arXiv subjects

Lin Zheng

Publications and source records attributed to Lin Zheng.

42 records · Page 3Linked to original sources

arXiv2020

Template Matching and Change Point Detection by M-estimation

We consider the fundamental problem of matching a template to a signal. We do so by M-estimation, which encompasses procedures that are robust to gross errors (i.e., outliers). Using standard results from empirical process theory, we derive the convergence rate and the asymptotic distribution of the M-estimator under relatively mild assumptions. We also discuss the optimality of the estimator, both in finite samples in the minimax sense and in the large-sample limit in terms of local minimaxity and relative efficiency. Although most of the paper is dedicated to the study of the basic shift model in the context of a random design, we consider many extensions towards the end of the paper, including more flexible templates, fixed designs, the agnostic setting, and more.

math.ST↗

arXiv2020

Generative Semantic Hashing Enhanced via Boltzmann Machines

Generative semantic hashing is a promising technique for large-scale information retrieval thanks to its fast retrieval speed and small memory footprint. For the tractability of training, existing generative-hashing methods mostly assume a factorized form for the posterior distribution, enforcing independence among the bits of hash codes. From the perspectives of both model representation and code space size, independence is always not the best assumption. In this paper, to introduce correlations among the bits of hash codes, we propose to employ the distribution of Boltzmann machine as the variational posterior. To address the intractability issue of training, we first develop an approximate method to reparameterize the distribution of a Boltzmann machine by augmenting it as a hierarchical concatenation of a Gaussian-like distribution and a Bernoulli distribution. Based on that, an asymptotically-exact lower bound is further derived for the evidence lower bound (ELBO). With these novel techniques, the entire model can be optimized efficiently. Extensive experimental results demonstrate that by effectively modeling correlations among different bits within a hash code, our model can achieve significant performance gains.

cs.LG↗

arXiv2018

Shifting Maximum Eigenvalue Detection in Low SNR Environment

Maximum eigenvalue detection (MED) is an important application of random matrix theory in spectrum sensing and signal detection. However, in small signal-to-noise ratio environment, the maximum eigenvalue of the representative signal is at the edge of Marchenko-Pastur (M-P) law bulk and meets the Tracy-Widom distribution. Since the distribution of Tracy-Widom has no closed-form expression, it brings great difficulty in processing. In this paper, we propose a shifting maximum eigenvalue (SMED) algorithm, which shifts the maximum eigenvalue out of the M-P law bulk by combining an auxiliary signal associated with the signal to be detected. According to the random matrix theory, the shifted maximum eigenvalue is consistent with Gaussian distribution. The proposed SMED not only simplifies the detection algorithm, but also greatly improve the detection performance. In this paper, the performance of SMED, MED and trace (FMD) algorithm is analyzed and the theoretical performance comparisons are obtained. The algorithm and theoretical results are verified by the simulations in different signal environments.

eess.SP↗

arXiv2017

Kinetic theory based force treatment in lattice Boltzmann equation

In the gas kinetic theory, it showed that the zeroth order of the density distribution function $f^{(0)}$ and local equilibrium density distribution function were the Maxwellian distribution $f^{(eq)}(ρ,\emph{\textbf{u}}, T)$ with an external force term, where $ρ$ the fluid density, $\emph{\textbf{u}}$ the physical velocity and $T$ the temperature, while in the lattice Boltzmann equation (LBE) method numerous force treatments were proposed with a discrete density distribution function $f_i$ apparently relaxed to a given state $f^{(eq)}_i(ρ,\emph{\textbf{u}}^*)$, where the given velocity $\emph{\textbf{u}}^*$ could be different with $\emph{\textbf{u}}$, and the Chapman-Enskog analysis showed that $f^{(0)}_i$ and local equilibrium density distribution function should be $f^{(eq)}_i(ρ,\emph{\textbf{u}}^*)$ in the literature. In this paper, we start from the kinetic theory and show that the $f^{(0)}_i$ and local equilibrium density distribution function in LBE should obey the Maxwellian distribution $f^{(eq)}_i(ρ,\emph{\textbf{u}})$ with $f_i$ relaxed to $f^{(eq)}_i(ρ,\emph{\textbf{u}}^*)$, which are consistent with kinetic theory, then the general requirements for the force term are derived, by which the correct hydrodynamic equations could be recovered at Navier-Stokes level, and numerical results confirm our theoretical analysis.

physics.comp-ph↗

arXiv2014

Continuous surface force based lattice Boltzmann equation method for simulating thermocapillary flow

In this paper, we extend a lattice Boltzmann equation (LBE) with continuous surface fore (CSF) to simulate thermocapillary flows. The model is designed on our previous CSF LBE for athermal two phase flow, in which the interfacial tension forces and the Marangoni stresses as the results of the interface interactions between different phases are described by a conception of CSF. In this model, the sharp interfaces between different phases are separated by a narrow transition layers, and the kinetics and morphology evolution of phase separation would be characterized by an order parameter visa Cahn-Hilliard equation which is solved in the frame work of LBE. The scalar convection-diffusion equation for temperature field is also solved by thermal LBE. The models are validated by thermal two layered Poiseuille flow, and a two superimposed planar fluids at negligibly small Reynolds and Marangoni numbers for the thermocapillary driven convection, which have analytical solutions for the velocity and temperature. Then thermocapillary migration of two dimensional deformable droplet are simulated. Numerical results show that the predictions of present LBE agreed with the analytical solution/other numerical results.

physics.comp-ph↗

arXiv2012

Multiple periodic oscillations in the radio light curves of NRAO 530

In this paper, the time series analysis method CLEANest is employed to search for characteristic periodicities in the radio light curves of the blazar NRAO 530 at 4.8, 8.0 and 14.5 GHz over a time baseline of three decades. Two prominent periodicities on time scales of about 6.3 and 9.5 yr are identified at all three frequencies, in agreement with previous results derived from different numerical techniques, confirming the multiplicity of the periodicities in NRAO 530. In addition to these two significant periods, there is also evidence of shorter-timescale periodicities of about 5.0 yr, 4.2 yr, 3.4 yr and 2.8 yr showing lower amplitude in the periodograms. The physical mechanisms responsible for the radio quasi-periodic oscillations and the multiplicity of the periods are discussed.

astro-ph.HE↗