TY - JOUR
TI - On the estimation of the consumption matrix from inexact data in the leontief model
AU - Ragni, S.
AU - Chu, M.T.
AU - Diele, F.
AU - Marangi, C.
T2 - Journal of Numerical Analysis, Industrial and Applied Mathematics
DA - 2007///
PY - 2007///
VL - 2
IS - 3-4
SP - 139-156
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84947050612&partnerID=MN8TOARS
ER -
TY - BOOK
TI - Inverse Eigenvalue Problems: Theory, Algorithms, and Applications
AU - Chu, Moody
AU - Golub, G.
AB - The basic goal of an inverse eigenvalue problem is to reconstruct the physical parameters of a certain system from the knowledge or desire of its dynamical behavior. Depending on the application, inverse eigenvalue problems appear in many different forms. This book discusses the fundamental questions, some known results, many applications, mathematical properties, a variety of numerical techniques, as well as several open problems.
DA - 2007///
PY - 2007///
DO - 10.1093/acprof:oso/9780198566649.001.0001
VL - 9780198566649
PB - Oxford: Oxford University Press
SE - 1-406
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84919596855&partnerID=MN8TOARS
ER -
TY - JOUR
TI - Low-dimensional polytope approximation and its applications to nonnegative matrix factorization
AU - Chu, M.T.
AU - Lin, M.M.
T2 - SIAM Journal on Scientific Computing
AB - In this study, nonnegative matrix factorization is recast as the problem of approximating a polytope on the probability simplex by another polytope with fewer facets. Working on the probability simplex has the advantage that data are limited to a compact set with a known boundary, making it easier to trace the approximation procedure. In particular, the supporting hyperplane that separates a point from a disjoint polytope, a fact asserted by the Hahn–Banach theorem, can be calculated in finitely many steps. This approach leads to a convenient way of computing the proximity map which, in contrast to most existing algorithms where only an approximate map is used, finds the unique and global minimum per iteration. This paper sets up a theoretical framework, outlines a numerical algorithm, and suggests an effective implementation. Testing results strongly evidence that this approach obtains a better low rank nonnegative matrix approximation in fewer steps than conventional methods.
DA - 2007///
PY - 2007///
DO - 10.1137/070680436
VL - 30
IS - 3
SP - 1131-1155
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-55549091744&partnerID=MN8TOARS
ER -
TY - CONF
TI - Lower bounds for approximate factorizations via semidefinite programming
AU - Kaltofen, Erich
AU - Li, Bin
AU - Sivaramakrishnan, Kartik
AU - Yang, Zhengfeng
AU - Zhi, Lihong
T2 - International Workshop on Symbolic-Numeric Computation
A2 - Verschelde, Jan
A2 - Watt, Stephen M.
C2 - 2007///
C3 - Proceedings of the 2007 International Workshop on Symbolic-Numeric Computation (SNC '07)
CY - London, Ontario, Canada
DA - 2007///
PY - 2007/7/25/
SP - 203–204
PB - ACM Press
SN - 9781595937445
ER -
TY - JOUR
TI - Approximate Radical for Clusters: A Global Approach Using Gaussian Elimination or SVD
AU - Janovitz-Freireich, Itnuit
AU - Rónyai, Lajos
AU - Szántó, Ágnes
T2 - Mathematics in Computer Science
AB - We introduce a matrix of traces, attached to a zero dimensional ideal
$$\tilde{I}$$
. We show that the matrix of traces can be a useful tool in handling systems of polynomial equations with clustered roots. We present a method based on Dickson’s lemma to compute the “approximate radical” of
$$\tilde{I}$$
in
$${\mathbb{C}}[x_1,\ldots, x_m]$$
which has zero clusters: the approximate radical ideal has exactly one root in each cluster for sufficiently small clusters. Our method is “global” in the sense that it works simultaneously for all clusters: the problem is reduced to the computation of the numerical nullspace of the matrix of traces, a matrix efficiently computable from the generating polynomials of
$$\tilde{I}$$
. To compute the numerical nullspace of the matrix of traces we propose to use Gaussian elimination with pivoting or singular value decomposition. We prove that if
$$\tilde{I}$$
has k distinct zero clusters each of radius at most ɛ in the ∞-norm, then k steps of Gaussian elimination on the matrix of traces yields a submatrix with all entries asymptotically equal to ɛ2. We also show that the (k + 1)-th singular value of the matrix of traces is proportional to ɛ2. The resulting approximate radical has one root in each cluster with coordinates which are the arithmetic mean of the cluster, up to an error term asymptotically equal to ɛ2. In the univariate case our method gives an alternative to known approximate square-free factorization algorithms which is simpler and its accuracy is better understood.
DA - 2007/10/5/
PY - 2007/10/5/
DO - 10.1007/S11786-007-0013-7
VL - 1
IS - 2
SP - 393-425
J2 - Math.comput.sci.
LA - en
OP -
SN - 1661-8270 1661-8289
UR - http://dx.doi.org/10.1007/S11786-007-0013-7
DB - Crossref
KW - Radical ideal
KW - clusters
KW - matrix of traces
KW - symbolic-numeric computation
ER -
TY - JOUR
TI - An augmented immersed interface-level set method for Stokes equations with discontinuous viscosity
AU - Li, Zhilin
AU - Lubkin, S.
AU - Wan, X.
T2 - Electronic Journal of Differential Equations, Conference
DA - 2007///
PY - 2007///
VL - 15
SP - 193–210
SN - 1072-6691
ER -
TY - BOOK
TI - Applied Numerical Mathematics for the International Conference on Scientific Computing
A3 - Li, Zhilin
DA - 2007///
PY - 2007///
VL - 57
M3 - Special Issues
PB - American Mathematical Society
ER -
TY - MGZN
TI - First SIAG linear algebra school slated for July 2008
AU - Ipsen, I.C.F.
T2 - SIAM News
DA - 2007/11/3/
PY - 2007/11/3/
VL - 40
M1 - 9
ER -
TY - JOUR
TI - Knots, Links, and Self-avoiding Curves
AU - Jablan, S.
AU - Sazdanović, R.
T2 - Forma
DA - 2007///
PY - 2007///
VL - 22
IS - 1
SP - 5–13
ER -
TY - JOUR
TI - UNLINKING NUMBER AND UNLINKING GAP
AU - JABLAN, SLAVIK
AU - SAZDANOVIĆ, RADMILA
T2 - Journal of Knot Theory and Its Ramifications
AB - Computing unlinking number is usually very difficult and complex problem, therefore we define BJ-unlinking number and recall Bernhard–Jablan conjecture stating that the classical unknotting/unlinking number is equal to the BJ-unlinking number. We compute BJ-unlinking number for various families of knots and links for which the unlinking number is unknown. Furthermore, we define BJ-unlinking gap and construct examples of links with arbitrarily large BJ-unlinking gap. Experimental results for BJ-unlinking gap of rational links up to 16 crossings, and all alternating links up to 12 crossings are obtained using programs LinKnot and K2K. Moreover, we propose families of rational links with arbitrarily large BJ-unlinking gap and polyhedral links with constant non-trivial BJ-unlinking gap. Computational results suggest existence of families of non-alternating links with arbitrarily large BJ-unlinking gap.
DA - 2007///
PY - 2007///
DO - 10.1142/s0218216507005828
VL - 16
IS - 10
SP - 1331-1355
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-38549182277&partnerID=MN8TOARS
KW - unknotting number
KW - unlinking number
KW - unknotting gap
KW - unlinking gap
KW - rational knot
KW - pretzel knot
KW - Conway notation
KW - n-move
ER -
TY - BOOK
TI - Linknot - Knot Theory by Computer
AU - Jablan, Slavik
AU - Sazdanović, Radmila
AB - Basic Graph Theory Shadows of KLs Notation of Knots and Links (KLs) Gauss and Dowker Code KL Diagrams Reidemeister Moves Conway Notation Classification of KLs Chirality of KLs Unlinking Number and Unlinking Gap KLs with Unlinking Number One Non-Invertible KLs Braids Braid Family Representatives Borromean Links Recognition and Generation of KLs Polynomial Invariants Experimenting with KLs Derivation and Classification of KLs Basic Polyhedra, Polyhedral KLs, and Non-Algebraic Tangles Non-Alternating and Almost Alternating KLs Families of Undetectable KLs Detecting Chirality of KLs by Polynomial Invariants History of Knot Theory and Its Applications Mirror Curves KLs and Fullerenes KLs and Mathematical Logic Self-Referential Systems KL Automata.
DA - 2007///
PY - 2007///
DO - 10.1142/9789812772244
PB - World Scientific Publishing Co. Pte. Ltd.
ER -
TY - JOUR
TI - The Disparate Effects of Microvascular Rarefaction and Reduced Compliance on Proximal Haemodynamics: Investigation with a Mathematical and Computational Model of the Circulation
AU - Vaughan, G.A.
AU - Johnson, M.K.
AU - Mark, P.B.
AU - Connell, J.M.C.
AU - Olufsen, M.S.
AU - Hill, N.A.
AU - Sainsbury, C.A.R.
T2 - Artery Research
DA - 2007/9//
PY - 2007/9//
DO - 10.1016/j.artres.2007.07.029
VL - 1
IS - 2
SP - 74
J2 - Artery Research
LA - en
OP -
SN - 1872-9312
UR - http://dx.doi.org/10.1016/j.artres.2007.07.029
DB - Crossref
ER -
TY - BOOK
TI - Special Issue for the International Conference on Scientific Computing
DA - 2007/5//
PY - 2007/5//
UR - https://www.sciencedirect.com/journal/applied-numerical-mathematics/vol/57/issue/5
ER -
TY - BOOK
TI - Moving Interface Problems and Applications in Fluid Dynamics
DA - 2007///
PY - 2007///
UR - https://books.google.com/books/about/Moving_Interface_Problems_and_Applicatio.html?id=fMYbCAAAQBAJ
ER -
TY - JOUR
TI - Foreword
AU - Yap, Chee K.
AU - Hong, Hoon
T2 - Mathematics in Computer Science
DA - 2007/12//
PY - 2007/12//
DO - 10.1007/s11786-007-0009-3
VL - 1
IS - 1
SP - 3-7
UR - http://dx.doi.org/10.1007/s11786-007-0009-3
ER -
TY - JOUR
TI - Counting subrings of Zn of index k
AU - Liu, Ricky Ini
T2 - Journal of Combinatorial Theory, Series A
AB - We consider the problem of determining the number of subrings of the ring Z n of a fixed index k , denoted f n ( k ) . We present a decomposition theorem for these subrings and calculate explicit expressions for the Dirichlet series generating function F n ( s ) = ∑ k = 1 ∞ f n ( k ) k − s for n ⩽ 4 and for the generating function Φ p ( x , y ) = ∑ e = 0 ∞ ∑ n = 0 ∞ f n ( p e ) x e y n / n ! modulo p . We also calculate f n ( k ) when k is not divisible by the sixth power of any prime.
DA - 2007/2//
PY - 2007/2//
DO - 10.1016/j.jcta.2006.05.002
VL - 114
IS - 2
SP - 278-299
J2 - Journal of Combinatorial Theory, Series A
LA - en
OP -
SN - 0097-3165
UR - http://dx.doi.org/10.1016/j.jcta.2006.05.002
DB - Crossref
KW - subrings
KW - lattices
KW - multiplicative lattices
ER -
TY - CONF
TI - Sparse signal recovery by iterative proximal thresholding
AU - Combettes, P.L.
AU - Pesquet, J.-C.
T2 - European Signal Processing Conference
C2 - 2007///
C3 - Proceedings of the European Signal Processing Conference
CY - Poznan, Poland
DA - 2007///
PY - 2007/9/3/
ER -
TY - CONF
TI - Opérateurs proximaux pour la restauration bayésienne de signaux
AU - Chaux, C.
AU - Combettes, P.L.
AU - Pesquet, J.-C.
AU - Wajs, V.R.
T2 - Proceedings of the Twenty First GRETSI Symposium
C2 - 2007/9/11/
C3 - Proceedings of the Twenty First GRETSI Symposium
CY - Troyes, France
DA - 2007/9/11/
PY - 2007/9/11/
SP - 1277–1280
UR - http://hdl.handle.net/2042/17744
ER -
TY - JOUR
TI - Matching and stabilization of discrete mechanical systems
AU - Bloch, Anthony M.
AU - Leok, Melvin
AU - Marsden, Jerrold E.
AU - Zenkov, Dmitry V.
T2 - PAMM
AB - Abstract Controlled Lagrangian and matching techniques are developed for the stabilization of equilibria of discrete mechanical systems with symmetry as well as broken symmetry. Interesting new phenomena arise in the controlled Lagrangian approach in the discrete context that are not present in the continuous theory. Specifically, a nonconservative force that is necessary for matching in the discrete setting is introduced. The paper also discusses digital and model predictive controllers. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
DA - 2007/12//
PY - 2007/12//
DO - 10.1002/pamm.200700390
VL - 7
IS - 1
SP - 1030603-1030604
J2 - Proc. Appl. Math. Mech.
LA - en
OP -
SN - 1617-7061 1617-7061
UR - http://dx.doi.org/10.1002/pamm.200700390
DB - Crossref
ER -
TY - JOUR
TI - Are Buchberger’s criteria necessary for the chain condition?
AU - Hong, Hoon
AU - Perry, John
T2 - Journal of Symbolic Computation
AB - Buchberger’s Gröbner basis theory plays a fundamental role in symbolic computation. The resulting algorithms essentially carry out several S-polynomial reductions. In his Ph.D. thesis and later publication Buchberger showed that sometimes one can skip S-polynomial reductions if the leading terms of polynomials satisfy certain criteria. A question naturally arises: Are Buchberger’s criteria also necessary for skipping S-polynomial reductions? In this paper, after making the question more precise (in terms of a chain condition), we show the answer to be “almost, but not quite”: necessary when there are four or more polynomials, but not necessary when there are exactly three polynomials. For that case, we found an extension to Buchberger’s criteria that is necessary as well as sufficient.
DA - 2007/7//
PY - 2007/7//
DO - 10.1016/j.jsc.2007.02.002
VL - 42
IS - 7
SP - 717-732
J2 - Journal of Symbolic Computation
LA - en
OP -
SN - 0747-7171
UR - http://dx.doi.org/10.1016/j.jsc.2007.02.002
DB - Crossref
KW - Grobner bases
KW - S-polynomials
KW - Buchberger criteria
ER -
TY - CONF
TI - Fundamental Limit of Sample Eigenvalue based Detection of Signals in Colored Noise using Relatively Few Samples
AU - Nadakuditi, Raj Rao
AU - Silverstein, Jack W.
T2 - 2007 41st Asilomar conference on Signals, Systems and Computers (ACSSC)
AB - Sample eigenvalue based estimators are often used for estimating the number of high-dimensional signals in colored noise when an independent estimate of the noise covariance matrix is available. We highlight a fundamental asymptotic limit of sample eigenvalue based detection that brings into sharp focus why in the large system, relatively large sample size limit, underestimation of the model order may be unavoidable for weak/closely spaced signals. We discuss the implication of these results for the detection of two weak, closely spaced signals.
C2 - 2007/11//
C3 - 2007 Conference Record of the Forty-First Asilomar Conference on Signals, Systems and Computers
DA - 2007/11//
DO - 10.1109/acssc.2007.4487301
PB - IEEE
SN - 9781424421091 9781424421107
UR - http://dx.doi.org/10.1109/acssc.2007.4487301
DB - Crossref
ER -
TY - JOUR
TI - CRITICAL POINTS OF NON-C2 FUNCTIONALS
T2 - Topological Methods in Nonlinear Analysis
DA - 2007///
PY - 2007///
ER -
TY - JOUR
TI - Morse-palais lemma for nonsmooth functionals on normed spaces
AU - Duc, D.M.
AU - Hung, T.V.
AU - Khai, N.T.
T2 - Proceedings of the American Mathematical Society
AB - Using elementary differential calculus we get a version of the Morse-Palais lemma. Since we do not use powerful tools in functional analysis such as the implicit theorem or flows and deformations in Banach spaces, our result does not require the C 1 -smoothness of functions nor the completeness of spaces. Therefore it is stronger than the classical one but its proof is very simple.
DA - 2007///
PY - 2007///
DO - 10.1090/S0002-9939-06-08662-X
VL - 135
IS - 3
SP - 921-927
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-77950647891&partnerID=MN8TOARS
KW - Morse-Palais lemma
KW - normed spaces
KW - directional differentiability
ER -
TY - JOUR
TI - Shape derivatives without taking the shape derivative
AU - Ito, K.
AU - Kunisch, K.
AU - Peichl, G.
T2 - PAMM
AB - Abstract A general framework for calculating shape derivatives for optimization problems with partial differential equations as constraints is presented. Exploiting the structure of the cost functional the proposed technique allows to obtain the shape derivative of the cost without the necessity to involve the shape derivative of the state variable. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
DA - 2007/12//
PY - 2007/12//
DO - 10.1002/pamm.200700780
VL - 7
IS - 1
SP - 1061005-1061006
J2 - Proc. Appl. Math. Mech.
LA - en
OP -
SN - 1617-7061 1617-7061
UR - http://dx.doi.org/10.1002/pamm.200700780
DB - Crossref
ER -
TY - JOUR
TI - An immersed interface method for the Navier-Stokes equations on irregular domains
AU - Li, Zhilin
AU - Lai, Ming-Chih
AU - Ito, Kazufumi
T2 - PAMM
AB - Abstract An augmented method based on a Cartesian grid is proposed for the incompressible Navier Stokes equations on an irregular domain. The irregular domain is embedded into a rectangular one so that a fast Poisson solver can be used in the projection method. Unlike several methods suggested in the literature that set the force strengths as unknowns, which often results an ill‐conditioned linear system, we set the jump in the normal derivative of the velocity as the augmented variable. The new approach improve the condition number of the system for the augmented variable significantly. Using the immersed interface method, we achieve second order accuracy for the velocity. Numerical results and comparisons are given to validate the new method. Some interesting new numerical experiments results are also presented. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
DA - 2007/12//
PY - 2007/12//
DO - 10.1002/pamm.200700758
VL - 7
IS - 1
SP - 1025401-1025402
J2 - Proc. Appl. Math. Mech.
LA - en
OP -
SN - 1617-7061 1617-7061
UR - http://dx.doi.org/10.1002/pamm.200700758
DB - Crossref
ER -
TY - JOUR
TI - Multiscale Considerations in Modeling of Nonlinear Elastomers
AU - Banks, H. T.
AU - Medhin, Negash G.
AU - Pinter, Gabriella A.
T2 - International Journal for Computational Methods in Engineering Science and Mechanics
AB - We present a survey of results from an extended project focused on the understanding of the dynamic behavior of elastomers or filled rubbers. This entailed experimental, modeling, computational and theoretical efforts. Of particular emphasis are the nonlinear and hysteretic aspects of dynamic deformations.
DA - 2007/2/13/
PY - 2007/2/13/
DO - 10.1080/15502280601149346
VL - 8
IS - 2
SP - 53-62
J2 - International Journal for Computational Methods in Engineering Science and Mechanics
LA - en
OP -
SN - 1550-2287 1550-2295
UR - http://dx.doi.org/10.1080/15502280601149346
DB - Crossref
KW - Nonlinear Partial Differential Equations
KW - Computational Methods
KW - Viscoelasticity
KW - Hysteresis
KW - Molecular Dynamics
KW - Multiscale Modeling
ER -
TY - JOUR
TI - Some software aspects of DAE simulation & optimization software
AU - Campbell, S. L.
AU - Betts, J. T.
AU - Engelsone, A.
AU - Nikoukhah, R.
AU - Najafi, M.
T2 - PAMM
AB - Considerable numerical software has been written for simulation and optimization of dynamical systems. From the beginning of their development, differential algebraic equations (DAEs) have often been proposed as a way to make modeling easier. The modeler need only write down equations relating the variables in the model. However, much DAE software requires at least as much user numerical and mathematical expertise as explicit methods. An important aspect of our research has been working toward helping the idea of DAEs achieve its promise in modeling and simulation by both pushing the software to handle more general problems and to also allow for less user expertise. Some recent examples are presented where this research impacts on software and their underlying algorithms. Space necessitates we assume the reader has a rough idea of what a DAE is. The examples are implicit Scicos, and optimization of DAE models. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
DA - 2007/12//
PY - 2007/12//
DO - 10.1002/pamm.200700495
VL - 7
IS - 1
SP - 1023103-1023104
SN - 1617-7061 1617-7061
UR - http://dx.doi.org/10.1002/pamm.200700495
ER -
TY - JOUR
TI - Problems and techniques: Introduction
AU - Ipsen, I.
T2 - SIAM Review
DA - 2007///
PY - 2007///
VL - 49
IS - 4
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-37249005235&partnerID=MN8TOARS
ER -
TY - JOUR
TI - Problems and techniques
AU - Ipsen, I.
T2 - SIAM Review
DA - 2007///
PY - 2007///
VL - 49
IS - 2
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-34249999151&partnerID=MN8TOARS
ER -
TY - JOUR
TI - Problems and Techniques
AU - Ipsen, Ilse
T2 - SIAM Review
AB - The three papers in this issue deal with how to describe spikes and plateaus; how to bound the probability that a random variable belongs to a particular set; and how to analyze thermodynamic properties of DNA and RNA. 1. If you had only a (mathematical) sound bite to explain the difference between the broad plateau of the Black Mesa in Arizona and the steep spike of the Matterhorn in Switzerland, what could you do? Thomas Hillen, in his paper “A Classification of Spikes and Plateaus,” proposes that you inspect fourth derivatives. In Flatland (a one‐dimensional domain, that is), the Black Mesa has a negative fourth derivative at its highest point, while the Matterhorn has a positive fourth derivative. For n‐dimensional domains it’s a little bit more complicated because one has to check whether the Hessian of the Laplacian is positive definite or negative definite. The author illustrates how the classification of plateaus and spikes benefits the qualitative analysis of several partial differential equations from mathematical physics and biology. 2. Given a random vector $X\in\real^n$ whose first two moments (the expected mean vector $\mathbf{E}X$ and the covariance matrix $\mathbf{E}XX^T$) are known, the problem considered in the second paper is to bound the probability that X lies in a particular subset C of $\real^n$. Here the set C is defined by m strict quadratic inequalities, $$C=\left\{x\in\real^n:\ x_i^TA_ix+2b_i^Tx+c_i<0, \quad 1\leq i\leq m\right\},$$ which involve symmetric matrices $A_i$, vectors $b_i$, and scalars $c_i$. The best possible (“sharp”) lower bound on the probability that X lies in C is an example of a generalized Chebyshev inequality. In general, generalized Chebyshev inequalities are sharp upper or lower bounds on the probability that a random vector with given moments lies in a particular set. The first such inequality was formulated in the nineteenth century by Chebyshev and proved by his student Markov. Almost a hundred years later duality theory and optimization emerged as powerful tools for deriving Chebyshev inequalities. Since then Chebyshev inequalities have appeared in decision analysis, statistics, finance, and machine learning. In their well‐written paper “Generalized Chebyshev Bounds via Semidefinite Programming,” Lieven Vandenberghe, Stephen Boyd, and Katherine Comanor construct two equivalent (dual) semidefinite programs for solving the above Chebyshev inequality. That is, the optimal value of these programs equals the best possible lower bound on the probability that a random vector X with given mean and covariance lies in the set C. If you have time, savor the well‐organized and constructive proofs, and check out the two simple examples to watch the semidefinite programs in action. 3. Nucleic acid technology is based on the design of molecular systems that self‐assemble out of strands of DNA or RNA, so as to implement functions relevant to robotics, biosensing, medicine, and many other applications. Fundamental to the success of this technology is a rigorous analysis of the thermodynamic properties of nucleic acid strands. In their paper “Thermodynamic Analysis of Interacting Nucleic Acid Strands,” Robert Dirks, Justin Bois, Joseph Schaeffer, Erik Winfree, and Niles Pierce make a significant advance by devising models and algorithms, not just for a single strand, but for an entire test tube of interacting strands of nucleic acids. They do this by combining an unusual variety of different mathematical techniques. A nucleic acid strand can be represented as a sequence of bases from a four‐letter alphabet (for DNA the bases are A, C, G, and T). Complementary bases can interact to form base pairs (for DNA these base pairs are C‐G and A‐T). The set of base pairs in a molecular conformation of interacting nucleic acid strands is called the secondary structure. In the simplest case, two fully‐complementary strands can base‐pair to each other completely, bringing to mind a ladder in which the rungs represent base pairs and the two sides of the ladder represent the backbones of the two strands. In practice, however, things are usually more complicated. Not every base is paired, and the strands might interact to form branched structures with various types of bulges and loops between the base pairs. For reasons of practicality, the authors disallow certain complicated secondary structures (pseudoknots). An important thermodynamic property, useful for the design of nucleic acids, is the equilibrium probability of a secondary structure. It can be calculated in a straightforward way from the partition function. Calculating the partition function for a single strand requires summing the partition functions of all smaller subsequences. This can be done by a dynamic program that computes the sums recursively. By contrast, calculating the partition function for a complex of several interacting strands is much more difficult, due to the physical and mathematical issues that arise when bases from different strands pair up. The authors present models and algorithms for computing the partition function for a complex of an arbitrary number of interacting strands. In particular, they use graph theory to map each allowed secondary structure to a unique ordering of strands (representation theorem). And they use group theory to eliminate symmetries and redundancies that would lead to overestimates of the partition function (distinguishability correction). Together, these results ensure that a dynamic program can again be used to recursively calculate the partition function. Now the authors are ready to extend their analysis to realistic experimental conditions where an arbitrary number of strand species interact (in a dilute solution) to form a variety of complexes. The authors use combinatorial arguments to determine how many times the dynamic program must be invoked to compute the partition function for such a system. They express the computation of the equilibrium concentration of each species of complex as a convex programming problem and use the concave dual problem as the basis for an efficient numerical implementation.
DA - 2007/1//
PY - 2007/1//
DO - 10.1137/siread000049000001000033000001
VL - 49
IS - 1
SP - 33-34
ER -
TY - JOUR
TI - Problems and Techniques
AU - Ipsen, Ilse
T2 - SIAM Review
DA - 2007/1//
PY - 2007/1//
DO - 10.1137/siread000049000002000209000001
VL - 49
IS - 2
SP - 209-209
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-34548494833&partnerID=MN8TOARS
ER -
TY - CONF
TI - Clusters, noncrossing partitions and the Coxeter plane
AU - Reading, N.
C2 - 2007///
C3 - FPSAC'07 - 19th International Conference on Formal Power Series and Algebraic Combinatorics
DA - 2007///
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84860725128&partnerID=MN8TOARS
ER -
TY - CONF
TI - Computer optimization of electron gun designs
AU - Ives, R.L.
AU - Bui, Thuc
AU - David, J.
AU - Tran, Hien
AU - Read, M.
T2 - 2007 Joint 32nd International Conference on Infrared and Millimeter Waves and the 15th International Conference on Terahertz Electronics (IRMMW-THz)
AB - Computer optimization is applied to three dimensional design of electron guns. The resulting designs exhibit improved performance with significantly reduced design cost compared to manual design. Design tables update geometric parameters in a solid modeling program, including dimensions for points defining spline surfaces. Algorithms then modified the geometry and other parameters based on goal functions defining the desired performance. Optimal designs were achieved by automatic execution of the optimization loop. Results for confined flow Pierce guns, sheet beam guns, and multiple beam guns will be described.
C2 - 2007/9//
C3 - 2007 Joint 32nd International Conference on Infrared and Millimeter Waves and the 15th International Conference on Terahertz Electronics
DA - 2007/9//
DO - 10.1109/icimw.2007.4516435
PB - IEEE
SN - 9781424414383
UR - http://dx.doi.org/10.1109/icimw.2007.4516435
DB - Crossref
ER -
TY - JOUR
TI - Subset selection for parameter estimation in an HIV model
AU - Fink, Martin
AU - Attarian, Adam
AU - Tran, Hien
T2 - PAMM
AB - Abstract This paper discusses methodologies for subset selection for nonlinear least squares parameter estimation. In particular, we will present approaches for partitioning the parameter space into well‐conditioned and ill‐conditioned subsets. The algorithms are applied to a simplified mathematical model of the physiologic response of the human immunodeficiency virus (HIV) in humans. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
DA - 2007/12//
PY - 2007/12//
DO - 10.1002/pamm.200700319
VL - 7
IS - 1
SP - 1121501-1121502
J2 - Proc. Appl. Math. Mech.
LA - en
OP -
SN - 1617-7061 1617-7061
UR - http://dx.doi.org/10.1002/pamm.200700319
DB - Crossref
ER -
TY -
ER -
TY - JOUR
TI - Providing easy access to radio networks
DA - 2007/5/3/
PY - 2007/5/3/
UR - http://appft.uspto.gov/netacgi/nph-Parser?Sect1=PTO2&Sect2=HITOFF&p=1&u=%2Fnetahtml%2FPTO%2Fsearch-bool.html&r=1&f=G&l=50&co1=AND&d=PG01&s1=%22Providing+easy+access+radio+networks%22.TTL.&OS=TTL/%22Providing+easy+access+to+radio+networks%22&RS=TTL/%22Providing+easy+access+to+radio+networks%22
ER -
TY - THES
TI - Comparison of local absorbing radiation conditions for scattering about elliptical body
DA - 2007///
PY - 2007///
UR - http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.728.1981&rep=rep1&type=pdf
ER -
TY - RPRT
TI - On Spectral Accuracy of Quadrature Formulae Based on
Piecewise Polynomial Interpolation
AU - Kurganov, A.
AU - Tsynkov, S.
A3 - Center for Research in Scientific Computation, North Carolina State University
DA - 2007///
PY - 2007///
M1 - CRSC-TR07-11
PB - Center for Research in Scientific Computation, North Carolina State University
SN - CRSC-TR07-11
UR - https://stsynkov.math.ncsu.edu/publications/a43e5.crsc.pdf
ER -
TY - CHAP
TI - Lacuna-based stabilization of PMLs
AU - Qasimov, H.
AU - Tsynkov, S.
T2 - Proceedings of the 8th International Conference on
Mathematical and Numerical Aspects of Wave Propagation, WAVES 2007,
University of Reading, UK, July 23 -- 27, 2007
A2 - Biggs, Nick
A2 - Bonnet-Bendhia, Anne-Sophie
A2 - Chamberlain, Peter
A2 - Chandler-Wildea, Simon
A2 - Cohen, Gary
A2 - Haddar, Houssem
A2 - Joly, Patrick
A2 - Langdon, Stephen
A2 - Lunéville, Eric
A2 - Pelloni, Beatrice
A2 - Potherat, Dominique
A2 - Potthast, Roland
PY - 2007///
SP - 298-300
UR - https://stsynkov.math.ncsu.edu/publications/Waves_2007_proceedings.pdf
ER -
TY - CHAP
TI - High-Order Numerical Method for the Nonlinear Helmholtz Equation
with Material Discontinuities
AU - Baruch, G.
AU - Fibich, G.
AU - Tsynkov, S. V.
T2 - Proceedings of the 8th International Conference on
Mathematical and Numerical Aspects of Wave Propagation, WAVES 2007,
University of Reading, UK, July 23 -- 27, 2007
A2 - Biggs, Nick
A2 - Bonnet-Bendhia, Anne-Sophie
A2 - Chamberlain, Peter
A2 - Chandler-Wildea, Simon
A2 - Cohen, Gary
A2 - Haddar, Houssem
A2 - Joly, Patrick
A2 - Langdon, Stephen
A2 - Lunéville, Eric
A2 - Pelloni, Beatrice
A2 - Potherat, Dominique
A2 - Potthast, Roland
PY - 2007///
SP - 455-457
UR - https://stsynkov.math.ncsu.edu/publications/Waves_2007_proceedings.pdf
ER -
TY - BOOK
TI - A Theoretical Introduction to Numerical Analysis
AU - Ryaben’kii, Victor S.
AU - Tsynkov, Semyon V.
AB - PREFACE ACKNOWLEDGMENTS INTRODUCTION Discretization Conditioning Error On Methods of Computation INTERPOLATION OF FUNCTIONS. QUADRATURES ALGEBRAIC INTERPOLATION Existence and Uniqueness of Interpolating Polynomial Classical Piecewise Polynomial Interpolation Smooth Piecewise Polynomial Interpolation (Splines) Interpolation of Functions of Two Variables TRIGONOMETRIC INTERPOLATION Interpolation of Periodic Functions Interpolation of Functions on an Interval. Relation between Algebraic and Trigonometric Interpolation COMPUTATION OF DEFINITE INTEGRALS. QUADRATURES Trapezoidal Rule, Simpson's Formula, and the Like Quadrature Formulae with No Saturation. Gaussian Quadratures Improper Integrals. Combination of Numerical and Analytical Methods Multiple Integrals SYSTEMS OF SCALAR EQUATIONS SYSTEMS OF LINEAR ALGEBRAIC EQUATIONS: DIRECT METHODS Different Forms of Consistent Linear Systems Linear Spaces, Norms, and Operators Conditioning of Linear Systems Gaussian Elimination and Its Tri-Diagonal Version Minimization of Quadratic Functions and Its Relation to Linear Systems The Method of Conjugate Gradients Finite Fourier Series ITERATIVE METHODS FOR SOLVING LINEAR SYSTEMS Richardson Iterations and the Like Chebyshev Iterations and Conjugate Gradients Krylov Subspace Iterations Multigrid Iterations OVERDETERMINED LINEAR SYSTEMS. THE METHOD OF LEAST SQUARES Examples of Problems that Result in Overdetermined Systems Weak Solutions of Full Rank Systems. QR Factorization Rank Deficient Systems. Singular Value Decomposition NUMERICAL SOLUTION OF NONLINEAR EQUATIONS AND SYSTEMS Commonly Used Methods of Rootfinding Fixed Point Iterations Newton's Method THE METHOD OF FINITE DIFFERENCES FOR THE NUMERICAL SOLUTION OF DIFFERENTIAL EQUATIONS NUMERCAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS Examples of Finite-Difference Schemes. Convergence Approximation of Continuous Problem by a Difference Scheme. Consistency Stability of Finite-Difference Schemes The Runge-Kutta Methods Solution of Boundary Value Problems Saturation of Finite-Difference Methods The Notion of Spectral Methods FINITE-DIFFERENCE SCHEMES FOR PARTIAL DIFFERENTIAL EQUATIONS Key Definitions and Illustrating Examples Construction of Consistent Difference Schemes Spectral Stability Criterion for Finite-Difference Cauchy Problems Stability for Problems with Variable Coefficients Stability for Initial Boundary Value Problems Explicit and Implicit Schemes for the Heat Equation DISCONTINUOUS SOLUTIONS AND METHODS OF THEIR COMPUTATION Differential Form of an Integral Conservation Law Construction of Difference Schemes DISCRETE METHODS FOR ELLIPTIC PROBLEMS A Simple Finite-Difference Scheme. The Maximum Principle The Notion of Finite Elements. Ritz and Galerkin Approximations THE METHODS OF BOUNDARY EQUATIONS FOR THE NUMERICAL SOLUTION OF BOUNDARY VALUE PROBLEMS BOUNDARY INTEGRAL EQUATIONS AND THE METHOD OF BOUNDARY ELEMENTS Reduction of Boundary Value Problems to Integral Equations Discretization of Integral Equations and Boundary Elements The Range of Applicability for Boundary Elements BOUNDARY EQUATIONS WITH PROJECTIONS AND THE METHOD OF DIFFERENCE POTENTIALS Formulation of Model Problems Difference Potentials Solution of Model Problems LIST OF FIGURES REFERENCED BOOKS REFERENCED JOURNAL ARTICLES INDEX
DA - 2007///
PY - 2007///
DO - 10.1201/9781420011166
PB - Chapman & Hall/CRC
SE - xiv+537
UR - https://doi.org/10.1201/9781420011166
ER -
TY - JOUR
TI - Convergence Analysis of the {DIRECT} Algorithm
AU - Finkel, D E
AU - Kelley, C T
DA - 2007///
PY - 2007///
ER -
TY - JOUR
TI - A Case Study in Using Local {I/O} and {GPFS} to Improve Simulation Scalability
T2 - 8th LCI International Conference on High-Performance Clustered Computing
DA - 2007///
PY - 2007///
ER -
TY - JOUR
TI - Analysis of A Scalable Preconditioner for the Wigner-Poisson Equation
AU - Lasater, M.S.
AU - Kelley, C.T.
AU - Salinger, A.
AU - Woolard, D.L.
AU - Recine, G.
AU - Zhao, P.
T2 - International Journal of Pure and Applied Mathematics
DA - 2007///
PY - 2007///
VL - 37
SP - 247–270
ER -
TY - JOUR
TI - Problems and Techniques
AU - Ipsen, Ilse
T2 - SIAM Review
AB - This issues features papers about mathematical genetics, data compression, and data assimilation in oceanography. 1. Computer algebra can help to predict the genetic makeup of a population. This is what we can conclude from the first paper, “Buchberger's Algorithm and the Two-Locus, Two-Allele Model.” With reproduction rates and probability of chromosome recombination as parameters, and one variable for each chromosome type, one can set up a system of polynomial equations. The solution value for a variable indicates how often this chromosome type occurs in the population. The question is now, over all parameter choices, how many different equilibrium solutions can there be? In other words, in the long term, can a chromosome type occur with any possible frequency? Arthur Copeland's answer is no: the number of solutions is almost always finite (and conjectured to be 15) in the special case when a population contains at most four different chromosome types. He arrives at his answer by means of affine varieties, ideals, and Gröbner bases. He also shows that the equilibrium solutions vary smoothly with the parameters. 2. The second paper, “A Direct Formulation for Sparse PCA Using Semidefinite Programming,” by Alexandre d'Aspremont, Laurent El Ghaoui, Michael I. Jordan, and Gert R. G. Lanckriet, is concerned with principal component analysis (PCA), a technique for compressing data so that as little information as possible is lost. PCA accomplishes this by finding directions of maximum variance in the data. In data analysis of gene expressions, for instance, different elements of a direction vector correspond to different genes. However, interpreting the meaning of a direction is much easier if only a few genes contribute to the direction. Such a direction vector has many zero elements and is called sparse. The authors propose a semidefinite programming method that maximizes variance as well as sparsity. The method is computationally efficient and robust. 3. The topic of the third paper, “A Reduced-Order Kalman Filter for Data Assimilation in Physical Oceanography,” by D. Rozier, F. Birol, E. Cosme, P. Brasseur, J. M. Brankart, and J. Verron, is a technique used by oceanographers to increase the accuracy of numerical models for predicting ocean circulation. Data assimilation combines the output of a simulation step with observed data and error statistics and then returns this “corrected” output to the simulation as the basis for the next step. Data assimilation based on Kalman filters assumes that measurement and model errors are unbiased and Gaussian. This is expensive, however, because an error covariance matrix must be constructed at every step. A reduced-order Kalman filter (called SEEK) is a cheaper version that reduces (or compresses) the size of the covariance matrix—the same key idea as in the paper described above. The authors give a very readable account of the issues associated with so-called ocean global circulation models: choice of vertical coordinate system (depending on the ocean region: shallow coastal shelf, steeply sloping ocean floors, stratified regions); limitations of models for ocean circulation simulations; sequential data assimilation techniques; adaptation of Kalman filters to geophysical applications; and modes of data acquisition (via satellites, ships, floats, mooring networks). The effectiveness of the SEEK filter is illustrated with numerical simulations of the Gulf Stream and the Bay of Biscay.
DA - 2007/1//
PY - 2007/1//
DO - 10.1137/siread000049000003000419000001
VL - 49
IS - 3
SP - 419-420
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-33847672254&partnerID=MN8TOARS
ER -
TY - JOUR
TI - Problems and techniques: Introduction
AU - Ipsen, I.
T2 - SIAM Review
DA - 2007///
PY - 2007///
VL - 49
IS - 4
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-37249005235&partnerID=MN8TOARS
ER -
TY - JOUR
TI - Problems and Techniques
AU - Ipsen, Ilse
T2 - SIAM Review
DA - 2007/1//
PY - 2007/1//
DO - 10.1137/siread000049000004000593000001
VL - 49
IS - 4
SP - 593-593
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-34548494833&partnerID=MN8TOARS
ER -
TY - JOUR
TI - Irreducible polynomials and barker sequences
AU - Borwein, Peter
AU - Kaltofen, Erich
AU - Mossinghoff, Michael J.
T2 - ACM Communications in Computer Algebra
AB - A Barker sequence is a finite sequence a o , ..., a n -1 , each term ±1, for which every sum Σ i a i a i +k with 0 < k < n is either 0, 1, or -- 1. It is widely conjectured that no Barker sequences of length n > 13 exist, and this conjecture has been verified for the case when n is odd. We show that in this case the problem can in fact be reduced to a question of irreducibility for a certain family of univariate polynomials: No Barker sequence of length 2 m + 1 exists if a particular integer polynomial of degree 4 m is irreducible over Q. A proof of irreducibility for this family would thus provide a short, alternative proof that long Barker sequences of odd length do not exist. However, we also prove that the polynomials in question are always reducible modulo p , for every prime p .
DA - 2007/12/1/
PY - 2007/12/1/
DO - 10.1145/1358183.1358185
VL - 41
IS - 4
SP - 118
J2 - ACM Commun. Comput. Algebra
LA - en
OP -
SN - 1932-2240
UR - http://dx.doi.org/10.1145/1358183.1358185
DB - Crossref
ER -
TY - CHAP
TI - Structured Low Rank Approximation of a Sylvester Matrix
AU - Kaltofen, Erich
AU - Yang, Zhengfeng
AU - Zhi, Lihong
T2 - Trends in Mathematics
AB - The task of determining the approximate greatest common divisor (GCD) of univariate polynomials with inexact coefficients can be formulated as computing for a given Sylvester matrix a new Sylvester matrix of lower rank whose entries are near the corresponding entries of that input matrix. We solve the approximate GCD problem by a new method based on structured total least norm (STLN) algorithms, in our case for matrices with Sylvester structure. We present iterative algorithms that compute an approximate GCD and that can certify an approximate ∈-GCD when a tolerance ∈ is given on input. Each single iteration is carried out with a number of floating point operations that is of cubic order in the input degrees. We also demonstrate the practical performance of our algorithms on a diverse set of univariate pairs of polynomials.
PY - 2007/6/24/
DO - 10.1007/978-3-7643-7984-1_5
SP - 69-83
OP -
PB - Birkhäuser Basel
SN - 9783764379834
UR - http://dx.doi.org/10.1007/978-3-7643-7984-1_5
DB - Crossref
KW - Sylvester matrix
KW - approximate greatest common divisor
KW - structured total least norm
KW - hybrid symbolic/numeric algorithm
ER -
TY - JOUR
TI - A variational formulation for frame-based inverse problems
AU - Chaux, Caroline
AU - Combettes, Patrick L
AU - Pesquet, Jean-Christophe
AU - Wajs, Valérie R
T2 - Inverse Problems
AB - A convex variational framework is proposed for solving inverse problems in Hilbert spaces with a priori information on the representation of the target solution in a frame. The objective function to be minimized consists of a separable term penalizing each frame coefficient individually, and a smooth term modelling the data formation model as well as other constraints. Sparsity-constrained and Bayesian formulations are examined as special cases. A splitting algorithm is presented to solve this problem and its convergence is established in infinite-dimensional spaces under mild conditions on the penalization functions, which need not be differentiable. Numerical simulations demonstrate applications to frame-based image restoration.
DA - 2007/6/14/
PY - 2007/6/14/
DO - 10.1088/0266-5611/23/4/008
VL - 23
IS - 4
SP - 1495-1518
J2 - Inverse Problems
OP -
SN - 0266-5611 1361-6420
UR - http://dx.doi.org/10.1088/0266-5611/23/4/008
DB - Crossref
ER -
TY - JOUR
TI - A Douglas–Rachford Splitting Approach to Nonsmooth Convex Variational Signal Recovery
AU - Combettes, Patrick L.
AU - Pesquet, Jean-Christophe
T2 - IEEE Journal of Selected Topics in Signal Processing
AB - Under consideration is the large body of signal recovery problems that can be formulated as the problem of minimizing the sum of two (not necessarily smooth) lower semicontinuous convex functions in a real Hilbert space. This generic problem is analyzed and a decomposition method is proposed to solve it. The convergence of the method, which is based on the Douglas-Rachford algorithm for monotone operator-splitting, is obtained under general conditions. Applications to non-Gaussian image denoising in a tight frame are also demonstrated.
DA - 2007/12//
PY - 2007/12//
DO - 10.1109/jstsp.2007.910264
VL - 1
IS - 4
SP - 564-574
J2 - IEEE J. Sel. Top. Signal Process.
OP -
SN - 1932-4553 1941-0484
UR - http://dx.doi.org/10.1109/jstsp.2007.910264
DB - Crossref
KW - Convex optimization
KW - denoising
KW - Douglas-Rachford
KW - frame
KW - nondifferentiable optimization
KW - Poisson noise
KW - proximal algorithm
KW - wavelets
ER -
TY - CONF
TI - College geometry students' uses of technology in the process of constructing arguments
AU - Smith, R.
AU - Hollebrands, K.
AU - Iwancio, K.
AU - Kogan, I.A.
A2 - Lamberg, T.
C2 - 2007///
C3 - Proceedings of the 29th Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education.
DA - 2007///
SP - 1153–1160
ER -
TY - JOUR
TI - Smooth and algebraic invariants of a group action. Local and global constructions.
AU - Hubert, E.
AU - Kogan, I.A.
T2 - Foundations of Computational Math.
DA - 2007///
PY - 2007///
VL - 7
IS - 4
SP - 345–383
ER -
TY - THES
TI - Comparison of local absorbing radiation conditions for scattering about elliptical body
AU - Medvinsky, M.
DA - 2007///
PY - 2007///
M3 - Master's thesis
PB - Tel Aviv University
ER -
TY - JOUR
TI - Counting subrings of Zn of index k
AU - Liu, Ricky Ini
T2 - Journal of Combinatorial Theory Series A
DA - 2007/2//
PY - 2007/2//
VL - 114
IS - 2
SP - 278–299
ER -
TY - JOUR
TI - Algebraic statistical models.
AU - Drton, Mathias
AU - Sullivant, Seth
T2 - Statistica Sinica
DA - 2007///
PY - 2007///
VL - 17
IS - 4
SP - 1273–1297
ER -
TY - JOUR
TI - Morse-Palais Lemma for nonsmooth functionals on normed spaces
AU - Nguyen, Tien Khai
AU - Duong, D.M.
AU - Tran, H.V.
T2 - Proceedings of the American Mathematical Society
DA - 2007///
PY - 2007///
VL - 135
IS - 3
SP - 921–927
ER -
TY - JOUR
TI - Fractal network model for simulating abdominal and lower extremity blood flow during resting and exercise conditions
AU - Steele, Brooke N.
AU - Olufsen, Mette S.
AU - Taylor, Charles A.
T2 - Computer Methods in Biomechanics and Biomedical Engineering
AB - We present a one-dimensional (1D) fluid dynamic model that can predict blood flow and blood pressure during exercise using data collected at rest. To facilitate accurate prediction of blood flow, we developed an impedance boundary condition using morphologically derived structured trees. Our model was validated by computing blood flow through a model of large arteries extending from the thoracic aorta to the profunda arteries. The computed flow was compared against measured flow in the infrarenal (IR) aorta at rest and during exercise. Phase contrast-magnetic resonance imaging (PC-MRI) data was collected from 11 healthy volunteers at rest and during steady exercise. For each subject, an allometrically-scaled geometry of the large vessels was created. This geometry extends from the thoracic aorta to the femoral arteries and includes the celiac, superior mesenteric, renal, inferior mesenteric, internal iliac and profunda arteries. During rest, flow was simulated using measured supraceliac (SC) flow at the inlet and a uniform set of impedance boundary conditions at the 11 outlets. To simulate exercise, boundary conditions were modified. Inflow data collected during steady exercise was specified at the inlet and the outlet boundaries were adjusted as follows. The geometry of the structured trees used to compute impedance was scaled to simulate the effective change in the cross-sectional area of resistance vessels and capillaries due to exercise. The resulting computed flow through the IR aorta was compared to measured flow. This method produces good results with a mean difference between paired data to be 1.1 +/- 7 cm(3) s(- 1) at rest and 4.0 +/- 15 cm(3) s(- 1) at exercise. While future work will improve on these results, this method provides groundwork with which to predict the flow distributions in a network due to physiologic regulation.
DA - 2007/2//
PY - 2007/2//
DO - 10.1080/10255840601068638
VL - 10
IS - 1
SP - 39-51
J2 - Computer Methods in Biomechanics and Biomedical Engineering
LA - en
OP -
SN - 1025-5842 1476-8259
UR - http://dx.doi.org/10.1080/10255840601068638
DB - Crossref
ER -
TY - CONF
TI - Integral invariants for 3D curves: an inductive approach
AU - Feng, Shuo
AU - Kogan, Irina A.
AU - Krim, Hamid
T2 - Electronic Imaging 2007
A2 - Chen, Chang Wen
A2 - Schonfeld, Dan
A2 - Luo, Jiebo
AB - In this paper we obtain, for the first time, explicit formulae for integral invariants for curves in 3D with respect
to the special and the full affine groups. Using an inductive approach we first compute Euclidean integral
invariants and use them to build the affine invariants. The motivation comes from problems in computer vision.
Since integration diminishes the effects of noise, integral invariants have advantage in such applications. We use
integral invariants to construct signatures that characterize curves up to the special affine transformations.
C2 - 2007/1/28/
C3 - Visual Communications and Image Processing 2007
DA - 2007/1/28/
DO - 10.1117/12.707278
VL - 6508
M1 - PART 1
PB - SPIE
UR - http://dx.doi.org/10.1117/12.707278
DB - Crossref
KW - 3D affine and Euclidean transformations
KW - integral affine invariants
KW - moving frames
KW - object classification
ER -
TY - CONF
TI - 3D Face Recognition using Euclidean Integral Invariants Signature
AU - Feng, S.
AU - Krim, H.
AU - Kogan, I. A.
T2 - 2007 IEEE/SP 14th Workshop on Statistical Signal Processing
AB - A novel 3D face representation and recognition approach is presented in this paper. We represent a 3D face by a set of level curves of geodesic function starting from the nose tip, which is invariant under isometric transformation of the surfaces. A pose change induces a special Euclidean transformation (a composition of a rotation and a translation) of the surface that represents a face and leads to the Euclidean transformation of the iso-geodesic curves. A change of facial expression induces isometric transformation of the iso-geodesic curves. Although the set of isometric transformations of a surface is larger than the set of Euclidean transformations in 3D, we assume that iso-geodesic curves undergo piecewise Euclidean transformations, i.e. the transformation of relatively small segments of the level curves is Euclidean. A Euclidean invariant integral signature for curves in 3D is presented in this paper. Euclidean invariant integral signature provides a classification of spatial curves which is independent of their position in 3D space and parameterization, and is not sensitive to noise. A recognition procedure based on comparing face feature in the invariant signature space is proposed. Substantiating examples are provided with an achieved classification accuracy of 95% for faces with various poses and facial expressions.
C2 - 2007/8//
C3 - 2007 IEEE/SP 14th Workshop on Statistical Signal Processing
DA - 2007/8//
DO - 10.1109/ssp.2007.4301238
SP - 156-160
PB - IEEE
SN - 9781424411979 9781424411986
UR - http://dx.doi.org/10.1109/ssp.2007.4301238
DB - Crossref
ER -
TY - CONF
TI - 3D Mixed Invariant and its Application on Object Classification
AU - Feng, S.
AU - Aouada, D.
AU - Krim, H.
AU - Kogan, I.
T2 - 2007 IEEE International Conference on Acoustics, Speech, and Signal Processing
AB - A new integro-differential invariant for curves in 3D transformed by affine group action is presented in this paper. The derivatives involved are of the first order, and therefore this invariant is significantly less sensitive to noise than classical affine differential invariants, the simplest of which involves derivatives of order 5. A classification procedure based on characteristic curves of an object surface is considered using our proposed mixed invariants. Substantiating examples are provided to verify efficiency and discriminant power of the characteristic spatial curve based 3D object classification.
C2 - 2007/4//
C3 - 2007 IEEE International Conference on Acoustics, Speech and Signal Processing - ICASSP '07
DA - 2007/4//
DO - 10.1109/icassp.2007.366716
VL - 1
PB - IEEE
SN - 1424407273
UR - http://dx.doi.org/10.1109/icassp.2007.366716
DB - Crossref
ER -
TY - CHAP
TI - Network models in epidemiology: an overview
AU - Lloyd, Alun L.
AU - Valeika, Steve
T2 - Complex Population Dynamics
PY - 2007/9//
DO - 10.1142/9789812771582_0008
SP - 189-214
OP -
PB - WORLD SCIENTIFIC
SN - 9789812771575 9789812771582
UR - http://dx.doi.org/10.1142/9789812771582_0008
DB - Crossref
ER -
TY - CONF
TI - The effects of a dynamic program for geometry on college students' understandings of properties of quadrilaterals in the Poincare Disk model
AU - Smith, R.
AU - Hollebrands, K.
AU - Iwancio, K.
AU - Kogan, I.A.
C2 - 2007///
C3 - Proceedings of the 9th International Conference on Mathematics Education in a Global Community
DA - 2007///
SP - 613–618
ER -
TY - JOUR
TI - Critical points of non-C2 functional
AU - Nguyen, Tien Khai
AU - Duong, D.M.
AU - Tran, H.V.
T2 - Topological Methods of Nonlinear Analysis
DA - 2007///
PY - 2007///
VL - 29
IS - 1
SP - 35–68
ER -
TY - CHAP
TI - Root systems and generalized
associahedra
AU - Fomin, Sergey
AU - Reading, Nathan
T2 - Geometric Combinatorics
PY - 2007/10/31/
DO - 10.1090/pcms/013/03
VL - 13
SP - 63-131
OP -
PB - American Mathematical
Society
SN - 9780821837368 9781470439125
UR - http://dx.doi.org/10.1090/pcms/013/03
DB - Crossref
ER -
TY - JOUR
TI - Chains of Modular Elements and Lattice Connectivity
AU - Hersh, Patricia
AU - Shareshian, John
T2 - Order
DA - 2007/1/24/
PY - 2007/1/24/
DO - 10.1007/s11083-006-9053-x
VL - 23
IS - 4
SP - 339-342
J2 - Order
LA - en
OP -
SN - 0167-8094 1572-9273
UR - http://dx.doi.org/10.1007/s11083-006-9053-x
DB - Crossref
ER -
TY - JOUR
TI - Combinatorics of multigraded Poincaré series for monomial rings
AU - Berglund, Alexander
AU - Blasiak, Jonah
AU - Hersh, Patricia
T2 - Journal of Algebra
AB - Backelin proved that the multigraded Poincaré series for resolving a residue field over a polynomial ring modulo a monomial ideal is a rational function. The numerator is simple, but until the recent work of Berglund there was no combinatorial formula for the denominator. Berglund's formula gives the denominator in terms of ranks of reduced homology groups of lower intervals in a certain lattice. We now express this lattice as the intersection lattice L A ( I ) of a subspace arrangement A ( I ) , use Crapo's Closure Lemma to drastically simplify the denominator in some cases (such as monomial ideals generated in degree two), and relate Golodness to the Cohen–Macaulay property for associated posets. In addition, we introduce a new class of finite lattices called complete lattices , prove that all geometric lattices are complete and provide a simple criterion for Golodness of monomial ideals whose lcm-lattices are complete.
DA - 2007/2//
PY - 2007/2//
DO - 10.1016/j.jalgebra.2006.08.020
VL - 308
IS - 1
SP - 73-90
J2 - Journal of Algebra
LA - en
OP -
SN - 0021-8693
UR - http://dx.doi.org/10.1016/j.jalgebra.2006.08.020
DB - Crossref
KW - Poincare series
KW - monomial rings
KW - poset homology
KW - diagonal arrangements
ER -
TY - JOUR
TI - Coloring complexes and arrangements
AU - Hersh, Patricia
AU - Swartz, Ed
T2 - Journal of Algebraic Combinatorics
AB - Steingrimsson’s coloring complex and Jonsson’s unipolar complex are interpreted in terms of hyperplane arrangements. This viewpoint leads to short proofs that all coloring complexes and a large class of unipolar complexes have convex ear decompositions. These convex ear decompositions impose strong new restrictions on the chromatic polynomials of all finite graphs. Similar results are obtained for characteristic polynomials of submatroids of type ℬ n arrangements.
DA - 2007/7/7/
PY - 2007/7/7/
DO - 10.1007/s10801-007-0086-z
VL - 27
IS - 2
SP - 205-214
J2 - J Algebr Comb
LA - en
OP -
SN - 0925-9899 1572-9192
UR - http://dx.doi.org/10.1007/s10801-007-0086-z
DB - Crossref
KW - convex ear decomposition
KW - chromatic polynomial
KW - coloring complex
ER -
TY - JOUR
TI - Automated Review of Prerequisite Material for Intermediate-Level Undergraduate Mathematics
AU - Levy, Rachel
AU - Shearer, Michael
AU - Taylor, Padraic
T2 - PRIMUS
AB - Abstract We describe a program that provides structured practice of prerequisite material to students in an ordinary differential equations course using an existing automated homework system originally designed for precalculus and calculus classes. The goal of the program is to improve students' comprehension of material presented in class by timing the review to occur just before the prerequisite material is relevant in class. The review is designed to gain class time that would otherwise be dedicated to review, with minimal involvement of the instructor. We report positive responses from both instructors and students in two sections of the course.
DA - 2007/5/2/
PY - 2007/5/2/
DO - 10.1080/10511970601131555
VL - 17
IS - 2
SP - 167-180
J2 - PRIMUS
LA - en
OP -
SN - 1051-1970 1935-4053
UR - http://dx.doi.org/10.1080/10511970601131555
DB - Crossref
ER -
TY - JOUR
TI - Toric fiber products
AU - Sullivant, Seth
T2 - Journal of Algebra
AB - We introduce and study the toric fiber product of two ideals in polynomial rings that are homogeneous with respect to the same multigrading. Under the assumption that the set of degrees of the variables form a linearly independent set, we can explicitly describe generating sets and Gröbner bases for these ideals. This allows us to unify and generalize some results in algebraic statistics.
DA - 2007/10//
PY - 2007/10//
DO - 10.1016/j.jalgebra.2006.10.004
VL - 316
IS - 2
SP - 560-577
J2 - Journal of Algebra
LA - en
OP -
SN - 0021-8693
UR - http://dx.doi.org/10.1016/j.jalgebra.2006.10.004
DB - Crossref
KW - Grobner basis
KW - algebraic statistics
KW - hierarchical model
KW - phylogenetic invariants
ER -
TY - JOUR
TI - A finiteness theorem for Markov bases of hierarchical models
AU - Hoşten, Serkan
AU - Sullivant, Seth
T2 - Journal of Combinatorial Theory, Series A
AB - We show that the complexity of the Markov bases of multidimensional tables stabilizes eventually if a single table dimension is allowed to vary. In particular, if this table dimension is greater than a computable bound, the Markov bases consist of elements from Markov bases of smaller tables. We give an explicit formula for this bound in terms of Graver bases. We also compute these Markov and Graver complexities for all K × 2 × 2 × 2 tables.
DA - 2007/2//
PY - 2007/2//
DO - 10.1016/j.jcta.2006.06.001
VL - 114
IS - 2
SP - 311-321
J2 - Journal of Combinatorial Theory, Series A
LA - en
OP -
SN - 0097-3165
UR - http://dx.doi.org/10.1016/j.jcta.2006.06.001
DB - Crossref
KW - contingency tables
KW - Markov bases
KW - hierarchical models
KW - graver complexity
ER -
TY - JOUR
TI - Asymptotic Evolution of Acyclic Random Mappings
AU - Evans, Steven
AU - Lidman, Tye
T2 - Electronic Journal of Probability
AB - An acyclic mapping from an $n$ element set into itself is a mapping $\varphi$ such that if $\varphi^k(x) = x$ for some $k$ and $x$, then $\varphi(x) = x$. Equivalently, $\varphi^\ell = \varphi^{\ell+1} = \ldots$ for $\ell$ sufficiently large. We investigate the behavior as $n \rightarrow \infty$ of a sequence of a Markov chain on the collection of such mappings. At each step of the chain, a point in the $n$ element set is chosen uniformly at random and the current mapping is modified by replacing the current image of that point by a new one chosen independently and uniformly at random, conditional on the resulting mapping being again acyclic. We can represent an acyclic mapping as a directed graph (such a graph will be a collection of rooted trees) and think of these directed graphs as metric spaces with some extra structure. Informal calculations indicate that the metric space valued process associated with the Markov chain should, after an appropriate time and ``space'' rescaling, converge as $n \rightarrow \infty$ to a real tree ($R$-tree) valued Markov process that is reversible with respect to a measure induced naturally by the standard reflected Brownian bridge. Although we don't prove such a limit theorem, we use Dirichlet form methods to construct a Markov process that is Hunt with respect to a suitable Gromov-Hausdorff-like metric and evolves according to the dynamics suggested by the heuristic arguments. This process is similar to one that appears in earlier work by Evans and Winter as a similarly informal limit of a Markov chain related to the subtree prune and regraft tree (SPR) rearrangements from phylogenetics.
DA - 2007///
PY - 2007///
DO - 10.1214/ejp.v12-437
VL - 12
IS - 0
SP - 1051-1180
J2 - Electron. J. Probab.
LA - en
OP -
SN - 1083-6489
UR - http://dx.doi.org/10.1214/ejp.v12-437
DB - Crossref
ER -
TY - JOUR
TI - Expectation, Conditional Expectation and Martingales in Local Fields
AU - Evans, Steven
AU - Lidman, Tye
T2 - Electronic Journal of Probability
AB - We investigate a possible definition of expectation and conditional expectation for random variables with values in a local field such as the $p$-adic numbers. We define the expectation by analogy with the observation that for real-valued random variables in $L^2$ the expected value is the orthogonal projection onto the constants. Previous work has shown that the local field version of $L^\infty$ is the appropriate counterpart of $L^2$, and so the expected value of a local field-valued random variable is defined to be its ``projection'' in $L^\infty$ onto the constants. Unlike the real case, the resulting projection is not typically a single constant, but rather a ball in the metric on the local field. However, many properties of this expectation operation and the corresponding conditional expectation mirror those familiar from the real-valued case; for example, conditional expectation is, in a suitable sense, a contraction on $L^\infty$ and the tower property holds. We also define the corresponding notion of martingale, show that several standard examples of martingales (for example, sums or products of suitable independent random variables or ``harmonic'' functions composed with Markov chains) have local field analogues, and obtain versions of the optional sampling and martingale convergence theorems.
DA - 2007///
PY - 2007///
DO - 10.1214/ejp.v12-405
VL - 12
IS - 0
SP - 498-515
J2 - Electron. J. Probab.
LA - en
OP -
SN - 1083-6489
UR - http://dx.doi.org/10.1214/ejp.v12-405
DB - Crossref
KW - local field
KW - expectation
KW - conditional expectation
KW - projection
KW - martingale
KW - martingale convergence
KW - optional sampling
ER -
TY - JOUR
TI - Immersed-interface finite-element methods for elliptic interface problems with nonhomogeneous jump conditions
AU - Gong, Y.
AU - Li, B.
AU - Li, Zhilin
T2 - SIAM Journal on Numerical Analysis
AB - In this work, a class of new finite-element methods, called immersed-interface finite-element methods, is developed to solve elliptic interface problems with nonhomogeneous jump conditions. Simple non-body-fitted meshes are used. A single function that satisfies the same nonhomogeneous jump conditions is constructed using a level-set representation of the interface. With such a function, the discontinuities across the interface in the solution and flux are removed, and an equivalent elliptic interface problem with homogeneous jump conditions is formulated. Special finite-element basis functions are constructed for nodal points near the interface to satisfy the homogeneous jump conditions. Error analysis and numerical tests are presented to demonstrate that such methods have an optimal convergence rate. These methods are designed as an efficient component of the finite-element level-set methodology for fast simulation of interface dynamics that does not require remeshing.
DA - 2007///
PY - 2007///
DO - 10.1137/060666482
VL - 46
IS - 1
SP - 472–495
KW - elliptic interface problems
KW - nonhomogeneous jump conditions
KW - immersed-interface finite-element method
KW - level-set functions
KW - error estimates
ER -
TY - BOOK
TI - Applications of abstract algebra with Maple and MATLAB2007
AU - Klima, R.E.
AU - Sigmon, N.P.
AU - Stitzinger, E.L.
DA - 2007///
PY - 2007///
PB - Boca Raton: Chapman & Hall/CRC
ER -
TY - BOOK
TI - Cardiovascular and respiratory systems modeling, analysis, and control
DA - 2007///
PY - 2007///
PB - Philadelphia: Society for Industrial and Applied Mathematics
ER -
TY - JOUR
TI - Sparse shearlet representation of Fourier integral operators
AU - Guo, K. H.
AU - Labate, D.
T2 - Electronic Research Announcements in Mathematical Sciences
DA - 2007///
PY - 2007///
VL - 14
SP - 7-19
ER -
TY - JOUR
TI - Perfect crystals for U-q (D-4((3)))
AU - Kashiwara, M.
AU - Misra, K. C.
AU - Okado, M.
AU - Yamada, D.
T2 - JOURNAL OF ALGEBRA
AB - A perfect crystal of any level is constructed for the Kirillov–Reshetikhin module of [Math Processing Error] corresponding to the middle vertex of the Dynkin diagram. The actions of Kashiwara operators are given explicitly. It is also shown that this family of perfect crystals is coherent. A uniqueness problem solved in this paper can be applied to other quantum affine algebras.
DA - 2007/11/1/
PY - 2007/11/1/
DO - 10.1016/j.jalgebra.2007.02.021
VL - 317
IS - 1
SP - 392-423
SN - 1090-266X
KW - combinatorial representation theory
KW - quantum affine algebra
KW - crystal bases
ER -
TY - JOUR
TI - High-order numerical method for the nonlinear Helmholtz equation with material discontinuities in one space dimension
AU - Baruch, G.
AU - Fibich, G.
AU - Tsynkov, S.
T2 - Journal of Computational Physics
AB - The nonlinear Helmholtz equation (NLH) models the propagation of electromagnetic waves in Kerr media, and describes a range of important phenomena in nonlinear optics and in other areas. In our previous work, we developed a fourth order method for its numerical solution that involved an iterative solver based on freezing the nonlinearity. The method enabled a direct simulation of nonlinear self-focusing in the nonparaxial regime, and a quantitative prediction of backscattering. However, our simulations showed that there is a threshold value for the magnitude of the nonlinearity, above which the iterations diverge. In this study, we numerically solve the one-dimensional NLH using a Newton-type nonlinear solver. Because the Kerr nonlinearity contains absolute values of the field, the NLH has to be recast as a system of two real equations in order to apply Newton’s method. Our numerical simulations show that Newton’s method converges rapidly and, in contradistinction with the iterations based on freezing the nonlinearity, enables computations for very high levels of nonlinearity. In addition, we introduce a novel compact finite-volume fourth order discretization for the NLH with material discontinuities. Our computations corroborate the design fourth order convergence of the method. The one-dimensional results of the current paper create a foundation for the analysis of multidimensional problems in the future.
DA - 2007/11//
PY - 2007/11//
DO - 10.1016/j.jcp.2007.08.022
VL - 227
IS - 1
SP - 820-850
J2 - Journal of Computational Physics
LA - en
OP -
SN - 0021-9991
UR - http://dx.doi.org/10.1016/j.jcp.2007.08.022
DB - Crossref
KW - Kerr nonlinearity
KW - nonlinear optics
KW - inhomogeneous medium
KW - discontinuous coefficients
KW - finite volume discretization
KW - C mpact scheme
KW - high-order method
KW - artificial boundary conditions (ABCs)
KW - two-way ABCs
KW - traveling waves
KW - complex valued solutior
KW - Frechet differentiability
KW - Newton's method
ER -
TY - JOUR
TI - Construction of regular and irregular shearlet frames
AU - Kutyniok, G.
AU - Labate, D.
T2 - Journal of Wavelet Theory and Applications
DA - 2007///
PY - 2007///
VL - 1
IS - 1
SP - 1-12
ER -
TY - JOUR
TI - Adaptive monitoring and accommodation of nonlinear actuator faults in positive real infinite dimensional systems
AU - Demetriou, Michael A.
AU - Ito, Kazufumi
AU - Smith, Ralph C.
T2 - IEEE TRANSACTIONS ON AUTOMATIC CONTROL
AB - We consider a class of positive real infinite dimensional systems which are subjected to incipient actuator faults. The actuator fault is modeled as a time varying transition from an initial (linear or even nonlinear) map into another unknown nonlinear map at the onset of the fault occurrence. An infinite dimensional adaptive detection observer is utilized to generate a residual signal in order to detect the fault occurrence and to assist in the fault accommodation. This is done via an automated control reconfiguration which utilizes information on the new actuator map and adjusts the controller via a right inverse of the new actuator map. A robust modification is utilized in order to avoid false alarms caused by unmodeled dynamics. An example is included to illustrate the applicability of the proposed detection scheme.
DA - 2007/12//
PY - 2007/12//
DO - 10.1109/TAC.2007.910694
VL - 52
IS - 12
SP - 2332-2338
SN - 1558-2523
KW - actuator faults
KW - distributed parameter systems
KW - fault accommodation
KW - nonlinear actuator dynamics
ER -
TY - JOUR
TI - The viscous-slip, diffusion-slip, and thermal-creep problems for a binary mixture of rigid spheres described by the linearized Boltzmann equation
AU - Garcia, R. D. M.
AU - Siewert, C. E.
T2 - EUROPEAN JOURNAL OF MECHANICS B-FLUIDS
AB - An analytical version of the discrete-ordinates method (the ADO method) is used with recently established analytical expressions for the rigid-sphere scattering kernels to develop concise and particularly accurate solutions to the viscous-slip, the diffusion-slip, and the half-space thermal-creep problems for a binary gas mixture described by the linearized Boltzmann equation. In addition to a computation of the viscous-slip, the diffusion-slip, and the 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 each species of particles. Numerical results are reported for two binary mixtures (Ne–Ar and He–Xe) with various molar concentrations.
DA - 2007///
PY - 2007///
DO - 10.1016/j.euromechflu.2006.12.002
VL - 26
IS - 6
SP - 749-778
SN - 1873-7390
KW - rarefied gas dynamics
KW - binary mixtures
KW - rigid spheres
KW - viscous slip
KW - thermal creep
KW - linearized Boltzmann equation
ER -
TY - JOUR
TI - Structured quadratic inverse eigenvalue problem, I. Serially linked systems
AU - Chu, Moody T.
AU - Del Buono, Nicoletta
AU - Yu, Bo
T2 - SIAM JOURNAL ON SCIENTIFIC COMPUTING
AB - Quadratic pencils arising from applications are often inherently structured. Factors contributing to the structure include the connectivity of elements within the underlying physical system and the mandatory nonnegativity of physical parameters. For physical feasibility, structural constraints must be respected. Consequently, they impose additional challenges on the inverse eigenvalue problems which intend to construct a structured quadratic pencil from prescribed eigeninformation. Knowledge of whether a structured quadratic inverse eigenvalue problem is solvable is interesting in both theory and applications. However, the issue of solvability is problem dependent and has to be addressed structure by structure. This paper considers one particular structure where the elements of the physical system, if modeled as a mass-spring system, are serially linked. The discussion recasts both undamped and damped problems in a framework of inequality systems that can be adapted for numerical computation. Some open questions are described.
DA - 2007///
PY - 2007///
DO - 10.1137/060672510
VL - 29
IS - 6
SP - 2668-2685
SN - 1095-7197
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-41849138387&partnerID=MN8TOARS
KW - quadratic pencil
KW - inverse eigenvalue problem
KW - linear oscillator
KW - inner-connectivity
KW - nonnegativity
KW - linear system of inequalities
ER -
TY - JOUR
TI - Response to perturbations for granular flow in a hopper
AU - Wambaugh, John F.
AU - Behringer, Robert P.
AU - Matthews, John V.
AU - Gremaud, Pierre A.
T2 - PHYSICAL REVIEW E
AB - We experimentally investigate the response to perturbations of circular symmetry for dense granular flow inside a three-dimensional right-conical hopper. These experiments consist of particle tracking velocimetry for the flow at the outer boundary of the hopper. We are able to test commonly used constitutive relations and observe granular flow phenomena that we can model numerically. Unperturbed conical hopper flow has been described as a radial velocity field with no azimuthal component. Guided by numerical models based upon continuum descriptions, we find experimental evidence for secondary, azimuthal circulation in response to perturbation of the symmetry with respect to gravity by tilting. For small perturbations we can discriminate between constitutive relations, based upon the agreement between the numerical predictions they produce and our experimental results. We find that the secondary circulation can be suppressed as wall friction is varied, also in agreement with numerical predictions. For large tilt angles we observe the abrupt onset of circulation for parameters where circulation was previously suppressed. Finally, we observe that for large tilt angles the fluctuations in velocity grow, independent of the onset of circulation.
DA - 2007/11//
PY - 2007/11//
DO - 10.1103/physreve.76.051303
VL - 76
IS - 5
SP -
SN - 1550-2376
ER -
TY - JOUR
TI - Pagerank computation, with special attention to dangling nodes
AU - Ipsen, Ilse C. F.
AU - Selee, Teresa M.
T2 - SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
AB - We present a simple algorithm for computing the PageRank (stationary distribution) of the stochastic Google matrix $G$. The algorithm lumps all dangling nodes into a single node. We express lumping as a similarity transformation of $G$ and show that the PageRank of the nondangling nodes can be computed separately from that of the dangling nodes. The algorithm applies the power method only to the smaller lumped matrix, but the convergence rate is the same as that of the power method applied to the full matrix $G$. The efficiency of the algorithm increases as the number of dangling nodes increases. We also extend the expression for PageRank and the algorithm to more general Google matrices that have several different dangling node vectors, when it is required to distinguish among different classes of dangling nodes. We also analyze the effect of the dangling node vector on the PageRank and show that the PageRank of the dangling nodes depends strongly on that of the nondangling nodes but not vice versa. Last we present a Jordan decomposition of the Google matrix for the (theoretical) extreme case when all Web pages are dangling nodes.
DA - 2007///
PY - 2007///
DO - 10.1137/060664331
VL - 29
IS - 4
SP - 1281-1296
SN - 1095-7162
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-38049017083&partnerID=MN8TOARS
KW - stochastic matrix
KW - stationary distribution
KW - lumping
KW - rank-one matrix
KW - power method
KW - Jordan decomposition
KW - similarity transformation
KW - Google
ER -
TY - JOUR
TI - Drinfeld realization of twisted quantum affine algebras
AU - Zhang, Honglian
AU - Jing, Naihuan
T2 - COMMUNICATIONS IN ALGEBRA
AB - The quantum affine algebra has two realizations, the usual Drinfeld–Jimbo definition and a new Drinfeld realization given by Drinfeld. In this article, we use the adjoint action to prove that these two realizations are isomorphic for the twisted quantum affine algebra.
DA - 2007///
PY - 2007///
DO - 10.1080/00927870701404713
VL - 35
IS - 11
SP - 3683-3698
SN - 0092-7872
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-35449000413&partnerID=MN8TOARS
KW - adjoint actions
KW - drinfeld realization
KW - quantum affine algebras
ER -
TY - JOUR
TI - Algorithms for computing characters for symmetric spaces
AU - Gagliardi, Daniel
AU - Helminck, Aloysius G.
T2 - ACTA APPLICANDAE MATHEMATICAE
DA - 2007/12//
PY - 2007/12//
DO - 10.1007/s10440-007-9171-5
VL - 99
IS - 3
SP - 339-365
SN - 1572-9036
KW - symmetric spaces
KW - Lie algebras of linear algebraic groups
ER -
TY - JOUR
TI - A recurrence relation for characters of highest weight integrable modules for affine Lie algebras
AU - Cook, William J.
AU - Li, Haisheng
AU - Misra, Kailash C.
T2 - COMMUNICATIONS IN CONTEMPORARY MATHEMATICS
AB - Using certain results for the vertex operator algebras associated with affine Lie algebras, we obtain recurrence relations for the characters of integrable highest weight irreducible modules for an affine Lie algebra. As an application we show that in the simply-laced level 1 case, these recurrence relations give the known characters, whose principal specializations naturally give rise to some multisum Macdonald identities.
DA - 2007/4//
PY - 2007/4//
DO - 10.1142/S0219199707002368
VL - 9
IS - 2
SP - 121-133
SN - 1793-6683
KW - affine Lie algebras
KW - vertex operator algebras
KW - highest weight representations
KW - recurrence relations
ER -
TY - JOUR
TI - A new sticky particle method for pressureless gas dynamics
AU - Chertock, Alina
AU - Kurganov, Alexander
AU - Rykov, Yurii
T2 - SIAM JOURNAL ON NUMERICAL ANALYSIS
AB - We first present a new sticky particle method for the system of pressureless gas dynamics. The method is based on the idea of sticky particles, which seems to work perfectly well for the models with point mass concentrations and strong singularity formations. In this method, the solution is sought in the form of a linear combination of $\delta$-functions, whose positions and coefficients represent locations, masses, and momenta of the particles, respectively. The locations of the particles are then evolved in time according to a system of ODEs, obtained from a weak formulation of the system of PDEs. The particle velocities are approximated in a special way using global conservative piecewise polynomial reconstruction technique over an auxiliary Cartesian mesh. This velocities correction procedure leads to a desired interaction between the particles and hence to clustering of particles at the singularities followed by the merger of the clustered particles into a new particle located at their center of mass. The proposed sticky particle method is then analytically studied. We show that our particle approximation satisfies the original system of pressureless gas dynamics in a weak sense, but only within a certain residual, which is rigorously estimated. We also explain why the relevant errors should diminish as the total number of particles increases. Finally, we numerically test our new sticky particle method on a variety of one- and two-dimensional problems as well as compare the obtained results with those computed by a high-resolution finite-volume scheme. Our simulations demonstrate the superiority of the results obtained by the sticky particle method that accurately tracks the evolution of developing discontinuities and does not smear the developing $\delta$-shocks.
DA - 2007///
PY - 2007///
DO - 10.1137/050644124
VL - 45
IS - 6
SP - 2408-2441
SN - 1095-7170
UR - https://doi-org.prox.lib.ncsu.edu/10.1137/050644124
KW - nonstrictly hyperbolic systems of conservation laws
KW - pressureless gas dynamics
KW - mass concentration
KW - strong singularities
KW - delta-shock
KW - sticky particle method
ER -
TY - JOUR
TI - Stochasticity and heterogeneity in host-vector models
AU - Lloyd, Alun L.
AU - Zhang, Ji
AU - Root, A. Morgan
T2 - JOURNAL OF THE ROYAL SOCIETY INTERFACE
AB - Demographic stochasticity and heterogeneity in transmission of infection can affect the dynamics of host-vector disease systems in important ways. We discuss the use of analytic techniques to assess the impact of demographic stochasticity in both well-mixed and heterogeneous settings. Disease invasion probabilities can be calculated using branching process methodology. We review the use of this theory for host-vector infections and examine its use in the face of heterogeneous transmission. Situations in which there is a marked asymmetry in transmission between host and vector are seen to be of particular interest. For endemic infections, stochasticity leads to variation in prevalence about the endemic level. If these fluctuations are large enough, disease extinction can occur via endemic fade-out. We develop moment equations that quantify the impact of stochasticity, providing insight into the likelihood of stochastic extinction. We frame our discussion in terms of the simple Ross malaria model, but discuss extensions to more realistic host-vector models.
DA - 2007/10/22/
PY - 2007/10/22/
DO - 10.1098/rsif.2007.1064
VL - 4
IS - 16
SP - 851-863
SN - 1742-5662
UR - https://publons.com/publon/2687695/
KW - vector-borne infection
KW - multi-group model
KW - heterogeneity
KW - stochasticity
KW - branching process
KW - moment equations
ER -
TY - JOUR
TI - Non-localizability of electric coupling and gravitational binding of charged objects
AU - Corne, Matthew
AU - Kheyfets, Arkady
AU - Miller, Warner A.
T2 - CLASSICAL AND QUANTUM GRAVITY
AB - The energy--momentum tensor in general relativity contains only localized contributions to the total energy--momentum. Here, we consider a static, spherically symmetric object consisting of a charged perfect fluid. For this object, the total gravitational mass contains a non--localizable contribution of electric coupling (ordinarily associated with electromagnetic mass). We derive an explicit expression for the total mass which implies that the non--localizable contribution of electric coupling is not bound together by gravity, thus ruling out existence of the objects with pure Lorentz electromagnetic mass in general relativity.
DA - 2007/12/7/
PY - 2007/12/7/
DO - 10.1088/0264-9381/24/23/019
VL - 24
IS - 23
SP - 5999-6005
SN - 1361-6382
ER -
TY - JOUR
TI - Monoids and cuspidal group characters
AU - Putcha, Mohan S.
T2 - SEMIGROUP FORUM
DA - 2007///
PY - 2007///
DO - 10.1007/s00233-007-0715-9
VL - 75
IS - 3
SP - 544-554
SN - 1432-2137
ER -
TY - JOUR
TI - Introducing transgenes into insect populations using combined gene-drive strategies: Modeling and analysis
AU - Huang, Yunxin
AU - Magori, Krisztian
AU - Lloyd, Alun L.
AU - Gould, Fred
T2 - INSECT BIOCHEMISTRY AND MOLECULAR BIOLOGY
AB - Engineered underdominance (EU), meiotic drive (MD) and Wolbachia have been proposed as mechanisms for driving anti-pathogen transgenes into natural populations of insect vectors of human diseases. EU can drive transgenes to high and stable frequencies but requires the release of sizeable numbers of engineered insects. MD and Wolbachia either cannot maintain high frequencies of transgenes or lack appropriate expression in critical tissues, but both can drive the transgenes to spread from very low initial frequencies. Here we use mathematical models to assess the utility of combining EU with MD or with Wolbachia. Under some conditions, the combination of EU and MD results in a more efficient transgene-drive strategy than either mechanism alone. This combined strategy could drive the transgenes to stable fixation and would require fewer released insects than EU alone, especially when only males are released. However, a combination of EU and Wolbachia does not work better than EU alone because it requires the release of even more engineered insects.
DA - 2007/10//
PY - 2007/10//
DO - 10.1016/j.ibmb.2007.06.002
VL - 37
IS - 10
SP - 1054-1063
SN - 0965-1748
KW - insect vectors
KW - anti-pathogen transgene
KW - gene-drive
KW - combined strategy
KW - release threshold
KW - theoretical assessment
ER -
TY - JOUR
TI - Gravity-driven thin liquid films with insoluble surfactant: smooth traveling waves
AU - Levy, Rachel
AU - Shearer, Michael
AU - Witelski, Thomas P.
T2 - EUROPEAN JOURNAL OF APPLIED MATHEMATICS
AB - The flow of a thin layer of fluid down an inclined plane is modified by the presence of insoluble surfactant. For any finite surfactant mass, traveling waves are constructed for a system of lubrication equations describing the evolution of the free-surface fluid height and the surfactant concentration. The one-parameter family of solutions is investigated using perturbation theory with three small parameters: the coefficient of surface tension, the surfactant diffusivity, and the coefficient of the gravity-driven diffusive spreading of the fluid. When all three parameters are zero, the nonlinear PDE system is hyperbolic/degenerate-parabolic, and admits traveling wave solutions in which the free-surface height is piecewise constant, and the surfactant concentration is piecewise linear and continuous. The jumps and corners in the traveling waves are regularized when the small parameters are nonzero; their structure is revealed through a combination of analysis and numerical simulation.
DA - 2007/12//
PY - 2007/12//
DO - 10.1017/S0956792507007218
VL - 18
SP - 679-708
SN - 1469-4425
ER -
TY - JOUR
TI - Gearhart-Pruss theorem and linear stability for riemann solutions of conservation laws
AU - Lin, Xiao-Biao
T2 - JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
DA - 2007/12//
PY - 2007/12//
DO - 10.1007/s10884-007-9098-6
VL - 19
IS - 4
SP - 1037-1074
SN - 1040-7294
KW - Gearhart Pruss theorem
KW - conservation laws
KW - Riemann solutions
KW - C-0-semigroup
KW - resonance values
ER -
TY - JOUR
TI - Empirical analysis of intraseasonal climate variability over the greater horn of Africa
AU - Bowden, Jared H.
AU - Semazzi, Fredrick H. M.
T2 - JOURNAL OF CLIMATE
AB - Abstract This study examines the intraseasonal climate variability over the Greater Horn of Africa (GHA) during the rainy season of October–December (OND). The investigation is primarily based on empirical orthogonal function (EOF) analysis of the pentad Climate Prediction Center Merged Analysis of Precipitation (CMAP) data for the period 1979–2001. The EOF analysis reveals two dominant modes of intraseasonal variability for the OND season: mixed El Niño–Southern Oscillation–Indian Ocean dipole (ENSO-IOD) and a decadal mode. The leading mode is associated with ENSO–IOD covariability. Case studies of several intraseasonal ENSO–IOD events within the recent decades indicate that during the warm (positive) events pentad rainfall is consistently above normal during the entire season despite fluctuations between pentads. However, case study analyses of negative ENSO–IOD events show that the negative cases are not mirror images of the warm events. The negative events exhibit pronounced wet and dry spells superimposed on the consistent dry anomaly background conditions. There is no large signal regarding the onset for either case, but the withdrawal of the positive (negative) events is anomalously wet (dry). The second mode of variability is associated with a decadal shift in the rainfall with the northern (southern) GHA becoming wetter (drier) in the recent decade. The decadal change in individual pentads can be quite different across the season and has a tendency to manifest itself through extreme events. The analysis underscores the need to exercise caution when applying seasonal-average-based statistics to infer the long-term behavior on subseasonal time scales. Additional analyses further confirm the decadal rainfall shift using four different rainfall datasets. Averaging the datasets to help aid in removing bias of individual datasets shows that, on average, northern (southern) portions of GHA are 29% (19%) wetter (drier) in the recent decade.
DA - 2007/12//
PY - 2007/12//
DO - 10.1175/2007JCLI1587.1
VL - 20
IS - 23
SP - 5715-5731
SN - 1520-0442
ER -
TY - JOUR
TI - Boundary-value problems for hyperbolic equations related to steady granular flow
AU - Schaeffer, David G.
AU - Shearer, Michael
AU - Witelski, Thomas P.
T2 - MATHEMATICS AND MECHANICS OF SOLIDS
AB - Boundary value problems for steady-state flow in elastoplasticity are a topic of mathematical and physical interest. In particular, the underlying PDE may be hyperbolic, and uncertainties surround the choice of physically appropriate stress and velocity boundary conditions. The analysis and numerical simulations of this paper address this issue for a model problem, a system of equations describing antiplane shearing of an elastoplastic material. This system retains the relevant mathematical structure of elastoplastic planar flow. Even if the flow rule is associative, two significant phenomena appear: (i) For boundary conditions suggestive of granular flow in a hopper, in which it seems physically natural to specify the velocity everywhere along a portion of the boundary, no such solutions of the equations exist; rather, we construct a solution with a shear band (velocity jump) along part of the boundary, and an appropriate relaxed boundary condition is satisfied there. (ii) Rigid zones appear inside deforming regions of the flow, and the stress field in such a zone is not uniquely determined. For a nonassociative flow rule, an extreme form of nonuniqueness—both velocity and stress—is encountered.
DA - 2007/12//
PY - 2007/12//
DO - 10.1177/1081286506067325
VL - 12
IS - 6
SP - 665-699
SN - 1741-3028
KW - granular materials
KW - nonlinear hyperbolic partial differential equations
ER -
TY - JOUR
TI - Weak Lacunae of Electromagnetic Waves in Dilute Plasma
AU - Tsynkov, S. V.
T2 - SIAM Journal on Applied Mathematics
AB - The propagation of waves is said to be diffusionless, and the corresponding governing PDE (or system) is said to satisfy Huygens' principle if the waves due to compactly supported sources have sharp aft fronts. The areas of no disturbance behind the aft fronts are called lacunae. Diffusionless propagation of waves is rare, whereas its opposite—diffusive propagation accompanied by aftereffects—is common. Nonetheless, lacunae can still be observed in a number of important applications, including the Maxwell equations in vacuum or in dielectrics with static response. In the framework of these applications, lacunae can be efficiently exploited for the numerical simulation of unsteady waves, and considerable progress has been made toward the development of lacunae-based methods for computational electromagnetism. Maxwell equations in vacuum are Huygens' because they reduce to a set of d'Alembert equations. Besides d'Alembert equations, there are no other scalar Huygens' equations in the standard $3+1$-dimensional Minkowski space-time. In terms of physics, this means that the mechanisms of dissipation and dispersion destroy the lacunae. In fact, all conventional low-frequency electromagnetic models, such as metals with Ohm conductivity, semiconductors, and magnetohydrodynamic media, are diffusive. An important case of the propagation of high-frequency electromagnetic waves in plasma is governed by the Klein–Gordon equation. It does not reduce to the d'Alembert equation either, and therefore the corresponding propagation is diffusive as well. However, one can still identify “weak lacunae” in the solutions of the Klein–Gordon equation, with the aft fronts that can be clearly observed, although they may not be as sharp as in the pure Huygens' case. Moreover, one can show that the “depth” of a weak lacuna is controlled by the dimensionless ratio of the Langmuir frequency to the primary carrying frequency of the waves.
DA - 2007/1//
PY - 2007/1//
DO - 10.1137/060655134
VL - 67
IS - 6
SP - 1548-1581
J2 - SIAM J. Appl. Math.
LA - en
OP -
SN - 0036-1399 1095-712X
UR - http://dx.doi.org/10.1137/060655134
DB - Crossref
KW - Huygens' principle
KW - wave diffusion
KW - aftereffects
KW - aft fronts
KW - lacunae
KW - ionospheric propagation
KW - isotropic plasma
KW - Langmuir frequency
KW - cold plasma
KW - transverse waves
KW - Maxwell equations
KW - Klein-Gordon equation
KW - weak dispersion
KW - short waves
KW - external magnetic field
KW - cyclotron frequency
KW - gyrotropy
KW - Faraday rotation
ER -
TY - JOUR
TI - Numerical investigation of cavitation in multidimensional compressible flows
AU - Devault, Kristen J.
AU - Gremaud, Pierre A.
AU - Jenssen, Helge Kristian
T2 - SIAM JOURNAL ON APPLIED MATHEMATICS
AB - The compressible Navier–Stokes equations for an ideal polytropic gas are considered in ${R}^n$, $n = 2,3$. The question of possible vacuum formation, an open theoretical problem, is investigated numerically using highly accurate computational methods. The flow is assumed to be symmetric about the origin with a purely radial velocity field. The numerical results indicate that there are weak solutions to the Navier–Stokes system in two and three space dimensions, which display formation of vacuum when the initial data are discontinuous and sufficiently large. The initial density is constant, while the initial velocity field is symmetric, points radially away from the origin, and belongs to $H^s_{loc}$ for all $s < n/2$. In addition, in the one-dimensional case, the numerical solutions are in agreement with known theoretical results.
DA - 2007///
PY - 2007///
DO - 10.1137/060652713
VL - 67
IS - 6
SP - 1675-1692
SN - 1095-712X
KW - Navier-Stokes
KW - Euler
KW - compressible fl ow
KW - cavitation
KW - pseudospectral
ER -
TY - JOUR
TI - Ergodic properties of multidimensional Brownian motion with rebirth
AU - Grigorescu, Ilie
AU - Kang, Min
T2 - ELECTRONIC JOURNAL OF PROBABILITY
AB - In a bounded open region of the $d$ dimensional space we consider a Brownian motion which is reborn at a fixed interior point as soon as it reaches the boundary. The evolution is invariant with respect to a density equal, modulo a constant, to the Green function of the Dirichlet Laplacian centered at the point of return. We calculate the resolvent in closed form, study its spectral properties and determine explicitly the spectrum in dimension one. Two proofs of the exponential ergodicity are given, one using the inverse Laplace transform and properties of analytic semigroups, and the other based on Doeblin's condition. Both methods admit generalizations to a wide class of processes.
DA - 2007/10/19/
PY - 2007/10/19/
DO - 10.1214/ejp.v12-450
VL - 12
SP - 1299-1322
SN - 1083-6489
ER -
TY - JOUR
TI - Class, dimension and length in nilpotent lie algebras
AU - Bradley, L. W.
AU - Stitzinger, Ernest
T2 - Electronic Journal of Linear Algebra
AB - The problem of finding the smallest order of a p-group of a given derived length hasa long history. Nilpotent Lie algebra versions of this and related problems are considered. Thus,the smallest order of a p-group is replaced by the smallest dimension of a nilpotent Lie algebra. Foreach length t, an upper bound for this smallest dimension is found. Also, it is shown that for eacht ≥ 5 there is a two generated Lie algebra of nilpotent class d = 21(2t−5) whose derived length is t.For two generated Lie algebras, this result is best possible. Results for small t are also found. Theresults are obtained by constructing Lie algebras of strictly upper triangular matrices.
DA - 2007///
PY - 2007///
DO - 10.13001/1081-3810.1212
VL - 16
SP - 429–434
ER -
TY - JOUR
TI - Active Control of Sound for Composite Regions
AU - Peterson, A. W.
AU - Tsynkov, S. V.
T2 - SIAM Journal on Applied Mathematics
AB - We present a methodology for the active control of time-harmonic wave fields, e.g., acoustic disturbances, in composite regions. This methodology extends our previous approach developed for the case of arcwise connected regions. The overall objective is to eliminate the effect of all outside field sources on a given domain of interest, i.e., to shield this domain. In this context, active shielding means introducing additional field sources, called active controls, that generate the annihilating signal and cancel out the unwanted component of the field. As such, the problem of active shielding can be interpreted as a special inverse source problem for the governing differential equation or system. For a composite domain, not only do the controls prevent interference from all exterior sources, but they can also enforce a predetermined communication pattern between the individual subdomains (as many as desired). In other words, they either allow the subdomains to communicate freely with one another or otherwise have them shielded from their peers. In the paper, we obtain a general solution for the composite active shielding problem and show that it reduces to solving a collection of auxiliary problems for arcwise connected domains. The general solution is constructed in two stages. Namely, if a particular subdomain is not allowed to hear another subdomain, then the supplementary controls are employed first. They communicate the required data prior to building the final set of controls. The general solution can be obtained with only the knowledge of the acoustic signals propagating through the boundaries of the subdomains. No knowledge of the field sources is required, nor is any knowledge of the properties of the medium needed.
DA - 2007/1//
PY - 2007/1//
DO - 10.1137/060662368
VL - 67
IS - 6
SP - 1582-1609
J2 - SIAM J. Appl. Math.
LA - en
OP -
SN - 0036-1399 1095-712X
UR - http://dx.doi.org/10.1137/060662368
DB - Crossref
KW - active shielding
KW - noise control
KW - inverse source problem
KW - time-harmonic acoustic fields
KW - composite domain
KW - communication pattern
KW - the Helmholtz equation
KW - generalized Calderon's potentials
KW - exact volumetric cancellation
KW - general solution
KW - incoming and outgoing waves
KW - wave split
ER -
TY - JOUR
TI - Smooth and algebraic invariants of a group action: Local and global constructions
AU - Hubert, Evelyne
AU - Kogan, Irina A.
T2 - FOUNDATIONS OF COMPUTATIONAL MATHEMATICS
AB - We provide an algebraic formulation of the moving frame method for constructing local smooth invariants on a manifold under an action of a Lie group. This formulation gives rise to algorithms for constructing rational and replacement invariants. The latter are algebraic over the field of rational invariants and play a role analogous to Cartan's normalized invariants in the smooth theory. The algebraic algorithms can be used for computing fundamental sets of differential invariants.
DA - 2007/11//
PY - 2007/11//
DO - 10.1007/s10208-006-0219-0
VL - 7
IS - 4
SP - 455-493
SN - 1615-3375
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-36549030235&partnerID=MN8TOARS
KW - rational and algebraic invariants
KW - smooth and differential invariants
KW - algebraic and Lie group actions
KW - cross-section
KW - moving frame method
KW - Grobner basis
ER -
TY - JOUR
TI - On the signal-to-interference ratio of CDMA systems in wireless communications
AU - Bai, Z. D.
AU - Silverstein, Jack W.
T2 - ANNALS OF APPLIED PROBABILITY
AB - Let {sij: i, j=1, 2, …} consist of i.i.d. random variables in ℂ with $\mathsf{E}s_{11}=0$, $\mathsf{E}|s_{11}|^{2}=1$. For each positive integer N, let sk=sk(N)=(s1k, s2k, …, sNk)T, 1≤k≤K, with K=K(N) and K/N→c>0 as N→∞. Assume for fixed positive integer L, for each N and k≤K, αk=(αk(1), …, αk(L))T is random, independent of the sij, and the empirical distribution of (α1, …, αK), with probability one converging weakly to a probability distribution H on ℂL. Let βk=βk(N)=(αk(1)skT, …, αk(L)skT)T and set C=C(N)=(1/N)∑k=2K βk βk*. Let σ2>0 be arbitrary. Then define SIR1=(1/N)β1*(C+σ2I)−1 β1, which represents the best signal-to-interference ratio for user 1 with respect to the other K−1 users in a direct-sequence code-division multiple-access system in wireless communications. In this paper it is proven that, with probability 1, SIR1 tends, as N→∞, to the limit ∑ℓ,ℓ'=1Lα̅1(ℓ)α1(ℓ')aℓ,ℓ', where A=(aℓ,ℓ') is nonrandom, Hermitian positive definite, and is the unique matrix of such type satisfying $A=\bigl(c\,\mathsf{E}\frac{\mathbf{\alpha}\mathbf{\alpha}^{*}}{1+\mathbf{\alpha}^{*}A\mathbf{\alpha}}+\sigma^{2}I_{L}\bigr)^{-1}$, where α∈ℂL has distribution H. The result generalizes those previously derived under more restricted assumptions.
DA - 2007/2//
PY - 2007/2//
DO - 10.1214/105051606000000637
VL - 17
IS - 1
SP - 81-101
SN - 1050-5164
KW - code-division multiple access (CDMA) systems
KW - random matrix
KW - empirical distributions
ER -
TY - CONF
TI - On probabilistic analysis of randomization in hybrid symbolic-numeric algorithms
AU - Kaltofen, E.
AU - Yang, Z.-F.
AU - Zhi, L.-H.
C2 - 2007///
C3 - International Workshop on Symbolic-Numeric Computation: Proceedings
DA - 2007///
PB - New York: ACM Press
SN - 9781595937445
ER -
TY - JOUR
TI - Model-Based Failure Detection on Nonlinear Systems: Theory and Transition
AU - Drake, Kimberly J.
AU - Campbell, Stephen L.
AU - Andjelkovic, Ivan
AU - Sweetingham, Kelly
T2 - Naval Engineers Journal
AB - Failure detection is an active area of Navy research due to its many important applications. Recently, an approach for multi-model identification and fault detection in the presence of bounded energy noise over finite time intervals has been introduced. This family of algorithms was originally designed to work on linear systems that can be modeled analytically. In this paper, efforts made toward extending this algorithm for fault detection to nonlinear systems along with efforts in testing this family of algorithms on real systems are discussed.
DA - 2007/10//
PY - 2007/10//
DO - 10.1111/j.0028-1425.2007.00022.x
VL - 119
IS - 2
SP - 93-107
LA - en
OP -
SN - 0028-1425 1559-3584
UR - http://dx.doi.org/10.1111/j.0028-1425.2007.00022.x
DB - Crossref
ER -
TY - JOUR
TI - Estimation of dynamic rate parameters in insect populations undergoing sublethal exposure to pesticides
AU - Banks, H. T.
AU - Banks, John E.
AU - Dick, Lara K.
AU - Stark, John D.
T2 - BULLETIN OF MATHEMATICAL BIOLOGY
AB - With newer, more environmentally friendly and, subsequently less lethal, pesticides in use, evaluating efficacy of a pesticide now requires more than simply counting deaths after treatment. A discrete, age-structured matrix model that incorporates a species' life history traits (such as birth rate, death rate and fecundity) has previously been used by ecologists. This model will be presented and discussed along with an alternative continuous, age-structured model which offers significant advantage in considering sublethal damage. We use this continuous model to estimate time-dependent mortality parameters in an ordinary least-squares technique. Confidence intervals are given and results from tests for statistical significance of added parameters are presented.
DA - 2007/10//
PY - 2007/10//
DO - 10.1007/s11538-007-9207-z
VL - 69
IS - 7
SP - 2139-2180
SN - 1522-9602
KW - population models
KW - Leslie
KW - Sinko-Streifer
KW - McKendrick-VonForester
KW - time-dependent parameters
ER -
TY - JOUR
TI - Using a signature function to determine resonant and attenuant 2-cycles in the Smith-Slatkin population model
AU - Franke, John E.
AU - Yakubu, Abdul-Aziz
T2 - JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS
AB - We study the responses of discretely reproducing populations to periodic fluctuations in three parameters: the carrying capacity and two demographic characteristics of the species. We prove that small 2-periodic fluctuations of the three parameters generate 2-cyclic oscillations of the population. We develop a signature function for predicting the responses of populations to 2-periodic fluctuations. Our signature function is the sign of a weighted sum of the relative strengths of the oscillations of the three parameters. Periodic environments are deleterious for populations when the signature function is negative, while positive signature functions signal favorable environments. We compute the signature function for the Smith–Slatkin model, and use it to determine regions in parameter space that are either favorable or detrimental to the species.
DA - 2007/4//
PY - 2007/4//
DO - 10.1080/10236190601078987
VL - 13
IS - 4
SP - 289-308
SN - 1563-5120
KW - attenuant
KW - periodic forcing
KW - resonant
KW - signature function
KW - Smith-Slatkin model
ER -
TY - JOUR
TI - Time delay systems with distribution dependent dynamics
AU - Banks, H. T.
AU - Dediu, Sava
AU - Nguyen, Hoan K.
T2 - ANNUAL REVIEWS IN CONTROL
AB - General delay dynamical systems in which uncertainty is present in the form of probability measure dependent dynamics are considered. Several motivating examples arising in biology are discussed. A functional analytic framework for investigating well-posedness (existence, uniqueness and continuous dependence of solutions), inverse problems, sensitivity analysis and approximations of the measures for computational purposes is surveyed.
DA - 2007///
PY - 2007///
DO - 10.1016/j.arcontrol.2007.02.002
VL - 31
IS - 1
SP - 17-26
SN - 1367-5788
KW - inverse dynamics problem
KW - probability distribution function
KW - sensitivity analysis
KW - biomedical systems
ER -
TY - JOUR
TI - The global attractor of a competitor-competitor-mutualist-reaction-diffusion system with time delays
AU - Pao, C. V.
T2 - NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
AB - Abstract The aim of this paper is to investigate the asymptotic behavior of time-dependent solutions of a three-species reaction–diffusion system in a bounded domain under a Neumann boundary condition. The system governs the population densities of a competitor, a competitor–mutualist and a mutualist, and time delays may appear in the reaction mechanism. It is shown, under a very simple condition on the reaction rates, that the reaction–diffusion system has a unique constant positive steady-state solution, and for any nontrivial nonnegative initial function the corresponding time-dependent solution converges to the positive steady-state solution. An immediate consequence of this global attraction property is that the trivial solution and all forms of semitrivial solutions are unstable. Moreover, the state–state problem has no nonuniform positive solution despite possible spatial dependence of the reaction and diffusion. All the conclusions for the time-delayed system are directly applicable to the system without time delays and to the corresponding ordinary differential system with or without time delays.
DA - 2007/11/1/
PY - 2007/11/1/
DO - 10.1016/j.na.2006.09.027
VL - 67
IS - 9
SP - 2623-2631
SN - 1873-5215
KW - reaction-diffusion system
KW - asymptotic behavior
KW - positive solutions
KW - global attraction
KW - time delays
KW - upper and lower solutions
ER -
TY - JOUR
TI - Sortable elements and Cambrian lattices
AU - Reading, Nathan
T2 - ALGEBRA UNIVERSALIS
AB - We show that the Coxeter-sortable elements in a finite Coxeter group W are the minimal congruence-class representatives of a lattice congruence of the weak order on W. We identify this congruence as the Cambrian congruence on W, so that the Cambrian lattice is the weak order on Coxeter-sortable elements. These results exhibit W-Catalan combinatorics arising in the context of the lattice theory of the weak order on W.
DA - 2007/6//
PY - 2007/6//
DO - 10.1007/s00012-007-2009-1
VL - 56
IS - 3-4
SP - 411-437
SN - 0002-5240
UR - https://doi.org/10.1007/s00012-007-2009-1
ER -
TY - JOUR
TI - Scalar discrete nonlinear multipoint boundary value problems
AU - Rodriguez, Jesus
AU - Taylor, Padraic
T2 - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
AB - In this paper we provide sufficient conditions for the existence of solutions to scalar discrete nonlinear multipoint boundary value problems. By allowing more general boundary conditions and by imposing less restrictions on the nonlinearities, we obtain results that extend previous work in the area of discrete boundary value problems [Debra L. Etheridge, Jesús Rodriguez, Periodic solutions of nonlinear discrete-time systems, Appl. Anal. 62 (1996) 119–137; Debra L. Etheridge, Jesús Rodriguez, Scalar discrete nonlinear two-point boundary value problems, J. Difference Equ. Appl. 4 (1998) 127–144].
DA - 2007/6/15/
PY - 2007/6/15/
DO - 10.1016/j.jmaa.2006.08.008
VL - 330
IS - 2
SP - 876-890
SN - 0022-247X
KW - boundary value problems
KW - Brouwer Fixed Point Theorem
KW - Lyapunov-Schmidt
KW - projection
ER -
TY - JOUR
TI - Nonlinear feedback controllers and compensators: a state-dependent Riccati equation approach
AU - Banks, H. T.
AU - Lewis, B. M.
AU - Tran, H. T.
T2 - COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
AB - State-dependent Riccati equation (SDRE) techniques are rapidly emerging as general design and synthesis methods of nonlinear feedback controllers and estimators for a broad class of nonlinear regulator problems. In essence, the SDRE approach involves mimicking standard linear quadratic regulator (LQR) formulation for linear systems. In particular, the technique consists of using direct parameterization to bring the nonlinear system to a linear structure having state-dependent coefficient matrices. Theoretical advances have been made regarding the nonlinear regulator problem and the asymptotic stability properties of the system with full state feedback. However, there have not been any attempts at the theory regarding the asymptotic convergence of the estimator and the compensated system. This paper addresses these two issues as well as discussing numerical methods for approximating the solution to the SDRE. The Taylor series numerical methods works only for a certain class of systems, namely with constant control coefficient matrices, and only in small regions. The interpolation numerical method can be applied globally to a much larger class of systems. Examples will be provided to illustrate the effectiveness and potential of the SDRE technique for the design of nonlinear compensator-based feedback controllers.
DA - 2007/6//
PY - 2007/6//
DO - 10.1007/s10589-007-9015-2
VL - 37
IS - 2
SP - 177-218
SN - 1573-2894
KW - nonlinear feedback control
KW - nonlinear compensator
KW - state-dependent Riccati equations
ER -
TY - JOUR
TI - Monotone iterative methods for numerical solutions of nonlinear integro-elliptic boundary problems
AU - Pao, C. V.
T2 - APPLIED MATHEMATICS AND COMPUTATION
AB - Abstract The aim of this paper is to obtain various monotone iterative schemes for numerical solutions of a class of nonlinear nonlocal reaction–diffusion–convection equations under linear boundary conditions. The boundary-value problem under consideration is discretized into a system of nonlinear algebraic equations by the finite difference method, and the iterative schemes are given for the finite difference system using upper and lower solutions as the initial iterations. The construction of the monotone sequences and the definition of upper and lower solutions depend on the quasimonotone property of the reaction function, and the iterative schemes are presented for each of the three types of quasimonotone functions. An application of the monotone iterations, including some numerical results, is given to a modified logistic diffusive equation where the kernel in the integral term may be positive, negative, or changing sign in its domain.
DA - 2007/3/15/
PY - 2007/3/15/
DO - 10.1016/j.amc.2006.08.074
VL - 186
IS - 2
SP - 1624-1642
SN - 1873-5649
KW - integro-differential equations
KW - reaction-diffusion-convection
KW - finite-difference solution
KW - monotone iterations
KW - upper and lower solutions
KW - existence-uniqueness theorem
ER -
TY - JOUR
TI - Global attractors for a discrete selection model with periodic immigration
AU - Selgrade, James F.
AU - Roberds, James H.
T2 - JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS
AB - A one-island selection-migration model is used to study the periodic immigration of a population of fixed allele frequency into a natural population. Density-dependent selection and immigration are the primary factors affecting the demographic and genetic change in the island population. With the assumptions of complete dominance (CD) or no dominance (ND) and homozygote superiority in fitness, the existence and location of global attractors are established. Analysis of this model provides rudimentary information about the migration of transgenes into a natural population.
DA - 2007/4//
PY - 2007/4//
DO - 10.1080/10236190601079100
VL - 13
IS - 4
SP - 275-287
SN - 1023-6198
KW - natural selection
KW - periodic immigration
KW - complete dominance
KW - no dominance
KW - global attractor
ER -
TY - JOUR
TI - Fast numerical methods for Bernoulli free boundary problems
AU - Kuster, Christopher M.
AU - Gremaud, Pierre A.
AU - Touzani, Rachid
T2 - SIAM JOURNAL ON SCIENTIFIC COMPUTING
AB - The numerical solution of the free boundary Bernoulli problem is addressed. An iterative method based on a level‐set formulation and boundary element method is proposed. Issues related to the implementation, the accuracy, and the generality of the method are discussed. The efficiency of the approach is illustrated by numerical results.
DA - 2007///
PY - 2007///
DO - 10.1137/06065444X
VL - 29
IS - 2
SP - 622-634
SN - 1064-8275
KW - Bernoulli
KW - free boundary
KW - level set
KW - boundary elements
ER -
TY - JOUR
TI - Comprehensive transcriptome profiling in tomato reveals a role for glycosyltransferase in Mi-mediated nematode resistance
AU - Schaff, Jennifer E.
AU - Nielsen, Dahlia M.
AU - Smith, Chris P.
AU - Scholl, Elizabeth H.
AU - Bird, David Mck.
T2 - PLANT PHYSIOLOGY
AB - Root-knot nematode (RKN; Meloidogyne spp.) is a major crop pathogen worldwide. Effective resistance exists for a few plant species, including that conditioned by Mi in tomato (Solanum lycopersicum). We interrogated the root transcriptome of the resistant (Mi+) and susceptible (Mi-) cultivars 'Motelle' and 'Moneymaker,' respectively, during a time-course infection by the Mi-susceptible RKN species Meloidogyne incognita and the Mi-resistant species Meloidogyne hapla. In the absence of RKN infection, only a single significantly regulated gene, encoding a glycosyltransferase, was detected. However, RKN infection influenced the expression of broad suites of genes; more than half of the probes on the array identified differential gene regulation between infected and uninfected root tissue at some stage of RKN infection. We discovered 217 genes regulated during the time of RKN infection corresponding to establishment of feeding sites, and 58 genes that exhibited differential regulation in resistant roots compared to uninfected roots, including the glycosyltransferase. Using virus-induced gene silencing to silence the expression of this gene restored susceptibility to M. incognita in 'Motelle,' indicating that this gene is necessary for resistance to RKN. Collectively, our data provide a picture of global gene expression changes in roots during compatible and incompatible associations with RKN, and point to candidates for further investigation.
DA - 2007/6//
PY - 2007/6//
DO - 10.1104/pp.106.090241
VL - 144
IS - 2
SP - 1079-1092
SN - 1532-2548
ER -
TY - JOUR
TI - Clusters, coxeter-sortable elements and noncrossing partitions
AU - Reading, Nathan
T2 - TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
AB - We introduce Coxeter-sortable elements of a Coxeter group W . W. For finite W , W, we give bijective proofs that Coxeter-sortable elements are equinumerous with clusters and with noncrossing partitions. We characterize Coxeter-sortable elements in terms of their inversion sets and, in the classical cases, in terms of permutations.
DA - 2007///
PY - 2007///
DO - 10.1090/s0002-9947-07-04319-x
VL - 359
IS - 12
SP - 5931-5958
SN - 0002-9947
UR - https://doi.org/10.1090/S0002-9947-07-04319-X
ER -
TY - JOUR
TI - Stochastic and deterministic models for agricultural production networks
AU - Bai, P.
AU - Banks, H. T.
AU - Dediu, S.
AU - Govan, A. Y.
AU - Last, M.
AU - Lloyd, Alun
AU - Nguyen, H. K.
AU - Olufsen, M. S.
AU - Rempala, G.
AU - Slenning, B. D.
T2 - Mathematical Biosciences and Engineering
AB - An approach to modeling the impact of disturbances in an agricultural production network is presented. A stochastic model and its approximate deterministic model for averages over sample paths of the stochastic system are developed. Simulations, sensitivity and generalized sensitivity analyses are given. Finally, it is shown how diseases may be introduced into the network and corresponding simulations are discussed.
DA - 2007///
PY - 2007///
DO - 10.3934/mbe.2007.4.373
VL - 4
IS - 3
SP - 373-402
UR - https://publons.com/publon/12886434/
ER -
TY - JOUR
TI - Some solutions (linear in the spatial variables) and generalized Chapman-Enskog functions basic to the linearized Boltzmann equations for a binary mixture of rigid spheres
AU - Garcia, R. D. M.
AU - Siewert, C. E.
T2 - ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
DA - 2007/3//
PY - 2007/3//
DO - 10.1007/s00033-006-0074-5
VL - 58
IS - 2
SP - 262-288
SN - 1420-9039
KW - rarefied gas dynamics
KW - binary mixtures
KW - rigid spheres
ER -
TY - JOUR
TI - Real-time implementation of a frequency shaping controller on a cantilever beam
AU - Lewis, B. M.
AU - Tran, H. T.
T2 - APPLIED NUMERICAL MATHEMATICS
AB - In this paper, we present the real time implementation of a control methodology for the attenuation of beam vibrations in a smart structure paradigm caused by a narrow-band exogenous force. By narrow-band exogenous force we mean a periodic force over a narrow frequency band or a particular harmonic. The particular control method is based on the minimization of a frequency dependent quadratic cost functional. This control method has been used successfully in various applications; however, this investigation differs from other works in that it emphasizes the real-time implementation of this model-based control methodology using real-time partial state measurements.
DA - 2007///
PY - 2007///
DO - 10.1016/j.apnum.2006.07.017
VL - 57
IS - 5-7
SP - 778-790
SN - 0168-9274
ER -
TY - JOUR
TI - Preface of the special issue of APNUM - International Conference on Scientific Computing in Nanjing, China
AU - Li, Zhilin
AU - Song, Yongzhong
AU - Tang, Tao
T2 - APPLIED NUMERICAL MATHEMATICS
DA - 2007///
PY - 2007///
DO - 10.1016/j.apnum.2006.07.023
VL - 57
IS - 5-7
SP - 473-474
SN - 0168-9274
ER -
TY - JOUR
TI - Positive solutions of quasilinear parabolic systems with nonlinear boundary conditions
AU - Pao, C. V.
AU - Ruan, W. H.
T2 - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
AB - The aim of this paper is to investigate the existence, uniqueness, and asymptotic behavior of solutions for a coupled system of quasilinear parabolic equations under nonlinear boundary conditions, including a system of quasilinear parabolic and ordinary differential equations. Also investigated is the existence of positive maximal and minimal solutions of the corresponding quasilinear elliptic system as well as the uniqueness of a positive steady-state solution. The elliptic operators in both systems are allowed to be degenerate in the sense that the density-dependent diffusion coefficients D i ( u i ) may have the property D i ( 0 ) = 0 for some or all i . Our approach to the problem is by the method of upper and lower solutions and its associated monotone iterations. It is shown that the time-dependent solution converges to the maximal solution for one class of initial functions and it converges to the minimal solution for another class of initial functions; and if the maximal and minimal solutions coincide then the steady-state solution is unique and the time-dependent solution converges to the unique solution. Applications of these results are given to three model problems, including a porous medium type of problem, a heat-transfer problem, and a two-component competition model in ecology. These applications illustrate some very interesting distinctive behavior of the time-dependent solutions between density-independent and density-dependent diffusions.
DA - 2007/9/1/
PY - 2007/9/1/
DO - 10.1016/j.jmaa.2006.10.005
VL - 333
IS - 1
SP - 472-499
SN - 1096-0813
KW - quasilinear parabolic systems
KW - nonlinear boundary conditions
KW - existence-uniqueness theorems
KW - asymptotic behavior of solutions
KW - degenerate diffusion
KW - porous medium problems
KW - upper and lower solutions
ER -
TY - JOUR
TI - Optimally sparse multidimensional representation using shearlets
AU - Guo, Kanghui
AU - Labate, Demetrio
T2 - SIAM JOURNAL ON MATHEMATICAL ANALYSIS
AB - In this paper we show that shearlets, an affine-like system of functions recently introduced by the authors and their collaborators, are essentially optimal in representing 2-dimensional functions f which are $C^2$ except for discontinuities along $C^2$ curves. More specifically, if $f_N^S$ is the N-term reconstruction of f obtained by using the N largest coefficients in the shearlet representation, then the asymptotic approximation error decays as $\norm{f-f_N^S}_2^2 \asymp N^{-2} (\log N)^3, N \to \infty,$ which is essentially optimal, and greatly outperforms the corresponding asymptotic approximation rate $N^{-1}$ associated with wavelet approximations. Unlike curvelets, which have similar sparsity properties, shearlets form an affine-like system and have a simpler mathematical structure. In fact, the elements of this system form a Parseval frame and are generated by applying dilations, shear transformations, and translations to a single well-localized window function.
DA - 2007///
PY - 2007///
DO - 10.1137/060649781
VL - 39
IS - 1
SP - 298-318
SN - 1095-7154
KW - affine systems
KW - curvelets
KW - geometric image processing
KW - shearlets
KW - sparse representation
KW - wavelets
ER -
TY - JOUR
TI - Optimal control of obstacle problems by H-1-obstacles
AU - Ito, Kazufumi
AU - Kunisch, Karl
T2 - APPLIED MATHEMATICS AND OPTIMIZATION
DA - 2007///
PY - 2007///
DO - 10.1007/s00245-007-0877-6
VL - 56
IS - 1
SP - 1-17
SN - 1432-0606
KW - control of variational inequalities
KW - optimality system
KW - Moreau-Yosida approximation
ER -
TY - CONF
TI - On exact and approximate interpolation of sparse rational functions
AU - Kaltofen, E.
AU - Yang, Z.-F.
AB - The black box algorithm for separating the numerator from the denominator of a multivariate rational function can be combined with sparse multivariate polynomial interpolation algorithms to interpolate a sparse rational function. domization and early termination strategies are exploited to minimize the number of black box evaluations. In addition, rational number coefficients are recovered from modular images by rational vector recovery. The need for separate numerator and denominator size bounds is avoided via correction, and the modulus is minimized by use of lattice basis reduction, a process that can be applied to sparse rational function vector recovery itself. Finally, one can deploy sparse rational function interpolation algorithm in the hybrid symbolic-numeric setting when the black box for the function returns real and complex values with noise. We present and analyze five new algorithms for the above problems and demonstrate their effectiveness on a mark implementation.
C2 - 2007///
C3 - ISSAC 2007: International Symposium for Symbolic and Algebraic Computation: Proceedings
DA - 2007///
DO - 10.1145/1277548.1277577
PB - New York: ACM Press
SN - 9781595937438
ER -
TY - JOUR
TI - On a nonlinear size-structured phytoplankton-zooplankton aggregation model
AU - Ackleh, A. S.
AU - Deng, K.
AU - Hu, S. H.
T2 - Dynamics of Continuous, Discrete & Impulsive Systems. Series A, Mathematical Analysis
DA - 2007///
PY - 2007///
VL - 14
IS - 2
SP - 265-285
ER -
TY - JOUR
TI - Numerical methods for quasi-linear elliptic equations with nonlinear boundary conditions
AU - Pao, C. V.
T2 - SIAM JOURNAL ON NUMERICAL ANALYSIS
AB - The purpose of this paper is to give a numerical treatment for a class of quasi-linear elliptic equations under nonlinear boundary conditions, including the three basic types of linear boundary conditions. The quasi-linear equation is discretized by the finite difference method, and the method of upper-lower solutions and its associated monotone iteration are used to compute the solutions of the finite difference system. This method leads to monotone iterative schemes for the computation of numerical solutions as well as some comparison results among the monotone iterative schemes. It also leads to the existence of a maximal and a minimal finite difference solution, including the uniqueness of the solution, and the convergence of the finite difference solution to the corresponding continuous solution. Applications are given to two physical problems in heat conduction and combustion theory, and numerical results for the heat-conduction problem are given, and are compared with the known true continuous solution.
DA - 2007///
PY - 2007///
DO - 10.1137/060653640
VL - 45
IS - 3
SP - 1081-1106
SN - 1095-7170
KW - density-dependent reaction diffusion
KW - nonlinear boundary condition
KW - monotone iterative schemes
KW - upper and lower solutions
KW - convergence of finite difference solution
KW - heat conduction
ER -
TY - JOUR
TI - Enhanced features for design of traveling wave tubes using CHRISTINE-1D
AU - David, John A.
AU - Kory, Carol L.
AU - Tran, Hien T.
AU - Ives, R. Lawrence
AU - Chernin, David
T2 - IEEE TRANSACTIONS ON PLASMA SCIENCE
AB - Traveling wave tubes (TWTs) are vacuum devices invented in the early 1940s for amplification of radio frequency power. These devices are critical for radar, communications, and electronic warfare missions in the military, as well as in commercial applications. The physics-based design and simulation code CHRISTINE-1D was used in the past to explore different TWT circuit designs and to automate the process of parameter estimation. However, the current capability of CHRISTINE-1D allows optimization of only helix TWT designs and includes a limited number of optimization goal functions. In addition, the current optimizer in CHRISTINE-1D employs a modified steepest descent method to carry out the optimization process. The objectives of this paper are threefold: (1) to investigate optimization techniques that may be better suited for this problem (for example, simplex type methods such as Nelder-Mead and Dividing Rectangles); (2) to allow optimization of nonhelix TWTs; and (3) to implement new optimization goal functions. Finally, to show the feasibility of our approach, we apply our optimization algorithms to the problem of designing a folded waveguide slow-wave circuit.
DA - 2007/8//
PY - 2007/8//
DO - 10.1109/TPS.2007.902128
VL - 35
IS - 4
SP - 1056-1064
SN - 0093-3813
KW - DIviding RECTangles (DIRECT)
KW - folded waveguide slow-wave circuit
KW - goal functions
KW - Nelder-Mead
KW - optimization
KW - traveling wave tubes (TWTs)
ER -
TY - JOUR
TI - Direct transcription solution of optimal control problems with higher order state constraints: theory vs practice
AU - Betts, J. T.
AU - Campbell, S. L.
AU - Engelsone, A.
T2 - OPTIMIZATION AND ENGINEERING
DA - 2007/3//
PY - 2007/3//
DO - 10.1007/s11081-007-9000-8
VL - 8
IS - 1
SP - 1-19
SN - 1573-2924
KW - optimal control
KW - numerical methods
KW - direct transcription
KW - constraints
ER -
TY - JOUR
TI - Computing the fine structure of real reductive symmetric spaces
AU - Daniel, Jennifer R.
AU - Helminck, Aloysius G.
T2 - JOURNAL OF SYMBOLIC COMPUTATION
AB - Much of the structure of Lie groups has been implemented in several computer algebra packages, including LiE , GAP4, Chevie, Magma and Maple. The structure of reductive symmetric spaces is very similar to that of the underlying Lie group and a computer algebra package for computations related to symmetric spaces would be an important tool for researchers in many areas of mathematics. Until recently only very few algorithms existed for computations in symmetric spaces due to the fact that their structure is much more complicated than that of the underlying group. In recent work, Daniel and Helminck [Daniel, J.R., Helminck, A.G., 2004. Algorithms for computations in local symmetric spaces. Comm. Algebra (in press)] gave a complete set of algorithms for computing the fine structure of Riemannian symmetric spaces. In this paper we make the first step in extending these results to general real reductive symmetric spaces and give a number of algorithms for computing some of their fine structure. This case is a lot more complicated since it involves the intricate relations of five root systems and their Weyl groups instead of just two as in the Riemannian case. We show first that this fine structure can be obtained from the setting of a complex reductive Lie group with a pair of commuting involutions. Then we proceed to give a number of algorithms for computing the fine structure of the latter.
DA - 2007/5//
PY - 2007/5//
DO - 10.1016/j.jsc.2006.08.003
VL - 42
IS - 5
SP - 497-510
SN - 0747-7171
KW - symmetric spaces
KW - Lie algebras of linear algebraic groups
KW - computational Lie theory
ER -
TY - JOUR
TI - Channel flow of a binary mixture of rigid spheres described by the linearized Boltzmann equation and driven by temperature, pressure, and concentration gradients
AU - Garcia, R. D. M.
AU - Siewert, C. E.
T2 - SIAM JOURNAL ON APPLIED MATHEMATICS
AB - An analytical version of the discrete‐ordinates method (the ADO method) is used with recently established analytical expressions for the rigid‐sphere scattering kernels in a study devoted to the flow of a binary gas mixture in a plane channel. In particular, concise and accurate solutions to basic flow problems in a plane channel driven by temperature, pressure, and concentration gradients and described by the linearized Boltzmann equation are established for the case of Maxwell boundary conditions for each of the two species. The velocity, heat‐flow, and shear‐stress profiles, as well as the mass‐ and heat‐flow rates, are established for each species of particles, and numerical results are reported for two binary mixtures (Ne‐Ar and He‐Xe).
DA - 2007///
PY - 2007///
DO - 10.1137/060673606
VL - 67
IS - 4
SP - 1041-1063
SN - 0036-1399
KW - rarefied gas dynamics
KW - binary mixtures
KW - rigid spheres
KW - channel flow
KW - linearized
KW - Boltzmann equation
ER -
TY - JOUR
TI - Are Buchberger's criteria necessary for the chain condition?
AU - Honga, H.
AU - Perry, J.
T2 - Journal of Symbolic Computation
DA - 2007///
PY - 2007///
DO - 10.1016/jjsc.2007.02.002
VL - 42
IS - 7
SP - 717-732
ER -
TY - JOUR
TI - Analysis of the limiting spectral distribution of large dimensional information-plus-noise type matrices
AU - Dozier, R. Brent
AU - Silverstein, Jack W.
T2 - JOURNAL OF MULTIVARIATE ANALYSIS
AB - A derivation of results on the analytic behavior of the limiting spectral distribution of sample covariance matrices of the “information-plus-noise” type, as studied in Dozier and Silverstein [On the empirical distribution of eigenvalues of large dimensional information-plus-noise type matrices, 2004, submitted for publication], is presented. It is shown that, away from zero, the limiting distribution possesses a continuous density. The density is analytic where it is positive and, for the most relevant cases of a in the boundary of its support, exhibits behavior closely resembling that of |x-a| for x near a. A procedure to determine its support is also analyzed.
DA - 2007/7//
PY - 2007/7//
DO - 10.1016/j.jmva.2006.12.005
VL - 98
IS - 6
SP - 1099-1122
SN - 0047-259X
KW - random matrix
KW - empirical distribution function of eigenvalues
KW - Stieltjes transform
ER -
TY - JOUR
TI - Affine Lie algebras and product-sum identities
AU - Jing, Naihuan
AU - Xia, Li-meng
T2 - JOURNAL OF ALGEBRA
AB - We provide four different decompositions for a special infinite product first studied by I. Schur. Our product–sum decomposition gives two more correspondences between subsets of partitions with parts congruent to 1 or 5 modulo 6. Our method uses a special vertex representation of affine Lie algebra C 3 ( 1 ) and admissible representations of A 1 ( 1 ) as well as quintuple product identity.
DA - 2007/8/15/
PY - 2007/8/15/
DO - 10.1016/j.jalgebra.2007.04.004
VL - 314
IS - 2
SP - 538-552
SN - 0021-8693
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-34250027840&partnerID=MN8TOARS
KW - Affine Lie algebras
KW - character formulas
KW - quintuple product identity
KW - vertex operators
ER -
TY - JOUR
TI - A two-scale model for an array of AFM's cantilever in the static case
AU - Lenczner, M.
AU - Smith, R. C.
T2 - MATHEMATICAL AND COMPUTER MODELLING
AB - The primary objective of this paper is to present a simplified model for an array of Atomic Force Microscopes (AFMs) operating in static mode. Its derivation is based on the asymptotic theory of thin plates initiated by P. Ciarlet and P. Destuynder and on the two-scale convergence introduced by M. Lenczner which generalizes the theory of G. Nguetseng and G. Allaire. As an example, we investigate in full detail a particular configuration, which leads to a very simple model for the array. Aspects of the theory for this configuration are illustrated through simulation results. Finally the formulation of our theory of two-scale convergence is fully revisited. All the proofs are reformulated in a significantly simpler manner.
DA - 2007/9//
PY - 2007/9//
DO - 10.1016/j.mcm.2006.12.028
VL - 46
IS - 5-6
SP - 776-805
SN - 1872-9479
KW - atomic force microscopy
KW - microsystems arrays
KW - multiscale modeling
KW - homogenization
ER -
TY - JOUR
TI - A study of numerical methods for the level set approach
AU - Gremaud, Pierre A.
AU - Kuster, Christopher M.
AU - Li, Zhilin
T2 - APPLIED NUMERICAL MATHEMATICS
AB - The computation of moving curves by the level set method typically requires reinitializations of the underlying level set function. Two types of reinitialization methods are studied: a high order “PDE” approach and a second order Fast Marching method. Issues related to the efficiency and implementation of both types of methods are discussed, with emphasis on the tube/narrow band implementation and accuracy considerations. The methods are also tested and compared. Fast Marching reinitialization schemes are faster but limited to second order, PDE based reinitialization schemes can easily be made more accurate but are slower, even with a tube/narrow band implementation.
DA - 2007///
PY - 2007///
DO - 10.1016/j.apnum.2006.07.022
VL - 57
IS - 5-7
SP - 837-846
SN - 0168-9274
ER -
TY - JOUR
TI - A fast iterative solver for scattering by elastic objects in layered media
AU - Ito, K.
AU - Toivanen, J.
T2 - APPLIED NUMERICAL MATHEMATICS
AB - We developed a fast iterative solver for computing time-harmonic acoustic waves scattered by an elastic object in layered media. The discretization of the problem was performed using a finite element method with linear elements based on a locally body-fitted uniform triangulation. We used a domain decomposition preconditioner in the iterative solution of the resulting system of linear equations. The preconditioner was based on a cyclic reduction type fast direct solver. The solution procedure reduces GMRES iterates onto a sparse subspace which decreases the storage and computational requirements essentially. The numerical results demonstrate the effectiveness of the proposed approach for two-dimensional domains that are hundreds of wavelengths wide and require the solution of linear systems with several millions of unknowns.
DA - 2007///
PY - 2007///
DO - 10.1016/j.apnum.2006.07.020
VL - 57
IS - 5-7
SP - 811-820
SN - 1873-5460
ER -
TY - JOUR
TI - A comparison of approximation methods for the estimation of probability distributions on parameters
AU - Banks, H. T.
AU - Davis, Jimena L.
T2 - APPLIED NUMERICAL MATHEMATICS
AB - In this paper, we compare two computationally efficient approximation methods for the estimation of growth rate distributions in size-structured population models. After summarizing the underlying theoretical framework, we present several numerical examples as validation of the theory. Furthermore, we compare the results from a spline based approximation method and a delta function based approximation method for the inverse problem involving the estimation of the distributions of growth rates in size-structured mosquitofish populations. Convergence as well as sensitivity of the estimates with respect to noise in the data are discussed for both approximation methods.
DA - 2007///
PY - 2007///
DO - 10.1016/j.apnum.2006.07.016
VL - 57
IS - 5-7
SP - 753-777
SN - 1873-5460
ER -
TY - JOUR
TI - Viscoelasticity in polymers: Phenomenological to molecular mathematical modeling
AU - Banks, H. T.
AU - Luke, N. S.
AU - Samuels, J. R., Jr.
T2 - NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
AB - We report on two recent advances in the modeling of viscoelastic polymers: (i) a new constitutive model that combines the virtual stick-slip continuum “molecular-based” ideas of Johnson and Stacer with the Rouse bead chain ideas; (ii) a two-dimensional version of a model that accounts for stenosis-driven shear wave propagation in biotissue. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 23: 817–831, 2007
DA - 2007/7//
PY - 2007/7//
DO - 10.1002/num.20250
VL - 23
IS - 4
SP - 817-831
SN - 1098-2426
KW - viscoelastic polymers
KW - constitutive models
KW - biotissue
KW - stenosis
KW - shear wave propagation
ER -
TY - JOUR
TI - Variability of East African rainfall based on multiyear RegCM3 simulations
AU - Anyah, Richard O.
AU - Semazzi, Fredrick H. M.
T2 - INTERNATIONAL JOURNAL OF CLIMATOLOGY
AB - The International Center for Theoretical Physics (ICTP) regional climate model version 3 (ICTP-RegCM3) multiyear simulations of East Africa rainfall during the October–December, short rains season are evaluated. Two parallel runs; based on NCEP reanalysis and NASA FvGCM lateral boundary conditions are performed. The simulated monthly and seasonal rainfall climatology as well as the interannual variability are found to be fairly consistent with the observations. The model climatology over specific homogeneous climate subregions, except central Kenya (CKE) highlands, also reasonably agrees with the observed. The latitude-time evolution (intraseasonal variability) of the simulated seasonal rainfall exhibits two distinct modes of behavior. The first is a quasistationary mode associated with high rainfall throughout the season within the equatorial belt between 1°S and 2°N. The second mode is associated with the intertropical convergence zone (ITCZ)-driven southward migration of regions of rainfall maxima as the season progresses, which is also consistent with the observed. Furthermore, observed rainfall variability over distinct homogeneous climate subregions is also fairly reproduced by the model, except over central Kenya highlands and northeastern parts of Kenya. The spatial correlation between the simulated seasonal rainfall and some of the global teleconnections (DMI and Nino3.4 indices) shows that the regional model conserves some of the observed regional ‘hot spots’ where rainfall-ENSO/DMI associations are strong. At the same time, unlike observations, the model reveals that along the East Africa Rift Valley and over western parts of the Lake Victoria Basin, the association is weak, perhaps an indication that nonlinear interactions between local forcing (captured by the model) and large-scale systems either suppress or obscur the dominant influence of the teleconnections on rainfall over certain parts. Copyright © 2006 Royal Meteorological Society.
DA - 2007/3/15/
PY - 2007/3/15/
DO - 10.1002/joc.1401
VL - 27
IS - 3
SP - 357-371
SN - 1097-0088
ER -
TY - JOUR
TI - The additional dynamics of least squares completions for linear differential algebraic equations
AU - Okay, Irfan
AU - Campbell, Stephen L.
AU - Kunkel, Peter
T2 - LINEAR ALGEBRA AND ITS APPLICATIONS
AB - Several approaches have been proposed for numerically solving lower dimensional, nonlinear, higher index differential algebraic equations (DAEs) for which more classical numerical methods such as backward differentiation or implicit Runge–Kutta may not be appropriate. One of these approaches is called explicit integration (EI). This approach is based on solving nonlinear DAE derivative arrays using nonlinear singular least squares methods. This results in a computed ODE, called the least squares completion, whose solutions contain those of the original DAE. This ODE is then integrated by a classical numerical method. The additional dynamics of the least squares completion can affect the numerical solution of the DAE. This paper begins the study of determining these extra dynamics.
DA - 2007/9/1/
PY - 2007/9/1/
DO - 10.1016/j.laa.2007.02.005
VL - 425
IS - 2-3
SP - 471-485
SN - 1873-1856
KW - differential algebraic equations
KW - DAEs
KW - extra dynamics
ER -
TY - JOUR
TI - On the empirical distribution of eigenvalues of large dimensional information-plus-noise-type matrices
AU - Dozier, R. Brent
AU - Silverstein, Jack W.
T2 - JOURNAL OF MULTIVARIATE ANALYSIS
AB - Let Xn be n×N containing i.i.d. complex entries and unit variance (sum of variances of real and imaginary parts equals 1), σ>0 constant, and Rn an n×N random matrix independent of Xn. Assume, almost surely, as n→∞, the empirical distribution function (e.d.f.) of the eigenvalues of 1NRnRn* converges in distribution to a nonrandom probability distribution function (p.d.f.), and the ratio nN tends to a positive number. Then it is shown that, almost surely, the e.d.f. of the eigenvalues of 1N(Rn+σXn)(Rn+σXn)* converges in distribution. The limit is nonrandom and is characterized in terms of its Stieltjes transform, which satisfies a certain equation.
DA - 2007/4//
PY - 2007/4//
DO - 10.1016/j.jmva.2006.09.006
VL - 98
IS - 4
SP - 678-694
SN - 0047-259X
KW - random matrix
KW - empirical distribution function of eigenvalues
KW - Stieltjes transform
ER -
TY - JOUR
TI - High-order numerical solution of the nonlinear Helmholtz equation with axial symmetry
AU - Baruch, G.
AU - Fibich, G.
AU - Tsynkov, S.
T2 - Journal of Computational and Applied Mathematics
AB - The nonlinear Helmholtz (NLH) equation models the propagation of intense laser beams in a Kerr medium. The NLH takes into account the effects of nonparaxiality and backward scattering that are neglected in the more common nonlinear Schrödinger model. In [G. Fibich, S. Tsynkov, High-order two-way artificial boundary conditions for nonlinear wave propagation with backscattering, J. Comput. Phys., 171 (2001) 632–677] and [G. Fibich, S. Tsynkov, Numerical solution of the nonlinear Helmholtz equation using nonorthogonal expansions, J. Comput. Phys., 210 (2005) 183–224], a novel high-order numerical method for solving the NLH was introduced and implemented in the case of a two-dimensional Cartesian geometry. The NLH was solved iteratively, using the separation of variables and a special nonlocal two-way artificial boundary condition applied to the resulting decoupled linear systems. In the current paper, we propose a major improvement to the previous method. Instead of using LU decomposition after the separation of variables, we employ an efficient summation rule that evaluates convolution with the discrete Green's function. We also extend the method to a three-dimensional setting with cylindrical symmetry, under both Dirichlet and Sommerfeld-type transverse boundary conditions.
DA - 2007/7//
PY - 2007/7//
DO - 10.1016/j.cam.2006.01.048
VL - 204
IS - 2
SP - 477-492
J2 - Journal of Computational and Applied Mathematics
LA - en
OP -
SN - 0377-0427
UR - http://dx.doi.org/10.1016/j.cam.2006.01.048
DB - Crossref
KW - Kerr media
KW - diffraction
KW - nonparaxiality
KW - nonlinear self-focusing
KW - backscattering
KW - critical and subcritical nonlinearity
KW - fourth-order approximation
KW - iterative solution
KW - separation of variables
KW - nonlocal artificial boundary conditions (ABCs)
KW - Sominerfeld radiation boundary conditions
KW - Green's function
KW - convolution
KW - cylindrical symmetry
ER -
TY - JOUR
TI - Computing the integer partition function
AU - Calkin, Neil
AU - Davis, Jimena
AU - James, Kevin
AU - Perez, Elizabeth
AU - Swannack, Charles
T2 - MATHEMATICS OF COMPUTATION
AB - In this paper we discuss efficient algorithms for com- puting the values of the partition function and implement these algorithms in order to conduct a numerical study of some conjec- tures related to the partition function. We present the distribution of p(N) for N ≤ 10 9 for primes up to 103 and small powers of 2 and 3.
DA - 2007///
PY - 2007///
DO - 10.1090/S0025-5718-07-01966-7
VL - 76
IS - 259
SP - 1619-1638
SN - 1088-6842
KW - partition function
KW - discrete fast Fourier transforms
ER -
TY - JOUR
TI - An elementary proof of Sylvester's double sums for subresultants
AU - D'Andrea, Carlos
AU - Hong, Hoon
AU - Krick, Teresa
AU - Szanto, Agnes
T2 - JOURNAL OF SYMBOLIC COMPUTATION
AB - In 1853 Sylvester stated and proved an elegant formula that expresses the polynomial subresultants in terms of the roots of the input polynomials. Sylvester’s formula was also recently proved by Lascoux and Pragacz using multi-Schur functions and divided differences. In this paper, we provide an elementary proof that uses only basic properties of matrix multiplication and Vandermonde determinants.
DA - 2007/3//
PY - 2007/3//
DO - 10.1016/j.jsc.2006.09.003
VL - 42
IS - 3
SP - 290-297
SN - 0747-7171
UR - http://dx.doi.org/10.1016/j.jsc.2006.09.003
KW - subresultants
KW - double-sum formula
KW - Vandermonde determinant
ER -
TY - JOUR
TI - An augmented approach for Stokes equations with a discontinuous viscosity and singular forces
AU - Li, Zhilin
AU - Ito, Kazufumi
AU - Lai, Ming-Chih
T2 - COMPUTERS & FLUIDS
AB - For Stokes equations with a discontinuous viscosity across an arbitrary interface or/and singular forces along the interface, it is known that the pressure is discontinuous and the velocity is non-smooth. It has been shown that these discontinuities are coupled together, which makes it difficult to obtain accurate numerical solutions. In this paper, a new numerical method that decouples the jump conditions of the fluid variables through two augmented variables has been developed. The GMRES iterative method is used to solve the Schur complement system for the augmented variables that are only defined on the interface. The augmented approach also rescales the Stokes equations in such a way that a fast Poisson solver can be used in each iteration. Numerical tests using examples that have analytic solutions show that the new method has average second order accuracy for the velocity in the infinity norm. An example of a moving interface problem is also presented.
DA - 2007/3//
PY - 2007/3//
DO - 10.1016/j.compfluid.2006.03.003
VL - 36
IS - 3
SP - 622-635
SN - 1879-0747
ER -
TY - JOUR
TI - A stress-dependent hysteresis model for ferroelectric materials
AU - Ball, Brian L.
AU - Smith, Ralph C.
AU - Kim, Sang-Joo
AU - Seelecke, Stefan
T2 - JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES
AB - This article addresses the development of a homogenized energy model which characterizes the ferroelastic switching mechanisms inherent to ferroelectric materials in a manner suitable for subsequent transducer and control design. In the first step of the development, we construct Helmholtz and Gibbs energy relations which quantify the potential and electrostatic energy associated with 90 and 180 dipole orientations. Equilibrium relations appropriate for homogeneous materials in the absence or presence of thermal relaxation are respectively determined by minimizing the Gibbs energy or balancing the Gibbs and relative thermal energies using Boltzmann principles. In the final step of the development, stochastic homogenization techniques are employed to construct macroscopic models suitable for nonhomogeneous, polycrystalline compounds. Attributes and limitations of the characterization framework are illustrated through comparison with experimental PLZT data.
DA - 2007/1//
PY - 2007/1//
DO - 10.1177/1045389X07070937
VL - 18
IS - 1
SP - 69-88
SN - 1530-8138
KW - PZT
KW - PLZT
KW - ferroelastic
KW - THUNDER
KW - hysteresis
KW - ferroelectric
KW - Helmholtz
ER -
TY - JOUR
TI - Using mathematical modeling and control to develop structured treatment interruption strategies for HIV infection
AU - Rosenberg, Eric S.
AU - Davidian, Marie
AU - Banks, H. Thomas
T2 - DRUG AND ALCOHOL DEPENDENCE
AB - The goal of this article is to suggest that mathematical models describing biological processes taking place within a patient over time can be used to design adaptive treatment strategies. We demonstrate using the key example of treatment strategies for human immunodeficiency virus type-1 (HIV) infection. Although there has been considerable progress in management of HIV infection using highly active antiretroviral therapies, continuous treatment with these agents involves significant cost and burden, toxicities, development of drug resistance, and problems with adherence; these latter complications are of particular concern in substance-abusing individuals. This has inspired interest in structured or supervised treatment interruption (STI) strategies, which involve cycles of treatment withdrawal and re-initiation. We argue that the most promising STI strategies are adaptive treatment strategies. We then describe how biological mechanisms governing the interaction over time between HIV and a patient's immune system may be represented by mathematical models and how control methods applied to these models can be used to design adaptive STI strategies seeking to maintain long-term suppression of the virus. We advocate that, when such mathematical representations of processes underlying a disease or disorder are available, they can be an important tool for suggesting adaptive treatment strategies for clinical study.
DA - 2007/5//
PY - 2007/5//
DO - 10.1016/j.drugalcdep.2006.12.024
VL - 88
SP - S41-S51
SN - 1879-0046
KW - STI
KW - CD4
KW - HIV dynamics
KW - drug resistance
KW - viral load
ER -
TY - JOUR
TI - Sensitivity of dynamical systems to parameters in a convex subset of a topological vector space
AU - Banks, H. T.
AU - Dediu, S.
AU - Nguyen, H. K.
T2 - Mathematical Biosciences and Engineering
AB - We develop a theory for sensitivity with respect to parameters in a convex subset of a topological vector space of dynamical systems in a Banach space. Specific motivating examples for probability measure dependent differential, partial differential and delay differential equations are given. Schemes that approximate the measures in the Prohorov sense are illustrated with numerical simulations for distributed delay differential equations.
DA - 2007///
PY - 2007///
DO - 10.3934/mbe.2007.4.403
VL - 4
IS - 3
SP - 403-430
ER -
TY - JOUR
TI - Optimal bilinear control of an abstract Schrodinger equation
AU - Ito, Kazufumi
AU - Kunisch, Karl
T2 - SIAM JOURNAL ON CONTROL AND OPTIMIZATION
AB - Well‐posedness of abstract quantum mechanical systems is considered and the existence of optimal control of such systems is proved. First order optimality systems are derived. Convergence of the monotone scheme for the solution of the optimality system is proved.
DA - 2007///
PY - 2007///
DO - 10.1137/05064254X
VL - 46
IS - 1
SP - 274-287
SN - 0363-0129
KW - Schrodinger equation
KW - C(0)-groups
KW - optimal control
KW - optimality systems
KW - monotone scheme
ER -
TY - JOUR
TI - Monotone approximation for a nonlinear size and class age structured epidemic model
AU - Banks, H. T.
AU - Bokil, V. A.
AU - Hu, Shuhua
T2 - NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
AB - In this paper, we study a nonautonomous size and class age structured epidemic model with nonlinear and nonlocal boundary conditions. We establish a comparison principle and construct convergent monotone sequences to prove the existence of solutions. Uniqueness of solutions is also established.
DA - 2007/7//
PY - 2007/7//
DO - 10.1016/j.nonrwa.2006.03.008
VL - 8
IS - 3
SP - 834-852
SN - 1468-1218
KW - size and class age structured models
KW - well-posedness
KW - monotone approximations
KW - comparison principle
ER -
TY - JOUR
TI - Inverse source problem and active shielding for composite domains
AU - Ryaben’kii, V.S.
AU - Tsynkov, S.V.
AU - Utyuzhnikov, S.V.
T2 - Applied Mathematics Letters
AB - The problem of active shielding (AS) for a multiply connected domain consists of constructing additional sources of the field (e.g., acoustic) so that all individual subdomains can either communicate freely with one another or otherwise be shielded from their peers. This problem can be interpreted as a special inverse source problem for the differential equation (or system) that governs the field. In the paper, we obtain general solution for a discretized composite AS problem and show that it reduces to solving a collection of auxiliary problems for simply connected domains.
DA - 2007/5//
PY - 2007/5//
DO - 10.1016/j.aml.2006.05.019
VL - 20
IS - 5
SP - 511-515
J2 - Applied Mathematics Letters
LA - en
OP -
SN - 0893-9659
UR - http://dx.doi.org/10.1016/j.aml.2006.05.019
DB - Crossref
KW - multiply connected domain
KW - inverse source
KW - active shielding
KW - control of sound
KW - Calderon's projection
KW - difference potentials method
ER -
TY - JOUR
TI - Direct transcription solution of high index optimal control problems and regular Euler-Lagrange equations
AU - Campbell, Stephen L.
AU - Maerz, Roswitha
T2 - JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
AB - Direct transcription methods are used to solve optimal control problems in many industrial settings. Models for physical systems often take the form of differential algebraic equations (DAEs). The index of the DAE traditionally is viewed as an important factor in deciding whether a particular numerical approach should be used. Recently it has been observed that what the user thinks is the index of the DAE may not be the same as the index available to the optimization software. An investigation of this fact is underway in order to develop guidelines to assist users of various numerical optimal control packages. This paper develops some theoretical results that will be needed for this development.
DA - 2007/5/15/
PY - 2007/5/15/
DO - 10.1016/j.cam.2006.02.024
VL - 202
IS - 2
SP - 186-202
SN - 1879-1778
KW - direct transcription
KW - optimal control
KW - control selection
KW - numerical algorithms
KW - differential algebraic equations
ER -
TY - JOUR
TI - Convergence of the primal-dual active set strategy for diagonally dominant systems
AU - Ito, Kazufumi
AU - Kunisch, Karl
T2 - SIAM JOURNAL ON CONTROL AND OPTIMIZATION
AB - Sufficient conditions for global convergence of the primal-dual active set strategy for finite and infinite dimensional quadratic, as well as nonlinear optimization, problems with affine equality and inequality constraints are presented. These conditions involve diagonal dominance and cone preserving properties of the operator defining the cost functional. Globalization strategies are also provided, and specific sufficient conditions for the primal-dual active set step to have a descent property are given.
DA - 2007///
PY - 2007///
DO - 10.1137/050632713
VL - 46
IS - 1
SP - 14-34
SN - 0363-0129
KW - primal-dual active set strategy
KW - diagonally dominant systems
KW - bilateral constraints
KW - globalization
ER -
TY - JOUR
TI - Application of a three-dimensional poroelastic BEM to modeling the biphasic mechanics of cell-matrix interactions in articular cartilage
AU - Haider, Mansoor A.
AU - Guilak, Farshid
T2 - COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
AB - Articular cartilage exhibits viscoelasticity in response to mechanical loading that is well described using biphasic or poroelastic continuum models. To date, boundary element methods (BEMs) have not been employed in modeling biphasic tissue mechanics. A three dimensional direct poroelastic BEM, formulated in the Laplace transform domain, is applied to modeling stress relaxation in cartilage. Macroscopic stress relaxation of a poroelastic cylinder in uni-axial confined compression is simulated and validated against a theoretical solution. Microscopic cell deformation due to poroelastic stress relaxation is also modeled. An extended Laplace inversion method is employed to accurately represent mechanical responses in the time domain.
DA - 2007///
PY - 2007///
DO - 10.1016/j.cma.2006.08.020
VL - 196
IS - 31-32
SP - 2999-3010
SN - 0045-7825
KW - boundary element method
KW - biphasic theory
KW - poroelasticity
KW - articular cartilage
KW - cells
ER -
TY - JOUR
TI - Unitary positive-energy representations of scalar bilocal quantum fields
AU - Bakalov, Bojko
AU - Nikolov, Nikolay M.
AU - Rehren, Karl-Henning
AU - Todorov, Ivan
T2 - COMMUNICATIONS IN MATHEMATICAL PHYSICS
AB - The superselection sectors of two classes of scalar bilocal quantum fields in D ≥ 4 dimensions are explicitly determined by working out the constraints imposed by unitarity. The resulting classification in terms of the dual of the respective gauge groups U(N) and O(N) confirms the expectations based on general results obtained in the framework of local nets in algebraic quantum field theory, but the approach using standard Lie algebra methods rather than abstract duality theory is complementary. The result indicates that one does not lose interesting models if one postulates the absence of scalar fields of dimension D−2 in models with global conformal invariance. Another remarkable outcome is the observation that, with an appropriate choice of the Hamiltonian, a Lie algebra embedded into the associative algebra of observables completely fixes the representation theory.
DA - 2007/4//
PY - 2007/4//
DO - 10.1007/s00220-006-0182-2
VL - 271
IS - 1
SP - 223-246
SN - 1432-0916
ER -
TY - JOUR
TI - Rational invariants of a group action. Construction and rewriting
AU - Hubert, Evelyne
AU - Kogan, Irina A.
T2 - JOURNAL OF SYMBOLIC COMPUTATION
AB - Geometric constructions applied to a rational action of an algebraic group lead to a new algorithm for computing rational invariants. A finite generating set of invariants appears as the coefficients of a reduced Gröbner basis. The algorithm comes in two variants. In the first construction the ideal of the graph of the action is considered. In the second one the ideal of a cross-section is added to the ideal of the graph. Zero-dimensionality of the resulting ideal brings a computational advantage. In both cases, reduction with respect to the computed Gröbner basis allows us to express any rational invariant in terms of the generators.
DA - 2007///
PY - 2007///
DO - 10.1016/j.jsc.2006.03.005
VL - 42
IS - 1-2
SP - 203-217
SN - 0747-7171
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-33751417574&partnerID=MN8TOARS
KW - rational invariants
KW - algebraic group actions
KW - cross-section
KW - Grobner basis
KW - differential invariants
KW - moving frame
ER -
TY - JOUR
TI - Rarely seen coleold phragmacone steinkerns from the Eocene Castle Hayne limestone of southeastern North Carolina
AU - Weaver, P.
AU - Ciampaglio, C.
AU - Chandler, R.
T2 - Palaeontographica. Abteilung A, Palaozoologie-Stratigraphie
DA - 2007///
PY - 2007///
DO - 10.1127/pala/279/2007/159
VL - 279
IS - 4-6
SP - 159-
ER -
TY - JOUR
TI - On Roth's pseudo equivalence over rings
AU - Hartwig, R. E.
AU - Patricio, P.
T2 - Electronic Journal of Linear Algebra
AB - The pseudo-equivalence of a block lower triangular matrix T = [Tij ] over a regular ring and its block diagonal matrix D(T)=[Tii] is characterized in terms of suitable Roth consistency conditions. The latter can in turn be expressed in terms of the solvability of certain matrix equations of the form TiiX − Y Tjj = Uij .
DA - 2007///
PY - 2007///
DO - 10.13001/1081-3810.1187
VL - 16
SP - 111-124
ER -
TY - JOUR
TI - Mechanism of electric fatigue crack growth in lead zirconate titanate
AU - Westrain, Ilona
AU - Oates, William S.
AU - Lupascu, Doru C.
AU - Roedel, Juergen
AU - Lynch, Christopher S.
T2 - ACTA MATERIALIA
AB - A series of experiments was performed with through-thickness cracks in ferroelectric double cantilever beam (DCB) specimens. Cyclic electric fields of different amplitudes were applied which resulted in cyclic crack propagation perpendicular to the electric field direction. Crack propagation was observed optically and three regimes were identified: a pop-in from a notch, steady-state crack growth and a decrease of the crack growth rate with increasing cycle number. Crack growth only occurred if the applied field exceeded the coercive field strength of the material. Furthermore, the crack extended during each field reversal and the crack growth rate increased with increasing field. Based on the experimental observations, a mechanistic understanding was developed and contrasted with a nonlinear finite element analysis which quantified the stress intensity in the DCB specimens. The driving forces for crack formation at the notch and subsequent fatigue crack growth were computed based on the distribution of residual stresses due to ferroelectric switching. The finite element results are in good agreement with the experimental observations and support the proposed mechanism.
DA - 2007/1//
PY - 2007/1//
DO - 10.1016/j.actamat.2006.08.029
VL - 55
IS - 1
SP - 301-312
SN - 1873-2453
KW - ferroelectricity
KW - fracture
KW - finite element analysis
KW - electroceramics
ER -
TY - JOUR
TI - Introducing desirable transgenes into insect populations using Y-linked meiotic drive - A theoretical assessment
AU - Huang, Yunxin
AU - Magori, Krisztian
AU - Lloyd, Alun L.
AU - Gould, Fred
T2 - EVOLUTION
AB - The use of genetic drive mechanisms to replace native mosquito genotypes with individuals bearing antipathogen transgenes is a potential strategy for repressing insect transmission of human diseases such as malaria and dengue. Antipathogen transgenes have been developed and tested, but efficient gene drive mechanisms are lacking. Here we theoretically assess the feasibility of introducing antipathogen genes into wild Aedes aegypti populations by using a naturally occurring meiotic drive system. We consider the release of males having both a Y-linked meiotic drive gene and an X-linked drive-insensitive response allele to which an antipathogen gene is linked. We use mathematical models and computer simulations to determine how the post-introduction dynamics of the antipathogen gene are affected by specific genetic characteristics of the system. The results show that when the natural population is uniformly sensitive to the meiotic drive gene, the antipathogen gene may be driven close to fixation if the fitness costs of the drive gene, the insensitive response allele, and the antipathogen gene are low. However, when the natural population has a small proportion of an X-linked insensitive response allele or an autosomal gene that strongly reduces the effect of the drive gene, the antipathogen gene does not spread if it has an associated fitness cost. Our modeling results provide a theoretical foundation for further experimental tests.
DA - 2007/4//
PY - 2007/4//
DO - 10.1111/j.1558-5646.2007.00075.x
VL - 61
IS - 4
SP - 717-726
SN - 1558-5646
UR - https://publons.com/publon/8533052/
KW - autosomal modifier
KW - sex-ratio distortion
KW - transgene
KW - X-chromosome responder
KW - Y-chromosome driver
ER -
TY - JOUR
TI - BRST extension of geometric quantization
AU - Fulp, Ronald
T2 - FOUNDATIONS OF PHYSICS
AB - Consider a physical system for which a mathematically rigorous geometric quantization procedure exists. Now subject the system to a finite set of irreducible first class (bosonic) constraints. It is shown that there is a mathematically rigorous BRST quantization of the constrained system whose cohomology at ghost number zero recovers the constrained quantum states. Moreover this space of constrained states has a well-defined Hilbert space structure inherited from that of the original system. Treatments of these ideas in the Physics literature are more general but suffer from having states with infinite or zero norms and thus are not admissible as states. Also the BRST operator for many systems require regularization to be well-defined. In our more restricted context we show that our treatment does not suffer from any of these difficulties. This work was submitted for publication March 21,2006.
DA - 2007/1//
PY - 2007/1//
DO - 10.1007/s10701-006-9090-8
VL - 37
IS - 1
SP - 103-124
SN - 0015-9018
KW - geometric quantization
KW - BRST quantization
ER -
TY - JOUR
TI - A note on radiative transfer in a finite layer
AU - Siewert, C. E.
T2 - JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
AB - An ADO (analytical discrete ordinates) solution is used to establish a concise and accurate result for a basic radiative transfer problem in a finite layer described by the grey equation of transfer with general anisotropic scattering. As a specific application, the solution is evaluated for the case of Fresnel boundary conditions to yield numerical results (of a high standard) for several specific cases.
DA - 2007/2/23/
PY - 2007/2/23/
DO - 10.1088/1751-8113/40/8/007
VL - 40
IS - 8
SP - 1785-1789
SN - 1751-8121
ER -
TY - JOUR
TI - The temperature-jump problem based on the linearized Boltzmann equation for a binary mixture of rigid spheres
AU - Garcia, R. D. M.
AU - Siewert, C. E.
T2 - EUROPEAN JOURNAL OF MECHANICS B-FLUIDS
AB - An analytical version of the discrete-ordinates method (the ADO method) is used with recently reported analytical forms for the rigid-sphere scattering kernels to establish a concise and particularly accurate solution to the temperature-jump problem for a binary gas mixture described by the linearized Boltzmann equation. The solution yields, in addition to the temperature-jump coefficient for the general (specular-diffuse) case of Maxwell boundary conditions for each of the two species, the density, the temperature and the heat-flow profiles for both types of particles. Numerical results are reported for two binary mixtures (Ne–Ar and He–Xe) with various molar concentrations.
DA - 2007///
PY - 2007///
DO - 10.1016/j.euromechflu.2006.04.001
VL - 26
IS - 1
SP - 132-153
SN - 1873-7390
KW - rarefied gas dynamics
KW - binary mixtures
KW - rigid spheres
KW - temperature-jump coefficient
ER -
TY - JOUR
TI - Quasilinear parabolic and elliptic equations with nonlinear boundary conditions
AU - Pao, C. V.
T2 - NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
AB - Abstract This paper is concerned with a class of quasilinear parabolic and elliptic equations in a bounded domain with both Dirichlet and nonlinear Neumann boundary conditions. The equation under consideration may be degenerate or singular depending on the property of the diffusion coefficient. The consideration of the class of equations is motivated by some heat-transfer problems where the heat capacity and thermal conductivity are both temperature dependent. The aim of the paper is to show the existence and uniqueness of a global time-dependent solution of the parabolic problem, existence of maximal and minimal steady-state solutions of the elliptic problem, including conditions for the uniqueness of a solution, and the asymptotic behavior of the time-dependent solution in relation to the steady-state solutions. Applications are given to some heat-transfer problems and an extended logistic reaction–diffusion equation.
DA - 2007/2/1/
PY - 2007/2/1/
DO - 10.1016/j.na.2005.12.007
VL - 66
IS - 3
SP - 639-662
SN - 1873-5215
KW - quasilinear parabolic and elliptic equations
KW - existence and uniqueness
KW - maximal and minimal solutions
KW - asymptotic behavior
KW - upper and lower solutions
KW - heat-transfer problems
ER -
TY - JOUR
TI - A dynamic model for induced reactivation of latent virus
AU - Kepler, G. M.
AU - Nguyen, H. K.
AU - Webster-Cyriaque, J.
AU - Banks, H. T.
T2 - JOURNAL OF THEORETICAL BIOLOGY
AB - We develop a deterministic mathematical model to describe reactivation of latent virus by chemical inducers. This model is applied to the reactivation of latent KSHV in BCBL-1 cell cultures with butyrate as the inducing agent. Parameters for the model are first estimated from known properties of the exponentially growing, uninduced cell cultures. Additional parameters that are necessary to describe induction are determined from fits to experimental data from the literature. Our initial model provides good agreement with two independent sets of experimental data, but also points to the need for a new class of experiments which are required for further understanding of the underlying mechanisms.
DA - 2007/2/7/
PY - 2007/2/7/
DO - 10.1016/j.jtbi.2006.08.020
VL - 244
IS - 3
SP - 451-462
SN - 1095-8541
KW - reactivation of latent virus
KW - mathematical model
KW - KSHV
KW - Herpes virus
ER -
TY - JOUR
TI - Weakly nonlinear discrete multipoint boundary value problems
AU - Rodriguez, Jesus
AU - Taylor, Padraic
T2 - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
AB - In this paper we study nonlinear, discrete, multipoint boundary value problems of the form x ( t + 1 ) = A ( t ) x ( t ) + ϵ f ( t , x ( t ) ) subject to B 0 x ( 0 ) + B 1 x ( 1 ) + ⋯ + B N x ( N ) = 0 . We provide sufficient conditions for the existence of solutions and we present a qualitative analysis of the way the solutions depend on the parameter ϵ.
DA - 2007/5/1/
PY - 2007/5/1/
DO - 10.1016/j.jmaa.2006.06.024
VL - 329
IS - 1
SP - 77-91
SN - 0022-247X
KW - boundary value problems
KW - implicit function theorem
KW - Lyapunov-Schmidt
KW - projection
ER -
TY - JOUR
TI - Updating quadratic models with no spillover effect on unmeasured spectral data
AU - Chu, Moody T.
AU - Lin, Wen-Wei
AU - Xu, Shu-Fang
T2 - INVERSE PROBLEMS
AB - Model updating concerns the modification of an existing but inaccurate model with measured data. For models characterized by quadratic pencils, the measured data usually involve incomplete knowledge of natural frequencies, mode shapes, or other spectral information. In conducting the updating, it is often desirable to match only the part of observed data without tampering with the other part of unmeasured or unknown eigenstructure inherent in the original model. Such an updating, if possible, is said to have no spillover. Model updating with no spillover has been a very challenging task in applications. This paper provides a complete theory on when such an updating with no spillover is possible.
DA - 2007/2//
PY - 2007/2//
DO - 10.1088/0266-5611/23/1/013
VL - 23
IS - 1
SP - 243-256
SN - 1361-6420
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-33947697703&partnerID=MN8TOARS
ER -
TY - JOUR
TI - Model-based robust control design for magnetostrictive transducers operating in hysteretic and nonlinear regimes
AU - Nealis, James M.
AU - Smith, Ralph C.
T2 - IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY
AB - This paper addresses the development of robust control designs for high-performance smart material transducers operating in nonlinear and hysteretic regimes. While developed in the context of a magnetostrictive transducer used for high-speed, high-accuracy milling, the resulting model-based control techniques can be directly extended to systems utilizing piezoceramic or shape memory alloy compounds due to the unified nature of models used to quantify hysteresis and nonlinearities inherent to all of these materials. When developing models and corresponding inverse filters or compensators, significant emphasis is placed on the utilization of the material's physics to provide the accuracy and efficiency required for real-time implementation of resulting model-based control designs. In the material models, this is achieved by combining energy analysis with stochastic homogenization techniques, whereas the efficiency of forward algorithms is combined with monotonicity properties of the material behavior to provide highly efficient inverse algorithms. These inverse filters are then incorporated in H _{2} and H _{infin} theory to provide robust control algorithms capable of providing high-accuracy tracking even though the actuators are operating in nonlinear and hysteretic regimes. Through numerical examples, it is illustrated that the robust designs incorporating inverse compensators can achieve the required tracking tolerance of 1-2 mum for the motivating milling application, whereas robust designs which treat the uncompensated hysteresis and nonlinearities as unmodeled disturbances cannot achieve design specifications
DA - 2007/1//
PY - 2007/1//
DO - 10.1109/TCST.2006.883235
VL - 15
IS - 1
SP - 22-39
SN - 1558-0865
KW - constitutive nonlinearities
KW - distributed parameter systems
KW - hysteresis
KW - inverse filter
KW - magnetostrictive devices
KW - robust control design
ER -
TY - JOUR
TI - L-infinity algebra structures from Lie algebra deformations
AU - Gao, Jining
T2 - JOURNAL OF PURE AND APPLIED ALGEBRA
AB - In this paper, we will show how to kill the obstructions to Lie algebra deformations via a method which essentially embeds a Lie algebra into a strong homotopy Lie algebra or L∞ algebra such that the sh-Lie algebra is the same homotopy type as the original Lie algebra.
DA - 2007/3//
PY - 2007/3//
DO - 10.1016/j.jpaa.2006.03.016
VL - 208
IS - 3
SP - 779-784
SN - 0022-4049
ER -
TY - JOUR
TI - Estimation and prediction with HIV-treatment interruption data
AU - Adams, B. M.
AU - Banks, H. T.
AU - Davidian, M.
AU - Rosenberg, E. S.
T2 - BULLETIN OF MATHEMATICAL BIOLOGY
DA - 2007/2//
PY - 2007/2//
DO - 10.1007/s11538-006-9140-6
VL - 69
IS - 2
SP - 563-584
SN - 0092-8240
KW - HIV models
KW - treatment interruptions
KW - censored data
KW - parameter estimation
KW - prediction
ER -
TY - JOUR
TI - Shifts of finite type and Fibonacci Harps
AU - Crannell, Annalisa
AU - May, Stephen
AU - Hilbert, Lindsay
T2 - APPLIED MATHEMATICS LETTERS
AB - We make an explicit connection between the Fibonacci Harp (or Fibonacci String) and two well-known dynamical systems: subshifts of finite type and the baker’s map on the unit interval. In particular, we show that the boundary of the Fibonacci Harp is an embedding of a commonly studied shift of finite type in the unit interval. Moreover, every shift of finite type embeds as the boundary of a lattice harp.
DA - 2007/2//
PY - 2007/2//
DO - 10.1016/j.aml.2006.03.007
VL - 20
IS - 2
SP - 138-141
SN - 0893-9659
KW - fractal strings
KW - lattice strings
KW - subshifts
KW - Cantor sets
KW - baker's map
KW - Fibonacci
ER -
TY - JOUR
TI - Model theory of partial differential fields: From commuting to noncommuting derivations
AU - Singer, Michael F.
T2 - PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
AB - McGrail (2000) has shown the existence of a model completion for the universal theory of fields on which a finite number of commuting derivations act and, independently, Yaffe (2001) has shown the existence of a model completion for the univeral theory of fields on which a fixed Lie algebra acts as derivations. We show how to derive the second result from the first.
DA - 2007///
PY - 2007///
DO - 10.1090/S0002-9939-07-08653-4
VL - 135
IS - 6
SP - 1929-1934
SN - 1088-6826
ER -
TY - JOUR
TI - Heat transfer between parallel plates: An approach based on the linearized Boltzmann equation for a binary mixture of rigid-sphere gases
AU - Garcia, R. D. M.
AU - Siewert, C. E.
T2 - PHYSICS OF FLUIDS
AB - An analytical version of the discrete-ordinates method is used to develop a concise and particularly accurate solution of the heat-transfer problem for a binary gas mixture confined between two parallel plates. The formulation of the problem allows general (specular-diffuse) Maxwell boundary conditions for each of the two types of particles and is based on a form of the linearized Boltzmann equation that incorporates recently established analytical expressions for the relevant rigid-sphere kernels. Numerical results are reported for the density, the temperature, and the heat-flow profiles relative to each species in Ne-Ar and He-Xe mixtures.
DA - 2007/2//
PY - 2007/2//
DO - 10.1063/1.2511039
VL - 19
IS - 2
SP -
SN - 2329-7778
ER -
TY - JOUR
TI - Direct transcription solution of higher-index optimal control problems and the virtual index
AU - Engelsone, A.
AU - Campbell, S. L.
AU - Betts, J. T.
T2 - APPLIED NUMERICAL MATHEMATICS
AB - Direct transcription methods are a popular approach for solving optimal control problems. They are sometimes able to solve problems that the classical numerical theory would suggest that they cannot solve. The dynamics of an equality constrained optimal control problem form a differential algebraic equation (DAE), and most numerical methods for solving these optimal control problems require solving this DAE for the states and algebraic variables, which would imply that the problem is unsolvable if this DAE is high index. We will demonstrate that direct transcription methods, which use a different approach, can successfully solve some higher index equality constrained optimal control problems and that the role of the index needs reinterpretation when using direct transcription methods. These results and observations have implications for software design and guidance provided to users.
DA - 2007/3//
PY - 2007/3//
DO - 10.1016/j.apnum.2006.03.012
VL - 57
IS - 3
SP - 281-296
SN - 1873-5460
KW - numerical methods
KW - optimal control
KW - direct transcription
ER -
TY - JOUR
TI - Condition estimates for pseudo-arclength continuation
AU - Dickson, K. I.
AU - Kelley, C. T.
AU - Ipsen, I. C. F.
AU - Kevrekidis, I. G.
T2 - SIAM JOURNAL ON NUMERICAL ANALYSIS
AB - We bound the condition number of the Jacobian in pseudo‐arclength continuation problems, and we quantify the effect of this condition number on the linear system solution in a Newton‐GMRES solve. Pseudo‐arclength continuation solves parameter dependent nonlinear equations $G(u,\lambda) = 0$ by introducing a new parameter s, which approximates arclength, and viewing the vector $x = (u,\lambda)$ as a function of s. In this way simple fold singularities can be computed directly by solving a larger system $F(x,s) = 0$ by simple continuation in the new parameter s. It is known that the Jacobian $F_x$ of F with respect to $x=(u,\lambda)$ is nonsingular if the path contains only regular points and simple fold singularities. We introduce a new characterization of simple folds in terms of the singular value decomposition, and we use it to derive a new bound for the norm of $F_x^{-1}$. We also show that the convergence rate of GMRES in a Newton step for $F(x,s)=0$ is essentially the same as that of the original problem $G(u,\lambda)=0$. In particular, we prove that the bounds on the degrees of the minimal polynomials of the Jacobians $F_x$ and $G_u$ differ by at most 2. We illustrate the effectiveness of our bounds with an example from radiative transfer theory.
DA - 2007///
PY - 2007///
DO - 10.1137/060654384
VL - 45
IS - 1
SP - 263-276
SN - 1095-7170
KW - pseudo-arclength continuation
KW - singularity
KW - GMRES
KW - singular vectors
KW - eigenvalues
KW - rank-one update
KW - turning point
KW - simple fold
KW - fold point
KW - limit point
ER -
TY - JOUR
TI - Comparison between stochastic and deterministic selection-mutation models
AU - Ackleh, Azmy S.
AU - Hu, Shuhua
T2 - MATHEMATICAL BIOSCIENCES AND ENGINEERING
AB - We present a deterministic selection-mutation model with a discrete trait variable. We show that for an irreducible selection-mutation matrix in the birth term the deterministic model has a unique interior equilibrium which is globally stable. Thus all subpopulations coexist. In the pure selection case, the outcome is known to be that of competitive exclusion, where the subpopulation with the largest growth-to-mortality ratio will survive and the remaining subpopulations will go extinct. We show that if the selection mutation matrix is reducible, then competitive exclusion or coexistence are possible outcomes. We then develop a stochastic population model based on the deterministic one. We show numerically that the mean behavior of the stochastic model in general agrees with the deterministic one. However, un like the deterministic one, if the differences in the growth-to-mortality ratios are small in the pure selection case, it cannot be determined a priori which subpopulation will have the highest probability of surviving and winning the competition.
DA - 2007/4//
PY - 2007/4//
DO - 10.3934/mbe.2007.4.133
VL - 4
IS - 2
SP - 133-157
SN - 1551-0018
KW - selection-mutation models
KW - competitive exclusion
KW - coexistence
KW - stochastic differential equations
ER -
TY - JOUR
TI - A delayed nonlinear PBPK model for genistein dosimetry in rats
AU - Zagera, Michael G.
AU - Schlosser, Paul M.
AU - Tran, Hien T.
T2 - BULLETIN OF MATHEMATICAL BIOLOGY
AB - Genistein is an endocrine-active compound (EAC) found in soy products. It has been linked to beneficial effects such as mammary tumor growth suppression and adverse endocrine-related effects such as reduced birth weight in rats and humans. In its conjugated form, genistein is excreted in the bile, which is a significant factor in its pharmacokinetics. Experimental data suggest that genistein induces a concentration-dependent suppression of biliary excretion. In this article, we describe a physiologically based pharmacokinetic (PBPK) model that focuses on biliary excretion with the goal of accurately simulating the observed suppression. The mathematical model is a system of nonlinear differential equations with state-dependent delay to describe biliary excretion. The model was analyzed to examine local existence and uniqueness of a solution to the equations. Furthermore, unknown parameters were estimated, and the mathematical model was compared against published experimental data.
DA - 2007/1//
PY - 2007/1//
DO - 10.1007/s11538-006-9068-x
VL - 69
IS - 1
SP - 93-117
SN - 1522-9602
KW - genistein
KW - biliary excretion
KW - pharmacokinetics
KW - delay-differential equations
ER -
TY - JOUR
TI - A Finite Difference Method and Analysis for 2D Nonlinear Poisson–Boltzmann Equations
AU - Li, Zhilin
AU - Pao, C. V.
AU - Qiao, Zhonghua
T2 - Journal of Scientific Computing
DA - 2007/1/31/
PY - 2007/1/31/
DO - 10.1007/s10915-005-9019-y
VL - 30
IS - 1
SP - 61–81
SN - 0885-7474 1573-7691
UR - http://dx.doi.org/10.1007/s10915-005-9019-y
KW - nonlinear Poisson-Boltzmann equation
KW - exterior problem
KW - immersed interface method
KW - monotone iterative method
ER -