is verified. First numerical tests are presented which show that the proposed approach is different from other methods in that it does not rely on a priori information about the switching structure.
DA - 2010///
PY - 2010///
DO - 10.1137/090753905
VL - 48
IS - 6
SP - 3997-4013
SN - 1095-7138
KW - semismooth Newton method
KW - time-optimal control
ER -
TY - JOUR
TI - On vertex operator realizations of Jack functions
AU - Cai, Wuxing
AU - Jing, Naihuan
T2 - JOURNAL OF ALGEBRAIC COMBINATORICS
AB - On the vertex operator algebra associated with a rank one lattice we derive a general formula for products of vertex operators in terms of generalized homogeneous symmetric functions. As an application we realize Jack symmetric functions of rectangular shapes as well as marked rectangular shapes.
DA - 2010/12//
PY - 2010/12//
DO - 10.1007/s10801-010-0228-6
VL - 32
IS - 4
SP - 579-595
SN - 0925-9899
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-78049527579&partnerID=MN8TOARS
KW - Symmetric functions
KW - Jack polynomials
KW - Vertex operators
ER -
TY - JOUR
TI - ON SCHUR MULTIPLIERS OF LIE ALGEBRAS AND GROUPS OF MAXIMAL CLASS
AU - Bosko, Lindsey R.
T2 - INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION
AB - The Lie algebra analogue to the Schur multiplier has been investigated in a number of recent articles. We consider the multipliers of Lie algebras of maximal class, classifying these algebras with a certain additional property. The classification leads to a conjecture about a bound on the dimension of the multiplier for each of these algebras and also for p-groups of maximal class. The conjectures are then shown to hold.
DA - 2010/9//
PY - 2010/9//
DO - 10.1142/s0218196710005881
VL - 20
IS - 6
SP - 807-821
SN - 0218-1967
KW - Schur multiplier
KW - maximal class
KW - filiform
ER -
TY - JOUR
TI - Marker-assisted selection for coupling phase resistance to tomato spotted wilt virus and phytophthora infestans (late blight) in tomato
AU - Robbins, M. D.
AU - Masud, M. A. T.
AU - Panthee, D. R.
AU - Gardner, R. G.
AU - Francis, D. M.
AU - Stevens, M. R.
T2 - HortScience
DA - 2010///
PY - 2010///
VL - 45
IS - 10
SP - 1424-1428
ER -
TY - JOUR
TI - Label structured cell proliferation models
AU - Banks, H. T.
AU - Charles, Frederique
AU - Jauffret, Marie Doumic
AU - Sutton, Karyn L.
AU - Thompson, W. Clayton
T2 - APPLIED MATHEMATICS LETTERS
AB - We present a general class of cell population models that can be used to track the proliferation of cells which have been labeled with a fluorescent dye. The mathematical models employ fluorescence intensity as a structure variable to describe the evolution in time of the population density of proliferating cells. While cell division is a major component of changes in cellular fluorescence intensity, models developed here also address overall label degradation.
DA - 2010/12//
PY - 2010/12//
DO - 10.1016/j.aml.2010.07.009
VL - 23
IS - 12
SP - 1412-1415
SN - 0893-9659
KW - Cell proliferation
KW - Label structured population dynamics
KW - Partial differential equations
KW - Moving coordinate systems
ER -
TY - JOUR
TI - Heteroclinic Orbits in Slow-Fast Hamiltonian Systems with Slow Manifold Bifurcations
AU - Schecter, Stephen
AU - Sourdis, Christos
T2 - JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
DA - 2010/12//
PY - 2010/12//
DO - 10.1007/s10884-010-9171-4
VL - 22
IS - 4
SP - 629-655
SN - 1040-7294
KW - Geometric singular perturbation theory
KW - Blow-up
KW - Pitchfork bifurcation
KW - Transcritical bifurcation
ER -
TY - JOUR
TI - Grape tomato breeding lines: NC 1 Grape, NC 2 Grape, and NC 3 Grape
AU - Gardner, R. G.
AU - Panthee, D. R.
T2 - HortScience
DA - 2010///
PY - 2010///
VL - 45
IS - 12
SP - 1887-1888
ER -
TY - JOUR
TI - DYNAMIC SOCIAL NETWORK MODELS INCORPORATING STOCHASTICITY AND DELAYS
AU - Banks, H. T.
AU - Rehm, Keri
AU - Sutton, Karyn L.
T2 - QUARTERLY OF APPLIED MATHEMATICS
AB - Networks are typically studied via computational models, and often investigations are restricted to the static case. Here we extend the work in Banks, Karr, Nguyen and Samuels (2008), which demonstrated a simple dynamical system framework in which to study social network behavior, to include a discrete delay. This delay represents the time lag that is likely required for an agent to change his/her own characteristics (e.g., opinions, viewpoints or behavior) after interacting with an agent possessing different characteristics. Thus this modification adds significantly to the relevance of the model in many potential applications. We have shown that the delays can be incorporated into a stochastic differential equations (SDE) framework in an efficient and computationally tractable way. Through numerical studies, we see novel outcomes when stochasticity, delay, or both are considered, demonstrating the need to include these features should they be present in the network application.
DA - 2010/12//
PY - 2010/12//
DO - 10.1090/s0033-569x-2010-01201-x
VL - 68
IS - 4
SP - 783-802
SN - 1552-4485
KW - Social networks
KW - stochastic differential equations
KW - delay differential equations
KW - clustering
ER -
TY - JOUR
TI - A Non-linear Optimal Control Design using Narrowband Perturbation Feedback for Magnetostrictive Actuators
AU - Oates, William S.
AU - Zrostlik, Rick
AU - Eichhorn, Scott
AU - Smith, Ralph
T2 - JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES
AB - Non-linear optimal and narrowband feedback control designs are developed and experimentally implemented on a magnetostrictive Terfenol-D actuator. The non-linear optimal control design incorporates a non-linear and hysteretic ferromagnetic homogenized energy model within an optimal control formulation to reduce displacement tracking errors and increase bandwidth. Improvements in robustness in the steady-state regime are achieved by utilizing narrowband feedback. A narrowband filter is implemented by treating the nonlinear and hysteretic magnetostrictive constitutive behavior as higher-order harmonic disturbances which are mitigated by tuning the narrowband filter to penalize these harmonics for displacement tracking control problems. The control designs are then combined into a hybrid optimal controller with perturbation narrowband feedback. Both transient and steady-state tracking control is assessed to illustrate performance attributes in different operating regimes. Narrowband perturbation feedback is shown to mitigate errors in the steady-state operating regime, while non-linear optimal control provides enhanced tracking control in the transient regime. The hybrid control design is relevant to a broad number of smart material actuators that exhibit non-linear and hysteretic field-coupled constitutive behavior.
DA - 2010/11//
PY - 2010/11//
DO - 10.1177/1045389x10386398
VL - 21
IS - 16
SP - 1681-1693
SN - 1530-8138
KW - magnetostrictive
KW - narrowband control
KW - hysteresis
KW - non-linear optimal control
ER -
TY - JOUR
TI - 'Mountain Merit': A late blight-resistant large-fruited tomato hybrid
AU - Panthee, D. R.
AU - Gardner, R. G.
T2 - HortScience
DA - 2010///
PY - 2010///
VL - 45
IS - 10
SP - 1547-1548
ER -
TY - JOUR
TI - TREK SEPARATION FOR GAUSSIAN GRAPHICAL MODELS
AU - Sullivant, Seth
AU - Talaska, Kelli
AU - Draisma, Jan
T2 - ANNALS OF STATISTICS
AB - Gaussian graphical models are semi-algebraic subsets of the cone of positive definite covariance matrices. Submatrices with low rank correspond to generalizations of conditional independence constraints on collections of random variables. We give a precise graph-theoretic characterization of when submatrices of the covariance matrix have small rank for a general class of mixed graphs that includes directed acyclic and undirected graphs as special cases. Our new trek separation criterion generalizes the familiar $d$-separation criterion. Proofs are based on the trek rule, the resulting matrix factorizations and classical theorems of algebraic combinatorics on the expansions of determinants of path polynomials.
DA - 2010/6//
PY - 2010/6//
DO - 10.1214/09-aos760
VL - 38
IS - 3
SP - 1665-1685
SN - 0090-5364
KW - Graphical model
KW - Bayesian network
KW - Gessel-Viennot-Lindstrom lemma
KW - trek rule
KW - linear regression
KW - conditional independence
ER -
TY - JOUR
TI - Standard error computations for uncertainty quantification in inverse problems: Asymptotic theory vs. bootstrapping
AU - Banks, H. T.
AU - Holm, Kathleen
AU - Robbins, Danielle
T2 - MATHEMATICAL AND COMPUTER MODELLING
AB - We computationally investigate two approaches for uncertainty quantification in inverse problems for nonlinear parameter dependent dynamical systems. We compare the bootstrapping and asymptotic theory approaches for problems involving data with several noise forms and levels. We consider both constant variance absolute error data and relative error which produces non-constant variance data in our parameter estimation formulations. We compare and contrast parameter estimates, standard errors, confidence intervals, and computational times for both bootstrapping and asymptotic theory methods.
DA - 2010/11//
PY - 2010/11//
DO - 10.1016/j.mcm.2010.06.026
VL - 52
IS - 9-10
SP - 1610-1625
SN - 0895-7177
KW - Parameter estimation
KW - Bootstrapping
KW - Asymptotic standard errors
ER -
TY - JOUR
TI - Shear-driven size segregation of granular materials: Modeling and experiment
AU - May, Lindsay B. H.
AU - Golick, Laura A.
AU - Phillips, Katherine C.
AU - Shearer, Michael
AU - Daniels, Karen E.
T2 - PHYSICAL REVIEW E
AB - Granular materials segregate by size under shear, and the ability to quantitatively predict the time required to achieve complete segregation is a key test of our understanding of the segregation process. In this paper, we apply the Gray-Thornton model of segregation (developed for linear shear profiles) to a granular flow with an exponential shear profile, and evaluate its ability to describe the observed segregation dynamics. Our experiment is conducted in an annular Couette cell with a moving lower boundary. The granular material is initially prepared in an unstable configuration with a layer of small particles above a layer of large particles. Under shear, the sample mixes and then resegregates so that the large particles are located in the top half of the system in the final state. During this segregation process, we measure the velocity profile and use the resulting exponential fit as input parameters to the model. To make a direct comparison between the continuum model and the observed segregation dynamics, we map the local concentration (from the model) to changes in packing fraction; this provides a way to make a semiquantitative comparison with the measured global dilation. We observe that the resulting model successfully captures the presence of a fast mixing process and relatively slower resegregation process, but the model predicts a finite resegregation time, while in the experiment resegregation occurs only exponentially in time.
DA - 2010/5//
PY - 2010/5//
DO - 10.1103/physreve.81.051301
VL - 81
IS - 5
SP -
SN - 1550-2376
ER -
TY - JOUR
TI - Normal binary graph models
AU - Sullivant, Seth
T2 - ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS
AB - We show that the marginal semigroup of a binary graph model is normal if and only if the graph is free of K 4 minors. The technique, based on the interplay of normality and the geometry of the marginal cone, has potential applications to other normality questions in algebraic statistics.
DA - 2010/8//
PY - 2010/8//
DO - 10.1007/s10463-010-0296-3
VL - 62
IS - 4
SP - 717-726
SN - 0020-3157
KW - Marginal cone
KW - Normal semigroup
KW - Algebraic statistics
ER -
TY - JOUR
TI - NC 1 CELBR and NC 2 CELBR: Early blight and late blight-resistant fresh market tomato breeding lines
AU - Gardner, R. G.
AU - Panthee, D. R.
T2 - HortScience
DA - 2010///
PY - 2010///
VL - 45
IS - 6
SP - 975-976
ER -
TY - JOUR
TI - Monte Carlo calibration of the response of the University of Chicago's Cosmic Ray Nuclei Experiment (CRNE) on IMP-8 to electrons above 0.5 MeV
AU - Novikova, E. I.
AU - Dietrich, W. F.
AU - Tylka, A. J.
AU - Collins, J.
AU - Phlips, B. F.
T2 - Journal of Engineered Fibers and Fabrics
DA - 2010///
PY - 2010///
VL - 46
IS - 1
SP - 31-43
ER -
TY - JOUR
TI - Filtering Turbulent Sparsely Observed Geophysical Flows
AU - Harlim, John
AU - Majda, Andrew J.
T2 - MONTHLY WEATHER REVIEW
AB - Abstract Filtering sparsely turbulent signals from nature is a central problem of contemporary data assimilation. Here, sparsely observed turbulent signals from nature are generated by solutions of two-layer quasigeostrophic models with turbulent cascades from baroclinic instability in two separate regimes with varying Rossby radius mimicking the atmosphere and the ocean. In the “atmospheric” case, large-scale turbulent fluctuations are dominated by barotropic zonal jets with non-Gaussian statistics while the “oceanic” case has large-scale blocking regime transitions with barotropic zonal jets and large-scale Rossby waves. Recently introduced, cheap radical linear stochastic filtering algorithms utilizing mean stochastic models (MSM1, MSM2) that have judicious model errors are developed here as well as a very recent cheap stochastic parameterization extended Kalman filter (SPEKF), which includes stochastic parameterization of additive and multiplicative bias corrections “on the fly.” These cheap stochastic reduced filters as well as a local least squares ensemble adjustment Kalman filter (LLS-EAKF) are compared on the test bed with 36 sparse regularly spaced observations for their skill in recovering turbulent spectra, spatial pattern correlations, and RMS errors. Of these four algorithms, the cheap SPEKF algorithm has the superior overall skill on the stringent test bed, comparable to LLS-EAKF in the atmospheric regime with and without model error and far superior to LLS-EAKF in the ocean regime. LLS-EAKF has special difficulty and high computational cost in the ocean regime with small Rossby radius, which creates stiffness in the perfect dynamics. The even cheaper mean stochastic model, MSM1, has high skill, which is comparable to SPEKF for the oceanic case while MSM2 has significantly worse filtering performance than MSM1 with the same inexpensive computational cost. This is interesting because MSM1 is based on a simple new regression strategy while MSM2 relies on the conventional regression strategy used in stochastic models for shear turbulence.
DA - 2010/4//
PY - 2010/4//
DO - 10.1175/2009mwr3113.1
VL - 138
IS - 4
SP - 1050-1083
SN - 1520-0493
ER -
TY - JOUR
TI - Application of Scale-Selective Data Assimilation to Regional Climate Modeling and Prediction
AU - Peng, Shiqiu
AU - Xie, Lan
AU - Liu, Bin
AU - Semazzi, Fredrick
T2 - MONTHLY WEATHER REVIEW
AB - Abstract A method referred to as scale-selective data assimilation (SSDA) is designed to inject the large-scale components of the atmospheric circulation from a global model into a regional model to improve regional climate simulations and predictions. The SSDA is implemented through the following procedure: 1) using a low-pass filter to extract the large-scale components of the atmospheric circulation from global analysis or model forecasts; 2) applying the filter to extract the regional-scale and the large-scale components of the atmospheric circulation from the regional model simulations or forecasts; 3) assimilating the large-scale circulation obtained from the global model into the corresponding component simulated by the regional model using the method of three-dimensional variational data assimilation (3DVAR) while maintaining the small-scale components from the regional model during the assimilation cycle; 4) combining the small-scale and the assimilated large-scale components as the adjusted forecasts by the regional climate model and allowing the two components to mutually adjust outside the data assimilation cycle. A case study of summer 2005 seasonal climate hindcasting for the regions of the Atlantic and the eastern United States indicates that the large-scale components from the Global Forecast System (GFS) analysis can be effectively assimilated into the regional model using the scale-selective data assimilation method devised in this study, resulting in an improvement in the overall results from the regional climate model.
DA - 2010/4//
PY - 2010/4//
DO - 10.1175/2009mwr2974.1
VL - 138
IS - 4
SP - 1307-1318
SN - 1520-0493
ER -
TY - JOUR
TI - The (2,2,0) group inverse problem
AU - Patricio, P.
AU - Hartwig, R. E.
T2 - APPLIED MATHEMATICS AND COMPUTATION
AB - Abstract We characterize the existence of the group inverse of a two by two matrix with zero (2, 2) entry, over a ring by means of the existence of the inverse of a suitable function of the other three entries. Some special cases are derived.
DA - 2010/9/15/
PY - 2010/9/15/
DO - 10.1016/j.amc.2010.05.084
VL - 217
IS - 2
SP - 516-520
SN - 0096-3003
KW - Group inverse
KW - Block matrices
ER -
TY - JOUR
TI - Quantitative Models for Germination and Infection of Pseudoperonospora cubensis in Response to Temperature and Duration of Leaf Wetness
AU - Arauz, L. F.
AU - Neufeld, K. N.
AU - Lloyd, A. L.
AU - Ojiambo, P. S.
T2 - PHYTOPATHOLOGY
AB - The influence of temperature and leaf wetness duration on germination of sporangia and infection of cantaloupe leaves by Pseudoperonospora cubensis was examined in three independent controlled-environment experiments by inoculating plants with a spore suspension and exposing them to a range of leaf wetness durations (2 to 24 h) at six fixed temperatures (5 to 30°C). Germination of sporangia was assessed at the end of each wetness period and infection was evaluated from assessments of disease severity 5 days after inoculation. Three response surface models based on modified forms of the Weibull function were evaluated for their ability to describe germination of sporangia and infection in response to temperature and leaf wetness duration. The models estimated 15.7 to 17.3 and 19.5 to 21.7°C as the optimum temperature (t) range for germination and infection, respectively, with little germination or infection at 5 or 30°C. For wetness periods of 4 to 8 h, a distinct optimum for infection was observed at t = 20°C but broader optimum curves resulted from wetness periods >8 h. Model 1 of the form f(w,t) = f(t) × (1 – exp{–[B × w] D }) resulted in smaller asymptotic standard errors and yielded higher correlations between observed and predicted germination and infection data than either model 2 of the form f(w,t) = A(1 – exp{– [f(t) × (w – C)] D }) or model 3 of the form f(w,t) = [1 – exp{–(B × w) 2 }]/cosh[(t – F)G/2]. Models 1 and 2 had nonsignificant lack-of-fit test statistics for both germination and infection data, whereas a lack-of-fit test was significant for model 3. The models accounted for ≈87% (model 3) to 98% (model 1) of the total variation in the germination and infection data. In the validation of the models using data generated with a different isolate of P. cubensis, slopes of the regression line between observed and predicted germination and infection data were not significantly different (P > 0.2487) and correlation coefficients between observed and predicted values were high (r 2 > 0.81). Models 1 and 2 were used to construct risk threshold charts that can be used to estimate the potential risk for infection based on observed or forecasted temperature and leaf wetness duration.
DA - 2010/9//
PY - 2010/9//
DO - 10.1094/phyto-100-9-0959
VL - 100
IS - 9
SP - 959-967
SN - 1943-7684
KW - cucurbit downy mildew
KW - disease forecasting
ER -
TY - JOUR
TI - Optimal control of parabolic variational inequalities
AU - Ito, Kazufumi
AU - Kunisch, Karl
T2 - JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES
AB - Optimal control of parabolic variational inequalities is studied in the case where the spatial domain is not necessarily bounded. First, strong and weak solutions concepts for the variational inequality are proposed and existence results are obtained by a monotone and a finite difference technique. An optimal control problem with the control appearing in the coefficient of the leading term is investigated and a first order optimality system in a Lagrangian framework is derived. On étudie le contrôle optimal d'inégalités variationnelles dans le cas où le domaine spatial n'est pas nécessairement borné. Tout d'abord, on introduit des concepts de solutions fortes et faibles pour l'inégalité variationnelle et on obtient des résultats d'existence par une méthode de différences finies et monotone. On examine ensuite un problème de contrôle optimal avec un contrôle apparaissant dans le coefficient du terme principal et on en déduit un système d'optimalité du premier ordre dans un cadre lagrangien.
DA - 2010/4//
PY - 2010/4//
DO - 10.1016/j.matpur.2009.10.005
VL - 93
IS - 4
SP - 329-360
SN - 0021-7824
KW - Variational inequalities
KW - Strong solutions
KW - Weak solutions
KW - Unbounded domain
KW - Difference schemes
KW - Optimal control
ER -
TY - JOUR
TI - Nonlinear fourth-order elliptic equations with nonlocal boundary conditions
AU - Pao, C. V.
AU - Wang, Yuan-Ming
T2 - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
AB - This paper is concerned with a class of fourth-order nonlinear elliptic equations with nonlocal boundary conditions, including a multi-point boundary condition in a bounded domain of Rn. Also considered is a second-order elliptic equation with nonlocal boundary condition, and the usual multi-point boundary problem in ordinary differential equations. The aim of the paper is to show the existence of maximal and minimal solutions, the uniqueness of a positive solution, and the method of construction for these solutions. Our approach to the above problems is by the method of upper and lower solutions and its associated monotone iterations. The monotone iterative schemes can be developed into computational algorithms for numerical solutions of the problem by either the finite difference method or the finite element method.
DA - 2010/12/15/
PY - 2010/12/15/
DO - 10.1016/j.jmaa.2010.07.027
VL - 372
IS - 2
SP - 351-365
SN - 1096-0813
KW - Fourth-order elliptic equation
KW - Nonlocal boundary condition
KW - Multi-point boundary condition
KW - Maximal and minimal solutions
KW - Method of upper and lower solutions
KW - Monotone iterations
ER -
TY - JOUR
TI - Inverse mode problems for real and symmetric quadratic models
AU - Lin, Matthew M.
AU - Dong, Bo
AU - Chu, Moody T.
T2 - INVERSE PROBLEMS
AB - Many natural phenomena can be modeled by a second-order dynamical system , where stands for an appropriate state variable and M, C, K are time-invariant, real and symmetric matrices. In contrast to the classical inverse vibration problem where a model is to be determined from natural frequencies corresponding to various boundary conditions, the inverse mode problem concerns the reconstruction of the coefficient matrices (M, C, K) from a prescribed or observed subset of natural modes. This paper set forth a mathematical framework for the inverse mode problem and resolves some open questions raised in the literature. In particular, it shows that given merely the desirable structure of the spectrum, namely given the cardinalities of real or complex eigenvalues but not of the actual eigenvalues, the set of eigenvectors can be completed via solving an under-determined nonlinear system of equations. This completion suffices to construct symmetric coefficient matrices (M, C, K) whereas the underlying system can have arbitrary eigenvalues. Generic conditions under which the real symmetric quadratic inverse mode problem is solvable are discussed. Applications to important tasks such as updating models without spill-over or constructing models with positive semi-definite coefficient matrices are discussed.
DA - 2010/6//
PY - 2010/6//
DO - 10.1088/0266-5611/26/6/065003
VL - 26
IS - 6
SP -
SN - 1361-6420
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-77952566534&partnerID=MN8TOARS
ER -
TY - JOUR
TI - Generalized sensitivities and optimal experimental design
AU - Banks, H. T.
AU - Dediu, S.
AU - Ernstberger, S. L.
AU - Kappel, F.
T2 - Journal of Inverse and Ill-Posed Problems
DA - 2010///
PY - 2010///
VL - 18
IS - 1
SP - 25-83
ER -
TY - JOUR
TI - Fermionic realization of toroidal Lie algebras of classical types
AU - Jing, Naihuan
AU - Misra, Kailash C.
T2 - JOURNAL OF ALGEBRA
AB - We use fermionic operators to construct toroidal Lie algebras of classical types, including in particular that of symplectic affine algebras, which is first realized by fermions.
DA - 2010/7/15/
PY - 2010/7/15/
DO - 10.1016/j.jalgebra.2010.03.021
VL - 324
IS - 2
SP - 183-194
SN - 1090-266X
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-77952959663&partnerID=MN8TOARS
KW - Clifford algebras
KW - Vertex operators
KW - Toroidal Lie algebras
ER -
TY - JOUR
TI - FINITE TIME EMERGENCE OF A SHOCK WAVE FOR SCALAR CONSERVATION LAWS
AU - Shearer, Michael
AU - Dafermos, Constantine
T2 - JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS
AB - For a convex conservation law [Formula: see text] bounded initial data u 0 (x), are considered that take on constant values u - to the left of a bounded interval, and u + to the right, with u - > u + . The solution of the initial value problem is shown to collapse in finite time to a single shock wave joining u - to u + . The proof involves comparison with a solution having piecewise constant initial data, for which the evolution to a single shock involves straightforward rarefaction-shock interactions. This result has a significant application to steady granular flow in a chute, and the result is reformulated to apply to the Lighthill–Whitham–Richards equation of traffic flow.
DA - 2010/3//
PY - 2010/3//
DO - 10.1142/s0219891610002037
VL - 7
IS - 1
SP - 107-116
SN - 0219-8916
KW - Shock waves
KW - conservation laws
ER -
TY - JOUR
TI - EIGENVALUE PROBLEMS OF A DEGENERATE QUASILINEAR ELLIPTIC EQUATION
AU - Pao, C. V.
T2 - ROCKY MOUNTAIN JOURNAL OF MATHEMATICS
DA - 2010///
PY - 2010///
DO - 10.1216/rmj-2010-40-1-305
VL - 40
IS - 1
SP - 305-311
SN - 0035-7596
KW - Positive eigenvalues and eigenfunctions
KW - degenerate quasilinear elliptic equations
KW - upper and lower solutions
ER -
TY - JOUR
TI - Collapsing and Explosion Waves in Phase Transitions with Metastability, Existence, Stability and Related Riemann Problems
AU - Fan, Haitao
AU - Lin, Xiao-Biao
T2 - JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
DA - 2010/6//
PY - 2010/6//
DO - 10.1007/s10884-009-9150-9
VL - 22
IS - 2
SP - 163-191
SN - 1572-9222
KW - Liquid/vapor phase transition
KW - Collapsing and explosion waves
KW - Phase boundary
KW - Reaction-diffusion-convection equation
KW - Admissibility criterion for Riemann solutions
ER -
TY - JOUR
TI - APPROXIMATE NULLSPACE ITERATIONS FOR KKT SYSTEMS
AU - Ito, Kazufumi
AU - Kunisch, Karl
AU - Schulz, Volker
AU - Gherman, Ilia
T2 - SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
AB - We investigate a linear iteration scheme for solving Karush–Kuhn–Tucker systems arising from optimization problems with linear equality constraints. The iterations are motivated by the simplicity of the proposed combination of iterations for the forward and adjoint systems that need to be solved and for which efficient solvers may already be available. Convergence results are derived, and their practical relevance is investigated by means of a numerical example.
DA - 2010///
PY - 2010///
DO - 10.1137/080724952
VL - 31
IS - 4
SP - 1835-1847
SN - 1095-7162
KW - KKT systems
KW - iterative solvers
KW - optimization
ER -
TY - JOUR
TI - A finite dimensional A(infinity) algebra example
AU - Allocca, M. P.
AU - Lada, T.
T2 - Georgian Mathematical Journal
DA - 2010///
PY - 2010///
VL - 17
IS - 1
SP - 1-12
ER -
TY - JOUR
TI - A fast quadrature-based numerical method for the continuous spectrum biphasic poroviscoelastic model of articular cartilage
AU - Stuebner, Michael
AU - Haider, Mansoor A.
T2 - Journal of Biomechanics
AB - A new and efficient method for numerical solution of the continuous spectrum biphasic poroviscoelastic (BPVE) model of articular cartilage is presented. Development of the method is based on a composite Gauss-Legendre quadrature approximation of the continuous spectrum relaxation function that leads to an exponential series representation. The separability property of the exponential terms in the series is exploited to develop a numerical scheme that can be reduced to an update rule requiring retention of the strain history at only the previous time step. The cost of the resulting temporal discretization scheme is O(N) for N time steps. Application and calibration of the method is illustrated in the context of a finite difference solution of the one-dimensional confined compression BPVE stress-relaxation problem. Accuracy of the numerical method is demonstrated by comparison to a theoretical Laplace transform solution for a range of viscoelastic relaxation times that are representative of articular cartilage.
DA - 2010/6//
PY - 2010/6//
DO - 10.1016/j.jbiomech.2010.02.023
VL - 43
IS - 9
SP - 1835-1839
J2 - Journal of Biomechanics
LA - en
OP -
SN - 0021-9290
UR - http://dx.doi.org/10.1016/j.jbiomech.2010.02.023
DB - Crossref
KW - Collagen
KW - Proteoglycan
KW - Stress relaxation
KW - Discrete spectrum
ER -
TY - JOUR
TI - Zero dynamics boundary control for regulation of the Kuramoto-Sivashinsky equation
AU - Byrnes, C. I.
AU - Gilliam, D. S.
AU - Hu, C.
AU - Shubov, V. I.
T2 - MATHEMATICAL AND COMPUTER MODELLING
AB - This work is concerned with a problem of tracking regulation for a one-dimensional Kuramoto–Sivashinsky equation. The objective is to design dynamic and static controllers to drive the state of the plant at the ends of the spatial domain to desired reference signals which may be time dependent. The particular case of constant reference signals is referred to as the set point control problem. To solve our tracking problem we employ the zero dynamics inverse design methodology recently developed to solve a variety of tracking and disturbance rejection problems for linear and nonlinear systems. In this paper we describe both dynamic and static control laws and prove that they provide the desired tracking of the reference signals. We also present two numerical examples which illustrate our theoretical results.
DA - 2010/9//
PY - 2010/9//
DO - 10.1016/j.mcm.2010.05.018
VL - 52
IS - 5-6
SP - 875-891
SN - 0895-7177
KW - Zero dynamics inverse
KW - Kuramoto-Sivashinsky equation
KW - Regulation
KW - Tracking
ER -
TY - JOUR
TI - Thermal-based damage detection in porous materials
AU - Banks, H. T.
AU - Boudreaux, Brittany
AU - Criner, Amanda Keck
AU - Foster, Krista
AU - Uttal, Cerena
AU - Vogel, Thomas
AU - Winfree, William P.
T2 - INVERSE PROBLEMS IN SCIENCE AND ENGINEERING
AB - We report here on the use of the heat equation to simulate a thermal interrogation method for detecting damage in a heterogeneous porous material. We first use probability schemes to randomly generate pores in a sample material; then we simulate flash heating of the compartment along one of its boundaries. Temperature data along the source and back boundaries are recorded and then analysed to distinguish differences between the undamaged and damaged materials. These results suggest that it is possible to detect damage of a certain size within a porous medium using thermal interrogation.
DA - 2010///
PY - 2010///
DO - 10.1080/17415977.2010.498912
VL - 18
IS - 6
SP - 835-851
SN - 1741-5977
KW - thermal interrogation
KW - material with porosity
KW - random porosity
KW - damage detection
KW - computational methods
ER -
TY - JOUR
TI - LUNG ORGANOGENESIS
AU - Warburton, David
AU - El-Hashash, Ahmed
AU - Carraro, Gianni
AU - Tiozzo, Caterina
AU - Sala, Frederic
AU - Rogers, Orquidea
AU - De Langhe, Stijn
AU - Kemp, Paul J.
AU - Riccardi, Daniela
AU - Torday, John
AU - Bellusci, Saverio
AU - Shi, Wei
AU - Lubkin, Sharon R.
AU - Jesudason, Edwin
T2 - ORGANOGENESIS IN DEVELOPMENT
AB - Developmental lung biology is a field that has the potential for significant human impact: lung disease at the extremes of age continues to cause major morbidity and mortality worldwide. Understanding how the lung develops holds the promise that investigators can use this knowledge to aid lung repair and regeneration. In the decade since the “molecular embryology” of the lung was first comprehensively reviewed, new challenges have emerged—and it is on these that we focus the current review. Firstly, there is a critical need to understand the progenitor cell biology of the lung in order to exploit the potential of stem cells for the treatment of lung disease. Secondly, the current familiar descriptions of lung morphogenesis governed by growth and transcription factors need to be elaborated upon with the reinclusion and reconsideration of other factors, such as mechanics, in lung growth. Thirdly, efforts to parse the finer detail of lung bud signaling may need to be combined with broader consideration of overarching mechanisms that may be therapeutically easier to target: in this arena, we advance the proposal that looking at the lung in general (and branching in particular) in terms of clocks may yield unexpected benefits.
DA - 2010///
PY - 2010///
DO - 10.1016/s0070-2153(10)90003-3
VL - 90
SP - 73-158
SN - 0070-2153
UR - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=ORCID&SrcApp=OrcidOrg&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=WOS:000281351100003&KeyUID=WOS:000281351100003
ER -
TY - JOUR
TI - Design of Doubly Convergent Multiple-Beam Electron Guns
AU - Ives, R. Lawrence
AU - Attarian, Adam
AU - Tallis, William
AU - Andujar, Cynthia
AU - Forstall, Virginia
AU - Tran, Hien
AU - Read, Michael
AU - Bui, Thuc
T2 - IEEE TRANSACTIONS ON PLASMA SCIENCE
AB - In an effort to achieve higher power RF source performance, designers are utilizing distributed beam devices, such as sheet beams and multiple beams. A limitation is the amount of current that can be emitted by the cathode while still achieving long cathode lifetimes. The desire is to develop distributed beam devices that utilize fundamental mode cavities in the RF circuit. For multiple-beam devices, where the individual beams propagate at the same radius as the cathode, a limitation is reached, where the size of the cathode becomes limited by the space available. A solution is to place the cathodes at a larger radius and compress the beams toward the radius required for fundamental mode cavities. This paper describes the design of a multiple-beam gun where the ensemble of beams is compressed toward the device axis while still achieving parallel propagation through the RF circuit.
DA - 2010/6//
PY - 2010/6//
DO - 10.1109/tps.2010.2046501
VL - 38
IS - 6
SP - 1337-1344
SN - 0093-3813
KW - Computer optimization
KW - electron guns
KW - multiple-beam gun
KW - multiple-beam klystron
ER -
TY - JOUR
TI - An augmented method for free boundary problems with moving contact lines
AU - Li, Zhilin
AU - Lai, Ming-Chih
AU - He, Guowei
AU - Zhao, Hongkai
T2 - COMPUTERS & FLUIDS
AB - An augmented immersed interface method (IIM) is proposed for simulating one-phase moving contact line problems in which a liquid drop spreads or recoils on a solid substrate. While the present two-dimensional mathematical model is a free boundary problem, in our new numerical method, the fluid domain enclosed by the free boundary is embedded into a rectangular one so that the problem can be solved by a regular Cartesian grid method. We introduce an augmented variable along the free boundary so that the stress balancing boundary condition is satisfied. A hybrid time discretization is used in the projection method for better stability. The resultant Helmholtz/Poisson equations with interfaces then are solved by the IIM in an efficient way. Several numerical tests including an accuracy check, and the spreading and recoiling processes of a liquid drop are presented in detail.
DA - 2010/6//
PY - 2010/6//
DO - 10.1016/j.compfluid.2010.01.013
VL - 39
IS - 6
SP - 1033-1040
SN - 1879-0747
KW - Moving contact line
KW - Free boundary problem
KW - Triple junction
KW - One-phase flow
KW - Navier-Stokes equations
KW - Embedding technique
KW - Immersed interface method
KW - Irregular domain
KW - Augmented method
ER -
TY - JOUR
TI - Theory for a dissipative droplet soliton excited by a spin torque nanocontact
AU - Hoefer, M. A.
AU - Silva, T. J.
AU - Keller, Mark W.
T2 - PHYSICAL REVIEW B
AB - A distinct type of solitary wave is predicted to form in spin torque oscillators when the free layer has a sufficiently large perpendicular anisotropy. In this structure, which is a dissipative version of the conservative droplet soliton originally studied in 1977 by Ivanov and Kosevich, spin torque counteracts the damping that would otherwise destroy the mode. Asymptotic methods are used to derive conditions on perpendicular anisotropy strength and applied current under which a dissipative droplet can be nucleated and sustained. Numerical methods are used to confirm the stability of the droplet against various perturbations that are likely in experiments, including tilting of the applied field, nonzero spin torque asymmetry, and nontrivial Oersted fields. Under certain conditions, the droplet experiences a drift instability in which it propagates away from the nanocontact and is then destroyed by damping.
DA - 2010/8/30/
PY - 2010/8/30/
DO - 10.1103/physrevb.82.054432
VL - 82
IS - 5
SP -
SN - 2469-9969
ER -
TY - JOUR
TI - Special issue in Memory of Alexander Rubinov
AU - Fukushima, M.
AU - Kelley, C. T.
AU - Qi, L. Q.
AU - Sun, J.
AU - Ye, Y. Y.
T2 - Pacific Journal of Optimization
DA - 2010///
PY - 2010///
VL - 6
IS - 2
ER -
TY - JOUR
TI - On the nonnegative rank of Euclidean distance matrices
AU - Lin, M.M.
AU - Chu, Moody
T2 - Linear Algebra and Its Applications
AB - The Euclidean distance matrix for n distinct points in ℝ r is generically of rank r + 2. It is shown in this paper via a geometric argument that its nonnegative rank for the case r = 1 is generically n.
DA - 2010///
PY - 2010///
DO - 10.1016/j.laa.2010.03.038
VL - 433
IS - 3
SP - 681-689
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-77953135527&partnerID=MN8TOARS
ER -
TY - JOUR
TI - Multivariate subresultants using Jouanolou matrices
AU - Szanto, A.
T2 - JOURNAL OF PURE AND APPLIED ALGEBRA
AB - Earlier results expressing multivariate subresultants as ratios of two subdeterminants of the Macaulay matrix are extended to Jouanolou matrices. These matrix constructions are generalizations of the classical Macaulay matrices and involve matrices of significantly smaller size. Equivalence of the various subresultant constructions is proved. The resulting subresultant method improves the efficiency of previous methods to compute the solution of over-determined polynomial systems.
DA - 2010/8//
PY - 2010/8//
DO - 10.1016/j.jpaa.2009.11.002
VL - 214
IS - 8
SP - 1347-1369
SN - 0022-4049
ER -
TY - JOUR
TI - Fundamental Limit of Sample Generalized Eigenvalue Based Detection of Signals in Noise Using Relatively Few Signal-Bearing and Noise-Only Samples
AU - Nadakuditi, Raj Rao
AU - Silverstein, Jack W.
T2 - IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING
AB - The detection problem in statistical signal processing can be succinctly formulated: given m (possibly) signal bearing, n -dimensional signal-plus-noise snapshot vectors (samples) and *N* statistically independent n-dimensional noise-only snapshot vectors, can one reliably infer the presence of a signal? This problem arises in the context of applications as diverse as radar, sonar, wireless communications, bioinformatics, and machine learning and is the critical first step in the subsequent signal parameter estimation phase. The signal detection problem can be naturally posed in terms of the sample generalized eigenvalues. The sample generalized eigenvalues correspond to the eigenvalues of the matrix formed by ?whitening? the signal-plus-noise sample covariance matrix with the noise-only sample covariance matrix. In this paper, we prove a fundamental asymptotic limit of sample generalized eigenvalue-based detection of signals in arbitrarily colored noise when there are relatively few signal bearing and noise-only samples. Specifically, we show why when the (eigen) signal-to-noise ratio (SNR) is below a critical value, that is a simple function of n , m, and N, then reliable signal detection, in an asymptotic sense, is not possible. If, however, the eigen-SNR is above this critical value then a simple, new random matrix theory-based algorithm, which we present here, will reliably detect the signal even at SNRs close to the critical value. Numerical simulations highlight the accuracy of our analytical prediction, permit us to extend our heuristic definition of the effective number of identifiable signals in colored noise and display the dramatic improvement in performance relative to the classical estimator by Zhao We discuss implications of our result for the detection of weak and/or closely spaced signals in sensor array processing, abrupt change detection in sensor networks, and clustering methodologies in machine learning.
DA - 2010/6//
PY - 2010/6//
DO - 10.1109/jstsp.2009.2038310
VL - 4
IS - 3
SP - 468-480
SN - 1932-4553
KW - Multivariate F distribution
KW - random matrices
KW - sample covariance matrix
KW - signal detection
KW - Wishart distribution
ER -
TY - JOUR
TI - Combinatorics on partial word correlations
AU - Blanchet-Sadri, F.
AU - Fowler, J.
AU - Gafni, J. D.
AU - Wilson, K. H.
T2 - Journal of Combinatorial Theory. Series A
DA - 2010///
PY - 2010///
VL - 117
IS - 6
SP - 607-624
ER -
TY - JOUR
TI - Bifurcation analysis of a model for hormonal regulation of the menstrual cycle
AU - Selgrade, James F.
T2 - MATHEMATICAL BIOSCIENCES
AB - A model for hormonal control of the menstrual cycle with 13 ordinary differential equations and 41 parameters is presented. Important changes in model behavior result from variations in two of the most sensitive parameters. One parameter represents the level of estradiol sufficient for significant synthesis of luteinizing hormone, which causes ovulation. By studying bifurcation diagrams in this parameter, an interval of parameter values is observed for which a unique stable periodic solution exists and it represent an ovulatory cycle. The other parameter measures mass transfer between the first two stages of ovarian development and is indicative of healthy follicular growth. Changes in this parameter affect the uniqueness interval defined with respect to the first parameter. Hopf, saddle-node and transcritical bifurcations are examined. To attain a normal ovulatory menstrual cycle in this model, a balance must be maintained between healthy development of the follicles and flexibility in estradiol levels needed to produce the surge in luteinizing hormone.
DA - 2010/6//
PY - 2010/6//
DO - 10.1016/j.mbs.2010.02.004
VL - 225
IS - 2
SP - 108-114
SN - 1879-3134
KW - Estradiol
KW - Follicle
KW - Parameter
KW - Transcritical bifurcation
ER -
TY - JOUR
TI - An approximation scheme for Black-Scholes equations with delays
AU - Chang, Mou-Hsiung
AU - Pang, Tao
AU - Pemy, Moustapha
T2 - JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
DA - 2010/6//
PY - 2010/6//
DO - 10.1007/s11424-010-0139-6
VL - 23
IS - 3
SP - 438-455
SN - 1009-6124
KW - Black-Scholes equation
KW - finite difference
KW - stochastic functional differential equations
KW - viscosity solutions
ER -
TY - JOUR
TI - A Fast Explicit Operator Splitting Method for Passive Scalar Advection
AU - Chertock, Alina
AU - Doering, Charles R.
AU - Kashdan, Eugene
AU - Kurganov, Alexander
T2 - JOURNAL OF SCIENTIFIC COMPUTING
DA - 2010/10//
PY - 2010/10//
DO - 10.1007/s10915-010-9381-2
VL - 45
IS - 1-3
SP - 200-214
SN - 1573-7691
UR - https://doi-org.prox.lib.ncsu.edu/10.1007/s10915-010-9381-2
ER -
TY - JOUR
TI - A Compact Fourth Order Scheme for the Helmholtz Equation in Polar Coordinates
AU - Britt, S.
AU - Tsynkov, S.
AU - Turkel, E.
T2 - Journal of Scientific Computing
DA - 2010/1/23/
PY - 2010/1/23/
DO - 10.1007/s10915-010-9348-3
VL - 45
IS - 1-3
SP - 26-47
J2 - J Sci Comput
LA - en
OP -
SN - 0885-7474 1573-7691
UR - http://dx.doi.org/10.1007/s10915-010-9348-3
DB - Crossref
KW - Helmholtz equation
KW - Variable coefficients
KW - Polar coordinates
KW - High order accuracy
KW - Compact finite differences
KW - Exact artificial boundary condition (ABC)
ER -
TY - JOUR
TI - Using inverse problem methods with surveillance data in pneumococcal vaccination
AU - Sutton, Karyn L.
AU - Banks, H. T.
AU - Castillo-Chavez, Carlos
T2 - MATHEMATICAL AND COMPUTER MODELLING
AB - The design and evaluation of epidemiological control strategies is central to public health policy. While inverse problem methods are routinely used in many applications, this remains an area in which their use is relatively rare, although their potential impact is great. We describe methods particularly relevant to epidemiological modeling at the population level. These methods are then applied to the study of pneumococcal vaccination strategies as a relevant example which poses many challenges common to other infectious diseases. We demonstrate that relevant yet typically unknown parameters may be estimated, and show that a calibrated model may used to assess implemented vaccine policies through the estimation of parameters if vaccine history is recorded along with infection and colonization information. Finally, we show how one might determine an appropriate level of refinement or aggregation in the age-structured model given age-stratified observations. These results illustrate ways in which the collection and analysis of surveillance data can be improved using inverse problem methods.
DA - 2010/3//
PY - 2010/3//
DO - 10.1016/j.mcm.2009.12.014
VL - 51
IS - 5-6
SP - 369-388
SN - 1872-9479
KW - Inverse problems
KW - Surveillance data
KW - Epidemiological models
KW - Pneumococcal diseases
KW - Age structure
ER -
TY - JOUR
TI - Electromagnetic interrogation and the Doppler shift using the method of mappings
AU - Banks, H. T.
AU - Hu, Shuhua
AU - Thompson, W. Clayton
T2 - MATHEMATICAL AND COMPUTER MODELLING
AB - We consider the electromagnetic detection of hidden moving or oscillating conductive targets. The resulting mathematical problem involves computation of a Doppler shift for an electromagnetic wave reflecting from a moving interface. This entails solving Maxwell’s equations on a domain changing in time. We employ the method of mappings to transform the problem to one of computing solutions of a Maxwell system with time dependent coefficients on a fixed reference domain. Thus we obtain a problem that is eminently tractable with finite element or finite difference time domain methods. The accuracy of numerical solutions is illustrated with computations for a number of different velocities for the moving interface.
DA - 2010/3//
PY - 2010/3//
DO - 10.1016/j.mcm.2009.12.013
VL - 51
IS - 5-6
SP - 389-399
SN - 0895-7177
KW - Electromagnetic Doppler shift
KW - Moving interfaces
KW - Method of mappings
KW - Finite elements
ER -
TY - JOUR
TI - BLOCK MONOTONE ITERATIVE METHOD FOR SEMILINEAR PARABOLIC EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS
AU - Pao, C. V.
AU - Lu, Xin
T2 - SIAM JOURNAL ON NUMERICAL ANALYSIS
AB - Two block monotone iterative schemes, called Jacobi and Gauss–Seidel monotone iterations, are presented for numerical solutions of a class of semilinear parabolic equations under nonlinear boundary conditions by the finite difference method. These iteration schemes extend the method for semilinear elliptic boundary value problems to parabolic equations, including a comparison result between them. It is shown that by using an upper solution and a lower solution as initial iterations each of the iterative schemes yields two sequences which converge monotonically from above and below, respectively, to a unique solution of the finite difference system. Some error estimates and a convergence theorem are given, and various sufficient conditions for the construction of upper and lower solutions are obtained. Numerical results are presented for some physical model problems, including some problems with known continuous solutions and two problems with L-shaped and trapezoidal domains.
DA - 2010///
PY - 2010///
DO - 10.1137/090748706
VL - 47
IS - 6
SP - 4581-4606
SN - 0036-1429
KW - semilinear parabolic equations
KW - nonlinear boundary conditions
KW - finite difference systems
KW - block monotone iterations
KW - upper and lower solutions
KW - Jacobi iterations and Gauss-Seidel iterations
KW - numerical solutions
KW - convergence
ER -
TY - JOUR
TI - An active approach for detection of incipient faults
AU - Nikoukhah, R.
AU - Campbell, S. L.
AU - Drake, K.
T2 - INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE
AB - The methodology of auxiliary signal design for robust fault detection based on a multi-model (MM) formulation of normal and faulty systems is used to study the problem of incipient fault detection. The fault is modelled as a drift in a system parameter, and an auxiliary signal is to be designed to enhance the detection of variations in this parameter. It is shown that it is possible to consider the model of the system with a drifted parameter as a second model and use the MM framework for designing the auxiliary signal by considering the limiting case as the parameter variation goes to zero. The result can be applied very effectively to many early detection problems where small parameter variations should be detected. Two different approaches for computing the test signal are given and compared on several computational examples.
DA - 2010///
PY - 2010///
DO - 10.1080/00207720903045817
VL - 41
IS - 2
SP - 241-257
SN - 1464-5319
KW - incipient fault detection
KW - fault detection
KW - auxiliary signal design
KW - identification
ER -
TY - JOUR
TI - A Multicompartment Liver-based Pharmacokinetic Model for Benzene and its Metabolites in Mice
AU - Manning, Cammey C.
AU - Schlosser, Paul M.
AU - Tran, Hien T.
T2 - BULLETIN OF MATHEMATICAL BIOLOGY
AB - Benzene is a highly flammable, colorless liquid. Ubiquitous exposures result from its presence in gasoline vapors, cigarette smoke, and industrial processes. After uptake into the body, benzene undergoes a series of metabolic transformations to multiple metabolites that exert toxic effects on the bone marrow. We developed a physiologically based pharmacokinetic model for the uptake and elimination of benzene in mice to relate the concentration of inhaled and orally administered benzene to the tissue doses of benzene and its key metabolites. This model takes into account the zonal distribution of enzymes and metabolism in the liver rather than treating the liver as one homogeneous compartment, and considers metabolism in tissues other than the liver. Analysis was done to examine the existence and uniqueness of solutions of the system. We then formulated an inverse problem to obtain estimates for the unknown parameters; data from multiple laboratories and experiments were used. Despite the sources of variability, the model simulations matched the data reasonably well in most cases. Our study shows that the multicompartment metabolism model does improve predictions over the previous model (Cole et al. in J. Toxicol. Environ. Health, 439–465, 2001) and that in vitro metabolic constants can be successfully extrapolated to predict in vivo data for benzene metabolism and dosimetry.
DA - 2010/4//
PY - 2010/4//
DO - 10.1007/s11538-009-9459-x
VL - 72
IS - 3
SP - 507-540
SN - 0092-8240
KW - Benzene metabolism model
KW - Ordinary differential equations
KW - Existence and uniqueness
KW - Inverse problems
ER -
TY - JOUR
TI - 'Plum Regal' fresh-market plum tomato hybrid and Its parents, NC 25P and NC 30P
AU - Gardner, R. G.
AU - Panthee, D. R.
T2 - HortScience
DA - 2010///
PY - 2010///
VL - 45
IS - 5
SP - 824-825
ER -
TY - JOUR
TI - Semi-definite programming techniques for structured quadratic inverse eigenvalue problems
AU - Lin, Matthew M.
AU - Dong, Bo
AU - Chu, Moody T.
T2 - NUMERICAL ALGORITHMS
AB - In the past decade or so, semi-definite programming (SDP) has emerged as a powerful tool capable of handling a remarkably wide range of problems. This article describes an innovative application of SDP techniques to quadratic inverse eigenvalue problems (QIEPs). The notion of QIEPs is of fundamental importance because its ultimate goal of constructing or updating a vibration system from some observed or desirable dynamical behaviors while respecting some inherent feasibility constraints well suits many engineering applications. Thus far, however, QIEPs have remained challenging both theoretically and computationally due to the great variations of structural constraints that must be addressed. Of notable interest and significance are the uniformity and the simplicity in the SDP formulation that solves effectively many otherwise very difficult QIEPs.
DA - 2010/4//
PY - 2010/4//
DO - 10.1007/s11075-009-9309-9
VL - 53
IS - 4
SP - 419-437
SN - 1572-9265
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-77950457631&partnerID=MN8TOARS
KW - Semi-definite programming
KW - Quadratic pencil
KW - Inverse eigenvalue problem
KW - Structural constraint
KW - Model updating
ER -
TY - JOUR
TI - SHOCK FORMATION AND BREAKING IN GRANULAR AVALANCHES
AU - Shearer, Michael
AU - Giffen, Nicholas
T2 - DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
AB - In this paper, we explore properties of shock wave solutions of the Gray-Thornton model for particle size segregation in granular avalanches.The model equation is a nonlinear scalar conservation law expressing conservation of mass under shear for the concentration of small particles in a bidisperse mixture. Shock waves are weak solutions of the partial differential equation across which the concentration jumps. We give precise criteria on smooth initial conditions under which a shock wave forms in the interior of the avalanche in finite time. Shocks typically lose stability as they are sheared by the flow, giving way to a complex structure in which a two-dimensional rarefaction wave interacts dynamically with a pair of shocks. The rarefaction represents a mixing zone, in which small and large particles are mixed as they are transported up and down (respectively) through the zone. The mixing zone expands and twice changes its detailed structure before reaching the boundary.
DA - 2010/6//
PY - 2010/6//
DO - 10.3934/dcds.2010.27.693
VL - 27
IS - 2
SP - 693-714
SN - 1553-5231
KW - avalanches
KW - conservation laws
KW - granular materials
KW - segregation
KW - shock waves
ER -
TY - JOUR
TI - On the use of a nascent delta function in radiative-transfer calculations for multi-layer media subject to Fresnel boundary and interface conditions
AU - Garcia, R. D. M.
AU - Siewert, C. E.
T2 - JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER
AB - Abstract The “pre-processing” procedure and the “break-point” analysis developed in a previous work based on the ADO (analytical discrete ordinates) method are used, along with a nascent delta function to describe the polar-angle dependence of an incident beam, to solve the classical albedo problem for radiative transfer in a plane-parallel, multi-layer medium subject to Fresnel boundary and interface conditions. As a result of the use of a nascent delta function, rather than the Dirac distribution, to model the polar-angle dependence of the incident beam, the computational work is significantly simplified (since a particular solution is not required) in comparison to an approach where both the polar-angle and the azimuthal-angle dependence of the incident beam are formulated in terms of Dirac delta distributions. The numerical results from this approach are (when a sufficiently small “narrowness” parameter is used to define the nascent delta) found to be in complete agreement with already reported (high-quality) results for a set of challenging multi-layer problems.
DA - 2010/1//
PY - 2010/1//
DO - 10.1016/j.jqsrt.2009.06.004
VL - 111
IS - 1
SP - 128-133
SN - 0022-4073
KW - Radiative transfer
KW - Nascent delta function
KW - Fresnel conditions
KW - Discrete-ordinates method
ER -
TY - JOUR
TI - MATHEMATICAL STRATEGIES FOR FILTERING TURBULENT DYNAMICAL SYSTEMS
AU - Majda, Andrew J.
AU - Harlim, John
AU - Gershgorin, Boris
T2 - DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
AB - The modus operandi of modern applied mathematics in developing very recent mathematical strategies for filtering turbulent dynamical systems isemphasized here. The approach involves the synergy of rigorous mathematical guidelines, exactly solvable nonlinear models with physical insight,and novel cheap algorithms with judicious model errors to filter turbulent signals with many degrees of freedom. A large number of new theoretical andcomputational phenomena such as 'catastrophic filter divergence' in finite ensemble filters are reviewed here with the intention to introduce mathematicians,applied mathematicians, and scientists to this remarkable emerging scientific discipline with increasing practical importance.
DA - 2010/6//
PY - 2010/6//
DO - 10.3934/dcds.2010.27.441
VL - 27
IS - 2
SP - 441-486
SN - 1553-5231
KW - stochastic parameter estimation
KW - Kalman filter
KW - filtering turbulent systems
KW - data assimilation
KW - model error
ER -
TY - JOUR
TI - Classification of Curves in 2D and 3D via Affine Integral Signatures
AU - Feng, Shuo
AU - Kogan, Irina
AU - Krim, Hamid
T2 - ACTA APPLICANDAE MATHEMATICAE
AB - We propose new robust classification algorithms for planar and spatial curves subjected to affine transformations. Our motivation comes from the problems in computer image recognition. To each planar or spatial curve, we assign a planar signature curve. Curves, equivalent under an affine transformation, have the same signature. The signatures are based on integral invariants, which are significantly less sensitive to small perturbations of curves and noise than classically known differential invariants. Affine invariants are derived in terms of Euclidean invariants. We present two types of signatures: the global and the local signature. Both signatures are independent of curve parameterization. The global signature depends on a choice of the initial point and, therefore, cannot be used for local comparison. The local signature, albeit being slightly more sensitive to noise, is independent of the choice of the initial point and can be used to solve local equivalence problem. An experiment that illustrates robustness of the proposed signatures is presented.
DA - 2010/3//
PY - 2010/3//
DO - 10.1007/s10440-008-9353-9
VL - 109
IS - 3
SP - 903-937
SN - 1572-9036
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-77949264986&partnerID=MN8TOARS
KW - Euclidean and affine transformations
KW - Equivalence problem for curves
KW - Integral invariants
KW - Signatures
KW - Image recognition
ER -
TY - JOUR
TI - A Quantized Tits-Kantor-Koecher Algebra
AU - Gao, Yun
AU - Jing, Naihuan
T2 - ALGEBRAS AND REPRESENTATION THEORY
AB - We propose a quantum analogue of a Tits–Kantor–Koecher algebra with a Jordan torus as an coordinated algebra by looking at the vertex operator construction over a Fock space.
DA - 2010/4//
PY - 2010/4//
DO - 10.1007/s10468-008-9115-4
VL - 13
IS - 2
SP - 207-217
SN - 1386-923X
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-77952096651&partnerID=MN8TOARS
KW - Quantum analogue
KW - Tits-Kantor-Koecher algebra
KW - Jordan torus
ER -
TY - JOUR
TI - Test models for improving filtering with model errors through stochastic parameter estimation
AU - Gershgorin, B.
AU - Harlim, J.
AU - Majda, A. J.
T2 - JOURNAL OF COMPUTATIONAL PHYSICS
AB - The filtering skill for turbulent signals from nature is often limited by model errors created by utilizing an imperfect model for filtering. Updating the parameters in the imperfect model through stochastic parameter estimation is one way to increase filtering skill and model performance. Here a suite of stringent test models for filtering with stochastic parameter estimation is developed based on the Stochastic Parameterization Extended Kalman Filter (SPEKF). These new SPEKF-algorithms systematically correct both multiplicative and additive biases and involve exact formulas for propagating the mean and covariance including the parameters in the test model. A comprehensive study is presented of robust parameter regimes for increasing filtering skill through stochastic parameter estimation for turbulent signals as the observation time and observation noise are varied and even when the forcing is incorrectly specified. The results here provide useful guidelines for filtering turbulent signals in more complex systems with significant model errors.
DA - 2010/1/1/
PY - 2010/1/1/
DO - 10.1016/j.jcp.2009.08.019
VL - 229
IS - 1
SP - 1-31
SN - 1090-2716
KW - Stochastic parameter estimation
KW - Kalman filter
KW - Filtering turbulence
KW - Data assimilation
KW - Model error
ER -
TY - JOUR
TI - Resolving the impact of waiting time distributions on the persistence of measles
AU - Conlan, Andrew J. K.
AU - Rohani, Pejman
AU - Lloyd, Alun L.
AU - Keeling, Matthew
AU - Grenfell, Bryan T.
T2 - Journal of The Royal Society Interface
AB - Measles epidemics in human populations exhibit what is perhaps the best empirically characterized, and certainly the most studied, stochastic persistence threshold in population biology. A critical community size (CCS) of around 250 000–500 000 separates populations where measles is predominantly persistent from smaller communities where there are frequent extinctions of measles between major epidemics. The fundamental mechanisms contributing to this pattern of persistence, which are long-lasting immunity to re-infection, recruitment of susceptibles, seasonality in transmission, age dependence of transmission and the spatial coupling between communities, have all been quantified and, to a greater or lesser level of success, captured by theoretical models. Despite these successes there has not been a consensus over whether simple models can successfully predict the value of the CCS, or indeed which mechanisms determine the persistence of measles over a broader range of population sizes. Specifically, the level of the CCS has been thought to be particularly sensitive to the detailed stochastic dynamics generated by the waiting time distribution (WTD) in the infectious and latent periods. We show that the relative patterns of persistence between models with different WTDs are highly sensitive to the criterion of comparison—in particular, the statistical measure of persistence that is employed. To this end, we introduce two new statistical measures of persitence—fade-outs post epidemic and fade-outs post invasion. Contrary to previous reports, we demonstrate that, no matter the choice of persistence measure, appropriately parametrized models of measles demonstrate similar predictions for the level of the CCS.
DA - 2010/4/6/
PY - 2010/4/6/
DO - 10.1098/rsif.2009.0284
VL - 7
IS - 45
SP - 623-640
J2 - J. R. Soc. Interface
LA - en
OP -
SN - 1742-5689 1742-5662
UR - http://dx.doi.org/10.1098/rsif.2009.0284
DB - Crossref
KW - measles
KW - stochasticity
KW - persistence
ER -
TY - JOUR
TI - Positive solutions of quasilinear parabolic systems with Dirichlet boundary condition
AU - Pao, C. V.
AU - Ruan, W. H.
T2 - JOURNAL OF DIFFERENTIAL EQUATIONS
AB - Coupled systems for a class of quasilinear parabolic equations and the corresponding elliptic systems, including systems of parabolic and ordinary differential equations are investigated. The aim of this paper is to show the existence, uniqueness, and asymptotic behavior of time-dependent solutions. Also investigated is the existence of positive maximal and minimal solutions of the corresponding quasilinear elliptic system. The elliptic operators in both systems are allowed to be degenerate in the sense that the density-dependent diffusion coefficients D i ( u i ) may have the property D i ( 0 ) = 0 for some or all i = 1 , … , N , and the boundary condition is u i = 0 . Using the method of upper and lower solutions, we show that a unique global classical time-dependent solution exists and converges to the maximal solution for one class of initial functions and it converges to the minimal solution for another class of initial functions; and if the maximal and minimal solutions coincide then the steady-state solution is unique and the time-dependent solution converges to the unique solution. Applications of these results are given to three model problems, including a scalar polynomial growth problem, a coupled system of polynomial growth problem, and a two component competition model in ecology.
DA - 2010/3/1/
PY - 2010/3/1/
DO - 10.1016/j.jde.2009.12.011
VL - 248
IS - 5
SP - 1175-1211
SN - 1090-2732
KW - Quasilinear parabolic and elliptic equations
KW - Degenerate reaction-diffusion system
KW - Maximal and minimal solutions
KW - Asymptotic behavior of solution
KW - Method of upper and lower solutions
ER -
TY - JOUR
TI - Neural Network Analysis Identifies Scaffold Properties Necessary for In Vitro Chondrogenesis in Elastin-like Polypeptide Biopolymer Scaffolds
AU - Nettles, Dana L.
AU - Haider, Mansoor A.
AU - Chilkoti, Ashutosh
AU - Setton, Lori A.
T2 - Tissue Engineering Part A
AB - The successful design of biomaterial scaffolds for articular cartilage tissue engineering requires an understanding of the impact of combinations of material formulation parameters on diverse and competing functional outcomes of biomaterial performance. This study sought to explore the use of a type of unsupervised artificial network, a self-organizing map, to identify relationships between scaffold formulation parameters (crosslink density, molecular weight, and concentration) and 11 such outcomes (including mechanical properties, matrix accumulation, metabolite usage and production, and histological appearance) for scaffolds formed from crosslinked elastin-like polypeptide (ELP) hydrogels. The artificial neural network recognized patterns in functional outcomes and provided a set of relationships between ELP formulation parameters and measured outcomes. Mapping resulted in the best mean separation amongst neurons for mechanical properties and pointed to crosslink density as the strongest predictor of most outcomes, followed by ELP concentration. The map also grouped formulations together that simultaneously resulted in the highest values for matrix production, greatest changes in metabolite consumption or production, and highest histological scores, indicating that the network was able to recognize patterns amongst diverse measurement outcomes. These results demonstrated the utility of artificial neural network tools for recognizing relationships in systems with competing parameters, toward the goal of optimizing and accelerating the design of biomaterial scaffolds for articular cartilage tissue engineering.
DA - 2010/1//
PY - 2010/1//
DO - 10.1089/ten.tea.2009.0134
VL - 16
IS - 1
SP - 11-20
J2 - Tissue Engineering Part A
LA - en
OP -
SN - 1937-3341 1937-335X
UR - http://dx.doi.org/10.1089/ten.tea.2009.0134
DB - Crossref
ER -
TY - JOUR
TI - Liouvillian solutions of linear difference-differential equations
AU - Feng, Ruyong
AU - Singer, Michael F.
AU - Wu, Min
T2 - JOURNAL OF SYMBOLIC COMPUTATION
AB - For a field k with an automorphism σ and a derivation δ, we introduce the notion of Liouvillian solutions of linear difference–differential systems {σ(Y)=AY,δ(Y)=BY} over k and characterize the existence of Liouvillian solutions in terms of the Galois group of the systems. In the forthcoming paper, we will propose an algorithm for deciding if linear difference–differential systems of prime order have Liouvillian solutions.
DA - 2010/3//
PY - 2010/3//
DO - 10.1016/j.jsc.2009.09.001
VL - 45
IS - 3
SP - 287-305
SN - 0747-7171
KW - Linear difference-differential equations
KW - Galois theory
KW - Liouvillian sequences
ER -
TY - JOUR
TI - Improving filtering and prediction of spatially extended turbulent systems with model errors through stochastic parameter estimation
AU - Gershgorin, B.
AU - Harlim, J.
AU - Majda, A. J.
T2 - JOURNAL OF COMPUTATIONAL PHYSICS
AB - The filtering and predictive skill for turbulent signals is often limited by the lack of information about the true dynamics of the system and by our inability to resolve the assumed dynamics with sufficiently high resolution using the current computing power. The standard approach is to use a simple yet rich family of constant parameters to account for model errors through parameterization. This approach can have significant skill by fitting the parameters to some statistical feature of the true signal; however in the context of real-time prediction, such a strategy performs poorly when intermittent transitions to instability occur. Alternatively, we need a set of dynamic parameters. One strategy for estimating parameters on the fly is a stochastic parameter estimation through partial observations of the true signal. In this paper, we extend our newly developed stochastic parameter estimation strategy, the Stochastic Parameterization Extended Kalman Filter (SPEKF), to filtering sparsely observed spatially extended turbulent systems which exhibit abrupt stability transition from time to time despite a stable average behavior. For our primary numerical example, we consider a turbulent system of externally forced barotropic Rossby waves with instability introduced through intermittent negative damping. We find high filtering skill of SPEKF applied to this toy model even in the case of very sparse observations (with only 15 out of the 105 grid points observed) and with unspecified external forcing and damping. Additive and multiplicative bias corrections are used to learn the unknown features of the true dynamics from observations. We also present a comprehensive study of predictive skill in the one-mode context including the robustness toward variation of stochastic parameters, imperfect initial conditions and finite ensemble effect. Furthermore, the proposed stochastic parameter estimation scheme applied to the same spatially extended Rossby wave system demonstrates high predictive skill, comparable with the skill of the perfect model for a duration of many eddy turnover times especially in the unstable regime.
DA - 2010/1/1/
PY - 2010/1/1/
DO - 10.1016/j.jcp.2009.09.022
VL - 229
IS - 1
SP - 32-57
SN - 1090-2716
KW - Stochastic parameter estimation
KW - Kalman filter
KW - Filtering turbulence
KW - Data assimilation
KW - Model error
KW - Predictability
ER -
TY - JOUR
TI - Combinatorial constructions of weight bases: The Gelfand-Tsetlin basis
AU - Hersh, P.
AU - Lenart, C.
T2 - Electronic Journal of Combinatorics
DA - 2010///
PY - 2010///
VL - 17
IS - 1
ER -
TY - JOUR
TI - An algorithm to compute Liouvillian solutions of prime order linear difference-differential equations
AU - Feng, R. Y.
AU - Singer, M. F.
AU - Wu, M.
T2 - Journal of Symbolic Computation
AB - A normal form is given for integrable linear difference–differential equations { σ ( Y ) = A Y , δ ( Y ) = B Y } , which is irreducible over C ( x , t ) and solvable in terms of Liouvillian solutions. We refine this normal form and devise an algorithm to compute all Liouvillian solutions of such kinds of systems of prime order.
DA - 2010///
PY - 2010///
DO - 10.1016/j.jsc.2009.09.002
VL - 45
IS - 3
SP - 306-323
ER -
TY - JOUR
TI - An Axisymmetric Boundary Element Model for Determination of Articular Cartilage Pericellular Matrix Properties In Situ via Inverse Analysis of Chondron Deformation
AU - Kim, Eunjung
AU - Guilak, Farshid
AU - Haider, Mansoor A.
T2 - Journal of Biomechanical Engineering
AB - The pericellular matrix (PCM) is the narrow tissue region surrounding all chondrocytes in articular cartilage and, together, the chondrocyte(s) and surrounding PCM have been termed the chondron. Previous theoretical and experimental studies suggest that the structure and properties of the PCM significantly influence the biomechanical environment at the microscopic scale of the chondrocytes within cartilage. In the present study, an axisymmetric boundary element method (BEM) was developed for linear elastic domains with internal interfaces. The new BEM was employed in a multiscale continuum model to determine linear elastic properties of the PCM in situ, via inverse analysis of previously reported experimental data for the three-dimensional morphological changes of chondrons within a cartilage explant in equilibrium unconfined compression (Choi, et al., 2007, “Zonal Changes in the Three-Dimensional Morphology of the Chondron Under Compression: The Relationship Among Cellular, Pericellular, and Extracellular Deformation in Articular Cartilage,” J. Biomech., 40, pp. 2596–2603). The microscale geometry of the chondron (cell and PCM) within the cartilage extracellular matrix (ECM) was represented as a three-zone equilibrated biphasic region comprised of an ellipsoidal chondrocyte with encapsulating PCM that was embedded within a spherical ECM subjected to boundary conditions for unconfined compression at its outer boundary. Accuracy of the three-zone BEM model was evaluated and compared with analytical finite element solutions. The model was then integrated with a nonlinear optimization technique (Nelder–Mead) to determine PCM elastic properties within the cartilage explant by solving an inverse problem associated with the in situ experimental data for chondron deformation. Depending on the assumed material properties of the ECM and the choice of cost function in the optimization, estimates of the PCM Young's modulus ranged from ∼24 kPa to 59 kPa, consistent with previous measurements of PCM properties on extracted chondrons using micropipette aspiration. Taken together with previous experimental and theoretical studies of cell-matrix interactions in cartilage, these findings suggest an important role for the PCM in modulating the mechanical environment of the chondrocyte.
DA - 2010///
PY - 2010///
DO - 10.1115/1.4000938
VL - 132
IS - 3
SP - 031011
J2 - J. Biomech. Eng.
LA - en
OP -
SN - 0148-0731
UR - http://dx.doi.org/10.1115/1.4000938
DB - Crossref
KW - osteoarthritis
KW - collagen
KW - proteoglycan
KW - aggrecan
KW - numerical model
KW - inverse problem
ER -
TY - JOUR
TI - A parallel interior point decomposition algorithm for block angular semidefinite programs
AU - Sivaramakrishnan, Kartik Krishnan
T2 - COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
DA - 2010/5//
PY - 2010/5//
DO - 10.1007/s10589-008-9187-4
VL - 46
IS - 1
SP - 1-29
SN - 1573-2894
KW - Block angular semidefinite programs
KW - Matrix completion
KW - Decomposition and nonsmooth optimization
KW - Interior point methods
KW - Parallel optimization
ER -
TY - JOUR
TI - Zero Action on Perfect Crystals for Uq(G(2)((1)))
AU - Misra, Kailash C.
AU - Mohamad, Mahathir
AU - Okado, Masato
T2 - SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS
AB - The actions of 0-Kashiwara operators on the $U'_q(G_2^{(1)})$-crystal $B_l$ in [Yamane S., J. Algebra 210 (1998), 440-486] are made explicit by using a similarity technique from that of a $U'_q(D_4^{(3)})$-crystal. It is shown that $\{B_l\}_{l\ge1}$ forms a coherent family of perfect crystals.
DA - 2010///
PY - 2010///
DO - 10.3842/sigma.2010.022
VL - 6
SP -
SN - 1815-0659
KW - combinatorial representation theory
KW - quantum affine algebra
KW - crystal bases
ER -
TY - JOUR
TI - Immersed Interface Finite Element Methods for Elasticity Interface Problems with Non-Homogeneous Jump Conditions
AU - Gong, Y.
AU - Li, Z. L.
T2 - Numerical Mathematics: Theory, Methods and Applications
DA - 2010///
PY - 2010///
VL - 3
IS - 1
SP - 23-39
ER -