Mathematics Grad: Publications since January 2020
List all publications in the database. :chronological alphabetical combined listing:
%% An, Chen
@article{fds355088,
Author = {An, C},
Title = {ℓtorsion in class groups of certain families of
D4quartic fields},
Journal = {Journal De Theorie Des Nombres De Bordeaux},
Volume = {32},
Number = {1},
Pages = {123},
Publisher = {Universite de Bordeaux},
Editor = {Wood, M},
Year = {2020},
Month = {August},
Key = {fds355088}
}
%% 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 = {3763},
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 RBMSVGD, 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 Wasserstein2 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}
}
%% 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
optimizationbased 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 KaneMele 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
TensorProduct Quantum States},
Journal = {Ieee International Symposium on Information Theory
Proceedings},
Volume = {2020June},
Pages = {19331938},
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
locallygreedy (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 tensorproduct
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 = {2020June},
Pages = {18971902},
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 minimalerror
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 locallyadaptive 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 testingpolicy achieves the same probability of
success as the optimal collective measurement.},
Doi = {10.1109/ISIT44484.2020.9174150},
Key = {fds355365}
}
%% 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
logconcave 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 L2convergence rate estimate for piecewise
deterministic Markov processes in MCMC algorithms},
Year = {2020},
Month = {July},
url = {http://arxiv.org/abs/ 2007.14927},
Key = {fds350883}
}
%% 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 = {B1B29},
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 highdimensional eigenvalue problems arising from
quantum manybody 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}
}
%% Zhou, Mo
@article{fds352917,
Author = {Han, J and Lu, J and Zhou, M},
Title = {Solving highdimensional 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 FeynmanKac formula in terms
of forwardbackward stochastic differential equations. The
method shares a similar spirit with diffusion Monte Carlo
but augments a direct approximation to the eigenfunction
through neuralnetwork 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 FokkerPlanck operator and the
linear and nonlinear Schrödinger operators in high
dimensions.},
Doi = {10.1016/j.jcp.2020.109792},
Key = {fds352917}
}
