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Mathematics Grad: Publications since January 2020

List all publications in the database.    :chronological  alphabetical  combined listing:
%% 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}
}


%% 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}
}


%% 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}
}


%% 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}
}


%% 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}
}


%% Zhou, Mo   
@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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