Mathematics Faculty: Publications since January 2014
List all publications in the database. :chronological alphabetical combined listing:
%% Addington, Nicolas
@article{fds225141,
Author = {N. Addington},
Title = {On two rationality conjectures for cubic
fourfolds},
Journal = {Math. Res. Lett.},
Year = {2014},
Month = {May},
url = {http://arxiv.org/abs/1405.4902},
Key = {fds225141}
}
@article{fds225601,
Author = {N. Addington and M. Lehn},
Title = {On the symplectic eightfold associated to a Pfaffian cubic
fourfold},
Journal = {J. Reine Angew. Math.},
Year = {2014},
Month = {April},
url = {http://arxiv.org/abs/1404.5657},
Key = {fds225601}
}
@article{fds225599,
Author = {N. Addington and W. Donovan and E. Segal},
Title = {The PfaffianGrassmannian equivalence revisited},
Journal = {Alg. Geom.},
Year = {2014},
Month = {January},
url = {http://arxiv.org/abs/1401.3661},
Key = {fds225599}
}
@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 = {18851927},
Year = {2014},
url = {http://arxiv.org/abs/1211.3758},
Key = {fds224079}
}
@article{fds225760,
Author = {N. Addington and E. Segal and E. Sharpe},
Title = {Dbrane probes, branched double covers, and noncommutative
resolutions},
Journal = {Adv. Theor. Math. Phys.},
Volume = {18},
Number = {6},
Pages = {13691436},
Year = {2014},
url = {http://arxiv.org/abs/1211.2446},
Key = {fds225760}
}
%% 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, SecondOrder in Time, PrimitiveVariable
Discontinuous Galerkin Schemes for a CahnHilliard 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 ReactionDiffusion Models of
Tissues.},
Journal = {Int. J. Numer. Meth. Biomed. Engng.},
Year = {2014},
Month = {February},
Key = {fds223441}
}
%% Aspinwall, Paul S
@article{fds225809,
Author = {P.S. Aspinwall and Ben Gaines},
Title = {Rational Curves and (0,2)Deformations},
Journal = {Journal of Geometry and Physics},
Year = {2014},
url = {http://arxiv.org/abs/1404.7802},
Key = {fds225809}
}
@article{fds225810,
Author = {P.S. Aspinwall},
Title = {Exoflops in Two Dimensions},
Year = {2014},
url = {http://arxiv.org/abs/1412.0612},
Key = {fds225810}
}
@article{fds225808,
Author = {P.S. Aspinwall},
Title = {A McKayLike Correspondence for (0,2)Deformations},
Journal = {Advances in Theoretical and Mathematical
Physics},
Volume = {18},
Number = {4},
Pages = {761797},
Year = {2014},
url = {http://arxiv.org/abs/1110.2524},
Key = {fds225808}
}
%% BarOn, Rann
@misc{fds178687,
Author = {R. BarOn},
Title = {105L106L Coursepack, Fall 2014 and Spring
2015},
Year = {2014},
Month = {August},
Key = {fds178687}
}
@article{fds225803,
Author = {Rann BarOn 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},
Volume = {83},
Series = {MAA Notes},
Pages = {5966},
Booktitle = {Doing the Scholarship of Teaching and Learning in
Mathematics},
Publisher = {The Mathematical Association of America},
Editor = {Jacqueline M. Dewar and Curtis D. Bennett},
Year = {2014},
ISBN = {9780883851937},
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 wellprepared 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 premed
students navigate a fourcourse Chemistry sequence through
Organic Chemistry, which trains TAs to monitor not only
content understanding, but selfregulation and metacognitive
development.},
Key = {fds225803}
}
%% Beale, J. Thomas
@article{fds225997,
Author = {J. T. Beale},
Title = {Uniform error estimates for NavierStokes flow with a moving
boundary using the immersed interface method},
Journal = {SIAM J. Numer. Anal.},
Year = {2015},
url = {http://www.math.duke.edu/faculty/beale/papers/nseiim.pdf},
Key = {fds225997}
}
%% Bertozzi, Andrea L
@booklet{Greer04a,
Author = {J. B. Greer and A. L. Bertozzi},
Title = {H1 solutions of a class of fourth order nonlinear equations
for image processing},
Journal = {Discrete And Continuous Dynamical Systems},
Volume = {10},
Number = {12},
Pages = {349  366},
Year = {2004},
Key = {Greer04a}
}
%% Bobrowski, Omer
@article{fds225074,
Author = {O. Bobrowski and M. Kahle},
Title = {Topology of Random Geometric Complexes: A
Survey},
Year = {2014},
Key = {fds225074}
}
@article{fds225075,
Author = {O. Bobrowski and S. Mukherjee and J. S. Taylor},
Title = {Topological Consistency via Kernel Estimation},
Year = {2014},
Key = {fds225075}
}
@article{fds225071,
Author = {O. Bobrowski and S. Mukherjee},
Title = {The Topology of Probability Distributions on
Manifolds},
Journal = {Probability Theory and Related Fields},
Year = {2014},
url = {http://dx.doi.org/10.1007/s004400140556x},
Doi = {10.1007/s004400140556x},
Key = {fds225071}
}
@article{fds225072,
Author = {R. J. Adler and O. Bobrowski and S. Weinberger},
Title = {Crackle: The Homology of Noise},
Journal = {Discrete and Computational Geometry},
Year = {2014},
url = {http://dx.doi.org/10.1007/s0045401496216},
Doi = {10.1007/s0045401496216},
Key = {fds225072}
}
@article{fds225073,
Author = {O. Bobrowski and R. J. Adler},
Title = {Distance Functions, Critical Points and the Topology of
Random Čech Complexes},
Journal = {Homology, Homotopy and Applications},
Year = {2014},
Key = {fds225073}
}
%% Bray, Hubert L.
@article{fds225574,
Author = {H.L. Bray and A.S. Goetz},
Title = {Wave Dark Matter and the TullyFisher Relation},
Year = {2014},
Month = {September},
url = {http://arxiv.org/abs/1409.7347},
Key = {fds225574}
}
@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
quasilocal mass of spacelike 2surfaces in the
spacetime.},
Key = {fds223121}
}
%% 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 notsotypical applications to illustrate their
use.},
Key = {fds223639}
}
@article{fds223640,
Author = {R.L. Bryant},
Title = {S.s. Chern's study of almostcomplex structures on the
sixsphere},
Year = {2014},
Month = {May},
url = {http://arxiv.org/abs/1405.3405},
Keywords = {6sphere complex structure exceptional geometry},
Abstract = {In 2003, S.s. Chern began a study of almostcomplex
structures on the 6sphere, with the idea of exploiting the
special properties of its wellknown almostcomplex
structure invariant under the exceptional group G2. While he
did not solve the (currently still open) problem of
determining whether there exists an integrable
almostcomplex structure on the 6sphere, he did prove a
significant identity that resolves the question for an
interesting class of almostcomplex structures on the
6sphere.},
Key = {fds223640}
}
%% Cahill, Jameson
@article{fds225806,
Author = {Jameson Cahill and Dustin G. Mixon},
Title = {Robust width: A characterization of uniformly stable and
robust compressed sensing},
Year = {2014},
url = {http://arxiv.org/abs/1408.4409},
Abstract = {http://arxiv.org/abs/1408.4409},
Key = {fds225806}
}
@article{fds225807,
Author = {Saeid Bahmanpour and Jameson Cahill and Peter G. Casazza and John
Jasper, Lindsey M. Woodland},
Title = {Phase retrieval and norm retrieval},
Year = {2014},
url = {http://arxiv.org/abs/1409.8266},
Key = {fds225807}
}
%% 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 = {225237},
Year = {2014},
url = {http://arxiv.org/abs/0711.0465},
Key = {fds223554}
}
%% Dolbow, John E.
@article{6333801,
Author = {Moes, N. and Dolbow, J. and Belytschko, T.},
Title = {A finite element method for crack growth without
remeshing},
Journal = {Int. J. Numer. Methods Eng. (UK)},
Volume = {46},
Number = {1},
Pages = {131  50},
Year = {10},
url = {http://dx.doi.org/10.1002/(SICI)10970207(19990910)46:1<131::AIDNME726>3.3.CO;2A},
Keywords = {crackedge stress field analysis;fatigue cracks;finite
element analysis;fracture mechanics;},
Abstract = {An improvement of a new technique for modelling cracks in
the finite element framework is presented. A standard
displacementbased approximation is enriched near a crack by
incorporating both discontinuous fields and the near tip
asymptotic fields through a partition of unity method. A
methodology that constructs the enriched approximation from
the interaction of the crack geometry with the mesh is
developed. This technique allows the entire crack to be
represented independently of the mesh, and so remeshing is
not necessary to model crack growth. Numerical experiments
are provided to demonstrate the utility and robustness of
the proposed technique},
Key = {6333801}
}
%% Fry, Brendan
@article{fds226007,
Author = {I Sgouralis and RG Evans and BS Gardiner and JA Smith and BC Fry and AT
Layton},
Title = {Renal hemodynamics, function, and oxygenation during cardiac
surgery performed on cardiopulmonary bypass: A modeling
study},
Journal = {Physiological Reports},
Volume = {3},
Pages = {e12260},
Year = {2015},
Key = {fds226007}
}
@article{fds226008,
Author = {BC Fry and A Edwards and AT Layton},
Title = {Impacts of nitric oxide and superoxide on renal medullary
oxygen transport and urine concentration},
Journal = {American Journal of Physiology  Renal Physiology},
Year = {2015},
Key = {fds226008}
}
@article{fds225212,
Author = {BC Fry and AT Layton},
Title = {Oxygen transport in a cross section of the rat inner
medulla: Impact of heterogeneous distribution of nephrons
and vessels},
Journal = {Mathematical Biosciences},
Volume = {258},
Pages = {6876},
Year = {2014},
Key = {fds225212}
}
@article{fds224574,
Author = {BC Fry and A Edwards and I Sgouralis and AT Layton},
Title = {Impact of renal medullary threedimensional architecture on
oxygen transport},
Journal = {American Journal of Physiology  Renal Physiology},
Volume = {307},
Pages = {F263F272},
Year = {2014},
Key = {fds224574}
}
%% Gasparovic, Ellen
@article{fds225255,
Author = {J. Damon and E. Gasparovic},
Title = {Shape and Positional Geometry of MultiObject
Configurations},
Year = {2014},
Key = {fds225255}
}
@article{fds225197,
Author = {P. Bendich and E. Gasparovic and J. Harer and R. Izmailov and L.
Ness},
Title = {Multiscale Local Shape Analysis and Feature Selection in
Machine Learning Applications},
Year = {2014},
url = {http://arxiv.org/abs/1410.3169},
Key = {fds225197}
}
@article{fds225256,
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 = {Skeletonbased recognition of shapes in images via longest
path matching},
Journal = {to appear in Research in Shape Analysis},
Year = {2014},
Key = {fds225256}
}
@article{fds223582,
Author = {J. Damon and E. Gasparovic},
Title = {Modeling MultiObject Configurations Via Medial/Skeletal
Linking Structures},
Year = {2014},
Key = {fds223582}
}
%% Getz, Jayce R.
@article{fds226265,
Author = {J.R. Getz and H. Hahn},
Title = {A general simple relative trace formula},
Journal = {Pacific J. Math},
Year = {2015},
Key = {fds226265}
}
@article{fds225245,
Author = {J.R. Getz},
Title = {Invariant fourvariable automorphic kernel
functions},
Year = {2014},
Key = {fds225245}
}
@article{fds225056,
Author = {J.R. Getz},
Title = {Automorphic kernel functions in four variables},
Year = {2014},
Key = {fds225056}
}
@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 = {161176},
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 ladic 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}
}
%% Hahn, Heekyoung
@article{fds226264,
Author = {J. R. Getz and H. Hahn},
Title = {A general simple relative trace formula},
Journal = {Pacific J. Math},
Year = {2015},
Key = {fds226264}
}
@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 = {161176},
Year = {2014},
Key = {fds222818}
}
%% Hain, Richard M
@article{fds225829,
Author = {D. Arapura and A. Dimca and R. Hain},
Title = {On the fundamental groups of normal varieties},
Year = {2014},
Month = {December},
url = {http://arxiv.org/abs/1412.1483},
Key = {fds225829}
}
@article{fds223909,
Author = {Richard Hain},
Title = {Genus 3 Mapping Class Groups are not Kähler},
Journal = {Journal of Topology},
Year = {2014},
Month = {June},
ISSN = {17538416},
url = {http://jtopol.oxfordjournals.org/content/early/2014/10/31/jtopol.jtu020.short},
Key = {fds223909}
}
@article{fds223317,
Author = {Richard Hain},
Title = {The Hodgede 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 = {805822},
Year = {2014},
url = {http://www.emsph.org/journals/show_abstract.php?issn=14359855&vol=16&iss=4&rank=6},
Key = {fds223449}
}
%% 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 = {Discrete and Computational Geometry},
Volume = {52},
Pages = {4470},
Year = {2014},
Month = {July},
url = {http://dx.doi.org/10.1007/s0045401496047},
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.},
Doi = {10.1007/s0045401496047},
Key = {fds221198}
}
@article{fds221210,
Author = {Jose Perea and J. Harer},
Title = {Sliding Windows and Persistence: An Application of
Topological Methods to Signal Analysis},
Journal = {Foundations of Computational Mathematics},
Year = {2014},
Month = {May},
ISSN = {16153375},
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 timedelay) embeddings, as seen through the lens
of persistent homology. In particular, we show that maximum
persistence at the pointcloud 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 stateoftheart
methods in gene expression analysis. We call this new method
SW1PerS which stands for Sliding Windows and 1dimensional
Persistence Scoring.},
Key = {fds221210}
}
@article{fds225820,
Author = {S. Bristow and A. Leman and L. Simmons Kovacs and A. Deckard and J.
Harer, S. B. Haase},
Title = {Checkpoints Couple Transcription Network Oscillator Dynamics
to CellCycle Progression},
Journal = {Genome Biology},
Volume = {15:446},
Year = {2014},
url = {http://dx.doi.org/doi:10.1186/s1305901404467},
Abstract = {Background The coupling of cyclin dependent kinases (CDKs)
to an intrinsically oscillating network of transcription
factors has been proposed to control progression through the
cell cycle in budding yeast, Saccharomyces cerevisiae. The
transcription network regulates the temporal expression of
many genes, including cyclins, and drives cellcycle
progression, in part, by generating successive waves of
distinct CDK activities that trigger the ordered program of
cellcycle events. Network oscillations continue
autonomously in mutant cells arrested by depletion of CDK
activities, suggesting the oscillator can be uncoupled from
cellcycle progression. It is not clear what mechanisms, if
any, ensure that the network oscillator is restrained when
progression in normal cells is delayed or arrested. A recent
proposal suggests CDK acts as a master regulator of
cellcycle processes that have the potential for autonomous
oscillatory behavior. Results Here we find that mitotic CDK
is not sufficient for fully inhibiting transcript
oscillations in arrested cells. We do find that activation
of the DNA replication and spindle assembly checkpoints can
fully arrest the network oscillator via overlapping but
distinct mechanisms. Further, we demonstrate that the DNA
replication checkpoint effector protein, Rad53, acts to
arrest a portion of transcript oscillations in addition to
its role in halting cellcycle progression. Conclusions Our
findings indicate that checkpoint mechanisms, likely via
phosphorylation of network transcription factors, maintain
coupling of the network oscillator to progression during
cellcycle arrest.},
Doi = {doi:10.1186/s1305901404467},
Key = {fds225820}
}
@article{fds225824,
Author = {P. Bendich and E. Gasparovic and J. Harer and R. Izmailov and L.
Ness},
Title = {MultiScale Local Shape Analysis and Feature Selection in
Machine Learning Applications},
Journal = {AISTATS},
Year = {2014},
Abstract = {We introduce a method called multiscale local shape
analysis for extracting features that describe the local
structure of points within a dataset. The method uses both
geometric and topological features at multiple levels of
granularity to capture diverse types of local information
for subsequent machine learning algorithms operating on the
dataset. Using synthetic and real dataset examples, we
demonstrate significant performance improvement of
classification algorithms constructed for these datasets
with correspondingly augmented features.},
Key = {fds225824}
}
@article{fds225825,
Author = {E. Munch and P. Bendich and K. Turner and S. Mukherjee and J. Mattingly and J. Harer},
Title = {Probabilistic Frechet Means and Statistics on
Vineyards},
Journal = {Foundations of Computational Math},
Year = {2014},
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 first study of the properties of the
Fr ́echet mean in (Dp,Wp), the space of persistence
diagrams equipped with the pth Wasserstein metric. In
particular, they showed that the Fr ́echet 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 continuouslyvarying set of diagrams do not
themselves vary continuously, which presents obvious
problems when trying to extend the Fr ́echet mean
definition to the realm of vineyards. We fix this problem by
altering the original definition of Fr ́echet 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 ́echet 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 = {fds225825}
}
@article{fds225821,
Author = {J. Perea and A. Deckard and S. Haase and J. Harer},
Title = {Sliding Windows and 1Persistence Scoring; Discovering
Periodicity in Gene Expression Time Series
Data},
Journal = {BMC Bioinformatics},
Year = {2014},
Abstract = {Motivation: Identifying periodically expressed genes across
different processes such as the cell cy cle, circadian
rhythms, and metabolic cycles, is a central problem in
computational biology. Biological time series data may
contain (multiple) unknown sig nal shapes, have
imperfections such as noise, damp ing, and trending, or
have limited sampling density. While many methods exist for
detecting periodicity, their design biases can limit their
applicability in one or more of these situations. Methods:
We present in this paper a novel method, SW1PerS, for
quantifying periodicity in time se ries data. The
measurement is performed directly, without presupposing a
particular shape or pattern, by evaluating the circularity
of a highdimensional representation of the signal. SW1PerS
is compared to other algorithms using synthetic data and
perfor mance is quantified under varying noise levels, sam
pling densities, and signal shapes. Results on biolog ical
data are also analyzed and compared; this data includes
different periodic processes from various or ganisms: the
cell and metabolic cycles in S. cere visiae, and the
circadian rhythms in M. musculus. ∗Department of
Mathematics, Duke University, USA and Institute for
Mathematics and its Applications, University of Minnesota,
USA. †Program in Computational Biology and Bioinformatics,
Duke University, USA. ‡Center for Systems Biology,
Institute for Genome Sciences & Policy, Duke University,
USA. §Departments of Mathematics, Computer Science and
Elec trical and Computer Engineering, Duke University, USA.
Results: On the task of periodic/notperiodic clas
sification, using synthetic data, SW1PerS performs on par
with successful methods in periodicity detec tion.
Moreover, it outperforms LombScargle and JTK CYCLE in the
highnoise/lowsampling range. SW1PerS is shown to be the
most shapeagnostic of the evaluated methods, and the only
one to consis tently classify damped signals as highly
periodic. On biological data, and for several experiments,
the lists of top 10% genes ranked with SW1PerS recover up to
67% of those generated with other popular algo rithms.
Moreover, lists of genes which are highly ranked only by
SW1PerS contain noncosine patterns (e.g. ECM33, CDC9,
SAM1,2 and MSH6 in the Yeast metabolic cycle data of Tu et
al. (2005)) which are highly periodic. In the Yeast cell
cycle data SW1PerS identifies genes not preferred by other
algorithms, not previously reported in Orlando et al.
(2008); Spell man et al. (1998), but found in other
experiments such as the universal growth rate response of
Slavov and Botstein (2011). These genes are BOP3, CDC10,
YIL108W, YER034W, MLP1, PAC2 and RTT101.},
Key = {fds225821}
}
@article{fds225822,
Author = {K.A. McGoff and X. Guo and A. Deckard and A.R. Leman and C.M. Kelliher and S.B. Haase and J.L. Harer},
Title = {The Local Edge Machine: Inference of dynamic models of gene
regulation},
Journal = {Nature Methods},
Year = {2014},
Abstract = {This paper develops the state of the art methodology for
inferring gene regulatory networks from gene expression data
for periodic processes. Application is made to finding
networks for cell cycle and circadian clocks.},
Key = {fds225822}
}
@article{fds225823,
Author = {P. Bendich and S. Chin and J. Clarke and J. deSena, J. Harer and E.
Munch, A. Newman and D. Porter and D. Rouse and N. Strawn and A.
Watkins},
Title = {Topological and Statistical Behavior Classifiers for
Tracking Applications},
Journal = {IEEE Trans. on Aerospace and Electronic Systems},
Year = {2014},
Abstract = {We introduce the first unified theory for target tracking
using Multiple Hypothesis Tracking, Topological Data
Analysis, and machine learning. Our string of innovations
are 1) robust topological features are used to encode
behavioral information, 2) statistical models are fitted to
distributions over these topological features, and 3) the
target type classification methods of Wigren and Bar Shalom
et al. are employed to exploit the resulting likelihoods for
topological features inside of the tracking procedure. To
demonstrate the efficacy of our approach, we test our
procedure on synthetic vehicular data generated by the
Simulation of Urban Mobility package.},
Key = {fds225823}
}
@article{fds225826,
Author = {P. Bendich and Jacob Harer and John Harer},
Title = {A Persistent Homology Based Geodesic Distance
Estimator},
Journal = {Journal of Machine Learning Research},
Year = {2014},
Key = {fds225826}
}
@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 = {2014},
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 pth 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 continuouslyvarying 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}
}
%% Herzog, David P
@article{fds223339,
Author = {D.P. Herzog and J.C. Mattingly},
Title = {NoiseInduced 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 = {NoiseInduced Stabilization of Planar Flows
II},
Year = {2014},
Month = {April},
url = {http://arxiv.org/pdf/1404.0955v1.pdf},
Key = {fds223340}
}
%% Layton, Anita T
@article{fds226016,
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 = {Physiol Report},
Volume = {3},
Number = {1},
Year = {2015},
Key = {fds226016}
}
@article{fds226266,
Author = {Ashlee N. Ford Versypt and Elizabeth Makerides and Julia C.
Arciero and Laura Ellwein and Anita T. Layton},
Title = {Bifurcation Study of Blood Flow Control in the
Kidney},
Journal = {Math Biosci, in press},
Year = {2015},
Key = {fds226266}
}
@article{fds226262,
Author = {Anita T. Layton},
Title = {Recent advances in renal hemodynamics: Insights from bench
experiments and computer simulations},
Journal = {Am J Physiol Renal Physiol, in press},
Year = {2015},
Key = {fds226262}
}
@article{fds226263,
Author = {Ioannis Sgouralis and Anita T. Layton},
Title = {Mathematical modeling of renal hemodynamics in physiology
and pathophysiology},
Journal = {Math Biosci, in press},
Year = {2015},
Key = {fds226263}
}
@article{fds225965,
Author = {Anita T. Layton and Volker Vallon and Aurelie
Edwards},
Title = {Modeling oxygen consumption in the proximal tubule: Effects
of NHE and SGLT2 inhibition},
Journal = {Am J Physiol Renal Physiol, submitted},
Year = {2015},
Key = {fds225965}
}
@article{fds226014,
Author = {Brendan Fry and Aurelie Edwards and Anita Layton},
Title = {Impacts of nitric oxide and superoxide on renal medullary
oxygen transport and urine concentration},
Journal = {Am J Physiol Renal Physiol, in press},
Year = {2014},
Key = {fds226014}
}
@article{fds226210,
Author = {Ioannis Sgouralis and Anita T. Layton},
Title = {Conduction of feedbackmediated signal in a computational
model of coupled nephron},
Journal = {Med Math Biol, in press},
Year = {2014},
Key = {fds226210}
}
@article{fds225249,
Author = {Anita T. Layton},
Title = {Mathematical physiology},
Journal = {Princeton Companion to Applied Mathematics},
Year = {2014},
Key = {fds225249}
}
@article{fds225219,
Author = {H. Nganguia and Y.N. Young and A.T. Layton and W.F. Hu and M.C.
Lai},
Title = {An immersed interface method for axisymmetric
electrohydrodynamic simulations in Stokes
flow},
Journal = {Comm Comput Phys},
Year = {2014},
Key = {fds225219}
}
@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 = {F34F48},
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 = {F1357F1371},
Year = {2014},
Key = {fds223975}
}
@article{fds224541,
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},
Volume = {306},
Pages = {F952F969},
Year = {2014},
Key = {fds224541}
}
@article{fds225657,
Author = {Anita T. Layton},
Title = {Mathematical modeling of urea transport in the
kidney},
Booktitle = {Urea Transporters},
Publisher = {Springer},
Editor = {Baoxue Yang},
Year = {2014},
Key = {fds225657}
}
@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},
Pages = {10231049},
Year = {2014},
Key = {fds223498}
}
@article{fds225250,
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},
Volume = {638},
Pages = {191208},
Year = {2014},
Key = {fds225250}
}
@article{fds225251,
Author = {Hwayeon Ryu and Anita T. Layton},
Title = {Feedbackmediated dynamics in a model of coupled nephrons
with compliant short loop of Henle},
Journal = {AMS Contemporary Mathematics, Biological Fluid Dynamics:
Modeling, Computations, and Applications},
Volume = {628},
Pages = {209238},
Year = {2014},
Key = {fds225251}
}
@article{fds226227,
Author = {Yi Li and Ioannis Sgouralis and Anita T. Layton},
Title = {Computing viscous flow in an elastic tube},
Journal = {Numer. Math. Theor. Meth. Appl.,},
Volume = {7},
Pages = {555574},
Year = {2014},
Key = {fds226227}
}
@article{fds225220,
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},
Volume = {307},
Number = {6},
Pages = {F649F655},
Year = {2014},
Key = {fds225220}
}
@article{fds225218,
Author = {Julia Arcerio and Laura Ellwein and Ashlee N. Ford Versypt and Elizabeth Markride and Anita T. Layton},
Title = {Modeling blood flow in the kidney},
Journal = {IMA volume},
Year = {2014},
Key = {fds225218}
}
@article{fds223468,
Author = {Gregory J. Herschlag and JianGuo Liu and Anita T.
Layton},
Title = {An exact solution for Stokes flow in an infinite channel
with permeable walls},
Journal = {SIAM Appl Math, submitted},
Year = {2014},
Key = {fds223468}
}
@article{fds226015,
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},
Volume = {258},
Pages = {68–76},
Year = {2014},
Key = {fds226015}
}
@article{fds224561,
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},
Volume = {307},
Pages = {F137F146},
Year = {2014},
Key = {fds224561}
}
@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{fds224542,
Author = {Brendan C. Fry and Aurelie Edward and Ioannis Sgouralis and Anita
T. Layton},
Title = {Impact of renal medullary threedimensional architecture on
oxygen transport},
Journal = {Am J Physiol Renal Physiol},
Volume = {307},
Pages = {F263F272},
Year = {2014},
Key = {fds224542}
}
%% Liao, Wenjing
@article{fds223442,
Author = {W. Liao and A. Fannjiang},
Title = {MUSIC for singlesnapshot spectral estimation: stability and
superresolution},
Year = {2014},
Key = {fds223442}
}
%% Lipnowski, Michael
@article{fds226181,
Author = {N. Bergeron and M. Lipnowski},
Title = {Twisted limit formula for torsion and cyclic base
change},
Year = {2015},
url = {http://arxiv.org/abs/1409.6749},
Key = {fds226181}
}
@article{fds226182,
Author = {J. Getz and H. Hahn and M. Lipnowski},
Title = {A relative Weyl law and spectral sparsity of distinguished
representations},
Year = {2015},
Key = {fds226182}
}
@article{fds226179,
Author = {M. Lipnowski},
Title = {The Equivariant CheegerMüller Theorem on Locally Symmetric
Spaces},
Journal = {Journal of the Institute of Mathematics of
Jussieu},
Year = {2014},
url = {http://arxiv.org/abs/1312.2543},
Key = {fds226179}
}
%% Liu, JianGuo
@article{fds225739,
Author = {F. Coquel and S. Jin and J.G. Liu and L. Wang},
Title = {Wellposedness and singular limit of a semilinear hyperbolic
relaxation system with a twoscale discontinuous relaxation
rate},
Journal = {Arch. Rat. Mech. Anal.},
Volume = {214},
Pages = {10511084},
Year = {2014},
Key = {fds225739}
}
@article{fds225738,
Author = {P. Degond and J.G. Liu and C. Ringhofer},
Title = {Evolution of wealth in a nonconservative economy driven by
local Nash equilibria},
Journal = {Phil. Trans. R. Soc. A},
Volume = {372},
Pages = {20130394},
Year = {2014},
Key = {fds225738}
}
@article{fds225737,
Author = {X. Chen and A. Jungel and J.G. Liu},
Title = {A note on AubinLionsDubinskii lemmas},
Journal = {Acta Appl. Math.},
Volume = {133},
Pages = {3343},
Year = {2014},
Key = {fds225737}
}
@article{fds225729,
Author = {P. Degond and J.G. Liu and C. Ringhofer},
Title = {Largescale dynamics of MeanField Games driven by local
Nash equilibria},
Journal = {J Nonlinear Sci.},
Volume = {24},
Pages = {93115},
Year = {2014},
Key = {fds225729}
}
@article{fds225730,
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.},
Volume = {154},
Pages = {751780},
Year = {2014},
Key = {fds225730}
}
@article{fds225731,
Author = {T. Goudon and S. Jin and J.G. Liu and B. Yan},
Title = {AsymptoticPreserving schemes for kineticfluid modeling of
disperse twophase flows with variable fluid
density},
Journal = {Internat. J. Numer. Methods Fluids},
Volume = {75},
Pages = {81154},
Year = {2014},
Key = {fds225731}
}
@article{fds225732,
Author = {P. Degond and M. Herty and J.G. Liu},
Title = {Flow on sweeping networks},
Journal = {Multiscale Model. Simul.},
Volume = {12},
Pages = {538565},
Year = {2014},
Key = {fds225732}
}
@article{fds225733,
Author = {D. Chae and P. Degond and J.G. Liu},
Title = {Wellposedness for Hallmagnetohydrodynamics},
Journal = {Ann. I. H. Poincare, AN},
Volume = {31},
Pages = {555565},
Year = {2014},
Key = {fds225733}
}
@article{fds225734,
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 rodlike
particles},
Journal = {Commun. Math. Sci.},
Volume = {12},
Pages = {15791601},
Year = {2014},
Key = {fds225734}
}
@article{fds225735,
Author = {H. Johnston and C. Wang and J.G. Liu},
Title = {A local pressure boundary condition spectral collocation
scheme for the threedimensional NavierStokes
equations},
Journal = {J. Sci. Comput.},
Volume = {60},
Pages = {612626},
Year = {2014},
Key = {fds225735}
}
@article{fds225726,
Author = {J.G. Liu and R.L. Pego},
Title = {On generating functions of Hausdorff moment
sequences},
Journal = {Trans. Amer. Math. Soc.},
Year = {2014},
Key = {fds225726}
}
@article{fds225727,
Author = {P. Degond and A. Frouvelle and J.G. Liu},
Title = {Phase transitions, hysteresis, and hyperbolicity for
selforganized alignment dynamics},
Journal = {Arch. Rat. Mech. Anal.},
Year = {2014},
Key = {fds225727}
}
@article{fds225728,
Author = {A. Chertock and J.G. Liu and T. Pendleton},
Title = {Elastic collisions among peakon solutions for the
CamassaHolm equation},
Journal = {Appl. Numer. Math.},
Year = {2014},
Key = {fds225728}
}
@article{fds220921,
Author = {S. Bian and J.G. Liu and C. Zou},
Title = {Ultracontractivity for KellerSegel model with diffusion
exponent m>12/d},
Journal = {Kinetic and Related Models},
Volume = {7},
Pages = {928},
Year = {2014},
Key = {fds220921}
}
@article{fds220121,
Author = {Y. Duan and J.G. Liu},
Title = {Convergence analysis of the vortex blob method for the
bequation},
Journal = {Discrete Contin. Dyn. Syst. Ser. A},
Volume = {34},
Pages = {19952011},
Year = {2014},
Key = {fds220121}
}
@article{fds225736,
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 = {2014},
Key = {fds225736}
}
%% Lu, Jianfeng
@article{fds226269,
Author = {J. Lu and James Nolen},
Title = {Reactive trajectories and the transition path
processes},
Journal = {Probab. Theory Related Fields},
Volume = {161},
Number = {12},
Pages = {195244},
Year = {2015},
url = {http://arxiv.org/abs/1303.1744},
Key = {fds226269}
}
@article{fds226046,
Author = {Yin Xian and Andrew Thompson and Qiang Qiu and Loren Nolte and Douglas
Nowacek, Jianfeng Lu and Robert Calderbank},
Title = {Classification of whale vocalizations using the Weyl
transform},
Booktitle = {ICASSP 2015},
Year = {2015},
Key = {fds226046}
}
@article{fds226225,
Author = {J. Lu and Chen Li and Weitao Yang},
Title = {Gentlest ascent dynamics for calculating first excited state
and exploring energy landscape of KohnSham density
functionals},
Year = {2015},
Key = {fds226225}
}
@article{fds226021,
Author = {J. Lu and Benedikt Wirth and Haizhao Yang},
Title = {Combining 2D synchrosqueezed wave packet transform with
optimization for crystal image analysis},
Year = {2015},
url = {http://arxiv.org/abs/1501.06254},
Key = {fds226021}
}
@article{fds226224,
Author = {Haizhao Yang and Jianfeng Lu and William Brown and Ingrid Daubechies and Lexing Ying},
Title = {Quantitative canvas weave analysis using 2D synchrosqueezed
transforms},
Journal = {IEEE Signal Process. Mag.},
Year = {2014},
Key = {fds226224}
}
@article{fds225365,
Author = {J. Lu and Jingrun Chen},
Title = {Analysis of the divideandconquer method for electronic
structure calculations},
Year = {2014},
url = {http://arxiv.org/abs/1411.0066},
Key = {fds225365}
}
@article{fds225257,
Author = {J. Lu and Lexing Ying},
Title = {Compression of the electron repulsion integral tensor in
tensor hypercontraction format with cubic scaling
cost},
Year = {2014},
url = {http://arxiv.org/abs/1410.7757},
Key = {fds225257}
}
@article{fds226220,
Author = {J. Lu and JianGuo Liu and Dionisios Margetis},
Title = {Emergence of step flow from atomistic scheme of epitaxial
growth in 1+1 dimensions},
Journal = {Phys. Rev. E},
Year = {2014},
url = {http://arxiv.org/abs/1409.0046},
Key = {fds226220}
}
@article{fds224958,
Author = {J. Lu and Qin Li and Weiran Sun},
Title = {Diffusion approximations of linear transport equations:
Asymptotics and numerics},
Year = {2014},
url = {http://arxiv.org/abs/1409.0476},
Key = {fds224958}
}
@article{fds224509,
Author = {J. Lu and Christian B. Mendl},
Title = {Numerical scheme for a spatially inhomogeneous matrixvalued
quantum Boltzmann equation},
Year = {2014},
url = {http://arxiv.org/abs/1408.1782},
Key = {fds224509}
}
@article{fds223301,
Author = {J. Lu and Lin Lin and Sihong Shao},
Title = {Analysis of the time reversible BornOppenheimer molecular
dynamics},
Journal = {Entropy},
Volume = {16},
Pages = {110137},
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 = {127},
Year = {2014},
url = {http://dx.doi.org/10.1007/s002200141943y},
Doi = {10.1007/s002200141943y},
Key = {fds223588}
}
@article{fds225180,
Author = {Yang Yang and Degao Peng and Jianfeng Lu and Weitao
Yang},
Title = {Excitation Energies from ParticleParticle Random Phase
Approximation: Davidson Algorithm and Benchmark
Studies},
Journal = {J. Chem. Phys.},
Volume = {141},
Pages = {124104},
Year = {2014},
url = {http://dx.doi.org/10.1063/1.4895792},
Doi = {10.1063/1.4895792},
Key = {fds225180}
}
@article{fds225182,
Author = {J. Lu and Felix Otto},
Title = {Nonexistence of minimizer for ThomasFermiDiracvon
Weizsacker model},
Journal = {Comm. Pure Appl. Math.},
Volume = {67},
Pages = {16051617},
Year = {2014},
url = {http://dx.doi.org/10.1002/cpa.21477},
Doi = {10.1002/cpa.21477},
Key = {fds225182}
}
@article{fds226047,
Author = {J. Lu and Pingbing Ming},
Title = {Stability of a forcebased hybrid method with planar sharp
interface},
Journal = {SIAM J. Numer. Anal.},
Volume = {52},
Number = {4},
Pages = {20052026},
Year = {2014},
url = {http://dx.doi.org/10.1137/130904843},
Doi = {10.1137/130904843},
Key = {fds226047}
}
@article{fds225507,
Author = {J. Lu and Rongjie Lai and Stanley Osher},
Title = {Density matrix minimization with $\ell_1$
regularization},
Journal = {Commun. Math. Sci.},
Year = {2014},
url = {http://arxiv.org/abs/1403.1525},
Key = {fds225507}
}
@article{fds223321,
Author = {J. Lu and Qin Li and Weiran Sun},
Title = {A convergent method for linear halfspace kinetic
equation},
Year = {2014},
url = {http://arxiv.org/abs/1408.6630},
Key = {fds223321}
}
@article{fds223237,
Author = {J. Lu and Bin Hu},
Title = {Dynamic production capacity management with price
skimming},
Year = {2014},
Key = {fds223237}
}
@article{fds223238,
Author = {J. Lu and Haizhao Yang and Lexing Ying},
Title = {Crystal image analysis using 2D synchrosqueezed
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 = {50855097},
Year = {2014},
url = {http://dx.doi.org/10.3934/dcds.2014.34.5085},
Doi = {10.3934/dcds.2014.34.5085},
Key = {fds224003}
}
@article{fds225181,
Author = {J. Lu and Eric VandenEijnden},
Title = {Exact dynamical coarsegraining without timescale
separation},
Journal = {J. Chem. Phys.},
Volume = {141},
Pages = {044109},
Year = {2014},
url = {http://dx.doi.org/10.1063/1.4890367},
Doi = {10.1063/1.4890367},
Key = {fds225181}
}
@article{fds225867,
Author = {J. Lu and Jingchen Liu and Xiang Zhou},
Title = {Efficient rare event simulation for failure problems in
random media},
Journal = {SIAM J. Sci. Comput.},
Year = {2014},
url = {http://arxiv.org/abs/1404.4729},
Key = {fds225867}
}
@article{fds223674,
Author = {J. Lu and Vitaly Moroz and Cyrill B. Muratov},
Title = {Orbitalfree density functional theory of outofplane
charge screening in graphene},
Year = {2014},
url = {http://arxiv.org/abs/1405.4949},
Key = {fds223674}
}
%% Maggioni, Mauro
@article{fds225842,
Author = {M. Maggioni and S. Minsker and N. Strawn},
Title = {Multiscale Dictionary and Manifold Learning: NonAsymptotic
Bounds for the Geometric MultiResolution
Analysis},
Booktitle = {Proc. iTWIST’14: international  Traveling Workshop on
Interactions between Sparse models and Technology},
Year = {2014},
Month = {August},
Key = {fds225842}
}
@article{fds225834,
Author = {Nicolas Altemose and Karen H. Miga and Mauro Maggioni and Huntington
F. Willard},
Title = {Genomic Characterization of Large Heterochromatic Gaps in
the Human Genome Assembly},
Journal = {PLOS Computational Biology},
Year = {2014},
Key = {fds225834}
}
@article{fds225832,
Author = {M. Crosskey and M. Maggioni},
Title = {ATLAS: A geometric approach to learning highdimensional
stochastic systems near manifolds},
Year = {2014},
url = {http://arxiv.org/abs/1404.0667},
Key = {fds225832}
}
@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 = {MultiScale Approximation with Hierarchical Radial Basis
Functions Networks,},
Journal = {IEEE Trans. on Neural Networks},
Volume = {15},
Number = {1},
Pages = {178188},
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 = {Hyperspectral 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/TR1289},
Organization = {Dept. Comp. Sci., Yale University},
Institution = {Dept. Comp. Sci., Yale University},
Year = {2004},
Key = {CMTech}
}
%% Mattingly, Jonathan C.
@article{fds225363,
Author = {J.C. Mattingly and Christy Vaughn},
Title = {Redistricting and the Will of the People},
Year = {2014},
Month = {October},
url = {http://www.math.duke.edu/~jonm/PaperArchive/14/gerrymandering.pdf},
Abstract = {We introduce a nonpartisan probability distribution on
congressional redistricting of North Carolina which
emphasizes the equal partition of the population and the
compactness of districts. When random districts are drawn
and the results of the 2012 election were retabulated under
the drawn districtings, we find that an average of 7.6
democratic representatives are elected. 95\% of the randomly
sampled redistrictings produced between 6 and 9 Democrats.
Both of these facts are in stark contrast with the 4
Democrats elected in the 2012 elections with the same vote
counts. This brings into serious question the idea that such
elections represent the ``will of the people.'' It
underlines the ability of redistricting to undermine the
democratic process, while on the face allowing democracy to
proceed.},
Key = {fds225363}
}
@article{fds225248,
Author = {J.C. Mattingly and Stephan Huckemann and Ezra Miller and James Nolen},
Title = {Sticky central limit theorems at isolated hyperbolic planar
singularities},
Year = {2014},
Month = {October},
url = {http://arxiv.org/abs/1410.6879},
Abstract = {We derive the limiting distribution of the barycenter bn of
an i.i.d. sample of n random points on a planar cone with
angular spread larger than 2π. There are three mutually
exclusive possibilities: (i) (fully sticky case) after a
finite random time the barycenter is almost surely at the
origin; (ii) (partly sticky case) the limiting distribution
of n‾√bn comprises a point mass at the origin, an open
sector of a Gaussian, and the projection of a Gaussian to
the sector's bounding rays; or (iii) (nonsticky case) the
barycenter stays away from the origin and the renormalized
fluctuations have a fully supported limit
distributionusually Gaussian but not always. We conclude
with an alternative, topological definition of stickiness
that generalizes readily to measures on general metric
spaces.},
Key = {fds225248}
}
@article{fds223434,
Author = {J.C. Mattingly and David P. Herzog},
Title = {NoiseInduced 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 = {NoiseInduced Stabilization of Planar Flows
I},
Year = {2014},
Month = {April},
url = {http://arxiv.org/abs/1404.0957},
Key = {fds223435}
}
@article{fds224075,
Author = {J.C. Mattingly and Yuri Bakhtin and Tobias Hurth},
Title = {Regularity of invariant densities for 1Dsystems with random
switching},
Year = {2014},
url = {http://arxiv.org/abs/1406.5425},
Abstract = {This is a detailed analysis of invariant measures for
onedimensional 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 righthand 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 = {42234257},
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 righthand 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}
}
%% McGoff, Kevin A
@article{fds225790,
Author = {K. McGoff and S. Mukherjee and A. Nobel and N. Pillai},
Title = {Consistency of maximum likelihood estimation for some
dynamical systems},
Journal = {Ann. Statist.},
Volume = {43},
Number = {1},
Pages = {129},
Year = {2015},
url = {http://arxiv.org/abs/1306.5603},
Key = {fds225790}
}
@article{fds225791,
Author = {M. Boyle and J. Buzzi and K. McGoff},
Title = {Bowen's entropyconjugacy conjecture is true up to finite
index},
Journal = {Proc. Amer. Math. Soc.},
Year = {2014},
url = {http://arxiv.org/abs/1310.2740},
Key = {fds225791}
}
@article{fds225792,
Author = {K. Lan and K. McGoff},
Title = {Coalescence and meeting times on nblock Markov
chains},
Journal = {J. Theoret. Probab.},
Year = {2014},
url = {http://arxiv.org/abs/1410.0099},
Key = {fds225792}
}
%% Ng, Lenhard L
@article{fds225794,
Author = {C. Cornwell and L. Ng and S. Sivek},
Title = {Obstructions to Lagrangian concordance},
Year = {2014},
url = {http://arxiv.org/abs/1411.1364},
Key = {fds225794}
}
@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 = {9783319020358},
url = {http://dx.doi.org/10.1007/9783319020365_10},
Doi = {10.1007/9783319020365_10},
Key = {fds223315}
}
@article{fds225797,
Author = {M. Aganagic and T. Ekholm and L. Ng and C. Vafa},
Title = {Topological strings, Dmodel, and knot contact
homology},
Journal = {Advances in Theoretical and Mathematical
Physics},
Volume = {18},
Number = {4},
Pages = {827956},
Year = {2014},
url = {http://dx.doi.org/10.4310/ATMP.2014.v18.n4.a3},
Doi = {10.4310/ATMP.2014.v18.n4.a3},
Key = {fds225797}
}
%% Nolen, James
@article{fds226268,
Author = {J.C. Mourrat and J. Nolen},
Title = {Scaling limit of the corrector in stochastic
homogenization},
Year = {2015},
url = {http://arxiv.org/abs/1502.07440},
Key = {fds226268}
}
@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/s004400140547y},
Key = {fds223681}
}
@article{fds225243,
Author = {A. Gloria and J. Nolen},
Title = {A quantitative central limit theorem for the effective
conductance on the discrete torus},
Year = {2014},
url = {http://arxiv.org/abs/1410.5734},
Key = {fds225243}
}
@article{fds225244,
Author = {S. Huckemann and E. Miller and J. Mattingly and J.
Nolen},
Title = {Sticky central limit theorems at isolated hyperbolic planar
singularities},
Year = {2014},
url = {http://arxiv.org/abs/1410.6879},
Key = {fds225244}
}
@article{fds218100,
Author = {J. Nolen},
Title = {Normal approximation for a random elliptic
equation},
Journal = {Probability Theory and Related Fields},
Volume = {159},
Number = {3},
Pages = {661700},
Year = {2014},
url = {http://math.duke.edu/~nolen/preprints/ellipfluctper_rev.pdf},
Doi = {10.1007/s0044001305179},
Key = {fds218100}
}
@article{fds225165,
Author = {J. Nolen and J.M. Roqujoffre and L. Ryzhik},
Title = {Powerlike delay in time inhomogeneous FisherKPP
equations},
Journal = {Communications in Partial Differential Equations},
Year = {2014},
url = {http://math.duke.edu/~nolen/preprints/bigdelaydraft.pdf},
Key = {fds225165}
}
@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}
}
%% Perea, Jose A.
@article{fds223841,
Author = {Jose A. Perea and Anastasia Deckard and Steve B. Haase and John
Harer},
Title = {SW1PerS: Sliding Windows and 1Persistence 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 = {16153375},
url = {http://dx.doi.org/10.1007/s102080149206z},
Doi = {10.1007/s102080149206z},
Key = {fds223454}
}
@article{fds223453,
Author = {Jose A. Perea and Gunnar Carlsson},
Title = {A KleinBottleBased Dictionary for Texture
Representation},
Journal = {International Journal of Computer Vision},
Volume = {107},
Number = {1},
Pages = {7597},
Year = {2014},
Month = {March},
ISSN = {09205691},
url = {http://dx.doi.org/10.1007/s1126301306762},
Doi = {10.1007/s1126301306762},
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 = {2016},
Month = {July},
Key = {fds15387}
}
@book{fds51036,
Author = {A. O. Petters and X. Dong},
Title = {An Introduction to Mathematical Finance: Understanding and
Building Financial Intuition},
Series = {SUMAT},
Publisher = {Springer, in preparation},
Year = {2015},
Month = {July},
Key = {fds51036}
}
%% Schoen, Chad
@article{fds225206,
Author = {C. Schoen},
Title = {An arithmetic ball quotient surface whose Albanese variety
is not of CM type},
Journal = {Electron. Res. Announc. Math. Sci.},
Volume = {21},
Pages = {132136},
Publisher = {American Institute of Mathematical Sciences},
Year = {2014},
Key = {fds225206}
}
%% Stern, Mark A
@article{fds225761,
Author = {M.A. Stern},
Title = {$C^{\infty}$ Stability, Canonical Maps, and Discrete
Dynamics},
Year = {2014},
Key = {fds225761}
}
@article{fds225762,
Author = {Mark Stern},
Title = {Nonlinear Harmonic Forms and an Exotic Bochner
Formula},
Year = {2014},
Key = {fds225762}
}
%% 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;twophase flow;},
Abstract = {Multicomponent twophase isothermal fluid flow in petroleum
reservoirs is described. The fluidflow 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 componentconservation 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
componentconservation 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{fds226041,
Author = {Stavros Komineas and Stephen P. Shipman and Stephanos
Venakides},
Title = {Lossless Polariton Solitons},
Journal = {arXiv},
Year = {2014},
url = {http://arxiv.org/abs/1409.4067},
Abstract = {Photons and excitons in a semiconductor microcavity interact
to form excitonpolariton condensates. These are governed by
a nonlinear quantummechanical system involving exciton and
photon wavefunctions. We calculate all nontraveling
harmonic soliton solutions for the onedimensional lossless
system. There are two frequency bands of bright solitons
when the interexciton interactions produce a repulsive
nonlinearity and two frequency bands of dark solitons when
the nonlinearity is attractive. In addition, there are two
frequency bands for which the exciton wavefunction is
discontinuous at its symmetry point, where it undergoes a
phase jump of π. A band of continuous dark solitons merges
with a band of discontinuous dark solitons, forming a larger
band over which the soliton farfield amplitude varies from
0 to ∞; the discontinuity is initiated when the operating
frequency exceeds the free exciton frequency. The far fields
of the solitons in the lowest and highest frequency bands
(one discontinuous and one continuous dark) are linearly
unstable, whereas the other four bands have linearly stable
far fields, including the merged band of dark
solitons.},
Key = {fds226041}
}
%% 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 = {17341753},
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{fds224474,
Author = {N.S. Hall Taylor and I.J. Hewitt and J.R. Ockendon and T.P.
Witelski},
Title = {A new model for disturbance waves},
Journal = {International Journal of Multiphase Flow},
Volume = {66},
Pages = {3845},
Year = {2014},
url = {http://dx.doi.org/10.1016/j.ijmultiphaseflow.2014.06.004},
Doi = {10.1016/j.ijmultiphaseflow.2014.06.004},
Key = {fds224474}
}
