arXiv subjects

Qiang Du

Publications and source records attributed to Qiang Du.

At least 109 records · Page 6Linked to original sources

arXiv2019

Maximum principle preserving exponential time differencing schemes for the nonlocal Allen-Cahn equation

The nonlocal Allen-Cahn (NAC) equation is a generalization of the classic Allen-Cahn equation by replacing the Laplacian with a parameterized nonlocal diffusion operator, and satisfies the maximum principle as its local counterpart. In this paper, we develop and analyze first and second order exponential time differencing (ETD) schemes for solving the NAC equation, which unconditionally preserve the discrete maximum principle. The fully discrete numerical schemes are obtained by applying the stabilized ETD approximations for time integration with the quadrature-based finite difference discretization in space. We derive their respective optimal maximum-norm error estimates and further show that the proposed schemes are asymptotically compatible, i.e., the approximate solutions always converge to the classic Allen-Cahn solution when the horizon, the spatial mesh size and the time step size go to zero. We also prove that the schemes are energy stable in the discrete sense. Various experiments are performed to verify these theoretical results and to investigate numerically the relation between the discontinuities and the nonlocal parameters.

math.NA↗

arXiv2019

Nonlocal Neural Networks, Nonlocal Diffusion and Nonlocal Modeling

Nonlocal neural networks have been proposed and shown to be effective in several computer vision tasks, where the nonlocal operations can directly capture long-range dependencies in the feature space. In this paper, we study the nature of diffusion and damping effect of nonlocal networks by doing spectrum analysis on the weight matrices of the well-trained networks, and then propose a new formulation of the nonlocal block. The new block not only learns the nonlocal interactions but also has stable dynamics, thus allowing deeper nonlocal structures. Moreover, we interpret our formulation from the general nonlocal modeling perspective, where we make connections between the proposed nonlocal network and other nonlocal models, such as nonlocal diffusion process and Markov jump process.

cs.LG↗

arXiv2019

Algorithm for distance list extraction from pair distribution functions

We present an algorithm to extract the distance list from atomic pair distribution functions (PDFs) in a highly automated way. The algorithm is constructed via curve fitting based on a Debye scattering equation model. Due to the non-convex nature of the resulting optimization problem, a number of techniques are developed to overcome various computational difficulties. A key ingredient is a new approach to obtain a reasonable initial guess based on the theoretical properties of the mathematical model. Tests on various nanostructured samples show the effectiveness of the initial guess and the accuracy and overall good performance of the extraction algorithm. This approach could be extended to any spectrum that is approximated as a sum of Gaussian functions.

cond-mat.mtrl-sci↗

arXiv2018

Stochastic Training of Residual Networks: a Differential Equation Viewpoint

During the last few years, significant attention has been paid to the stochastic training of artificial neural networks, which is known as an effective regularization approach that helps improve the generalization capability of trained models. In this work, the method of modified equations is applied to show that the residual network and its variants with noise injection can be regarded as weak approximations of stochastic differential equations. Such observations enable us to bridge the stochastic training processes with the optimal control of backward Kolmogorov's equations. This not only offers a novel perspective on the effects of regularization from the loss landscape viewpoint but also sheds light on the design of more reliable and efficient stochastic training strategies. As an example, we propose a new way to utilize Bernoulli dropout within the plain residual network architecture and conduct experiments on a real-world image classification task to substantiate our theoretical findings.

cs.LG↗

arXiv2018

Stochastic representation of solution to nonlocal-in-time diffusion

The aim of this paper is to give a stochastic representation for the solution to a natural extension of the Caputo-type evolution equation. The nonlocal-in-time operator is defined by a hypersingular integral with a (possibly time-dependent) kernel function, and it results in a model which serves a bridge between normal diffusion and anomalous diffusion. We derive the stochastic representation for the weak solution of the nonlocal-in-time problem in case of nonsmooth data. We do so by starting from an auxiliary Caputo-type evolution equation with a specific forcing term. Numerical simulations are also provided to support our theoretical results.

math.AP↗

arXiv2018

New error bounds for deep networks using sparse grids

We prove a theorem concerning the approximation of multivariate functions by deep ReLU networks. We present new error estimates for which the curse of the dimensionality is lessened by establishing a connection with sparse grids.

math.NA↗

arXiv2018

A spectral method for nonlocal diffusion operators on the sphere

We present algorithms for solving spatially nonlocal diffusion models on the unit sphere with spectral accuracy in space. Our algorithms are based on the diagonalizability of nonlocal diffusion operators in the basis of spherical harmonics, the computation of their eigenvalues to high relative accuracy using quadrature and asymptotic formulas, and a fast spherical harmonic transform. These techniques also lead to an efficient implementation of high-order exponential integrators for time-dependent models. We apply our method to the nonlocal Poisson, Allen--Cahn and Brusselator equations.

math.NA↗

arXiv2018

Hierarchical Attention-Based Recurrent Highway Networks for Time Series Prediction

Time series prediction has been studied in a variety of domains. However, it is still challenging to predict future series given historical observations and past exogenous data. Existing methods either fail to consider the interactions among different components of exogenous variables which may affect the prediction accuracy, or cannot model the correlations between exogenous data and target data. Besides, the inherent temporal dynamics of exogenous data are also related to the target series prediction, and thus should be considered as well. To address these issues, we propose an end-to-end deep learning model, i.e., Hierarchical attention-based Recurrent Highway Network (HRHN), which incorporates spatio-temporal feature extraction of exogenous variables and temporal dynamics modeling of target variables into a single framework. Moreover, by introducing the hierarchical attention mechanism, HRHN can adaptively select the relevant exogenous features in different semantic levels. We carry out comprehensive empirical evaluations with various methods over several datasets, and show that HRHN outperforms the state of the arts in time series prediction, especially in capturing sudden changes and sudden oscillations of time series.

cs.LG↗

arXiv2018

Direct measurement of neutrons induced in lead by cosmic muons at a shallow underground site

Neutron production in lead by cosmic muons has been studied with a Gadolinium doped liquid scintillator detector. The detector was installed next to the Muon-Induced Neutron Indirect Detection EXperiment (MINIDEX), permanently located in the Tübingen shallow underground laboratory where the mean muon energy is approximately 7 GeV. The MINIDEX plastic scintillators were used to tag muons; the neutrons were detected through neutron capture and neutron-induced nuclear recoil signals in the liquid scintillator detector. Results on the rates of observed neutron captures and nuclear recoils are presented and compared to predictions from GEANT4-9.6 and GEANT4-10.3. The predicted rates are significantly too low for both versions of GEANT4. For neutron capture events, the observation exceeds the predictions by factors of $ 1.65\,\pm\,0.02\,\textrm{(stat.)}\,\pm\,0.07\,\textrm{(syst.)} $ and $ 2.58\,\pm\,0.03\,\textrm{(stat.)}\,\pm\,0.11\,\textrm{(syst.)} $ for GEANT4-9.6 and GEANT4-10.3, respectively. For neutron nuclear recoil events, which require neutron energies above approximately 5 MeV, the factors are even larger, $ 2.22\,\pm\,0.05\,\textrm{(stat.)}\,\pm\,0.25\,\textrm{(syst.)} $ and $ 3.76\,\pm\,0.09\,\textrm{(stat.)}\,\pm\,0.41\,\textrm{(syst.)} $, respectively. Also presented is the first statistically significant measurement of the spectrum of neutrons induced by cosmic muons in lead between 5 and 40 MeV. It was obtained by unfolding the nuclear recoil spectrum. The observed neutron spectrum is harder than predicted by GEANT4. An investigation of the distribution of the time difference between muon tags and nuclear recoil signals confirms the validity of the unfolding procedure and shows that GEANT4 cannot properly describe the time distribution of nuclear recoil events. In general, the description of the data is worse for GEANT4-10.3 than for GEANT4-9.6.

physics.ins-det↗

arXiv2018

Response of gadolinium doped liquid scintillator to charged particles: measurement based on intrinsic U/Th contamination

A measurement is reported for the response to charged particles of a liquid scintillator named EJ-335 doped with 0.5% gadolinium by weight. This liquid scintillator was used as the detection medium in a neutron detector. The measurement is based on the in-situ $α$-particles from the intrinsic Uranium and Thorium contamination in the scintillator. The $β$-$α$ and the $α$-$α$ cascade decays from the U/Th decay chains were used to select $α$-particles. The contamination levels of U/Th were consequently measured to be $(5.54\pm0.15)\times 10^{-11}$ g/g, $(1.45\pm0.01)\times 10^{-10}$ g/g and $(1.07\pm0.01)\times 10^{-11}$ g/g for $^{232}$Th, $^{238}$U and $^{235}$U, respectively, assuming secular equilibrium. The stopping power of $α$-particles in the liquid scintillator was simulated by the TRIM software. Then the Birks constant, $kB$, of the scintillator for $α$-particles was determined to be $(7.28\pm0.23)$ mg/(cm$^{2}\cdot$MeV) by Birks' formulation. The response for protons is also presented assuming the $kB$ constant is the same as for $α$-particles.

physics.ins-det↗

arXiv2017

A New Phase-Field Approach to Variational Implicit Solvation of Charged Molecules with the Coulomb-Field Approximation

We construct a new phase-field model for the solvation of charged molecules with a variational implicit solvent. Our phase-field free-energy functional includes the surface energy, solute-solvent van der Waals dispersion energy, and electrostatic interaction energy that is described by the Coulomb-field approximation, all coupled together self-consistently through a phase field. By introducing a new phase-field term in the description of the solute-solvent van der Waals and electrostatic interactions, we can keep the phase-field values closer to those describing the solute and solvent regions, respectively, making it more accurate in the free-energy estimate. We first prove that our phase-field functionals $Γ$-converge to the corresponding sharp-interface limit. We then develop and implement an efficient and stable numerical method to solve the resulting gradient-flow equation to obtain equilibrium conformations and their associated free energies of the underlying charged molecular system. Our numerical method combines a linear splitting scheme, spectral discretization, and exponential time differencing Runge-Kutta approximations. Applications to the solvation of single ions and a two-plate system demonstrate that our new phase-field implementation improves the previous ones by achieving the localization of the system forces near the solute-solvent interface and maintaining more robustly the desirable hyperbolic tangent profile for even larger interfacial width. This work provides a scheme to resolve the possible unphysical feature of negative values in the phase-field function found in the previous phase-field modeling (cf. H. Sun, et al. J. Chem. Phys., 2015) of charged molecules with the Poisson--Boltzmann equation for the electrostatic interaction.

math.NA↗

arXiv2017

A quasinonlocal coupling method for nonlocal and local diffusion models

In this paper, we extend the idea of "geometric reconstruction" to couple a nonlocal diffusion model directly with the classical local diffusion in one dimensional space. This new coupling framework removes interfacial inconsistency, ensures the flux balance, and satisfies energy conservation as well as the maximum principle, whereas none of existing coupling methods for nonlocal-to-local coupling satisfies all of these properties. We establish the well-posedness and provide the stability analysis of the coupling method. We investigate the difference to the local limiting problem in terms of the nonlocal interaction range. Furthermore, we propose a first order finite difference numerical discretization and perform several numerical tests to confirm the theoretical findings. In particular, we show that the resulting numerical result is free of artifacts near the boundary of the domain where a classical local boundary condition is used, together with a coupled fully nonlocal model in the interior of the domain.

math.NA↗

arXiv2017

Measurement of the fast neutron background at the China Jinping Underground Laboratory

We report on the measurements of the fluxes and spectra of the environmental fast neutron background at the China Jinping Underground Laboratory (CJPL) with a rock overburden of about 6700 meters water equivalent, using a liquid scintillator detector doped with 0.5% gadolinium. The signature of a prompt nuclear recoil followed by a delayed high energy $γ$-ray cascade is used to identify neutron events. The large energy deposition of the delayed $γ$-rays from the $(n, γ)$ reaction on gadolinium, together with the excellent n-$γ$ discrimination capability provides a powerful background suppression which allows the measurement of a low intensity neutron flux. The neutron flux of $(1.51\pm0.03(stat.)\pm0.10(syst.))\times10^{-7}$ cm$^{-2}$s$^{-1}$ in the energy range of 1 -- 10 MeV in the Hall A of CJPL was measured based on 356 days of data. In the same energy region, measurement with the same detector placed in a one meter thick polyethylene room gives a significantly lower flux of $(4.9\pm0.9(stat.)\pm0.5(syst.))\times10^{-9}$ cm$^{-2}$s$^{-1}$ with 174 days of data. This represents a measurement of the lowest environmental fast neutron background among the underground laboratories in the world, prior to additional experiment-specific attenuation. Additionally, the fast neutron spectra both in the Hall A and the polyethylene room were reconstructed with the help of GEANT4 simulation.

physics.ins-det↗

arXiv2017

Stability of nonlocal Dirichlet integrals and implications for peridynamic correspondence material modeling

Nonlocal gradient operators are basic elements of nonlocal vector calculus that play important roles in nonlocal modeling and analysis. In this work, we extend earlier analysis on nonlocal gradient operators. In particular, we study a nonlocal Dirichlet integral that is given by a quadratic energy functional based on nonlocal gradients. Our main finding, which differs from claims made in previous studies, is that the coercivity and stability of this nonlocal continuum energy functional may hold for some properly chosen nonlocal interaction kernels but may fail for some other ones. This can be significant for possible applications of nonlocal gradient operators in various nonlocal models. In particular, we discuss some important implications for the peridynamic correspondence material models.

physics.comp-ph↗

arXiv2017

General neck condition for the limit shape of budding vesicles

The shape equation and linking conditions for a vesicle with two-phase domains are derived. We refine the conjecture on the general neck condition for the limit shape of a budding vesicle proposed by Jülicher and Lipowsky [Phys. Rev. Lett. \textbf{70}, 2964 (1993); Phys. Rev. E \textbf{53}, 2670 (1996)], and then we use the shape equation and linking conditions to prove that this conjecture holds not only for axisymmetric budding vesicles, but also for asymmetric ones. Our study reveals that the mean curvature at any point on the membrane segments adjacent to the neck satisfies the general neck condition for the limit shape of a budding vesicle when the length scale of the membrane segments is much larger than the characteristic size of the neck but still much smaller than the characteristic size of the vesicle.

cond-mat.soft↗

arXiv2017

The first result on 76Ge neutrinoless double beta decay from CDEX-1 experiment

We report the first result on Ge-76 neutrinoless double beta decay from CDEX-1 experiment at China Jinping Underground Laboratory. A mass of 994 g p-type point-contact high purity germanium detector has been installed to search the neutrinoless double beta decay events, as well as to directly detect dark matter particles. An exposure of 304 kg*day has been analyzed. The wideband spectrum from 500 keV to 3 MeV was obtained and the average event rate at the 2.039 MeV energy range is about 0.012 count per keV per kg per day. The half-life of Ge-76 neutrinoless double beta decay has been derived based on this result as: T 1/2 > 6.4*10^22 yr (90% C.L.). An upper limit on the effective Majorana-neutrino mass of 5.0 eV has been achieved. The possible methods to further decrease the background level have been discussed and will be pursued in the next stage of CDEX experiment.

hep-ex↗

arXiv2016

Nonlocal conservation laws. I. A new class of monotonicity-preserving models

We introduce a new class of nonlocal nonlinear conservation laws in one space dimension that allow for nonlocal interactions over a finite horizon. The proposed model, which we refer to as the nonlocal pair interaction model, inherits at the continuum level the unwinding feature of finite difference schemes for local hyperbolic conservation laws, so that the maximum principle and certain monotonicity properties hold and, consequently, the entropy inequalities are naturally satisfied. We establish a global-in-time well-posedness theory for these models which covers a broad class of initial data. Moreover, in the limit when the horizon parameter approaches zero, we are able to prove that our nonlocal model reduces to the conventional class of local hyperbolic conservation laws. Furthermore, we propose a numerical discretization method adapted to our nonlocal model, which relies on a monotone numerical flux and a uniform mesh, and we establish that these numerical solutions converge to a solution, providing as by-product both the existence theory for the nonlocal model and the convergence property relating the nonlocal regime and the asymptotic local regime.

math.AP↗

arXiv2014

Temperature Effect and Correction Method of White Rabbit Timing Link

To guarantee the angular resolution, the Large High Altitude Air Shower Observatory (LHAASO) requires a 500ps (rms) timing synchronization among the 6866 detect units for its KM2A sub-detector array. The White Rabbit technology is applied which combines sub-nanosecond precision timing transfer and gigabit Ethernet data transfer over the same fiber media. Deployed on a wild field at 4300m a.s.l. altitude, the WR network must maintain the precision over a wide temperature range. The temperature effect on a small WR link is measured, and contributions from different components like optical fiber, SFP module, fixed delay on PCB and ICs are separately studied and analyzed. An online real-time temperature correction method was applied based on the result which significantly reduce the synchronization variation from 300 ps to 50 ps in a temperature range of 50 degrees centigrade.

physics.ins-det↗