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Mathematics Faculty: Publications since January 2013

List all publications in the database.    :chronological  alphabetical  combined listing:
%% Addington, Nicolas   
@article{fds223834,
   Author = {N. Addington},
   Title = {On two rationality conjectures for cubic
             fourfolds},
   Year = {2014},
   Month = {May},
   url = {http://arxiv.org/abs/1405.4902},
   Key = {fds223834}
}

@article{fds223671,
   Author = {N. Addington and M. Lehn},
   Title = {On the symplectic eightfold associated to a Pfaffian cubic
             fourfold},
   Year = {2014},
   Month = {April},
   url = {http://arxiv.org/abs/1404.5657},
   Key = {fds223671}
}

@article{fds223672,
   Author = {N. Addington and W. Donovan and E. Segal},
   Title = {The Pfaffian-Grassmannian equivalence revisited},
   Year = {2014},
   Month = {January},
   url = {http://arxiv.org/abs/1401.3661},
   Key = {fds223672}
}

@article{fds224079,
   Author = {N. Addington and R. P. Thomas},
   Title = {Hodge theory and derived categories of cubic
             fourfolds},
   Journal = {Duke Math. J.},
   Volume = {163},
   Number = {10},
   Pages = {1885-1927},
   Year = {2014},
   url = {http://arxiv.org/abs/1211.3758},
   Key = {fds224079}
}

@article{fds223991,
   Author = {N. Addington and E. Segal and E. Sharpe},
   Title = {D-brane probes, branched double covers, and noncommutative
             resolutions},
   Journal = {Adv. Theor. Math. Phys.},
   Volume = {18},
   Number = {6},
   Year = {2014},
   url = {http://arxiv.org/abs/1211.2446},
   Key = {fds223991}
}

@article{fds223494,
   Author = {N. Addington},
   Title = {The Brauer group is not a derived invariant},
   Year = {2013},
   Month = {June},
   url = {http://arxiv.org/abs/1306.6538},
   Key = {fds223494}
}

@article{fds219852,
   Author = {N. Addington and P. Aspinwall},
   Title = {Categories of massless D-branes and del Pezzo
             surfaces},
   Journal = {J. High Energy Phys.},
   Volume = {2013},
   Number = {7},
   Pages = {front matter + 39pp.},
   Year = {2013},
   url = {http://arxiv.org/abs/1305.5767},
   Key = {fds219852}
}


%% Aristotelous, Andreas   
@article{fds224099,
   Author = {Aristotelous, A. C. and Durrett, R.},
   Title = {Fingering in Stochastic Growth Models.},
   Journal = {Experimental Mathematics},
   Year = {2014},
   Month = {July},
   Key = {fds224099}
}

@article{fds223440,
   Author = {Andreas C. Aristotelous and Ohannes A. Karakashian and Steven
             M.Wise},
   Title = {Adaptive, Second-Order in Time, Primitive-Variable
             Discontinuous Galerkin Schemes for a Cahn-Hilliard Equation
             with a Mass Source},
   Journal = {IMA Journal of Numerical Analysis},
   Year = {2014},
   Month = {March},
   Key = {fds223440}
}

@article{fds223439,
   Author = {A. C. Aristotelous and M. A. Haider},
   Title = {Evaluation of Diffusive Transport and Cellular Uptake of
             Nutrients in Tissue Engineered Constructs using a Hybrid
             Discrete Model},
   Journal = {Processes},
   Year = {2014},
   Month = {March},
   Key = {fds223439}
}

@article{fds223438,
   Author = {Andreas C. Aristotelous and Richard Durrett},
   Title = {Chemical Evolutionary Games},
   Journal = {Theoretical Population Biology},
   Year = {2014},
   Month = {February},
   Key = {fds223438}
}

@article{fds223441,
   Author = {Andreas C. Aristotelous and Mansoor A. Haider},
   Title = {Use of Hybrid Discrete Cellular Models for Identification of
             Macroscopic Nutrient Loss in Reaction-Diffusion Models of
             Tissues.},
   Journal = {Int. J. Numer. Meth. Biomed. Engng.},
   Year = {2014},
   Month = {February},
   Key = {fds223441}
}

@article{fds219212,
   Author = {Andreas C. Aristotelous and Ohannes A. Karakashian and Steven
             M.Wise},
   Title = {A Mixed Discontinuous Galerkin, Convex Splitting Scheme for
             a Modified Cahn-Hilliard Equation and an Efficient Nonlinear
             Multigrid Solver.},
   Journal = {DCDS-B},
   Volume = {18},
   Number = {9},
   Pages = {2211–2238},
   Year = {2013},
   Month = {November},
   Key = {fds219212}
}


%% Aspinwall, Paul S   
@article{fds221207,
   Author = {N. Addington and P.S. Aspinwall},
   Title = {Categories of Massless D-Branes and del Pezzo
             Surfaces},
   Journal = {JHEP},
   Volume = {2013},
   Number = {176},
   Year = {2013},
   Key = {fds221207}
}

@article{fds221208,
   Author = {P.S. Aspinwall},
   Title = {Some Applications of Commutative Algebra to String
             Theory},
   Booktitle = {Commutative Algebra, Expository Papers Dedicated to David
             Eisenbud on the Occasion of His 65th Birthday},
   Year = {2013},
   Abstract = {The topological B-model, which is a simplified model of
             string theory, is essentially algebraic in nature. We
             describe how some calculations in this model may be
             performed using methods of commutative algebra. In
             particular, we consider the B-model associated with a
             Calabi– Yau threefold in the form of a complete
             intersection in a toric variety. There is a category of
             D-branes associated to matrix factorizations, and we show
             how to compute certain products and some Hochschild
             cohomology associated to this category. Mirror symmetry and
             the notion of stability lead to a notion of monodromy on
             this D-brane category. In general this monodromy can be
             awkward to compute, but we show how much of the
             combinatorial data associated to the monodromy can be
             accessed using commutative algebra.},
   Key = {fds221208}
}


%% Bar-On, Rann   
@misc{fds205138,
   Author = {Rann Bar-On and Jack Bookman and Benjamin Cooke and Donna Hall and Sarah
             Schott},
   Title = {(Re)discovering SoTL Through a Fundamental Challenge:
             Helping Students Transition to College Calculus},
   Year = {2014},
   Keywords = {SoTL calculus undergraduate education},
   Abstract = {Teaching and learning occur both inside and outside of the
             classroom, but undergraduates' transition to college
             mathematics are affected by many factors outside of the
             classroom. A collaboration at Duke between mathematics
             faculty and the Academic Resource Center (ARC) originally
             designed to fill knowledge gaps gradually adapted into a
             tool to help less well-prepared students transition to the
             calculus curriculum. The collaboration to monitor student
             progress and the adaptation of research tools grew initial
             voluntary algebra review sessions into an algebra review and
             study group program that supports students through the two
             course sequence of Laboratory Calculus with Functions I and
             II. The collaborators have applied for an NSF grant proposal
             to transition the program into the structure of the course
             labs to build a formative feedback loop between the
             students, undergraduate TAs, and mathematics and ARC
             instructors. The grant proposal builds on a collaboration
             between the ARC and Chemistry faculty to help pre-med
             students navigate a four-course Chemistry sequence through
             Organic Chemistry, which trains TAs to monitor not only
             content understanding, but self-regulation and metacognitive
             development.},
   Key = {fds205138}
}


%% Beale, J. Thomas   
@article{fds219617,
   Author = {S. Tlupova and J. T. Beale},
   Title = {Nearly singular integrals in 3D Stokes flow},
   Journal = {Commun. Comput. Phys.},
   Volume = {14},
   Pages = {1207-27},
   Year = {2013},
   url = {http://www.math.duke.edu/faculty/beale/papers/stokes3d2.pdf},
   Key = {fds219617}
}

@article{fds219618,
   Author = {W. Ying and J. T. Beale},
   Title = {A fast accurate boundary integral method for potentials on
             closely packed cells},
   Journal = {Commun. Comput. Phys.},
   Volume = {14},
   Pages = {1073-93},
   Year = {2013},
   url = {http://www.math.duke.edu/faculty/beale/papers/cpcells2.pdf},
   Key = {fds219618}
}


%% Bendich, Paul L.   
@article{fds220713,
   Author = {Paul Bendich and Herbert Edelsbrunner and Dmitriy Morozov and Amit Patel},
   Title = {Homology and Robustness of Level and Interlevel
             Sets},
   Journal = {Homology, Homotopy, and Applications},
   Volume = {15},
   Number = {1},
   Pages = {51-72},
   Editor = {Gunnar Carlsson},
   Year = {2013},
   Month = {March},
   Abstract = {Given a continuous function f : X → R on a topological
             space, we consider the preimages of intervals and their
             homol- ogy groups and show how to read the ranks of these
             groups from the extended persistence diagram of f. In
             addition, we quan- tify the robustness of the homology
             classes under perturbations of f using well groups, and we
             show how to read the ranks of these groups from the same
             extended persistence diagram. The special case X = R^3 has
             ramifications in the fields of medical imaging and
             scientific visualization.},
   Key = {fds220713}
}

@article{fds220715,
   Author = {Liz Munch and Paul Bendich and Kate Turner and Sayan Mukherjee and Jonathan Mattingly and John Harer},
   Title = {Probabalistic Frechet Means and Statistics on
             Vineyards},
   Year = {2013},
   url = {http://arxiv.org/abs/1307.6530},
   Abstract = {In order to use persistence diagrams as a true statistical
             tool, it would be very useful to have a good notion of mean
             and variance for a set of diagrams. In [21], Mileyko and his
             collaborators made the rst study of the properties of the
             Frechet mean in (Dp;Wp), the space of persistence diagrams
             equipped with the p-th Wasserstein metric. In particular,
             they showed that the Frechet mean of a nite set of diagrams
             always exists, but is not necessarily unique. As an
             unfortunate consequence, one sees that the means of a
             continuously-varying set of diagrams do not themselves vary
             continuously, which presents obvious problems when trying to
             extend the Frechet mean de nition to the realm of
             vineyards. We x this problem by altering the original de
             nition of Frechet mean so that it now becomes a probability
             measure on the set of persistence diagrams; in a nutshell,
             the mean of a set of diagrams will be a weighted sum of
             atomic measures, where each atom is itself the (Frechet
             mean) persistence diagram of a perturbation of the input
             diagrams. We show that this new de nition de nes a (Holder)
             continuous map, for each k, from (Dp)k ! P(Dp), and we
             present several examples to show how it may become a useful
             statistic on vineyards.},
   Key = {fds220715}
}


%% 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{fds220485,
   Author = {Lewis Blake and Michael Reed},
   Title = {Laboratory Calculus (2013-2014)},
   Year = {2013},
   Month = {August},
   Key = {fds220485}
}


%% Bobrowski, Omer   
@article{fds221191,
   Author = {O. Bobrowski and S. Mukherjee},
   Title = {The Topology of Probability Distributions on
             Manifolds},
   Journal = {arXiv: 1307.1123},
   Year = {2013},
   Key = {fds221191}
}

@article{fds221192,
   Author = {R. J. Adler and O. Bobrowski and S. Weinberger},
   Title = {Crackle: The Persistent Homology of Noise},
   Journal = {arXiv:1301.1466},
   Year = {2013},
   Key = {fds221192}
}


%% Bookman, Jack   
@article{fds218390,
   Author = {Emily Lardner and Jack Bookman},
   Title = {Lessons Learned in Interdisciplinary Professional
             Development Designed to Promote the Teaching of Quantitative
             Literacy},
   Journal = {Journal of Faculty Development},
   Volume = {27},
   Number = {2},
   Year = {2013},
   Month = {May},
   Key = {fds218390}
}

@article{fds219344,
   Author = {Narayan, Aditee Pradhan and Whicker, Shari A and Staples, Betty and Bookman, Jack and Bartlett, Kathleen and McGann, Kathleen
             A},
   Title = {The Clinical Skills Fair - An Innovative Curriculum
             Evaluation Tool},
   Journal = {Journal of Graduate Medical Education},
   Year = {2013},
   Month = {April},
   Key = {fds219344}
}

@article{fds219345,
   Author = {Rann Bar-On and Jack Bookman and Benjamin Cooke and Donna Hall and Sarah Schott},
   Title = {(Re)discovering SoTL Through a Fundamental Challenge:
             Helping Students Transition to College Calculus},
   Journal = {MAA Notes},
   Year = {2013},
   Key = {fds219345}
}


%% Bray, Hubert L.   
@article{fds223450,
   Author = {H.L. Bray and J. L. Jauregui},
   Title = {Time Flat Surfaces and the Monotonicity of the Spacetime
             Hawking Mass},
   Journal = {Communications in Mathematical Physics},
   Year = {2014},
   Month = {April},
   url = {http://arxiv.org/abs/1310.8638},
   Key = {fds223450}
}

@article{fds223121,
   Author = {H.L. Bray and J. L. Jauregui and M. Mars},
   Title = {Time Flat Surfaces and the Monotonicity of the Spacetime
             Hawking Mass II},
   Year = {2014},
   Month = {February},
   url = {http://arxiv.org/abs/1402.3287},
   Abstract = {In this sequel paper we give a shorter, second proof of the
             monotonicity of the Hawking mass for time flat surfaces
             under spacelike uniformly area expanding flows in spacetimes
             that satisfy the dominant energy condition. We also include
             a third proof which builds on a known formula and describe a
             class of sufficient conditions of divergence type for the
             monotonicity of the Hawking mass. These flows of surfaces
             may have connections to the problem in general relativity of
             bounding the total mass of a spacetime from below by the
             quasi-local mass of spacelike 2-surfaces in the
             spacetime.},
   Key = {fds223121}
}

@article{fds220311,
   Author = {H.L. Bray and J. L. Jauregui},
   Title = {On Curves with Nonnegative Torsion},
   Year = {2013},
   Month = {December},
   url = {http://arxiv.org/abs/1312.5171},
   Key = {fds220311}
}

@article{fds220312,
   Author = {H.L. Bray and J.L. Jauregui},
   Title = {A Geometric Theory of Zero Area Singularities in General
             Relativity},
   Journal = {Asian Journal of Mathematics},
   Volume = {17},
   Number = {3},
   Pages = {525-560},
   Year = {2013},
   Month = {September},
   url = {http://arxiv.org/abs/0909.0522v1},
   Key = {fds220312}
}

@article{fds214520,
   Author = {H.L. Bray and A. R. Parry},
   Title = {Modeling Wave Dark Matter in Dwarf Elliptical
             Galaxies},
   Year = {2013},
   Month = {January},
   url = {http://www.math.duke.edu/~bray/darkmatter/darkmatter.html},
   Key = {fds214520}
}

@article{fds220313,
   Author = {H.L. Bray},
   Title = {On Dark Matter, Spiral Galaxies, and the Axioms of General
             Relativity},
   Journal = {AMS Contemporary Mathematics Volume, "Geometric Analysis,
             Mathematical Relativity, and Nonlinear Partial Differential
             Equations"},
   Volume = {599},
   Publisher = {American Mathematical Society},
   Year = {2013},
   url = {http://www.math.duke.edu/~bray/darkmatter/darkmatter.html},
   Key = {fds220313}
}


%% Bryant, Robert L   
@article{fds223639,
   Author = {R.L. Bryant},
   Title = {Notes on Exterior Differential Systems},
   Year = {2014},
   Month = {May},
   url = {http://arxiv.org/abs/1405.3116},
   Keywords = {exterior differential systems Lie theory differential
             geometry},
   Abstract = {These are notes for a very rapid introduction to the basics
             of exterior differential systems and their connection with
             what is now known as Lie theory, together with some typical
             and not-so-typical applications to illustrate their
             use.},
   Key = {fds223639}
}

@article{fds223640,
   Author = {R.L. Bryant},
   Title = {S.-s. Chern's study of almost-complex structures on the
             six-sphere},
   Year = {2014},
   Month = {May},
   url = {http://arxiv.org/abs/1405.3405},
   Keywords = {6-sphere complex structure exceptional geometry},
   Abstract = {In 2003, S.-s. Chern began a study of almost-complex
             structures on the 6-sphere, with the idea of exploiting the
             special properties of its well-known almost-complex
             structure invariant under the exceptional group G2. While he
             did not solve the (currently still open) problem of
             determining whether there exists an integrable
             almost-complex structure on the 6-sphere, he did prove a
             significant identity that resolves the question for an
             interesting class of almost-complex structures on the
             6-sphere.},
   Key = {fds223640}
}


%% Cahill, Jason   
@article{fds221006,
   Author = {J. Cahill and P.G. Casazza and M. Ehler and S. Li},
   Title = {Tight and random nonorthogonal fusion frames},
   Year = {2013},
   url = {http://http://arxiv.org/abs/1309.0532},
   Abstract = {First we show that tight nonorthogonal fusion frames are
             relatively easy to com by. In order to do this we need to
             establish a classification of how to to wire a self adjoint
             operator as a product of (nonorthogonal) projection
             operators. We also discuss the link between nonorthogonal
             fusion frames and positive operator valued measures, we
             define and study a nonorthogonal fusion frame potential, and
             we introduce the idea of random nonorthogonal fusion
             frames.},
   Key = {fds221006}
}

@article{fds221008,
   Author = {J. Cahill and D.G. Mixon and N. Strawn},
   Title = {Connectivity and Irreducibility of Algebraic Varieties of
             Finite Unit Norm Tight Frames},
   Year = {2013},
   url = {http://arxiv.org/abs/1311.4748},
   Abstract = {In this paper, we settle a long-standing problem on the
             connectivity of spaces of finite unit norm tight frames
             (FUNTFs), essentially affirming a conjecture first appearing
             in Dykema and Strawn (2003). Our central technique involves
             continuous liftings of paths from the polytope of eigensteps
             (see Cahill et al. (2012)) to spaces of FUNTFs. After
             demonstrating this connectivity result, we refine our
             analysis to show that the set of nonsingular points on these
             spaces is also connected, and we use this result to show
             that spaces of FUNTFs are irreducible in the
             algebro-geometric sense, and that generic FUNTFs are full
             spark.},
   Key = {fds221008}
}


%% Cornwell, Christopher R   
@article{fds220821,
   Author = {C.R. Cornwell},
   Title = {Knot contact homology and representations of knot
             groups},
   Year = {2013},
   url = {http://arxiv.org/abs/1303.4943},
   Abstract = {We study certain linear representations of the knot group
             that induce augmentations of knot contact homology. This
             perspective on augmentations enhances our understanding of
             the relationship between the augmentation polynomial and the
             A-polynomial of the knot. For example, we show that for
             2-bridge knots the polynomials agree and that this is never
             the case for (non-2-bridge) torus knots, nor for a family of
             3-bridge pretzel knots. In addition, we obtain a lower bound
             on the meridional rank of the knot. As a consequence, our
             results give another proof that torus knots and a family of
             pretzel knots have meridional rank equal to their bridge
             number.},
   Key = {fds220821}
}

@article{fds220823,
   Author = {C.R. Cornwell},
   Title = {KCH representations, augmentations, and A-polynomials},
   Year = {2013},
   url = {http://arxiv.org/abs/1310.7526},
   Abstract = {Knot contact homology is an invariant of knots in $\mathbb
             R^3$, defined via the geometry of the cotangent bundle.
             Augmentations of knot contact homology are quite useful for
             relating it to other knot invariants. We describe a
             correspondence between augmentations and certain
             representations of the knot group. The correspondence
             implies the 2-variable augmentation polynomial equals a
             generalization of the classical A-polynomial. It also
             associates to each augmentation a rank, which is bounded by
             the bridge number. Like the bridge number, augmentation rank
             minus 1 is additive under connect sums. We also describe
             properties of augmentations with rank equal to the braid
             index.},
   Key = {fds220823}
}


%% Daubechies, Ingrid   
@article{fds215103,
   Author = {B. Cornelis and T.Ruzic, E.Gezels and A.Dooms, A.Pizurica and L.Platisa, J.Cornelis and M. Martens and M.DeMey, I.Daubechies},
   Title = {Crack detection and inpainting for virtual restoration of
             paintings: The case of the Ghent Altarpiece},
   Journal = {Signal Processing},
   Volume = {93},
   Pages = {605-619},
   Publisher = {Elsevier},
   Year = {2013},
   url = {http://www.sciencedirect.com/science/article/pii/S0165168412002526},
   Abstract = {Digital image processing is proving to be of great help in
             the analysis and documenta- tion of our vast cultural
             heritage. In this paper, we present a new method for the
             virtual restoration of digitized paintings with
             specialattention for the Ghent Altarpiece (1432), a large
             polyptych panel painting of which very few digital
             reproductions exist. We achieve our objective by detecting
             and digitally removing cracks. The detection of cracks is
             particularly difficult because of the varying content
             features in different parts of the polyptych. Three new
             detection methods are proposed and combined in order to
             detect cracks of different sizes as well as varying
             brightness. Semi-supervised clustering based post-processing
             is used to remove objects falsely labelled as cracks. For
             the subsequent inpainting stage, a patch-based technique is
             applied to handle the noisy nature of the images and to
             increase the performance for crack removal. We demonstrate
             the usefulness of our method by means of a case study where
             the goal is to improve readability of the depiction of text
             in a book, present in one of the panels, in order to assist
             paleographers in its deciphering.},
   Key = {fds215103}
}


%% Di Cerbo, Luca F.   
@article{fds224000,
   Author = {G. Di Cerbo and L.F. Di Cerbo},
   Title = {A sharp cusp count for complex hyperbolic surfaces and
             related results},
   Journal = {Arch. Math. (Basel)},
   Year = {2014},
   Month = {July},
   url = {http://arxiv.org/abs/1312.5368},
   Key = {fds224000}
}

@article{fds223554,
   Author = {L.F. Di Cerbo},
   Title = {Generic Properties of Homogeneous Ricci Solitons},
   Journal = {Adv. Geom.},
   Volume = {14},
   Number = {2},
   Pages = {225-237},
   Year = {2014},
   url = {http://arxiv.org/abs/0711.0465},
   Key = {fds223554}
}

@article{fds219797,
   Author = {L.F. Di Cerbo},
   Title = {Classification of Toroidal Compactifications with
             3\bar{c}_{2}=\bar{c}^{2}_{1} and \bar{c}_{2}=1},
   Year = {2013},
   Month = {September},
   url = {http://arxiv.org/abs/1309.5516},
   Key = {fds219797}
}

@article{fds215945,
   Author = {G. Di Cerbo and L.F. Di Cerbo},
   Title = {Positivity questions in K\"ahler-Einstein
             theory},
   Year = {2013},
   Month = {February},
   url = {http://arxiv.org/abs/1210.0218},
   Key = {fds215945}
}

@article{fds215526,
   Author = {G. Di Cerbo and L.F. Di Cerbo},
   Title = {Effective results for complex hyperbolic
             manifolds},
   Year = {2013},
   Month = {February},
   url = {http://arxiv.org/abs/1212.0501v5},
   Key = {fds215526}
}

@article{fds222369,
   Author = {L.F. Di Cerbo},
   Title = {Seiberg-Witten equations on surfaces of logarithmic general
             type},
   Journal = {Internat. J. Math.},
   Volume = {24},
   Number = {9},
   Pages = {23},
   Year = {2013},
   url = {http://arxiv.org/abs/1112.0694},
   Key = {fds222369}
}


%% Durrett, Rick   
@article{fds220505,
   Author = {C. Varghese and R. Durrett},
   Title = {Phase transition in the quadratic contact process on complex
             networks},
   Journal = {Physical Review E},
   Volume = {87},
   Pages = {paper 062819},
   Year = {2013},
   Key = {fds220505}
}

@article{fds220506,
   Author = {Feng Shi and Peter Mucha and R. Durrett},
   Title = {Multi-opinion coevolving voter model with infinitely many
             phase transitions},
   Journal = {Physical Review E},
   Year = {2013},
   Key = {fds220506}
}

@article{fds220504,
   Author = {S. Magura and V. Pong and D. Sivakoff and R. Durrett},
   Title = {Two evolving social network models},
   Year = {2013},
   Key = {fds220504}
}

@article{fds220507,
   Author = {R. Durrett and T. Liggett and Y. Zhang},
   Title = {The contact process with fast voting},
   Journal = {Electronic Journal of Probability},
   Year = {2013},
   Key = {fds220507}
}

@article{fds220508,
   Author = {Andreas Aristotelos and R. Durrett},
   Title = {Chemical evolutionary games},
   Journal = {Theoretical Population Biology},
   Year = {2013},
   Key = {fds220508}
}

@article{fds220499,
   Author = {R. Durrett and S. Chatterjee},
   Title = {A first order phase transition in the threshold theta
             contact process on random r-regular graphs and
             trees},
   Journal = {Stoch. Proc. Appl.},
   Volume = {123},
   Pages = {561-578},
   Year = {2013},
   Key = {fds220499}
}

@article{fds220500,
   Author = {K. Danesh and R. Durrett and L. Havrilesky and E.
             Myers},
   Title = {A branching process model of ovarian cancer},
   Journal = {J. Theor. Biol.},
   Volume = {314},
   Pages = {10-15},
   Year = {2013},
   Key = {fds220500}
}

@article{fds220501,
   Author = {J.T. Cox and R. Durrett and E. Perkins},
   Title = {Voter model perturbations and reaction diffusion
             equations},
   Journal = {Asterique},
   Volume = {349},
   Pages = {1-113},
   Year = {2013},
   url = {http://arxiv.org/abs/math/1103.1676},
   Key = {fds220501}
}

@article{fds220503,
   Author = {R. Durrett and S. Moseley},
   Title = {Spatial Moran Models. I. Tunneling in the Neutral
             Case},
   Journal = {Annals Applied Probability},
   Year = {2013},
   Key = {fds220503}
}


%% Fry, Brendan   
@article{fds218670,
   Author = {BC Fry and TK Roy and TW Secomb},
   Title = {Capillary recruitment in a theoretical model for blood flow
             regulation in heterogeneous microvessel networks},
   Journal = {Physiological Reports},
   Volume = {1},
   Number = {3},
   Pages = {e00050},
   Year = {2013},
   Key = {fds218670}
}


%% Gasparovic, Ellen   
@article{fds223290,
   Author = {G. Bal and J. Bergbauer and E. W. Chambers and E. Gasparovic and R. Hu and K. Leonard and M. Shaker and C. Wenk},
   Title = {Skeleton-based recognition of shapes in images via longest
             path matching},
   Year = {2014},
   Key = {fds223290}
}

@article{fds223582,
   Author = {James Damon and Ellen Gasparovic},
   Title = {Modeling Multi-Object Configurations Via Medial/Skeletal
             Linking Structures},
   Year = {2014},
   Key = {fds223582}
}

@article{fds220590,
   Author = {James Damon and Ellen Gasparovic},
   Title = {Medial/Skeletal Linking Structures for Multi-Region
             Configurations},
   Year = {2013},
   url = {http://arxiv.org/abs/1402.5517},
   Key = {fds220590}
}


%% Getz, Jayce R.   
@article{fds223281,
   Author = {J.R. Getz and H. Hahn},
   Title = {Algebraic cycles and Tate classes on Hilbert modular
             varieties},
   Journal = {Int. J. Number Theory},
   Volume = {10},
   Number = {1},
   Pages = {161-176},
   Year = {2014},
   Abstract = {Let E be a totally real number field that is Galois, and
             consider a cuspidal, nondihedral automorphic representation
             of GL(2) over E that is in the lowest weight discrete series
             at every real place of E. The representation cuts out a
             ``motive'' M from the l-adic middle degree intersection
             cohomology of an appropriate Hilbert modular variety. If l
             is sufficiently large in a sense that depends on the
             representation we compute the dimension of the space of Tate
             classes in M. Moreover if the space of Tate classes on this
             motive over all finite abelian extensions k/E is at most of
             rank one as a Hecke module, we prove that the space of Tate
             classes in M is spanned by algebraic cycles.},
   Key = {fds223281}
}

@article{fds223471,
   Author = {J.R. Getz and H. Hahn},
   Title = {A general simple relative trace formula and a relative Weyl
             law},
   Year = {2014},
   Key = {fds223471}
}

@article{fds220702,
   Author = {J.R. Getz and P. E. Herman},
   Title = {A nonabelian trace formula},
   Year = {2013},
   Abstract = {Let E/F be an extension of number fi elds with Gal(E/F)
             simple and nonabelian. In a recent paper the fi rst named
             author suggested an approach to nonsolvable base change and
             descent of automorphic representations of GL(2) along such
             an extension. Motivated by this we prove a trace formula
             whose spectral side is a weighted sum over cuspidal
             automorphic representations of GL(2) over E that are
             isomorphic to their Gal(E/F)-conjugates.},
   Key = {fds220702}
}

@article{fds218668,
   Author = {J.R. Getz and E. Wambach},
   Title = {Twisted relative trace formulae with a view towards unitary
             groups},
   Journal = {Amer. J. Math.},
   Volume = {135},
   Pages = {1-57},
   Year = {2013},
   url = {http://www.math.duke.edu/~jgetz/BCRT_Final_AJM.pdf},
   Abstract = {We introduce a twisted relative trace formula which
             simultaneously generalizes the twisted trace formula of
             Langlands et. al. (in the quadratic case) and the relative
             trace formula of Jacquet and Lai [JL]. Certain matching
             statements relating this twisted relative trace formula to a
             relative trace formula are also proven (including the
             relevant fundamental lemma in the "biquadratic case"). Using
             recent work of Jacquet, Lapid and their collaborators [J1]
             and the Rankin-Selberg integral representation of the Asai
             L-function (obtained by Flicker using the theory of Jacquet,
             Piatetskii-Shapiro, and Shalika [Fl2]), we give the
             following application: Let E/F be a totally real quadratic
             extension, let U' be a quasi-split unitary group with
             respect to a CM extension M/F, and let U := U'_E. Under
             suitable local hypotheses, we show that a cuspidal
             cohomological automorphic representation  of U whose Asai
             L-function has a pole at the edge of the critical strip is
             nearly equivalent to a cuspidal cohomological automorphic
             representation 0 of U that is U'-distinguished in the
             sense that there is a form in the space of 0 admitting a
             nonzero period over U. This provides cohomologically
             nontrivial cycles of middle dimension on unitary Shimura
             varieties analogous to those on Hilbert modular surfaces
             studied by Harder, Langlands, and Rapoport
             [HLR].},
   Key = {fds218668}
}

@article{fds219239,
   Author = {J.R. Getz and J. Klassen},
   Title = {Isolating Rankin-Selberg lifts},
   Journal = {Proc. Amer. Math. Soc.},
   Year = {2013},
   Key = {fds219239}
}


%% Hahn, Heekyoung   
@article{fds222818,
   Author = {J. R. Getz and H. Hahn},
   Title = {Algebraic cycles and Tate classes on Hilbert modular
             varieties},
   Journal = {Int. J. Number Theory},
   Volume = {10},
   Number = {1},
   Pages = {161-176},
   Year = {2014},
   Key = {fds222818}
}

@article{fds223470,
   Author = {J. R. Getz and H. Hahn},
   Title = {A general simple relative trace formula and a relative Weyl
             law},
   Year = {2014},
   Key = {fds223470}
}

@article{fds222461,
   Author = {S. Akhtari and C. David and H. Hahn and L. Thompson},
   Title = {Distribution of square-free values of sequences associated
             with elliptic curves},
   Journal = {Contemp. Math.},
   Volume = {606},
   Series = {Women in Numbers 2},
   Pages = {171-188},
   Publisher = {Amer. Math. Soc.},
   Address = {Providence, RI},
   Year = {2013},
   Key = {fds222461}
}


%% Hain, Richard M   
@article{fds223909,
   Author = {Richard Hain},
   Title = {Genus 3 Mapping Class Groups are not Kähler},
   Journal = {Journal of Topology},
   Year = {2014},
   Month = {June},
   ISSN = {1753-8416},
   url = {http://arxiv.org/abs/1305.2052},
   Key = {fds223909}
}

@article{fds223317,
   Author = {Richard Hain},
   Title = {The Hodge-de Rham theory of modular groups},
   Year = {2014},
   Month = {March},
   url = {http://arxiv.org/abs/1403.6443},
   Key = {fds223317}
}

@article{fds223449,
   Author = {Alexandru Dimca and Richard Hain and Stefan Papadima},
   Title = {The abelianization of the Johnson kernel},
   Journal = {Journal of the European Mathematical Society},
   Volume = {16},
   Number = {4},
   Pages = {805-822},
   Year = {2014},
   url = {http://www.ems-ph.org/journals/show_abstract.php?issn=1435-9855&vol=16&iss=4&rank=6},
   Key = {fds223449}
}

@article{fds218754,
   Author = {Richard Hain},
   Title = {Notes on the Universal Elliptic KZB Equation},
   Year = {2013},
   Month = {September},
   url = {http://arxiv.org/abs/1309.0580},
   Key = {fds218754}
}

@article{fds217200,
   Author = {Richard Hain},
   Title = {Normal Functions and the Geometry of Moduli Spaces of
             Curves},
   Volume = {I},
   Pages = {527-578},
   Booktitle = {Handbook of Moduli},
   Publisher = {International Press},
   Editor = {Gavril Farkas and Ian Morrison},
   Year = {2013},
   Month = {March},
   url = {http://arxiv.org/abs/1102.4031},
   Key = {fds217200}
}

@book{fds212861,
   Author = {Benson Farb and Richard Hain and Eduard Looijenga},
   Title = {Moduli Spaces of Riemann Surfaces},
   Series = {IAS/Park City Mathematics Series},
   Publisher = {American Mathematical Society},
   Year = {2013},
   ISBN = {ISBN-13: 978-0-8218-9887-1},
   url = {http://www.ams.org/bookstore-getitem/item=PCMS-20},
   Key = {fds212861}
}

@article{fds217199,
   Author = {Richard Hain},
   Title = {Remarks on non-abelian cohomology of proalgebraic
             groups},
   Journal = {J. Algebraic Geom.},
   Volume = {22},
   Pages = {581-598},
   Year = {2013},
   url = {http://arxiv.org/abs/1009.3662},
   Key = {fds217199}
}


%% Harer, John   
@article{fds221198,
   Author = {Katharine Turner and Yuriy Mileyko and Sayan Mukherjee and John
             Harer},
   Title = {Fréchet Means for Distributions of Persistence
             diagrams},
   Journal = {arXiv:1206.2790},
   Year = {2013},
   Abstract = {Given a distribution ρ on persistence diagrams and
             observations X1,...Xn∼iidρ we introduce an algorithm in
             this paper that estimates a Fr\'echet mean from the set of
             diagrams X1,...Xn. If the underlying measure ρ is a
             combination of Dirac masses ρ=1m∑mi=1δZi then we prove
             the algorithm converges to a local minimum and a law of
             large numbers result for a Fr\'echet mean computed by the
             algorithm given observations drawn iid from ρ. We
             illustrate the convergence of an empirical mean computed by
             the algorithm to a population mean by simulations from
             Gaussian random fields.},
   Key = {fds221198}
}

@article{fds221199,
   Author = {Elizabeth Munch and Paul Bendich and Katharine Turner and Sayan
             Mukherjee, Jonathan Mattingly and John Harer},
   Title = {Probabilistic Fréchet Means and Statistics on
             Vineyards},
   Year = {2013},
   Abstract = {In order to use persistence diagrams as a true statistical
             tool, it would be very useful to have a good notion of mean
             and variance for a set of diagrams. Mileyko and his
             collaborators made the first study of the properties of the
             Fr\'{e}chet mean in (Dp,Wp), the space of persistence
             diagrams equipped with the p-th Wasserstein metric. In
             particular, they showed that the Fr\'{e}chet mean of a
             finite set of diagrams always exists, but is not necessarily
             unique. As an unfortunate consequence, one sees that the
             means of a continuously-varying set of diagrams do not
             themselves vary continuously, which presents obvious
             problems when trying to extend the Fr\'{e}chet mean
             definition to the realm of vineyards. We fix this problem by
             altering the original definition of Fr\'{e}chet mean so that
             it now becomes a probability measure on the set of
             persistence diagrams; in a nutshell, the mean of a set of
             diagrams will be a weighted sum of atomic measures, where
             each atom is itself the (Fr\'{e}chet mean) persistence
             diagram of a perturbation of the input diagrams. We show
             that this new definition defines a (H\"older) continuous
             map, for each k, from (Dp)k→P(Dp), and we present several
             examples to show how it may become a useful statistic on
             vineyards.},
   Key = {fds221199}
}

@article{fds221210,
   Author = {Jose Perea and J. Harer},
   Title = {Sliding Windows and Persistence: An Application of
             Topological Methods to Signal Analysis},
   Journal = {arXiv:1307.6188},
   Year = {2013},
   Abstract = {We develop in this paper a theoretical framework for the
             topological study of time series data. Broadly speaking, we
             describe geometrical and topological properties of sliding
             window (or time-delay) embeddings, as seen through the lens
             of persistent homology. In particular, we show that maximum
             persistence at the point-cloud level can be used to quantify
             periodicity at the signal level, prove structural and
             convergence theorems for the resulting persistence diagrams,
             and derive estimates for their dependency on window size and
             embedding dimension. We apply this methodology to
             quantifying periodicity in synthetic data sets, and compare
             the results with those obtained using state-of-the-art
             methods in gene expression analysis. We call this new method
             SW1PerS which stands for Sliding Windows and 1-dimensional
             Persistence Scoring.},
   Key = {fds221210}
}

@article{fds221197,
   Author = {Christopher N Topp and Anjali S Iyer-Pascuzzi and Jill T Anderson and Cheng-Ruei Lee and Paul R Zurek and Olga Symonova and Ying Zheng and Alexander Bucksch and Yuriy Milyeko and Taras Galkovskyi and Brad
             Moore, John Harer and Herbert Edelsbrunner and Thomas Mitchell
             Olds and Joshua S Weitz and Philip N Benfey},
   Title = {3-dimensional phenotyping of growing root systems combined
             with QTL mapping identifies core regions of the rice genome
             controlling root architecture},
   Journal = {PNAS},
   Year = {2013},
   Abstract = {Identification of genes that control root system
             architecture in crop plants requires innovations that enable
             high-throughput and accurate measurements of root system
             architecture through time. We demonstrate the ability of a
             semiautomated 3D in vivo imaging and digital phenotyping
             pipeline to interrogate the quantitative genetic basis of
             root system growth in a rice biparental mapping population,
             Bala × Azucena. We phenotyped >1,400 3D root models and
             >57,000 2D images for a suite of 25 traits that quantified
             the distribution, shape, extent of exploration, and the
             intrinsic size of root networks at days 12, 14, and 16 of
             growth in a gellan gum medium. From these data we identified
             89 quantitative trait loci, some of which correspond to
             those found previously in soil-grown plants, and provide
             evidence for genetic tradeoffs in root growth allocations,
             such as between the extent and thoroughness of exploration.
             We also developed a multivariate method for generating and
             mapping central root architecture phenotypes and used it to
             identify five major quantitative trait loci (r2 = 24–37%),
             two of which were not identified by our univariate analysis.
             Our imaging and analytical platform provides a means to
             identify genes with high potential for improving root traits
             and agronomic qualities of crops.},
   Key = {fds221197}
}

@article{fds221196,
   Author = {Anastasia Deckard and Ron C. Anafi and John B. Hogenesch and Steven
             B. Haase and John Harer},
   Title = {Design and Analysis of Large-Scale Biological Rhythm
             Studies: A Comparison of Algorithms for Detecting Periodic
             Signals in Biological Data},
   Journal = {PLOS Computational Biology},
   Year = {2013},
   Abstract = {The results of a major year-long DARPA funded project to
             study the performance of a large collection of algorithms
             for finding periodic gene expression.},
   Key = {fds221196}
}

@article{fds221211,
   Author = {J. Perea and A. Deckard and S. Haase and J. Harer},
   Title = {Applications of SWiPerS to the discovery of periodic
             genes},
   Year = {2013},
   Key = {fds221211}
}

@article{fds221202,
   Author = {Sara Bristow and Laura A. Simmons Kovacs and Anastasia Deckard and John Harer and Steven B. Haase},
   Title = {Checkpoint Pathways Couple the CDK-Independent
             Transcriptional Oscillations to Cell Cycle
             Progression},
   Year = {2013},
   Abstract = {A study of how checkpoint pathways control the yeast cell
             cycle, derived from methods of finding periodic genes and
             cell cycle experiments from the Haase Lab.},
   Key = {fds221202}
}


%% Herschlag, Gregory   
@article{fds220747,
   Author = {G. Herschlag and G.J.M. Garcia and B. Button and R. Tarran and B.
             Lindley, B. Reinhardt and T.C. Elston and M.G.
             Forest},
   Title = {A mechanochemical model for auto-regulation of lung airway
             surface layer volume},
   Journal = {Journal of Theoretical Biology},
   Volume = {325},
   Pages = {42-51},
   Year = {2013},
   Month = {May},
   url = {http://www.sciencedirect.com/science/article/pii/S0022519313000489},
   Abstract = {http://www.sciencedirect.com/science/article/pii/S0022519313000489},
   Key = {fds220747}
}


%% Herzog, David P   
@article{fds223339,
   Author = {D.P. Herzog and J.C. Mattingly},
   Title = {Noise-Induced Stabilization of Planar Flows
             I},
   Year = {2014},
   Month = {April},
   url = {http://arxiv.org/pdf/1404.0957v1.pdf},
   Key = {fds223339}
}

@article{fds223340,
   Author = {D.P. Herzog and J.C. Mattingly},
   Title = {Noise-Induced Stabilization of Planar Flows
             II},
   Year = {2014},
   Month = {April},
   url = {http://arxiv.org/pdf/1404.0955v1.pdf},
   Key = {fds223340}
}

@article{fds221189,
   Author = {D.P. Herzog and Nathan Totz},
   Title = {An extension of H\"{o}rmander's hypoellipticity
             theorem},
   Year = {2013},
   Month = {February},
   url = {http://arxiv.org/pdf/1312.3557v1.pdf},
   Abstract = {Motivated by applications to stochastic differential
             equations, an extension of H\"{o}rmander's hypoellipticity
             theorem is proved for second-order degenerate elliptic
             operators with non-smooth coefficients. The main results are
             established using point-wise Bessel kernel estimates and a
             weighted Sobolev inequality of Stein and Weiss. Of
             particular interest is that our results apply to operators
             with quite general first-order terms.},
   Key = {fds221189}
}

@article{fds221190,
   Author = {D.P. Herzog and Marc Ryser and David Sivakoff and Kevin McGoff and Evan
             Myers},
   Title = {Impact of coverage-dependent marginal costs on optimal HPV
             vaccination strategies},
   Year = {2013},
   Month = {February},
   Key = {fds221190}
}


%% Lawlor, David   
@article{fds218102,
   Author = {D. Lawlor and Y. Wang and A. Christlieb},
   Title = {A Multiscale Sub-linear Time Fourier Algorithm for Noisy
             Data},
   Year = {2013},
   Month = {Spring},
   url = {http://arxiv.org/abs/1304.4517},
   Abstract = {We extend the recent sparse Fourier algorithm of (Lawlor,
             Christlieb, and Wang, 2013) to the noisy setting. We present
             two such extensions, the second of which exhibits a novel
             form of error-correction not unlike that of the
             beta-encoders in analog-to-digital conversion (Daubechies et
             al, 2006). The algorithm runs in time O(k log(k) log(N/k))
             on average, provided the noise is not overwhelming. The
             error-correction property allows the algorithm to outperform
             FFTW over a wide range of sparsity and noise values, and is
             to the best of our knowledge novel in the sparse Fourier
             transform context.},
   Key = {fds218102}
}

@article{fds220376,
   Author = {D. Lawlor and Y. Wang and A. Christlieb},
   Title = {Adaptive sub-linear Fourier algorithms},
   Journal = {Advances in Adaptive Data Analysis},
   Volume = {5},
   Number = {1},
   Publisher = {World Scientific},
   Year = {2013},
   Month = {January},
   ISSN = {1793-5369},
   url = {http://arxiv.org/abs/1207.6368},
   Abstract = {We present a new deterministic algorithm for the sparse
             Fourier transform problem, in which we seek to identify k <<
             N significant Fourier coefficients from a signal of
             bandwidth N. Previous deterministic algorithms exhibit
             quadratic runtime scaling, while our algorithm scales
             linearly with k in the average case. Underlying our
             algorithm are a few simple observations relating the Fourier
             coefficients of time-shifted samples to unshifted samples of
             the input function. This allows us to detect when aliasing
             between two or more frequencies has occurred, as well as to
             determine the value of unaliased frequencies. We show that
             empirically our algorithm is orders of magnitude faster than
             competing algorithms.},
   Key = {fds220376}
}


%% Layton, Anita T   
@article{fds223269,
   Author = {Aurelie Edwards and Anita T. Layton},
   Title = {Calcium dynamics underlying the myogenic response of the
             renal afferent arteriole},
   Journal = {Am J Physiol Renal Physiol},
   Volume = {306},
   Number = {F34-F48},
   Year = {2014},
   Key = {fds223269}
}

@article{fds223975,
   Author = {Ioannis Sgouralis and Anita T. Layton},
   Title = {Theoretical assessment of renal autoregulatory
             mechanisms},
   Journal = {Am J Physiol Renal Physiol},
   Volume = {306},
   Pages = {F1357-F1371},
   Year = {2014},
   Key = {fds223975}
}

@article{fds222881,
   Author = {Yi Li and Ioannis Sgouralis and Anita T. Layton},
   Title = {Computing viscous flow in an elastic tube},
   Journal = {Numer. Math. Theor. Meth. Appl., in press},
   Year = {2014},
   Key = {fds222881}
}

@article{fds223235,
   Author = {Robert Moss and Anita T. Layton},
   Title = {Dominant factors that govern pressure natriuresis in
             diuresis and antidiuresis: a mathematical
             model},
   Journal = {Am J Physiol Renal Physiol, in press},
   Year = {2014},
   Key = {fds223235}
}

@article{fds224021,
   Author = {Thomas L. Pannabecker and Anita T. Layton},
   Title = {Targeted delivery of solutes and oxygen in the renal
             medulla: role of microvessel architecture},
   Journal = {Am J Physiol Renal Physiol, in press},
   Year = {2014},
   Key = {fds224021}
}

@article{fds223973,
   Author = {Julia Arcerio and Laura Ellwein and Ashley N. Ford Versypt and Elizabeth Markride and Anita T. Layton},
   Title = {Modeling blood flow in the kidney},
   Journal = {IMA volume, submitted},
   Year = {2014},
   Key = {fds223973}
}

@article{fds223680,
   Author = {Ioannis Sgouralis and Roger Evans and Bruce S. Gardiner and Julian A
             Smith and Brendan C. Fry and Anita T. Layton},
   Title = {Renal hemodynamics, function and oxygenation during cardiac
             Surgery performed on cardiopulmonary bypass: A modeling
             study},
   Journal = {Am J Physiol Renal Physiol, submitted},
   Year = {2014},
   Key = {fds223680}
}

@article{fds223468,
   Author = {Gregory J. Herschlag and Jian-Guo Liu and Anita T.
             Layton},
   Title = {An exact solution for Stokes flow in an in nite channel with
             permeable walls},
   Journal = {J Fluid Mech, submitted},
   Year = {2014},
   Key = {fds223468}
}

@article{fds223291,
   Author = {Brendan C. Fry and Anita T. Layton},
   Title = {Oxygen transport in a cross section of the rat inner
             medulla: Impact of heterogeneous distribution of nephrons
             and vessels},
   Journal = {Math Biosci, submitted},
   Year = {2014},
   Key = {fds223291}
}

@article{fds223679,
   Author = {Aurelie Edwards and Hayo Castrop and Kamel Laghmani and Volker
             Vallon and Anita T. Layton},
   Title = {Regulation of NKCC2 isoform expression and NaCl transport in
             the thick ascending limb and macula densa
             cells},
   Journal = {Am J Physiol Renal Physiol, in press},
   Year = {2014},
   Key = {fds223679}
}

@book{fds223268,
   Author = {Anita T. Layton and Sarah D. Olson},
   Title = {Biological Fluid Dynamics: Modeling, Computation, and
             Applications},
   Journal = {AMS Contemporary Mathematics},
   Year = {2014},
   Key = {fds223268}
}

@article{fds223501,
   Author = {Brendan C. Fry and Aurelie Edward and Ioannis Sgouralis and Anita
             T. Layton},
   Title = {Impact of renal medullary three-dimensional architecture on
             oxygen transport},
   Journal = {Am J Physiol Renal Physiol, in press},
   Year = {2014},
   Key = {fds223501}
}

@article{fds219930,
   Author = {Anta T. Layton},
   Title = {Mathematical modeling of urea transport in the
             kidney},
   Booktitle = {Urea Transporters, in press},
   Publisher = {Springer},
   Editor = {Baoxue Yang},
   Year = {2013},
   Key = {fds219930}
}

@article{fds214468,
   Author = {Karin Leiderman and Elizabeth L. Bouzarth and Ricardo Cortez and Anita T. Layton},
   Title = {A regularization method for the numerical solution of
             periodic Stokes flow},
   Journal = {J Comput Phys},
   Volume = {236},
   Number = {187-202},
   Year = {2013},
   Key = {fds214468}
}

@article{fds216651,
   Author = {Aniel Nieves-Gonzalez and Chris Clausen and Anita .T. Layton and Harold E. Layton and Leon C. Moore},
   Title = {Transport efficiency and workload distribution in a
             mathematical model of the thick ascending
             limb},
   Journal = {Am J Physiol Renal Physiol},
   Volume = {304},
   Number = {F653-F664},
   Year = {2013},
   Key = {fds216651}
}

@article{fds216652,
   Author = {Aniel Nieves-Gonzalez and Chris Clausen and Mariano Marcano and Anita
             .T. Layton and Harold E. Layton and Leon C.
             Moore},
   Title = {Fluid dilution and efficiency of Na+ transport in a
             mathematical model of a thick ascending limb
             cell},
   Journal = {Am J Physiol Renal Physiol},
   Volume = {304},
   Number = {F634-F652},
   Year = {2013},
   Key = {fds216652}
}

@article{fds218841,
   Author = {Anita T. Layton and Lise Bankir},
   Title = {Impacts of active urea secretion into pars recta on urine
             concentrating mechanism},
   Journal = {Physiol Report},
   Volume = {1},
   Number = {3},
   Pages = {e00034},
   Year = {2013},
   Key = {fds218841}
}

@article{fds218844,
   Author = {Hwayeon Ryu and Anita T. Layton},
   Title = {Effect of tubular inhomogeneities on feedback-mediated
             dynamics of a model of a thick ascending
             limb},
   Journal = {Med Math Biol},
   Volume = {30},
   Number = {191-212},
   Year = {2013},
   Key = {fds218844}
}

@article{fds219207,
   Author = {William H. Dantzler and Anita T. Layton and Harold E. Layton and Thomas L. Pannabecker},
   Title = {Urine concentrating mechanism in the inner medulla: function
             of the thin limbs of Henle’s loops},
   Journal = {Clin J Am Soc Nephrol},
   Pages = {doi:10.2215/CJN.08750812},
   Year = {2013},
   Key = {fds219207}
}

@article{fds219490,
   Author = {Yi Li and Sarah A. Williams and Anita T. Layton},
   Title = {A hybrid immersed interface method for driven stokes flow in
             an elastic tube},
   Journal = {Numer. Math. Theor. Meth. Appl.},
   Volume = {6},
   Number = {4},
   Pages = {600-616},
   Year = {2013},
   Key = {fds219490}
}

@article{fds223502,
   Author = {Ioannis Sgouralis and Anita T. Layton},
   Title = {Control and modulation of fluid flow in the rat
             kidney},
   Journal = {Bull Math Biol},
   Volume = {75},
   Pages = {2551-2574},
   Year = {2013},
   Key = {fds223502}
}

@article{fds223236,
   Author = {Sarah D. Olson and Anita T. Layton},
   Title = {Simulating Fluid-Structure Interactions --- A
             Review},
   Journal = {AMS Contemporary Mathematics, Biological Fluid Dynamics:
             Modeling, Computations, and Applications, in
             press},
   Year = {2013},
   Key = {fds223236}
}

@book{fds216729,
   Author = {Anita T. Layton and Aurelie Edwards},
   Title = {Mathematical Modeling of Renal Physiology},
   Series = {Lecture Notes on Mathematical Modelling in the Life
             Sciences},
   Publisher = {Springer},
   Editor = {Angela Stevens and Michael C. Mackey},
   Year = {2013},
   Key = {fds216729}
}

@article{fds218854,
   Author = {Anita T. Layton},
   Title = {Impacts of facilitated urea transporters on the urine
             concentrating mechanism in the rat kidney},
   Journal = {AMS Contemporary Mathematics, Biological Fluid Dynamics:
             Modeling, Computations, and Applications, in
             press},
   Year = {2013},
   Key = {fds218854}
}

@article{fds217955,
   Author = {Hwayeon Ryu and Anita T. Layton},
   Title = {Feedback-mediated dynamics in a model of coupled nephrons
             with compliant short loop of Henle},
   Journal = {AMS Contemporary Mathematics, Biological Fluid Dynamics:
             Modeling, Computations, and Applications, in
             press},
   Year = {2013},
   Key = {fds217955}
}

@article{fds219491,
   Author = {Anita T. Layton},
   Title = {Mathematical modeling of kidney transport},
   Journal = {WIRESs Syst Biol Med},
   Volume = {5},
   Pages = {557-573},
   Year = {2013},
   Key = {fds219491}
}

@article{fds223498,
   Author = {Hwayeon Ryu and Anita T. Layton},
   Title = {Tubular fluid flow and distal NaCl delivery mediated by
             tubuloglomerular feedback in the rat kidney},
   Journal = {J Math Biol},
   Volume = {68},
   Number = {1023–1049},
   Key = {fds223498}
}


%% Liao, Wenjing   
@article{fds223442,
   Author = {W. Liao and A. Fannjiang},
   Title = {MUSIC for single-snapshot spectral estimation: stability and
             super-resolution},
   Year = {2014},
   Key = {fds223442}
}

@article{fds223270,
   Author = {A. Fannjiang and W. Liao},
   Title = {Fourier phasing with phase-uncertain mask},
   Journal = {Inverse problems},
   Volume = {29},
   Number = {12},
   Year = {2013},
   Key = {fds223270}
}


%% Lipnowski, Michael   
@article{fds220725,
   Author = {M. Lipnowski},
   Title = {Equivariant Torsion and Base Change},
   Year = {2013},
   url = {http://arxiv.org/abs/1312.2540},
   Key = {fds220725}
}

@article{fds220726,
   Author = {M. Lipnowski},
   Title = {The Equivariant Cheeger-Müller Theorem on Locally Symmetric
             Spaces},
   Year = {2013},
   url = {http://arxiv.org/abs/1312.2543},
   Key = {fds220726}
}


%% Liu, Jian-Guo   
@article{fds220921,
   Author = {S. Bian and J.-G. Liu and C. Zou},
   Title = {Ultra-contractivity for Keller-Segel model with diffusion
             exponent m>1-2/d},
   Journal = {Kinetic and Related Models},
   Volume = {7},
   Pages = {9-28},
   Year = {2014},
   Key = {fds220921}
}

@article{fds220121,
   Author = {Y. Duan and J.-G. Liu},
   Title = {Convergence analysis of the vortex blob method for the
             b-equation},
   Journal = {Discrete Contin. Dyn. Syst. Ser. A},
   Volume = {34},
   Pages = {1995-2011},
   Year = {2014},
   Key = {fds220121}
}

@article{fds220922,
   Author = {H. Johnston and C. Wang and J.-G. Liu},
   Title = {A local pressure boundary condition spectral collocation
             scheme for the three-dimensional Navier-Stokes
             equations},
   Journal = {J. Sci. Comput.},
   Year = {2013},
   Key = {fds220922}
}

@article{fds220114,
   Author = {X. Chen and J.-G. Liu},
   Title = {Global weak entropy solution to Doi-Saintillan-Shelley model
             for active and passive rod-like and ellipsoidal particle
             suspensions},
   Journal = {J Diff Eqs},
   Volume = {254},
   Pages = {2764-2802},
   Year = {2013},
   Key = {fds220114}
}

@article{fds220115,
   Author = {T. Goudon and S. Jin and J.-G. Liu and B. Yan},
   Title = {Asymptotic-Preserving schemes for kinetic-fluid modeling of
             disperse two-phase flows},
   Journal = {J. Comput. Phy.},
   Volume = {246},
   Pages = {145-164},
   Year = {2013},
   Key = {fds220115}
}

@article{fds220116,
   Author = {X. Chen and J.-G. Liu},
   Title = {Analysis of polymeric flow models and related compactness
             theorems in weighted spaces},
   Journal = {SIAM J Math Anal},
   Volume = {45},
   Pages = {1179-1215},
   Year = {2013},
   Key = {fds220116}
}

@article{fds220117,
   Author = {P. Degond and A. Frouvelle and J.-G. Liu and S Motsch and L
             Navoret},
   Title = {Macroscopic models of collective motion and
             self-organization},
   Journal = {Seminaire Laurent Schwartz -- EDP et applicatios},
   Volume = {2012 - 2013},
   Pages = {1-27},
   Year = {2013},
   Key = {fds220117}
}

@article{fds220118,
   Author = {Y.L. Huang and J.-G. Liu and W.-C. Wang},
   Title = {A generalized MAC scheme on curvilinear domains},
   Journal = {SIAM J. Sci. Comput.},
   Volume = {35},
   Pages = {B953-B986},
   Year = {2013},
   Key = {fds220118}
}

@article{fds220119,
   Author = {P. Degond and J.-G, Liu and S. Motsch and V. Panferov},
   Title = {Hydrodynamic models of self-organized dynamics: derivation
             and existence theory},
   Journal = {Methods Anal. Appl.},
   Volume = {20},
   Pages = {89-114},
   Year = {2013},
   Key = {fds220119}
}

@article{fds220120,
   Author = {S. Bian and J.-G. Liu},
   Title = {Dynamic and steady states for multi-dimensional Keller-Segel
             model with diffusion exponent m > 0},
   Journal = {Comm Math Phy},
   Volume = {323},
   Pages = {1017-1070},
   Year = {2013},
   Key = {fds220120}
}

@article{fds220122,
   Author = {D. Chae and P. Degond and J.-G. Liu},
   Title = {Well-posedness for Hall-magnetohydrodynamics},
   Journal = {Ann. I. H. Poincare, AN},
   Year = {2013},
   Key = {fds220122}
}

@article{fds220123,
   Author = {P. Degond and A. Frouvelle and J.-G. Liu},
   Title = {A note on phase transitions for the Smoluchowski equation
             with dipolar potential},
   Booktitle = {Proceedings of the Fourteenth International Conference on
             Hyperbolic Problems: Theory, Numerics and
             Application},
   Year = {2013},
   Key = {fds220123}
}

@article{fds220124,
   Author = {X. Chen and X. Liu and J.-G. Liu},
   Title = {Existence and uniqueness of global weak solution to a
             kinetic model for the sedimentation of rod-like
             particles},
   Journal = {Commun. Math. Sci.},
   Year = {2013},
   Key = {fds220124}
}

@article{fds220126,
   Author = {P. Degond and J.-G. Liu and C. Ringhofer},
   Title = {Large-scale dynamics of Mean-Field Games driven by local
             Nash equilibria},
   Journal = {J Nonlinear Sci.},
   Year = {2013},
   Key = {fds220126}
}

@article{fds220127,
   Author = {P. Degond and J.-G. Liu and C. Ringhofer},
   Title = {Evolution of the distribution of wealth in an economic
             environment driven by local Nash equilibria},
   Journal = {J. Stat. Phys.},
   Year = {2013},
   Key = {fds220127}
}

@article{fds220128,
   Author = {X. Chen and A. Jungel and J.-G. Liu},
   Title = {A note on Aubin-Lions-Dubinskii lemmas},
   Journal = {Acta Applicanda Mathematicae},
   Year = {2013},
   Key = {fds220128}
}

@article{fds220111,
   Author = {P. Degond and A. Frouvell and J.-G. Liu},
   Title = {Macroscopic limits and phase transition in a system of
             self-propelled particles},
   Journal = {J Nonlinear Sci.},
   Volume = {23},
   Pages = {427-456},
   Year = {2013},
   Key = {fds220111}
}

@article{fds220113,
   Author = {S. Jin and J.-G. Liu and L. Wang},
   Title = {A domain decomposition method for semilinear hyperbolic
             systems with two-scale relaxations},
   Journal = {Math. Comp.},
   Volume = {82},
   Pages = {749-779},
   Year = {2013},
   Key = {fds220113}
}


%% Lu, Jianfeng   
@article{fds223301,
   Author = {J. Lu and Lin Lin and Sihong Shao},
   Title = {Analysis of the time reversible Born-Oppenheimer molecular
             dynamics},
   Journal = {Entropy},
   Volume = {16},
   Pages = {110-137},
   Editor = {G. Ciccotti and M. Ferrario and Ch. Schuette},
   Year = {2014},
   url = {http://dx.doi.org/10.3390/e16010110},
   Doi = {10.3390/e16010110},
   Key = {fds223301}
}

@article{fds223588,
   Author = {J. Lu and Robert V. Kohn and Ben Schweizer and Michael I.
             Weinstein},
   Title = {A variational perspective on cloaking by anomalous localized
             resonance},
   Journal = {Comm. Math. Phys.},
   Volume = {328},
   Number = {1},
   Pages = {1-27},
   Year = {2014},
   url = {http://dx.doi.org/10.1007/s00220-014-1943-y},
   Doi = {10.1007/s00220-014-1943-y},
   Key = {fds223588}
}

@article{fds209290,
   Author = {J. Lu and Felix Otto},
   Title = {Nonexistence of minimizer for Thomas-Fermi-Dirac-von
             Weizsacker model},
   Journal = {Comm. Pure Appl. Math.},
   Year = {2014},
   Key = {fds209290}
}

@article{fds223239,
   Author = {J. Lu and James Nolen},
   Title = {Reactive trajectories and the transition path
             processes},
   Journal = {Probab. Theory Related Fields},
   Year = {2014},
   Key = {fds223239}
}

@article{fds223321,
   Author = {J. Lu and Qin Li and Weiran Sun},
   Title = {A convergent method for linear half-space kinetic
             equation},
   Year = {2014},
   Key = {fds223321}
}

@article{fds223237,
   Author = {J. Lu and Bin Hu},
   Title = {Dynamic production capacity management with price
             skimming},
   Year = {2014},
   Key = {fds223237}
}

@article{fds223256,
   Author = {J. Lu and Rongjie Lai and Stanley Osher},
   Title = {Density matrix minimization with $\ell_1$
             regularization},
   Year = {2014},
   url = {http://arxiv.org/abs/1403.1525},
   Key = {fds223256}
}

@article{fds223238,
   Author = {J. Lu and Haizhao Yang and Lexing Ying},
   Title = {Crystal image analysis using 2D synchrosqueezing
             transforms},
   Year = {2014},
   url = {http://arxiv.org/abs/1402.1262},
   Key = {fds223238}
}

@article{fds224003,
   Author = {J. Lu and Weinan E},
   Title = {Mathematical theory of solids: from quantum mechanics to
             continuum models},
   Journal = {Discret. Contin. Dyn. Sys.},
   Volume = {34},
   Pages = {5085-5097},
   Year = {2014},
   url = {http://dx.doi.org/10.3934/dcds.2014.34.5085},
   Doi = {10.3934/dcds.2014.34.5085},
   Key = {fds224003}
}

@article{fds224002,
   Author = {J. Lu and Eric Vanden-Eijnden},
   Title = {Exact dynamical coarse-graining without time-scale
             separation},
   Journal = {J. Chem. Phys.},
   Year = {2014},
   url = {http://arxiv.org/abs/1404.4225},
   Key = {fds224002}
}

@article{fds223482,
   Author = {J. Lu and Jingchen Liu and Xiang Zhou},
   Title = {Efficient rare event simulation for failure problems in
             random media},
   Year = {2014},
   url = {http://arxiv.org/abs/1404.4729},
   Key = {fds223482}
}

@article{fds223674,
   Author = {J. Lu and Vitaly Moroz and Cyrill B. Muratov},
   Title = {Orbital-free density functional theory of out-of-plane
             charge screening in graphene},
   Year = {2014},
   url = {http://arxiv.org/abs/1405.4949},
   Key = {fds223674}
}

@article{fds223485,
   Author = {J. Lu and Jeremy L. Marzuola},
   Title = {Strang splitting methods for a quasilinear Schrodinger
             equation - convergence, instability and dynamics},
   Journal = {Commun. Math. Sci.},
   Year = {2013},
   Month = {May},
   Key = {fds223485}
}

@article{fds223466,
   Author = {J. Lu and Weinan E and Yuan Yao},
   Title = {The Landscape of Complex Networks -- Critical Nodes and a
             Hierarchical Decomposition},
   Journal = {Methods Appl. Anal.},
   Volume = {20},
   Number = {4},
   Pages = {383--404},
   Year = {2013},
   url = {http://dx.doi.org/10.4310/MAA.2013.v20.n4.a5},
   Doi = {10.4310/MAA.2013.v20.n4.a5},
   Key = {fds223466}
}

@article{fds223300,
   Author = {J. Lu and Sergey Fomel and Xu Yang},
   Title = {Seismic modeling using the frozen Gaussian
             approximation},
   Pages = {4677-4682},
   Booktitle = {SEG Technical Program Expanded Abstracts
             2013},
   Year = {2013},
   url = {http://arxiv.org/abs/1304.3542},
   Key = {fds223300}
}

@article{fds211935,
   Author = {J. Lu and Pingbing Ming},
   Title = {Convergence of a force-based hybrid method for atomistic and
             continuum models in three dimension},
   Journal = {Comm. Pure Appl. Math.},
   Volume = {66},
   Pages = {83-108},
   Year = {2013},
   url = {http://dx.doi.org/10.1002/cpa.21429},
   Doi = {10.1002/cpa.21429},
   Key = {fds211935}
}

@article{fds211936,
   Author = {J. Lu and Weinan E},
   Title = {The Kohn-Sham equation for deformed crystals},
   Journal = {Mem. Amer. Math. Soc.},
   Volume = {221},
   Number = {1040},
   Year = {2013},
   url = {http://dx.doi.org/10.1090/S0065-9266-2012-00659-9},
   Doi = {10.1090/S0065-9266-2012-00659-9},
   Key = {fds211936}
}

@article{fds215935,
   Author = {J. Lu and Eric Vanden-Eijnden},
   Title = {Infinite swapping replica exchange molecular dynamics leads
             to a simple simulation patch using mixture
             potentials},
   Journal = {J. Chem. Phys.},
   Volume = {138},
   Pages = {084105},
   Year = {2013},
   url = {http://dx.doi.org/10.1063/1.4790706},
   Doi = {10.1063/1.4790706},
   Key = {fds215935}
}

@article{fds220491,
   Author = {J. Lu and Weinan E and Xu Yang},
   Title = {Asymptotic analysis of the quantum dynamics: Bloch-Wigner
             transform and Bloch dynamics},
   Journal = {Acta Math. Appl. Sin. Engl. Ser.},
   Volume = {29},
   Pages = {465--476},
   Year = {2013},
   url = {http://dx.doi.org/10.1007/s10255-011-0095-5},
   Doi = {10.1007/s10255-011-0095-5},
   Key = {fds220491}
}


%% Maggioni, Mauro   
@article{fds221112,
   Author = {M. Maggioni},
   Title = {Geometric Estimation of Probability Measures in
             High-Dimensions},
   Journal = {Proc. IEEE Asilomar Conference},
   Year = {2013},
   Month = {November},
   Key = {fds221112}
}

@article{fds221106,
   Author = {M. Iwen and M. Maggioni},
   Title = {Approximation of Points on Low-Dimensional Manifolds Via
             Random Linear Projections},
   Journal = {Inference & Information},
   Volume = {2},
   Year = {2013},
   Month = {February},
   url = {http://dx.doi.org/10.1093/imaiai/iat001},
   Doi = {10.1093/imaiai/iat001},
   Key = {fds221106}
}

@article{fds221105,
   Author = {A. Coppola and B. Wenner and R. Stevens and O. Ilkayeva and M. Maggioni and T. Slotkin and E. Levin and C. Newgard},
   Title = {Branched-chain amino acids alter neurobehavioral function in
             rats},
   Journal = {American Journal of Physiology - Endocrinology and
             Metabolism},
   Volume = {304},
   Number = {4},
   Year = {2013},
   Month = {February},
   url = {http://dx.doi.org/10.1152/ajpendo.00373.2012},
   Doi = {10.1152/ajpendo.00373.2012},
   Key = {fds221105}
}

@article{fds221113,
   Author = {S. Gerber and M. Maggioni},
   Title = {Multiscale dictionaries, transforms, and learning in
             high-dimensions},
   Journal = {Proc. SPIE 8858, Wavelets and Sparsity XV},
   Year = {2013},
   url = {http://dx.doi.org/10.1117/12.2021984},
   Doi = {10.1117/12.2021984},
   Key = {fds221113}
}

@article{fds221121,
   Author = {Kalyani Krishnamurthy and Alex Mrozack and Mauro Maggioni and David Brady},
   Title = {Multiscale, dictionary-based speckle denoising},
   Booktitle = {Proc. Computational Optical Sensing and Imaging},
   Year = {2013},
   ISBN = {978-1-55752-975-6},
   url = {http://dx.doi.org/http://dx.doi.org/10.1364/COSI.2013.CM2C.2},
   Doi = {http://dx.doi.org/10.1364/COSI.2013.CM2C.2},
   Key = {fds221121}
}

@article{fds221122,
   Author = {G. Chen and A.V. Little and M. Maggioni},
   Title = {Multi-Resolution Geometric Analysis for Data in High
             Dimensions},
   Volume = {1},
   Booktitle = {Excursions in Harmonic Analysis},
   Publisher = {Birkhaüser Boston},
   Year = {2013},
   ISBN = {978-0-8176-8375-7},
   url = {http://dx.doi.org/10.1007/978-0-8176-8376-4_13},
   Doi = {10.1007/978-0-8176-8376-4_13},
   Key = {fds221122}
}

@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},
   Institution = {Dept. Comp. Sci., Yale University},
   Year = {2004},
   Key = {CMTech}
}


%% Mattingly, Jonathan C.   
@article{fds223434,
   Author = {J.C. Mattingly and David P. Herzog},
   Title = {Noise-Induced Stabilization of Planar Flows
             II},
   Year = {2014},
   Month = {April},
   url = {http://arxiv.org/abs/1404.0955},
   Key = {fds223434}
}

@article{fds223435,
   Author = {J.C. Mattingly and David P. Herzog},
   Title = {Noise-Induced Stabilization of Planar Flows
             I},
   Year = {2014},
   Month = {April},
   url = {http://arxiv.org/abs/1404.0957},
   Key = {fds223435}
}

@article{fds224075,
   Author = {J.C. Mattingly},
   Title = {Regularity of invariant densities for 1D-systems with random
             switching},
   Year = {2014},
   url = {http://arxiv.org/abs/1406.5425},
   Abstract = {This is a detailed analysis of invariant measures for
             one-dimensional dynamical systems with random switching. In
             particular, we prove smoothness of the invariant densities
             away from critical points and describe the asymptotics of
             the invariant densities at critical points.},
   Key = {fds224075}
}

@article{fds224076,
   Author = {J.C. Mattingly and Sean D. Lawley and Michael C. Reed},
   Title = {Stochastic switching in infinite dimensions with
             applications to random parabolic PDEs},
   Year = {2014},
   url = {http://arxiv.org/abs/1407.2264},
   Abstract = {We consider parabolic PDEs with randomly switching boundary
             conditions. In order to analyze these random PDEs, we
             consider more general stochastic hybrid systems and prove
             convergence to, and properties of, a stationary
             distribution. Applying these general results to the heat
             equation with randomly switching boundary conditions, we
             find explicit formulae for various statistics of the
             solution and obtain almost sure results about its regularity
             and structure. These results are of particular interest for
             biological applications as well as for their significant
             departure from behavior seen in PDEs forced by disparate
             Gaussian noise. Our general results also have applications
             to other types of stochastic hybrid systems, such as ODEs
             with randomly switching right-hand sides.},
   Key = {fds224076}
}

@article{fds224078,
   Author = {Jonathan C. Mattingly and Etienne Pardoux},
   Title = {Invariant measure selection by noise: An
             Example},
   Journal = {Discrete and Continuous Dynamical Systems. Series
             A},
   Volume = {34},
   Number = {10},
   Pages = {4223--4257},
   Year = {2014},
   url = {http://arxiv.org/abs/1403.3593},
   Abstract = {We consider a deterministic system with two conserved
             quantities and infinity many invariant measures. However the
             systems possess a unique invariant measure when enough
             stochastic forcing and balancing dissipation are added. We
             then show that as the forcing and dissipation are removed a
             unique limit of the deterministic system is selected. The
             exact structure of the limiting measure depends on the
             specifics of the stochastic forcing.},
   Key = {fds224078}
}

@article{fds224074,
   Author = {J.C. Mattingly and Sean D. Lawley and Michael C. Reed},
   Title = {Sensitivity to switching rates in stochastically switched
             ODEs},
   Year = {2014},
   url = {http://arxiv.org/abs/1310.2525},
   Abstract = {We consider a stochastic process driven by a linear ordinary
             differential equation whose right-hand side switches at
             exponential times between a collection of different
             matrices. We construct planar examples that switch between
             two matrices where the individual matrices and the average
             of the two matrices are all Hurwitz (all eigenvalues have
             strictly negative real part), but nonetheless the process
             goes to infinity at large time for certain values of the
             switching rate. We further construct examples in higher
             dimensions where again the two individual matrices and their
             averages are all Hurwitz, but the process has arbitrarily
             many transitions between going to zero and going to infinity
             at large time as the switching rate varies. In order to
             construct these examples, we first prove in general that if
             each of the individual matrices is Hurwitz, then the process
             goes to zero at large time for sufficiently slow switching
             rate and if the average matrix is Hurwitz, then the process
             goes to zero at large time for sufficiently fast switching
             rate. We also give simple conditions that ensure the process
             goes to zero at large time for all switching
             rates.},
   Key = {fds224074}
}

@article{fds224077,
   Author = {Thomas Hotz and Sean Skwerer and Stephan Huckemann and Huiling Le and J.
             S. Marron and Jonathan C. Mattingly and Ezra Miller and James Nolen and Megan Owen and Vic Patrangenaru},
   Title = {Sticky central limit theorems on open books},
   Journal = {Ann. Appl. Probab.},
   Volume = {23},
   Number = {6},
   Pages = {2238--2258},
   Year = {2013},
   url = {http://arxiv.org/abs/1202.4267},
   Abstract = {Given a probability distribution on an open book (a metric
             space obtained by gluing a disjoint union of copies of a
             half-space along their boundary hyperplanes), we define a
             precise concept of when the Fr\'{e}chet mean (barycenter) is
             sticky. This nonclassical phenomenon is quantified by a law
             of large numbers (LLN) stating that the empirical mean
             eventually almost surely lies on the (codimension 1 and
             hence measure 0) spine that is the glued hyperplane, and a
             central limit theorem (CLT) stating that the limiting
             distribution is Gaussian and supported on the spine. We also
             state versions of the LLN and CLT for the cases where the
             mean is nonsticky (i.e., not lying on the spine) and partly
             sticky (i.e., is, on the spine but not sticky).},
   Key = {fds224077}
}

@article{fds221260,
   Author = {Elizabeth Munch and Paul Bendich and Katharine Turner and Sayan
             Mukherjee, Jonathan Mattingly and John Harer},
   Title = {Probabilistic Fréchet Means and Statistics on
             Vineyards},
   Year = {2013},
   url = {http://arxiv.org/abs/1307.6530},
   Abstract = {In order to use persistence diagrams as a true statistical
             tool, it would be very useful to have a good notion of mean
             and variance for a set of diagrams. Mileyko and his
             collaborators made the first study of the properties of the
             Fr\'{e}chet mean in (Dp,Wp), the space of persistence
             diagrams equipped with the p-th Wasserstein metric. In
             particular, they showed that the Fr\'{e}chet mean of a
             finite set of diagrams always exists, but is not necessarily
             unique. As an unfortunate consequence, one sees that the
             means of a continuously-varying set of diagrams do not
             themselves vary continuously, which presents obvious
             problems when trying to extend the Fr\'{e}chet mean
             definition to the realm of vineyards. We fix this problem by
             altering the original definition of Fr\'{e}chet mean so that
             it now becomes a probability measure on the set of
             persistence diagrams; in a nutshell, the mean of a set of
             diagrams will be a weighted sum of atomic measures, where
             each atom is itself the (Fr\'{e}chet mean) persistence
             diagram of a perturbation of the input diagrams. We show
             that this new definition defines a (H\"older) continuous
             map, for each k, from (Dp)k→P(Dp), and we present several
             examples to show how it may become a useful statistic on
             vineyards.},
   Key = {fds221260}
}


%% Miller, Ezra   
@article{fds221013,
   Author = {Sean Skwerer and Elizabeth Bullitt and Stephan Huckemann and Ezra
             Miller, Ipek Oguz and Megan Owen and Vic Patrangenaru and Scott
             Provan and J.S. Marron},
   Title = {Tree-oriented analysis of brain artery structure},
   Journal = {Journal of Mathematical Imaging and Vision},
   Year = {2013},
   Abstract = {Statistical analysis of magnetic resonance angiography (MRA)
             brain artery trees is performed using two methods for
             mapping brain artery trees to points in phylogenetic
             treespace: cortical landmark correspondence and descendant
             correspondence. The differences in end results based on
             these mappings are highlighted to emphasize the importance
             of correspondence in tree-oriented data analysis.
             Representation of brain artery systems as points in
             phylogenetic tree space, a mathematical space developed by
             Billera, Holmes, and Vogtmann, facilitates this analysis.
             Phylogenetic tree space is a rich setting for tree-oriented
             data analysis. The Fréchet sample mean or an approximation
             is reported. Multidimensional scaling is used to explore
             structure in the data set based on pairwise distances
             between data points. This analysis of MRA data shows a
             statistically significant effect of age and sex on brain
             artery structure. Variation in the proximity of brain
             arteries to the cortical surface results in strong
             statistical difference between sexes and statistically
             significant age effect. That particular observation is
             possible with cortical correspondence but did not appear in
             the descendant correspondence.},
   Key = {fds221013}
}

@article{fds220838,
   Title = {Affine stratifications from finite misère
             quotients},
   Journal = {Journal of Algebraic Combinatorics},
   Volume = {37},
   Pages = {1-9},
   Year = {2013},
   url = {http://dx.doi.org/10.1007/s10801-012-0355-3},
   Abstract = {Given a morphism from an affine semigroup Q to an arbitrary
             commutative monoid, it is shown that every fiber possesses
             an affine stratification: a partition into a finite disjoint
             union of translates of normal affine semigroups. The proof
             rests on mesoprimary decomposition of monoid congruences
             [arXiv:1107.4699] and a novel list of equivalent conditions
             characterizing the existence of an affine stratification.
             The motivating consequence of the main result is a special
             case of a conjecture due to Guo and the author
             [arXiv:0908.3473, arXiv:1105.5420] on the existence of
             affine stratifications for (the set of winning positions of)
             any lattice game. The special case proved here assumes that
             the lattice game has finite mis&egrave;re quotient, in the
             sense of Plambeck and Siegel [arXiv:math/0501315,
             arXiv:math/0609825v5].},
   Key = {fds220838}
}

@article{fds220839,
   Author = {First Miller and Alan Guo},
   Title = {Algorithms for lattice games},
   Journal = {International Journal of Game Theory},
   Volume = {42},
   Number = {4},
   Pages = {777-788},
   Year = {2013},
   url = {http://dx.doi.org/10.1007/s00182-012-0319-9},
   Abstract = {This paper provides effective methods for the polyhedral
             formulation of impartial finite combinatorial games as
             lattice games. Given a rational strategy for a lattice game,
             a polynomial time algorithm is presented to decide (i)
             whether a given position is a winning position, and to find
             a move to a winning position, if not; and (ii) to decide
             whether two given positions are congruent, in the sense of
             misère quotient theory. The methods are based on the theory
             of short rational generating functions.},
   Key = {fds220839}
}

@article{fds220949,
   Author = {First Miller and Thomas Hotz and Stephan Huckemann and Huiling Le and J. S. Marron and Jonathan C. Mattingly and James Nolen and Megan Owen and Vic
             Patrangenaru and Sean Skwerer},
   Title = {Sticky central limit theorems on open books},
   Journal = {Annals of Applied Probability},
   Volume = {23},
   Number = {6},
   Pages = {2238-2258},
   Year = {2013},
   url = {http://dx.doi.org/10.1214/12-AAP899},
   Abstract = {Given a probability distribution on an open book (a metric
             space obtained by gluing a disjoint union of copies of a
             half-space along their boundary hyperplanes), we define a
             precise concept of when the Fr&eacute;chet mean (barycenter)
             is <i>sticky</i>. This non-classical phenomenon is
             quantified by a law of large numbers (LLN) stating that the
             empirical mean eventually almost surely lies on the
             (codimension 1 and hence measure 0) <i>spine</i> that is the
             glued hyperplane, and a central limit theorem (CLT) stating
             that the limiting distribution is Gaussian and supported on
             the spine. We also state versions of the LLN and CLT for the
             cases where the mean is nonsticky (that is, not lying on the
             spine) and partly sticky (that is, on the spine but not
             sticky).},
   Key = {fds220949}
}

@article{fds220950,
   Author = {First Miller and Manoj Gopalkrishnan and Anne Shiu},
   Title = {A projection argument for differential inclusions, with
             applications to persistence of mass-action
             kinetics},
   Journal = {SIGMA (Symmetry, Integrability, and Geometry: Methods and
             Applications)},
   Volume = {9},
   Year = {2013},
   url = {http://dx.doi.org/10.3842/SIGMA.2013.025},
   Abstract = {Motivated by questions in mass-action kinetics, we introduce
             the notion of <i>vertexical family</i> of differential
             inclusions. Defined on open hypercubes, these families are
             characterized by particular good behavior under projection
             maps. The motivating examples are certain families of
             reaction networks&mdash;including reversible, weakly
             reversible, endotactic, and <i>strongly endotactic</i>
             reaction networks&mdash;that give rise to vertexical
             families of mass-action differential inclusions. We prove
             that vertexical families are amenable to structural
             induction. Consequently, a trajectory of a vertexical family
             approaches the boundary if and only if either the trajectory
             approaches a vertex of the hypercube, or a trajectory in a
             lower-dimensional member of the family approaches the
             boundary. With this technology, we make progress on the
             global attractor conjecture, a central open problem
             concerning mass-action kinetics systems. Additionally, we
             phrase mass-action kinetics as a functor on reaction
             networks with variable rates.},
   Key = {fds220950}
}

@article{fds221011,
   Author = {First Miller and Manoj Gopalkrishnan and Anne Shiu},
   Title = {A geometric approach to the Global Attractor
             Conjecture},
   Journal = {SIADS (SIAM Journal on Applied Dynamical
             Systems)},
   Year = {2013},
   url = {http://arxiv.org/abs/math/1305.5303},
   Abstract = {This paper introduces the class of "strongly endotactic
             networks", a subclass of the endotactic networks introduced
             by G. Craciun, F. Nazarov, and C. Pantea. The main result
             states that the global attractor conjecture holds for
             complex-balanced systems that are strongly endotactic: every
             trajectory with positive initial condition converges to the
             unique positive equilibrium allowed by conservation laws.
             This extends a recent result by D. F. Anderson for systems
             where the reaction diagram has only one linkage class
             (connected component). The results here are proved using
             differential inclusions, a setting that includes power-law
             systems. The key ideas include a perspective on reaction
             kinetics in terms of combinatorial geometry of reaction
             diagrams, a projection argument that enables analysis of a
             given system in terms of systems with lower dimension, and
             an extension of Birch's theorem, a well-known result about
             intersections of affine subspaces with manifolds
             parameterized by monomials.},
   Key = {fds221011}
}


%% Minsker, Stanislav   
@article{fds220272,
   Author = {S. Minsker},
   Title = {Estimation of Extreme Values and Associated Level Sets of a
             Regression Function via Selective Sampling},
   Journal = {In Proceedings of the Conference on Learning Theory (COLT
             2013)},
   Pages = {105-121},
   Year = {2013},
   url = {http://jmlr.org/proceedings/papers/v30/Minsker13.html},
   Abstract = {We propose a new method for estimating the locations and the
             value of an absolute maximum (minimum) of a function from
             the observations contaminated by random noise. Our goal is
             to solve the problem under minimal regularity and shape
             constraints. In particular, we do not assume
             differentiability of a function nor that its maximum is
             attained at a single point. We provide tight upper and lower
             bounds for the performance of proposed estimators. Our
             method is adaptive with respect to the unknown parameters of
             the problem over a large class of underlying
             distributions.},
   Key = {fds220272}
}

@article{fds220270,
   Author = {V. Koltchinskii and S. Minsker},
   Title = {L1-Penalization in Functional Linear Regression with
             Subgaussian Design},
   Journal = {Submitted},
   Year = {2013},
   url = {http://arxiv.org/abs/1307.8137},
   Abstract = {We study functional regression with random subgaussian
             design and real-valued response. The focus is on the
             problems in which the regression function can be well
             approximated by a functional linear model with the slope
             function being "sparse" in the sense that it can be
             represented as a sum of a small number of well separated
             "spikes". This can be viewed as an extension of now
             classical sparse estimation problems to the case of infinite
             dictionaries. We study an estimator of the regression
             function based on penalized empirical risk minimization with
             quadratic loss and the complexity penalty defined in terms
             of L1-norm (a continuous version of LASSO). The main goal is
             to introduce several important parameters characterizing
             sparsity in this class of problems and to prove sharp oracle
             inequalities showing how the L2-error of the continuous
             LASSO estimator depends on the underlying sparsity of the
             problem.},
   Key = {fds220270}
}

@article{fds220271,
   Author = {S. Minsker},
   Title = {Geometric Median and Robust Estimation in Banach
             Spaces},
   Year = {2013},
   url = {http://arxiv.org/abs/1308.1334},
   Abstract = {In many real-world applications, collected data is
             contaminated by the noise with heavy-tailed distribution and
             might contain outliers of large magnitude. In this
             situation, it is necessary to apply methods which produce
             reliable outcomes even if the input contains corrupted
             measurements. We describe a general method which allows one
             to obtain estimators with tight concentration around the
             true parameter of interest taking values in a Banach space.
             Suggested construction relies on the fact that the geometric
             median of a collection of independent "weakly concentrated"
             estimators satisfies a much stronger deviation bound than
             each individual element in the collection. Our approach is
             illustrated through several examples, including sparse
             linear regression and low-rank matrix recovery
             problems.},
   Key = {fds220271}
}


%% Moss, Robert   
@article{fds219949,
   Author = {R. Moss and S. R. Thomas},
   Title = {Hormonal regulation of salt and water excretion: a
             mathematical model of whole-kidney function and
             pressure-natriuresis},
   Journal = {AJP Renal Physiol},
   Year = {2013},
   url = {http://ajprenal.physiology.org/content/early/2013/10/03/ajprenal.00089.2013},
   Abstract = {We present a lumped-nephron model that explicitly represents
             the main features of the underlying physiology,
             incorporating the major hormonal regulatory effects on both
             tubular and vascular function, and which accurately
             simulates hormonal regulation of renal salt and water
             excretion. This is the first model to explicitly couple
             glomerulovascular and medullary dynamics, and it is much
             more detailed in structure than existing whole-organ models
             and renal portions of multi-organ models. In contrast to
             previous medullary models, which have only considered the
             antidiuretic state, our model is able to regulate water and
             sodium excretion over a variety of experimental conditions
             in good agreement with data from experimental studies of the
             rat. Since the properties of the vasculature and epithelia
             are explicitly represented, they can be altered to simulate
             pathophysiological conditions and pharmacological
             interventions. The model serves as an appropriate starting
             point for simulations of physiological, pathophysiological
             and pharmacological renal conditions, and for exploring the
             relationship between the extra-renal environment and renal
             excretory function in physiological and pathophysiological
             contexts.},
   Doi = {10.1152/ajprenal.00089.2013},
   Key = {fds219949}
}


%% Ng, Lenhard L   
@article{fds223315,
   Author = {L. Ng},
   Title = {A topological introduction to knot contact
             homology},
   Booktitle = {Contact and Symplectic Topology},
   Editor = {F. Bourgeois and V. Colin and A. Stipsicz},
   Year = {2014},
   ISBN = {978-3-319-02035-8},
   url = {http://dx.doi.org/10.1007/978-3-319-02036-5_10},
   Doi = {10.1007/978-3-319-02036-5_10},
   Key = {fds223315}
}

@article{fds218592,
   Author = {T. Ekholm and L. Ng},
   Title = {Legendrian contact homology in the boundary of a subcritical
             Weinstein 4-manifold},
   Year = {2013},
   url = {http://arxiv.org/abs/1307.8436},
   Key = {fds218592}
}

@article{fds218591,
   Author = {L. Ng and D. Rutherford},
   Title = {Satellites of Legendrian knots and representations of the
             Chekanov-Eliashberg algebra},
   Journal = {Algebraic & Geometric Topology},
   Volume = {13},
   Number = {5},
   Pages = {3047–3097},
   Year = {2013},
   url = {http://dx.doi.org/10.2140/agt.2013.13.3047},
   Doi = {10.2140/agt.2013.13.3047},
   Key = {fds218591}
}

@article{fds217173,
   Author = {W. Chongchitmate and L. Ng},
   Title = {An atlas of Legendrian knots},
   Journal = {Experimental Mathematics},
   Volume = {22},
   Number = {1},
   Pages = {26-37},
   Year = {2013},
   url = {http://dx.doi.org/10.1080/10586458.2013.750221},
   Doi = {10.1080/10586458.2013.750221},
   Key = {fds217173}
}

@article{fds217174,
   Author = {J. Etnyre and L. Ng and V. Vertesi},
   Title = {Legendrian and transverse twist knots},
   Journal = {Journal of the European Mathematical Society},
   Volume = {15},
   Number = {3},
   Pages = {451-512},
   Year = {2013},
   url = {http://dx.doi.org/10.4171/JEMS/383},
   Doi = {10.4171/JEMS/383},
   Key = {fds217174}
}

@article{fds217175,
   Author = {T. Ekholm and J. Etnyre and L. Ng and M. Sullivan},
   Title = {Filtrations on the knot contact homology of transverse
             knots},
   Journal = {Mathematische Annalen},
   Volume = {355},
   Number = {4},
   Pages = {1561-1691},
   Year = {2013},
   url = {http://dx.doi.org/10.1007/s00208-012-0832-y},
   Doi = {10.1007/s00208-012-0832-y},
   Key = {fds217175}
}

@article{fds217177,
   Author = {T. Ekholm and J. Etnyre and L. Ng and M. Sullivan},
   Title = {Knot contact homology},
   Journal = {Geometry & Topology},
   Volume = {17},
   Pages = {975-1112},
   Year = {2013},
   url = {http://dx.doi.org/10.2140/gt.2013.17.975},
   Doi = {10.2140/gt.2013.17.975},
   Key = {fds217177}
}

@article{fds218616,
   Author = {M. Aganagic and T. Ekholm and L. Ng and C. Vafa},
   Title = {Topological strings, D-model, and knot contact
             homology},
   Year = {2013},
   url = {http://arxiv.org/abs/1304.5778},
   Key = {fds218616}
}

@article{fds223316,
   Author = {R. Lipshitz and L. Ng and S. Sarkar},
   Title = {On transverse invariants from Khovanov homology},
   Journal = {Quantum Topology},
   Year = {2013},
   url = {http://arxiv.org/abs/1303.6371},
   Key = {fds223316}
}


%% Nolen, James   
@article{fds223681,
   Author = {J. Lu and J. Nolen},
   Title = {Reactive trajectories and the transition path
             process.},
   Journal = {Probability Theory and Related Fields},
   Year = {2014},
   Month = {January},
   url = {http://arxiv.org/abs/1303.1744},
   Doi = {10.1007/s00440-014-0547-y},
   Key = {fds223681}
}

@article{fds218100,
   Author = {J. Nolen},
   Title = {Normal approximation for a random elliptic
             equation},
   Journal = {Probability Theory and Related Fields},
   Volume = {159},
   Number = {3},
   Pages = {661-700},
   Year = {2014},
   url = {http://math.duke.edu/~nolen/preprints/ellipfluctper_rev.pdf},
   Doi = {10.1007/s00440-013-0517-9},
   Key = {fds218100}
}

@article{fds223716,
   Author = {J. Nolen},
   Title = {Normal approximation for the net flux through a random
             conductor},
   Year = {2014},
   url = {http://arxiv.org/abs/1406.2186},
   Key = {fds223716}
}

@article{fds216732,
   Author = {F. Hamel and J. Nolen and J.-M. Roquejoffre and L.
             Ryzhik},
   Title = {A short proof of the logarithmic Bramson correction in
             Fisher-KPP equations},
   Journal = {Networks and Heterogeneous Media},
   Volume = {8},
   Number = {1},
   Pages = {275-289},
   Year = {2013},
   url = {http://math.duke.edu/~nolen/preprints/hnrr1_submit.pdf},
   Doi = {doi:10.3934/nhm.2013.8.275},
   Key = {fds216732}
}

@article{fds219489,
   Author = {T. Hotz and S. Huckemann and H. Le and J. Marron and J. Mattingly and E.
             Miller, J. Nolen and M. Owen and V. Patrangenaru and S.
             Skwere},
   Title = {Sticky central limit theorem on open books},
   Journal = {Annals of Applied Probability},
   Volume = {23},
   Number = {6},
   Pages = {2238-2258},
   Year = {2013},
   url = {http://arxiv.org/abs/1202.4267},
   Doi = {doi:10.1214/12-AAP899},
   Key = {fds219489}
}

@article{fds217615,
   Author = {J. Nolen and J.-M. Roqujoffre and L. Ryzhik},
   Title = {Power-like delay in time inhomogeneous Fisher-KPP
             equations},
   Year = {2013},
   url = {http://math.duke.edu/~nolen/preprints/bigdelay-draft.pdf},
   Key = {fds217615}
}

@article{fds215981,
   Author = {S. Bhamidi and J. Hannig and C. Lee and J. Nolen},
   Title = {The importance sampling technique for understanding rare
             events in Erdős-Rényi random graphs},
   Year = {2013},
   url = {http://arxiv.org/abs/1302.6551},
   Key = {fds215981}
}


%% Patel, Mainak   
@article{fds218652,
   Author = {M. Patel and B. Joshi},
   Title = {Decoding synchronized oscillations within the brain:
             Phase-delayed inhibition provides a robust mechanism for
             creating a sharp synchrony filter},
   Journal = {Journal of Theoretical Biology},
   Volume = {334C},
   Pages = {13-25},
   Year = {2013},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/23747525},
   Abstract = {The widespread presence of synchronized neuronal
             oscillations within the brain suggests that a mechanism must
             exist that is capable of decoding such activity. Two
             realistic designs for such a decoder include: (1) a read-out
             neuron with a high spike threshold, or (2) a phase-delayed
             inhibition network motif. Despite requiring a more elaborate
             network architecture, phase-delayed inhibition has been
             observed in multiple systems, suggesting that it may provide
             inherent advantages over simply imposing a high spike
             threshold. In this work, we use a computational and
             mathematical approach to investigate the efficacy of the
             phase-delayed inhibition motif in detecting synchronized
             oscillations. We show that phase-delayed inhibition is
             capable of creating a synchrony detector with sharp
             synchrony filtering properties that depend critically on the
             time course of inputs. Additionally, we show that
             phase-delayed inhibition creates a synchrony filter that is
             far more robust than that created by a high spike
             threshold.},
   Key = {fds218652}
}

@article{fds218653,
   Author = {M. Patel and B. Joshi},
   Title = {Switching mechanisms and bout times in a pair of
             reciprocally inhibitory neurons},
   Journal = {Journal of Computational Neuroscience [ePub ahead of
             print]},
   Year = {2013},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/23820857},
   Abstract = {Within the appropriate parameter regime, a deterministic
             model of a pair of mutually inhibitory neurons receiving
             excitatory driving currents exhibits bistability-each of the
             two stable states corresponds to one neuron being active and
             the other being quiescent. The presence of noise in the
             driving currents results in a system that randomly switches
             back and forth between these two states, causing alternating
             bouts of spiking activity. In this work, we examine the
             random bout durations of the two neurons and dependence on
             system parameters. We find that bout durations of each
             neuron are exponentially distributed, with changes in system
             parameters altering only the mean of the distribution.
             Synaptic inhibition independently controls the bout
             durations of the two neurons-the mean bout time of a neuron
             is a function of efferent (or outgoing) inhibition, and is
             independent of afferent (or incoming) inhibition.
             Furthermore, we find that the mean bout time of a neuron
             exhibits a critical dependence on the time course (rather
             than amplitude) of efferent inhibition-mean bout time of a
             neuron grows exponentially with the time course of efferent
             inhibition, and the growth rate of this exponential function
             depends only on the excitatory driving current to that
             neuron (and not on any other system parameters). We discuss
             the relevance of our results to the regulation of sleep-wake
             cycling by medullary and pontine structures within the
             brain.},
   Key = {fds218653}
}

@article{fds217324,
   Author = {M. Patel},
   Title = {Stimulus encoding within the barn owl optic tectum using
             gamma oscillations vs. spike rate: A modeling
             approach.},
   Journal = {Network},
   Volume = {24},
   Number = {2},
   Pages = {52-74},
   Year = {2013},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/23406211},
   Abstract = {The optic tectum of the barn owl is a multimodal structure
             with multiple layers, with each layer topographically
             organized according to spatial receptive field. The response
             of a site to a stimulus can be measured as either spike rate
             or local field potential (LFP) gamma (25-90 Hz) power;
             within superficial layers, spike rate and gamma power
             spatial tuning curves are narrow and contrast-response
             functions rise slowly. Within deeper layers, however, spike
             rate tuning curves broaden and gamma power contrast-response
             functions sharpen. In this work, we employ a computational
             model to describe the inputs required to generate these
             transformations from superficial to deep layers and show
             that gamma power and spike rate can act as parallel
             information processing streams.},
   Key = {fds217324}
}

@article{fds217323,
   Author = {B. Joshi and M. Patel},
   Title = {Encoding with synchrony: Phase-delayed inhibition allows for
             reliable and specific stimulus detection.},
   Journal = {Journal of Theoretical Biology},
   Volume = {328},
   Pages = {26-32},
   Year = {2013},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/23524360},
   Abstract = {Synchronized oscillations are observed in a diverse array of
             neuronal systems, suggesting that synchrony represents a
             common mechanism used by the brain to encode and relay
             information. Coherent population activity can be deciphered
             by a decoder neuron with a high spike threshold or by a
             decoder using phase-delayed inhibition. These two mechanisms
             are fundamentally different - a high spike threshold detects
             a minimum number of synchronous input spikes (absolute
             synchrony), while phase-delayed inhibition requires a fixed
             fraction of incoming spikes to be synchronous (relative
             synchrony). We show that, in a system with noisy encoders
             where stimuli are encoded through synchrony, phase-delayed
             inhibition enables the creation of a decoder that can
             respond both reliably and specifically to a stimulus, while
             a high spike threshold does not.},
   Key = {fds217323}
}

@article{fds217322,
   Author = {M. Patel and AV Rangan and D Cai},
   Title = {Coding of odors by temporal binding within a model network
             of the locust antennal lobe.},
   Journal = {Frontiers in Computational Neuroscience},
   Volume = {7},
   Pages = {50-67},
   Year = {2013},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/23630495},
   Abstract = {The locust olfactory system interfaces with the external
             world through antennal receptor neurons (ORNs), which
             represent odors in a distributed, combinatorial manner. ORN
             axons bundle together to form the antennal nerve, which
             relays sensory information centrally to the antennal lobe
             (AL). Within the AL, an odor generates a dynamically
             evolving ensemble of active cells, leading to a
             stimulus-specific temporal progression of neuronal spiking.
             This experimental observation has led to the hypothesis that
             an odor is encoded within the AL by a dynamically evolving
             trajectory of projection neuron (PN) activity that can be
             decoded piecewise to ascertain odor identity. In order to
             study information coding within the locust AL, we developed
             a scaled-down model of the locust AL using
             Hodgkin-Huxley-type neurons and biologically realistic
             connectivity parameters and current components. Using our
             model, we examined correlations in the precise timing of
             spikes across multiple neurons, and our results suggest an
             alternative to the dynamic trajectory hypothesis. We propose
             that the dynamical interplay of fast and slow inhibition
             within the locust AL induces temporally stable correlations
             in the spiking activity of an odor-dependent neural subset,
             giving rise to a temporal binding code that allows rapid
             stimulus detection by downstream elements.},
   Key = {fds217322}
}


%% Perea, Jose A.   
@article{fds223841,
   Author = {Jose A. Perea and Anastasia Deckard and Steve B. Haase and John
             Harer},
   Title = {SW1PerS: Sliding Windows and 1-Persistence Scoring;
             Discovering Periodicity in Gene Expression Time Series
             Data},
   Year = {2014},
   Month = {June},
   Key = {fds223841}
}

@article{fds223454,
   Author = {Jose A. Perea and John Harer},
   Title = {Sliding Windows and Persistence: An Application of
             Topological Methods to Signal Analysis},
   Journal = {Foundations of Computational Mathematics},
   Year = {2014},
   Month = {May},
   ISSN = {1615-3375},
   url = {http://dx.doi.org/10.1007/s10208-014-9206-z},
   Doi = {10.1007/s10208-014-9206-z},
   Key = {fds223454}
}

@article{fds223453,
   Author = {Jose A. Perea and Gunnar Carlsson},
   Title = {A Klein-Bottle-Based Dictionary for Texture
             Representation},
   Journal = {International Journal of Computer Vision},
   Volume = {107},
   Number = {1},
   Pages = {75-97},
   Year = {2014},
   Month = {March},
   ISSN = {0920-5691},
   url = {http://dx.doi.org/10.1007/s11263-013-0676-2},
   Doi = {10.1007/s11263-013-0676-2},
   Key = {fds223453}
}


%% Petters, Arlie O   
@book{fds15387,
   Author = {A. O. Petters and M. C. Werner},
   Title = {Gravitational Lensing and Black Holes},
   Publisher = {Springer, in preparation},
   Year = {2015},
   Month = {July},
   Key = {fds15387}
}

@book{fds51036,
   Author = {A. O. Petters and X. Dong},
   Title = {Mathematical Finance with Applications: Understanding and
             Buiding Financial Intuition},
   Series = {SUMAT},
   Publisher = {Springer, in preparation},
   Year = {2014},
   Month = {July},
   Key = {fds51036}
}


%% Reed, Michael C   
@article{fds221130,
   Author = {L. Rios-Avila and H. F. Nijhout and M. C. Reed and H. S. Sitren and J.
             F. Gregory III},
   Title = {A mathematical model of tryptophan metabolism via the
             kynurenine pathway provides insights into the effects of
             vitamin B-6 deficiency, tryptophan loading and induction of
             tryptophan 2,3-dioxygenase on tryptophan
             metabolites},
   Journal = {J. Nutrition},
   Volume = {143},
   Pages = {1509-1519},
   Year = {2013},
   Key = {fds221130}
}

@article{fds221131,
   Author = {M. Reed and H. F. Nijhout and J. Best},
   Title = {Computational studies of the role of serotonin in the basal
             ganglia},
   Journal = {Frontiers in Integrative Neuroscience},
   Volume = {7},
   Pages = {1-8},
   Year = {2013},
   Key = {fds221131}
}

@article{fds221133,
   Author = {T. Duncan and M. Reed and H. F. Nijhout},
   Title = {A population model of folate-mediated one-carbon
             metabolism},
   Journal = {Nutrients},
   Volume = {5},
   Pages = {2457-2474},
   Year = {2013},
   Key = {fds221133}
}

@article{fds221135,
   Author = {M. Reed and H. F. Nijhout and J. Best},
   Title = {Projecting biochemistry over long distances},
   Journal = {Math. Models Natural Phenomena},
   Year = {2013},
   Key = {fds221135}
}

@article{fds221136,
   Author = {S. Lawley and J. Mattingly and M. Reed},
   Title = {Sensitivity to switching rates on stochastically switched
             ODEs},
   Year = {2013},
   Key = {fds221136}
}

@article{fds212606,
   Author = {T. Duncan and M. Reed and H. F. Nijhout},
   Title = {The relationship between intracellular and plasma levels of
             folate and metabolites in the methionine cycle: A
             model},
   Journal = {Mol. Food Nutr. Res.},
   Volume = {DOI 10.1002/mnfr.201200125},
   Pages = {628-636},
   Year = {2013},
   Key = {fds212606}
}

@article{fds221124,
   Author = {R. Ben-Shachar and Y, Chen and S. Luo and C. Hartman and M. Reed and H. F.
             Nijhout},
   Title = {The biochemistry of acetaminophen hepatotoxicity and rescue:
             a mathematical model},
   Journal = {Theoretical Biology and Medical Modeling},
   Volume = {9},
   Pages = {1-22},
   Year = {2013},
   Key = {fds221124}
}

@article{fds221127,
   Author = {M. Patel and M. Reed},
   Title = {Stimulus Encoding Within the Barn Owl Optic Tectum Using
             Gamma Oscillations versus Spike Rate: A Modeling
             Approach.},
   Journal = {Network},
   Volume = {24},
   Pages = {52-74},
   Year = {2013},
   Key = {fds221127}
}


%% Ryser, Marc D   
@article{fds221213,
   Author = {S. Payne and B. Li and Y. Cao and D. Schaeffer and M.D. Ryser and L.
             You},
   Title = {Temporal control of self-organized pattern formation without
             morphogen gradients in bacteria},
   Journal = {Molecular Systems Biology},
   Volume = {9},
   Number = {697},
   Year = {2013},
   Key = {fds221213}
}

@article{fds221214,
   Author = {J. Foo and K. Leder and M.D. Ryser},
   Title = {Multifocality and recurrence risk: a quantitative model of
             field cancerization},
   Year = {2013},
   Key = {fds221214}
}

@article{fds221216,
   Author = {M.D. Ryser and K. McGoff and D. Herzog and D. Sivakoff and E.
             Myers},
   Title = {Impact of coverage-dependent marginal costs on optimal HPV
             vaccination strategies},
   Year = {2013},
   Key = {fds221216}
}

@book{fds215731,
   Author = {M.D. Ryser and S.V. Komarova},
   Title = {Mathematical modeling of cancer metastases},
   Booktitle = {Computational Bioengineering},
   Publisher = {CRC/Taylor & Francis},
   Key = {fds215731}
}


%% Schoen, Chad   
@article{fds218712,
   Author = {C. Schoen},
   Title = {Invariants of regular models of the product of two elliptic
             curves at a place of multiplicative reduction},
   Series = {Fields Institute Communications 67},
   Pages = {461-487},
   Booktitle = {Arithmetic and Geometry of K3 surfaces and Calabi-Yau
             Threefolds},
   Publisher = {Springer},
   Editor = {Laza, R. and Schuett, M and and Yui, N.},
   Year = {2013},
   ISBN = {978-1-4614-6402-0},
   Key = {fds218712}
}

@article{fds215558,
   Author = {C. Schoen},
   Title = {The geometric genus of a desingularized fiber product of
             elliptic surfaces},
   Journal = {Proceedings of the American Mathematical
             Society},
   Volume = {141},
   Number = {3},
   Pages = {745-752},
   Year = {2013},
   Key = {fds215558}
}

@article{fds216477,
   Author = {C. Schoen},
   Title = {Torsion in the Cohomology of Desingularized Fiber Products
             of Elliptic Surfaces},
   Journal = {Michigan Math. J.},
   Volume = {62},
   Pages = {81-115},
   Year = {2013},
   Key = {fds216477}
}


%% Schott, Sarah   
@article{fds220537,
   Author = {Mark Huber, and Sarah Schott},
   Title = {Random Construction of Interpolating Sets for High
             Dimensional Integration},
   Journal = {Journal of Applied Probability},
   Year = {2013},
   Key = {fds220537}
}


%% Stern, Mark A   
@article{fds219287,
   Author = {Anda Degeratu and M.A. Stern},
   Title = {Witten spinors on nonspin manifolds},
   Journal = {Communications of Mathematical Physics 2013},
   Year = {2013},
   Month = {October},
   url = {http://xxx.lanl.gov/abs/1112.0194},
   Abstract = {Motivated by Witten's spinor proof of the positive mass
             theorem, we analyze asymptotically constant harmonic spinors
             on complete asymptotically flat nonspin manifolds with
             nonnegative scalar curvature.},
   Key = {fds219287}
}

@article{fds199121,
   Author = {B. Charbonneau and M. Stern},
   Title = {Asymptotic Hodge Theory of Vector Bundles},
   Journal = {Communications in Analysis and Geometry},
   Year = {2013},
   Month = {August},
   url = {http://xxx.lanl.gov/abs/1111.0591},
   Abstract = {We introduce several families of filtrations on the space of
             vector bundles over a smooth projective variety. These
             filtrations are defined using the large k asymptotics of the
             kernel of the Dolbeault Dirac operator on a bundle twisted
             by the kth power of an ample line bundle. The filtrations
             measure the failure of the bundle to admit a holomorphic
             structure. We study compatibility under the Chern
             isomorphism of these filtrations with the Hodge filtration
             on cohomology.},
   Key = {fds199121}
}


%% Strawn, Nathaniel K   
@article{fds220457,
   Author = {J. Cahill and D. Mixon and N. Strawn},
   Title = {Connectivity and Irreducibility of Algebraic Varieties of
             Finite Unit Norm Tight Frames},
   Year = {2013},
   Key = {fds220457}
}

@article{fds220455,
   Author = {A. Armagan and D. Dunson and J. Lee and W. Bajwa and N.
             Strawn},
   Title = {Posterior consistency in linear models under shrinkage
             priors},
   Journal = {Biometrika},
   Year = {2013},
   Key = {fds220455}
}


%% Thompson, Andrew   
@article{fds220947,
   Author = {C. Cartis and A. Thompson},
   Title = {An exact tree projection algorithm for wavelets},
   Journal = {IEEE Signal Processing Letters},
   Volume = {20},
   Number = {11},
   Pages = {1028-1031},
   Year = {2013},
   Key = {fds220947}
}


%% 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{fds220956,
   Author = {Oscar P. Bruno and Stephen P. Shipman and Catalin Turc and Stephanos
             Venakides},
   Title = {Efficient Evaluation of Doubly Periodic Green Functions in
             3D Scattering, Including Wood Anomaly Frequencies},
   Journal = {ArXiv>Mathematics > Analysis of PDEs},
   Year = {2013},
   Month = {July},
   url = {http://arxiv.org/abs/1307.1176},
   Abstract = {We present efficient methods for computing wave scattering
             by diffraction gratings that exhibit two-dimensional
             periodicity in three dimensional (3D) space. Applications
             include scattering in acoustics, electromagnetics and
             elasticity. Our approach uses boundary-integral equations.
             The quasi-periodic Green function is a doubly infinite sum
             of scaled 3D free-space outgoing Helmholtz Green functions.
             Their source points are located at the nodes of a
             periodicity lattice of the grating. For efficient numerical
             computation of the lattice sum, we employ a smooth
             truncation. Super-algebraic convergence to the Green
             function is achieved as the truncation radius increases,
             except at frequency-wavenumber pairs at which a Rayleigh
             wave is at exactly grazing incidence to the grating. At
             these "Wood frequencies", the term in the Fourier series
             representation of the Green function that corresponds to the
             grazing Rayleigh wave acquires an infinite coefficient and
             the lattice sum blows up. At Wood frequencies, we modify the
             Green function by adding two types of terms to it. The first
             type adds weighted spatial shifts of the Green function to
             itself with singularities below the grating; this yields
             algebraic convergence. The second-type terms are
             quasi-periodic plane wave solutions of the Helmholtz
             equation. They reinstate (with controlled coefficients) the
             grazing modes, effectively eliminated by the terms of first
             type. These modes are needed in the Green function for
             guaranteeing the well-posedness of the boundary-integral
             equation that yields the scattered field. We apply this
             approach to acoustic scattering by a doubly periodic 2D
             grating near and at Wood frequencies and scattering by a
             doubly periodic array of scatterers away from Wood
             frequencies.},
   Key = {fds220956}
}

@article{fds221201,
   Author = {Jackson AD and Huang D and Gauthier DJ and Venakides
             S.},
   Title = {Destructive impact of imperfect beam collimation in
             extraordinary optical transmission.},
   Journal = {J. Opt. Soc. Am A},
   Volume = {30},
   Number = {6},
   Pages = {1281-1290},
   Year = {2013},
   Month = {June},
   Abstract = {We investigate the difference between analytic predictions,
             numerical simulations, and experiments measuring the
             transmission of energy through subwavelength, periodically
             arranged holes in a metal film. At normal incidence, theory
             predicts a sharp transmission minimum when the wavelength is
             equal to the periodicity, and sharp transmission maxima at
             one or more nearby wavelengths. In experiments, the sharpest
             maximum from the theory is not observed, while the others
             appear less sharp. In numerical simulations using commercial
             electromagnetic field solvers, we find that the sharpest
             maximum appears and approaches our predictions as the
             computational resources are increased. To determine possible
             origins of the destruction of the sharp maximum, we
             incorporate additional features in our model. Incorporating
             imperfect conductivity and imperfect periodicity in our
             model leaves the sharp maximum intact. Imperfect
             collimation, on the other hand, incorporated into the model
             causes the destruction of the sharp maximum as happens in
             experiments. We provide analytic support through an
             asymptotic calculation for both the existence of the sharp
             maximum and the destructive impact of imperfect collimation.
             © 2013 Optical Society of America},
   Key = {fds221201}
}

@article{fds220953,
   Author = {S. Belov and S. Venakides},
   Title = {Smooth parametric dependence of asymptotics of the
             semiclassical focusing NLS},
   Journal = {APDE (Analysis and PDE)},
   Year = {2013},
   Abstract = {We consider the one dimensional focusing (cubic) Nonlinear
             Schrodinger equation (NLS) in the semiclassical limit with
             a one parameter family of exponentially decaying in absolute
             value initial conditions. We prove smooth parametric
             dependence of the asymptotic solution on the parameter
             utilizing the Riemann-Hilbert approach. Nu- merical
             computations supporting our estimates of important
             quantities are presented.},
   Key = {fds220953}
}


%% Wang, Yi (Grace)   
@article{fds221742,
   Author = {Y. Wang},
   Title = {K mappings and regression trees},
   Year = {2013},
   Month = {October},
   Key = {fds221742}
}


%% Witelski, Thomas P.   
@article{fds222260,
   Author = {T.P. Witelski and L.N. Virgin and C. George},
   Title = {A driven system of impacting pendulums: Experiments and
             simulations},
   Journal = {Journal of Sound and Vibration},
   Volume = {333},
   Number = {6},
   Pages = {1734-1753},
   Year = {2014},
   Month = {March},
   url = {http://dx.doi.org/10.1016/j.jsv.2013.11.004},
   Doi = {10.1016/j.jsv.2013.11.004},
   Key = {fds222260}
}

@article{fds215741,
   Author = {S.J.Chapman, P.H.Trinh and T.P. Witelski},
   Title = {Exponential asymptotics for thin film rupture},
   Journal = {SIAM Journal on Applied Mathematics},
   Volume = {73},
   Number = {1},
   Pages = {232-253},
   Year = {2013},
   url = {http://dx.doi.org/10.1137/120872012},
   Doi = {10.1137/120872012},
   Key = {fds215741}
}

@article{fds218639,
   Author = {L.B.Smolka and T.P. Witelski},
   Title = {Biaxial extensional motion of an inertially driven
             radially-expanding liquid sheet},
   Journal = {Physics of Fluids},
   Volume = {25},
   Number = {062105},
   Year = {2013},
   url = {http://dx.doi.org/10.1063/1.4811389},
   Doi = {10.1063/1.4811389},
   Key = {fds218639}
}

 

dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320