arXiv subjects

Liping Li

Publications and source records attributed to Liping Li.

At least 73 records · Page 4Linked to original sources

arXiv2021

3D modelling of survey scene from images enhanced with a multi-exposure fusion

In current practice, scene survey is carried out by workers using total stations. The method has high accuracy, but it incurs high costs if continuous monitoring is needed. Techniques based on photogrammetry, with the relatively cheaper digital cameras, have gained wide applications in many fields. Besides point measurement, photogrammetry can also create a three-dimensional (3D) model of the scene. Accurate 3D model reconstruction depends on high quality images. Degraded images will result in large errors in the reconstructed 3D model. In this paper, we propose a method that can be used to improve the visibility of the images, and eventually reduce the errors of the 3D scene model. The idea is inspired by image dehazing. Each original image is first transformed into multiple exposure images by means of gamma-correction operations and adaptive histogram equalization. The transformed images are analyzed by the computation of the local binary patterns. The image is then enhanced, with each pixel generated from the set of transformed image pixels weighted by a function of the local pattern feature and image saturation. Performance evaluation has been performed on benchmark image dehazing datasets. Experimentations have been carried out on outdoor and indoor surveys. Our analysis finds that the method works on different types of degradation that exist in both outdoor and indoor images. When fed into the photogrammetry software, the enhanced images can reconstruct 3D scene models with sub-millimeter mean errors.

cs.CV↗

arXiv2021

SN 2015bq: A Luminous Type Ia Supernova with Early Flux Excess

We present optical and ultraviolet (UV) observations of a luminous type Ia supernova (SN Ia) SN 2015bq characterized by the early flux excess. This SN reaches a B-band absolute magnitude at $M_B = -19.68 \pm 0.41$ mag and a peak bolometric luminosity at $L = (1.75 \pm 0.37) \times 10^{43}$ erg s$^{-1}$, with a relatively small post-maximum decline rate [$Δm_{15}(B) = 0.82 \pm 0.05$ mag]. The flux excess observed in the light curves of SN 2015bq a few days after the explosion, especially seen in the UV bands, might be due to the radioactive decay of $^{56}$Ni mixed into the surface. The radiation from the decay of the surface $^{56}$Ni heats the outer layer of this SN. It produces blue $U-B$ color followed by monotonically reddening in the early phase, dominated iron-group lines, and weak intermediate-mass elements absorption features in the early spectra. The scenario of enhanced $^{56}$Ni in the surface is consistent with a large amount of $^{56}$Ni ($M_{ \rm ^{56}{\rm Ni}}$ = 0.97 $\pm 0.20$ $M_{\odot}$) synthesized during the explosion. The properties of SN 2015bq are found to locate between SN 1991T and SN 1999aa, suggesting the latter two subclasses of SNe Ia may have a common origin.

astro-ph.HE↗

arXiv2021

Analysis for full face mechanical behaviors through spatial deduction model with real-time monitoring data

Mechanical analysis for the full face of tunnel structure is crucial to maintain stability, which is a challenge in classical analytical solutions and data analysis. Along this line, this study aims to develop a spatial deduction model to obtain the full-faced mechanical behaviors through integrating mechanical properties into pure data-driven model. The spatial tunnel structure is divided into many parts and reconstructed in a form of matrix. Then, the external load applied on structure in the field was considered to study the mechanical behaviors of tunnel. Based on the limited observed monitoring data in matrix and mechanical analysis results, a double-driven model was developed to obtain the full-faced information, in which the data-driven model was the dominant one and the mechanical constraint was the secondary one. To verify the presented spatial deduction model, cross-test was conducted through assuming partial monitoring data are unknown and regarding them as testing points. The well agreement between deduction results with actual monitoring results means the proposed model is reasonable. Therefore, it was employed to deduct both the current and historical performance of tunnel full face, which is crucial to prevent structural disasters.

cs.LG↗

arXiv2021

Quantum Computational Advantage via 60-Qubit 24-Cycle Random Circuit Sampling

To ensure a long-term quantum computational advantage, the quantum hardware should be upgraded to withstand the competition of continuously improved classical algorithms and hardwares. Here, we demonstrate a superconducting quantum computing systems \textit{Zuchongzhi} 2.1, which has 66 qubits in a two-dimensional array in a tunable coupler architecture. The readout fidelity of \textit{Zuchongzhi} 2.1 is considerably improved to an average of 97.74\%. The more powerful quantum processor enables us to achieve larger-scale random quantum circuit sampling, with a system scale of up to 60 qubits and 24 cycles. The achieved sampling task is about 6 orders of magnitude more difficult than that of Sycamore [Nature \textbf{574}, 505 (2019)] in the classic simulation, and 3 orders of magnitude more difficult than the sampling task on \textit{Zuchongzhi} 2.0 [arXiv:2106.14734 (2021)]. The time consumption of classically simulating random circuit sampling experiment using state-of-the-art classical algorithm and supercomputer is extended to tens of thousands of years (about $4.8\times 10^4$ years), while \textit{Zuchongzhi} 2.1 only takes about 4.2 hours, thereby significantly enhancing the quantum computational advantage.

quant-ph↗

arXiv2021

Completeness of the induced cotorsion pairs in functor categories

This paper focuses on a question raised by Holm and Jørgensen, who asked if the induced cotorsion pairs $(Φ({\sf X}),Φ({\sf X})^{\perp})$ and $(^{\perp}Ψ({\sf Y}),Ψ({\sf Y}))$ in $\mathrm{Rep}(Q,{\sf{A}})$ -- the category of all $\sf{A}$-valued representations of a quiver $Q$ -- are complete whenever $(\sf X,\sf Y)$ is a complete cotorsion pair in an abelian category $\sf{A}$ satisfying some mild conditions. Recently, Odabaşı gave an affirmative answer if the quiver $Q$ is rooted and the cotorsion pair $(\sf X,\sf Y)$ is further hereditary. In this paper, we improve Odabaşı's work by removing the hereditary assumption on the cotorsion pair. As an application, we show under certain mild conditions that if a subcategory $\sf L$, which is not necessarily closed under direct summands, of $\sf A$ is special precovering (resp., preenveloping), then $Φ(\sf L)$ (resp., $Ψ(\sf L)$) is special precovering (resp., preenveloping) in $\mathrm{Rep}(Q,{\sf{A}})$.

math.RT↗

arXiv2021

On trace of Brownian motion on the boundary of a strip

The trace of a Markov process is the time changed process of the original process on the support of the Revuz measure used in the time change. In this paper, we will concentrate on the reflecting Brownian motions on certain closed strips. On one hand, we will formulate the concrete expression of the Dirichlet forms associated with the traces of such reflecting Brownian motions on the boundary. On the other hand, the limits of these traces as the distance between the upper and lower boundaries tends to $0$ or $\infty$ will be further obtained.

math.PR↗

arXiv2021

On a stiff problem in two-dimensional space

In this paper we will study a stiff problem in two-dimensional space and especially its probabilistic counterpart. Roughly speaking, the heat equation with a parameter $\varepsilon>0$ is under consideration: \[ \partial_t u^\varepsilon(t,x)=\frac{1}{2}\nabla \cdot \left(\mathbf{A}_\varepsilon(x)\nabla u^\varepsilon(t,x) \right),\quad t\geq 0, x\in \mathbb{R}^2, \] where $\mathbf{A}_\varepsilon(x)=\text{Id}_2$, the identity matrix, for $x\notin Ω_\varepsilon:=\{x=(x_1,x_2)\in \mathbb{R}^2: |x_2|<\varepsilon\}$ while $$\mathbf{A}_\varepsilon(x):=\begin{pmatrix} a_\varepsilon^- & 0 \\ 0 & a^\shortmid_\varepsilon \end{pmatrix}$$ with two positive constants $a^-_\varepsilon, a^\shortmid_\varepsilon$ for $x\in Ω_\varepsilon$. There exists a diffusion process $X^\varepsilon$ on $\mathbb{R}^2$ associated to this heat equation in the sense that $u^\varepsilon(t,x):=\mathbf{E}^xu^\varepsilon(0,X_t^\varepsilon)$ is its unique weak solution. Note that $Ω_\varepsilon$ collapses to the $x_1$-axis, a barrier of zero volume, as $\varepsilon\downarrow 0$. The main purpose of this paper is to derive all possible limiting process $X$ of $X^\varepsilon$ as $\varepsilon\downarrow 0$. In addition, the limiting flux $u$ of the solution $u^\varepsilon$ as $\varepsilon\downarrow 0 $ and all possible boundary conditions satisfied by $u$ will be also characterized.

math.PR↗

arXiv2021

Hunt's hypothesis and symmetrization for general 1-dimensional diffusions

In this paper, we will consider the problem that how far from Hunt's hypothesis (H) to symmetrization for a general 1-dimensional diffusion. A characterization of (H) involving the classification of points for this diffusion will be first obtained. Then the main result shows that such a process is symmetrizable, if and only if (H) holds and a certain family of asymmetric shunt points is empty. Furthermore, we will also derive the representation of associated Dirichlet forms of general 1-dimensional diffusions under symmetry.

math.PR↗

arXiv2021

Strong quantum computational advantage using a superconducting quantum processor

Scaling up to a large number of qubits with high-precision control is essential in the demonstrations of quantum computational advantage to exponentially outpace the classical hardware and algorithmic improvements. Here, we develop a two-dimensional programmable superconducting quantum processor, \textit{Zuchongzhi}, which is composed of 66 functional qubits in a tunable coupling architecture. To characterize the performance of the whole system, we perform random quantum circuits sampling for benchmarking, up to a system size of 56 qubits and 20 cycles. The computational cost of the classical simulation of this task is estimated to be 2-3 orders of magnitude higher than the previous work on 53-qubit Sycamore processor [Nature \textbf{574}, 505 (2019)]. We estimate that the sampling task finished by \textit{Zuchongzhi} in about 1.2 hours will take the most powerful supercomputer at least 8 years. Our work establishes an unambiguous quantum computational advantage that is infeasible for classical computation in a reasonable amount of time. The high-precision and programmable quantum computing platform opens a new door to explore novel many-body phenomena and implement complex quantum algorithms.

quant-ph↗

arXiv2021

Adjoint functors on the representation category of $\mathscr{OI}$

In this paper we study adjunction relations between some natural functors on the representation category of the category of finite linearly ordered sets and order-preserving injections. We also prove that the Nakayama functor induces an equivalence from the Serre quotient of the category of finitely generated modules by the category of finitely generated torsion modules to the category of finite dimensional modules.

math.RT↗

arXiv2020

Sufficient and necessary conditions for hereditary of infinite category algebras

We describe necessary and sufficient conditions for the hereditarity of the category algebra of an infinite EI category satisfying certain combinatorial assumptions. More generally, we discuss conditions such that the left global dimension of a category algebra equals the maximal left global dimension of the endomorphism algebras of its objects, and classify its projective modules in this case. As applications, we completely classify transporter categories, orbit categories, and Quillen categories with left hereditary category algebras over a field.

math.RT↗

arXiv2020

Distorted Brownian motions on space with varying dimension

Roughly speaking, a space with varying dimension consists of at least two components with different dimensions. In this paper we will concentrate on the one, which can be treated as $\mathbb{R}^3$ tying a half line not contained by $\mathbb{R}^3$ at the origin. The aim is twofold. On one hand, we will introduce so-called distorted Brownian motions on this space with varying dimension (dBMVDs in abbreviation) and study their basic properties by means of Dirichlet forms. On the other hand, we will prove the joint continuity of the transition density functions of these dBMVDs and derive the short-time heat kernel estimates for them.

math.PR↗

arXiv2020

A Communication Efficient Collaborative Learning Framework for Distributed Features

We introduce a collaborative learning framework allowing multiple parties having different sets of attributes about the same user to jointly build models without exposing their raw data or model parameters. In particular, we propose a Federated Stochastic Block Coordinate Descent (FedBCD) algorithm, in which each party conducts multiple local updates before each communication to effectively reduce the number of communication rounds among parties, a principal bottleneck for collaborative learning problems. We analyze theoretically the impact of the number of local updates and show that when the batch size, sample size, and the local iterations are selected appropriately, within $T$ iterations, the algorithm performs $\mathcal{O}(\sqrt{T})$ communication rounds and achieves some $\mathcal{O}(1/\sqrt{T})$ accuracy (measured by the average of the gradient norm squared). The approach is supported by our empirical evaluations on a variety of tasks and datasets, demonstrating advantages over stochastic gradient descent (SGD) approaches.

cs.LG↗

arXiv2020

An inductive method for $\mathrm{OI}$-modules

In this paper we introduce an inductive method to study $\mathrm{OI}$-modules presented in finite degrees, where $\mathrm{OI}$ is a skeleton of the category of finitely totally ordered sets and strictly increasing maps. As an application, we obtain an explicit upper bound for the Castelnuovo-Mumford regularity of $\mathrm{OI}$-modules.

math.RT↗

arXiv2020

Castelnuovo-Mumford regularity of representations of certain product categories

We show in this paper that representations of a finite product of categories satisfying certain combinatorial conditions have finite Castelnuovo-Mumford regularity if and only if they are presented in finite degrees, and hence the category consisting of them is abelian. These results apply to examples such as the categories $\mathrm{FI}^m$ and $\mathrm{FI}_G^m$.

math.RT↗

arXiv2020

Communication-Censored Distributed Stochastic Gradient Descent

This paper develops a communication-efficient algorithm to solve the stochastic optimization problem defined over a distributed network, aiming at reducing the burdensome communication in applications such as distributed machine learning.Different from the existing works based on quantization and sparsification, we introduce a communication-censoring technique to reduce the transmissions of variables, which leads to our communication-Censored distributed Stochastic Gradient Descent (CSGD) algorithm. Specifically, in CSGD, the latest mini-batch stochastic gradient at a worker will be transmitted to the server if and only if it is sufficiently informative. When the latest gradient is not available, the stale one will be reused at the server. To implement this communication-censoring strategy, the batch-size is increasing in order to alleviate the effect of stochastic gradient noise. Theoretically, CSGD enjoys the same order of convergence rate as that of SGD, but effectively reduces communication. Numerical experiments demonstrate the sizable communication saving of CSGD.

stat.ML↗

arXiv2019

RSA: Byzantine-Robust Stochastic Aggregation Methods for Distributed Learning from Heterogeneous Datasets

In this paper, we propose a class of robust stochastic subgradient methods for distributed learning from heterogeneous datasets at presence of an unknown number of Byzantine workers. The Byzantine workers, during the learning process, may send arbitrary incorrect messages to the master due to data corruptions, communication failures or malicious attacks, and consequently bias the learned model. The key to the proposed methods is a regularization term incorporated with the objective function so as to robustify the learning task and mitigate the negative effects of Byzantine attacks. The resultant subgradient-based algorithms are termed Byzantine-Robust Stochastic Aggregation methods, justifying our acronym RSA used henceforth. In contrast to most of the existing algorithms, RSA does not rely on the assumption that the data are independent and identically distributed (i.i.d.) on the workers, and hence fits for a wider class of applications. Theoretically, we show that: i) RSA converges to a near-optimal solution with the learning error dependent on the number of Byzantine workers; ii) the convergence rate of RSA under Byzantine attacks is the same as that of the stochastic gradient descent method, which is free of Byzantine attacks. Numerically, experiments on real dataset corroborate the competitive performance of RSA and a complexity reduction compared to the state-of-the-art alternatives.

cs.LG↗

arXiv2019

A General Construction and Encoder Implementation of Polar Codes

Similar to existing codes, puncturing and shortening are two general ways to obtain an arbitrary code length and code rate for polar codes. When some of the coded bits are punctured or shortened, it is equivalent to a situation in which the underlying channels of the polar codes are different. Therefore, the quality of bit channels with puncturing or shortening differ from the original qualities, which can greatly affect the construction of polar codes. In this paper, a general construction of polar codes is studied in two aspects: 1) the theoretical foundation of the construction; and 2) the hardware implementation of polar codes encoders. In contrast to the original identical and independent binary-input, memoryless, symmetric (BMS) channels, these underlying BMS channels can be different. For binary erasure channel (BEC) channels, recursive equations can be employed assuming independent BMS channels. For all other channel types, the proposed general construction of polar codes is based on the existing Tal-Vardy's procedure. The symmetric property and the degradation relationship are shown to be preserved under the general setting, rendering the possibility of a modification of Tal-Vardy's procedure. Simulation results clearly show improved error performance with re-ordering using the proposed new procedures. In terms of hardware, a novel pruned folded encoder architecture is proposed which saves the computation for the beginning frozen bits. Implementation results show the pruned encoder achieve 28% throughput improvement.

cs.IT↗