Mathematics : Publications since January 2008
List all publications in the database. :chronological combined listing:
%% Aazami, Amir
@article{fds163846,
Author = {A. Aazami and A. O. Petters},
Title = {A Universal Magnification Theorem III. Caustics Beyond
Codimension Five},
Journal = {to appear in J. Math. Phys.},
Year = {2009},
Key = {fds163846}
}
@article{fds151900,
Author = {A. Aazami and A. O. Petters},
Title = {A Universal Magnification Theorem for Higher-Order Caustic
Singularities},
Journal = {J. Math. Phys. 50, 032501},
Year = {2009},
Key = {fds151900}
}
@article{fds157959,
Author = {A. Aazami and A. O. Petters},
Title = {A Universal Magnification Theorem II. Generic Caustics up to
Codimension Five},
Journal = {J. Math. Phys. 50, 082501},
Year = {2009},
Key = {fds157959}
}
%% Aguado, Alex
@article{fds146627,
Author = {Alejandro Aguado and Saad I. El-Zanati},
Title = {On σ-labeling the union of three cycles.},
Journal = {Journal of Combinatorial Mathematics and Combinatorial
Computing},
Volume = {64},
Pages = {33-48},
Year = {2008},
MRNUMBER = {MR2389065},
Key = {fds146627}
}
%% Allard, William K
@article{fds152504,
Author = {W.K. Allard},
Title = {Total variation regularization for image denoising: II.
Examples.},
Journal = {SIAM Journal on Imaging Sciences},
Year = {2008},
Key = {fds152504}
}
%% Aspinwall, Paul S
@article{fds152804,
Author = {P.S. Aspinwall},
Title = {D-Branes on Toric Calabi-Yau Varieties},
Year = {2008},
Key = {fds152804}
}
%% Beale, J. Thomas
@article{fds159910,
Author = {J. T. Beale},
Title = {Smoothing properties of implicit finite difference methods
for a diffusion equation in maximum norm},
Journal = {SIAM J. Numer. Anal.},
Volume = {47},
Pages = {2476-95},
Year = {2009},
Month = {April},
url = {http://www.math.duke.edu/faculty/beale/papers/parab.pdf},
Key = {fds159910}
}
@article{fds157267,
Author = {J. T. Beale and A. T. Layton},
Title = {A velocity decomposition approach for moving interfaces in
viscous fluids},
Journal = {J. Comput. Phys. 228, 3358-67},
Year = {2009},
url = {http://www.math.duke.edu/faculty/beale/papers/velcomp.pdf},
Key = {fds157267}
}
@article{fds148392,
Author = {J. T. Beale and D. Chopp and R LeVeque and Z.
Li},
Title = {Correction to the article A comparison of the extended
finite element method with the immersed interface method for
elliptic equations with discontinuous coefficients and
singular sources by Vaughan et al.},
Journal = {Commun. Appl. Math. Comput. Sci.},
Volume = {3},
Pages = {95-100},
Year = {2008},
Month = {August},
url = {http://www.math.duke.edu/faculty/beale/papers/camcoscorr.pdf},
Key = {fds148392}
}
@article{fds144448,
Author = {J. T. Beale},
Title = {A proof that a discrete delta function is second-order
accurate},
Journal = {J. Comput. Phys.},
Volume = {227},
Pages = {2195-97},
Year = {2008},
url = {http://www.math.duke.edu/faculty/beale/papers/ddel.pdf},
Key = {fds144448}
}
@article{fds144449,
Author = {J. T. Beale and J. Strain},
Title = {Locally corrected semi-Lagrangian methods for Stokes flow
with moving elastic interfaces},
Journal = {J. Comput. Phys.},
Volume = {227},
Pages = {3896-3920},
Year = {2008},
url = {http://www.math.duke.edu/faculty/beale/papers/bealestrain.pdf},
Key = {fds144449}
}
%% Bertozzi, Andrea L
@booklet{Greer04a,
Author = {J. B. Greer and A. L. Bertozzi},
Title = {H-1 solutions of a class of fourth order nonlinear equations
for image processing},
Journal = {Discrete And Continuous Dynamical Systems},
Volume = {10},
Number = {1-2},
Pages = {349 -- 366},
Year = {2004},
Key = {Greer04a}
}
%% Blake, Lewis D
@book{fds152837,
Author = {Lewis Blake and Michael Reed},
Title = {Laboratory Calculus, 2008-2009},
Year = {2008},
Month = {August},
Key = {fds152837}
}
%% Bookman, Jack
@article{fds152945,
Author = {Jack Bookman and Susan Ganter and Rick Morgan},
Title = {Developing Assessment Methodologies for Quantitative
Literacy - A Formative Study},
Journal = {American Mathematical Monthly},
Year = {2008},
Month = {December},
Key = {fds152945}
}
%% Bray, Clark B
@book{fds163009,
Author = {C.B. Bray},
Title = {Multivariable Calculus},
Year = {2009},
Abstract = {This is a textbook on multivariable calculus.},
Key = {fds163009}
}
%% Bray, Hubert L.
@article{fds152866,
Author = {H.L. Bray and Pengzi Miao},
Title = {On the Capacity of Surfaces in Manifolds with Nonnegative
Scalar Curvature},
Journal = {Inventiones Mathematicae},
Volume = {172},
Number = {3},
Year = {2008},
Month = {June},
url = {http://xxx.lanl.gov/abs/0707.3337},
Key = {fds152866}
}
@article{fds152867,
Author = {H.L. Bray and D.A. Lee},
Title = {On the Riemannian Penrose Inequality in Dimension Less Than
Eight},
Journal = {Duke Math Journal},
Year = {2008},
Month = {May},
Key = {fds152867}
}
%% Bryant, Robert L
@article{fds146224,
Author = {R.L. Bryant and G. Manno and V. Matveev},
Title = {A solution of a problem of Sophus Lie: Normal forms of
2-dimensional metrics admitting two projective vector
fields},
Journal = {Mathematische Annalen},
Volume = {340},
Number = {2},
Pages = {437--463},
Year = {2008},
Month = {Spring},
url = {http://www.arxiv.org/abs/0705.3592},
Abstract = {We give a complete list of normal forms for the
2-dimensional metrics that admit a transitive Lie
pseudogroup of geodesic-preserving transformations and we
show that these normal forms are mutually non-isometric.
This solves a problem posed by Sophus Lie.},
Key = {fds146224}
}
@article{fds141021,
Author = {R.L. Bryant and M. Dunajski and M. Eastwood},
Title = {Metrisability of two-dimensional projective
structures},
Year = {2008},
Abstract = {We carry out the programme of R. Liouville \cite{Liouville}
to construct an explicit local obstruction to the existence
of a Levi--Civita connection within a given projective
structure $[\Gamma]$ on a surface. The obstruction is of
order 5 in the components of a connection in a projective
class. It can be expressed as a point invariant for a second
order ODE whose integral curves are the geodesics of
$[\Gamma]$ or as a weighted scalar projective invariant of
the projective class. If the obstruction vanishes we find
the sufficient conditions for the existence of a metric in
the real analytic case. In the generic case they are
expressed by the vanishing of two invariants of order 6 in
the connection. In degenerate cases the sufficient
obstruction is of order at most 8.},
Key = {fds141021}
}
%% Charbonneau, Benoit
@article{fds164885,
Author = {J.A. van Meel and B. Charbonneau and A. Fortini and P.
Charbonneau},
Title = {Hard-sphere crystallization gets rarer with increasing
dimension},
Journal = {Phys. Rev. E},
Year = {2009},
Month = {November},
url = {http://arxiv.org/abs/0907.3100},
Abstract = {We recently found that crystallization of monodisperse hard
spheres from the bulk fluid faces a much higher free energy
barrier in four than in three dimensions at equivalent
supersaturation, due to the increased geometrical
frustration between the simplex-based fluid order and the
crystal [J.A. van Meel, D. Frenkel, and P. Charbonneau,
Phys. Rev. E 79, 030201(R) (2009)]. Here, we analyze the
microscopic contributions to the fluid-crystal interfacial
free energy to understand how the barrier to crystallization
changes with dimension. We find the barrier to grow with
dimension and we identify the role of polydispersity in
preventing crystal formation. The increased fluid stability
allows us to study the jamming behavior in four, five, and
six dimensions and compare our observations with two recent
theories [C. Song, P. Wang, and H. A. Makse, Nature 453, 629
(2008); G. Parisi and F. Zamponi, Rev. Mod. Phys, in press
(2009)].},
Key = {fds164885}
}
@article{fds158601,
Author = {Juli Atherton and Benoit Charbonneau and Xiaojie Zhou and David
Wolfson, Lawrence Joseph and Alain C. Vandal},
Title = {Bayesian optimal design for changepoint problems},
Journal = {Canadian Journal of Statistics},
Year = {2009},
Month = {May},
url = {http://dx.doi.org/10.1002/cjs.10037},
Abstract = {We propose, for the first time, optimal design for
changepoint problems. Suppose that a sequence of
observations is taken in some subinterval of the real axis.
If the distribution of the sequence changes at some unknown
location then we refer to this location as a changepoint.
Changepoint inference usually concerns location testing for
a change and/or estimating the location of the change and
the unknown parameters of the distributions before and after
any change. In this paper, we investigate Bayesian optimal
designs for changepoint problems. We find robust optimal
designs which allow for arbitrary distributions before and
after the change, arbitrary prior densities on the
parameters before and after the change, and any log-concave
prior density on the changepoint. We define a new design
measure for Bayesian optimal design problems as a means of
finding the optimal design itself. Our results apply to any
design criterion function concave in the design measure. We
show that our method extends directly to a setting in which
there are several paths all with the same
changepoint.},
Key = {fds158601}
}
@article{fds156863,
Author = {Benoit Charbonneau and Yuriy Svyrydov and P.F.
Tupper},
Title = {Convergence in the Prokhorov Metric of Weak Methods for
Stochastic Differential Equations},
Journal = {IMA Journal of Numerical Analysis},
Year = {2009},
Month = {February},
url = {http://imajna.oxfordjournals.org/cgi/content/abstract/drn067?ijkey=oQbKpjUZWUEfl4K&keytype=ref},
Keywords = {stochastic differential equations numerical methods
convergence in distribution weak convergence Prokhorov
metric Strassen–Dudley theorem Wasserstein
distance},
Key = {fds156863}
}
@article{benoitjacques3,
Author = {Benoit Charbonneau and Jacques Hurtubise},
Title = {Singular Hermitian-Einstein monopoles on the product of a
circle and a Riemann surface},
Year = {2009},
Month = {January},
url = {http://arxiv.org/abs/0812.0221},
Key = {benoitjacques3}
}
@article{benoitjacques1,
Author = {Benoit Charbonneau and Jacques Hurtubise},
Title = {Calorons, Nahm's equations on S^1 and bundles over
P^1xP^1},
Journal = {Communications in Mathematical Physics},
Volume = {280},
Number = {2},
Pages = {315--349},
Year = {2008},
ISSN = {0010-3616},
MRCLASS = {53C07 (14D21 58D27)},
MRNUMBER = {MR2395473},
url = {http://dx.doi.org/10.1007/s00220-008-0468-7},
Abstract = {The moduli space of solutions to Nahm's equations of rank
(k,k+j) on the circle, and hence, of SU(2) calorons of
charge (k,j), is shown to be equivalent to the moduli of
holomorphic rank 2 bundles on P^1xP^1 trivialized at
infinity with c_2=k and equipped with a flag of degree j
along P^1x{0}. An explicit matrix description of these
spaces is given by a monad construction.},
Key = {benoitjacques1}
}
@article{benoitjacques2,
Author = {Benoit Charbonneau and Jacques Hurtubise},
Title = {The Nahm transform for calorons},
Booktitle = {The many facets of geometry: a tribute to Nigel
Hitchin},
Publisher = {Oxford University Press},
Editor = {Jean-Pierre Bourguignon and Oscar Garcia-Prada and Simon
Salamon},
Year = {2008},
url = {http://arxiv.org/pdf/0705.2412},
Abstract = {In this paper, we complete the proof of an equivalence given
by Nye and Singer of the equivalence between calorons
(instantons on $S^1\times R^3$) and solutions to Nahm's
equations over the circle, both satisfying appropriate
boundary conditions. Many of the key ingredients are
provided by a third way of encoding the same data which
involves twistors and complex geometry. Dedicated to Nigel
Hitchin on the occasion of his sixtieth birthday},
Key = {benoitjacques2}
}
%% Chen, Guangliang
@article{fds160728,
Author = {G. Chen and G. Lerman},
Title = {Spectral Curvature Clustering (SCC)},
Journal = {International Journal of Computer Vision},
Volume = {81},
Pages = {317-330},
Year = {2009},
url = {http://www.springerlink.com/content/e120x08k21341784/fulltext.pdf},
Key = {fds160728}
}
@article{fds160729,
Author = {G. Chen and G. Lerman},
Title = {Foundations of a Multi-way Spectral Clustering Framework for
Hybrid Linear Modeling},
Journal = {Foundations of Computational Mathematics},
Year = {2009},
url = {http://www.springerlink.com/content/243860078k1183l3/fulltext.pdf},
Key = {fds160729}
}
@article{fds160731,
Author = {G. Chen and S. Atev and G. Lerman},
Title = {Kernel Spectral Curvature Clustering (KSCC)},
Journal = {2009 ICCV Workshop on Dynamical Vision},
Year = {2009},
Key = {fds160731}
}
@article{fds160732,
Author = {G. Chen and G. Lerman},
Title = {Motion Segmentation for Hopkins 155 Database via
SCC},
Journal = {2009 ICCV Workshop on Dynamical Vision},
Year = {2009},
Key = {fds160732}
}
%% Chuang, Jer-Chin (Luke)
@article{fds158904,
Author = {Jer-Chin Chuang},
Title = {Minimal Rational and Integral Solutions to the Box
Problem},
Journal = {The College Mathematics Journal},
Year = {2008},
Key = {fds158904}
}
@article{fds148129,
Author = {Jer-Chin Chuang},
Title = {Analytic subdivision invariants},
Year = {2008},
Key = {fds148129}
}
@article{fds152553,
Author = {Jer-Chin Chuang},
Title = {Subdivisions and transgressive chains},
Year = {2008},
Key = {fds152553}
}
%% Dai, Shu
@article{fds150138,
Author = {S. Dai and D. G. Schaeffer},
Title = {Spectrum of a linearized amplitude equation for alternans in
a cardiac fiber},
Journal = {SIAM J. Appl. Math.},
Year = {2008},
Abstract = {Under rapid periodic pacing, cardiac cells typically undergo
a period-doubling bifurcation in which action potentials of
short and long duration alternate with one another. If these
action potentials propagate in a fiber, the short-long
alternation may suffer reversals of phase at various points
along the fiber, a phenomenon called (spatially) discordant
alternans. Either stationary or moving patterns are
possible. Using a weak approximation, Echebarria and Karma
proposed an equation to describe the spatiotemporal dynamics
of small-amplitude alternans in a class of simple cardiac
models, and they showed that an instability in this equation
predicts the spontaneous formation of discordant alternans.
To study the bifurcation, they computed the spectrum of the
relevant linearized operator numerically, supplemented with
partial analytical results. In the present paper we
calculate this spectrum with purely analytical methods in
two cases where a small parameter may be exploited: (i)
small dispersion or (ii) a long fiber. From this analysis we
estimate the parameter ranges in which the phase reversals
of discordant alternans are stationary or
moving.},
Key = {fds150138}
}
@article{fds150136,
Author = {S. Dai and D. G. Schaeffer},
Title = {Bifurcations in a modulation equation for alternans in a
cardiac fiber},
Journal = {Math. Modelling and Num. Analysis},
Year = {2008},
Abstract = {While alternans in a single cardiac cell appears through a
simple period-doubling bifurcation, in extended tissue the
exact nature of the bifurcation is unclear. In particular,
the phase of alternans can exhibit wave-like spatial
dependence, either stationary or traveling, which is known
as discordant alternans. We study these phenomena in simple
cardiac models through a modulation equation proposed by
Echebarria-Karma. As shown in our previous paper, the zero
solution of their equation may lose stability, as the pacing
rate is increased, through either a Hopf or steady-state
bifurcation. Which bifurcation occurs first depends on
parameters in the equation, and for one critical case both
modes bifurcate together at a degenerate (codimension 2)
bifurcation. For parameters close to the degenerate case, we
investigate the competition between modes, both numerically
and analytically. We find that at sufficiently rapid pacing
(but assuming a 1:1 response is maintained), steady patterns
always emerge as the only stable solution. However, in the
parameter range where Hopf bifurcation occurs first, the
evolution from periodic solution (just after the
bifurcation) to the eventual standing wave solution occurs
through an interesting series of secondary
bifurcations.},
Key = {fds150136}
}
%% Diaz Espinosa, Oliver R
@book{fds163557,
Author = {O.R. Diaz Espinosa and de la Llave},
Title = {Renormalization of arbitrary weak noises for one-dimensional
critical dynamical systems: summary of results and numerical
explorations},
Volume = {53},
Series = {Fields Inst. Commun.},
Pages = {331--359},
Booktitle = {Holomorphic dynamics and renormalization.},
Publisher = {American Mathematical Society},
Year = {2008},
Key = {fds163557}
}
@article{fds163555,
Author = {O.R. Diaz Espinosa and A. de Bouard and W. Craig and P. Guyenne and C.
Sulem},
Title = {Long wave expansions for water waves over random
topography},
Journal = {Nonlinearity},
Volume = {21},
Number = {9},
Pages = {2143--2178},
Year = {2008},
Key = {fds163555}
}
%% Gratton, Michael B.
@article{coarse-grav,
Author = {M.B. Gratton and T.P. Witelski},
Title = {Coarsening of dewetting thin films subject to
gravity},
Journal = {Phys. Rev. E.},
Volume = {77},
Pages = {016301},
Year = {2008},
Month = {January},
Key = {coarse-grav}
}
%% Hain, Richard M
@article{fds158815,
Author = {Richard Hain and Makoto Matsumoto},
Title = {Relative pro-l completions of mapping class
groups},
Journal = {J. Algebra},
Volume = {321},
Pages = {3335-3374},
Year = {2009},
Key = {fds158815}
}
@article{fds153572,
Author = {Richard Hain},
Title = {Relative weight filtrations on completions of mapping
class groups},
Volume = {52},
Series = {Advanced Studies in Pure Mathematics},
Pages = {309--368},
Booktitle = {Groups of Diffeomorphisms},
Publisher = {Mathematical Society of Japan},
Year = {2008},
Month = {May},
Key = {fds153572}
}
@article{fds165315,
Author = {Richard Hain},
Title = {Lectures on Moduli Spaces of Elliptic Curves},
Series = {Advanced
Lectures in Mathematics},
Publisher = {International Press},
Address = {Boston},
Year = {2008},
Key = {fds165315}
}
%% Harer, John
@article{fds152558,
Author = {D. Cohen-Steiner and H. Edelsbrunner and J. Harer and D.
Morozov.},
Title = {Persistent homology for kernels, images, and
cokernels.},
Journal = {Proc. Sympos. Discret Alg.},
Year = {2009},
url = {http://www.cs.duke.edu/~edels/Topology/},
Abstract = {The persistence algorithms are extended to the study of
kernels and images of homology maps. Applications include
the study of stratifications of point clouds.},
Key = {fds152558}
}
@article{fds152560,
Author = {P. Bendich and D. Cohen-Steiner and H. Edelsbrunner and J. Harer and D. Morozov.},
Title = {Inferring local homology from sampled stratified
spaces.},
Journal = {Proc. 48th Ann. Sympos. Found. Comput. Sci.},
Pages = {536-546},
Year = {2008},
url = {http://www.cs.duke.edu/~edels/Topology/},
Abstract = {http://www.cs.duke.edu/~edels/Topology/},
Key = {fds152560}
}
@article{fds152559,
Author = {D. Cohen-Steiner and H. Edelsbrunner and J. Harer and Y.
Mileyko.},
Title = {Lipschitz functions have L_p-stable persistence.},
Journal = {Foundations of Computional Mathematics},
Year = {2008},
url = {http://www.cs.duke.edu/~edels/Topology/},
Abstract = {This paper shows that persistence diagrams of Lipschitz
functions are stable in a stronger sense than proved in the
paper by Cohen-Steiner, Edelsbrunner and Harer. The stronger
version is more useful in the study of gene expression
data.},
Key = {fds152559}
}
@article{fds152561,
Author = {D. Cohen-Steiner and H. Edelsbrunner and J.
Harer.},
Title = {Extending persistence using Poincare and Lefschetz
duality.},
Journal = {Found. Comput. Math.},
Year = {2008},
url = {http://www.cs.duke.edu/~edels/Topology/},
Abstract = {We extend the methods of persistence and persistence
diagrams to essential homology classes using Poincare'
duality. We show that this extended definition satisfies
duality and symmetry compatible with usual persistence, find
a fast algorithm to compute it and discuss a variety of
applications including the extension of the elevation
function which is used to establish initial placements in
protein docking prediction.},
Key = {fds152561}
}
@article{fds152566,
Author = {P. Bendich and J. Harer and H. King},
Title = {Persistent Intersection Homology},
Year = {2008},
Key = {fds152566}
}
@article{fds152569,
Author = {Mehak Aziz and Siobhan M. Brady and David Orlando and Appu Kuruvilla and Scott Spillias and José R. Dinneny and Terri A. Long and John Harer and Uwe Ohler and Philip N. Benfey},
Title = {Gene Expression Clustering Analysis: How to Choose the Best
Parameters and Clustering Algorithm},
Year = {2008},
Abstract = {This paper is the result of a summer research project
supported by the Howard Hughes summer program in systems
biology.},
Key = {fds152569}
}
@article{fds152571,
Author = {A. HB and J. Harer},
Title = {Persistent Steifel Whitney Classes},
Year = {2008},
Abstract = {Cohomology classes are used in Algebraic Topology as a tool
that computes the complexity of n-plane bundles over a
manifold. This paper introduces a method of including a
general cohomology class into study and practice of
Persistence for homology. Using a combinatorial formula, we
illustrate our new algorithm for Stiefel-Whitney
classes.},
Key = {fds152571}
}
@book{fds51656,
Author = {H. Edelsbrunner and J. Harer},
Title = {Computational Topology, An Introduction},
Year = {2008},
Abstract = {This book is an introduction to computational topology for
students in Computer Science and Mathematics. Currently 183
pages, it is in its second draft - submission for
publication is expected in Summer 2007.},
Key = {fds51656}
}
@article{fds51476,
Author = {P. Bendich and J. Harer},
Title = {Persistence for Intersection Homology - Theoretical
Foundations},
Year = {2008},
Abstract = {We show that the theory of persistence extends naturally to
intersection homology and give a fast algorithm to compute
it. We also describe a methodology based on local-systems
for characterizing when a point cloud has the structure of a
stratified space.},
Key = {fds51476}
}
@article{fds51657,
Author = {H. Edelsbrunner and J. Harer and A. Patel},
Title = {Reeb Surfaces},
Year = {2008},
Abstract = {This paper studies a generalization of the Reeb graph called
the Reeb surface. It characterizes the surface and gives an
efficient algorithm for its computation.},
Key = {fds51657}
}
%% Heymann, Matthias
@article{fds153301,
Author = {M. Heymann and E. Vanden-Eijnden},
Title = {The Geometric Minimum Action Method - A Least Action
Principle on the Space of Curves},
Journal = {CPAM},
Volume = {61},
Number = {8},
Pages = {1052-1117},
Publisher = {Wiley InterScience},
Year = {2008},
Month = {August},
Key = {fds153301}
}
@article{fds153305,
Author = {E. Vanden-Eijnden and M. Heymann},
Title = {The Geometric Minimum Action Method for Computing Minimum
Energy Paths},
Journal = {Journal of Chemical Physics},
Volume = {128},
Number = {061103},
Year = {2008},
Month = {February},
Key = {fds153305}
}
%% Huber, Mark
@article{fds150242,
Author = {M. L. Huber and R. L. Wolpert},
Title = {Perfect Simulation of Matern Type III Repulsive Point
Processes},
Year = {2008},
Month = {September},
Abstract = {In a repulsive point process, points act as if they are
repelling one another, leading to configurations that are
overdispersed when compared to a standard Poisson point
process. These models are useful wherever competition for
resources exists, such as in the locations of towns and
trees. Bertil Matern introduced three approaches to modeling
repulsive point processes but described only two in detail,
now called the Matern processes of Types I and II; the third
he regarded as overly complex. In fact it is only this third
process, which we call Matern Type III, which has a
tractable likelihood function. In this paper a perfect
simulation method is developed that allows for arbitrarily
accurate approximation of the likelihood for data modeled by
the Matern Type III, thereby enabling its use for inference.
This method is shown to be fast in practice, generating
samples in time that grows nearly linearly in the intensity
parameter of the model, while the running times for more
naive methods grow exponentially.},
Key = {fds150242}
}
@article{fds147643,
Author = {M. Huber},
Title = {Perfect simulation with exponential tails},
Journal = {Random Structures and Algorithms},
Volume = {33},
Number = {1},
Pages = {29--43},
Publisher = {Wiley InterScience},
Year = {2008},
Month = {August},
Abstract = {Monte Carlo algorithms typically need to generate random
variates from a probability distribution described by an
unnormalized density or probability mass function. Perfect
simulation algorithms generate random variates exactly from
these distributions, but have a running time T that is
itself an unbounded random variable. This paper shows that
commonly used protocols for creating perfect simulation
algorithms, such as Coupling From the Past can be used in
such a fashion that the running time is unlikely to be very
much larger than the expected running time.},
Key = {fds147643}
}
@article{fds69197,
Author = {M. Huber},
Title = {Spatial Birth-Death-Swap Chains},
Journal = {Bernoulli},
Year = {2008},
Month = {May},
Abstract = {Markov chains have long been used for generating random
variates from spatial point processes. Broadly speaking,
these chains fall into two categories: Metropolis-Hastings
type chains running in discrete time and spatial birth death
chains running in continuous time. These birth death chains
only allow for removal of a point or addition of a point. In
this work it is shown that the addition of transitions where
a point is moved from one location to the other can aid in
shortening the mixing time of the chain. Here the mixing
time of the chain is analyzed through coupling, and use of
the swap moves allows for analysis of a broader class of
chains. Furthermore, these swap moves can be employed in
perfect sampling algorithms via the dominated Coupling from
the Past procedure of Kendall and Møller. This method can
be applied to any pairwise interaction model with repulsion.
In particular, an application to the Strauss process is
developed in detail, and the swap chains are shown to be
much faster than standard birth death chains.},
Key = {fds69197}
}
@article{fds148510,
Author = {M. Huber},
Title = {Spatial point processes},
Booktitle = {Handbook of MCMC},
Editor = {Brooks, Gelman and Jones, Meng},
Year = {2008},
Month = {April},
Key = {fds148510}
}
@article{fds146748,
Author = {M. Huber and J. Law},
Title = {Fast approximation of the permanent for very dense
problems},
Pages = {681--689},
Booktitle = {Proceedings of the nineteenth annual ACM-SIAM Symposium on
Discrete Algorithms},
Publisher = {SIAM},
Address = {Philadelphia, PA, USA},
Year = {2008},
Abstract = {Approximation of the permanent of a matrix with nonnegative
entries is a well studied problem. The most successful
approach to date for general matrices uses Markov chains to
approximately sample from a distribution on weighted
permuations, and Jerrum, Sinclair, and Vigoda developed such
a method they proved runs in polynomial time in the input.
The current bound on the running time of their method is
O(n^7(ln n)^4). Here we present a very different approach
using sequential acceptance/rejection, and show that for a
class of very dense problems, this method has an O(n^4 ln n)
running time. In the process we prove a more general form of
Bregman's theorem that applies not just to 0-1 matrices, but
ot any matrix with entries in [0,1].},
Key = {fds146748}
}
@article{fds10385,
Author = {James A. Fill and Mark L. Huber},
Title = {Linear expected time perfect generation of proper colorings
of low degree graphs},
Year = {2008},
Abstract = {A proper coloring assigns colors to nodes of a graph so that
no two endpoints of an edge receive the same color. Here we
present the first algorithm for sampling uniformly from the
set of proper colorings of a graph (in expected linear time)
when the number of colors is linear in the maximum degree of
the graph.},
Key = {fds10385}
}
%% Jauregui, Jeff
@article{fds163797,
Author = {Hubert L. Bray and Jeffrey L. Jauregui},
Title = {A geometric theory of zero area singularities in general
relativity},
Year = {2009},
Month = {September},
url = {http://arxiv.org/abs/0909.0522},
Key = {fds163797}
}
%% Layton, Anita T
@article{fds163974,
Author = {Jing Chen and Aurelie Edwards and Anita T.
Layton},
Title = {Effects of pH and medullary blood flow on oxygen transport
and sodium reabsorption in the rat outer
medulla},
Journal = {Am J Physiol Renal Physiol, submitted},
Year = {2009},
Key = {fds163974}
}
@article{fds151520,
Author = {Anita T. Layton},
Title = {Using integral equations and the immersed interface method
to solve immersed boundary problems with stiff
forces},
Journal = {Comput. Fluids.},
Volume = {38},
Pages = {266-272},
Year = {2009},
Key = {fds151520}
}
@article{fds157874,
Author = {J. Thomas Beale and Anita T. Layton},
Title = {A velocity decomposition approach for moving interfaces in
viscous fluids},
Journal = {J. Comput. Phys.},
Volume = {228},
Pages = {3358-3367},
Year = {2009},
Key = {fds157874}
}
@article{fds157006,
Author = {Anita T. Layton and Leon C. Moore and Harold E.
Layton},
Title = {Multistable dynamics mediated by tubuloglomerular feedback
in a model of coupled nephrons},
Journal = {Bull Math Biol},
Volume = {71},
Number = {3},
Pages = {515-555},
Year = {2009},
Key = {fds157006}
}
@article{fds157875,
Author = {Anita T. Layton},
Title = {On the efficiency of spectral deferred correction methods
for time-dependent partial differential equations},
Journal = {Appl. Numer. Math.},
Volume = {59},
Pages = {1629-1643},
Year = {2009},
Key = {fds157875}
}
@article{fds159929,
Author = {Jing Chen and Anita T. Layton and Aurelie Edwards},
Title = {A mathematical model of oxygen transport in the rat outer
medulla: I. Model formulation and baseline
results},
Journal = {Am J Physiol Renal Physiol},
Volume = {297},
Pages = {F517-F536},
Year = {2009},
Key = {fds159929}
}
@article{fds159930,
Author = {Jing Chen and Aurelie Edwards and Anita T.
Layton},
Title = {A mathematical model of oxygen transport in the rat outer
medulla: II. Impacts of outer medullary architecture},
Journal = {Am J Physiol Renal Physiol},
Volume = {297},
Pages = {F537-F548},
Year = {2009},
Key = {fds159930}
}
@article{fds164723,
Author = {Milargros Loreto and Anita T. Layton},
Title = {An optimization study of a mathematical model of the urine
concentrating mechanism of the rat kidney},
Journal = {Math. Biosci., in press},
Year = {2009},
Key = {fds164723}
}
@article{fds164724,
Author = {Anita T. Layton and Yusuke Toyama and Guo-Qiang Yang and Glenn S.
Edwards and Daniel P. Kiehart and Stephanos
Venakides},
Title = {Drosophila morphogenesis: tissue force laws and the modeling
of dorsal closure},
Journal = {HFSP, in press},
Year = {2009},
Key = {fds164724}
}
@article{fds158201,
Author = {Anita T. Layton and Aurelie Edwards},
Title = {Tubuloglomerular feedback signal transduction in a short
loop of Henle},
Journal = {Bull. Math. Biol., in press},
Year = {2009},
Key = {fds158201}
}
@article{fds159894,
Author = {Mariano Marcano and Anita T. Layton and Harold E.
Layton},
Title = {Maximum urine concentrating capability for transport
parameters and urine flow within prescribed
ranges},
Journal = {Bull. Math. Biol., in press},
Year = {2009},
Key = {fds159894}
}
@article{fds158380,
Author = {Anita T. Layton and Thomas L. Pannabecker and William H. Dantzler and Harold E. Layton},
Title = {Functional implications of the three-dimensional
architecture of the rat renal inner medulla},
Journal = {Am. J. Physiol. Renal Physiol., submitted},
Year = {2009},
Key = {fds158380}
}
@article{fds159374,
Author = {Anita T. Layton and Leon C. Moore and Harold E.
Layton},
Title = {Tubuloglomerular Feedback signal transduction in a compliant
thick ascending limb},
Journal = {Am. J. Physiol. Renal Physiol.},
Year = {2009},
Key = {fds159374}
}
@article{fds159079,
Author = {Jin Wang and Anita T. Layton},
Title = {New numerical methods for Burgers' equation based on
semi-Lagrangian and modified equation approaches},
Journal = {Appl. Numer. Math., submitted},
Year = {2009},
Key = {fds159079}
}
@article{fds164039,
Author = {Mark A. Hallen and Anita T. Layton},
Title = {Expanding the scope of quantitative FRAP
analysis},
Journal = {J. Theor. Biol., in press},
Year = {2009},
Key = {fds164039}
}
@article{fds159895,
Author = {Anita T. Layton and Harold E. Layton and William H. Dantzler and Thomas L. Pannabecker},
Title = {The mammalian urine concentrating mechanism: hypotheses and
uncertainties},
Journal = {Physiol.},
Volume = {24},
Pages = {250-256},
Year = {2009},
Key = {fds159895}
}
@article{fds158381,
Author = {Anita T. Layton and Thomas L. Pannabecker and William H. Dantzler and Harold E. Layton},
Title = {Hyperfiltration and inner-stripe hypertrophy may explain
findings by Gamble and co-workers},
Journal = {Am. J. Physiol. Renal Physiol., submitted},
Year = {2009},
Key = {fds158381}
}
@article{fds145760,
Author = {Anita T. Layton},
Title = {On the choice of correctors for semi-implicit Picard
deferred correction methods},
Journal = {Appl. Numer. Math.},
Volume = {58},
Number = {6},
Pages = {845-858},
Year = {2008},
Key = {fds145760}
}
@article{fds148405,
Author = {Jin Wang and Anita T. Layton},
Title = {Numerical simulations of fiber sedimentation in
Navier-Stokes flows},
Journal = {Comm. Comput. Phys.},
Volume = {5},
Pages = {61-83},
Year = {2008},
Key = {fds148405}
}
@article{fds151478,
Author = {Thomas L. Pannabecker and William H. Dantzler and Harold E.
Layton and Anita T. Layton},
Title = {Role of three-dimensional architecture in the urine
concentrating mechanism of the rat renal inner
medulla},
Journal = {Am. J. Physiol. Renal Physiol.},
Volume = {295},
Pages = {F1271 - F1285},
Year = {2008},
Key = {fds151478}
}
%% Layton, Harold
@article{fds157877,
Author = {Anita T. Layton and Leon C. Moore and Harold E.
Layton},
Title = {Multistable dynamics mediated by tubuloglomerular feedback
in a model of coupled nephrons},
Journal = {Bulletin of Mathematical Biology. 71(3):515-555,
2009.},
Year = {2009},
Month = {April},
Key = {fds157877}
}
@article{fds159030,
Author = {Jeff M. Sands and Harold E. Layton},
Title = {The physiology of urinary concentration: an
update},
Journal = {Seminars in Nephrology, 29 (2): 178-195,
2009.},
Year = {2009},
Key = {fds159030}
}
@article{fds152096,
Author = {Thomas L. Pannabecker and William H. Dantzler and Harold E.
Layton and Anita T. Layton},
Title = {Role of three-dimensional architecture in the urine
concentrating mechanism of the rat renal inner
medulla},
Journal = {American Journal of Physiology--Renal Physiology, 295: F1271
- F1285, 2008},
Year = {2008},
Month = {November},
Key = {fds152096}
}
@article{fds160443,
Author = {Mariano Marcano and Anita T. Layton and Harold E.
Layton},
Title = {Maximum urine concentrating capability for transport
parameters and urine flow within prescribed
ranges},
Year = {2008},
Key = {fds160443}
}
%% Liu, Jian-Guo
@book{fds165493,
Title = {Multi-scale phenomena in complex fluids, Modeling, Analysis
and Numerical Simulations},
Publisher = {World Scientific},
Editor = {T. Hou and C. Liu and J.-G. Liu},
Year = {2009},
ISBN = {978-981-4273-25-1},
Key = {fds165493}
}
@book{fds165494,
Title = {Hyperbolic Problems: Theory, Numerics and Applications,
volume I: Plenary & Invited Talks; volume II: Contributed
Talks},
Volume = {67},
Series = {Proceedings of Symposia in Applied Mathematics},
Publisher = {American Mathematical Society},
Editor = {E. Tadmor and J.-G. Liu and A.E. Tzavaras},
Year = {2009},
ISBN = {978-0-8218-4728-2},
Key = {fds165494}
}
@article{fds165495,
Author = {S.-Y. Ha and J.-G. Liu},
Title = {A simple proof of the Cucker-Smale flocking dynamics and
mean-field limit},
Journal = {Commun. Math. Sci.},
Volume = {7},
Pages = {297-325},
Year = {2009},
Key = {fds165495}
}
@article{fds165496,
Author = {J.-G. Liu and W.-C. Wang},
Title = {Characterization and regularity for axisymmetric solenoidal
vector elds with application to Navier-Stokes
equation},
Journal = {SIAM J. Math. Anal.},
Volume = {41},
Pages = {1825-1850},
Year = {2009},
Key = {fds165496}
}
@article{fds165499,
Author = {J.-G. Liu and J. Liu and R. Pego},
Title = {Error estimates for finite-element Navier-Stokes solvers
without standard inf-sup conditions},
Journal = {Chin. Ann. Math. Ser. B},
Volume = {30},
Pages = {743-768},
Year = {2009},
Key = {fds165499}
}
@article{fds165497,
Author = {Y.-L. Huang and J.-G. Liu and W.-C. Wang},
Title = {An FFT based fast Poisson solver on spherical
shells},
Journal = {Commun. Comput. Phy.},
Year = {2009},
Key = {fds165497}
}
@article{fds165498,
Author = {J.-G. Liu and R. Pego},
Title = {Stable discretization of magnetohydrodynamics in bounded
domains},
Journal = {Commun. Math. Sci.},
Year = {2009},
Key = {fds165498}
}
@article{fds165489,
Author = {X. Lu and P. Lin and J.-G. Liu},
Title = {Analysis of a sequential regularization method for the
unsteady Navier-Stokes equations},
Journal = {Math. Comp.},
Volume = {77},
Pages = {1467-1494},
Year = {2008},
Keywords = {Navier-Stokes equations iterative penalty method implicit
parabolic PDE error estimates constrained dynamical system
stabilization method},
Abstract = {The incompressibility constraint makes Navier-Stokes
equations dicult. A reformulation to a better posed problem
is needed before solving it numerically. The sequential
regularization method (SRM) is a reformulation which
combines the penalty method with a stabilization method in
the context of constrained dynamical systems and has the
bene t of both methods. In the paper, we study the existence
and uniqueness for the solution of the SRM and provide a
simple proof of the convergence of the solution of the SRM
to the solution of the Navier-Stokes equations. We also give
error estimates for the time discretized SRM
formulation.},
Key = {fds165489}
}
@article{fds165491,
Author = {P. Degond and J.-G. Liu and M.H. Vignal},
Title = {Analysis of an asymptotic preserving scheme for the
Euler-Poisson system in the quasineutral
limit},
Journal = {SIAM J. Num. Anal.},
Volume = {46},
Pages = {1298-1322},
Year = {2008},
Keywords = {stiffness Debye length electron plasma period
Burgers-Poisson sheath problem Klein-Gordon},
Abstract = {In a previous work, a new numerical discretization of the
Euler-Poisson system has been proposed. This scheme is
'Asymptotic Preserving' in the quasineutral limit (i.e. when
the Debye length epsilon tends to zero), which means that it
becomes consistent with the limit model when epsilon tends
to zero$. In the present work, we show that the stability
domain of the present scheme is independent of epsilon. This
stability analysis is performed on the Fourier transformed
(with respect to the space variable) linearized system. We
show that the stability property is more robust when a
space-decentered scheme is used (which brings in some
numerical dissipation) rather than with a space-centered
one. The linearization is first performed about a zero mean
velocity, and then about a non-zero mean velocity. At the
various stages of the analysis, our scheme is compared with
more classical schemes and its improved stability property
is outlined. The analysis of a fully discrete (in space and
time) version of the scheme is also given. Finally, some
considerations about a model nonlinear problem, the
Burgers-Poisson problem, are also given.},
Key = {fds165491}
}
@article{fds165500,
Author = {J.-G. Liu and C. Wang},
Title = {A fourth order numerical method for the primitive equations
formulated in mean vorticity},
Journal = {Commun. Comput. Phys.},
Volume = {4},
Pages = {26-55},
Year = {2008},
Key = {fds165500}
}
@article{fds165501,
Author = {P. Lin and J.-G. Liu and X. Lu},
Title = {Long time numerical solutyion of the Navier-Stokes equations
based on a sequential regularization formulation},
Journal = {SIAM J. Sci. Comput.},
Volume = {31},
Pages = {398-419},
Year = {2008},
Key = {fds165501}
}
@article{fds165502,
Author = {C.-H. Hsia and J.-G. Liu and C. Wang},
Title = {Structural stability and bifurcation for 2D incompressible
ows with symmetry},
Journal = {Meth. Appl. Anal.},
Volume = {15},
Pages = {495-512},
Year = {2008},
Key = {fds165502}
}
%% Maggioni, Mauro
@article{fds152199,
Author = {A.D. Szlam and R.R. Coifman and M. Maggioni},
Title = {A general framework for adaptive regularization based on
diffusion processes},
Journal = {Journ. Mach. Learn. Res.},
Number = {9},
Pages = {1711-1739},
Year = {2008},
Month = {August},
Key = {fds152199}
}
@article{MM:DiffusionPolynomialFrames,
Author = {Mauro Maggioni and Hrushikesh Mhaskar},
Title = {Diffusion polynomial frames on metric measure
spaces},
Journal = {Appl. Comp. Harm. Anal.},
Volume = {3},
Pages = {329-353},
Year = {2008},
Month = {May},
Key = {MM:DiffusionPolynomialFrames}
}
@article{fds152198,
Author = {P.W. Jones and M. Maggioni and R. Schul},
Title = {Manifold parametrizations by eigenfunctions of the Laplacian
and heat kernels},
Journal = {Proc. Nat. Acad. Sci.},
Volume = {105},
Number = {6},
Year = {2008},
Key = {fds152198}
}
@article{fds152202,
Author = {R R Coifman and I G Kevrekidis and S Lafon and M Maggioni and B.
Nadler},
Title = {Diffusion Maps, reduction coordinates and low dimensional
representation of stochastic systems},
Journal = {J.M.M.S.},
Year = {2008},
Key = {fds152202}
}
@inproceedings{MM:EEG,
Author = {E Causevic and R~R Coifman and R Isenhart and A Jacquin and E~R John and M Maggioni and L~S Prichep and F~J
Warner},
Title = {{QEEG}-based classification with wavelet packets and
microstate features for triage applications in the
{ER}},
Year = {2005},
Key = {MM:EEG}
}
@article{MRA_HRBF2004,
Author = {S. Ferrari and M. Maggioni and N. A. Borghese},
Title = {Multi-Scale Approximation with Hierarchical Radial Basis
Functions Networks,},
Journal = {IEEE Trans. on Neural Networks},
Volume = {15},
Number = {1},
Pages = {178--188},
Year = {2004},
Key = {MRA_HRBF2004}
}
@misc{PathNIH2004,
Author = {GL Davis and Mauro Maggioni and FJ Warner and FB Geshwind and AC Coppi and RA DeVerse and RR Coifman},
Title = {Hyper-spectral Analysis of normal and malignant colon tissue
microarray sections using a novel DMD system},
Year = {2004},
Key = {PathNIH2004}
}
@techreport{CMTech,
Author = {Ronald R Coifman and Mauro Maggioni},
Title = {Multiresolution Analysis associated to diffusion semigroups:
construction and fast algorithms},
Number = {YALE/DCS/TR-1289},
Organization = {Dept. Comp. Sci., Yale University},
Year = {2004},
Key = {CMTech}
}
%% Mattingly, Jonathan C.
@article{fds164683,
Author = {J.C. Mattingly and Andrew M. Stuart and M.V. Tretyakov},
Title = {Convergence of Numerical Time-Averaging and Stationary
Measures via Poisson Equations},
Year = {2009},
Abstract = {Numerical approximation of the long time behavior of a
stochastic differential equation (SDE) is considered. Error
estimates for time-averaging estimators are obtained and
then used to show that the stationary behavior of the
numerical method converges to that of the SDE. The error
analysis is based on using an associated Poisson equation
for the underlying SDE. The main advantage of this approach
is its simplicity and universality. It works equally well
for a range of explicit and implicit schemes including those
with simple simulation of random variables, and for general
hypoelliptic SDEs. An analogy between this approach and
Stein's method is indicated. Some practical implications of
the results are discussed.},
Key = {fds164683}
}
@article{fds160937,
Author = {J.C. Mattingly and David Anderson},
Title = {A weak trapezoidal method for a class of stochastic
differential equations},
Year = {2009},
Abstract = {We present a numerical method for the approximation of
solutions for the class of stochastic differential equations
driven by Brownian motions which induce stochastic variation
in fixed directions. This class of equations arises
naturally in the study of population processes and chemical
reaction kinetics. We show that the method constructs paths
that are second order accurate in the weak sense. The method
is simpler than many second order methods in that it neither
requires the construction of iterated Ito integrals nor the
evaluation of any derivatives. The method consists of two
steps. In the first an explicit Euler step is used to take a
fractional step. This fractional point is then combined with
the initial point to obtain a higher order, trapezoidal
like, approximation. The higher order of accuracy stems from
the fact that both the drift and the quadratic variation of
the underlying SDE are approximated to second
order.},
Key = {fds160937}
}
@article{fds163255,
Author = {J.C. Mattingly and Martin Hairer and Michael Scheutzow},
Title = {Asymptotic coupling and a weak form of Harris' theorem with
applications to stochastic delay equations},
Year = {2009},
Abstract = {There are many Markov chains on infinite dimensional spaces
whose one-step transition kernels are mutually singular when
starting from different initial conditions. We give results
which prove unique ergodicity under minimal assumptions on
one hand and the existence of a spectral gap under
conditions reminiscent of Harris' theorem. The first uses
the existence of couplings which draw the solutions together
as time goes to infinity. Such "asymptotic couplings" were
central to recent work on SPDEs on which this work builds.
The emphasis here is on stochastic differential delay
equations.Harris' celebrated theorem states that if a Markov
chain admits a Lyapunov function whose level sets are
"small" (in the sense that transition probabilities are
uniformly bounded from below), then it admits a unique
invariant measure and transition probabilities converge
towards it at exponential speed. This convergence takes
place in a total variation norm, weighted by the Lyapunov
function. A second aim of this article is to replace the
notion of a "small set" by the much weaker notion of a
"d-small set," which takes the topology of the underlying
space into account via a distance-like function d. With this
notion at hand, we prove an analogue to Harris' theorem,
where the convergence takes place in a Wasserstein-like
distance weighted again by the Lyapunov function. This
abstract result is then applied to the framework of
stochastic delay equations.},
Key = {fds163255}
}
@article{fds156904,
Author = {J.C. Mattingly and Scott A. McKinley and Natesh S. Pillai},
Title = {Geometric ergodicity of a bead-spring pair with stochastic
Stokes forcing},
Year = {2009},
Abstract = {We consider a simple model for the fluctuating hydrodynamics
of a flexible polymer in dilute solution, demonstrating
geometric ergodicity for a pair of particles that interact
with each other through a nonlinear spring potential while
being advected by a stochastic Stokes fluid velocity field.
This is a generalization of previous models which have used
linear spring forces as well as white-in-time fluid velocity
fields. We follow previous work combining control theoretic
arguments, Lyapunov functions, and hypo-elliptic diffusion
theory to prove exponential convergence via a Harris chain
argument. To this, we add the possibility of excluding
certain "bad" sets in phase space in which the assumptions
are violated but from which the systems leaves with a
controllable probability. This allows for the treatment of
singular drifts, such as those derived from the
Lennard-Jones potential, which is an novel feature of this
work.},
Key = {fds156904}
}
@article{fds163256,
Author = {Hairer, Martin and Mattingly, Jonathan C.},
Title = {Slow energy dissipation in anharmonic oscillator
chains},
Journal = {Communications on Pure and Applied Mathematics},
Volume = {62},
Number = {8},
Pages = {999--1032},
Year = {2009},
ISSN = {0010-3640},
MRCLASS = {82C20 (35K55 37Lxx)},
MRNUMBER = {MR2531551},
Abstract = {We study the dynamic behaviour at high energies of a chain
of anharmonic oscillators coupled at its ends to heat baths
at possibly different temperatures. In our setup, each
oscillator is subject to a homogeneous anharmonic pinning
potential $V_1(q_i) =|q_i|^{2k}/2k$ and harmonic coupling
potentials $V_2(q_i- q_{i-1}) = (q_i- q_{i-1})^2/2$ between
itself and its nearest neighbours. We consider the case $k >
1$ when the pinning potential is stronger then the coupling
potential. At high energy, when a large fraction of the
energy is located in the bulk of the chain, breathers appear
and block the transport of energy through the system, thus
slowing its convergence to equilibrium. In such a regime, we
obtain equations for an effective dynamics by averaging out
the fast oscillation of the breather. Using this
representation and related ideas, we can prove a number of
results. When the chain is of length three and $k> 3/2$ we
show that there exists a unique invariant measure. If $k >
2$ we further show that the system does not relax
exponentially fast to this equilibrium by demonstrating that
zero is in the essential spectrum of the generator of the
dynamics. When the chain has five or more oscillators and
$k> 3/2$ we show that the generator again has zero in its
essential spectrum. In addition to these rigorous results, a
theory is given for the rate of decrease of the energy when
it is concentrated in one of the oscillators without
dissipation. Numerical simulations are included which
confirm the theory.},
Key = {fds163256}
}
@article{fds163257,
Author = {J.C. Mattingly and Martin Hairer},
Title = {Yet another look at Harris' ergodic theorem for Markov
chains},
Year = {2008},
Month = {August},
Abstract = {The aim of this note is to present an elementary proof of a
variation of Harris' ergodic theorem of Markov chains. This
theorem, dating back to the fifties essentially states that
a Markov chain is uniquely ergodic if it admits a "small"
set which is visited infinitely often. This gives an
extension of the ideas of Doeblin to the unbounded state
space setting. Often this is established by finding a
Lyapunov function with "small" level sets. This topic has
been studied by many authors (cf. Harris, Hasminskii,
Nummelin, Meyn and Tweedie). If the Lyapunov function is
strong enough, one has a spectral gap in a weighted supremum
norm (cf. Meyn and Tweedie). Traditional proofs of this
result rely on the decomposition of the Markov chain into
excursions away from the small set and a careful analysis of
the exponential tail of the length of these excursions.
There have been other variations which have made use of
Poisson equations or worked at getting explicit constants.
The present proof is very direct, and relies instead on
introducing a family of equivalent weighted norms indexed by
a parameter $\beta$ and to make an appropriate choice of
this parameter that allows to combine in a very elementary
way the two ingredients (existence of a Lyapunov function
and irreducibility) that are crucial in obtaining a spectral
gap. The original motivation of this proof was the authors'
work on spectral gaps in Wasserstein metrics. The proof
presented in this note is a version of our reasoning in the
total variation setting which we used to guide the
calculations in arXiv:math/0602479. While we initially
produced it for that purpose, we hope that it will be of
interest in its own right.},
Key = {fds163257}
}
@article{fds151344,
Author = {J.C. Mattingly and Martin Hairer},
Title = {A Theory of Hypoellipticity and Unique Ergodicity for
Semilinear Stochastic PDEs},
Year = {2008},
Key = {fds151344}
}
@article{fds152882,
Author = {J.C. Mattingly and Martin Hairer},
Title = {Spectral gaps in Wasserstein distances and the 2D stochastic
Navier-Stokes equations},
Journal = {Annals of Probability},
Number = {6},
Pages = {993--1032},
Year = {2008},
MRNUMBER = {2478676},
Abstract = {We develop a general method that allows to show the
existence of spectral gaps for Markov semigroups on Banach
spaces. Unlike most previous work, the type of norm we
consider for this analysis is neither a weighted supremum
norm nor an L^p-type norm, but involves the derivative of
the observable as well and hence can be seen as a type of
1--Wasserstein distance. This turns out to be a suitable
approach for infinite-dimensional spaces where the usual
Harris or Doeblin conditions, which are geared to total
variation convergence, regularly fail to hold. In the first
part of this paper, we consider semigroups that have uniform
behaviour which one can view as an extension of Doeblin's
condition. We then proceed to study situations where the
behaviour is not so uniform, but the system has a suitable
Lyapunov structure, leading to a type of Harris condition.
We finally show that the latter condition is satisfied by
the two-dimensional stochastic Navier-Stokers equations,
even in situations where the forcing is extremely
degenerate. Using the convergence result, we show shat the
stochastic Navier-Stokes equations' invariant measures
depend continuously on the viscosity and the structure of
the forcing.},
Key = {fds152882}
}
@article{fds155602,
Author = {J.C. Mattingly and Iyer, Gautam and Mattingly, Jonathan},
Title = {A stochastic-{L}agrangian particle system for the
{N}avier-{S}tokes equations},
Journal = {Nonlinearity},
Volume = {21},
Number = {11},
Pages = {2537--2553},
Year = {2008},
ISSN = {0951-7715},
MRCLASS = {76D05 (35Q30 35R60 60H10 60H30)},
MRNUMBER = {MR2448230 (2009h:76060)},
Key = {fds155602}
}
@article{fds157004,
Author = {Mattingly, Jonathan C. and Suidan, Toufic
M.},
Title = {Transition measures for the stochastic {B}urgers
equation},
Journal = {, Integrable systems and random matrices},
Volume = {458},
Series = {Contemp. Math.},
Pages = {409--418},
Booktitle = {Integrable systems and random matrices},
Publisher = {Amer. Math. Soc.},
Address = {Providence, RI},
Year = {2008},
MRCLASS = {60Hxx (35Q53 35R60 60Jxx 76M35)},
MRNUMBER = {MR2411921},
Key = {fds157004}
}
%% McKinley, Scott A
@article{fds164672,
Author = {Jonathan C. Mattingly and Scott A. McKinley and Natesh S.
Pillai},
Title = {Geometric ergodicity of a bead-spring system advected by a
stochastic Stokes fluid},
Year = {2009},
Month = {Winter},
url = {http://arxiv.org/abs/0902.4496},
Key = {fds164672}
}
@article{fds164673,
Author = {Scott A. McKinley and Lingxing Yao and M. Gregory
Forest},
Title = {Transient Anomalous Diffusion of Tracer Particles in Soft
Matter},
Journal = {Journal of Rheology},
Year = {2009},
Key = {fds164673}
}
@article{fds164674,
Author = {Scott A. McKinley and Lea Popovic and Michael C.
Reed},
Title = {A Spatial Markov Model for Fast Axonal Transport},
Year = {2009},
Key = {fds164674}
}
@article{fds164675,
Author = {Scott A. McKinley},
Title = {Anomalous Diffusion of Distinguished Particles in
Bead-Spring Systems},
Year = {2009},
Key = {fds164675}
}
%% Mihalcea, Leonardo Constantin
@article{fds151401,
Author = {Anders S. Buch and Leonardo C. Mihalcea},
Title = {Quantum K-theory of Grassmannians},
Journal = {submitted},
Year = {2008},
Key = {fds151401}
}
@article{fds151402,
Author = {Takeshi Ikeda and Leonardo C. Mihalcea and Hiroshi
Naruse},
Title = {Double Schubert polynomials for the classical
groups},
Year = {2008},
Key = {fds151402}
}
%% Narkawicz, Anthony J.
@article{fds142516,
Author = {A.J. Narkawicz},
Title = {Cohomology jumping loci and relative malcev
completion},
Year = {2008},
Key = {fds142516}
}
%% Ng, Lenhard L
@article{fds152632,
Author = {T. Khandhawit and L. Ng},
Title = {A family of transversely nonsimple knots},
Year = {2008},
Key = {fds152632}
}
@article{fds152630,
Author = {L. Ng},
Title = {Rational Symplectic Field Theory for Legendrian
knots},
Year = {2008},
Key = {fds152630}
}
@article{fds70598,
Author = {L. Ng},
Title = {Framed knot contact homology},
Journal = {Duke Mathematical Journal},
Volume = {141},
Number = {2},
Pages = {365-406},
Year = {2008},
Key = {fds70598}
}
@article{fds152626,
Author = {L. Ng},
Title = {A skein approach to Bennequin type inequalities},
Journal = {International Mathematics Research Notices},
Volume = {2008},
Year = {2008},
Key = {fds152626}
}
@article{fds155120,
Author = {L. Ng and P. Ozsvath and D. Thurston},
Title = {Transverse knots distinguished by knot Floer
homology},
Journal = {Journal of Symplectic Geometry},
Volume = {6},
Number = {4},
Pages = {461-490},
Year = {2008},
Key = {fds155120}
}
%% Nolen, James
@article{fds159547,
Author = {J. Nolen and J. Xin},
Title = {Bounds on front speeds for inviscid and viscous
G-equations},
Year = {2009},
Month = {July},
Key = {fds159547}
}
@article{fds164667,
Author = {J. Nolen and G. Papanicolaou},
Title = {Fine scale uncertainty in parameter estimation for elliptic
equations},
Year = {2009},
Month = {June},
url = {http://math.duke.edu/~nolen/preprints/uq_elliptic.pdf},
Key = {fds164667}
}
@article{fds155119,
Author = {J. Nolen},
Title = {An invariance principle for random traveling waves in one
dimension},
Year = {2009},
Month = {January},
url = {http://math.duke.edu/~nolen/preprints/clt_front.pdf},
Key = {fds155119}
}
@article{fds160665,
Author = {J. Nolen and L. Ryzhik},
Title = {Traveling waves in a one-dimensional heterogeneous
medium},
Journal = {Annales de l'institut Henri Poincare -- Analyse Non
Lineaire},
Volume = {26},
Number = {3},
Pages = {1021-1047},
Year = {2009},
url = {http://math.duke.edu/~nolen/preprints/rand-tw-sub2.pdf},
Key = {fds160665}
}
@article{fds154866,
Author = {J. Nolen and J. Xin},
Title = {KPP Fronts in 1D Random Drift},
Journal = {Discrete and Continuous Dynamical Systems
B},
Volume = {11},
Number = {2},
Year = {2009},
url = {http://math.duke.edu/~nolen/preprints/nx1D_final.pdf},
Key = {fds154866}
}
@article{fds160664,
Author = {A. Mellet and J. Nolen and J.-M. Roquejoffre and L.
Ryzhik},
Title = {Stability of generalized transition fronts},
Journal = {Comm. PDE},
Volume = {34},
Number = {6},
Pages = {521-552},
Year = {2009},
url = {http://math.duke.edu/~nolen/preprints/stab-submit.pdf},
Key = {fds160664}
}
@article{fds156650,
Author = {J. Nolen and J. Xin},
Title = {Variational principle and reaction-diffusion front speeds in
random flows},
Journal = {ICIAM07-Proceedings},
Pages = {1040701-1040702},
Year = {2008},
Month = {December},
Key = {fds156650}
}
@article{fds154862,
Author = {J. Nolen and G. Papanicolaou and O. Pironneau},
Title = {A Framework for Adaptive Multiscale Methods for Elliptic
Problems},
Journal = {SIAM Multiscale Modeling and Simulation},
Volume = {7},
Pages = {171-196},
Publisher = {SIAM},
Year = {2008},
url = {http://math.duke.edu/~nolen/preprints/multiscale_npp_final.pdf},
Key = {fds154862}
}
@article{fds155499,
Author = {J. Nolen and J. Xin},
Title = {Computing reactive front speeds in random flows by
variational principle},
Journal = {Physica D},
Volume = {237},
Pages = {3172-3177},
Year = {2008},
Key = {fds155499}
}
@article{fds160663,
Author = {J. Nolen and J. Xin},
Title = {Asymptotic Spreading of KPP Reactive Fronts in
Incompressible Space-Time Random Flows},
Journal = {Annales de l'institut Henri Poincare -- Analyse Non
Lineaire},
Volume = {26},
Number = {3},
Pages = {815-839},
Year = {2008},
url = {http://math.duke.edu/~nolen/preprints/rand_fronts_sub2.pdf},
Key = {fds160663}
}
%% Petters, Arlie O
@article{fds157741,
Author = {A. M. Aazami and A.O. Petters},
Title = {A Universal Magnification Theorem for Higher-Order Caustic
Singularities},
Journal = {J. Math. Phys.},
Volume = {50},
Pages = {032501},
Year = {2009},
Month = {November},
url = {http://arxiv.org/abs/0811.3447},
Key = {fds157741}
}
@book{fds15387,
Author = {A. O. Petters},
Title = {Gravitational Lensing and Black Holes},
Publisher = {in preparation},
Year = {2009},
Month = {August},
Key = {fds15387}
}
@book{fds51036,
Author = {X. Dong and A. O. Petters},
Title = {Mathematical Finance II},
Publisher = {in preparation},
Year = {2009},
Month = {June},
Key = {fds51036}
}
@article{fds157980,
Author = {A. B. Aazami and A.O. Petters},
Title = {A Universal Magnification Theorem II. Generic Caustics up to
Codimension Five},
Year = {2009},
Key = {fds157980}
}
@book{fds28898,
Author = {X. Dong and A.O. Petters},
Title = {Mathematical Finance I},
Publisher = {in preparation},
Year = {2008},
Month = {June},
Key = {fds28898}
}
@article{fds148864,
Author = {A.O. Petters and B. Rider and A. M. Teguia},
Title = {A Mathematical Theory of Stochastic Microlensing II. Random
Images, Shear, and the Kac-Rice Formula},
Year = {2008},
Key = {fds148864}
}
@article{fds148865,
Author = {A.O. Petters and B. Rider and A. M. Teguia},
Title = {A Mathematical Theory of Stochastic Microlensing I. Random
Time Delay Functions and Lensing Maps},
Year = {2008},
Key = {fds148865}
}
%% Reed, Michael C
@article{fds152579,
Author = {Nijhout HF and Reed M and Ulrich C},
Title = {Mathematical Models of One-Carbon Metabolism},
Volume = {79},
Pages = {42-85},
Booktitle = {Vitamins and Hormones, Folic Acid},
Publisher = {Elsevier},
Editor = {G. Litwack},
Year = {2008},
Key = {fds152579}
}
@article{fds152578,
Author = {Ulrich CM and Reed MC and Nijhout HF},
Title = {Modeling folate, one-carbon metabolism, and DNA
methylation},
Journal = {Nutrition Reviews},
Volume = {66, Supp1},
Pages = {S27-S30},
Year = {2008},
Key = {fds152578}
}
@article{fds152573,
Author = {Nijhout HF and Reed MC},
Title = {A Mathematical Model for Juvenile Hormone
Titers},
Journal = {Journal of Insect Physiology},
Volume = {54},
Number = {255-264},
Year = {2008},
Key = {fds152573}
}
@article{fds152574,
Author = {Nijhout HF and Reed M and Ulrich C},
Title = {A day in the life of cell metabolism},
Journal = {Journal of Biological Theory},
Volume = {2},
Pages = {124-127},
Year = {2008},
Key = {fds152574}
}
@article{fds152576,
Author = {Reed M and Thomas R and Pavisic J and Nijhout HF and James SJ and Ulrich
CM},
Title = {A Mathematical Model of Glutathione Metabolism},
Journal = {Theoretical Biology and Medical Modelling},
Volume = {5},
Pages = {1-16},
Year = {2008},
Key = {fds152576}
}
@article{fds152577,
Author = {Ulrich CM and Neuhouser M and Liu A and Boynton A and Gregory JF and Shane
B, James SJ and Reed MC and Nijhout HF},
Title = {Mathematical modeling of folate metabolism: Predicted
effects of genetic polymorphisms on mechanisms and
biomarkers relevant to carcinogenesis},
Journal = {Cancer Epidemiology Biomarkers and Prevention},
Volume = {17},
Pages = {1822-1831},
Year = {2008},
Key = {fds152577}
}
@article{fds152581,
Author = {H. Frederik Nijhout and Jesse F. Gregory and Courtney Fitzpatrick and Eugenia Cho and Cornelia M. Ulrich and Michael C.
Reed},
Title = {A Mathematical Model Gives Insights into the Effects of B6
Deficiency on One-Carbon and Glutathione
Metabolism},
Journal = {Journal of Nutrition},
Year = {2008},
Key = {fds152581}
}
@article{fds152580,
Author = {Mitchell C and Reed M},
Title = {Do Real Neurons Have Time Windows?},
Journal = {Journal of Neural Computation},
Year = {2008},
Key = {fds152580}
}
@article{fds139742,
Author = {M.C. Reed},
Title = {Mathematical Biology},
Booktitle = {The Princeton Companion to Mathematics},
Publisher = {Princeton University Press, Princeton},
Year = {2008},
Key = {fds139742}
}
%% Rose, David E.
@article{fds142083,
Author = {David E. V. Rose and Ilya M. Spitkovsky},
Title = {On the stabilization of the Aluthge sequence},
Journal = {International Journal of Information and Systems
Sciences},
Volume = {4},
Number = {1},
Pages = {178-189},
Year = {2008},
Month = {Spring},
ISSN = {1708-296X},
Key = {fds142083}
}
@article{fds139616,
Author = {David E. V. Rose and Ilya M. Spitkovsky},
Title = {On the numerical range behavior under the generalized
Aluthge transform},
Journal = {Linear and Multilinear Algebra},
Volume = {56},
Number = {1&2},
Pages = {163-177},
Publisher = {Taylor and Francis},
Year = {2008},
Month = {January},
Keywords = {Aluthge transform Numerical range},
Key = {fds139616}
}
%% Schaeffer, David G
@article{fds151400,
Author = {S. Dai and D.G. Schaeffer},
Title = {Bifurcation in a modulation equation for alternans in a
cardiac fiber},
Journal = {Math. Modeling and Num. Anal.},
Year = {2008},
Key = {fds151400}
}
@article{fds151397,
Author = {D.G. Schaeffer and J. Cain},
Title = {Shortening of action potential duraction near an insulating
boundary},
Journal = {Math Medicine and Biology},
Volume = {25},
Number = {21--36},
Year = {2008},
Key = {fds151397}
}
@article{fds151398,
Author = {D.G. Schaeffer and A. Catlla and T. Witelski and E. Monson and A.
Lin},
Title = {On spiking models of synaptic activity and impulsive
differential equations},
Journal = {SIAM Review},
Volume = {50},
Number = {553--569},
Year = {2008},
Key = {fds151398}
}
@article{fds151399,
Author = {D.G. Schaeffer and W. Ying and X. Zhao},
Title = {Asymptotic approximation of an ionic model for cardiac
restitution},
Journal = {Nonlinear Dynamics},
Volume = {51},
Pages = {189--198},
Year = {2008},
Key = {fds151399}
}
@article{fds151393,
Author = {D.G. Schaeffer and M. Beck and C. Jones and M.
Wechselberger},
Title = {Electrical waves in a one-dimensional model of cardiac
tissue},
Journal = {SIAM Applied Dynamical Systems},
Year = {2008},
Key = {fds151393}
}
@article{fds151394,
Author = {D.G. Schaeffer and Shu Dai},
Title = {Spectrum of a linearized amplitude equation for alternans in
a cardiac fiber},
Journal = {SIAM Analysis},
Year = {2008},
Key = {fds151394}
}
@article{fds151395,
Author = {D.G. Schaeffer and R. Iverson},
Title = {Steady and intermittent slipping in a model of landslide
motion regulated by pore-pressure feedback},
Journal = {SIAM Applied Math},
Year = {2008},
Key = {fds151395}
}
@article{fds139451,
Author = {D.G. Schaeffer and A. Catlla and T. Witelski and E. Monson and A.
Lin},
Title = {Annular patterns in reaction-diffusion systems and their
implications for neural-glial interactions},
Year = {2008},
Key = {fds139451}
}
%% Schoen, Chad
@article{fds156905,
Author = {C. Schoen},
Title = {Desingularized fiber products of semi-stable elliptic
surfaces with vanishing third Betti number},
Journal = {Compositio Mathematica},
Volume = {145},
Pages = {89-111},
Year = {2009},
Key = {fds156905}
}
%% Smith, David A
@article{fds151530,
Author = {David Tall and David A. Smith and Cynthia Piez},
Title = {Technology and Calculus},
Pages = {207-258},
Booktitle = {Research on Technology and the Teaching and Learning of
Mathematics: Volume 1, Research Syntheses},
Publisher = {Information Age Publishing, Inc.},
Address = {Charlotte, NC},
Editor = {M. Kathleen Heid and Glendon W. Blume},
Year = {2008},
Month = {Summer},
ISBN = {978-1-931576-19-2},
Key = {fds151530}
}
%% Stern, Mark A
@article{fds156409,
Author = {M.A. Stern},
Title = {Spectral asymmetry for manifolds of special
holonomy},
Year = {2009},
Key = {fds156409}
}
@article{fds152685,
Author = {M.A. Stern},
Title = {Geometry of minimal energy Yang-Mills connections},
Year = {2008},
Month = {August},
Abstract = {We study the converse to the statement that instantons are
minimizers of the Yang--Mills energy in four dimensions. We
show that given an energy minimizing connection, A, the
curvature of A takes values in a subbundle of the adjoint
bundle which decomposes as a sum of instantons.},
Key = {fds152685}
}
@article{fds153432,
Author = {M.A. Stern},
Title = {Fixed point theorems from a de Rham perspective},
Journal = {Asian Journal of Mathematics},
Year = {2008},
Key = {fds153432}
}
%% Teguia, Alberto M.
@article{fds142537,
Author = {A.M. Teguia and J. Gardner and A. Godbole and A. Vuong and N. Watson and C.
Yerger},
Title = {Domination Cover Pebbling: Graph Families},
Journal = {Journal of Combinatorial Mathematics and Combinatorial
Computing},
Year = {2008},
Month = {November},
Key = {fds142537}
}
@article{fds147485,
Author = {A.M. Teguia and Arlie O. Petters and Brian Rider},
Title = {A Mathematical Theory of Stochastic Microlensing I. Random
Time-Delay Functions and Lensing Maps},
Year = {2008},
Month = {July},
Key = {fds147485}
}
@article{fds149174,
Author = {A.M. Teguia and Arlie O. Petters and Brian Rider},
Title = {A Mathematical Theory of Stochastic Microlensing II. Random
Images, Shear, and the Kac-Rice Formula},
Year = {2008},
url = {http://arxiv.org/abs/0807.4984},
Key = {fds149174}
}
%% Thomas, Rachel L.
@article{fds147056,
Author = {Reed M and Thomas R and Pavisic J and James SJ and Ulrich C and Nijhout
HF},
Title = {A Mathematical Model of Glutathione Metabolism},
Journal = {Theoretical Biology & Medical Modelling},
Year = {2008},
Month = {April},
url = {http://www.tbiomed.com/content/5/1/8},
Key = {fds147056}
}
%% Trangenstein, John
@article{3547392,
Author = {Trangenstein, J.A. and Bell, J.B.},
Title = {Mathematical structure of compositional reservoir
simulation},
Journal = {SIAM J. Sci. Stat. Comput. (USA)},
Volume = {10},
Number = {5},
Pages = {817 - 45},
Keywords = {chemical technology;numerical methods;petroleum
industry;two-phase flow;},
Abstract = {Multicomponent two-phase isothermal fluid flow in petroleum
reservoirs is described. The fluid-flow model consists of
component conservation equations. Darcy's law for the
volumetric flow rates, balance between the fluid volume and
the rock void, and the conditions of thermodynamic
equilibrium that determine the distribution of the chemical
components into phases. Thermodynamic equilibrium is
described by means of a mathematical model for the chemical
potentials of each component in each phase of the fluid. The
flow equations are manipulated to form a pressure equation
and a modified component-conservation equation: these form
the basis for the sequential method. It is shown that the
pressure equation is parabolic under reasonable assumptions
on the thermodynamic equilibrium model, and that the
component-conservation equations are hyperbolic in the
absence of diffusive forces such as capillary pressure and
mixing. A numerical method based on the sequential
formulation of the flow equations is outlined and used to
illustrate the kinds of flow behavior that occur during
miscible gas injection},
Key = {3547392}
}
%% Venakides, Stephanos
@article{fds153395,
Author = {N. Ptitsyna and S. P. Shipman and S. Venakides},
Title = {Fano resonance of waves in periodic slabs},
Journal = {Proceedings of the 12th International Conference on
Mathematical Methods in Electrodynamic Theory (MMET08 Odesa)
(2008) 73-78},
Year = {2008},
Abstract = {We investigate Fano-type anomalous transmission of energy of
plane waves across lossless slab scatterers with periodic
structure in the presence of non-robust guided modes. Our
approach is based on rigorous analytic perturbation of the
scattering problem near a guided mode and applies to very
general structures, continuous and discrete.},
Key = {fds153395}
}
@article{fds153396,
Author = {A. Tovbis and S. Venakides},
Title = {Determinant form of modulation equations for the
semiclassical focusing Nonlinear Schr\" odinger
equation.},
Journal = {International Mathematics Research Notices
IMRN},
Year = {2008},
Abstract = {We derive a determinant formula for the WKB exponential of
singularly perturbed Zakharov-Shabat system that corresponds
to the semiclassical (zero dispersion) limit of the focusing
Nonlinear Schr\" odinger equation. The derivation is based
on the Riemann-Hilbert Problem (RHP) representation of the
WKB exponential. We also prove its independence of the
branchpoints of the corresponding hyperelliptic surface
assuming that the modulation equations are
satisfied.},
Key = {fds153396}
}
%% Witelski, Thomas P
@article{fds158293,
Author = {T.P. Witelski},
Title = {The subtle art of blowing bubbles (News and Views: Fluid
Dynamics)},
Journal = {Nature Physics},
Volume = {5},
Pages = {315-316},
Year = {2009},
Month = {May},
url = {http://links.ealert.nature.com/ctt?kn=65&m=32736150&r=MTc2NjI2MDg2NwS2&b=2&j},
Key = {fds158293}
}
@article{fds154256,
Author = {H.-J. Hwang and T.P. Witelski},
Title = {Short-time Pattern formation in thin film
equations},
Journal = {Discrete and Continuous Dynamical Systems
A},
Volume = {23},
Number = {3},
Pages = {867-885},
Year = {2009},
Month = {March},
ISSN = {1078-0947},
url = {http://aimsciences.org/journals/displayArticles.jsp?paperID=3829},
Key = {fds154256}
}
@article{fds165136,
Author = {M. B. Gratton and T.P. Witelski},
Title = {Transient and self-similar dynamics in thin film
coarsening},
Journal = {Physica D},
Volume = {238},
Number = {23-24},
Pages = {2380-2394},
Year = {2009},
Key = {fds165136}
}
@article{fds157908,
Author = {L. B. Smolka and T. P. Witelski},
Title = {On the planar extensional motion of an inertially driven
liquid sheet},
Journal = {Physics of Fluids},
Volume = {21},
Number = {4},
Pages = {042101},
Year = {2009},
url = {http://link.aip.org/link/?PHF/21/042101},
Key = {fds157908}
}
@article{fds157864,
Author = {T.P. Witelski and M. Bowen},
Title = {Singular perturbation theory},
Journal = {Scholarpedia},
Volume = {4},
Number = {4},
Pages = {3951},
Year = {2009},
url = {http://www.scholarpedia.org/article/Singular_perturbation_theory},
Key = {fds157864}
}
@article{fds159830,
Author = {A.J.Bernoff and T.P. Witelski},
Title = {Stability and dynamics of self-similarity in evolution
equations},
Journal = {Journal of Engineering Mathematics},
Year = {2009},
ISSN = {1573-2703},
url = {http://dx.doi.org/10.1007/s10665-009-9309-8},
Key = {fds159830}
}
@article{fds145237,
Author = {DiCarlo DA and Juanes R and LaForce T and Witelski
TP},
Title = {Nonmonotonic traveling wave solutions of infiltration into
porous media},
Journal = {Water Resources Research},
Volume = {44},
Number = {2},
Pages = {W02406},
Year = {2008},
Month = {February},
ISSN = {0043-1397},
url = {DOI: 10.1029/2007WR005975},
Key = {fds145237}
}
@article{fds151811,
Author = {M. Aguareles and S. J. Chapman and T.P. Witelski},
Title = {Interaction of spiral waves in the Complex Ginzburg-Landau
equation},
Journal = {PRL},
Volume = {101},
Number = {224101},
Year = {2008},
url = {http://link.aps.org/abstract/PRL/v101/e224101},
Key = {fds151811}
}
@article{fds148596,
Author = {S. T. Santillian and R. H. Plaut and T. P. Witelski and L. N.
Virgin},
Title = {Large oscillations of beams and columns including
self-weight},
Journal = {International Journal of Nonlinear mechanics},
Volume = {43},
Pages = {761-771},
Year = {2008},
ISSN = {0020-7462},
url = {doi:10.1016/j.ijnonlinmec.2008.04.007},
Key = {fds148596}
}
@article{fds141438,
Author = {M.B. Gratton and T.P. Witelski},
Title = {Coarsening of dewetting thin films subject to
gravity},
Journal = {Physical Review E},
Volume = {77},
Number = {016301},
Pages = {1--11},
Year = {2008},
url = {http://link.aps.org/abstract/PRE/v77/e016301},
Key = {fds141438}
}
@article{fds148304,
Author = {A.J. Catlla and D.G. Schaeffer and T.P. Witelski and E. E. Monson and A.
L. Lin},
Title = {On spiking models for synaptic activity and impulsive
differential equations},
Journal = {SIAM Review},
Volume = {50},
Number = {3},
Pages = {553-569},
Year = {2008},
url = {http://link.aip.org/link/?SIR/50/553},
Key = {fds148304}
}
%% Zhou, Xin
@article{fds152874,
Author = {K. T.-R. McLaughlin and A. H. Vartanian and X.
Zhou},
Title = {Asymptotics of Orthogonal Laurent Polynomials of even Degree
with Respect to Varying Exponential Weights},
Year = {2008},
Key = {fds152874}
}
@article{fds152870,
Author = {X. Zhou and K. T.-R. McLaughlin and A. H. Vartanian},
Title = {Asymptotics of Coefficients of Recurrence Relations, Hankel
Determinants Ratios, and Root Products Associated with
Orthogonal Laurent Polynomials with Respect to Varying
Exponential Weights},
Journal = {journal Acta Applicandae Mathematicae},
Volume = {100},
Pages = {39-104},
Year = {2008},
Key = {fds152870}
}
@article{fds152869,
Author = {X. Zhou and K. McLaughlin and A.H. Vartanian},
Title = {Asymptotics of Orthogonal Laurent Polynomials of Odd Degree
with Respect to Varying Exponential Weights},
Journal = {Constructive Approximation},
Volume = {27},
Pages = {149-202},
Year = {2008},
Key = {fds152869}
}
@article{fds152871,
Author = {B. Rider and X. Zhou},
Title = {Janossy densities for unitary ensembles at the spectral
edge},
Journal = {IMRN},
Year = {2008},
Key = {fds152871}
}
@article{fds152873,
Author = {K. T.-R. McLaughlin and A. H. Vartanian and X.
Zhou},
Title = {Rational functions with a general distribution of poles on
the real line orthogonal with respect to varying exponential
weights},
Journal = {Math. Phys. Anal. Geom.},
Year = {2008},
Key = {fds152873}
}
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Mathematics Department