arXiv subjects

Lei Liu

Publications and source records attributed to Lei Liu.

At least 361 records · Page 20Linked to original sources

arXiv2019

On the $j$-th Eigenvalue of Sturm-Liouville Problem and the Maslov Index

In the previous papers \cite{HLWZ,KWZ}, the jump phenomena of the $j$-th eigenvalue were completely characterized for Sturm-Liouville problems. In this paper, we show that the jump number of these eigenvalue branches is exactly the Maslov index for the path of corresponding boundary conditions. Then we determine the sharp range of the $j$-th eigenvalue on each layer of the space of boundary conditions. Finally, we prove that the graph of monodromy matrix tends to the Dirichlet boundary condition as the spectral parameter goes to $-\infty$.

math.FA↗

arXiv2019

Dimension Engineering of Single-Layer PtN$_2$ with the Cairo Tessellation

Single-layer PtN$_2$ exhibits an intriguing structure consisting of a tessellation pattern called the Cairo tessellation of type 2 pentagons, which belong to one of the existing 15 types of convex pentagons discovered so far that can monohedrally tile a plane. Single-layer PtN$_2$ has also been predicted to show semiconducting behavior with direct band gaps. Full exploration of the structure-property relationship awaits the successful exfoliation or synthesis of this novel single-layer material, which depends on the structure of its bulk counterpart with the same stoichiometry to some extent. Bulk PtN$_2$ with the pyrite structure is commonly regarded as the most stable structure in the literature. But comparing the energies of single-layer PtN$_2$ and bulk PtN$_2$ leads to a dilemma that a single-layer material is more stable than its bulk counterpart. To solve this dilemma, we propose stacking single-layer PtN$_2$ sheets infinitely to form a new bulk structure of PtN$_2$. The resulting tetrahedral layered structure is energetically more stable than the pyrite structure and single-layer PtN$_2$. We also find that the predicted bulk structure is metallic, in contrast to the semiconducting pyrite structure. In addition to predicting the 3D structure, we explore the possibility of rolling single-layer PtN$_2$ sheets into nanotubes. The required energies are comparable to those needed to form carbon or boron nitride nanotubes from their single-layer sheets, implying the feasibility of obtaining PtN$_2$ nanotubes. We finally study the electronic structures of PtN$_2$ nanotubes and find that the band gaps of PtN$_2$ nanotubes are tunable by changing the number of unit cells $N$ of single-layer PtN$_2$ used to construct the nanotubes. Our work shows that dimension engineering of PtN$_2$ not only leads to a more stable 3D structure but also 1D materials with novel properties.

cond-mat.mtrl-sci↗

arXiv2019

The localization of single pulse in VLBI observation

In our previous work, we propose a cross spectrum based method to extract single pulse signals from RFI contaminated data, which is originated from geodetic VLBI postprocessing. This method fully utilizes fringe phase information of the cross spectrum and hence maximizes signal power, however the localization was not discussed in that work yet. As the continuation of that work, in this paper, we further study how to localize single pulses using astrometric solving method. Assuming that the burst is a point source, we derive the burst position by solving a set of linear equations given the relation between residual delay and offset to a priori position. We find that the single pulse localization results given by both astrometric solving and radio imaging are consistent within 3 sigma level. Therefore we claim that it is possible to derive the position of a single pulse with reasonable precision based on only 3 or even 2 baselines with 4 milliseconds integration. The combination of cross spectrum based detection and the localization proposed in this work then provide a thorough solution for searching single pulse in VLBI observation. According to our calculation, our pipeline gives comparable accuracy as radio imaging pipeline. Moreover, the computational cost of our pipeline is much smaller, which makes it more practical for FRB search in regular VLBI observation. The pipeline is now publicly available and we name it as "VOLKS", which is the acronym of "VLBI Observation for frb Localization Keen Searcher".

astro-ph.IM↗

arXiv2019

Capacity-Achieving MIMO-NOMA: Iterative LMMSE Detection

This paper considers a low-complexity iterative Linear Minimum Mean Square Error (LMMSE) multi-user detector for the Multiple-Input and Multiple-Output system with Non-Orthogonal Multiple Access (MIMO-NOMA), where multiple single-antenna users simultaneously communicate with a multiple-antenna base station (BS). While LMMSE being a linear detector has a low complexity, it has suboptimal performance in multi-user detection scenario due to the mismatch between LMMSE detection and multi-user decoding. Therefore, in this paper, we provide the matching conditions between the detector and decoders for MIMO-NOMA, which are then used to derive the achievable rate of the iterative detection. We prove that a matched iterative LMMSE detector can achieve (i) the optimal capacity of symmetric MIMO-NOMA with any number of users, (ii) the optimal sum capacity of asymmetric MIMO-NOMA with any number of users, (iii) all the maximal extreme points in the capacity region of asymmetric MIMO-NOMA with any number of users, (iv) all points in the capacity region of two-user and three-user asymmetric MIMO-NOMA systems. In addition, a kind of practical low-complexity error-correcting multiuser code, called irregular repeat-accumulate code, is designed to match the LMMSE detector. Numerical results shows that the bit error rate performance of the proposed iterative LMMSE detection outperforms the state-of-art methods and is within 0.8dB from the associated capacity limit.

cs.IT↗

arXiv2019

Background subtraction on depth videos with convolutional neural networks

Background subtraction is a significant component of computer vision systems. It is widely used in video surveillance, object tracking, anomaly detection, etc. A new data source for background subtraction appeared as the emergence of low-cost depth sensors like Microsof t Kinect, Asus Xtion PRO, etc. In this paper, we propose a background subtraction approach on depth videos, which is based on convolutional neural networks (CNNs), called BGSNet-D (BackGround Subtraction neural Networks for Depth videos). The method can be used in color unavailable scenarios like poor lighting situations, and can also be applied to combine with existing RGB background subtraction methods. A preprocessing strategy is designed to reduce the influences incurred by noise from depth sensors. The experimental results on the SBM-RGBD dataset show that the proposed method outperforms existing methods on depth data.

cs.CV↗

arXiv2019

Global existence of the harmonic map heat flow into Lorentzian manifolds

We investigate a parabolic-elliptic system for maps $(u,v)$ from a compact Riemann surface $M$ into a Lorentzian manifold $N\times{\mathbb{R}}$ with a warped product metric. That system turns the harmonic map type equations into a parabolic system, but keeps the $v$-equation as a nonlinear second order constraint along the flow. We prove a global existence result of the parabolic-elliptic system by assuming either some geometric conditions on the target Lorentzian manifold or small energy of the initial maps. The result implies the existence of a Lorentzian harmonic map in a given homotopy class with fixed boundary data.

math.DG↗

arXiv2018

Compact and low-cost structured illumination microscopy using an optical fiber coupler

In this paper, a compact and low-cost structured illumination microscope (SIM) based on a 2X2 fiber coupler is presented. Fringe illumination is achieved by placing two output fiber tips at a conjugate Fourier plane of the sample plane as the point sources. Raw structured illumination (SI) images in different pattern orientations are captured when rotating the fiber mount. Following this, high resolution images are reconstructed from no-phase-shift raw SI images by using a joint Richardson-Lucy (jRL) deconvolution algorithm. Compared with an SLM-based SIM system, our method provides a much shorter illumination path, high power efficiency, and low cost.

physics.ins-det↗

arXiv2018

Auto-tuning Neural Network Quantization Framework for Collaborative Inference Between the Cloud and Edge

Recently, deep neural networks (DNNs) have been widely applied in mobile intelligent applications. The inference for the DNNs is usually performed in the cloud. However, it leads to a large overhead of transmitting data via wireless network. In this paper, we demonstrate the advantages of the cloud-edge collaborative inference with quantization. By analyzing the characteristics of layers in DNNs, an auto-tuning neural network quantization framework for collaborative inference is proposed. We study the effectiveness of mixed-precision collaborative inference of state-of-the-art DNNs by using ImageNet dataset. The experimental results show that our framework can generate reasonable network partitions and reduce the storage on mobile devices with trivial loss of accuracy.

cs.DC↗

arXiv2018

Single-Layer Ferromagnetic and Piezoelectric CoAsS with Pentagonal Structure

Single-layer pentagonal materials are an emerging family of two-dimensional (2D) materials that could exhibit novel properties due to the building blocks being pentagons instead of hexagons as in numerous 2D materials. Based on our recently predicted single-layer pentagonal CoS$_2$ that is an antiferromagnetic (AFM) semiconductor, we replace two S atoms by As atoms in a unit cell to form single-layer pentagonal CoAsS. The resulting single-layer material is dynamically stable ac-cording to the phonon calculations. We find two drastic changes in the properties of single-layer pentagonal CoAsS in comparison with those of CoS$_2$. First, we find a magnetic transition from the AFM to FM ordering. We understand that the transition is caused by the lower electronegativity of As atoms, leading to the weakened bridging roles on the superexchange interactions be-tween Co ions. Single-layer pentagonal CoAsS also shows significantly stronger magnetocrystalline anisotropy energy due to stronger spin-orbit coupling. We additionally perform Monte Carlo simulations to calculate the Curie temperature of single-layer pentagonal CoAsS and the predicted Curie temperature is 103 K. Second, we find that single-layer pentagonal CoAsS exhibits piezoelectricity, which is absent in single-layer pentagonal CoS$_2$ due to its center of symmetry. The computed piezoelectric coefficients are also sizable. The rare coexistence of FM ordering and piezoelectric properties makes single-layer pentagonal CoAsS a promising multifunctional 2D material.

cond-mat.mtrl-sci↗

arXiv2018

Iterative Channel Estimation Using LSE and Sparse Message Passing for MmWave MIMO Systems

We propose an iterative channel estimation algorithm based on the Least Square Estimation (LSE) and Sparse Message Passing (SMP) algorithm for the Millimeter Wave (mmWave) MIMO systems. The channel coefficients of the mmWave MIMO are approximately modeled as a Bernoulli-Gaussian distribution and the channel matrix is sparse with only a few non-zero entries. By leveraging the advantage of sparseness, we propose an algorithm that iteratively detects the exact locations and values of non-zero entries of the sparse channel matrix. At each iteration, the locations are detected by the SMP, and values are estimated with the LSE. We also analyze the Cramér-Rao Lower Bound (CLRB), and show that the proposed algorithm is a minimum variance unbiased estimator under the assumption that we have the partial priori knowledge of the channel. Furthermore, we employ the Gaussian approximation for message densities under density evolution to simplify the analysis of the algorithm, which provides a simple method to predict the performance of the proposed algorithm. Numerical experiments show that the proposed algorithm has much better performance than the existing sparse estimators, especially when the channel is sparse. In addition, our proposed algorithm converges to the CRLB of the genie-aided estimation of sparse channels with only five turbo iterations.

cs.IT↗

arXiv2018

Gaussian Message Passing for Overloaded Massive MIMO-NOMA

This paper considers a low-complexity Gaussian Message Passing (GMP) scheme for a coded massive Multiple-Input Multiple-Output (MIMO) systems with Non-Orthogonal Multiple Access (massive MIMO-NOMA), in which a base station with $N_s$ antennas serves $N_u$ sources simultaneously in the same frequency. Both $N_u$ and $N_s$ are large numbers, and we consider the overloaded cases with $N_u>N_s$. The GMP for MIMO-NOMA is a message passing algorithm operating on a fully-connected loopy factor graph, which is well understood to fail to converge due to the correlation problem. In this paper, we utilize the large-scale property of the system to simplify the convergence analysis of the GMP under the overloaded condition. First, we prove that the \emph{variances} of the GMP definitely converge to the mean square error (MSE) of Linear Minimum Mean Square Error (LMMSE) multi-user detection. Secondly, the \emph{means} of the traditional GMP will fail to converge when $ N_u/N_s< (\sqrt{2}-1)^{-2}\approx5.83$. Therefore, we propose and derive a new convergent GMP called scale-and-add GMP (SA-GMP), which always converges to the LMMSE multi-user detection performance for any $N_u/N_s>1$, and show that it has a faster convergence speed than the traditional GMP with the same complexity. Finally, numerical results are provided to verify the validity and accuracy of the theoretical results presented.

cs.IT↗

arXiv2018

Energy identity for a class of approximate Dirac-harmonic maps from surfaces with boundary

For a sequence of coupled fields $\{(ϕ_n,ψ_n)\}$ from a compact Riemann surface $M$ with smooth boundary to a general compact Riemannian manifold with uniformly bounded energy and satisfying the Dirac-harmonic system up to some uniformly controlled error terms, we show that the energy identity holds during a blow-up process near the boundary. As an application to the heat flow of Dirac-harmonic maps from surfaces with boundary, when such a flow blows up at infinite time, we obtain an energy identity.

math.DG↗

arXiv2018

The qualitative behavior at the free boundary for approximate harmonic maps from surfaces

Let $\{u_n\}$ be a sequence of maps from a compact Riemann surface $M$ with smooth boundary to a general compact Riemannian manifold $N$ with free boundary on a smooth submanifold $K\subset N$ satisfying \[ \sup_n \ \left(\|\nabla u_n\|_{L^2(M)}+\|τ(u_n)\|_{L^2(M)}\right)\leq Λ, \] where $τ(u_n)$ is the tension field of the map $u_n$. We show that the energy identity and the no neck property hold during a blow-up process. The assumptions are such that this result also applies to the harmonic map heat flow with free boundary, to prove the energy identity at finite singular time as well as at infinity time. Also, the no neck property holds at infinity time.

math.DG↗

arXiv2018

A global weak solution to the Lorentzian harmonic map flow

We investigate a parabolic-elliptic system which is related to a harmonic map from a compact Riemann surface with a smooth boundary into a Lorentzian manifold with a warped product metric. We prove that there exists a unique global weak solution for this system which is regular except for at most finitely many singular points.

math.DG↗

arXiv2018

Single-layer antiferromagnetic semiconductor CoS2 with the pentagonal structure

Structure-property relationships have always been guiding principles in discovering new materials. Here we explore the relationships to discover novel two-dimensional (2D) materials with the goal of identifying 2D magnetic semiconductors for spintronics applications. In particular, we report a density functional theory + $U$ study of single-layer antiferromagnetic (AFM) semiconductor CoS$_2$ with the pentagonal structure forming the so-called Cairo Tessellation. We find that this single-layer magnet exhibits an indirect bandgap of 1.06 eV with light electron and hole effective masses of 0.03 and 0.10 $m_0$, respectively, which may lead to high carrier mobilities. The hybrid density functional theory calculations correct the bandgap to 2.24 eV. We also compute the magnetocrystalline anisotropy energy (MAE), showing that the easy axis of the AFM ordering is out of plane with a sizable MAE of 153 $μ$eV per Co ion. We further calculate the magnon frequencies at different spin-spiral vectors, based on which we estimate the N$\acute{e}$el temperatures to be 20.4 and 13.3 K using the mean field and random phase approximations, respectively. We then apply biaxial strains to tune the bandgap of single-layer pentagonal CoS$_2$. We find that the energy difference between the ferromagnetic and AFM structures strongly depends on the biaxial strain, but the ground state remains the AFM ordering. Although the low critical temperature prohibits the magnetic applications of single-layer pentagonal CoS$_2$ at room temperature, the excellent electrical properties may find this novel single-layer semiconductor applications in optoelectronic nanodevices.

cond-mat.mtrl-sci↗

arXiv2018

TreeGAN: Syntax-Aware Sequence Generation with Generative Adversarial Networks

Generative Adversarial Networks (GANs) have shown great capacity on image generation, in which a discriminative model guides the training of a generative model to construct images that resemble real images. Recently, GANs have been extended from generating images to generating sequences (e.g., poems, music and codes). Existing GANs on sequence generation mainly focus on general sequences, which are grammar-free. In many real-world applications, however, we need to generate sequences in a formal language with the constraint of its corresponding grammar. For example, to test the performance of a database, one may want to generate a collection of SQL queries, which are not only similar to the queries of real users, but also follow the SQL syntax of the target database. Generating such sequences is highly challenging because both the generator and discriminator of GANs need to consider the structure of the sequences and the given grammar in the formal language. To address these issues, we study the problem of syntax-aware sequence generation with GANs, in which a collection of real sequences and a set of pre-defined grammatical rules are given to both discriminator and generator. We propose a novel GAN framework, namely TreeGAN, to incorporate a given Context-Free Grammar (CFG) into the sequence generation process. In TreeGAN, the generator employs a recurrent neural network (RNN) to construct a parse tree. Each generated parse tree can then be translated to a valid sequence of the given grammar. The discriminator uses a tree-structured RNN to distinguish the generated trees from real trees. We show that TreeGAN can generate sequences for any CFG and its generation fully conforms with the given syntax. Experiments on synthetic and real data sets demonstrated that TreeGAN significantly improves the quality of the sequence generation in context-free languages.

cs.CL↗

arXiv2018

PtP$_2$: An Example of Exploring the Hidden Cairo Tessellation in the Pyrite Structure for Discovering Novel Two-Dimensional Materials

The Cairo tessellation refers to a pattern of type 2 pentagons that can pave an infinite plane without creating a gap or overlap. We reveal the hidden, layered Cairo tessellations in the pyrite structure with a general chemical formula of $AB_2$ and space group $pa\bar3$. We use this hidden tessellation along with density functional theory calculations to examine the possibility of obtaining a two-dimensional (2D) material with the Cairo tessellation from the bulk, using PtP$_2$ as an example. Unlike previously reported single-layer materials such as PdSe$_2$ with a buckled, pentagonal structure-strictly speaking, not belonging to the Cairo tessellation, we find that single-layer PtP$_2$ is completely planar exhibiting dynamically stable phonon modes. We also observe a reduction in the bandgaps PtP$_2$ from bulk to single layer using the Heyd-Scuseria-Ernzerhof (HSE) hybrid density functional, and the bandgap type switches from indirect to direct. By contrast, using the standard Perdew-Burke-Ernzerhof functional leads to the conclusion of single-layer PtP$_2$ being metallic. We further study the bonding characteristics of this novel single-layer material by computing the Bader charge transfer, the electron localization function, and the crystal orbit overlap population, which show mixed P-P covalent bonding and Pt-P ionic bonding, with the former being stronger. Finally, we study the surface states of single-layer PtP$_2$ and consider the spin-orbit coupling. We observe no spin-helical Dirac cone states, therefore ruling out single-layer PtP$_2$ as a topological insulator. We expect the example demonstrated in this work will stimulate interest in computationally identifying novel 2D materials from a variety of bulk materials with the pyrite structure.

cond-mat.mtrl-sci↗

arXiv2018

Encoding Quantum Mechanics into Pentagonal Geometries for Discovering Novel Two-Dimensional Materials

Imagine that there is a gapless plane tessellated by irregular, convex pentagons with their side lengths at the sub-nanoscale, and tiny balls are placed at the vertices of each pentagon. If there are no interactions among these balls, one would expect that they stand still at the vertices of the pentagons. But what if these balls symbolize atoms? The electrons and nuclei of the atoms will start to interact following the laws of quantum mechanics. As a result, the atoms will relocate leading to a system of energy minimum. While performing an experiment of manipulating individual atoms and observing the resulting configurations may be challenging, we apply ab initio density functional theory (DFT) calculations to carry out a virtual experiment, where we assign carbon atoms at the vertices of 14 types of convex pentagons and then optimize the positions of these atoms. We obtain a variety of unexpected structures; almost all of them except types 2 and 4 structures{these two structures are equivalent{differ from the initial pentagonal geometries. We compute the band structure of each resulting geometry representing the crystal structure of a two-dimensional (2D) material. We find diverse electrical properties among these 2D materials: metallic, semiconducting, and semi-metallic with a Dirac cone. Our work shows that encoding quantum mechanics into the geometries of irregular, convex pentagons and with the help of DFT calculations open up a novel route for accelerating discovery of new 2D materials.

cond-mat.mtrl-sci↗