Mathematics Grad: All Publications (in the database)
List most recent publications in the database. :chronological alphabetical combined listing:
%% Aguado, Alex
@misc{fds208064,
Author = {Alejandro Aguado},
Title = {A short note on mapping cylinders},
Journal = {arXiv:1206.1277v2 [math.AT]},
Year = {2012},
Month = {June},
Key = {fds208064}
}
@misc{fds204392,
Author = {Alejandro Aguado},
Title = {On the cardinality of the Kuratowski family},
Journal = {Mathematics Magazine (Problem 1888)},
Volume = {85 (1) & 86 (1)},
Year = {2012},
Month = {February},
url = {http://www.jstor.org/stable/10.4169/math.mag.85.1.61},
Key = {fds204392}
}
@misc{fds208066,
Author = {Alejandro Aguado},
Title = {On group designs and the social golfer problem},
Year = {2012},
Key = {fds208066}
}
@article{fds146627,
Author = {Alejandro Aguado and Saad I. El-Zanati},
Title = {On σ-labeling the union of three cycles.},
Journal = {Journal of Combinatorial Mathematics and Combinatorial
Computing},
Volume = {64},
Pages = {33-48},
Year = {2008},
MRNUMBER = {MR2389065},
url = {http://www.ams.org/mathscinet-getitem?mr=2389065},
Key = {fds146627}
}
@article{fds146626,
Author = {Alejandro Aguado and Saad I. El-Zanati and et al.},
Title = {On ρ-labeling the union of three cycles},
Journal = {The Australasian Journal of Combinatorics},
Volume = {37},
Pages = {155-170},
Year = {2007},
MRNUMBER = {MR2284379 (2007k:05190)},
url = {http://www.ams.org/mathscinet-getitem?mr=2284379},
Key = {fds146626}
}
@misc{fds146628,
Author = {Alejandro Aguado},
Title = {Cantor Sets, Antoine's Necklace and p-Adic
Numbers},
Series = {Undergraduate Thesis (unpublished)},
Publisher = {22 figures, 48 pages},
Year = {2006},
Key = {fds146628}
}
@article{fds146625,
Author = {Alejandro Aguado},
Title = {A 10 days solution to the social golfer problem},
Series = {Math games: Social Golfer problem},
Publisher = {MAA Online},
Editor = {Ed Pegg Jr.},
Year = {2004},
url = {http://www.maa.org/editorial/mathgames/mathgames_08_14_07.html},
Key = {fds146625}
}
%% Ambrose, David M.
@article{fds10435,
Author = {David M. Ambrose},
Title = {Well-posedness of vortex sheets with surface
tension},
Journal = {SIAM J. Math. Analysis},
Key = {fds10435}
}
%% An, Chen
@article{fds355088,
Author = {An, C},
Title = {ℓ-torsion in class groups of certain families of
D4-quartic fields},
Journal = {Journal De Theorie Des Nombres De Bordeaux},
Volume = {32},
Number = {1},
Pages = {1-23},
Publisher = {Universite de Bordeaux},
Editor = {Wood, M},
Year = {2020},
Month = {August},
Key = {fds355088}
}
%% Arya, Shreya
@article{fds371223,
Author = {Arya, S and Boissonnat, J-D and Dutta, K and Lotz,
M},
Title = {Dimensionality reduction for k-distance applied to
persistent homology},
Journal = {Journal of Applied and Computational Topology},
Volume = {5},
Number = {4},
Pages = {671-691},
Publisher = {Springer Science and Business Media LLC},
Year = {2021},
Month = {December},
url = {http://dx.doi.org/10.1007/s41468-021-00079-x},
Abstract = {<jats:title>Abstract</jats:title><jats:p>Given a set
<jats:italic>P</jats:italic> of <jats:italic>n</jats:italic>
points and a constant <jats:italic>k</jats:italic>, we are
interested in computing the persistent homology of the Čech
filtration of <jats:italic>P</jats:italic> for the
<jats:italic>k</jats:italic>-distance, and investigate the
effectiveness of dimensionality reduction for this problem,
answering an open question of Sheehy (The persistent
homology of distance functions under random projection. In
Cheng, Devillers (eds), 30th Annual Symposium on
Computational Geometry, SOCG’14, Kyoto, Japan, June
08–11, p 328, ACM, 2014). We show that
<jats:italic>any</jats:italic> linear transformation that
preserves pairwise distances up to a <jats:inline-formula><jats:alternatives><jats:tex-math>$$(1\pm
{\varepsilon })$$</jats:tex-math>?? <mml:mrow>
<mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>±</mml:mo>
<mml:mi>ε</mml:mi> <mml:mo>)</mml:mo> </mml:mrow>
</mml:math></jats:alternatives></jats:inline-formula>
multiplicative factor, must preserve the persistent homology
of the Čech filtration up to a factor of
<jats:inline-formula><jats:alternatives><jats:tex-math>$$(1-{\varepsilon
})^{-1}$$</jats:tex-math>?? <mml:msup> <mml:mrow>
<mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>-</mml:mo>
<mml:mi>ε</mml:mi> <mml:mo>)</mml:mo> </mml:mrow>
<mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow>
</mml:msup> </mml:math></jats:alternatives></jats:inline-formula>.
Our results also show that the Vietoris-Rips and Delaunay
filtrations for the <jats:italic>k</jats:italic>-distance,
as well as the Čech filtration for the approximate
<jats:italic>k</jats:italic>-distance of Buchet et al. [J
Comput Geom, 58:70–96, 2016] are preserved up to a
<jats:inline-formula><jats:alternatives><jats:tex-math>$$(1\pm
{\varepsilon })$$</jats:tex-math>?? <mml:mrow>
<mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>±</mml:mo>
<mml:mi>ε</mml:mi> <mml:mo>)</mml:mo> </mml:mrow>
</mml:math></jats:alternatives></jats:inline-formula>
factor. We also prove extensions of our main theorem, for
point sets (<jats:italic>i</jats:italic>) lying in a region
of bounded Gaussian width or (<jats:italic>ii</jats:italic>)
on a low-dimensional submanifold, obtaining embeddings
having the dimension bounds of Lotz (Proc R Soc A Math Phys
Eng Sci, 475(2230):20190081, 2019) and Clarkson (Tighter
bounds for random projections of manifolds. In Teillaud (ed)
Proceedings of the 24th ACM Symposium on Computational Geom-
etry, College Park, MD, USA, June 9–11, pp 39–48, ACM,
2008) respectively. Our results also work in the
<jats:italic>terminal dimensionality reduction</jats:italic>
setting, where the distance of any point in the original
ambient space, to any point in <jats:italic>P</jats:italic>,
needs to be approximately preserved. </jats:p>},
Doi = {10.1007/s41468-021-00079-x},
Key = {fds371223}
}
%% Beckman, Erin
@article{fds343710,
Author = {Beckman, E and Frank, N and Jiang, Y and Junge, M and Tang,
S},
Title = {The frog model on trees with drift},
Journal = {Electronic Communications in Probability},
Volume = {24},
Publisher = {Institute of Mathematical Statistics},
Year = {2019},
Month = {January},
url = {http://dx.doi.org/10.1214/19-ECP235},
Abstract = {© 2019, Institute of Mathematical Statistics. All rights
reserved. We provide a uniform upper bound on the minimal
drift so that the one-per-site frog model on a d-ary tree is
recurrent. To do this, we introduce a subprocess that
couples across trees with different degrees. Finding
couplings for frog models on nested sequences of graphs is
known to be difficult. The upper bound comes from combining
the coupling with a new, simpler proof that the frog model
on a binary tree is recurrent when the drift is sufficiently
strong. Additionally, we describe a coupling between frog
models on trees for which the degree of the smaller tree
divides that of the larger one. This implies that the
critical drift has a limit as d tends to infinity along
certain subsequences.},
Doi = {10.1214/19-ECP235},
Key = {fds343710}
}
@article{fds339575,
Author = {Beckman, E and Dinan, E and Durrett, R and Huo, R and Junge,
M},
Title = {Asymptotic behavior of the brownian frog
model},
Journal = {Electronic Journal of Probability},
Volume = {23},
Publisher = {Institute of Mathematical Statistics},
Year = {2018},
Month = {January},
url = {http://dx.doi.org/10.1214/18-EJP215},
Abstract = {© 2018, University of Washington. All rights reserved. We
introduce an extension of the frog model to Euclidean space
and prove properties for the spread of active particles. Fix
r>0 and place a particle at each point x of a unit intensity
Poisson point process P⊆ℝd−B(0,r). Around each point
in P, put a ball of radius r. A particle at the origin
performs Brownian motion. When it hits the ball around x for
some x ∈ P, new particles begin independent Brownian
motions from the centers of the balls in the cluster
containing x. Subsequent visits to the cluster do nothing.
This waking process continues indefinitely. For r smaller
than the critical threshold of continuum percolation, we
show that the set of activated points in P approximates a
linearly expanding ball. Moreover, in any fixed ball the set
of active particles converges to a unit intensity Poisson
point process.},
Doi = {10.1214/18-EJP215},
Key = {fds339575}
}
@article{fds340893,
Author = {Cristali, I and Ranjan, V and Steinberg, J and Beckman, E and Durrett,
R and Junge, M and Nolen, J},
Title = {Block size in geometric(P)-biased permutations},
Journal = {Electronic Communications in Probability},
Volume = {23},
Year = {2018},
Month = {January},
url = {http://dx.doi.org/10.1214/18-ECP182},
Abstract = {© 2018, University of Washington. All rights reserved. Fix
a probability distribution p = (p1, p2, …) on the positive
integers. The first block in a p-biased permutation can be
visualized in terms of raindrops that land at each positive
integer j with probability pj. It is the first point K so
that all sites in [1, K] are wet and all sites in (K, ∞)
are dry. For the geometric distribution pj = p(1 − p)j−1
we show that p log K converges in probability to an explicit
constant as p tends to 0. Additionally, we prove that if p
has a stretch exponential distribution, then K is infinite
with positive probability.},
Doi = {10.1214/18-ECP182},
Key = {fds340893}
}
%% Belov, Sergey
@article{fds31885,
Author = {Sergei Belov and Alexei Rybkin},
Title = {On the existence of WKB-type asymptotics for the generalized
eigenvectors of discrete string operators},
Journal = {Bull. London Math. Soc.},
Volume = {36},
Number = {2},
Pages = {241-251},
Year = {2004},
MRNUMBER = {2026899},
url = {http://www.ams.org/mathscinet-getitem?mr=2026899},
Key = {fds31885}
}
@article{fds31887,
Author = {S.M. Belov and N.B. Avdonina and Z. Felfli and M. Marletta and A. Z.
Msezane and S.N. Naboko},
Title = {Semiclassical approach to Regge poles trajectories
calculations for nonsingular potentials: Thomas-Fermi
type},
Journal = {J. Phys. A},
Volume = {37},
Number = {27},
Pages = {6943–6954},
Year = {2004},
MRNUMBER = {2078324},
url = {http://www.ams.org/mathscinet-getitem?mr=2078324},
Key = {fds31887}
}
@article{fds31884,
Author = {S.M. Belov and A.V. Rybkin},
Title = {Higher order trace formulas of the Buslaev-Faddeev type for
the half-line Schrodinger operator with long-range
potentials},
Journal = {J. Math. Phys.},
Volume = {44},
Number = {7},
Pages = {2748–2761},
Year = {2003},
MRNUMBER = {1982789},
url = {http://www.ams.org/mathscinet-getitem?mr=1982789},
Key = {fds31884}
}
@article{fds31883,
Author = {N.B. Avdonina and S. Belov and Z. Felfli and A.Z. Msezane and S.N.
Naboko},
Title = {Semiclassical approach for calculating Regge-pole
trajectories for singular potentials},
Journal = {Phys. Rev. A (3)},
Volume = {66},
Number = {2},
Pages = {022713},
Year = {2002},
MRNUMBER = {1955150},
url = {http://link.aps.org/abstract/PRA/v66/e022713},
Key = {fds31883}
}
%% Cain, John
@misc{fds32393,
Author = {D.G. Schaeffer and J.W. Cain and D.J. Gauthier and S.S. Kalb and W.
Krassowska, R.A. Oliver and E.G. Tolkacheva and W.
Ying},
Title = {An ionically based mapping model with memory for cardiac
restitution},
Year = {2005},
Month = {February},
Key = {fds32393}
}
@article{fds38248,
Author = {J.W. Cain and D.G. Schaeffer},
Title = {Two-term asymptotic approximation of a cardiac restitution
curve},
Year = {2005},
Key = {fds38248}
}
@misc{fds36954,
Author = {J. Cain},
Title = {Issues in the one-dimensional dynamics of a paced cardiac
fiber},
Journal = {Ph.D. Dissertation, Duke University},
Year = {2005},
Key = {fds36954}
}
@misc{fds26554,
Author = {J.W. Cain and E.G. Tolkacheva and D.G. Schaeffer and D.J.
Gauthier},
Title = {Rate-dependent waveback velocity of cardiac action
potentials in a one-dimensional cable},
Journal = {International Conference for Mathematics in Biology and
Medicine: Annual Meeting for the Society for Mathematical
Biology},
Year = {2004},
Month = {July},
Key = {fds26554}
}
@article{fds26048,
Author = {D.G. Schaeffer and J.W. Cain and D.J. Gauthier and S.S. Kalb and W.
Krassowska, R.A. Oliver and E.G. Tolkacheva},
Title = {An ionically based mapping model with memory for cardiac
restitution},
Journal = {Bull. Math. Bio.},
Year = {2004},
Key = {fds26048}
}
@article{fds30212,
Author = {J.W. Cain and E.G. Tolkacheva and D.G. Schaeffer and D.J.
Gauthier},
Title = {Rate-dependent propagation of cardiac action potentials in a
one-dimensional fiber},
Journal = {Phys. Rev. E.},
Volume = {70},
Number = {6},
Pages = {061906},
Year = {2004},
Key = {fds30212}
}
@misc{fds26555,
Author = {J.W. Cain},
Title = {Simulating discordant alternans with a two-current
model},
Journal = {International School on Biomathematics, Bioengineering and
Clinical Aspects of Blood Flow, MSRI},
Year = {2002},
Month = {August},
Key = {fds26555}
}
%% Cao, Yu
@article{fds344622,
Author = {Cao, Y and Lu, J and Lu, Y},
Title = {Exponential Decay of Rényi Divergence Under Fokker–Planck
Equations},
Journal = {Journal of Statistical Physics},
Volume = {176},
Number = {5},
Pages = {1172-1184},
Year = {2019},
Month = {September},
url = {http://dx.doi.org/10.1007/s10955-019-02339-8},
Abstract = {© 2019, Springer Science+Business Media, LLC, part of
Springer Nature. We prove the exponential convergence to the
equilibrium, quantified by Rényi divergence, of the
solution of the Fokker–Planck equation with drift given by
the gradient of a strictly convex potential. This extends
the classical exponential decay result on the relative
entropy for the same equation.},
Doi = {10.1007/s10955-019-02339-8},
Key = {fds344622}
}
@article{fds343501,
Author = {Cao, Y and Lu, J and Lu, Y},
Title = {Gradient flow structure and exponential decay of the
sandwiched Rényi divergence for primitive Lindblad
equations with GNS-detailed balance},
Journal = {Journal of Mathematical Physics},
Volume = {60},
Number = {5},
Pages = {052202-052202},
Publisher = {AIP Publishing},
Year = {2019},
Month = {May},
url = {http://dx.doi.org/10.1063/1.5083065},
Abstract = {© 2019 Author(s). We study the entropy production of the
sandwiched Rényi divergence under the primitive Lindblad
equation with Gel'fand-Naimark-Segal-detailed balance. We
prove that the Lindblad equation can be identified as the
gradient flow of the sandwiched Rényi divergence of any
order α ∈ (0, ∞). This extends a previous result by
Carlen and Maas [J. Funct. Anal. 273(5), 1810-1869 (2017)]
for the quantum relative entropy (i.e., α = 1). Moreover,
we show that the sandwiched Rényi divergence of any order
α ∈ (0, ∞) decays exponentially fast under the time
evolution of such a Lindblad equation.},
Doi = {10.1063/1.5083065},
Key = {fds343501}
}
@article{fds337049,
Author = {Cao, Y and Lu, J},
Title = {Stochastic dynamical low-rank approximation
method},
Journal = {Journal of Computational Physics},
Volume = {372},
Pages = {564-586},
Publisher = {Elsevier BV},
Year = {2018},
Month = {November},
url = {http://dx.doi.org/10.1016/j.jcp.2018.06.058},
Abstract = {© 2018 Elsevier Inc. In this paper, we extend the dynamical
low-rank approximation method to the space of finite signed
measures. Under this framework, we derive stochastic
low-rank dynamics for stochastic differential equations
(SDEs) coming from classical stochastic dynamics or
unraveling of Lindblad quantum master equations. We justify
the proposed method by error analysis and also numerical
examples for applications in solving high-dimensional SDE,
stochastic Burgers' equation, and high-dimensional Lindblad
equation.},
Doi = {10.1016/j.jcp.2018.06.058},
Key = {fds337049}
}
@article{fds337050,
Author = {Cao, Y and Lu, J},
Title = {Lindblad equation and its semiclassical limit of the
Anderson-Holstein model},
Journal = {Journal of Mathematical Physics},
Volume = {58},
Number = {12},
Pages = {122105-122105},
Publisher = {AIP Publishing},
Year = {2017},
Month = {December},
url = {http://dx.doi.org/10.1063/1.4993431},
Abstract = {© 2017 Author(s). For multi-level open quantum systems, the
interaction between different levels could pose a challenge
to understand the quantum system both analytically and
numerically. In this work, we study the approximation of the
dynamics of the Anderson-Holstein model, as a model of the
multi-level open quantum system, by Redfield and Lindblad
equations. Both equations have a desirable property that if
the density operators for different levels are diagonal
initially, they remain to be diagonal for any time. Thanks
to this nice property, the semiclassical limit of both
Redfield and Lindblad equations could be derived explicitly;
the resulting classical master equations share similar
structures of transport and hopping terms. The Redfield and
Lindblad equations are also compared from the angle of time
dependent perturbation theory.},
Doi = {10.1063/1.4993431},
Key = {fds337050}
}
@article{fds337051,
Author = {Cao, Y and Lin, L and Zhou, X},
Title = {Explore stochastic instabilities of periodic points by
transition path theory},
Journal = {Journal of Nonlinear Science},
Volume = {26},
Number = {3},
Pages = {755-786},
Publisher = {Springer Nature},
Year = {2016},
Month = {March},
url = {http://dx.doi.org/10.1007/s00332-016-9289-6},
Abstract = {© Springer Science+Business Media New York 2016. We
consider the noise-induced transitions from a linearly
stable periodic orbit consisting of T periodic points in
randomly perturbed discrete logistic map. Traditional large
deviation theory and asymptotic analysis at small noise
limit cannot distinguish the quantitative difference in
noise-induced stochastic instabilities among the T periodic
points. To attack this problem, we generalize the transition
path theory to the discrete-time continuous-space stochastic
process. In our first criterion to quantify the relative
instability among T periodic points, we use the distribution
of the last passage location related to the transitions from
the whole periodic orbit to a prescribed disjoint set. This
distribution is related to individual contributions to the
transition rate from each periodic points. The second
criterion is based on the competency of the transition paths
associated with each periodic point. Both criteria utilize
the reactive probability current in the transition path
theory. Our numerical results for the logistic map reveal
the transition mechanism of escaping from the stable
periodic orbit and identify which periodic point is more
prone to lose stability so as to make successful transitions
under random perturbations.},
Doi = {10.1007/s00332-016-9289-6},
Key = {fds337051}
}
%% Cruz, Joshua
@article{fds341431,
Author = {Cruz, J and Giusti, C and Itskov, V and Kronholm,
B},
Title = {On Open and Closed Convex Codes},
Journal = {Discrete & Computational Geometry},
Volume = {61},
Number = {2},
Pages = {247-270},
Publisher = {Springer Science and Business Media LLC},
Year = {2019},
Month = {March},
url = {http://dx.doi.org/10.1007/s00454-018-00050-1},
Doi = {10.1007/s00454-018-00050-1},
Key = {fds341431}
}
%% Dai, Shu
@article{fds150138,
Author = {S. Dai and D. G. Schaeffer},
Title = {Spectrum of a linearized amplitude equation for alternans in
a cardiac fiber},
Journal = {SIAM J. Appl. Math.},
Year = {2008},
Abstract = {Under rapid periodic pacing, cardiac cells typically undergo
a period-doubling bifurcation in which action potentials of
short and long duration alternate with one another. If these
action potentials propagate in a fiber, the short-long
alternation may suffer reversals of phase at various points
along the fiber, a phenomenon called (spatially) discordant
alternans. Either stationary or moving patterns are
possible. Using a weak approximation, Echebarria and Karma
proposed an equation to describe the spatiotemporal dynamics
of small-amplitude alternans in a class of simple cardiac
models, and they showed that an instability in this equation
predicts the spontaneous formation of discordant alternans.
To study the bifurcation, they computed the spectrum of the
relevant linearized operator numerically, supplemented with
partial analytical results. In the present paper we
calculate this spectrum with purely analytical methods in
two cases where a small parameter may be exploited: (i)
small dispersion or (ii) a long fiber. From this analysis we
estimate the parameter ranges in which the phase reversals
of discordant alternans are stationary or
moving.},
Key = {fds150138}
}
@article{fds150136,
Author = {S. Dai and D. G. Schaeffer},
Title = {Bifurcations in a modulation equation for alternans in a
cardiac fiber},
Journal = {Math. Modelling and Num. Analysis},
Year = {2008},
Abstract = {While alternans in a single cardiac cell appears through a
simple period-doubling bifurcation, in extended tissue the
exact nature of the bifurcation is unclear. In particular,
the phase of alternans can exhibit wave-like spatial
dependence, either stationary or traveling, which is known
as discordant alternans. We study these phenomena in simple
cardiac models through a modulation equation proposed by
Echebarria-Karma. As shown in our previous paper, the zero
solution of their equation may lose stability, as the pacing
rate is increased, through either a Hopf or steady-state
bifurcation. Which bifurcation occurs first depends on
parameters in the equation, and for one critical case both
modes bifurcate together at a degenerate (codimension 2)
bifurcation. For parameters close to the degenerate case, we
investigate the competition between modes, both numerically
and analytically. We find that at sufficiently rapid pacing
(but assuming a 1:1 response is maintained), steady patterns
always emerge as the only stable solution. However, in the
parameter range where Hopf bifurcation occurs first, the
evolution from periodic solution (just after the
bifurcation) to the eventual standing wave solution occurs
through an interesting series of secondary
bifurcations.},
Key = {fds150136}
}
%% Diaz, Humberto
@article{fds299458,
Author = {H. Diaz},
Title = {The motive of a smooth Theta divisor},
Year = {2015},
Key = {fds299458}
}
@article{fds227122,
Author = {H. Diaz},
Title = {The motive of the Fano surface of lines},
Year = {2015},
Key = {fds227122}
}
%% Duncan, William
@article{fds346636,
Author = {Duncan, W and Best, J and Golubitsky, M and Nijhout, HF and Reed,
M},
Title = {Homeostasis despite instability.},
Journal = {Mathematical Biosciences},
Volume = {300},
Pages = {130-137},
Year = {2018},
Month = {June},
url = {http://dx.doi.org/10.1016/j.mbs.2018.03.025},
Abstract = {We have shown previously that different homeostatic
mechanisms in biochemistry create input-output curves with a
"chair" shape. At equilibrium, for intermediate values of a
parameter (often an input), a variable, Z, changes very
little (the homeostatic plateau), but for low and high
values of the parameter, Z changes rapidly (escape from
homeostasis). In all cases previously studied, the steady
state was stable for each value of the input parameter. Here
we show that, for the feedback inhibition motif, stability
may be lost through a Hopf bifurcation on the homeostatic
plateau and then regained by another Hopf bifurcation. If
the limit cycle oscillations are relatively small in the
unstable interval, then the variable Z maintains homeostasis
despite the instability. We show that the existence of an
input interval in which there are oscillations, the length
of the interval, and the size of the oscillations depend in
interesting and complicated ways on the properties of the
inhibition function, f, the length of the chain, and the
size of a leakage parameter.},
Doi = {10.1016/j.mbs.2018.03.025},
Key = {fds346636}
}
%% Feist, Andrew
@article{fds13550,
Author = {Andrew Feist},
Title = {Fun With the Sigma-Function},
Journal = {Missouri Journal of Mathematical Sciences},
Volume = {15},
Number = {3},
Pages = {173-177},
Year = {2003},
Month = {Fall},
url = {http://www.math-cs.cmsu.edu/~mjms/mjms.html},
Key = {fds13550}
}
@article{fds10468,
Author = {McCune, Veroff and Fitelson, Harris and Feist, Wos},
Title = {Short Single Axioms for Boolean Algebra},
Journal = {Journal of Automated Reasoning, vol. 29, (2002), pp.
1-16},
Year = {2002},
Month = {July},
MRNUMBER = {2003i:68119},
url = {http://www.kluweronline.com/issn/0168-7433},
Abstract = {We present short single equational axioms for Boolean
algebra in terms of disjunction and negation and in terms of
the Sheffer stroke. Previously known single axioms for these
theories are much longer than the ones we present. We show
that there is no shorter axiom in terms of the Sheffer
stroke. Automated deduction techniques were used in several
parts of the work.},
Key = {fds10468}
}
@article{fds9787,
Author = {Andrew Feist},
Title = {On the Density of Birthday Sets},
Journal = {The Pentagon, vol. 60 (2000), no. 1, pp.
31-35},
Key = {fds9787}
}
%% Fox, Daniel
@article{fds31610,
Author = {Jennie Traschen and Daniel Fox},
Title = {Tension perturbations of black brane spacetimes},
Journal = {Class. Quantum Grav.},
Volume = {21},
Pages = {289-306},
Year = {2004},
Abstract = {Abstract. We consider black brane spacetimes that have at
least one spatial translation Killing field that is tangent
to the brane. A new parameter, the tension of a spacetime,
is defined. The tension parameter is associated with spatial
translations in much the same way that the ADM mass is
associated with the time translation Killing field. In this
work, we explore the implications of the spatial translation
symmetry for small perturbations around a background black
brane. For static-charged black branes we derive a law which
relates the tension perturbation to the surface gravity
times the change in the horizon area, plus terms that
involve variations in the charges and currents. We find that
as a black brane evaporates the tension decreases. We also
give a simple derivation of a first law for black brane
spacetimes. These constructions hold when the background
stress–energy is governed by a Hamiltonian, and the
results include arbitrary perturbative stress–energy
sources.},
Key = {fds31610}
}
%% Gjoneski, Oliver
@misc{fds182407,
Author = {O. Gjoneski},
Title = {Three Variable Period Polynomials associated to Cusp
Forms},
Journal = {in preparation},
Year = {2010},
Key = {fds182407}
}
@unpublished{author = "Oliver Gjoneski",
Author = {O. Gjoneski},
Title = {Cohomology of GL4(Z)},
Journal = {in preparation},
Year = {2010},
Key = {author = "Oliver Gjoneski"}
}
@misc{fds182411,
Author = {O. Gjoneski},
Title = {Degenerate Tilings and Invariant Spines},
Journal = {in preparation},
Year = {2010},
Key = {fds182411}
}
@misc{fds182410,
Author = {O. Gjoneski and K. Smith},
Title = {On the nonexistence of a (176, 50, 14) difference
set},
Journal = {unpublished manuscript},
Year = {2005},
Key = {fds182410}
}
%% Goetz, Andrew
@article{fds226222,
Author = {A. S. Goetz},
Title = {Tully-Fisher Scalings and Boundary Conditions for Wave Dark
Matter},
Year = {2015},
Month = {February},
url = {http://arxiv.org/abs/1502.04976},
Abstract = {We investigate a theory of dark matter called wave dark
matter, also known as scalar field dark matter (SFDM) and
boson star dark matter or Bose-Einstein condensate (BEC)
dark matter (also see axion dark matter), and its relation
to the Tully-Fisher relation. We exhibit two boundary
conditions that give rise to Tully-Fisher-like relations for
spherically symmetric static wave dark matter halos: (BC1)
Fixing a length scale at the outer edge of wave dark matter
halos gives rise to a Tully-Fisher-like relation of the form
M/v^4=const. (BC2) Fixing the density of dark matter at the
outer edge of wave dark matter halos gives rise to a
Tully-Fisher-like relation of the form M/v^3.4=const.},
Key = {fds226222}
}
@article{fds225134,
Author = {H.L. Bray and A.S. Goetz},
Title = {Wave Dark Matter and the Tully-Fisher Relation},
Year = {2014},
Month = {October},
url = {http://arxiv.org/abs/1409.7347},
Abstract = {We investigate a theory of dark matter called wave dark
matter, also known as scalar field dark matter (SFDM) and
boson star dark matter or Bose-Einstein condensate (BEC)
dark matter, in spherical symmetry and its relation to the
Tully-Fisher relation. We show that fixing the oscillation
frequency of wave dark matter near the edge of dark galactic
halos implies a Tully-Fisher-like relation for those halos.
We then describe how this boundary condition, which is
roughly equivalent to fixing the half-length of the
exponentially decaying tail of each galactic halo mass
profile, may yield testable predictions for this theory of
dark matter.},
Key = {fds225134}
}
%% Gratton, Michael B.
@article{coarse-grav,
Author = {M.B. Gratton and T.P. Witelski},
Title = {Coarsening of dewetting thin films subject to
gravity},
Journal = {Phys. Rev. E.},
Volume = {77},
Pages = {016301},
Year = {2008},
Month = {January},
Key = {coarse-grav}
}
@article{fds70307,
Author = {M.B. Gratton et. al.},
Title = {Backward Diffusion methods for digital halftoning},
Pages = {1 -- 15},
Booktitle = {Proceedings of the Twenty-Second Annual Workshop on
Mathematical Problems in Industry},
Year = {2006},
Month = {June},
Key = {fds70307}
}
%% Greer, John B.
@article{fds13521,
Author = {Andrea L. Bertozzi and John B. Greer},
Title = {Low curvature image simplifiers: global regularity of smooth
solutions and Laplacian limiting schemes},
Journal = {Comm. Pure Appl. Math., submitted 2003},
url = {http://www.math.duke.edu/~jbg33/lcis.ps},
Key = {fds13521}
}
@article{fds10475,
Author = {J. B. Greer and A. L. Bertozzi},
Title = {Traveling Wave Solutions of Fourth Order PDES for Image
Processing},
url = {http://www.math.duke.edu/~jbg33/paper/tw.ps},
Key = {fds10475}
}
@article{fds10219,
Author = {John B. Greer and Andrea L. Bertozzi},
Title = {H^1 Solutions of a Class of Fourth Order Nonlinear Equations
for Image Processing},
Journal = {Journal of Discrete and Continuous Dynamical
Systems},
url = {http://www.math.duke.edu/~jbg33/fourthorder.ps},
Abstract = {Recently fourth order equations of the form u_t =
-\nabla\cdot(({\mathcal G}(J_\sigma u)) \nabla \Delta u)
have been proposed for noise reduction and simplification of
two dimensional images. The operator \mathcal G is a
nonlinear functional involving the gradient or Hessian of
its argument, with decay in the far field. The operator
J_\sigma is a standard mollifier. Using ODE methods on
Sobolev spaces, we prove existence and uniqueness of
solutions of this problem for H^1 initial
data.},
Key = {fds10219}
}
%% Gu, Miao
@article{fds341820,
Author = {Gu, M and Martin, GG},
Title = {Factorization tests and algorithms arising from counting
modular forms and automorphic representations},
Journal = {Canadian Mathematical Bulletin},
Volume = {62},
Number = {1},
Pages = {81-97},
Publisher = {Canadian Mathematical Society},
Year = {2019},
Month = {March},
url = {http://dx.doi.org/10.4153/CMB-2018-035-0},
Abstract = {A theorem of Gekeler compares the number of non-isomorphic
automorphic representations associated with the space of
cusp forms of weight k on Γ 0 (N) to a simpler function of
k and N, showing that the two are equal whenever N is
squarefree. We prove the converse of this theorem (with one
small exception), thus providing a characterization of
squarefree integers. We also establish a similar
characterization of prime numbers in terms of the number of
Hecke newforms of weight k on Γ 0 (N). It follows that a
hypothetical fast algorithm for computing the number of such
automorphic representations for even a single weight k would
yield a fast test for whether N is squarefree. We also show
how to obtain bounds on the possible square divisors of a
number N that has been found not to be squarefree via this
test, and we show how to probabilistically obtain the
complete factorization of the squarefull part of N from the
number of such automorphic representations for two different
weights. If in addition we have the number of such Hecke
newforms for even a single weight k, then we show how to
probabilistically factor N entirely. All of these
computations could be performed quickly in practice, given
the number(s) of automorphic representations and modular
forms as input.},
Doi = {10.4153/CMB-2018-035-0},
Key = {fds341820}
}
%% Gunderson, Ryan
@article{fds225241,
Author = {D. Campos and R. Gunderson and S. Morey and C. Paulsen and T.
Polstra},
Title = {Depths and Cohen-Macaulay properties of path
ideals},
Journal = {Journal of Pure and Applied Algebra},
Volume = {218},
Number = {8},
Pages = {1537–1543},
Year = {2014},
Month = {August},
Key = {fds225241}
}
%% Haskett, Ryan P.
@article{fds26926,
Author = {Ryan P. Haskett and Thomas P. Witelski and Jeanman
Sur},
Title = {Localized Marangoni Forcing in Driven Thin
Films},
Journal = {Physica D},
Year = {2004},
Keywords = {thin films fluid dynamics thermocapillary valve Marangoni
forcing lubrication theory},
Abstract = {We consider the use of localized Marangoni forcing to
produce a thermocapillary ``microfluidic valve'' that allows
us to control the downstream flow of a thin film of viscous
fluid. To this end, we analyze the influence of this
localized forcing on a flow driven by a combination of
uniform Marangoni stresses and gravity in a one-dimensional
model. Long-time solutions approach states that can be
categorized in two classes, where the film thickness
downstream of the forcing is: (I) determined by the upstream
thickness, or (II) controlled by the forcing amplitude. The
type~II solutions are stable stationary hydraulic jumps for
thin films. We give careful attention to the relation
between the forcing and the downstream film flow for the
resulting bi-stable solutions. Comparison of the
one-dimensional theory with two-dimensional computations and
experimental results is given.},
Key = {fds26926}
}
%% Hsu, Chun-Hsien
@article{fds373473,
Author = {Getz, J and Hsu, C-H and Leslie, S},
Title = {Harmonic analysis on certain spherical varieties},
Journal = {Journal of the European Mathematical Society},
Publisher = {EMS Press},
Year = {2023},
Month = {October},
url = {http://dx.doi.org/10.4171/JEMS/1381},
Doi = {10.4171/JEMS/1381},
Key = {fds373473}
}
%% Huo, Ran
@article{fds338635,
Author = {Huo, R and Durrett, R},
Title = {Latent voter model on locally tree-like random
graphs},
Journal = {Stochastic Processes and Their Applications},
Volume = {128},
Number = {5},
Pages = {1590-1614},
Publisher = {Elsevier BV},
Year = {2018},
Month = {May},
url = {http://dx.doi.org/10.1016/j.spa.2017.08.004},
Abstract = {© 2017 Elsevier B.V. In the latent voter model, individuals
who have just changed their choice have a latent period,
which is exponential with rate λ, during which they will
not change their opinion. We study this model on random
graphs generated by a configuration model with degrees
3≤d(x)≤M. We show that if the number of vertices n→∞
and logn≪λn≪n then there is a quasi-stationary state in
which each opinion has probability ≈1∕2 and persists in
this state for a time that is ≥nm for any
m<∞.},
Doi = {10.1016/j.spa.2017.08.004},
Key = {fds338635}
}
@article{fds339579,
Author = {Beckman, E and Dinan, E and Durrett, R and Huo, R and Junge,
M},
Title = {Asymptotic behavior of the brownian frog
model},
Journal = {Electronic Journal of Probability},
Volume = {23},
Publisher = {Institute of Mathematical Statistics},
Year = {2018},
Month = {January},
url = {http://dx.doi.org/10.1214/18-EJP215},
Abstract = {© 2018, University of Washington. All rights reserved. We
introduce an extension of the frog model to Euclidean space
and prove properties for the spread of active particles. Fix
r>0 and place a particle at each point x of a unit intensity
Poisson point process P⊆ℝd−B(0,r). Around each point
in P, put a ball of radius r. A particle at the origin
performs Brownian motion. When it hits the ball around x for
some x ∈ P, new particles begin independent Brownian
motions from the centers of the balls in the cluster
containing x. Subsequent visits to the cluster do nothing.
This waking process continues indefinitely. For r smaller
than the critical threshold of continuum percolation, we
show that the set of activated points in P approximates a
linearly expanding ball. Moreover, in any fixed ball the set
of active particles converges to a unit intensity Poisson
point process.},
Doi = {10.1214/18-EJP215},
Key = {fds339579}
}
%% Jauregui, Jeff
@article{fds163797,
Author = {Hubert L. Bray and Jeffrey L. Jauregui},
Title = {A geometric theory of zero area singularities in general
relativity},
Year = {2009},
Month = {September},
url = {http://arxiv.org/abs/0909.0522},
Key = {fds163797}
}
%% Ji, Hangjie
@article{fds322248,
Author = {Y. Gao and H. Ji and J. Liu and T. P. Witelski},
Title = {Global existence of solutions to a tear film model with
locally elevated evaporation rates},
Year = {2017},
url = {http://arxiv.org/abs/1701.00853},
Key = {fds322248}
}
@article{fds322247,
Author = {H. Ji and T. P. Witelski},
Title = {Finite-time thin film rupture driven by generalized
evaporative loss},
Journal = {Physica D: Nonlinear Phenomena},
Year = {2016},
url = {http://arxiv.org/abs/1601.03625},
Key = {fds322247}
}
%% Laurent, Thomas
@article{fds46038,
Author = {T. Laurent and B. Rider and M.C. Reed},
Title = {Parabolic Behavior of a Hyperbolic Delay
Equation},
Journal = {SIAM J. Mathematical Analysis},
Year = {2006},
Key = {fds46038}
}
%% Lawley, Sean D.
@article{fds223274,
Author = {SD Lawley and JC Mattingly and MC Reed},
Title = {Sensitivity to switching rates in stochastically switched
ODEs},
Journal = {Commun. Math. Sci.},
Year = {2014},
url = {http://arxiv.org/abs/1310.2525},
Key = {fds223274}
}
@article{fds223275,
Author = {SD Lawley and J Yun and M Gamble and M Hall and MC Reed and HF
Nijhout},
Title = {Mathematical modeling of the effects of glutathione on
arsenic methylation},
Year = {2014},
Key = {fds223275}
}
@article{fds194478,
Author = {SD Lawley and M Cinderella and M Hall and M Gamble and HF Nijhout and MC
Reed},
Title = {Mathematical model insights into arsenic
methylation},
Journal = {Theoretical Biology and Medical Modelling},
Year = {2011},
Key = {fds194478}
}
%% Leete, Jessica
@article{fds346829,
Author = {Ahmed, S and Hu, R and Leete, J and Layton, AT},
Title = {Understanding sex differences in long-term blood pressure
regulation: insights from experimental studies and
computational modeling.},
Journal = {American Journal of Physiology Heart and Circulatory
Physiology},
Volume = {316},
Number = {5},
Pages = {H1113-H1123},
Year = {2019},
Month = {May},
url = {http://dx.doi.org/10.1152/ajpheart.00035.2019},
Abstract = {Sex differences in blood pressure and the prevalence of
hypertension are found in humans and animal models.
Moreover, there has been a recent explosion of data
concerning sex differences in nitric oxide, the
renin-angiotensin-aldosterone system, inflammation, and
kidney function. These data have the potential to reveal the
mechanisms underlying male-female differences in blood
pressure control. To elucidate the interactions among the
multitude of physiological processes involved, one may apply
computational models. In this review, we describe published
computational models that represent key players in blood
pressure regulation, and highlight sex-specific models and
their findings.},
Doi = {10.1152/ajpheart.00035.2019},
Key = {fds346829}
}
@article{fds339743,
Author = {Leete, J and Layton, AT},
Title = {Sex-specific long-term blood pressure regulation: Modeling
and analysis.},
Journal = {Computers in Biology and Medicine},
Volume = {104},
Pages = {139-148},
Year = {2019},
Month = {January},
url = {http://dx.doi.org/10.1016/j.compbiomed.2018.11.002},
Abstract = {Hypertension is a global health challenge: it affects one
billion people worldwide and is estimated to account for
>60% of all cases or types of cardiovascular disease. In
part because sex differences in blood pressure regulation
mechanisms are not sufficiently well understood, fewer
hypertensive women achieve blood pressure control compared
to men, even though compliance and treatment rates are
generally higher in women. Thus, the objective of this study
is to identify which factors contribute to the sexual
dimorphism in response to anti-hypertensive therapies
targeting the renin angiotensin system (RAS). To accomplish
that goal, we develop sex-specific blood pressure regulation
models. Sex differences in the RAS, baseline adosterone
level, and the reactivity of renal sympathetic nervous
activity (RSNA) are represented. A novel aspect of the model
is the representation of sex-specific vasodilatory effect of
the bound angiotensin II type two receptor (AT2R-bound Ang
II) on renal vascular resistance. Model simulations suggest
that sex differences in RSNA are the largest cause of female
resistance to developing hypertension due to the direct
influence of RSNA on afferent arteriole resistance.
Furthermore, the model predicts that the sex-specific
vasodilatory effects of AT2R-bound Ang II on renal vascular
resistance may explain the higher effectiveness of
angiotensin receptor blockers in treating hypertensive women
(but not men), compared to angiotensin converting enzyme
inhibitors.},
Doi = {10.1016/j.compbiomed.2018.11.002},
Key = {fds339743}
}
@article{fds346830,
Author = {Leete, J and Gurley, S and Layton, A},
Title = {Modeling Sex Differences in the Renin Angiotensin System and
the Efficacy of Antihypertensive Therapies.},
Journal = {Computers & Chemical Engineering},
Volume = {112},
Pages = {253-264},
Year = {2018},
Month = {April},
url = {http://dx.doi.org/10.1016/j.compchemeng.2018.02.009},
Abstract = {The renin angiotensin system is a major regulator of blood
pressure and a target for many anti-hypertensive therapies;
yet the efficacy of these treatments varies between the
sexes. We use published data for systemic RAS hormones to
build separate models for four groups of rats: male
normotensive, male hypertensive, female normotensive, and
female hypertensive rats. We found that plasma renin
activity, angiotensinogen production rate, angiotensin
converting enzyme activity, and neutral endopeptidase
activity differ significantly among the four groups of rats.
Model results indicate that angiotensin converting enzyme
inhibitors and angiotensin receptor blockers induce similar
percentage decreases in angiotensin I and II between groups,
but substantially different absolute decreases. We further
propose that a major difference between the male and female
RAS may be the strength of the feedback mechanism, by which
receptor bound angiotensin II impacts the production of
renin.},
Doi = {10.1016/j.compchemeng.2018.02.009},
Key = {fds346830}
}
%% Leverson, Caitlin
@article{fds311182,
Author = {C. Leverson},
Title = {Augmentations and Rulings of Legendrian Links in
$\#^k(S^1\times S^2)$},
Year = {2015},
url = {http://arxiv.org/abs/1510.06071},
Key = {fds311182}
}
@article{fds311183,
Author = {C. Leverson},
Title = {Augmentations and Rulings of Legendrian Knots},
Journal = {Journal of Symplectic Geometry},
Year = {2014},
url = {http://arxiv.org/abs/1403.4982},
Key = {fds311183}
}
%% Li, Didong
@article{fds341808,
Author = {Didong Li and David B Dunson},
Title = {Classification via local manifold approximation},
Year = {2019},
url = {http://arxiv.org/abs/1903.00985},
Key = {fds341808}
}
@article{fds341807,
Author = {D. Li and Minerva Mukhopadhyay and David Dunson},
Title = {Efficient Manifold and Subspace Approximations with
Spherelets},
Year = {2018},
url = {http://arxiv.org/abs/1706.08263},
Key = {fds341807}
}
@article{fds337143,
Author = {Wang, J and Sun, H and Li, D},
Title = {A Geodesic-Based Riemannian Gradient Approach to Averaging
on the Lorentz Group},
Journal = {Entropy},
Volume = {19},
Number = {12},
Pages = {698-698},
Publisher = {MDPI AG},
Year = {2017},
Month = {December},
url = {https://www.mdpi.com/1099-4300/19/12/698/},
Doi = {10.3390/e19120698},
Key = {fds337143}
}
@article{fds346337,
Author = {Cao, L and Li, D and Zhang, E and Zhang, Z and Sun, H},
Title = {A Statistical Cohomogeneity One Metric on the Upper Plane
with Constant Negative Curvature},
Journal = {Advances in Mathematical Physics},
Volume = {2014},
Pages = {1-6},
Publisher = {Hindawi Limited},
Year = {2014},
url = {https://www.hindawi.com/journals/amp/2014/832683/abs/},
Abstract = {<jats:p>we analyze the geometrical structures of statistical
manifold<jats:italic>S</jats:italic>consisting of all the
wrapped Cauchy distributions. We prove that<jats:italic>S</jats:italic>is
a simply connected manifold with constant negative
curvature??<mml:mi>K</mml:mi><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mn>2</mml:mn></mml:math>.
However, it is not isometric to the hyperbolic space
because<jats:italic>S</jats:italic>is noncomplete. In
fact,<jats:italic>S</jats:italic>is approved to be a
cohomogeneity one manifold. Finally, we use several tricks
to get the geodesics and explore the divergence performance
of them by investigating the Jacobi vector
field.</jats:p>},
Doi = {10.1155/2014/832683},
Key = {fds346337}
}
@article{fds341320,
Author = {Dongxiao Yang and Didong Li and Huafei Sun},
Title = {2D Dubins Path in Environments with Obstacle},
Journal = {Mathematical Problems in Engineering},
Volume = {2013},
Year = {2013},
url = {https://www.hindawi.com/journals/mpe/2013/291372/},
Doi = {10.1155/2013/291372},
Key = {fds341320}
}
%% Li, Yi
@article{fds217611,
Author = {Y. Li and Anita T. Layton},
Title = {Accurate computation of Stokes flow driven by an open
immersed interface},
Journal = {J. Compute. Phys.},
Volume = {231},
Number = {15},
Pages = {5195-5215},
Year = {2012},
Key = {fds217611}
}
@article{fds217612,
Author = {Y. Li and Sarah A. Williams and Anita T. Layton},
Title = {A hybrid immersed interface method for driven stokes flow in
an elastic tube},
Journal = {Numerical Mathematics: Theory, Methods and
Applications},
Year = {2012},
Key = {fds217612}
}
@article{fds217613,
Author = {Y. Li and Ioannis Sgouralis and Anita T. Layton},
Title = {Computing viscous flow in an elastic tube},
Journal = {SIAM Journal on Scientific Computing},
Year = {2012},
Key = {fds217613}
}
%% Little, Anna V.
@article{fds141693,
Author = {Tammy Ladner and Anna Little and Ken Marks and Amber
Russell},
Title = {Positive Solutions to a Diffusive Logistic Equation with
Constant Yield Harvesting},
Journal = {Rose-Hulman Undergraduate Math Journal},
Year = {2005},
ISSN = {Vol. 6, Issue 1, 2005},
url = {http://www.rose-hulman.edu/mathjournal/v6n1.php},
Abstract = {We consider a reaction diffusion equation which models the
constant yield harvesting of a spatially heterogeneous
population which satisfies a logistic growth. In particular,
we study the existence of positive solutions subject to a
class of nonlinear boundary conditions. We also provide
results for the case of Neumann and Robin boundary
conditions. We obtain our results via a quadrature method
and Mathematica computations.},
Key = {fds141693}
}
%% Liu, Zibu
@article{fds349537,
Author = {Li, L and Li, Y and Liu, JG and Liu, Z and Lu, J},
Title = {A stochastic version of stein variational gradient descent
for efficient sampling},
Journal = {Communications in Applied Mathematics and Computational
Science},
Volume = {15},
Number = {1},
Pages = {37-63},
Publisher = {Mathematical Sciences Publishers},
Year = {2020},
Month = {January},
url = {http://dx.doi.org/10.2140/camcos.2020.15.37},
Abstract = {We propose in this work RBM-SVGD, a stochastic version of
the Stein variational gradient descent (SVGD) method for
efficiently sampling from a given probability measure, which
is thus useful for Bayesian inference. The method is to
apply the random batch method (RBM) for interacting particle
systems proposed by Jin et al. to the interacting particle
systems in SVGD. While keeping the behaviors of SVGD, it
reduces the computational cost, especially when the
interacting kernel has long range. We prove that the one
marginal distribution of the particles generated by this
method converges to the one marginal of the interacting
particle systems under Wasserstein-2 distance on fixed time
interval T0; T U. Numerical examples verify the efficiency
of this new version of SVGD.},
Doi = {10.2140/camcos.2020.15.37},
Key = {fds349537}
}
%% Melikechi, Omar
@article{fds367257,
Author = {Melikechi, O and Young, AL and Tang, T and Bowman, T and Dunson, D and Johndrow, J},
Title = {Limits of epidemic prediction using SIR models.},
Journal = {Journal of Mathematical Biology},
Volume = {85},
Number = {4},
Pages = {36},
Year = {2022},
Month = {September},
url = {http://dx.doi.org/10.1007/s00285-022-01804-5},
Abstract = {The Susceptible-Infectious-Recovered (SIR) equations and
their extensions comprise a commonly utilized set of models
for understanding and predicting the course of an epidemic.
In practice, it is of substantial interest to estimate the
model parameters based on noisy observations early in the
outbreak, well before the epidemic reaches its peak. This
allows prediction of the subsequent course of the epidemic
and design of appropriate interventions. However, accurately
inferring SIR model parameters in such scenarios is
problematic. This article provides novel, theoretical
insight on this issue of practical identifiability of the
SIR model. Our theory provides new understanding of the
inferential limits of routinely used epidemic models and
provides a valuable addition to current simulate-and-check
methods. We illustrate some practical implications through
application to a real-world epidemic data
set.},
Doi = {10.1007/s00285-022-01804-5},
Key = {fds367257}
}
%% Narkawicz, Anthony J.
@article{fds142516,
Author = {A.J. Narkawicz},
Title = {Cohomology jumping loci and relative malcev
completion},
Year = {2008},
Key = {fds142516}
}
%% O'Neill, Christopher
@article{fds221103,
Author = {C. O'Neill and R. Pelayo},
Title = {On the Linearity of Omega-Primality in Numerical
Monoids},
Journal = {Journal of Pure and Applied Algebra},
Year = {2013},
url = {http://arxiv.org/abs/1309.7476},
Abstract = {In an atomic, cancellative, commutative monoid, the
omega-value measures how far an element is from being prime.
In numerical monoids, we show that this invariant exhibits
eventual quasilinearity (i.e., periodic linearity). We apply
this result to describe the asymptotic behavior of the
omega-function for a general numerical monoid and give an
explicit formula when the monoid has embedding dimension
2.},
Key = {fds221103}
}
@article{fds219347,
Author = {J. Haarmann and A. Kalauli and A. Moran and C. O'Neill and R.
Pelayo},
Title = {Factorization Properties of Leamer Monoids},
Journal = {Semigroup Forum},
Year = {2013},
url = {http://arxiv.org/abs/1309.7477},
Abstract = {The Huneke-Wiegand conjecture has prompted much recent
research in Commutative Algebra. In studying this conjecture
for certain classes of rings, Garcia-Sanchez and Leamer
construct a monoid S_Gamma^s whose elements correspond to
arithmetic sequences in a numerical monoid Gamma of step
size s. These monoids, which we call Leamer monoids, possess
a very interesting factorization theory that is
significantly different from the numerical monoids from
which they are derived. In this paper, we offer much of the
foundational theory of Leamer monoids, including an analysis
of their atomic structure, and investigate certain
factorization invariants. Furthermore, when S_Gamma^s is an
arithmetical Leamer monoid, we give an exact description of
its atoms and use this to provide explicit formulae for its
Delta set and catenary degree.},
Key = {fds219347}
}
%% Pan, Yu
@article{fds317667,
Author = {Y. Pan},
Title = {Exact Lagrangian fillings of Legendrian (2,n) torus
links},
Year = {2016},
Month = {July},
url = {http://arxiv.org/abs/ 1607.03167},
Key = {fds317667}
}
@article{fds317666,
Author = {Y. Pan},
Title = {The augmentation category map induced by exact Lagrangian
cobordisms.},
Year = {2016},
Month = {June},
url = {http://arxiv.org/abs/ArXiv 1606.05884},
Key = {fds317666}
}
@article{fds222948,
Author = {Y. Pan and Q. Liu and C.M. Bai and L. Guo},
Title = {PostLie algebra structures on the Lie algebra
sl(2,C)},
Journal = {Electron. J. Linear Algebra},
Volume = {23 (2012)},
Pages = {180-197},
url = {http://arxiv.org/abs/1111.6128},
Key = {fds222948}
}
%% Parry, Alan R.
@phdthesis{fds215989,
Author = {Alan R. Parry},
Title = {Wave Dark Matter and Dwarf Spheroidal Galaxies},
Publisher = {Duke University},
Address = {Durham, NC},
Year = {2013},
Month = {March},
Key = {fds215989}
}
@article{fds214514,
Author = {Hubert L. Bray and Alan R. Parry},
Title = {Modeling Wave Dark Matter in Dwarf Spheroidal
Galaxies},
Year = {2013},
Month = {January},
url = {http://arxiv.org/abs/1301.0255},
Key = {fds214514}
}
@article{fds214513,
Author = {Alan R. Parry},
Title = {Spherically Symmetric Static States of Wave Dark
Matter},
Year = {2012},
Month = {December},
url = {http://arxiv.org/abs/1212.6426},
Key = {fds214513}
}
@article{fds214515,
Author = {Alan R. Parry},
Title = {A Survey of Spherically Symmetric Spacetimes},
Year = {2012},
Month = {October},
url = {http://arxiv.org/abs/1210.5269},
Keywords = {General Relativity Spherical Symmetry Einstein-Klein-Gordon
Equations},
Abstract = {We present several different ways of describing a
spherically symmetric spacetime and the resulting metrics.
We then focus our discussion on an especially useful form of
the metric of a spherically symmetric spacetime in
polar-areal coordinates and its properties. In particular,
we show how the metric component functions chosen are
extremely compatible with notions in Newtonian mechanics. We
also show the monotonicity of the Hawking mass in these
coordinates. Finally, we discuss how these coordinates and
the metric can be used to solve the spherically symmetric
Einstein-Klein-Gordon equations and how this will be useful
in our future work.},
Key = {fds214515}
}
@mastersthesis{fds159065,
Author = {Alan R. Parry},
Title = {A Classification of Real Indecomposable Solvable Lie
Algebras of Small Dimension with Codimension One
Nilradicals},
Publisher = {Utah State University},
Address = {Logan, UT},
Year = {2007},
Month = {August},
url = {http://gradworks.umi.com/14/48/1448067.html},
Keywords = {Lie Algebras},
Key = {fds159065}
}
%% Player, Kevin J.
@article{fds9853,
Author = {K.T. Arasu and Kevin J. Player},
Title = {A New Family of Cyclic Difference Sets with Singer
Parameters in Characteristic Three},
Journal = {Designs Codes and Cryptography},
Key = {fds9853}
}
@article{fds9854,
Author = {K.T Arasu and Henk D. L. Hollmann and Kevin J. Player and Qing
Xiang},
Title = {On the p-Ranks of GWM Difference Sets},
Journal = {"Special issue in honor of Prof. Ray-Chaudhuri's 65th
birthday" of OSU math research monograph
series},
Key = {fds9854}
}
%% Potter, Harrison
@article{fds296271,
Author = { Harrison Potter},
Title = {On Conformal Mappings and Vector Fields},
Journal = {OhioLINK Electronic Theses and Dissertations
Center},
Year = {2008},
Month = {May},
url = {http://etd.ohiolink.edu/view.cgi?acc_num=marhonors1210888378},
Abstract = {We seek to extend the applicability of the tools of complex
analysis that have been developed to deal with problems in
two-dimensional harmonic field theory. In order to ease the
reader who has only a basic understanding of complex
analysis into a working knowledge of its relevant
applications to field theory, this material is introduced
through the use of vector fields as common ground.
Opportunities for using the mathematical tools being
developed to solve physical problems are also highlighted by
examples in order to aid comprehension and foster intuition.
Established techniques used in solving problems involving
point sources are then generalized to handle those involving
interval sources.},
Key = {fds296271}
}
@article{fds296272,
Author = {VX Dang and H Potter and S Glasgow and S Taylor},
Title = {Pricing the Asian Call Option},
Journal = {Electronic Proceedings of Undergraduate Mathematics
Day},
Volume = {3},
Number = {3},
Pages = {26},
Year = {2008},
Month = {February},
url = {http://academic.udayton.edu/EPUMD/},
Abstract = {Background material on measure-theoretic probability theory
and stochastic calculus is provided in order to clarify
notation and inform the reader unfamiliar with these
concepts. These fields are then employed in exploring two
distinct but related approaches to fair option pricing:
developing a partial differential equation whose solution,
given specified boundary conditions, is the desired fair
option price and evaluating a riskneutral conditional
expectation whose value is the fair option price. Both
approaches are illustrated by example before being applied
to the Asian call option. Two results are obtained by
applying the latter option pricing approach to the Asian
call option. The price of an Asian call option is shown to
be equal to an integral of an unknown joint distribution
function. This exact formula is then made approximate by
allowing one of the random variables to become a parameter
of the system. This modified Asian call option is then
priced explicitly, leading to a formula that is strikingly
similar to the Black- Scholes-Merton formula, which prices
the European call option. Finally, possible methods of
generalizing the procedure to price the Asian call option
both exactly and explicitly are speculated.},
Key = {fds296272}
}
%% Rose, David E.
@misc{fds194842,
Author = {David E. V. Rose},
Title = {A categorification of quantum $\mathfrak{sl}_3$ projectors
and the $\mathfrak{sl}_3$ Reshetikhin-Turaev invariant of
tangles},
Journal = {arXiv:1109.1745v1 [math.GT]},
Year = {2011},
Key = {fds194842}
}
@misc{fds194843,
Author = {David E. V. Rose},
Title = {A note on the Grothendieck group of an additive
category},
Journal = {arXiv:1109.2040v1 [math.CT]},
Year = {2011},
Key = {fds194843}
}
@article{fds142083,
Author = {David E. V. Rose and Ilya M. Spitkovsky},
Title = {On the stabilization of the Aluthge sequence},
Journal = {International Journal of Information and Systems
Sciences},
Volume = {4},
Number = {1},
Pages = {178-189},
Year = {2008},
Month = {Spring},
ISSN = {1708-296X},
Key = {fds142083}
}
@article{fds139616,
Author = {David E. V. Rose and Ilya M. Spitkovsky},
Title = {On the numerical range behavior under the generalized
Aluthge transform},
Journal = {Linear and Multilinear Algebra},
Volume = {56},
Number = {1&2},
Pages = {163-177},
Publisher = {Taylor and Francis},
Year = {2008},
Month = {January},
Keywords = {Aluthge transform Numerical range},
Key = {fds139616}
}
%% Ryu, Hwayeon
@article{fds218275,
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},
Year = {2013},
Month = {March},
Key = {fds218275}
}
@article{fds215979,
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},
Year = {2013},
Month = {March},
Key = {fds215979}
}
@article{fds218850,
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 = {Math Med Biol},
Volume = {30},
Number = {3},
Pages = {191-212},
Year = {2013},
Key = {fds218850}
}
@article{fds204653,
Author = {Anita T. Layton and Philip Pham and Hwayeon
Ryu},
Title = {Signal transduction in a compliant short loop of
Henle},
Journal = {Int J Numer Methods Biomed Eng, vol. 28 no. 3 (2012), pp.
369-380},
Key = {fds204653}
}
%% Sgouralis, Ioannis
@article{fds223258,
Author = {Ioannis Sgouralis, and Anita T. Layton},
Title = {Theoretical Assessment of Renal Autoregulatory
Mechanisms},
Journal = {Am J Physiol Renal Physiol},
Year = {2014},
Month = {March},
Key = {fds223258}
}
@article{fds222884,
Author = {Yi Li and Ioannis Sgouralis and Anita T. Layton},
Title = {Computing viscous flow in an elastic tube},
Journal = {Numer Math Theor Meth Appl},
Year = {2014},
Key = {fds222884}
}
@article{fds223280,
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},
Year = {2014},
Key = {fds223280}
}
@article{fds219527,
Author = {Ioannis Sgouralis, and Anita T. Layton},
Title = {Control and modulation of fluid flow in the rat
kidney},
Journal = {Bull Math Biol (2013) 75:2551-2574  },
Year = {2013},
Month = {December},
url = {http://dx.doi.org/10.1007/s11538-013-9907-5},
Doi = {10.1007/s11538-013-9907-5},
Key = {fds219527}
}
@article{fds208425,
Author = {Ioannis Sgouralis, and Anita T. Layton},
Title = {Autoregulation and conduction of vasomotor responses in a
mathematical model of the rat afferent arteriole},
Journal = {Am J Physiol Renal Physiol},
Volume = {303},
Pages = {F229-F239},
Year = {2012},
Month = {July},
url = {http://dx.doi.org/10.1152/ajprenal.00589.2011},
Doi = {10.1152/ajprenal.00589.2011},
Key = {fds208425}
}
@article{fds196319,
Author = {Jing Chen and Ioannis Sgouralis and Leon C. Moore and Harold E.
Layton and Anita T. Layton},
Title = {A Mathematical Model of the Myogenic Response to Systolic
Pressure in the Afferent Arteriole},
Journal = {Am J Physiol Renal Physiol},
Volume = {300},
Pages = {F669-F681},
Year = {2011},
Month = {March},
url = {http://dx.doi.org/10.1152/ajprenal.00382.2010},
Doi = {10.1152/ajprenal.00382.2010},
Key = {fds196319}
}
%% Shan, Shan
@article{fds346319,
Author = {Shan, S and Kovalsky, SZ and Winchester, JM and Boyer, DM and Daubechies, I},
Title = {ariaDNE: A robustly implemented algorithm for Dirichlet
energy of the normal},
Journal = {Methods in Ecology and Evolution},
Volume = {10},
Number = {4},
Pages = {541-552},
Year = {2019},
Month = {April},
url = {http://dx.doi.org/10.1111/2041-210X.13148},
Abstract = {© 2019 The Authors. Methods in Ecology and Evolution ©
2019 British Ecological Society Shape characterizers are
metrics that quantify aspects of the overall geometry of a
three-dimensional (3D) digital surface. When computed for
biological objects, the values of a shape characterizer are
largely independent of homology interpretations and often
contain a strong ecological and functional signal. Thus,
shape characterizers are useful for understanding
evolutionary processes. Dirichlet normal energy (DNE) is a
widely used shape characterizer in morphological studies.
Recent studies found that DNE is sensitive to various
procedures for preparing 3D mesh from raw scan data, raising
concerns regarding comparability and objectivity when
utilizing DNE in morphological research. We provide a
robustly implemented algorithm for computing the Dirichlet
energy of the normal (ariaDNE) on 3D meshes. We show through
simulation that the effects of preparation-related mesh
surface attributes, such as triangle count, mesh
representation, noise, smoothing and boundary triangles, are
much more limited on ariaDNE than DNE. Furthermore, ariaDNE
retains the potential of DNE for biological studies,
illustrated by its effectiveness in differentiating species
by dietary preferences. Use of ariaDNE can dramatically
enhance the assessment of the ecological aspects of
morphological variation by its stability under different 3D
model acquisition methods and preparation procedure. Towards
this goal, we provide scripts for computing ariaDNE and
ariaDNE values for specimens used in previously published
DNE analyses.},
Doi = {10.1111/2041-210X.13148},
Key = {fds346319}
}
%% Smith, Abraham D
@misc{fds139484,
Author = {Rann Bar-On and Paul Bendich and Benjamin Cooke and Michael Gratton and Timothy Lucas and Michael Nicholas and Nicholas Robbins and Abraham
Smith, Joseph Spivey},
Title = {Graduate Calculus Curriculum Review, Spring
2007},
Year = {2007},
Month = {March},
url = {http://www.math.duke.edu/~adsmith/proposal.pdf},
Abstract = {This document is the end result of a several-month-long
study of the calculus curriculum by a group of experienced
graduate instructors. Herein, we propose specific changes to
each course as well as significant changes to the curriculum
as a whole. We arrived at these proposals after carefully
considering the mathematical content of each class, its
intended audience, and the mathematical requirements of the
various physical, biological, and social sciences. In the
course of gathering this information, we interviewed
graduate instructors, teaching faculty, and teachers of
concurrent courses in many other departments. <p> For each
of 25L, 26L, 31L, 32L and the multivariable courses, we
suggest shifting the position or emphasis of various topics,
and we suggest alterations to specific lab assignments. In
several cases, we have replacement labs in concept or in
outline, and expect to write the new labs during Spring and
Summer. <p> Most significantly, we propose replacing 32 and
41 with 41L, a course we designed specifically for incoming
freshmen who have gained AP credit for 31. The course is a
careful balance of rigorous mathematics, computational
techniques, and physical applications.},
Key = {fds139484}
}
%% Spivey, Joseph A.
@misc{fds139511,
Author = {J.A. Spivey and J.Bookman},
Title = {Approximating Definite Integrals},
Year = {2007},
Month = {Summer},
url = {http://www.math.duke.edu/~jaspive/Joseph},
Key = {fds139511}
}
%% Steenbergen, John J
@article{fds210553,
Author = {J.J. Steenbergen and Caroline Klivans and Sayan
Mukherjee.},
Title = {“A Cheeger-Type Inequality on Simplicial
Complexes”},
Year = {2012},
Month = {September},
url = {http://arxiv.org/abs/1209.5091},
Key = {fds210553}
}
%% Streets, Jeffrey D.
@article{fds51322,
Author = {J.D. Streets},
Title = {The Gradient Flow of $\int_M | \Rm|^2$},
Journal = {Journal of Geometric Analysis},
Year = {2006},
url = {http://math.duke.edu/~streets/L2gradflow.pdf},
Key = {fds51322}
}
@article{fds53441,
Author = {J.D. Streets},
Title = {Quasi-Local Mass Functionals and Generalized Inverse Mean
Curvature Flow},
Journal = {Communications in Analysis and Geometry},
Year = {2006},
url = {http://math.duke.edu/~streets/gimcf.pdf},
Key = {fds53441}
}
%% Stubbs, Kevin
@article{fds355604,
Author = {Stubbs, KD and Watson, AB and Lu, J},
Title = {Iterated projected position algorithm for constructing
exponentially localized generalized Wannier functions for
periodic and nonperiodic insulators in two dimensions and
higher},
Journal = {Physical Review B},
Volume = {103},
Number = {7},
Year = {2021},
Month = {February},
url = {http://dx.doi.org/10.1103/PhysRevB.103.075125},
Abstract = {Localized bases play an important role in understanding
electronic structure. In periodic insulators, a natural
choice of localized basis is given by the Wannier functions
which depend on a choice of unitary transform known as a
gauge transformation. Over the past few decades, there have
been many works that have focused on optimizing the choice
of the gauge so that the corresponding Wannier functions are
maximally localized or reflect some symmetry of the
underlying system. In this work, we consider fully
nonperiodic materials where the usual Wannier functions are
not well defined and gauge optimization is impractical. To
tackle the problem of calculating exponentially localized
generalized Wannier functions in both periodic and
nonperiodic systems, we discuss the 'iterated projected
position (IPP)"algorithm. The IPP algorithm is based on
matrix diagonalization and therefore unlike
optimization-based approaches, it does not require
initialization and cannot get stuck at a local minimum.
Furthermore, the IPP algorithm is guaranteed by a rigorous
analysis to produce exponentially localized functions under
certain mild assumptions. We numerically demonstrate that
the IPP algorithm can be used to calculate exponentially
localized bases for the Haldane model, the Kane-Mele model
(in both Z2 invariant even and Z2 invariant odd phases), and
the px+ipy model on a quasicrystal lattice.},
Doi = {10.1103/PhysRevB.103.075125},
Key = {fds355604}
}
@article{fds355364,
Author = {Brandsen, S and Lian, M and Stubbs, KD and Rengaswamy, N and Pfister,
HD},
Title = {Adaptive Procedures for Discriminating Between Arbitrary
Tensor-Product Quantum States},
Journal = {Ieee International Symposium on Information Theory
Proceedings},
Volume = {2020-June},
Pages = {1933-1938},
Year = {2020},
Month = {June},
url = {http://dx.doi.org/10.1109/ISIT44484.2020.9174234},
Abstract = {Discriminating between quantum states is a fundamental task
in quantum information theory. Given two quantum states, ρ
and ρ , the Helstrom measurement distinguishes between them
with minimal probability of error. However, finding and
experimentally implementing the Helstrom measurement can be
challenging for quantum states on many qubits. Due to this
difficulty, there is a great interest in identifying local
measurement schemes which are close to optimal. In the first
part of this work, we generalize previous work by Acin et
al. (Phys. Rev. A 71, 032338) and show that a locally greedy
(LG) scheme using Bayesian updating can optimally
distinguish between any two states that can be written as a
tensor product of arbitrary pure states. We then show that
the same algorithm cannot distinguish tensor products of
mixed states with vanishing error probability (even in a
large subsystem limit), and introduce a modified
locally-greedy (MLG) scheme with strictly better
performance. In the second part of this work, we compare
these simple local schemes with a general dynamic
programming (DP) approach. The DP approach finds the optimal
series of local measurements and optimal order of subsystem
measurement to distinguish between the two tensor-product
states. + - 1},
Doi = {10.1109/ISIT44484.2020.9174234},
Key = {fds355364}
}
@article{fds355365,
Author = {Brandsen, S and Stubbs, KD and Pfister, HD},
Title = {Reinforcement Learning with Neural Networks for Quantum
Multiple Hypothesis Testing},
Journal = {Ieee International Symposium on Information Theory
Proceedings},
Volume = {2020-June},
Pages = {1897-1902},
Year = {2020},
Month = {June},
ISBN = {9781728164328},
url = {http://dx.doi.org/10.1109/ISIT44484.2020.9174150},
Abstract = {Reinforcement learning with neural networks (RLNN) has
recently demonstrated great promise for many problems,
including some problems in quantum information theory. In
this work, we apply reinforcement learning to quantum
hypothesis testing, where one designs measurements that can
distinguish between multiple quantum states j = 1 while
minimizing the error probability. Although the Helstrom
measurement is known to be optimal when there are m=2
states, the general problem of finding a minimal-error
measurement is challenging. Additionally, in the case where
the candidate states correspond to a quantum system with
many qubit subsystems, implementing the optimal measurement
on the entire system may be impractical. In this work, we
develop locally-adaptive measurement strategies that are
experimentally feasible in the sense that only one quantum
subsystem is measured in each round. RLNN is used to find
the optimal measurement protocol for arbitrary sets of
tensor product quantum states. Numerical results for the
network performance are shown. In special cases, the neural
network testing-policy achieves the same probability of
success as the optimal collective measurement.},
Doi = {10.1109/ISIT44484.2020.9174150},
Key = {fds355365}
}
@article{fds340299,
Author = {Czaja, W and Manning, B and Murphy, JM and Stubbs,
K},
Title = {Discrete directional Gabor frames},
Journal = {Applied and Computational Harmonic Analysis},
Volume = {45},
Number = {1},
Pages = {1-21},
Publisher = {Elsevier BV},
Year = {2018},
Month = {July},
url = {http://dx.doi.org/10.1016/j.acha.2016.07.004},
Doi = {10.1016/j.acha.2016.07.004},
Key = {fds340299}
}
%% Su, Langxuan
@article{fds361539,
Author = {Mattingly, JC and Romito, M and Su, L},
Title = {The Gaussian structure of the singular stochastic Burgers
equation},
Journal = {Forum of Mathematics, Sigma},
Volume = {10},
Publisher = {Cambridge University Press (CUP)},
Year = {2022},
Month = {September},
url = {http://dx.doi.org/10.1017/fms.2022.64},
Abstract = {We consider the stochastically forced Burgers equation with
an emphasis on spatially rough driving noise. We show that
the law of the process at a fixed time t, conditioned on no
explosions, is absolutely continuous with respect to the
stochastic heat equation obtained by removing the
nonlinearity from the equation. This establishes a form of
ellipticity in this infinite-dimensional setting. The
results follow from a recasting of the Girsanov Theorem to
handle less spatially regular solutions while only proving
absolute continuity at a fixed time and not on path-space.
The results are proven by decomposing the solution into the
sum of auxiliary processes, which are then shown to be
absolutely continuous in law to a stochastic heat equation.
The number of levels in this decomposition diverges to
infinite as we move to the stochastically forced Burgers
equation associated to the KPZ equation, which we conjecture
is just beyond the validity of our results (and certainly
the current proof). The analysis provides insights into the
structure of the solution as we approach the regularity of
KPZ. A number of techniques from singular SPDEs are
employed, as we are beyond the regime of classical solutions
for much of the paper.},
Doi = {10.1017/fms.2022.64},
Key = {fds361539}
}
@article{fds362666,
Author = {Su, L and Mukherjee, S},
Title = {Large Deviation Asymptotics and Bayesian Posterior
Consistency on Stochastic Processes and Dynamical
Systems},
Year = {2021},
Month = {June},
Abstract = {We consider generalized Bayesian inference on stochastic
processes and dynamical systems with potentially long-range
dependency. Given a sequence of observations, a class of
parametrized model processes with a prior distribution, and
a loss function, we specify the generalized posterior
distribution. The problem of frequentist posterior
consistency is concerned with whether as more and more
samples are observed, the posterior distribution on
parameters will asymptotically concentrate on the "right"
parameters. We show that posterior consistency can be
derived using a combination of classical large deviation
techniques, such as Varadhan's lemma, conditional/quenched
large deviations, annealed large deviations, and exponential
approximations. We show that the posterior distribution will
asymptotically concentrate on parameters that minimize the
expected loss and a divergence term, and we identify the
divergence term as the Donsker-Varadhan relative entropy
rate from process-level large deviations. As an application,
we prove new quenched and annealed large deviation
asymptotics and new Bayesian posterior consistency results
for a class of mixing stochastic processes. In the case of
Markov processes, one can obtain explicit conditions for
posterior consistency, whenever estimates for log-Sobolev
constants are available, which makes our framework
essentially a black box. We also recover state-of-the-art
posterior consistency on classical dynamical systems with a
simple proof. Our approach has the potential of proving
posterior consistency for a wide range of Bayesian
procedures in a unified way.},
Key = {fds362666}
}
%% Teguia, Alberto M
@article{fds185162,
Author = {A.M. Teguia and A Petters},
Title = {A Mathematical Theory of Stochastic Microlensing III.
Densities for Radial, Spatial Distributions with General
Random Mass Spectrum},
Year = {2010},
Key = {fds185162}
}
@article{fds185163,
Author = {A. Petters},
Title = {A Mathematical Theory of Stochastic Microlensing. IV. Global
Expectations and Shear for Radial Distributions with a
General Mass Spectrum},
Year = {2010},
Key = {fds185163}
}
@article{fds175315,
Author = {A.M. Teguia and A. Petters and B. Rider},
Title = {A Mathematical Theory of Stochastic Microlensing II. Random
Images, Shear, and the Kac-Rice Formula},
Journal = {Journal of Mathematical Physics},
Volume = {50},
Pages = {122501},
Year = {2009},
Month = {December},
Key = {fds175315}
}
@article{fds175316,
Author = {A.M. Teguia and A. Petters and B. Rider},
Title = {A Mathematical Theory of Stochastic Microlensing I. Random
Time-Delay Functions and Lensing Maps},
Journal = {Journal of Mathematical Physics},
Volume = {50},
Pages = {072503},
Year = {2009},
Month = {October},
Key = {fds175316}
}
@article{fds185165,
Author = {A.M. Teguia and J. Gardner and A. Godbole and A. Vuong and N. Watson and C.
Yerger},
Title = {Domination Cover Pebbling: Graph Families},
Journal = {Journal of Combinatorial Mathematics and Combinatorial
Computing},
Year = {2008},
Month = {November},
url = {http://arxiv.org/abs/math/0507271v1},
Key = {fds185165}
}
@article{fds142536,
Author = {A.M. Teguia and A. Godbole},
Title = {Sierpinski Gasket Graphs and Some of their
Properties},
Journal = {Australasian Journal of Combinatorics},
Volume = {35},
Pages = {181-192},
Year = {2006},
Month = {June},
url = {http://arxiv.org/abs/math/0509259v1},
Key = {fds142536}
}
%% Thomas, Ashleigh
@article{fds223719,
Author = {J. Brindza and A. Thomas and S. Lee and W. McDermid and Y. He and D.
Lee},
Title = {Active Sound Localization in a Symmetric
Environment},
Journal = {Int J Adv Robot Syst},
Volume = {10},
Number = {301},
Year = {2013},
url = {http://cdn.intechopen.com/pdfs/45523/InTechActive_sound_localization_in_a_symmetric_environment.pdf},
Keywords = {localization},
Key = {fds223719}
}
%% Thomas, Rachel L.
@article{fds147056,
Author = {Reed M and Thomas R and Pavisic J and James SJ and Ulrich C and Nijhout
HF},
Title = {A Mathematical Model of Glutathione Metabolism},
Journal = {Theoretical Biology & Medical Modelling},
Year = {2008},
Month = {April},
url = {http://www.tbiomed.com/content/5/1/8},
Key = {fds147056}
}
@article{fds164044,
Author = {Petronella SA and Thomas RL and Stone JA and Goldblum RM and Brooks
EG},
Title = {Clearing the Air: A Model for Investigating Indoor Air
Quality in Texas Schools},
Journal = {Journal of Environmental Health},
Volume = {67},
Year = {2005},
Month = {June},
Key = {fds164044}
}
@article{fds164045,
Author = {Rhoades RC and Thomas RL},
Title = {When Abelian Groups Split},
Journal = {Rose-Hulman Mathematical Sciences Technical Report
Series},
Volume = {03-01},
Year = {2003},
Key = {fds164045}
}
%% Vagner, Dmitry
@article{fds317684,
Author = {Dmitry Vagner and David I. Spivak and Eugene Lerman},
Title = {Algebras of Open Dynamical Systems on the Operad of Wiring
Diagrams},
Journal = {Theory and Application of Categories},
Volume = {30},
Number = {51},
Pages = {1793-1822},
Year = {2015},
Month = {December},
url = {http://www.tac.mta.ca/tac/volumes/30/51/30-51abs.html},
Key = {fds317684}
}
%% Wang, Lihan
@article{fds355588,
Author = {Yu Cao and Jianfeng Lu and Lihan wang},
Title = {Complexity of randomized algorithms for underdamped Langevin
dynamics},
Journal = {Communications in Mathematical Sciences},
Year = {2021},
Month = {March},
url = {http://arxiv.org/abs/2003.09906},
Key = {fds355588}
}
@article{fds355587,
Author = {Lei Li and Jianfeng Lu and Jonathan Mattingly and Lihan
Wang},
Title = {Numerical methods for stochastic differential equations
based on Gaussian mixture},
Journal = {Communications in Mathematical Sciences},
Year = {2021},
Month = {February},
url = {http://arxiv.org/abs/1812.11932},
Key = {fds355587}
}
@article{fds354148,
Author = {Jianfeng Lu and Lihan Wang},
Title = {Complexity of zigzag sampling algorithm for strongly
log-concave distributions},
Year = {2020},
Month = {December},
url = {http://arxiv.org/abs/ 2012.11094},
Key = {fds354148}
}
@article{fds350883,
Author = {Jianfeng Lu and Lihan Wang},
Title = {On explicit L2-convergence rate estimate for piecewise
deterministic Markov processes in MCMC algorithms},
Year = {2020},
Month = {July},
url = {http://arxiv.org/abs/ 2007.14927},
Key = {fds350883}
}
@article{fds345493,
Author = {Yu Cao and Jianfeng Lu and Lihan Wang},
Title = {On explicit L2-convergence rate estimate for underdamped
Langevin dynamics},
Year = {2019},
Month = {August},
url = {http://arxiv.org/abs/1908.04746},
Key = {fds345493}
}
%% Wang, Zhe
@article{fds349535,
Author = {Lu, J and Wang, Z},
Title = {The full configuration interaction quantum monte carlo
method through the lens of inexact power
iteration},
Journal = {Siam Journal on Scientific Computing},
Volume = {42},
Number = {1},
Pages = {B1-B29},
Year = {2020},
Month = {January},
url = {http://dx.doi.org/10.1137/18M1166626},
Abstract = {© 2020 Society for Industrial and Applied Mathematics. In
this paper, we propose a general analysis framework for
inexact power iteration, which can be used to efficiently
solve high-dimensional eigenvalue problems arising from
quantum many-body problems. Under this framework, we
establish the convergence theorems for several recently
proposed randomized algorithms, including full configuration
interaction quantum Monte Carlo and fast randomized
iteration. The analysis is consistent with numerical
experiments for physical systems such as the Hubbard model
and small chemical molecules. We also compare the algorithms
both in convergence analysis and numerical
results.},
Doi = {10.1137/18M1166626},
Key = {fds349535}
}
@article{fds342764,
Author = {Wang, Z and Li, Y and Lu, J},
Title = {Coordinate Descent Full Configuration Interaction.},
Journal = {Journal of Chemical Theory and Computation},
Volume = {15},
Number = {6},
Pages = {3558-3569},
Year = {2019},
Month = {June},
url = {http://dx.doi.org/10.1021/acs.jctc.9b00138},
Abstract = {We develop an efficient algorithm, coordinate descent FCI
(CDFCI), for the electronic structure ground-state
calculation in the configuration interaction framework.
CDFCI solves an unconstrained nonconvex optimization
problem, which is a reformulation of the full configuration
interaction eigenvalue problem, via an adaptive coordinate
descent method with a deterministic compression strategy.
CDFCI captures and updates appreciative determinants with
different frequencies proportional to their importance. We
show that CDFCI produces accurate variational energy for
both static and dynamic correlation by benchmarking the
binding curve of nitrogen dimer in the cc-pVDZ basis with
10-3 mHa accuracy. We also demonstrate the efficiency and
accuracy of CDFCI for strongly correlated chromium dimer in
the Ahlrichs VDZ basis and produce state-of-the-art
variational energy.},
Doi = {10.1021/acs.jctc.9b00138},
Key = {fds342764}
}
@article{fds345877,
Author = {Yingzhou, LI and Jianfeng, LU and Wang, AZHE},
Title = {Coordinatewise descent methods for leading eigenvalue
problem},
Journal = {Siam Journal on Scientific Computing},
Volume = {41},
Number = {4},
Pages = {A2681-A2716},
Publisher = {Society for Industrial & Applied Mathematics
(SIAM)},
Year = {2019},
Month = {January},
url = {http://dx.doi.org/10.1137/18M1202505},
Abstract = {© 2019 Society for Industrial and Applied Mathematics
Leading eigenvalue problems for large scale matrices arise
in many applications. Coordinatewise descent methods are
considered in this work for such problems based on a
reformulation of the leading eigenvalue problem as a
nonconvex optimization problem. The convergence of several
coordinatewise methods is analyzed and compared. Numerical
examples of applications to quantum many-body problems
demonstrate the efficiency and provide benchmarks of the
proposed coordinatewise descent methods.},
Doi = {10.1137/18M1202505},
Key = {fds345877}
}
%% Watanabe, Tatsunari
@article{fds226201,
Author = {T. Watanabe},
Title = {Rational points of universal curves in positive
characteristics},
Year = {2014},
url = {http://arxiv.org/abs/arxiv/abs/1410.3020},
Key = {fds226201}
}
%% Williamson, Brendan
@article{fds218909,
Author = {B. Williamson},
Title = {Large deviation theory: estimating the probabilities of rare
events},
Journal = {Irish Undergraduate Mathematical Magazine},
Year = {2013},
Month = {Summer},
Key = {fds218909}
}
%% Xu, Feng
@article{fds142520,
Author = {F. Xu},
Title = {SU(3) structures and special Lagrangian geometries},
Year = {2006},
Month = {November},
Key = {fds142520}
}
%% Xu, Hangjun
@misc{fds223718,
Author = {H. Xu},
Title = {Uniformly Area Expanding Flows in Spacetimes (theis, Duke
University)},
Year = {2014},
Month = {April},
url = {http://dukespace.lib.duke.edu/dspace/bitstream/handle/10161/8732/Xu_duke_0066D_12371.pdf?sequence=1},
Key = {fds223718}
}
%% Yao, Dong
@article{fds337128,
Author = {van der Hoorn, P and Yao, D and Litvak, N},
Title = {Average nearest neighbor degrees in scale-free
networks},
Journal = {Internet Mathematics},
Publisher = {Internet Mathematics},
Year = {2018},
Month = {January},
url = {http://dx.doi.org/10.24166/im.02.2018},
Doi = {10.24166/im.02.2018},
Key = {fds337128}
}
%% Zhang, Yuan
@article{fds226441,
Author = {Y. Zhang and J. Liu},
Title = {Convergence of Diffusion-Drift Many Particle Systems in
Probability under Sobolev Norm},
Year = {2015},
Month = {April},
Key = {fds226441}
}
@article{fds225992,
Author = {Y. Zhang and A, Lloyd},
Title = {Weak Convergence of a Seasonally Forced Stochastic Epidemic
Model},
Year = {2015},
url = {http://arxiv.org/abs/ 1412.0964},
Key = {fds225992}
}
@article{fds225208,
Author = {Y. Zhang and R. Durrett},
Title = {Exact solution for a metapopulation version of Schelling’s
model},
Journal = {Proceedings of the National Academy of Science},
Volume = {111},
Number = {39},
Pages = {14036–14041},
Year = {2014},
Month = {September},
url = {http://www.math.duke.edu/~rtd/sch/schfinal.pdf},
Doi = {10.1073/pnas.1414915111},
Key = {fds225208}
}
@article{fds225209,
Author = {Y. Zhang and R. Durrett and T. Liggett},
Title = {Contact Process with Fast Voting},
Journal = {Electronic Journal of Probability},
Volume = {19},
Number = {28},
Year = {2014},
Month = {March},
url = {http://www.math.duke.edu/~rtd/candv/cplusv-4.pdf},
Key = {fds225209}
}
@article{fds225210,
Author = {Y. Zhang and N. Lanchier},
Title = {Some rigorous results for the stacked contact
process},
Year = {2014},
url = {http://arxiv.org/abs/1410.3842},
Key = {fds225210}
}
@article{fds224033,
Author = {Y. Zhang and X. Yin and W. Nolte and S. Tantum},
Title = {On marine mammal acoustic detection performance bounds
(conference version)},
Journal = {167th Meeting of the Acoustical Society of
America},
Year = {2014},
Key = {fds224033}
}
@article{fds225370,
Author = {Y. Zhang and R. Durrett},
Title = {Coexistence of Grass, Saplings and Trees in the Staver-Levin
Forest Model},
Journal = {Annals of Applied Probability},
Year = {2014},
Key = {fds225370}
}
%% Zhou, Mo
@article{fds360561,
Author = {Zhou, M and Han, J and Lu, J},
Title = {ACTOR-CRITIC METHOD FOR HIGH DIMENSIONAL STATIC
HAMILTON-JACOBI-BELLMAN PARTIAL DIFFERENTIAL EQUATIONS BASED
ON NEURAL NETWORKS},
Journal = {Siam Journal on Scientific Computing},
Volume = {43},
Number = {6},
Pages = {A4043-A4066},
Publisher = {Society for Industrial & Applied Mathematics
(SIAM)},
Year = {2021},
Month = {January},
url = {http://dx.doi.org/10.1137/21M1402303},
Abstract = {We propose a novel numerical method for high dimensional
Hamilton-Jacobi-Bellman (HJB) type elliptic partial
differential equations (PDEs). The HJB PDEs, reformulated as
optimal control problems, are tackled by the actor-critic
framework inspired by reinforcement learning, based on
neural network parametrization of the value and control
functions. Within the actor-critic framework, we employ a
policy gradient approach to improve the control, while for
the value function, we derive a variance reduced
least-squares temporal difference method using stochastic
calculus. To numerically discretize the stochastic control
problem, we employ an adaptive step size scheme to improve
the accuracy near the domain boundary. Numerical examples up
to 20 spatial dimensions including the linear quadratic
regulators, the stochastic Van der Pol oscillators, the
diffusive Eikonal equations, and fully nonlinear elliptic
PDEs derived from a regulator problem are presented to
validate the effectiveness of our proposed
method.},
Doi = {10.1137/21M1402303},
Key = {fds360561}
}
@article{fds352917,
Author = {Han, J and Lu, J and Zhou, M},
Title = {Solving high-dimensional eigenvalue problems using deep
neural networks: A diffusion Monte Carlo like
approach},
Journal = {Journal of Computational Physics},
Volume = {423},
Year = {2020},
Month = {December},
url = {http://dx.doi.org/10.1016/j.jcp.2020.109792},
Abstract = {We propose a new method to solve eigenvalue problems for
linear and semilinear second order differential operators in
high dimensions based on deep neural networks. The
eigenvalue problem is reformulated as a fixed point problem
of the semigroup flow induced by the operator, whose
solution can be represented by Feynman-Kac formula in terms
of forward-backward stochastic differential equations. The
method shares a similar spirit with diffusion Monte Carlo
but augments a direct approximation to the eigenfunction
through neural-network ansatz. The criterion of fixed point
provides a natural loss function to search for parameters
via optimization. Our approach is able to provide accurate
eigenvalue and eigenfunction approximations in several
numerical examples, including Fokker-Planck operator and the
linear and nonlinear Schrödinger operators in high
dimensions.},
Doi = {10.1016/j.jcp.2020.109792},
Key = {fds352917}
}
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Mathematics Department