TY - RPRT TI - The effect of ties on convergence in the k-modes variants for clustering categorical data AU - Chu, Moody T. AU - Orlowski, N. AU - Schlorff, D. AU - Blevins, J. AU - Canas, D. AU - Funderlic, R. DA - 2004/// PY - 2004/// M3 - Preprint ER - TY - RPRT TI - On the least squares Euclidean distance matrix approximation and completion AU - Chu, Moody T. AU - Chu, D.I. AU - Brown, H. DA - 2004/// PY - 2004/// M3 - Preprint ER - TY - RPRT TI - Group theory, linear transformations, and flows: Dynamical systems on manifolds AU - Chu, Moody DA - 2004/// PY - 2004/// M3 - Preprint ER - TY - JOUR TI - SINGULAR VALUE REASSIGNMENT WITH LOW RANK MATRICES (DRAFT: June 11, 2004) AU - Chu, Delin AU - Chu, Moody DA - 2004/// PY - 2004/// UR - http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.61.6384 ER - TY - JOUR TI - SINGULAR VALUE REASSIGNMENT WITH LOW RANK MATRICES AU - Chu, Delin AU - Chu, Moody DA - 2004/// PY - 2004/// UR - http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.71.8290 ER - TY - JOUR TI - On inverse quadratic eigenvalue problems with partially prescribed eigenstructure AU - Chu, M.T. AU - Kuo, Y.-C. AU - Lin, W.-W. T2 - SIAM Journal on Matrix Analysis and Applications AB - The inverse eigenvalue problem of constructing real and symmetric square matrices M, C, and K of size $n \times n$ for the quadratic pencil $Q(\lambda) = \lambda^2 M + \lambda C + K$ so that $Q(\lambda)$ has a prescribed subset of eigenvalues and eigenvectors is considered. This paper consists of two parts addressing two related but different problems. The first part deals with the inverse problem where M and K are required to be positive definite and semidefinite, respectively. It is shown via construction that the inverse problem is solvable for any k, given complex conjugately closed pairs of distinct eigenvalues and linearly independent eigenvectors, provided $k \leq n$. The construction also allows additional optimization conditions to be built into the solution so as to better refine the approximate pencil. The eigenstructure of the resulting $Q(\lambda)$ is completely analyzed. The second part deals with the inverse problem where M is a fixed positive definite matrix (and hence may be assumed to be the identity matrix $I_n$). It is shown via construction that the monic quadratic pencil $Q(\lambda)=\lambda^2 I_n + \lambda C + K$, with $n + 1$ arbitrarily assigned complex conjugately closed pairs of distinct eigenvalues and column eigenvectors which span the space $\mathbb{C}^n$, always exists. Sufficient conditions under which this quadratic inverse eigenvalue problem is uniquely solvable are specified. DA - 2004/// PY - 2004/// DO - 10.1137/S0895479803404484 VL - 25 IS - 4 SP - 995-1020 UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-8344269351&partnerID=MN8TOARS ER - TY - JOUR TI - Early termination in Shoup's algorithm for the minimum polynomial of an algebraic AU - Eberly, Wayne AU - Kaltofen, Erich DA - 2004/// PY - 2004/// ER - TY - CONF TI - Design of a Detection Signal for Fault Detection and Model Identification on Systems with Multiple Delays AU - Drake, K. AU - Campbell, S.L. T2 - American Society of Naval Engineers Day C2 - 2004/6/28/ C3 - Proceedings of the American Society of Naval Engineers Day 2004 CY - Alexandria, VA DA - 2004/6/28/ PY - 2004/6/28/ ER - TY - CONF TI - ODE and DAE integrators in Scicos environment AU - Najafi, M. AU - Nikoukhah, R. AU - Campbell, S.L. T2 - IASTED International Conference on Applied Simulation and Modeling A2 - Hamza, M.H. C2 - 2004/// C3 - Proceedings of the IASTED International Conference on Applied Simulation and Modelling and Simulation : June 28-30, 2004, Rhodes, Greece CY - Rhodes, Greece DA - 2004/// PY - 2004/6/28/ PB - ACTA Press SN - 0889863970 9780889863972 ER - TY - MGZN TI - Accurate eigenvalues for fast trains AU - Ipsen, I.C.F. T2 - SIAM News DA - 2004/11// PY - 2004/11// VL - 37 SP - 1–2 M1 - 9 ER - TY - JOUR TI - Visualizing symmetry of knots by using program LinKnot, Symmetry: Art and Science AU - Jablan, S. AU - Sazdanovic, R. T2 - The Journal of ISIS-Symmetry DA - 2004/// PY - 2004/// VL - 1-4 SP - 106–110 ER - TY - CONF TI - Modularity in Medieval Persian Mosaics: Textual, Empirical, Analytical and Theoretical Considerations, Bridges AU - Sarhangi, R. AU - Jablan, S. AU - Sazdanovic, R. C2 - 2004/// C3 - Mathematical Connections in Art, Music and Science, Conference Proceedings DA - 2004/// SP - 281–293 ER - TY - JOUR TI - Hyperbolic Tessellations by tess AU - Sazdanovic, R. AU - Sremcević, M. T2 - Symmetry: Art and Science (The Quarterly of ISIS Symmetry) DA - 2004/// PY - 2004/// SP - 1–4 226–229 ER - TY - JOUR TI - Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices AU - Kappraff, J. AU - Jablan, S. AU - Adamson, G.W. AU - Sazdanović, R. T2 - Forma DA - 2004/// PY - 2004/// VL - 19 IS - 4 SP - 367–387 ER - TY - JOUR TI - Discovering symmetry of knots by using program LinKnot AU - Jablan, S. AU - Sazdanovic, R. T2 - The Journal of ISIS-Symmetry DA - 2004/// PY - 2004/// VL - 1-4 SP - 102–106 ER - TY - CONF TI - Twisted modules over lattice vertex algebras AU - Bakalov, Bojko AU - Kac, Victor G. T2 - Proceedings of the Fifth International Workshop A2 - Doebner, H.-D. A2 - Dobrev, V.K. AB - For any integral lattice $Q$, one can construct a vertex algebra $V_Q$ called a lattice vertex algebra. If $\sigma$ is an automorphism of $Q$ of finite order, it can be lifted to an automorphism of $V_Q$. In this paper we classify the irreducible $\sigma$-twisted $V_Q$-modules. We show that the category of $\sigma$-twisted $V_Q$-modules is a semisimple abelian category with finitely many isomorphism classes of simple objects. C2 - 2004/7// C3 - Lie Theory and Its Applications in Physics V DA - 2004/7// DO - 10.1142/9789812702562_0001 SP - 3–26 PB - World Scientific Publishing Company SN - 9789812389367 9789812702562 UR - http://dx.doi.org/10.1142/9789812702562_0001 ER - TY - CONF TI - From Concept to Real-time Implementation: POD Based Reduced Order Control of a Cantilever Beam AU - Tran, H. AU - Lewis, B.M. T2 - 16th International Symposium on Mathematical Theory of Networks and Systems(MTNS 2004) A2 - De Moor, B. A2 - Motmans, Bart A2 - Willems, J. A2 - Van Dooren, Paul A2 - Blondel, Vincent C2 - 2004/// C3 - Proceedings of the 16th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2004) CY - Catholic University of Leuven (K.U.Leuven-Belgium) DA - 2004/// PY - 2004/7/5/ ER - TY - CONF TI - Analysis of spline based auxiliary signal design for failure detection in delay systems AU - Campbell, SL AU - Drake, K. AU - Nikoukhah, R. T2 - SMC '03 2003IEEE International Conference on Systems, Man and Cybernetics AB - In an active approach for model detection and its use in failure detection, an auxiliary control is applied in order to assist in model identification. An active approach for robust multi-model identification and failure detection in the presence of disturbances over possibly short time intervals has been introduced. Previous papers extended the original design procedure to problems with several delays and additive noise. The infinite dimensional delay problem was approximated by a finite dimensional system without delays and numerical examples were worked. The numerical examples seemed to converge better than was expected. In this paper we explain that convergence. In addition we discuss the extension of the previous results for delay systems with additive noise to those with small model uncertainties and explain why this additional assumption of small uncertainty, which was not present in the case without delays, is now needed for the analysis. C2 - 2004/5/25/ C3 - SMC'03 Conference Proceedings. 2003 IEEE International Conference on Systems, Man and Cybernetics. Conference Theme - System Security and Assurance (Cat. No.03CH37483) DA - 2004/5/25/ DO - 10.1109/icsmc.2003.1244267 PB - IEEE SN - 0780379527 UR - http://dx.doi.org/10.1109/icsmc.2003.1244267 DB - Crossref ER - TY - CONF TI - Direct transcription solution of inequality constrained optimal control problems AU - Betts, J.T. AU - Campbell, S.L. AU - Engelsone, A. T2 - Proceedings of the 2004 American Control Conference AB - Direct transcription is a popular way to solve the complex optimal control problems that arise in industry. With a direct transcription approach, the problem is fully discretized and then the discrete problem is solved numerically. Recently, it has been shown that the theory for direct transcription differs in several key ways from the theory for other approaches. These differences have implications for numerical algorithms and the interpretation of solutions to practical problems. This paper examines some of those differences. C2 - 2004/// C3 - Proceedings of the 2004 American Control Conference DA - 2004/// DO - 10.23919/acc.2004.1386809 PB - IEEE SN - 0780383354 UR - http://dx.doi.org/10.23919/acc.2004.1386809 DB - Crossref ER - TY - JOUR TI - Deeper Inside PageRank AU - Langville, Amy AU - Meyer, Carl T2 - Internet Mathematics AB - This paper serves as a companion or extension to the "Inside PageRank" paper by Bianchini et al. [Bianchini et al. 03]. It is a comprehensive survey of all issues associated with PageRank, covering the basic PageRank model, available and recommended solution methods, storage issues, existence, uniqueness, and convergence properties, possible alterations to the basic model, suggested alternatives to the traditional solution methods, sensitivity and conditioning, and finally the updating problem. We introduce a few new results, provide an extensive reference list, and speculate about exciting areas of future research. DA - 2004/1/1/ PY - 2004/1/1/ DO - 10.1080/15427951.2004.10129091 VL - 1 IS - 3 SP - 335-380 J2 - UINM LA - en OP - SN - 1542-7951 UR - http://dx.doi.org/10.1080/15427951.2004.10129091 DB - Crossref ER - TY - CONF TI - Approximate factorization of multivariate polynomials via differential equations AU - Gao, Shuhong AU - Kaltofen, Erich AU - May, John AU - Yang, Zhengfeng AU - Zhi, Lihong T2 - the 2004 international symposium AB - The input to our algorithm is a multivariate polynomial, whose complex rational coefficients are considered imprecise with an unknown error that causes f to be irreducible over the complex numbers C. We seek to perturb the coefficients by a small quantitity such that the resulting polynomial factors over C. Ideally, one would like to minimize the perturbation in some selected distance measure, but no efficient algorithm for that is known. We give a numerical multivariate greatest common divisor algorithm and use it on a numerical variant of algorithms by W. M. Ruppert and S. Gao. Our numerical factorizer makes repeated use of singular value decompositions. We demonstrate on a significant body of experimental data that our algorithm is practical and can find factorizable polynomials within a distance that is about the same in relative magnitude as the input error, even when the relative error in the input is substantial (10-3). C2 - 2004/// C3 - Proceedings of the 2004 international symposium on Symbolic and algebraic computation - ISSAC '04 DA - 2004/// DO - 10.1145/1005285.1005311 PB - ACM Press SN - 158113827X UR - http://dx.doi.org/10.1145/1005285.1005311 DB - Crossref ER - TY - JOUR TI - Estimating variability in models for recurrent epidemics: assessing the use of moment closure techniques AU - Lloyd, Alun L T2 - Theoretical population biology AB - The major role played by demographic stochasticity in determining the dynamics and persistence of childhood diseases, such as measles, chickenpox and pertussis, has long been realized. Techniques which can be used to estimate the magnitude of this stochastic effect are of clear importance. In this study, we assess and compare the use of two moment closure approximations to estimate the variability seen about the average behavior of stochastic models for the recurrent epidemics seen in childhood diseases. The performance of the approximations are assessed using analytic techniques available for the simplest epidemiological model and using numerical simulations in more complex settings. We also present epidemiologically important extensions of previous work, considering variability in the SEIR model and in situations for which there is seasonal variation in disease transmission. Important implications of stochastic effects for the dynamics of childhood diseases are highlighted, including serious deficiencies of deterministic descriptions of dynamical behavior. DA - 2004/// PY - 2004/// DO - http://dx.doi.org/10.1016/j.tpb.2003.07.002 VL - 65 IS - 1 SP - 49-65 ER - TY - JOUR TI - Spatiotemporal dynamics of epidemics: synchrony in metapopulation models AU - Lloyd, Alun L AU - Jansen, Vincent AA T2 - Mathematical biosciences AB - Multi-patch models - also known as metapopulation models - provide a simple framework within which the role of spatial processes in disease transmission can be examined. An n-patch model which distinguishes between k different classes of individuals is considered. The linear stability of spatially homogeneous solutions of such models is studied using an extension of an analysis technique previously described for a population setting in which individuals migrate between patches according to a simple linear term. The technique considerably simplifies the analysis as it decouples the nk dimensional linearized system into n distinct k-dimensional systems. An important feature of the spatial epidemiological model is that the spatial coupling may involve non-linear terms. As an example of the use of this technique, the dynamical behavior in the vicinity of the endemic equilibrium of a symmetric SIR model is decomposed into spatial modes. For parameter values appropriate for childhood diseases, expressions for the eigenvalues corresponding to in-phase and out-of-phase modes are obtained, and it is shown that the dominant mode of the system is an in-phase mode. Furthermore, the out-of-phase modes are shown to decay much more rapidly than the in-phase mode for a broad range of coupling strengths. DA - 2004/// PY - 2004/// DO - http://dx.doi.org/10.1016/j.mbs.2003.09.003 VL - 188 IS - 1-2 SP - 1-16 ER - TY - JOUR TI - Practical methods for optimal control using nonlinear programming, John T. Betts, SIAM, Philadelphia, PA, 2001, ISBN 0-89871-488-5 AU - Campbell, Stephen L. T2 - International Journal of Robust and Nonlinear Control AB - International Journal of Robust and Nonlinear ControlVolume 14, Issue 11 p. 1019-1021 Book ReviewFree Access Practical methods for optimal control using nonlinear programming, John T. Betts, SIAM, Philadelphia, PA, 2001, ISBN 0-89871-488-5 Stephen L. Campbell, Stephen L. Campbell slc@math.ncsu.edu Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, U.S.A.Search for more papers by this author Stephen L. Campbell, Stephen L. Campbell slc@math.ncsu.edu Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, U.S.A.Search for more papers by this author First published: 11 June 2004 https://doi.org/10.1002/rnc.874AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article. Volume14, Issue11Special Issue: Robust control design from data: direct and model-based approaches25 July 2004Pages 1019-1021 ReferencesRelatedInformation DA - 2004/6/18/ PY - 2004/6/18/ DO - 10.1002/rnc.874 VL - 14 IS - 11 SP - 1019-1021 J2 - Int. J. Robust Nonlinear Control LA - en OP - SN - 1049-8923 1099-1239 UR - http://dx.doi.org/10.1002/rnc.874 DB - Crossref ER - TY - JOUR TI - Well-posedness for a nonsmooth acoustic system AU - Banks, H.T AU - Raye, J.K T2 - Applied Mathematics Letters AB - We consider an acoustic wave system with discontinuous coefficients and nonsmooth inputs. Existence, uniqueness, and continuous dependence on input data of weak solutions are established. DA - 2004/3// PY - 2004/3// DO - 10.1016/S0893-9659(04)90069-9 VL - 17 IS - 3 SP - 317-322 J2 - Applied Mathematics Letters LA - en OP - SN - 0893-9659 UR - http://dx.doi.org/10.1016/S0893-9659(04)90069-9 DB - Crossref KW - well-posedness KW - wave equations KW - acoustics ER - TY - CONF TI - Initialization of direct transcription optimal control software AU - Betts, J.T. AU - Campbell, S.L. AU - Kalla, N.N. T2 - 42nd IEEE International Conference on Decision and Control AB - Direct transcription optimal control codes have been very successful. One common source of numerical difficulty is getting a feasible solution on the first iteration. Overcoming this often requires a high level of expertise on the user's part. This paper discusses research aimed at the development of a collection of utilities to assist users in solving complex industrial optimal control problems with direct transcription codes. C2 - 2004/4/23/ C3 - 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475) DA - 2004/4/23/ DO - 10.1109/cdc.2003.1271741 PB - IEEE SN - 0780379241 UR - http://dx.doi.org/10.1109/cdc.2003.1271741 DB - Crossref ER - TY - CONF TI - A numerical integrator for simulation of unstructured implicit models AU - Campbell, S.L. AU - Selva, M. AU - Arevalo, C. T2 - Proceedings of the 2004 American Control Conference AB - Object oriented modeling naturally leads to implicitly defined dynamical systems or, as they are also called, differential algebraic equations (DAEs). Most existing DAE integrators require the equations defining the dynamical system to have a special structure. Progress on the development of a new integrator for general unstructured DAEs is presented. The new integrator is called UCP. Computational tests are given to show that the new method can successfully integrate problems that other methods have trouble with. C2 - 2004/// C3 - Proceedings of the 2004 American Control Conference DA - 2004/// DO - 10.23919/acc.2004.1384754 PB - IEEE SN - 0780383354 UR - http://dx.doi.org/10.23919/acc.2004.1384754 DB - Crossref ER - TY - CONF TI - Software for auxiliary signal design AU - Campbell, S.L. AU - Nikoukhah, R. T2 - Proceedings of the 2004 American Control Conference AB - An approach for multi-model identification and failure detection in the presence of model uncertainty and bounded energy noise over finite time intervals has been introduced in the literature. This approach involved offline computation of an auxiliary signal and online application of a hyperplane test. This paper discusses progress in developing a software package to carry out this procedure. C2 - 2004/// C3 - Proceedings of the 2004 American Control Conference DA - 2004/// DO - 10.23919/acc.2004.1384004 PB - IEEE SN - 0780383354 UR - http://dx.doi.org/10.23919/acc.2004.1384004 DB - Crossref ER - TY - JOUR TI - The cd-index of Bruhat intervals AU - Reading, N. T2 - Electronic Journal of Combinatorics DA - 2004/// PY - 2004/// VL - 11 IS - 1 R SP - 1-25 UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-8744221555&partnerID=MN8TOARS ER - TY - JOUR TI - The cd-index of Bruhat intervals AU - Reading, Nathan T2 - The Electronic Journal of Combinatorics AB - We study flag enumeration in intervals in the Bruhat order on a Coxeter group by means of a structural recursion on intervals in the Bruhat order. The recursion gives the isomorphism type of a Bruhat interval in terms of smaller intervals, using basic geometric operations which preserve PL sphericity and have a simple effect on the cd-index. This leads to a new proof that Bruhat intervals are PL spheres as well a recursive formula for the cd-index of a Bruhat interval. This recursive formula is used to prove that the cd-indices of Bruhat intervals span the space of cd-polynomials. The structural recursion leads to a conjecture that Bruhat spheres are "smaller" than polytopes. More precisely, we conjecture that if one fixes the lengths of $x$ and $y$, then the cd-index of a certain dual stacked polytope is a coefficientwise upper bound on the cd-indices of Bruhat intervals $[x,y]$. We show that this upper bound would be tight by constructing Bruhat intervals which are the face lattices of these dual stacked polytopes. As a weakening of a special case of the conjecture, we show that the flag h-vectors of lower Bruhat intervals are bounded above by the flag h-vectors of Boolean algebras (i. e. simplices). DA - 2004/// PY - 2004/// DO - 10.37236/1827 VL - 11 IS - 1 SP - R74 UR - http://www.combinatorics.org/Volume_11/Abstracts/v11i1r74.html ER - TY - CONF TI - Total variation information in image recovery AU - Combettes, P.L. AU - Pesquet, J.C. T2 - International Conference on Image Processing AB - Total variation has proven to be a valuable concept in connection with the recovery of images featuring piecewise smooth components. So far, however, it has been used exclusively as an objective to be minimized under a single constraint. In this paper, we propose an alternative framework in which total variation is used as a constraint in a general quadratic programming context. The advantage of this approach is that it allows for a wider range of constraints to be easily incorporated in the recovery process. C2 - 2004/6/3/ C3 - Proceedings 2003 International Conference on Image Processing (Cat. No.03CH37429) CY - Barcelona, Spain DA - 2004/6/3/ PY - 2003/9/14/ DO - 10.1109/icip.2003.1247259 PB - IEEE SN - 0780377508 UR - http://dx.doi.org/10.1109/icip.2003.1247259 ER - TY - CONF TI - Constraint construction in convex set theoretic signal recovery via Stein's principle [image denoising example] AU - Combettes, P.L. AU - Pesquet, J.-C. T2 - 2004 IEEE International Conference on Acoustics, Speech, and Signal Processing AB - Convex set theoretic estimation methods have been shown to be effective in numerous signal recovery problems due to their ability to incorporate a wide range of deterministic and probabilistic information in the form of constraints on the solution. To date, probabilistic information has been used exclusively to constrain statistics of the estimation residual to be consistent with known properties of the noise. In this paper, we propose a new technique to construct constraint sets from probabilistic information based on Stein's identity. In this framework, probabilistic attributes of the signal to be recovered are estimated from the data. The proposed approach is applicable to signal formation models involving additive Gaussian noise and it leads to geometrically simple sets that can easily be handled via projection methods. An application to image denoising is demonstrated. C2 - 2004/9/28/ C3 - 2004 IEEE International Conference on Acoustics, Speech, and Signal Processing CY - Montreal, Quebec, Canada DA - 2004/9/28/ PY - 2004/5/17/ DO - 10.1109/icassp.2004.1326382 PB - IEEE SN - 0780384849 UR - http://dx.doi.org/10.1109/icassp.2004.1326382 ER - TY - JOUR TI - Wavelet-constrained image restoration AU - Combettes, Patrick L. AU - Pesquet, Jean Christophe T2 - International Journal of Wavelets, Multiresolution and Information Processing AB - Image restoration problems can naturally be cast as constrained convex programming problems in which the constraints arise from a priori information and the observation of signals physically related to the image to be recovered. In this paper, the focus is placed on the construction of constraints based on wavelet representations. Using a mix of statistical and convex-analytical tools, we propose a general framework to construct wavelet-based constraints. The resulting optimization problem is then solved with a block-iterative parallel algorithm which offers great flexibility in terms of implementation. Numerical results illustrate an application of the proposed framework. DA - 2004/12// PY - 2004/12// DO - 10.1142/s0219691304000688 VL - 2 IS - 4 SP - 371-389 SN - 0219-6913 1793-690X UR - http://dx.doi.org/10.1142/s0219691304000688 ER - TY - JOUR TI - On wavelet-based numerical homogenization AU - Chertock, Alina AU - Levy, Doron T2 - Multiscale Model. Simul. AB - Recently, a wavelet-based method was introduced for the systematic derivation of subgrid scale models in the numerical solution of partial differential equations. Starting from a discretization of the multiscale differential operator, the discrete operator is represented in a wavelet space and projected onto a coarser subspace. The coarse (homogenized) operator is then replaced by a sparse approximation to increase the efficiency of the resulting algorithm. In this work we show how to improve the efficiency of this numerical homogenization method by choosing a different compact representation of the homogenized operator. In two dimensions our approach for obtaining a sparse representation is significantly simpler than the alternative sparse representations. $L^{\infty}$ error estimates are derived for a sample elliptic problem. An additional improvement we propose is a natural fine-scales correction that can be implemented in the final homogenization step. This modification of the scheme improves the resolution of the approximation without any significant increase in the computational cost. We apply our method to a variety of test problems including one- and two-dimensional elliptic models as well as wave propagation problems in materials with subgrid inhomogeneities. DA - 2004/// PY - 2004/// DO - 10.1137/030600783 VL - 3 IS - 1 SP - 65-88 UR - https://doi-org.prox.lib.ncsu.edu/10.1137/030600783 KW - numerical homogenization KW - wavelets KW - Helmholtz equation ER - TY - JOUR TI - On the application of lacunae-based methods to Maxwell's equations AU - Tsynkov, S.V. T2 - Journal of Computational Physics AB - A straightforward application of the previously designed lacunae-based numerical methods to unsteady electromagnetic problems would encounter certain difficulties, as it may violate the continuity of the charges and currents, which is a necessary solvability condition for the Maxwell equations. In the paper, we prove existence of the special auxiliary charges and currents that satisfy the continuity equations identically. We also show that using such charges and currents as a part of the numerical procedure provides a clear and unobstructed venue toward implementation of the lacunae-based methods in electromagnetics. DA - 2004/9// PY - 2004/9// DO - 10.1016/j.jcp.2004.02.003 VL - 199 IS - 1 SP - 126-149 J2 - Journal of Computational Physics LA - en OP - SN - 0021-9991 UR - http://dx.doi.org/10.1016/j.jcp.2004.02.003 DB - Crossref KW - electromagnetic waves KW - continuity equation KW - solenoidal currents KW - partition of unity KW - unsteady propagation KW - unbounded domains KW - truncation KW - finite computational domain KW - sharp aft fronts KW - Huygens' principle KW - non-deteriorating method KW - long-term numerical integration ER - TY - CONF TI - Parallel Solution of the {Wigner-Poisson} Equations for {RTDs} AU - Lasater, M S AU - Kelley, C T AU - Salinger, A AU - Woolard, D L AU - Zhao, P A2 - Qingping, Quo C2 - 2004/// C3 - 2004 International Symposium on Distributed Computing and Applications to Business, Engineering and Science CY - Wuhan, China DA - 2004/// SP - 672-676 PB - Hubei Science and Technology Press ER - TY - CONF TI - Simulation of Nondifferentiable Models for Groundwater Flow and Transport AU - Kelley, C T AU - Fowler, K R AU - Kees, C E A2 - Miller, C T A2 - Farthing, M. W. A2 - Gray, W G A2 - Pinter, G F C2 - 2004/// C3 - Proceedings of Computational Methods in Water Resources XV CY - Amsterdam DA - 2004/// SP - 939-952 PB - Elsevier ER - TY - JOUR TI - Implicit Filtering Revisited AU - Conn, A R AU - Kelley, C T AU - Scheinberg, K AU - Vicente, L N DA - 2004/// PY - 2004/// ER - TY - CONF TI - Enhancement of Numerical Computations of the {W}igner-{P}oisson Equations for Application to the Simulation of {TH}z-Frequency {RTD} Oscillators AU - Lasater, M S AU - Kelley, C T AU - Salinger, A AU - Woolard, D L AU - Zhao, P T2 - North Carolina State University, Center for Research in Scientific Computation A2 - Jensen, J O A2 - Theriault, J-M C2 - 2004/// C3 - Proceedings of SPIE: Chemical and Biological Standoff Detection II Volume 5584, paper number 07 DA - 2004/// SP - 42-51 ER - TY - CONF TI - A Hydraulic Capture Application for Optimal Remeidation Design AU - Fowler, K R AU - Kelley, C T AU - Kees, C E AU - Miller, C T A2 - Miller, C T A2 - Farthing, M. W. A2 - Gray, W G A2 - Pinter, G F C2 - 2004/// C3 - Proceedings of Computational Methods in Water Resources XV CY - Amsterdam DA - 2004/// SP - 1149-1158 PB - Elsevier ER - TY - JOUR TI - A Fast Algorithm for the {Ornstein-Zernike} Equations AU - Kelley, C T AU - Pettitt, B Montgomery T2 - J. Comp. Phys. DA - 2004/// PY - 2004/// VL - 197 SP - 491-591 ER - TY - BOOK TI - Characterization and Computation of a "Good Control" AB - Models for physical systems often take the form of implicit or behavioral models. One important problem is the identification of which combinations of variables are good candidtates for control variables. This paper first provides one solution to this problem for linear time varying systems. The solution is shown to be related to a general optimization problem. It is then shown how these same algorithms can be extended to a large and important class of nonlinear systems. DA - 2004/5/3/ PY - 2004/5/3/ DO - 10.18452/2583 ER - TY - JOUR TI - Finding best approximation pairs relative to two closed convex sets in Hilbert spaces AU - Bauschke, Heinz H. AU - Combettes, Patrick L. AU - Luke, D.Russell T2 - Journal of Approximation Theory AB - We consider the problem of finding a best approximation pair, i.e., two points which achieve the minimum distance between two closed convex sets in a Hilbert space. When the sets intersect, the method under consideration, termed AAR for averaged alternating reflections, is a special instance of an algorithm due to Lions and Mercier for finding a zero of the sum of two maximal monotone operators. We investigate systematically the asymptotic behavior of AAR in the general case when the sets do not necessarily intersect and show that the method produces best approximation pairs provided they exist. Finitely many sets are handled in a product space, in which case the AAR method is shown to coincide with a special case of Spingarn's method of partial inverses. DA - 2004/4// PY - 2004/4// DO - 10.1016/j.jat.2004.02.006 VL - 127 IS - 2 SP - 178-192 J2 - Journal of Approximation Theory LA - en OP - SN - 0021-9045 UR - http://dx.doi.org/10.1016/j.jat.2004.02.006 DB - Crossref KW - best approximation pair KW - convex set KW - firmly nonexpansive map KW - Hilbert space KW - hybrid projection-reflection method KW - method of partial inverses KW - normal cone KW - projection KW - reflection KW - weak convergence ER - TY - JOUR TI - Image Restoration Subject to a Total Variation Constraint AU - Combettes, P.L. AU - Pesquet, J.-C. T2 - IEEE Transactions on Image Processing AB - Total variation has proven to be a valuable concept in connection with the recovery of images featuring piecewise smooth components. So far, however, it has been used exclusively as an objective to be minimized under constraints. In this paper, we propose an alternative formulation in which total variation is used as a constraint in a general convex programming framework. This approach places no limitation on the incorporation of additional constraints in the restoration process and the resulting optimization problem can be solved efficiently via block-iterative methods. Image denoising and deconvolution applications are demonstrated. DA - 2004/9// PY - 2004/9// DO - 10.1109/tip.2004.832922 VL - 13 IS - 9 SP - 1213-1222 J2 - IEEE Trans. on Image Process. LA - en OP - SN - 1057-7149 UR - http://dx.doi.org/10.1109/tip.2004.832922 DB - Crossref ER - TY - JOUR TI - Proximal Methods for Cohypomonotone Operators AU - Combettes, Patrick L. AU - Pennanen, Teemu T2 - SIAM Journal on Control and Optimization AB - Conditions are given for the viability and the weak convergence of an inexact, relaxed proximal point algorithm for finding a common zero of countably many cohypomonotone operators in a Hilbert space. In turn, new convergence results are obtained for an extended version of the proximal method of multipliers in nonlinear programming. DA - 2004/1// PY - 2004/1// DO - 10.1137/s0363012903427336 VL - 43 IS - 2 SP - 731-742 J2 - SIAM J. Control Optim. LA - en OP - SN - 0363-0129 1095-7138 UR - http://dx.doi.org/10.1137/s0363012903427336 DB - Crossref KW - cohypomonotone operator KW - common zero problem KW - hypomonotone operator KW - method of multipliers KW - nonlinear programming KW - proximal point method KW - weak convergence ER - TY - JOUR TI - Solving monotone inclusions via compositions of nonexpansive averaged operators AU - Combettes, Patrick L. T2 - Optimization AB - Abstract A unified fixed point theoretic framework is proposed to investigate the asymptotic behavior of algorithms for finding solutions to monotone inclusion problems. The basic iterative scheme under consideration involves nonstationary compositions of perturbed averaged nonexpansive operators. The analysis covers proximal methods for common zero problems as well as for various splitting methods for finding a zero of the sum of monotone operators. Keywords: Averaged operatorDouglas–Rachford methodForward–backward methodMonotone inclusionMonotone operatorProximal point algorithmMathematics Subject Classifications 2000: 47B3347H0547H1054H25 Notes E-mail: plc@math.jussieu.fr Additional informationNotes on contributorsPatrick L. Combettes Footnote* E-mail: plc@math.jussieu.fr DA - 2004/10// PY - 2004/10// DO - 10.1080/02331930412331327157 VL - 53 IS - 5-6 SP - 475–504 SN - 0233-1934 1029-4945 UR - http://dx.doi.org/10.1080/02331930412331327157 KW - averaged operator KW - Douglas-Rach ford method KW - forward-backward method KW - monotone inclusion KW - monotone operator KW - proximal point algorithm ER - TY - BOOK TI - Applied Mathematical Models in Human Physiology AU - Ottesen, Johnny T. AU - Olufsen, Mette S. AU - Larsen, Jesper K. AB - Preface 1. Introduction 2. Cardiovascular and pulmonary physiology and anatomy 3. Blood flow in the heart 4. The ejection effect of the pumping heart 5. Modeling flow and pressure in the systemic arteries 6. A cardiovascular model 7. A baroreceptor model 8. Respiration Appendices Bibliography Index. DA - 2004/1// PY - 2004/1// DO - 10.1137/1.9780898718287 OP - PB - Society for Industrial and Applied Mathematics SN - 9780898715392 9780898718287 UR - http://dx.doi.org/10.1137/1.9780898718287 DB - Crossref ER - TY - JOUR TI - Modeling Cerebral Blood Flow Control During Posture Change from Sitting to Standing AU - Olufsen, Mette AU - Tran, Hien AU - Ottesen, Johnny T2 - Cardiovascular Engineering AB - Hypertension, decreased cerebral blood flow, and diminished cerebral blood flow velocity regulation, are among the first signs indicating the presence of cerebral vascular disease. In this paper, we will present a mathematical model that can predict blood flow and pressure during posture change from sitting to standing. The mathematical model uses a compartmental approach to describe pulsatile blood flow velocity and pressure in a number of compartments representing the systemic circulation. Our model includes compartments representing the trunk and upper extremities, the lower extremities, the brain, and the heart. We use physiologically based control mechanisms to describe the regulation of cerebral blood flow velocity and arterial pressure in response to orthostatic hypotension resulting from postural change. To justify the fidelity of our mathematical model and control mechanisms development, we will show validation results of our model against experimental data from a young subject. DA - 2004/3// PY - 2004/3// DO - 10.1023/b:care.0000025122.46013.1a VL - 4 IS - 1 SP - 47-58 J2 - Cardiovascular Engineering LA - en OP - SN - 1567-8822 UR - http://dx.doi.org/10.1023/b:care.0000025122.46013.1a DB - Crossref ER - TY - JOUR TI - Non-negative cd-coefficients of Gorenstein∗ posets AU - Reading, Nathan T2 - Discrete Mathematics AB - We give a convolution formula for cd-index coefficients. The convolution formula, together with the proof by Davis and Okun of the Charney–Davis Conjecture in dimension 3, imply that certain cd-coefficients are non-negative for all Gorenstein∗ posets. Additional coefficients are shown to be non-negative by interpreting them in terms of the top homology of certain Cohen–Macaulay complexes. In particular we verify, up to rank 6, Stanley's conjecture that the coefficients in the cd-index of a Gorenstein∗ ranked poset are non-negative. DA - 2004/1// PY - 2004/1// DO - 10.1016/j.disc.2003.07.001 VL - 274 IS - 1-3 SP - 323-329 J2 - Discrete Mathematics LA - en OP - SN - 0012-365X UR - http://dx.doi.org/10.1016/j.disc.2003.07.001 DB - Crossref KW - cd-index KW - Charney-Davis conjecture KW - eulerian poset KW - flag f-vector KW - Gorenstein ER - TY - JOUR TI - Lattice Congruences of the Weak Order AU - Reading, Nathan T2 - Order AB - We study the congruence lattice of the poset of regions of a hyperplane arrangement, with particular emphasis on the weak order on a finite Coxeter group. Our starting point is a theorem from a previous paper which gives a geometric description of the poset of join-irreducibles of the congruence lattice of the poset of regions in terms of certain polyhedral decompositions of the hyperplanes. For a finite Coxeter system (W,S) and a subset $K\subseteq S$ , let ηK: w↦wK be the projection onto the parabolic subgroup WK. We show that the fibers of ηK constitute the smallest lattice congruence with 1≡s for every s∈(S−K). We give an algorithm for determining the congruence lattice of the weak order for any finite Coxeter group and for a finite Coxeter group of type A or B we define a directed graph on subsets or signed subsets such that the transitive closure of the directed graph is the poset of join-irreducibles of the congruence lattice of the weak order. DA - 2004/11// PY - 2004/11// DO - 10.1007/s11083-005-4803-8 VL - 21 IS - 4 SP - 315-344 J2 - Order LA - en OP - SN - 0167-8094 1572-9273 UR - http://dx.doi.org/10.1007/s11083-005-4803-8 DB - Crossref KW - Cambrian lattice KW - congruence uniform KW - Coxeter group KW - parabolic subgroup KW - poset of regions KW - shard KW - simplicial hyperplane arrangement KW - Tamari lattice KW - weak order ER - TY - JOUR TI - Connectivity of h-complexes AU - Hersh, Patricia T2 - Journal of Combinatorial Theory, Series A AB - This paper verifies a conjecture of Edelman and Reiner regarding the homology of the h -complex of a Boolean algebra. A discrete Morse function with no low-dimensional critical cells is constructed, implying a lower bound on connectivity. This together with an Alexander duality result of Edelman and Reiner implies homology vanishing also in high dimensions. Finally, possible generalizations to certain classes of supersolvable lattices are suggested. DA - 2004/1// PY - 2004/1// DO - 10.1016/j.jcta.2003.10.006 VL - 105 IS - 1 SP - 111-126 J2 - Journal of Combinatorial Theory, Series A LA - en OP - SN - 0097-3165 UR - http://dx.doi.org/10.1016/j.jcta.2003.10.006 DB - Crossref KW - discrete morse function KW - h-vector KW - Charney-Davis quantity ER - TY - JOUR TI - A Hodge decomposition for the complex of injective words AU - Hanlon, Phil AU - Hersh, Patricia T2 - Pacific Journal of Mathematics AB - llReiner and Webb (preprint, 2002) compute the S n -module structure for the complex of injective words. This paper refines their formula by providing a Hodge type decomposition. Along the way, this paper proves that the simplicial boundary map interacts in a nice fashion with the Eulerian idempotents. The Laplacian acting on the top chain group in the complex of injective words is also shown to equal the signed random to random shuffle operator. Uyemura-Reyes, 2002, conjectured that the (unsigned) random to random shuffle operator has integral spectrum. We prove that this conjecture would imply that the Laplacian on (each chain group in) the complex of injective words has integral spectrum. DA - 2004/3/1/ PY - 2004/3/1/ DO - 10.2140/pjm.2004.214.109 VL - 214 IS - 1 SP - 109-125 J2 - Pacific J. Math. LA - en OP - SN - 0030-8730 UR - http://dx.doi.org/10.2140/pjm.2004.214.109 DB - Crossref ER - TY - JOUR TI - Ideals of adjacent minors AU - Hoşten, Serkan AU - Sullivant, Seth T2 - Journal of Algebra AB - We give a description of the minimal primes of the ideal generated by the 2×2 adjacent minors of a generic matrix. We also compute the complete prime decomposition of the ideal of adjacent m×m minors of an m×n generic matrix when the characteristic of the ground field is zero. A key intermediate result is the proof that the ideals which appear as minimal primes are, in fact, prime ideals. This introduces a large new class of mixed determinantal ideals that are prime. DA - 2004/7// PY - 2004/7// DO - 10.1016/j.jalgebra.2004.01.027 VL - 277 IS - 2 SP - 615-642 J2 - Journal of Algebra LA - en OP - SN - 0021-8693 UR - http://dx.doi.org/10.1016/j.jalgebra.2004.01.027 DB - Crossref ER - TY - JOUR TI - A Divide-and-Conquer Algorithm for Generating Markov Bases of Multi-way Tables AU - Dobra, Adrian AU - Sullivant, Seth T2 - Computational Statistics DA - 2004/9// PY - 2004/9// DO - 10.1007/bf03372101 VL - 19 IS - 3 SP - 347-366 J2 - CompStat LA - en OP - SN - 0943-4062 1613-9658 UR - http://dx.doi.org/10.1007/bf03372101 DB - Crossref KW - contingency tables KW - decomposable graphical models KW - disclosure limitation KW - exact distributions KW - Grobner bases KW - Markov bases ER - TY - CONF TI - The North Carolina State University women in science and engineering program: a community for living and learning AU - Rajala, S. A. AU - Bottomley, L.J. AU - Parry, E. A. AU - Cohen, J. D. AU - Grant, S. C. AU - Thomas, C. J. AU - Doxey, T. M. AU - Perez, G. AU - Collins, R. E. AU - Spurlin, J. E. C2 - 2004/// C3 - American Society for Engineering Education DA - 2004/// ER - TY - JOUR TI - Oversampling, quasi-affine frames, and wave packets AU - Hernandez, E. AU - Labate, D. AU - Weiss, G. AU - al., T2 - Applied and Computational Harmonic Analysis AB - In [E. Hernández, D. Labate, G. Weiss, J. Geom. Anal. 12 (4) (2002) 615–662], three of the authors obtained a characterization of certain types of reproducing systems. In this work, we apply these results and methods to various affine-like, wave packets and Gabor systems to determine their frame properties. In particular, we study how oversampled systems inherit properties (like the frame bounds) of the original systems. Moreover, our approach allows us to study the phenomenon of oversampling in much greater generality than is found in the literature. DA - 2004/// PY - 2004/// DO - 10.1016/j.acha.2003.12.002 VL - 16 IS - 2 SP - 111-147 ER - TY - JOUR TI - Polymorphism in the interleukin-10 promoter affects both provirus load and the risk of human T lymphotropic virus type I-associated myelopathy/tropical spastic paraparesis AU - Sabouri, AH AU - Saito, M AU - Lloyd, AL AU - Vine, AM AU - Witkover, AW AU - Furukawa, Y AU - Izumo, S AU - Arimura, K AU - Marshall, SEF AU - Usuku, K AU - Bangham, CRM AU - Osame, M T2 - JOURNAL OF INFECTIOUS DISEASES AB - To investigate non-human leukocyte antigen candidate genes that influence the outcome of human T cell lymphotropic virus (HTLV) type I infection, we analyzed 6 single-nucleotide polymorphisms in the interleukin (IL)-10 promoter region in 280 patients with HTLV-I-associated myelopathy/tropical spastic paraparesis (HAM/TSP) and 255 HTLV-I-seropositive asymptomatic carriers from an area where HTLV-I is endemic. The IL-10 -592 A allele, which shows lower HTLV-I Tax-induced transcriptional activity than the C allele in the Jurkat T cell line, was associated with a >2-fold reduction in the odds of developing HAM/TSP (P=.011; odds ratio [OR], 0.50 [95% confidence interval, 0.30-0.86]) by reducing the provirus load in the whole cohort (P=.009, analysis of variance). Given the OR and the observed frequency of IL-10 -592 A, we demonstrate that this allele prevents approximately 44.7% (standard deviation, +/-13.1%) of potential cases of HAM/TSP, which indicates that it defines one component of the genetic susceptibility to HAM/TSP in the cohort. DA - 2004/10/1/ PY - 2004/10/1/ DO - 10.1086/423942 VL - 190 IS - 7 SP - 1279-1285 SN - 1537-6613 ER - TY - JOUR TI - Variance reduction for Monte Carlo methods to evaluate option prices under multi-factor stochastic volatility models AU - Fouque, JP AU - Han, CH T2 - QUANTITATIVE FINANCE AB - We present variance reduction methods for Monte Carlo simulations to evaluate European and Asian options in the context of multiscale stochastic volatility models. European option price approximations, obtained from singular and regular perturbation analysis [Fouque J P, Papanicolaou G, Sircar R and Solna K 2003 Multiscale stochastic volatility asymptotics, SIAM J. Multiscale Modeling and Simulation 2], are used in importance sampling techniques, and their efficiencies are compared. Then we investigate the problem of pricing arithmetic average Asian options (AAOs) by Monte Carlo simulations. A two-step strategy is proposed to reduce the variance where geometric average Asian options (GAOs) are used as control variates. Due to the lack of analytical formulas for GAOs under stochastic volatility models, it is then necessary to consider efficient Monte Carlo methods to estimate the unbiased means of GAOs. The second step consists in deriving formulas for approximate prices based on perturbation techniques, a... DA - 2004/10// PY - 2004/10// DO - 10.1080/14697680400020317 VL - 4 IS - 5 SP - 597-606 SN - 1469-7696 ER - TY - JOUR TI - Modeling and optimal regulation of erythropoiesis subject to benzene intoxication AU - Banks, HT AU - Cole, CE AU - Schlosser, PM AU - Tran, HT T2 - MATHEMATICAL BIOSCIENCES AND ENGINEERING AB - Benzene (C(6)H(6)) is a highly flammable, colorless liquid. Ubiquitous exposures result from its presence in gasoline vapors, cigarette smoke, and industrial processes. Benzene increases the incidence of leukemia in humans when they are exposed to high doses for extended periods; however, leukemia risks in humans subjected to low exposures are uncertain. The exposure-dose- response relationship of benzene in humans is expected to be nonlinear because benzene undergoes a series of metabolic transformations, detoxifying and activating, resulting in various metabolites that exert toxic effects on the bone marrow. Since benzene is a known human leukemogen, the toxicity of benzene in the bone marrow is of most importance. And because blood cells are produced in the bone marrow, we investigated the effects of benzene on hematopoiesis (blood cell production and development). An age-structured model was used to examine the process of erythropoiesis, the development of red blood cells. This investigation proved the existence and uniqueness of the solution of the system of coupled partial and ordinary differential equations. In addition, we formulated an optimal control problem for the control of erythropoiesis and performed numerical simulations to compare the performance of the optimal feedback law and another feedback function based on the Hill function. DA - 2004/6// PY - 2004/6// DO - 10.3934/mbe.2004.1.15 VL - 1 IS - 1 SP - 15-48 SN - 1547-1063 KW - hematopoiesis KW - age-structured model KW - existence and uniqueness KW - optimal control ER - TY - JOUR TI - Dynamic multidrug therapies for HIV: Optimal and STI control approaches AU - Adams, B. M. AU - Banks, H. T. AU - Kwon, H. D. AU - Tran, Hien T2 - Mathematical Biosciences and Engineering AB - We formulate a dynamic mathematical model that describes the interaction of the immune system with the human immunodeficiency virus (HIV) and that permits drug ''cocktail'' therapies. We derive HIV therapeutic strategies by formulating and analyzing an optimal control problem using two types of dynamic treatments representing reverse transcriptase (RT) inhibitors and protease inhibitors (PIs). Continuous optimal therapies are found by solving the corresponding optimality systems. In addition, using ideas from dynamic programming, we formulate and derive suboptimal structured treatment interruptions (STI) in antiviral therapy that include drug-free periods of immune-mediated control of HIV. Our numerical results support a scenario in which STI therapies can lead to long-term control of HIV by the immune response system after discontinuation of therapy. DA - 2004/// PY - 2004/// DO - 10.3934/mbe.2004.1.223 VL - 1 IS - 2 SP - 223–241 ER - TY - JOUR TI - Gradient driven and singular flux blowup of smooth solutions to hyperbolic systems of conservation laws AU - Jenssen, HK AU - Young, R T2 - JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS AB - We consider two new classes of examples of sup-norm blowup in finite time for strictly hyperbolic systems of conservation laws. The explosive growth in amplitude is caused either by a gradient catastrophe or by a singularity in the flux function. The examples show that solutions of uniformly strictly hyperbolic systems can remain as smooth as the initial data until the time of blowup. Consequently, blowup in amplitude is not necessarily strictly preceded by shock formation. DA - 2004/12// PY - 2004/12// DO - 10.1142/S021989160400024X VL - 1 IS - 4 SP - 627-641 SN - 1793-6993 KW - blowup KW - smoothness KW - systems of hyperbolic conservation laws ER - TY - JOUR TI - Comparison of two dynamic contact line models for driven thin liquid films AU - Levy, R AU - Shearer, M T2 - EUROPEAN JOURNAL OF APPLIED MATHEMATICS AB - The modeling of the motion of a contact line, the triple point at which solid, liquid and air meet, is a major outstanding problem in the fluid mechanics of thin films [2, 9]. In this paper, we compare two well-known models in the specific context of Marangoni driven films. The precursor model replaces the contact line by a sharp transition between the bulk fluid and a thin layer of fluid, effectively pre-wetting the solid; the Navier slip model replaces the usual no-slip boundary condition by a singular slip condition that is effective only very near the contact line. We restrict attention to traveling wave solutions of the thin film PDE for a film driven up an inclined planar solid surface by a thermally induced surface tension gradient. This involves analyzing third order ODE that depend on several parameters. The two models considered here have subtle differences in their description, requiring a careful treatment when comparing traveling waves and effective contact angles. Numerical results exhibit broad agreement between the two models, but the closest comparison can be done only for a rather restricted range of parameters. The driven film context gives contact angle results quite different from the case of a film moving under the action of gravity alone. The numerical technique for exploring phase portraits for the third order ODE is also used to tabulate the kinetic relation and nucleation condition, information that can be used with the underlying hyperbolic conservation law to explain the rich combination of wave structures observed in simulations of the PDE and in experiments [3, 15]. DA - 2004/12// PY - 2004/12// DO - 10.1017/S0956792504005741 VL - 15 SP - 625-642 SN - 1469-4425 ER - TY - JOUR TI - Control of mobile communication systems with time-varying channels via stability methods AU - Buche, R AU - Kushner, HJ T2 - IEEE TRANSACTIONS ON AUTOMATIC CONTROL AB - Consider the forward link of a mobile communications system with a single transmitter and connecting to K destinations via randomly varying channels. Data arrives in some random way and is queued according to the K destinations until transmitted. Time is divided into small scheduling intervals. Current systems can estimate the channel (e.g, via pilot signals) and use this information for scheduling. The issues are the allocation of transmitter power and/or time and bandwidth to the various queues in a queue and channel-state dependent way to assure stability and good operation. The decisions are made at the beginning of the scheduling intervals. Stochastic stability methods are used both to assure that the system is stable and to get appropriate allocations, under very weak conditions. The choice of Lyapunov function allows a choice of the effective performance criteria. The resulting controls are readily implementable and allow a range of tradeoffs between current rates and queue lengths. The various extensions allow a large variety of schemes of current interest to be covered. All essential factors are incorporated into a "mean rate" function, so that the results cover many different systems. Because of the non-Markovian nature of the problem, we use the perturbed Stochastic Lyapunov function method, which is well adapted to such problems. The method is simple and effective. DA - 2004/11// PY - 2004/11// DO - 10.1109/TAC.2004.837590 VL - 49 IS - 11 SP - 1954-1962 SN - 0018-9286 KW - mobile communications KW - perturbed Lyapunov function KW - stability KW - time-varying systems ER - TY - JOUR TI - Non-classical Riemann solvers with nucleation AU - LeFloch, PG AU - Shearer, M T2 - PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS AB - We introduce a new non-classical Riemann solver for scalar conservation laws with concave–convex flux-function. This solver is based on both a kinetic relation, which determines the propagation speed of (under-compressive) non-classical shock waves, and a nucleation criterion, which makes a choice between a classical Riemann solution and a non-classical one. We establish the existence of (non-classical entropy) solutions of the Cauchy problem and discuss several examples of wave interactions. We also show the existence of a class of solutions, called splitting–merging solutions, which are made of two large shocks and small bounded-variation perturbations. The nucleation solvers, as we call them, are applied to (and actually motivated by) the theory of thin-film flows; they help explain numerical results observed for such flows. DA - 2004/// PY - 2004/// DO - 10.1017/s0308210500003577 VL - 134 IS - 2004 SP - 961-984 SN - 1473-7124 ER - TY - BOOK TI - Computational mathematics: Models, methods, and analysis with MATLAB and MPI AU - White, R. E. CN - QA297 .W495 2004 DA - 2004/// PY - 2004/// PB - Boca Raton, Fla.: Chapman & Hall/CRC SN - 1584883642 ER - TY - JOUR TI - Wavelets with composite dilations AU - Guo, KH AU - Labate, D AU - Lim, WQ AU - Weiss, G AU - Wilson, E T2 - ELECTRONIC RESEARCH ANNOUNCEMENTS OF THE AMERICAN MATHEMATICAL SOCIETY AB - A wavelet with composite dilations is a function generating an orthonormal basis or a Parseval frame for L 2 ( R n ) L^2({\mathbb R}^n) under the action of lattice translations and dilations by products of elements drawn from non-commuting matrix sets A A and B B . Typically, the members of B B are shear matrices (all eigenvalues are one), while the members of A A are matrices expanding or contracting on a proper subspace of R n {\mathbb R}^n . These wavelets are of interest in applications because of their tendency to produce “long, narrow” window functions well suited to edge detection. In this paper, we discuss the remarkable extent to which the theory of wavelets with composite dilations parallels the theory of classical wavelets, and present several examples of such systems. DA - 2004/// PY - 2004/// DO - 10.1090/S1079-6762-04-00132-5 VL - 10 SP - 78-87 SN - 1079-6762 KW - affine systems KW - frames KW - multiresolution analysis (MRA) KW - multiwavelets KW - wavelets ER - TY - JOUR TI - Radiographic and clinical changes of the tibial tuberosity after tibial plateau leveling osteotomy AU - Kergosien, DH AU - Barnhart, MD AU - Kees, CE AU - Danielson, BG AU - Brourman, JD AU - Dehoff, WD AU - Schertel, ER T2 - VETERINARY SURGERY AB - Objective— To investigate radiographic changes of the tibial tuberosity after tibial plateau leveling osteotomy (TPLO) surgery and identify clinical findings and risk factors associated with such changes. Study Design— Retrospective study. Sample Population— Hundred and eighty‐six client‐owned dogs (219 stifles) that had TPLO surgery. Methods— Patient data retrieved included radiographic changes of the tibial tuberosity during re‐examination, age, body weight, whether unilateral or single‐session bilateral surgery had been performed, location of the anti‐rotational pin, approximate tibial tuberosity area, and approximate average tibial tuberosity width. Results— Fracture with resulting caudal displacement of the proximal tibial tuberosity (1.4%; 3 of 219) occurred less frequently than non‐displaced tibial tuberosity fractures (7.3%; 16 of 219). Age, weight, average tibial tuberosity width, location of the anti‐rotational pin, and single session bilateral surgery were identified as risks factors for non‐displaced fracture. Weight divided by the square of the average tibial tuberosity width may be a stronger risk factor than either weight or average tibial tuberosity width alone. Conclusions— Dogs undergoing single session bilateral TPLO surgery are at greater risk for developing non‐displaced tibial tuberosity fractures. The non‐displaced tibial tuberosity fracture does not appear to adversely affect outcome or lead to tibial tuberosity avulsion. Significant risk factors for fracture of the proximal tibial tuberosity with caudal displacement were not identified. Clinical Relevance— Factors including age, weight, tibial tuberosity thickness, and conditions that may enhance strain on the tibial tuberosity, such as single‐session bilateral procedures, may increase risk of fracture. DA - 2004/// PY - 2004/// DO - 10.1111/j.1532-950X.2004.04066.x VL - 33 IS - 5 SP - 468-474 SN - 0161-3499 KW - tibial plateau leveling osteotomy KW - tibial tuberosity KW - radiographic change KW - cranial cruciate ligament KW - dog ER - TY - JOUR TI - On the semigroup of standard symplectic matrices and its applications AU - Chu, M AU - Del Buono, N AU - Diele, F AU - Politi, T AU - Ragni, S T2 - LINEAR ALGEBRA AND ITS APPLICATIONS AB - A matrix Z∈R2n×2n is said to be in the standard symplectic form if Z enjoys a block LU-decomposition in the sense of A0−HIZ=IG0AT, where A is nonsingular and both G and H are symmetric and positive definite in Rn×n. Such a structure arises naturally in the discrete algebraic Riccati equations. This note contains two results: First, by means of a parameter representation it is shown that the set of all 2n×2n standard symplectic matrices is closed under multiplication and, thus, forms a semigroup. Secondly, block LU-decompositions of powers of Z can be derived in closed form which, in turn, can be employed recursively to induce an effective structure-preserving algorithm for solving the Riccati equations. The computational cost of doubling and tripling of the powers is investigated. It is concluded that doubling is the better strategy. DA - 2004/9/15/ PY - 2004/9/15/ DO - 10.1016/j.laa.2004.03.017 VL - 389 IS - 1-3 SP - 215-225 SN - 1873-1856 UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-3943079249&partnerID=MN8TOARS KW - standard symplectic form KW - discrete algebraic Riccati equation KW - structure preserving KW - power method KW - block LU decomposition KW - semigroup ER - TY - JOUR TI - On the application of lacunae-based methods to Maxwell's equations AU - Tsynkov, Semyon T2 - Journal of Computational Physics DA - 2004/// PY - 2004/// DO - 10.1016/.jcp.2004.02.003 VL - 199 IS - 1 SP - 126–149 ER - TY - JOUR TI - Approximate solution of singular integro-differential equations by reduction over Faber-Laurent polynomials AU - Zolotarevskii, VA AU - Li, ZL AU - Caraus, I T2 - DIFFERENTIAL EQUATIONS DA - 2004/12// PY - 2004/12// DO - 10.1007/s10625-005-0108-3 VL - 40 IS - 12 SP - 1764-1769 SN - 0012-2661 ER - TY - JOUR TI - Probabilities of extinction, weak extinction, permanence, and mutual exclusion in discrete, competitive, Lotka-Volterra systems that involve invading species AU - Chan, DM AU - Franke, JE T2 - MATHEMATICAL AND COMPUTER MODELLING AB - The probabilities of various biological asymptotic dynamics are computed for a stable system that is invaded by another competing species. The asymptotic behaviors studied include extinction, weak extinction, permanence, and mutual exclusion. The model used is a discrete Lotka-Volterra system that models species that compete for the same resources. Among the results found are that the chance of permanence occurring in the invaded system is significantly higher than the probability of permanence in a purely random system, and that multiple extinctions that include the invading species and one of the original species are impossible. DA - 2004/10// PY - 2004/10// DO - 10.1016/j.mcm.2004.10.013 VL - 40 IS - 7-8 SP - 809-821 SN - 1872-9479 KW - extinction KW - permanence KW - mutual exclusion KW - competition KW - Lotka-Volterra KW - weak extinction KW - invader KW - strongly permanent ER - TY - JOUR TI - Path collapse for multidimensional Brownian motion with rebirth AU - Grigorescu, I AU - Kang, M T2 - STATISTICS & PROBABILITY LETTERS AB - In a bounded open region of the d-dimensional Euclidean space we consider a Brownian motion which is reborn at a fixed interior point as soon as it reaches the boundary. It was shown that in dimension one coupled paths starting at different points but driven by the same Brownian motion either collapse with probability one or never meet. In higher dimensions, for convex or polyhedral regions, the paths with positive probability of collapse differ at start by a vector from a set of codimension one. The problem can be interpreted in terms of the long term mixing properties of the payoff of a portfolio of knock-out barrier options in derivatives markets. DA - 2004/12/1/ PY - 2004/12/1/ DO - 10.1016/j.spl.2004.10.006 VL - 70 IS - 3 SP - 199-209 SN - 1879-2103 KW - absorbing Brownian motion KW - harmonic measure KW - collapsing paths KW - barrier options ER - TY - JOUR TI - LBIC imaging of semiconductor arrays: The cross-sectional model AU - Fang, WF AU - Ito, K AU - Redfern, DA T2 - MATHEMATICAL AND COMPUTER MODELLING AB - Laser beam induced current (LBIC)/nondestructive technique that has been used for a number of years to qualitatively examine large arrays of p-n junctions, especially in HgCdTe infrared focal plane arrays. In this paper, we quantitatively study the application of the LBIC imaging technique to semiconductor arrays Based on a previous mathematical model for LBIC applied to individual devices, we employ the homogenization method to derive approximations of the LBIC images of large arrays. Such approximations reduce the computational burden in simulations of these LBIC bouges. We then illustrate the application of our approximations for the purpose of recovering array parameters from the LBIC images. DA - 2004/7// PY - 2004/7// DO - 10.1016/j.mcm.2003.10.045 VL - 40 IS - 1-2 SP - 127-136 SN - 1872-9479 KW - homogenization KW - LBIC KW - semiconductor arrays KW - inverse problem KW - parameter identification ER - TY - JOUR TI - Kronecker product approximate preconditioner for SANs AU - Langville, AN AU - Stewart, WJ T2 - NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS AB - Abstract Many very large Markov chains can be modelled efficiently as stochastic automata networks (SANs). A SAN is composed of individual automata which, for the most part, act independently, requiring only infrequent interaction. SANs represent the generator matrix Q of the underlying Markov chain compactly as the sum of Kronecker products of smaller matrices. Thus, storage savings are immediate. The benefit of a SAN's compact representation, known as the descriptor, is often outweighed by its tendency to make analysis of the underlying Markov chain tough. While iterative or projections methods have been used to solve the system π Q =0, the time until these methods converge to the stationary solution π is still unsatisfactory. SAN's compact representation has made the next logical research step of preconditioning thorny. Several preconditioners for SANs have been proposed and tested, yet each has enjoyed little or no success. Encouraged by the recent success of approximate inverses as preconditioners, we have explored their potential as SAN preconditioners. One particularly relevant finding on approximate inverse preconditioning is the nearest Kronecker product approximation discovered by Pitsianis and Van Loan. In this paper, we extend the nearest Kronecker product technique to approximate the Q matrix for an SAN with a Kronecker product, A 1 ⊗ A 2 ⊗…⊗ A N . Then, we take M = A ⊗ A ⊗…⊗ A as our SAN NKP preconditioner. Copyright © 2004 John Wiley & Sons, Ltd. DA - 2004/// PY - 2004/// DO - 10.1002/nla.344 VL - 11 IS - 8-9 SP - 723-752 SN - 1099-1506 KW - stochastic automata networks KW - nearest Kronecker products KW - inultilinear alaebra KW - preconditioning ER - TY - JOUR TI - Existence of Dafermos profiles for singular shocks AU - Schecter, S. T2 - Journal of Differential Equations DA - 2004/// PY - 2004/// DO - 10.1016/j.ide.2004.06.013 VL - 205 IS - 1 SP - 185-210 ER - TY - JOUR TI - Time-reversal simulations for detection in randomly layered media AU - Haider, MA AU - Mehta, KJ AU - Fouque, JP T2 - WAVES IN RANDOM MEDIA AB - Abstract A time-reversal mirror is, roughly speaking, a device which is capable of receiving an acoustic signal in time, keeping it in memory and sending it back into the medium in the reversed direction of time. In this paper, we employ an accurate numerical method for simulating waves propagating in complex one-dimensional media. We use numerical simulations to reproduce the time-reversal self-averaging effect which takes place in randomly layered media. This is done in the regime where the inhomogeneities are smaller than the pulse, which propagates over long distances compared to its width. We show numerical evidence for possible use of an expanding window time-reversal technique for detecting anomalies buried in the medium. DA - 2004/4// PY - 2004/4// DO - 10.1088/0959-7174/14/2/007 VL - 14 IS - 2 SP - 185-198 SN - 0959-7174 ER - TY - JOUR TI - The McCormack model: channel flow of a binary gas mixture driven by temperature, pressure and density gradients AU - Siewert, CE AU - Valougeorgis, D T2 - EUROPEAN JOURNAL OF MECHANICS B-FLUIDS AB - An analytical version of the discrete-ordinates method (the ADO method) is used to establish concise and particularly accurate solutions to the problems of Poiseuille flow, thermal-creep flow and diffusion flow for a binary gas mixture confined between parallel walls. The kinetic equations used to describe the flow are based on the McCormack model for mixtures. The analysis yields, for the general (specular-diffuse) case of Maxwell boundary conditions for each of the two species, the velocity, heat-flow and shear-stress profiles for both types of particles. Numerical results are reported for two binary mixtures (Ne–Ar and He–Xe) with various molar concentrations. The complete solution requires only a (matrix) eigenvalue/eigenvector routine and a solver of a system of linear algebraic equations, and thus the algorithm is considered especially easy to use. The developed (FORTRAN) code requires typically less than a second on a 2.2 GHz Pentium IV machine to solve all three problems. DA - 2004/// PY - 2004/// DO - 10.1016/j.euromechflu.2004.03.003 VL - 23 IS - 4 SP - 645-664 SN - 1873-7390 ER - TY - JOUR TI - Stochastic volatility corrections for interest rate derivatives AU - Cotton, P. AU - Fouque, J. P. AU - Papanicolaou, G. AU - Sircar, R. T2 - Mathematical Finance: An International Journal of Mathematics, Statistics, and Financial Theory DA - 2004/// PY - 2004/// VL - 14 IS - 2 SP - 173-200 ER - TY - JOUR TI - Special issue devoted to papers presented at the Conference on the Numerical Solution of Markov Chains 2003 - Preface AU - Langville, AN AU - Stewart, WJ T2 - LINEAR ALGEBRA AND ITS APPLICATIONS DA - 2004/7/15/ PY - 2004/7/15/ DO - 10.1016/j.laa.2004.02.016 VL - 386 SP - 1-2 SN - 1873-1856 ER - TY - JOUR TI - Solution of a well-field design problem with implicit filtering AU - Fowler, KR AU - Kelley, CT AU - Miller, CT AU - Kees, CE AU - Darwin, RW AU - Reese, JP AU - Farthing, MW AU - Reed, MSC T2 - OPTIMIZATION AND ENGINEERING AB - Problems involving the management of groundwater resources occur routinely, and management decisions based upon optimization approaches offer the potential to save substantial amounts of money. However, this class of application is notoriously difficult to solve due to non-convex objective functions with multiple local minima and both nonlinear models and nonlinear constraints. We solve a subset of community test problems from this application field using MODFLOW, a standard groundwater flow model, and IFFCO, an implicit filtering algorithm that was designed to solve problems similar to those of focus in this work. While sampling methods have received only scant attention in the groundwater optimization literature, we show encouraging results that suggest they are deserving of more widespread consideration for this class of problems. In keeping with our objectives for the community problems, we have packaged the approaches used in this work to facilitate additional work on these problems by others and the application of implicit filtering to other problems in this field. We provide the data for our formulation and solution on the web. DA - 2004/6// PY - 2004/6// DO - 10.1023/B:OPTE.0000033375.33183.e7 VL - 5 IS - 2 SP - 207-234 SN - 1573-2924 KW - implicit filtering KW - well field design KW - groundwater flow and transport ER - TY - JOUR TI - Maturity cycles in implied volatility AU - Fouque, JP AU - Papanicolaou, G AU - Sircar, R AU - Solna, K T2 - FINANCE AND STOCHASTICS AB - The skew effect in market implied volatility can be reproduced by option pricing theory based on stochastic volatility models for the price of the underlying asset. Here we study the performance of the calibration of the S&P 500 implied volatility surface using the asymptotic pricing theory under fast mean-reverting stochastic volatility described in [8]. The time-variation of the fitted skew-slope parameter shows a periodic behaviour that depends on the option maturity dates in the future, which are known in advance. By extending the mathematical analysis to incorporate model parameters which are time-varying, we show this behaviour can be explained in a manner consistent with a large model class for the underlying price dynamics with time-periodic volatility coefficients. DA - 2004/11// PY - 2004/11// DO - 10.1007/s00780-004-0126-7 VL - 8 IS - 4 SP - 451-477 SN - 1432-1122 KW - implied volatilities KW - maturity cycles KW - fast mean-reverting stochastic volatility KW - asymptotic expansions ER - TY - JOUR TI - L-infinity structures on spaces with three one-dimensional components AU - Daily, M T2 - COMMUNICATIONS IN ALGEBRA AB - Abstract L ∞ structures have been a subject of recent interest in physics, where they occur in closed string theory and in gauge theory. This paper provides a class of easily constructible examples of L n and L ∞ structures on graded vector spaces with three one-dimensional components. In particular, it demonstrates a way to classify all possible L n and L ∞ structures on V = V m ⊕ V m+1 ⊕ V m+2 when each of the three components is one-dimensional. Included are necessary and sufficient conditions under which a space with an L 3 structure is a differential graded Lie algebra. It is also shown that some of these differential graded Lie algebras possess a nontrivial L n structure for higher n. DA - 2004/// PY - 2004/// DO - 10.1081/AGB-120029922 VL - 32 IS - 5 SP - 2041-2059 SN - 0092-7872 KW - L-intinity algebras KW - strongly homotopy Lie algebras ER - TY - JOUR TI - Injective properties of complex matrices AU - Meyer, C. T2 - American Mathematical Monthly DA - 2004/// PY - 2004/// DO - 10.2307/4145059 VL - 111 IS - 8 SP - 728 ER - TY - JOUR TI - Deterministic distinct-degree factorization of polynomials over finite fields AU - Gao, SH AU - Kaltofen, E AU - Lauder, AGB T2 - JOURNAL OF SYMBOLIC COMPUTATION AB - A deterministic polynomial time algorithm is presented for finding the distinct-degree factorization of multivariate polynomials over finite fields. As a consequence, one can count the number of irreducible factors of polynomials over finite fields in deterministic polynomial time, thus resolving a theoretical open problem of Kaltofen from 1987. DA - 2004/12// PY - 2004/12// DO - 10.1016/j.jsc.2004.05.004 VL - 38 IS - 6 SP - 1461-1470 SN - 0747-7171 KW - multivariate polynomial KW - deterministic algorithm KW - distinct-degree factorization ER - TY - JOUR TI - Determinantal identities over commutative semirings AU - Poplin, PL AU - Hartwig, RE T2 - LINEAR ALGEBRA AND ITS APPLICATIONS AB - We present a development of determinantal identities over commutative semirings. This includes a generalization of the Cauchy–Binet and Laplace Theorems, as well as results on compound matrices and adjoints. It is further shown that Laplace's Theorem is a special case of the grade-s-adjoint identity. DA - 2004/8/1/ PY - 2004/8/1/ DO - 10.1016/j.laa.2004.02.019 VL - 387 SP - 99-132 SN - 0024-3795 KW - semiring KW - determinant KW - laplace KW - Cauchy-Binet ER - TY - JOUR TI - Variability of the recent climate of eastern Africa AU - Schreck, CJ AU - Semazzi, FHM T2 - INTERNATIONAL JOURNAL OF CLIMATOLOGY AB - Abstract The primary objective of this study is to investigate the recent variability of the eastern African climate. The region of interest is also known as the Greater Horn of Africa (GHA), and comprises the countries of Burundi, Djibouti, Eritrea, Ethiopia, Kenya, Rwanda, Somalia, Sudan, Uganda, and Tanzania. The analysis was based primarily on the construction of empirical orthogonal functions (EOFs) of gauge rainfall data and on CPC Merged Analysis of Precipitation (CMAP) data, derived from a combination of rain‐gauge observations and satellite estimates. The investigation is based on the period 1961–2001 for the ‘short rains’ season of eastern Africa of October through to December. The EOF analysis was supplemented by projection of National Centers for Environmental Prediction wind data onto the rainfall eigenmodes to understand the rainfall–circulation relationships. Furthermore, correlation and composite analyses have been performed with the Climatic Research Unit globally averaged surface‐temperature time series to explore the potential relationship between the climate of eastern Africa and global warming. The most dominant mode of variability (EOF1) based on CMAP data over eastern Africa corresponds to El Niño–southern oscillation (ENSO) climate variability. It is associated with above‐normal rainfall amounts during the short rains throughout the entire region, except for Sudan. The corresponding anomalous low‐level circulation is dominated by easterly inflow from the Indian Ocean, and to a lesser extent the Congo tropical rain forest, into the positive rainfall anomaly region that extends across most of eastern Africa. The easterly inflow into eastern Africa is part of diffluent outflow from the maritime continent during the warm ENSO events. The second eastern African EOF (trend mode) is associated with decadal variability. In distinct contrast from the ENSO mode pattern, the trend mode is characterized by positive rainfall anomalies over the northern sector of eastern Africa and opposite conditions over the southern sector. This rainfall trend mode eluded detection in previous studies that did not include recent decades of data, because the signal was still relatively weak. The wind projection onto this mode indicates that the primary flow that feeds the positive anomaly region over the northern part of eastern Africa emanates primarily from the rainfall‐deficient southern region of eastern Africa and Sudan. Although we do not assign attribution of the trend mode to global warming (in part because of the relatively short period of analysis), the evidence, based on our results and previous studies, strongly suggests a potential connection. Copyright © 2004 Royal Meteorological Society. DA - 2004/5// PY - 2004/5// DO - 10.1002/joc.1019 VL - 24 IS - 6 SP - 681-701 SN - 1097-0088 KW - eastern Africa KW - climate variability KW - climate change KW - CMAP KW - El Nino-southern oscillation KW - Greater Horn of Africa KW - Indian Ocean KW - zonal mode ER - TY - JOUR TI - Probabilistic methods for addressing uncertainty and variability in biological models: application to a toxicokinetic model AU - Banks, HT AU - Potter, LK T2 - MATHEMATICAL BIOSCIENCES AB - Population variability and uncertainty are important features of biological systems that must be considered when developing mathematical models for these systems. In this paper we present probability-based parameter estimation methods that account for such variability and uncertainty. Theoretical results that establish well-posedness and stability for these methods are discussed. A probabilistic parameter estimation technique is then applied to a toxicokinetic model for trichloroethylene using several types of simulated data. Comparison with results obtained using a standard, deterministic parameter estimation method suggests that the probabilistic methods are better able to capture population variability and uncertainty in model parameters. DA - 2004/12// PY - 2004/12// DO - 10.1016/j.mbs.2004.11.008 VL - 192 IS - 2 SP - 193-225 SN - 1879-3134 KW - parameter estimation KW - biological modeling KW - population variability KW - model uncertainty KW - toxicokinetics KW - trichloroethylene ER - TY - JOUR TI - Concise and accurate solutions to half-space binary-gas flow problems defined by the McCormack model and specular-diffuse wall conditions AU - Siewert, CE AU - Valougerogis, D T2 - EUROPEAN JOURNAL OF MECHANICS B-FLUIDS AB - An analytical version of the discrete-ordinates method (the ADO method) is used to establish concise and particularly accurate solutions to the viscous-slip and the half-space thermal-creep problems for a binary gas mixture. The kinetic equations used to describe the flow are based on the McCormack model for mixtures. In addition to a computation of the viscous-slip and thermal-slip coefficients, for the case of Maxwell boundary conditions for each of the two species, the velocity, heat-flow and shear-stress profiles are established for both types of particles. Numerical results are reported for three binary mixtures (Ne–Ar, He–Ar and He–Xe) with various molar concentrations. The complete solution requires only a (matrix) eigenvalue/eigenvector routine and the solution of a system of linear algebraic equations, and thus the algorithm is considered especially easy to use. The developed (FORTRAN) code requires typically less than 0.1 seconds on a 1.2 GHz Pentium-based PC to solve both problems. DA - 2004/// PY - 2004/// DO - 10.1016/j.euromechflu.2003.12.002 VL - 23 IS - 5 SP - 709-726 SN - 0997-7546 ER - TY - JOUR TI - Volume determination for bulk materials in bunkers AU - Ahmed, SA AU - Buckingham, R AU - Gremaud, PA AU - Hauck, CD AU - Kuster, CM AU - Prodanovic, M AU - Royal, TA AU - Silantyev, V T2 - INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING AB - A simple model for the determination of the shape of large granular piles in complicated geometries is discussed. An eikonal formulation of the problem is proposed. Two distinct cases arise. In cylindrical geometries, i.e., if both container and possible obstacles have vertical walls, the problem is equivalent to a two-dimensional travel time problem with obstacles, while in general geometries, this analogy breaks down. In the first case, classical one-sided discretizations are generalized to handle obstacles without loss in accuracy. In the second case, a fast and efficient numerical method is proposed, implemented and tested. The discrete problems are solved through fast marching. Copyright © 2004 John Wiley & Sons, Ltd. DA - 2004/12/7/ PY - 2004/12/7/ DO - 10.1002/nme.1144 VL - 61 IS - 13 SP - 2239-2249 SN - 0029-5981 KW - granular KW - eikonal formulation KW - ordered upwind methods ER - TY - JOUR TI - Time reversal for dispersive waves in random media AU - Fouque, JP AU - Garnier, J AU - Nachbin, A T2 - SIAM JOURNAL ON APPLIED MATHEMATICS AB - Refocusing for time reversed waves propagating in disordered media has recently been observed experimentally and studied mathematically. This surprising effect has many potential applications in domains such as medical imaging, underwater acoustics, and wireless communications. Time refocusing for one-dimensional acoustic waves is now mathematically well understood. In this paper the important case of one-dimensional dispersive waves is addressed. Time reversal is studied in reflection and in transmission. In both cases we derive the self-averaging properties of time reversed refocused pulses. An asymptotic analysis allows us to derive a precise description of the combined effects of randomness and dispersion. In particular, we study an important regime in transmission, where the coherent front wave is destroyed while time reversal of the incoherent transmitted wave still enables refocusing. DA - 2004/// PY - 2004/// DO - 10.1137/S0036139903422371 VL - 64 IS - 5 SP - 1810-1838 SN - 1095-712X KW - dispersive waves KW - inhomogeneous media KW - asymptotic theory KW - time reversal ER - TY - JOUR TI - The McCormack model for gas mixtures: Heat transfer in a plane channel AU - Garcia, RDM AU - Siewert, CE T2 - PHYSICS OF FLUIDS AB - An analytical version of the discrete-ordinates method (the ADO method) is used to establish a concise and particularly accurate solution to the heat-transfer problem in a plane channel for a binary gas mixture described by the McCormack kinetic model. The solution yields for the general (specular-diffuse) case of Maxwell boundary conditions for each of the two species, the density and temperature profiles for both types of particles, as well as the overall heat flow associated with each of the two species of gas particles. Numerical results are reported for two binary mixtures (Ne–Ar and He–Xe). The algorithm is considered especially easy to use, and the developed (FORTRAN) code requires typically less than a second on a 2.2 GHz Pentium 4 machine to compute all quantities of interest. DA - 2004/9// PY - 2004/9// DO - 10.1063/1.1773711 VL - 16 IS - 9 SP - 3393-3402 SN - 1070-6631 ER - TY - JOUR TI - Symmetry reduction of sh-Lie structures and of local functionals AU - Al-Ashhab, S T2 - DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS AB - Reduced sh-Lie structures have been studied for the case when a Lie group acts on the fibers of a vector bundle while preserving the base space of the bundle. In this paper we investigate how one obtains a reduced sh-Lie structure using the ideas of symmetry reduction where the action of the Lie group is transversal to the fibers of the bundle. We also show how local functionals are reduced using these ideas. DA - 2004/9// PY - 2004/9// DO - 10.1016/j.difgeo.2004.05.002 VL - 21 IS - 2 SP - 215-227 SN - 1872-6984 KW - reduction KW - sh-lie algebra KW - jet bundle KW - Poisson bracket ER - TY - JOUR TI - Reconstruction of magnetic charge densities using regularization of bounded variations under noisy observations AU - Kojima, F AU - Ito, K T2 - INTERNATIONAL JOURNAL OF APPLIED ELECTROMAGNETICS AND MECHANICS AB - This paper is concerned with computational and regularization techniques for recovering induced magnetic fields due to the existence of cracks. The problem is formulated as an inverse problem with a set of source functions of the distribution type. The regularization of bounded variatio n is effectively used for solving the severe ill-posed problem. A iterative solver is proposed by a integro-differential equation with time marching scheme. For the practical implementation of the numerical treatment, a finite difference scheme is adopted to the proposed method with the aid of discrete fast Fourier transform. Some successful numerical experiments are demonstrated for the validity of the proposed method. DA - 2004/// PY - 2004/// DO - 10.3233/jae-2004-582 VL - 19 IS - 1-4 SP - 309-313 SN - 1383-5416 KW - inverse problem KW - regularization KW - fast fourier transform ER - TY - JOUR TI - Low temperature saturation of p-n junction laser beam induced current signals AU - Redfern, DA AU - Fang, W AU - Ito, K AU - Musca, CA AU - Dell, JM AU - Faraone, L T2 - SOLID-STATE ELECTRONICS AB - To date, most studies of the use of laser beam induced current (LBIC) for non-destructive characterisation of photodiodes have been qualitative and/or empirical, due in part to the difficulty of isolating the influence of the large number of material and device parameters on which the LBIC signal is dependent. The development of methodologies whereby these parameters can be determined quantitatively from the LBIC measurements is important for the technique to gain wider acceptance. This work describes, for the first time, the specific experimental conditions under which some of the variable parameters can be eliminated, substantially reducing the complexity of the analysis. In particular, temperature dependence of the peak-to-peak LBIC measurements on p–n junctions is examined for the first time, revealing that a saturation state is reached at low temperatures. When measurements are performed under these saturation conditions, the peak-to-peak LBIC signal becomes independent of doping density and bulk recombination parameters, allowing other parameters including device geometry to be examined with less ambiguity. This concept represents a crucial step towards a quantitative procedure for extraction of p–n junction material and device parameters using LBIC. DA - 2004/3// PY - 2004/3// DO - 10.1016/j.sse.2003.09.008 VL - 48 IS - 3 SP - 409-414 SN - 1879-2405 KW - laser beam induced current KW - LBIC KW - photodiode KW - non-destructive characterisation KW - temperature dependence ER - TY - JOUR TI - Existence-uniqueness and monotone approximation for an erythropoiesis age-structured model AU - Ackleh, AS AU - Deng, K AU - Cole, CE AU - Tran, HT T2 - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS AB - We develop a monotone approximation to the solution of an age-structured model which describes the regulation of erythropoiesis, the process in which red blood cells are developed. The convergence of this approximation to the unique solution of the model is also established. DA - 2004/1/15/ PY - 2004/1/15/ DO - 10.1016/j.jmaa.2003.08.037 VL - 289 IS - 2 SP - 530-544 SN - 0022-247X KW - erythropoiesis KW - age-structured model KW - monotone approximation KW - existence uniqueness ER - TY - JOUR TI - A radial biphasic model for local cell-matrix mechanics in articular cartilage AU - Haider, MA T2 - SIAM JOURNAL ON APPLIED MATHEMATICS AB - Analytical and numerical solutions are presented for an interface problem that models deformation in the local cell-matrix unit (chondron) of articular cartilage. The cell and its protective pericellular matrix layer are modeled as isotropic biphasic continua deforming in small strain. A spherical geometry with purely radial deformation is assumed. Enforcement of the boundary and interface conditions results in an eigenvalue problem that is self-adjoint when the permeabilities of the cell and the layer are the same. In this case, a series solution of the interface problem is presented for a time-varying displacement prescribed at the boundary of the pericellular layer. The case of nonuniform permeability is considered via a numerical finite difference solution. The analytical and numerical solutions are used to conduct a parametric analysis of mechanical signal transmission due to an applied sinusoidal displacement. The dual role of the pericellular matrix as a mechanical signal transmitter and a protective layer is analyzed. For frequencies in the range 0-3Hz, transmission of transient-free radial displacement, solid stress, and strain are evaluated with varying pericellular stiffness and permeability in biphasic models of normal and osteoarthritic chondrons. DA - 2004/// PY - 2004/// DO - 10.1137/S0036139902417700 VL - 64 IS - 5 SP - 1588-1608 SN - 0036-1399 KW - articular cartilage KW - chondrocyte KW - chondron KW - pericellular matrix KW - cartilage mechanics KW - mechanical signal transduction KW - biphasic theory KW - interface problem KW - eigenvalue problem ER - TY - JOUR TI - Testing the nearest Kronecker product preconditioner on Markov chains and stochastic automata networks AU - Langville, AN AU - Stewart, WJ T2 - INFORMS JOURNAL ON COMPUTING AB - This paper is the experimental follow-up to Langville and Stewart (2002), where the theoretical background for the nearest Kronecker product (NKP) preconditioner was developed. Here we test the NKP preconditioner on both Markov chains (MCs) and stochastic automata networks (SANs). We conclude that the NKP preconditioner is not appropriate for general MCs, but is very effective for a MC stored as a SAN. DA - 2004/// PY - 2004/// DO - 10.1287/ijoc.1030.0041 VL - 16 IS - 3 SP - 300-315 SN - 1526-5528 KW - probability KW - Markov processes KW - queues KW - Markovian KW - algorithms ER - TY - JOUR TI - On-bark behavior of Dendroctonus frontalis: a Markov chain analysis AU - Bishir, J AU - Roberds, JH AU - Strom, BL T2 - JOURNAL OF INSECT BEHAVIOR DA - 2004/5// PY - 2004/5// DO - 10.1023/B:JOIR.0000031531.07035.10 VL - 17 IS - 3 SP - 281-301 SN - 0892-7553 KW - Scolytidae KW - southern pine beetle KW - host selection KW - host recognition KW - transition probabilities KW - absorbing states ER - TY - JOUR TI - Design of an electron gun using computer optimization AU - Lewis, BM AU - Tran, HT AU - Read, ME AU - Ives, RL T2 - IEEE TRANSACTIONS ON PLASMA SCIENCE AB - This paper considers an optimization technique in which the objective is attained via alterations to the physical geometry of the system. This optimization framework, to be considered in the context of electron guns, is known as optimal shape design. Optimal shape design has been used in a number of applications including wing design, magnetic tape design, and nozzle design, among others. In this investigation, we use the methods of shape optimization to design the cathode of an electron gun. The dynamical equations modeling the electron particle path as well as the generalized shape optimization problem will be presented. Illustrative examples of the technique on gun designs that were previously limited to spherical cathodes will be given. DA - 2004/6// PY - 2004/6// DO - 10.1109/TPS.2004.827572 VL - 32 IS - 3 SP - 1242-1250 SN - 1939-9375 KW - cathode shape optimization KW - electron gun KW - optimal shape design KW - optimization techniques ER - TY - JOUR TI - Mobius function on cross-section lattices AU - Putcha, MS T2 - JOURNAL OF COMBINATORIAL THEORY SERIES A AB - Let M be an irreducible algebraic monoid with a reductive unit group G . Then there is an idempotent cross-section Λ of G × G -orbits that preserves the Zariski closure ordering. The purpose of this paper is to compute the Möbius function on the cross-section lattice Λ . This is accomplished by analyzing an associated boolean family of face lattices of polytopes and then solving a resulting system of linear equations. DA - 2004/5// PY - 2004/5// DO - 10.1016/j.jcta.2004.03.001 VL - 106 IS - 2 SP - 287-297 SN - 0097-3165 KW - Mobius function KW - cross section lattice KW - reductive monoid ER - TY - JOUR TI - Computation of Riemann solutions using the Dafermos regularization and continuation AU - Schecter, S. AU - Plohr, B. J. AU - Marchesin, D. T2 - Discrete and Continuous Dynamical Systems AB - We present a numerical method, based on the Dafermos regularization,for computing a one-parameter family of Riemann solutions of a system ofconservation laws. The family is obtained by varying either the left orright state of the Riemann problem. The Riemann solutions are requiredto have shock waves that satisfy the viscous profile criterion prescribedby the physical model. The system is not required to satisfy strict hyperbolicity or genuine nonlinearity; the left and right states need not be close; and the Riemann solutions may contain an arbitrary number of waves, including composite waves and nonclassical shock waves. The method uses standard continuation softwareto solve a boundary-value problem in which the left and right states ofthe Riemann problem appear as parameters. Because the continuation methodcan proceed around limit point bifurcations, it can sucessfully computemultiple solutions of a particular Riemann problem, including ones thatcorrespond to unstable asymptotic states of the viscous conservation laws. DA - 2004/// PY - 2004/// DO - 10.3934/dcds.2004.10.965 VL - 10 IS - 4 SP - 965-986 ER - TY - JOUR TI - An immersed finite element space and its approximation capability AU - Li, Z. AU - Lin, T. AU - Lin, Y. AU - Rogers, R. C. T2 - Numerical Methods for Partial Differential Equations AB - Abstract This article discusses an immersed finite element (IFE) space introduced for solving a second‐order elliptic boundary value problem with discontinuous coefficients (interface problem). The IFE space is nonconforming and its partition can be independent of the interface. The error estimates for the interpolation of a function in the usual Sobolev space indicate that this IFE space has an approximation capability similar to that of the standard conforming linear finite element space based on body‐fit partitions. Numerical examples of the related finite element method based on this IFE space are provided. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 338–367, 2004 DA - 2004/// PY - 2004/// DO - 10.1002/num.10092 VL - 20 IS - 3 SP - 338-367 J2 - Numer. Methods Partial Differential Eq. LA - en OP - SN - 0749-159X 1098-2426 UR - http://dx.doi.org/10.1002/num.10092 DB - Crossref KW - interface problems KW - immersed interface KW - finite element KW - error estimates ER - TY - JOUR TI - A coupled regional climate model for the Lake Victoria basin of East Africa AU - Song, Y AU - Semazzi, FHM AU - Xie, L AU - Ogallo, LJ T2 - INTERNATIONAL JOURNAL OF CLIMATOLOGY AB - Abstract A nested coupled model has been developed to investigate the two‐way interactions between the regional climate of eastern Africa and Lake Victoria. The atmospheric component of the model is the North Carolina State University (NCSU) version of the National Center for Atmospheric Research (NCAR) regional climate model (NCSU‐RegCM2). The lake component of the model is based on the Princeton ocean model (POM). Three simulations, each 4 months long, have been performed for the short rains of eastern Africa of September through to December. The control experiment is based on the standard NCSU‐RegCM2 model coupled to a one‐dimensional model of Lake Victoria. The second experiment was based on the stand‐alone three‐dimensional primitive equation POM–Lake Victoria model forced by output from the atmospheric component of the control run. The third experiment is based on the integration of the coupled system of the NCSU‐RegCM2 model where the one‐dimensional lake model in the control run has been replaced by the three‐dimensional POM hydrodynamical model for Lake Victoria. The results confirm that adopting the traditional modelling approach, in which the lake hydrodynamics are neglected and the formulation is based entirely on thermodynamics alone, is not entirely satisfactory for the Lake Victoria basin. Such a strategy precludes the transport of heat realistically within the lake, from the heat surplus regions to the cooler regions, and thereby results in a degraded simulation of the climate downstream over the rest of the lake and the surrounding land regions. The numerical simulations show that the southwestern region of the lake is an important source of warm water because it is relatively shallower and the water column is heated up much more quickly during the day than the rest of the lake. The result is that the surface temperature anomaly field from the all‐lake area average consists of a gradient pattern with warmer water over the shallow region of the lake over the southeastern sector and a colder pool of water over the northeastern region, where the lake is relatively deeper. This pattern is also reproduced by the one‐dimensional lake model. Some of the excess heat over the southeastern region is transported to the colder and deeper region over the northeastern part of the lake by prevailing surface wind flow. Through the lake–atmosphere coupling, the resulting asymmetric lake‐surface temperature distribution modifies the overlying wind circulation, which in turn reduces the cloud cover and rainfall. This secondary feature in the surface temperature structure cannot be generated by the traditional nested climate models, such as the standard version of the NCAR‐RegCM2 model, since the simple static lake model formulation is not capable of supporting horizontal mixing of water. Comparisons show that this feature is weaker in the RegCM2‐POM coupled model than the corresponding pattern that we obtained in our previous study based on the ‘stand‐alone’ POM lake model. In contrast, from the simple classical text‐book theoretical model of the lake–land breeze phenomena, the simulated surface wind circulation and rainfall distribution are highly asymmetric across the lake. Copyright © 2004 Royal Meteorological Society DA - 2004/1// PY - 2004/1// DO - 10.1002/joc.983 VL - 24 IS - 1 SP - 57-75 SN - 1097-0088 KW - Lake Victoria KW - regional climate modelling KW - eastern Africa KW - climate variability KW - RegCM2 KW - POM ER - TY - JOUR TI - The temperature-jump problem based on the CES model of the linearized Boltzmann equation AU - Siewert, CE T2 - ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK DA - 2004/1// PY - 2004/1// DO - 10.1007/s00033-003-1140-x VL - 55 IS - 1 SP - 92-104 SN - 1420-9039 KW - Boltzmann equation KW - rarefied gas dynamics KW - temperature-jump problem ER - TY - JOUR TI - Spatiotemporal dynamics of epidemics: synchrony in metapopulation models AU - Lloyd, AL AU - Jansen, VAA T2 - MATHEMATICAL BIOSCIENCES AB - Multi-patch models - also known as metapopulation models - provide a simple framework within which the role of spatial processes in disease transmission can be examined. An n-patch model which distinguishes between k different classes of individuals is considered. The linear stability of spatially homogeneous solutions of such models is studied using an extension of an analysis technique previously described for a population setting in which individuals migrate between patches according to a simple linear term. The technique considerably simplifies the analysis as it decouples the nk dimensional linearized system into n distinct k-dimensional systems. An important feature of the spatial epidemiological model is that the spatial coupling may involve non-linear terms. As an example of the use of this technique, the dynamical behavior in the vicinity of the endemic equilibrium of a symmetric SIR model is decomposed into spatial modes. For parameter values appropriate for childhood diseases, expressions for the eigenvalues corresponding to in-phase and out-of-phase modes are obtained, and it is shown that the dominant mode of the system is an in-phase mode. Furthermore, the out-of-phase modes are shown to decay much more rapidly than the in-phase mode for a broad range of coupling strengths. DA - 2004/// PY - 2004/// DO - 10.1016/j.mbs.2003.09.003 VL - 188 IS - 2004 Mar-Apr SP - 1-16 SN - 1879-3134 KW - epidemiological model KW - metapopulation KW - spatial dynamics KW - linear stability analysis ER - TY - JOUR TI - Probabilities of extinction, weak extinction permanence, and mutual exclusion in discrete, competitive, Lotka-Volterra systems AU - Chan, D. M. AU - Franke, J. E. T2 - Computers & Mathematics With Applications DA - 2004/// PY - 2004/// DO - 10.1016/S0898-1221(04)00018-5 VL - 47 IS - 03-Feb SP - 365-379 ER - TY - JOUR TI - On computing the Chapman-Enskog and Burnett functions AU - Barichello, LB AU - Rodrigues, P AU - Siewert, CE T2 - JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER AB - An expansion and projection technique based on Legendre polynomials is used to solve, in an efficient and accurate way, the Chapman-Enskog equations for viscosity and heat transfer and to compute the Burnett functions required, for example, for Poiseuille-flow problems based on rigid-sphere collisions and the linearized Boltzmann equation. DA - 2004/6/1/ PY - 2004/6/1/ DO - 10.1016/j.jqsrt.2003.10.001 VL - 86 IS - 1 SP - 109-114 SN - 1879-1352 KW - Boltzmann equation KW - rarefied-gas dynamics KW - Chapman-Enskog KW - Burnett ER - TY - JOUR TI - Gradient flow methods for matrix completion with prescribed eigenvalues AU - Chu, MT AU - Diele, F AU - Sgura, I T2 - LINEAR ALGEBRA AND ITS APPLICATIONS AB - Matrix completion with prescribed eigenvalues is a special type of inverse eigenvalue problem. The goal is to construct a matrix subject to both the structural constraint of prescribed entries and the spectral constraint of prescribed spectrum. The challenge of such a completion problem lies in the intertwining of the cardinality and the location of the prescribed entries so that the inverse problem is solvable. An intriguing question is whether matrices can have arbitrary entries at arbitrary locations with arbitrary eigenvalues and how to complete such a matrix. Constructive proofs exist to a certain point (and those proofs, such as the classical Schur–Horn theorem, are amazingly elegant enough in their own right) beyond which very few theories or numerical algorithms are available. In this paper the completion problem is recast as one of minimizing the distance between the isospectral matrices with the prescribed eigenvalues and the affined matrices with the prescribed entries. The gradient flow is proposed as a numerical means to tackle the construction. This approach is general enough that it can be used to explore the existence question when the prescribed entries are at arbitrary locations with arbitrary cardinalities. DA - 2004/3/1/ PY - 2004/3/1/ DO - 10.1016/S0024-3795(03)00393-8 VL - 379 IS - 1-3 SPEC. ISS SP - 85-112 SN - 1873-1856 UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-0742268367&partnerID=MN8TOARS KW - matrix completion KW - inverse eigenvalue problem KW - prescribed entries KW - isospectral matrices KW - gradient flow KW - ODE solvers KW - restart ER - TY - JOUR TI - Computing the sign or the value of the determinant of an integer matrix, a complexity survey AU - Kaltofen, E AU - Villard, G T2 - JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS AB - Computation of the sign of the determinant of a matrix and the determinant itself is a challenge for both numerical and exact methods. We survey the complexity of existing methods to solve these problems when the input is an n×n matrix A with integer entries. We study the bit-complexities of the algorithms asymptotically in n and the norm of A. Existing approaches rely on numerical approximate computations, on exact computations, or on both types of arithmetic in combination. DA - 2004/1/1/ PY - 2004/1/1/ DO - 10.1016/j.cam.2003.08.019 VL - 162 IS - 1 SP - 133-146 SN - 1879-1778 KW - determinant KW - bit-complexity KW - integer matrix KW - approximate computation KW - exact computation KW - randomized algorithms ER - TY - JOUR TI - Altered flower retention and developmental patterns in nine tomato cultivars under elevated temperature AU - Sato, S AU - Peet, MM AU - Gardner, RG T2 - SCIENTIA HORTICULTURAE AB - Moderately elevated temperature effects on flower development were examined in nine tomato cultivars (Lycopersicon esculentum Mill.). Plants were grown under high (HT, 32/28 °C day/night temperatures) and control (CT, 26/22 °C) temperature conditions. Fate of flowers developed was categorized as seeded fruit, parthenocarpic fruit, undeveloped flowers, or aborted flowers. Although HT decreased seeded fruit set in all nine cultivars, the degree of sensitivity and the pattern of reaction to the elevated temperature differed among cultivars. FLA7156 was the most tolerant cultivar, although under HT seeded fruit set was less than half that at CT (22.5% compared to 46.8%). The remaining cultivars had very few or no seeded fruit set at all at HT. The percentage of parthenocarpic fruit increased at HT compared to CT in all cultivars. Aborted flowers also increased in FLA7156, NC8288, NCHS1 and NC46E, but did not change in ‘Piedmont’, NC279HS, and NC403HS, or decreased in ‘Fresh Market 9’ and TH318. Reduction of flower abortion and increase of parthenocarpic fruit set can be advantageous traits for breeding of high temperature tolerant tomato cultivars. DA - 2004/5/3/ PY - 2004/5/3/ DO - 10.1016/j.scienta.2003.10.008 VL - 101 IS - 1-2 SP - 95-101 SN - 0304-4238 KW - Lycopersicon esculentum Mill KW - parthenocarpy KW - undeveloped flowers KW - flower abortion KW - high temperature stress ER - TY - JOUR TI - Global asymptotic stability of Lotka-Volterra competition systems with diffusion and time delays AU - Pao, CV T2 - NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS AB - In the Lotka–Volterra competition system with N-competing species if the effect of dispersion and time-delays are both taken into consideration, then the densities of the competing species are governed by a coupled system of reaction–diffusion equations with time-delays. The aim of this paper is to investigate the asymptotic behavior of the time-dependent solution in relation to a positive uniform solution of the corresponding steady-state problem in a bounded domain with Neumann boundary condition, including the existence and uniqueness of a positive steady-state solution. A simple and easily verifiable condition is given to the competing rate constants to ensure the global asymptotic stability of the positive steady-state solution. This result leads to the permanence of the competing system, the instability of the trivial and all forms of semitrivial solutions, and the nonexistence of nonuniform steady-state solution. The condition for the global asymptotic stability is independent of diffusion and time-delays, and the conclusions for the reaction–diffusion system are directly applicable to the corresponding ordinary differential system. DA - 2004/2// PY - 2004/2// DO - 10.1016/S1468-1218(03)00018-X VL - 5 IS - 1 SP - 91-104 SN - 1468-1218 KW - Lotka-Volterra competition KW - reaction-diffusion system KW - ordinary differential system KW - time-delays KW - global asymptotic stability KW - permanence ER - TY - JOUR TI - Estimating variability in models for recurrent epidemics: assessing the use of moment closure techniques AU - Lloyd, AL T2 - THEORETICAL POPULATION BIOLOGY AB - The major role played by demographic stochasticity in determining the dynamics and persistence of childhood diseases, such as measles, chickenpox and pertussis, has long been realized. Techniques which can be used to estimate the magnitude of this stochastic effect are of clear importance. In this study, we assess and compare the use of two moment closure approximations to estimate the variability seen about the average behavior of stochastic models for the recurrent epidemics seen in childhood diseases. The performance of the approximations are assessed using analytic techniques available for the simplest epidemiological model and using numerical simulations in more complex settings. We also present epidemiologically important extensions of previous work, considering variability in the SEIR model and in situations for which there is seasonal variation in disease transmission. Important implications of stochastic effects for the dynamics of childhood diseases are highlighted, including serious deficiencies of deterministic descriptions of dynamical behavior. DA - 2004/2// PY - 2004/2// DO - 10.1016/j.tpb.2003.07.002 VL - 65 IS - 1 SP - 49-65 SN - 1096-0325 KW - demographic stochasticity KW - moment closure KW - epidemic models KW - nonlinear dynamics ER - TY - JOUR TI - U-q (gl(N)) action on gl(N)-modules and quantum toroidal algebras AU - Gao, Y AU - Jing, NH T2 - JOURNAL OF ALGEBRA AB - We construct a vertex representation for the quantum toroidal algebra through the quantum general linear algebra. Using a new realization of the quantum general linear algebra we construct vertex operators for root vectors on the basic representation of the affine Lie algebra $gl_n$ and show that the simple generators give rise a realization of the quantum toroidal algebra with two parameters. DA - 2004/3/1/ PY - 2004/3/1/ DO - 10.1016/j.jalgebra.2003.09.046 VL - 273 IS - 1 SP - 320-343 SN - 0021-8693 UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-1342268342&partnerID=MN8TOARS ER - TY - BOOK TI - Auxiliary Signal Design for Failure Detection AU - Campbell, Stephen L. AU - Nikoukhah, Ramine CN - TA169.5 .C36 2004 DA - 2004/1// PY - 2004/1// DO - 10.1515/9781400880041 PB - Princeton University Press SN - 0691099871 ER - TY - JOUR TI - On deriving lumped models for blood flow and pressure in the systemic arteries AU - Olufsen, MS AU - Nadim, A T2 - MATHEMATICAL BIOSCIENCES AND ENGINEERING AB - Windkessel and similar lumped models are often used to represent blood flow and pressure in systemic arteries. The windkessel model was originally developed by Stephen Hales (1733) and Otto Frank (1899) who used it to describe blood flow in the heart. In this paper we start with the one-dimensional axisymmetric Navier-Stokes equations for time-dependent blood flow in a rigid vessel to derive lumped models relating flow and pressure. This is done through Laplace transform and its inversion via residue theory. Upon keeping contributions from one, two, or more residues, we derive lumped models of successively higher order. We focus on zeroth, first and second order models and relate them to electrical circuit analogs, in which current is equivalent to flow and voltage to pressure. By incorporating e ffects of compliance through addition of capacitors, windkessel and related lumped models are obtained. Our results show that given the radius of a blood vessel, it is possible to determine the order of the model that would be appropriate for analyzing the flow and pressure in that vessel. For instance, in small rigid vessels ($R <$ 0.2 cm) it is adequate to use Poiseuille's law to express the relation between flow and pressure, whereas for large vessels it might be necessary to incorporate spatial dependence by using a one-dimensional model accounting for axial variations. DA - 2004/6// PY - 2004/6// DO - 10.3934/mbe.2004.1.61 VL - 1 IS - 1 SP - 61-80 SN - 1551-0018 KW - arterial modeling KW - lumped arterial models ER - TY - JOUR TI - Unitary partitioning in general constraint preserving DAE integrators AU - Arevalo, C AU - Campbell, SL AU - Selva, M T2 - MATHEMATICAL AND COMPUTER MODELLING AB - A number of numerical algorithms have been developed for various special classes of DAEs. This paper describes a new variable step size, constraint preserving integrator for general nonlinear fully implicit higher index DAEs. Numerical implementation issues are discussed. Numerical examples illustrate the effectiveness of the new method. DA - 2004/12// PY - 2004/12// DO - 10.1016/j.mcm.2005.01.018 VL - 40 IS - 11-12 SP - 1273-1284 SN - 0895-7177 KW - differential algebraic equati ons KW - numerical integration KW - constraint preservation KW - singular system ER - TY - JOUR TI - Symmetric nonbarotropic flows with large data and forces AU - Hoff, D AU - Jenssen, HK T2 - ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS AB - We prove the global existence of weak solutions of the Navier-Stokes equations of compressible, nonbarotropic flow in three space dimensions with initial data and external forces which are large, discontinuous, and spherically or cylindrically symmetric. The analysis allows for the possibility that a vacuum state emerges at the origin or axis of symmetry, and the equations hold in the sense of distributions in the set where the density is positive. In addition, the mass and momentum equations hold weakly in the entire space-time domain, but with a nonstandard interpretation of the viscosity terms as distributions. Solutions are obtained as limits of solutions in annular regions between two balls or cylinders, and the analysis allows for the possibility that energy is absorbed into the origin or axis, and is lost in the limit as the inner radius goes to zero. DA - 2004/9// PY - 2004/9// DO - 10.1007/s00205-004-0318-5 VL - 173 IS - 3 SP - 297-343 SN - 0003-9527 ER - TY - JOUR TI - Simulation of the sensitivity of Lake Victoria basin climate to lake surface temperatures AU - Anyah, RO AU - Semazzi, FHM T2 - THEORETICAL AND APPLIED CLIMATOLOGY DA - 2004/10// PY - 2004/10// DO - 10.1007/s00704-004-0057-4 VL - 79 IS - 1-2 SP - 55-69 SN - 1434-4483 ER - TY - JOUR TI - On the computation of steady Hopper flows II: von Mises materials in various geometries AU - Gremaud, PA AU - Matthews, JV AU - M O'Malley, T2 - JOURNAL OF COMPUTATIONAL PHYSICS AB - Similarity solutions are constructed for the flow of granular materials through hoppers. Unlike previous work, the present approach applies to nonaxisymmetric containers. The model involves ten unknowns (stresses, velocity, and plasticity function) determined by nine nonlinear first order partial differential equations together with a quadratic algebraic constraint (yield condition). A pseudospectral discretization is applied; the resulting problem is solved with a trust region method. The important role of the hopper geometry on the flow is illustrated by several numerical experiments of industrial relevance. DA - 2004/11/1/ PY - 2004/11/1/ DO - 10.1016/j.jcp.2004.04.021 VL - 200 IS - 2 SP - 639-653 SN - 1090-2716 KW - elliptic KW - granular KW - similarity KW - spectral ER - TY - JOUR TI - On a hybrid finite-volume-particle method AU - Chertock, A AU - Kurganov, A T2 - ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE AB - We present a hybrid finite-volume-particle numerical method for computing the transport of a passive pollutant by a flow. The flow is modeled by the one- and two-dimensional Saint-Venant system of shallow water equations and the pollutant propagation is described by a transport equation. This paper is an extension of our previous work [Chertock, Kurganov and Petrova, J. Sci. Comput. (to appear)], where the one-dimensional finite-volume-particle method has been proposed. The core idea behind the finite-volume-particle method is to use different schemes for the flow and pollution computations: the shallow water equations are numerically integrated using a finite-volume scheme, while the transport equation is solved by a particle method. This way the specific advantages of each scheme are utilized at the right place. A special attention is given to the recovery of the point values of the numerical solution from its particle distribution. The reconstruction is obtained using a dual equation for the pollutant concentration. This results in a significantly enhanced resolution of the computed solution and also makes it much easier to extend the finite-volume-particle method to the two-dimensional case. DA - 2004/// PY - 2004/// DO - 10.1051/m2an:2004051 VL - 38 IS - 6 SP - 1071-1091 SN - 1290-3841 UR - https://doi-org.prox.lib.ncsu.edu/10.1051/m2an:2004051 KW - shallow water equations KW - transport of passive pollutant KW - finite-volume schemes KW - particle method ER - TY - JOUR TI - Nonlinear reptation in molecular based hysteresis models for polymers AU - Banks, HT AU - Medhin, NG AU - Pinter, GA T2 - QUARTERLY OF APPLIED MATHEMATICS AB - We extend the linear “stick-slip” models of Doi-Edwards and Johnson-Stacer to nonlinear tube reptation models. We then show that such models, when combined with probabilistic formulations allowing distributions of relaxation times, provide a good description of dynamic experiments with highly filled rubber in tensile deformations. A connection to other applications including dielectric polarization and reptation in other viscoelastic materials (e.g., living tissue) is noted. DA - 2004/12// PY - 2004/12// DO - 10.1090/qam/2104273 VL - 62 IS - 4 SP - 767-779 SN - 1552-4485 KW - viscoelastic KW - hysteresis KW - polymers KW - molecular models KW - relaxation times KW - probability KW - distributions KW - uncertainty ER - TY - JOUR TI - High-frequency pulse propagation in nonlinear dielectric materials AU - Banks, HT AU - Pinter, GA T2 - NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS AB - Abstract We consider a variational formulation based on Maxwell's equations for the propagation of high-frequency (gigahertz to terahertz) ultrashort input pulses in dielectric materials modeled by a linear Debye medium. We demonstrate computationally the emergence of Brillouin precursors in the material (water) and the fact that the peak of this transient is attenuated at a much slower rate than is the carrier frequency. In the 0.1– 1 THz regime the carrier frequency does not propagate in our calculations. Only the precursors enter the material, and this is in line with experiments reported by Pleshko and Palocz (Phys. Rev. Lett. 22 (1969) 1201). We also implement models that include nonlinearly forced Debye and nonlinear Debye polarization dynamics and demonstrate the importance of nonlinear effects, especially when the amplitude of the input signal is large. This is an important step in understanding high-frequency pulse propagation, and it has potential applications in the assessment of safety standards and in extending current imaging capabilities in both civilian and military uses. DA - 2004/9// PY - 2004/9// DO - 10.1016/j.nonrwa.2003.10.002 VL - 5 IS - 4 SP - 597-612 SN - 1468-1218 KW - Maxwell's equations KW - nonlinear dielectrics KW - terahertz pulse propagation ER - TY - JOUR TI - Bruhat-Chevalley order in reductive monoids AU - Putcha, MS T2 - JOURNAL OF ALGEBRAIC COMBINATORICS AB - Let M be a reductive monoid with unit group G. Let Λ denote the idempotent cross-section of the G × G-orbits on M. If W is the Weyl group of G and e, f ∈ Λ with e ≤ f, we introduce a projection map from WeW to WfW. We use these projection maps to obtain a new description of the Bruhat-Chevalley order on the Renner monoid of M. For the canonical compactification X of a semisimple group G 0 with Borel subgroup B 0 of G 0, we show that the poset of B 0 × B 0-orbits of X (with respect to Zariski closure inclusion) is Eulerian. DA - 2004/7// PY - 2004/7// DO - 10.1023/B:JACO.0000047291.42015.a6 VL - 20 IS - 1 SP - 33-53 SN - 1572-9192 KW - reductive monoid KW - Renner monoid KW - Bruhat-Chevalley order KW - projections ER - TY - JOUR TI - Behavior dominated by slow particles in a disordered asymmetric exclusion process AU - Grigorescu, I AU - Kang, M AU - Seppalainen, T T2 - ANNALS OF APPLIED PROBABILITY AB - We study the large space and time scale behavior of a totally asymmetric, nearest-neighbor exclusion process in one dimension with random jump rates attached to the particles. When slow particles are sufficiently rare, the system has a phase transition. At low densities there are no equilibrium distributions, and on the hydrodynamic scale the initial profile is transported rigidly. We elaborate this situation further by finding the correct order of the correction from the hydrodynamic limit, together with distributional bounds averaged over the disorder. We consider two settings, a macroscopically constant low density profile and the outflow from a large jam. DA - 2004/8// PY - 2004/8// DO - 10.1214/105051604000000387 VL - 14 IS - 3 SP - 1577-1602 SN - 1050-5164 KW - asymmetric exclusion process KW - hydrodynamic limit KW - random rates ER - TY - JOUR TI - Well-posedness for a nonsmooth acoustic system AU - Banks, H. T. AU - Raye, J. K. T2 - Applied Mathematics Letters DA - 2004/// PY - 2004/// DO - 10.1016/S0893-9659(04)00013-8 VL - 17 IS - 3 SP - 317-322 ER - TY - JOUR TI - Vertex Representations and McKay Correspondence AU - Jing, N. T2 - Algebra Colloquium DA - 2004/// PY - 2004/// VL - 11 IS - 1 SP - 53-70 UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-1842528779&partnerID=MN8TOARS ER - TY - JOUR TI - The constraints as evolution equations for numerical relativity AU - Gentle, AP AU - George, ND AU - Kheyfets, A AU - Miller, WA T2 - CLASSICAL AND QUANTUM GRAVITY AB - The Einstein equations have proved surprisingly difficult to solve numerically. A standard diagnostic of the problems which plague the field is the failure of computational schemes to satisfy the constraints, which are known to be mathematically conserved by the evolution equations. We describe a new approach to rewriting the constraints as first-order evolution equations, thereby guaranteeing that they are satisfied to a chosen accuracy by any discretization scheme. This introduces a set of four subsidiary constraints which are far simpler than the standard constraint equations and which should be more easily conserved in computational applications. We explore the manner in which the momentum constraints are already incorporated in several existing formulations of the Einstein equations, and demonstrate the ease with which our new constraint-conserving approach can be incorporated into these schemes. DA - 2004/1/7/ PY - 2004/1/7/ DO - 10.1088/0264-9381/21/1/006 VL - 21 IS - 1 SP - 83-91 SN - 0264-9381 ER - TY - JOUR TI - Smoothness of quotients associated with a pair of commuting involutions AU - Helminck, AG AU - Schwarz, GW T2 - CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES AB - Abstract Let σ, θ be commuting involutions of the connected semisimple algebraic group G where σ, θ and G are defined over an algebraically closed field , char = 0. Let H := G σ and K := G θ be the fixed point groups. We have an action ( H × K ) × G → G , where (( h , k ), g ) ⟼ hgk –1 , h ∈ H , k ∈ K , g ∈ G . Let G //( H × K ) denote the categorical quotient Spec ( G ) H × K . We determine when this quotient is smooth. Our results are a generalization of those of Steinberg [Ste75], Pittie [Pit72] and Richardson [Ric82] in the symmetric case where σ = θ and H = K . DA - 2004/10// PY - 2004/10// DO - 10.4153/CJM-2004-043-7 VL - 56 IS - 5 SP - 945-962 SN - 1496-4279 ER - TY - JOUR TI - Shock structure due to stochastic forcing and the time reversal of nonlinear waves AU - Fouque, JP AU - Garnier, J AU - Nachbin, A T2 - PHYSICA D-NONLINEAR PHENOMENA AB - This paper is concerned with the study of the deformation of a nonlinear pulse traveling in a random medium. We consider shallow water waves with a spatially random depth. We demonstrate that in the presence of properly scaled stochastic forcing the solution to the nonlinear conservation law is regularized leading to a viscous shock profile. This enables us to perform time-reversal experiments beyond the critical time for shock formation. DA - 2004/8/15/ PY - 2004/8/15/ DO - 10.1016/j.physd.2004.05.003 VL - 195 IS - 3-4 SP - 324-346 SN - 1872-8022 KW - nonlinear waves KW - inhomogeneous media KW - viscous shock KW - time reversal ER - TY - JOUR TI - Robustness of time reversal for waves in time-dependent random media AU - Vigo, DGA AU - Fouque, JP AU - Garnier, J AU - Nachbin, A T2 - STOCHASTIC PROCESSES AND THEIR APPLICATIONS AB - This paper addresses the impact of time fluctuations of a random medium on refocusing during a time-reversal experiment. Even in the presence of moderate time perturbations a coherent refocused pulse is observed. The theory predicts the level of recompression observed as well as the conditions for the loss of statistical stabilization. It is shown that the statistical properties of the refocused pulse depend on a simple set of parameters that describe the correlation degree of the medium. The refocused pulse has in general a random shape that can be described in terms of a system of stochastic transport equations driven by a single Brownian motion. Pulse stabilization is also demonstrated for some particular configurations, and the convolution kernel that describes the pulse reshaping is explicitly computed. Numerical simulations are presented and show a very good agreement with the theoretical predictions, thus providing a clear illustration of the robustness of time reversal. DA - 2004/10// PY - 2004/10// DO - 10.1016/j.spa.2004.04.002 VL - 113 IS - 2 SP - 289-313 SN - 1879-209X KW - inhomogeneous media KW - asymptotic theory KW - time reversal ER - TY - JOUR TI - Portfolio optimization models on infinite-time horizon AU - Pang, T T2 - JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS DA - 2004/9// PY - 2004/9// DO - 10.1023/B:JOTA.0000042596.26927.2d VL - 122 IS - 3 SP - 573-597 SN - 1573-2878 KW - portfolio optimization KW - dynamic programming equations KW - subsolutions and supersolutions ER - TY - JOUR TI - Optimization of power in the problems of active control of sound AU - Lončarić, J. AU - Tsynkov, S.V. T2 - Mathematics and Computers in Simulation AB - We analyze the problem of suppressing the unwanted component of a time-harmonic acoustic field (noise) on a predetermined region of interest. The suppression is rendered by active means, i.e., by introducing the additional acoustic sources called controls that generate the appropriate anti-sound. Previously, we have obtained general solutions for active controls in both continuous and discrete formulation of the problem. We have also obtained optimal solutions that minimize the L1 or L2 norm of the control sources; the physical interpretation of the former being the overall absolute acoustic source strength. In the current paper, we minimize the power required for the operation of the active control system. It turns out that the corresponding analysis necessarily involves interaction between the sources of sound and the surrounding acoustic field, which was not the case for either L1 or L2. Even though it may first seem counterintuitive, one can build a control system (a particular combination of surface monopoles and dipoles) that would require no power input for operation and would even produce a net power gain while providing the exact noise cancellation. This usually comes at the expense of having the original sources of noise produce even more energy. DA - 2004/5// PY - 2004/5// DO - 10.1016/j.matcom.2004.01.005 VL - 65 IS - 4-5 SP - 323-335 J2 - Mathematics and Computers in Simulation LA - en OP - SN - 0378-4754 UR - http://dx.doi.org/10.1016/j.matcom.2004.01.005 DB - Crossref KW - noise cancellation KW - active control sources KW - volumetric and surface controls KW - general solution KW - monopoles and dipoles KW - radiation of waves KW - complex-valued quantities KW - load on the sources by the field KW - net power gain ER - TY - JOUR TI - On the nilpotency of certain subalgebras of Kac-Moody Lie algebras AU - Kim, Y. AU - Misra, K. C. AU - Stitzinger, E. T2 - Journal of Lie Theory DA - 2004/// PY - 2004/// VL - 14 IS - 1 SP - 23- ER - TY - JOUR TI - On computing the thermal-slip coefficient from Kramers' problem AU - Siewert, CE T2 - PHYSICS OF FLUIDS AB - Classical techniques are used to derive a variant of an Onsager relation (used typically for Poiseuille flow and thermal-creep flow) that yields a convenient relationship between the heat flow of Kramers’ problem and the thermal-slip coefficient. The analysis is based on the linearized Boltzmann equation for rigid-sphere interactions, and wall interactions are described by a general law that includes, for example, the Maxwell model (a mixture of specular and diffuse reflection) and the Cercignani–Lampis model. DA - 2004/6// PY - 2004/6// DO - 10.1063/1.1728157 VL - 16 IS - 6 SP - 2132-2135 SN - 1089-7666 ER - TY - JOUR TI - Note on Jacobi's method for approximating dominant roots AU - Hong, H T2 - JOURNAL OF SYMBOLIC COMPUTATION AB - In 1834 Jacobi gave a method for approximating dominant roots of a polynomial. In 2002 Mignotte and Stefanescu showed that Jacobi’s method works only when the dominant roots are simple. In this note, we show that Jacobi’s method can still be useful even when the dominant roots are not simple, if we use it for approximating the “distinct” dominant roots. DA - 2004/4// PY - 2004/4// DO - 10.1016/j.jsc.2003.07.003 VL - 37 IS - 4 SP - 449-453 SN - 0747-7171 UR - http://dx.doi.org/10.1016/j.jsc.2003.07.003 KW - dominant roots KW - root bounds ER - TY - JOUR TI - Immune responses and the emergence of drug-resistant virus strains in vivo AU - Wodarz, D AU - Lloyd, AL T2 - PROCEEDINGS OF THE ROYAL SOCIETY B-BIOLOGICAL SCIENCES AB - The treatment of viral infections using antiviral drugs has had a significant public health benefit in the setting of human immunodeficiency virus (HIV) infection, and newly developed drugs offer potential benefits in the management of other viral infections, including acute self-limiting infections such as influenza and picornaviruses (including the rhinoviruses that are responsible for a large proportion of 'common colds'). A serious concern with such treatments is that they may lead to the selection of drug-resistant strains. This has been a significant problem in the case of HIV infection. Existing mathematical-modelling studies of drug resistance have focused on the interactions between virus, target cells and infected cells, ignoring the impact of immune responses. Here, we present a model that explores the role of immune responses in the rise of drug-resistant mutants in vivo. We find that drug resistance is unlikely to be a problem if immune responses are maintained above a threshold level during therapy. Alternatively, if immune responses decline at a fast rate and fall below a threshold level during treatment (indicating impaired immunity), the rise of drug-resistant mutants is more likely. This indicates an important difference between HIV, which impairs immunity and for which immune responses have been observed to vanish during treatment, and viral infections such as influenza and rhinoviruses, for which such immune impairment is not present. Drug resistance is much more likely to be a problem in HIV than in acute and self-limiting infections. DA - 2004/6/7/ PY - 2004/6/7/ DO - 10.1098/rspb.2003.2664 VL - 271 IS - 1544 SP - 1101-1109 SN - 0962-8452 KW - mathematical models KW - drug resistance KW - acute infection KW - HIV KW - rhinoviruses KW - common cold ER - TY - JOUR TI - Hydrodynamic limit for a Fleming-Viot type system AU - Grigorescu, I AU - Kang, M T2 - STOCHASTIC PROCESSES AND THEIR APPLICATIONS AB - We consider a system of N Brownian particles evolving independently in a domain D. As soon as one particle reaches the boundary it is killed and one of the other particles is chosen uniformly and splits into two independent particles resuming a new cycle of independent motion until the next boundary hit. We prove the hydrodynamic limit for the joint law of the empirical measure process and the average number of visits to the boundary as N approaches infinity. DA - 2004/3// PY - 2004/3// DO - 10.1016/j.spa.2003.10.010 VL - 110 IS - 1 SP - 111-143 SN - 1879-209X KW - Fleming-Viot KW - hydrodynamic limit KW - catalytic branching KW - absorbing Brownian motion ER - TY - JOUR TI - Constraints in quantum geometrodynamics AU - Gentle, AP AU - George, ND AU - Miller, WA AU - Kheyfets, A T2 - INTERNATIONAL JOURNAL OF MODERN PHYSICS A AB - We compare different treatments of the constraints in canonical quantum gravity. The standard approach on the superspace of 3-geometries treats the constraints as the sole carriers of the dynamic content of the theory, thus rendering the traditional dynamical equations obsolete. Quantization of the constraints in both the Dirac and ADM square root Hamiltonian approaches leads to the well known problems of time evolution. These problems of time are of both an interpretational and technical nature. In contrast, the geometrodynamic quantization procedure on the superspace of the true dynamical variables separates the issues of quantization from the enforcement of the constraints. The resulting theory takes into account states that are off-shell with respect to the constraints, and thus avoids the problems of time. We develop, for the first time, the geometrodynamic quantization formalism in a general setting and show that it retains all essential features previously illustrated in the context of homogeneous cosmologies. DA - 2004/4/20/ PY - 2004/4/20/ DO - 10.1142/S0217751X04017008 VL - 19 IS - 10 SP - 1609-1638 SN - 0217-751X KW - quantum gravity KW - canonical quantum gravity ER - TY - JOUR TI - CLT for linear spectral statistics of large-dimensional sample covariance matrices AU - Bai, Z. D. AU - Silverstein, J. W. T2 - Annals of Probability DA - 2004/// PY - 2004/// VL - 32 IS - 1A SP - 553–605 ER - TY - JOUR TI - Brauer characters of finite monoids AU - Putcha, MS T2 - ALGEBRAS AND REPRESENTATION THEORY DA - 2004/3// PY - 2004/3// DO - 10.1023/B:ALGE.0000019387.07748.9b VL - 7 IS - 1 SP - 59-66 SN - 1386-923X KW - monoid KW - Brauer character KW - quiver ER - TY - JOUR TI - An application of stochastic control theory to financial economics AU - Fleming, WH AU - Pang, T T2 - SIAM JOURNAL ON CONTROL AND OPTIMIZATION AB - We consider a portfolio optimization problem which is formulated as a stochastic control problem. Risky asset prices obey a logarithmic Brownian motion, and interest rates vary according to an ergodic Markov diffusion process. The goal is to choose optimal investment and consumption policies to maximize the infinite horizon expected discounted hyperbolic absolute risk aversion (HARA) utility of consumption. A dynamic programming principle is used to derive the dynamic programming equation (DPE). The subsolution--supersolution method is used to obtain existence of solutions of the DPE. The solutions are then used to derive the optimal investment and consumption policies. DA - 2004/// PY - 2004/// DO - 10.1137/S0363012902419060 VL - 43 IS - 2 SP - 502-531 SN - 1095-7138 KW - portfolio optimization KW - dynamic programming equations KW - subsolutions KW - supersolutions ER - TY - JOUR TI - A fast solver for the Ornstein-Zernike equations AU - Kelley, CT AU - Pettitt, BM T2 - JOURNAL OF COMPUTATIONAL PHYSICS AB - In this paper, we report on the design and analysis of a multilevel method for the solution of the Ornstein–Zernike Equations and related systems of integro-algebraic equations. Our approach is based on an extension of the Atkinson–Brakhage method, with Newton-GMRES used as the coarse mesh solver. We report on several numerical experiments to illustrate the effectiveness of the method. The problems chosen are related to simple short ranged fluids with continuous potentials. Speedups over traditional methods for a given accuracy are reported. The new multilevel method is roughly six times faster than Newton-GMRES and 40 times faster than Picard. DA - 2004/7/1/ PY - 2004/7/1/ DO - 10.1016/j.jcp.2003.12.006 VL - 197 IS - 2 SP - 491-501 SN - 1090-2716 ER - TY - JOUR TI - The primal-dual active set method for nonlinear optimal control problems with bilateral constraints AU - Ito, K AU - Kunisch, K T2 - SIAM JOURNAL ON CONTROL AND OPTIMIZATION AB - The primal-dual active set method has proved to be an efficient numerical tool in the context of diverse applications. So far it has been investigated mainly for linear problems. This paper is devoted to the study of global convergence of the primal-dual active set method for nonlinear problems with bilateral constraints. Utilizing the close relationship between the primal-dual active set method and semismooth Newton methods, local superlinear convergence of the method is investigated as well. DA - 2004/// PY - 2004/// DO - 10.1137/S0363012902411015 VL - 43 IS - 1 SP - 357-376 SN - 1095-7138 KW - primal-dual active set method KW - semismooth Newton method KW - optimal control KW - bilateral constraints ER - TY - JOUR TI - The life and work of A.A. Markov AU - Basharin, G. P. AU - Langville, A. N. AU - Naumov, V. A. T2 - Linear Algebra and Its Applications DA - 2004/// PY - 2004/// VL - 386 IS - Jul 15 2004 SP - 26- ER - TY - JOUR TI - The Kronecker product and stochastic automata networks AU - Langville, AN AU - Stewart, WJ T2 - JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS AB - This paper can be thought of as a companion paper to Van Loan's The Ubiquitous Kronecker Product paper (J. Comput. Appl. Math. 123 (2000) 85). We collect and catalog the most useful properties of the Kronecker product and present them in one place. We prove several new properties that we discovered in our search for a stochastic automata network preconditioner. We conclude by describing one application of the Kronecker product, omitted from Van Loan's list of applications, namely stochastic automata networks. DA - 2004/6/1/ PY - 2004/6/1/ DO - 10.1016/j.cam.2003.10.010 VL - 167 IS - 2 SP - 429-447 SN - 1879-1778 KW - stochastic automata networks KW - Kronecker products KW - Kronecker product properties KW - preconditioning ER -