arXiv subjects

Nan Li

Publications and source records attributed to Nan Li.

At least 289 records · Page 16Linked to original sources

arXiv2020

A Game Theoretic Approach for Parking Spot Search with Limited Parking Lot Information

We propose a game theoretic approach to address the problem of searching for available parking spots in a parking lot and picking the ``optimal'' one to park. The approach exploits limited information provided by the parking lot, i.e., its layout and the current number of cars in it. Considering the fact that such information is or can be easily made available for many structured parking lots, the proposed approach can be applicable without requiring major updates to existing parking facilities. For large parking lots, a sampling-based strategy is integrated with the proposed approach to overcome the associated computational challenge. The proposed approach is compared against a state-of-the-art heuristic-based parking spot search strategy in the literature through simulation studies and demonstrates its advantage in terms of achieving lower cost function values.

cs.RO↗

arXiv2020

Off-road Autonomous Vehicles Traversability Analysis and Trajectory Planning Based on Deep Inverse Reinforcement Learning

Terrain traversability analysis is a fundamental issue to achieve the autonomy of a robot at off-road environments. Geometry-based and appearance-based methods have been studied in decades, while behavior-based methods exploiting learning from demonstration (LfD) are new trends. Behavior-based methods learn cost functions that guide trajectory planning in compliance with experts' demonstrations, which can be more scalable to various scenes and driving behaviors. This research proposes a method of off-road traversability analysis and trajectory planning using Deep Maximum Entropy Inverse Reinforcement Learning. To incorporate vehicle's kinematics while solving the problem of exponential increase of state-space complexity, two convolutional neural networks, i.e., RL ConvNet and Svf ConvNet, are developed to encode kinematics into convolution kernels and achieve efficient forward reinforcement learning. We conduct experiments in off-road environments. Scene maps are generated using 3D LiDAR data, and expert demonstrations are either the vehicle's real driving trajectories at the scene or synthesized ones to represent specific behaviors such as crossing negative obstacles. Different cost functions of traversability analysis are learned and tested at various scenes of capability in guiding the trajectory planning of different behaviors. We also demonstrate the performance and computation efficiency of the proposed method.

cs.RO↗

arXiv2020

On algebraic differential equations concerning the Riemann-zeta function and the Euler-gamma function

In this paper, we prove that $ζ$ is not a solution of any non-trivial algebraic differential equation whose coefficients are polynomials in $Γ, Γ^{(n)}, Γ^{(l)}$ over the ring of polynomials in $\mathbb{C}$, $l>n\geq 1$ are positive integers. We extended the result that $ζ$ does not satisfy any non-trivial algebraic differential equation whose coefficients are polynomials in $Γ, Γ', Γ''$ over the field of complex numbers, which is proved by Li and Ye[7].

math.CV↗

arXiv2020

The Hawking-Page phase transitions in the extended phase space in the Gauss-Bonnet gravity

In this paper, the Hawking-Page phase transitions between the black holes and thermal anti-de Sitter (AdS) space are studied with the Gauss-Bonnet term in the extended phase space, in which the varying cosmological constant plays the role of an effective thermodynamic pressure. The Gauss-Bonnet term exhibits its effects via introducing the corrections to the black hole entropy and Gibbs free energy. The global phase structures, especially the phase transition temperature $T_{\rm HP}$ and the Gibbs free energy $G$, are systematically investigated, first for the Schwarzschild-AdS black holes and then for the charged and rotating AdS black holes in the grand canonical ensembles, with both analytical and numerical methods. It is found that there are terminal points in the coexistence lines, and $T_{\rm HP}$ decreases at large electric potentials and angular velocities and also decreases with the Gauss-Bonnet coupling constant $α$.

gr-qc↗

arXiv2020

Identifying Strong Lenses with Unsupervised Machine Learning using Convolutional Autoencoder

In this paper we develop a new unsupervised machine learning technique comprised of a feature extractor, a convolutional autoencoder (CAE), and a clustering algorithm consisting of a Bayesian Gaussian mixture model (BGM). We apply this technique to visual band space-based simulated imaging data from the Euclid Space Telescope using data from the Strong Gravitational Lenses Finding Challenge. Our technique promisingly captures a variety of lensing features such as Einstein rings with different radii, distorted arc structures, etc, without using predefined labels. After the clustering process, we obtain several classification clusters separated by different visual features which are seen in the images. Our method successfully picks up $\sim$63\ percent of lensing images from all lenses in the training set. With the assumed probability proposed in this study, this technique reaches an accuracy of $77.25\pm 0.48$\% in binary classification using the training set. Additionally, our unsupervised clustering process can be used as the preliminary classification for future surveys of lenses to efficiently select targets and to speed up the labelling process. As the starting point of the astronomical application using this technique, we not only explore the application to gravitationally lensed systems, but also discuss the limitations and potential future uses of this technique.

astro-ph.IM↗

arXiv2020

ReADS: A Rectified Attentional Double Supervised Network for Scene Text Recognition

In recent years, scene text recognition is always regarded as a sequence-to-sequence problem. Connectionist Temporal Classification (CTC) and Attentional sequence recognition (Attn) are two very prevailing approaches to tackle this problem while they may fail in some scenarios respectively. CTC concentrates more on every individual character but is weak in text semantic dependency modeling. Attn based methods have better context semantic modeling ability while tends to overfit on limited training data. In this paper, we elaborately design a Rectified Attentional Double Supervised Network (ReADS) for general scene text recognition. To overcome the weakness of CTC and Attn, both of them are applied in our method but with different modules in two supervised branches which can make a complementary to each other. Moreover, effective spatial and channel attention mechanisms are introduced to eliminate background noise and extract valid foreground information. Finally, a simple rectified network is implemented to rectify irregular text. The ReADS can be trained end-to-end and only word-level annotations are required. Extensive experiments on various benchmarks verify the effectiveness of ReADS which achieves state-of-the-art performance.

cs.CV↗

arXiv2020

A Neural Architecture Search based Framework for Liquid State Machine Design

Liquid State Machine (LSM), also known as the recurrent version of Spiking Neural Networks (SNN), has attracted great research interests thanks to its high computational power, biological plausibility from the brain, simple structure and low training complexity. By exploring the design space in network architectures and parameters, recent works have demonstrated great potential for improving the accuracy of LSM model with low complexity. However, these works are based on manually-defined network architectures or predefined parameters. Considering the diversity and uniqueness of brain structure, the design of LSM model should be explored in the largest search space possible. In this paper, we propose a Neural Architecture Search (NAS) based framework to explore both architecture and parameter design space for automatic dataset-oriented LSM model. To handle the exponentially-increased design space, we adopt a three-step search for LSM, including multi-liquid architecture search, variation on the number of neurons and parameters search such as percentage connectivity and excitatory neuron ratio within each liquid. Besides, we propose to use Simulated Annealing (SA) algorithm to implement the three-step heuristic search. Three datasets, including image dataset of MNIST and NMNIST and speech dataset of FSDD, are used to test the effectiveness of our proposed framework. Simulation results show that our proposed framework can produce the dataset-oriented optimal LSM models with high accuracy and low complexity. The best classification accuracy on the three datasets is 93.2%, 92.5% and 84% respectively with only 1000 spiking neurons, and the network connections can be averagely reduced by 61.4% compared with a single LSM. Moreover, we find that the total quantity of neurons in optimal LSM models on three datasets can be further reduced by 20% with only about 0.5% accuracy loss.

cs.NE↗

arXiv2020

Gluing of multiple Alexandrov spaces

In this paper we discuss the sufficient and necessary conditions for multiple Alexandrov spaces being glued to an Alexandrov space. We propose a Gluing Conjecture, which says that the finite gluing of Alexandrov spaces is an Alexandrov space, if and only if the gluing is by path isometry along the boundaries and the tangent cones are glued to Alexandrov spaces. This generalizes Petrunin's Gluing Theorem. Under the assumptions of the Gluing Conjecture, we classify the $2$-point gluing over $(n-1,ε)$-regular points as local separable gluing and the gluing near un-glued $(n-1,ε)$-regular points as local involutional gluing. We also prove that the Gluing Conjecture is true if the complement of $(n-1,ε)$-regular points is discrete in the glued boundary. In particular, this implies the general Gluing Conjecture as well as a new Gluing Theorem in dimension 2.

math.DG↗

arXiv2020

End-to-End Learnable Geometric Vision by Backpropagating PnP Optimization

Deep networks excel in learning patterns from large amounts of data. On the other hand, many geometric vision tasks are specified as optimization problems. To seamlessly combine deep learning and geometric vision, it is vital to perform learning and geometric optimization end-to-end. Towards this aim, we present BPnP, a novel network module that backpropagates gradients through a Perspective-n-Points (PnP) solver to guide parameter updates of a neural network. Based on implicit differentiation, we show that the gradients of a "self-contained" PnP solver can be derived accurately and efficiently, as if the optimizer block were a differentiable function. We validate BPnP by incorporating it in a deep model that can learn camera intrinsics, camera extrinsics (poses) and 3D structure from training datasets. Further, we develop an end-to-end trainable pipeline for object pose estimation, which achieves greater accuracy by combining feature-based heatmap losses with 2D-3D reprojection errors. Since our approach can be extended to other optimization problems, our work helps to pave the way to perform learnable geometric vision in a principled manner. Our PyTorch implementation of BPnP is available on http://github.com/BoChenYS/BPnP.

cs.CV↗

arXiv2020

Estimation of genomic characteristics by analyzing k-mer frequency in de novo genome projects

Background: With the fast development of next generation sequencing technologies, increasing numbers of genomes are being de novo sequenced and assembled. However, most are in fragmental and incomplete draft status, and thus it is often difficult to know the accurate genome size and repeat content. Furthermore, many genomes are highly repetitive or heterozygous, posing problems to current assemblers utilizing short reads. Therefore, it is necessary to develop efficient assembly-independent methods for accurate estimation of these genomic characteristics. Results: Here we present a framework for modeling the distribution of k-mer frequency from sequencing data and estimating the genomic characteristics such as genome size, repeat structure and heterozygous rate. By introducing novel techniques of k-mer individuals, float precision estimation, and proper treatment of sequencing error and coverage bias, the estimation accuracy of our method is significantly improved over existing methods. We also studied how the various genomic and sequencing characteristics affect the estimation accuracy using simulated sequencing data, and discussed the limitations on applying our method to real sequencing data. Conclusion: Based on this research, we show that the k-mer frequency analysis can be used as a general and assembly-independent method for estimating genomic characteristics, which can improve our understanding of a species genome, help design the sequencing strategy of genome projects, and guide the development of assembly algorithms. The programs developed in this research are written using C/C++, and freely accessible at Github URL (https://github.com/fanagislab/GCE) or BGI ftp ( ftp://ftp.genomics.org.cn/pub/gce).

q-bio.GN↗

arXiv2020

Optimising Automatic Morphological Classification of Galaxies with Machine Learning and Deep Learning using Dark Energy Survey Imaging

There are several supervised machine learning methods used for the application of automated morphological classification of galaxies; however, there has not yet been a clear comparison of these different methods using imaging data, or a investigation for maximising their effectiveness. We carry out a comparison between several common machine learning methods for galaxy classification (Convolutional Neural Network (CNN), K-nearest neighbour, Logistic Regression, Support Vector Machine, Random Forest, and Neural Networks) by using Dark Energy Survey (DES) data combined with visual classifications from the Galaxy Zoo 1 project (GZ1). Our goal is to determine the optimal machine learning methods when using imaging data for galaxy classification. We show that CNN is the most successful method of these ten methods in our study. Using a sample of $\sim$2,800 galaxies with visual classification from GZ1, we reach an accuracy of $\sim$0.99 for the morphological classification of Ellipticals and Spirals. The further investigation of the galaxies that have a different ML and visual classification but with high predicted probabilities in our CNN usually reveals an the incorrect classification provided by GZ1. We further find the galaxies having a low probability of being either spirals or ellipticals are visually Lenticulars (S0), demonstrating that supervised learning is able to rediscover that this class of galaxy is distinct from both Es and Spirals. We confirm that $\sim$2.5\% galaxies are misclassified by GZ1 in our study. After correcting these galaxies' labels, we improve our CNN performance to an average accuracy of over 0.99 (accuracy of 0.994 is our best result).

astro-ph.GA↗

arXiv2020

Three results on transcendental meromorphic solutions of certain nonlinear differential equations

In this paper, we study the transcendental meromorphic solutions for the nonlinear differential equations: $f^{n}+P(f)=R(z)e^{α(z)}$ and $f^{n}+P_{*}(f)=p_{1}(z)e^{α_{1}(z)}+p_{2}(z)e^{α_{2}(z)}$ in the complex plane, where $P(f)$ and $P_{*}(f)$ are differential polynomials in $f$ of degree $n-1$ with coefficients being small functions and rational functions respectively, $R$ is a non-vanishing small function of $f$, $α$ is a nonconstant entire function, $p_{1}, p_{2}$ are non-vanishing rational functions, and $α_{1}, α_{2}$ are nonconstant polynomials. Particularly, we consider the solutions of the second equation when $p_{1}, p_{2}$ are nonzero constants, and $°α_{1}=°α_{2}=1$. Our results are improvements and complements of Liao (Complex Var. Elliptic Equ. 2015, 60(6): 748--756), and Rong-Xu (Mathematics 2019, 7, 539), etc., which partially answer a question proposed by Li (J. Math. Anal. Appl. 2011, 375: 310--319).

math.CV↗

arXiv2019

ICDAR 2019 Robust Reading Challenge on Reading Chinese Text on Signboard

Chinese scene text reading is one of the most challenging problems in computer vision and has attracted great interest. Different from English text, Chinese has more than 6000 commonly used characters and Chinesecharacters can be arranged in various layouts with numerous fonts. The Chinese signboards in street view are a good choice for Chinese scene text images since they have different backgrounds, fonts and layouts. We organized a competition called ICDAR2019-ReCTS, which mainly focuses on reading Chinese text on signboard. This report presents the final results of the competition. A large-scale dataset of 25,000 annotated signboard images, in which all the text lines and characters are annotated with locations and transcriptions, were released. Four tasks, namely character recognition, text line recognition, text line detection and end-to-end recognition were set up. Besides, considering the Chinese text ambiguity issue, we proposed a multi ground truth (multi-GT) evaluation method to make evaluation fairer. The competition started on March 1, 2019 and ended on April 30, 2019. 262 submissions from 46 teams are received. Most of the participants come from universities, research institutes, and tech companies in China. There are also some participants from the United States, Australia, Singapore, and Korea. 21 teams submit results for Task 1, 23 teams submit results for Task 2, 24 teams submit results for Task 3, and 13 teams submit results for Task 4. The official website for the competition is http://rrc.cvc.uab.es/?ch=12.

cs.CV↗

arXiv2019

Quantitative Estimates on the Singular Sets of Alexandrov Spaces

Let $X\in\text{Alex}\,^n(-1)$ be an $n$-dimensional Alexandrov space with curvature $\ge -1$. Let the $r$-scale $(k,ε)$-singular set $\mathcal S^k_{ε,\,r}(X)$ be the collection of $x\in X$ so that $B_r(x)$ is not $εr$-close to a ball in any splitting space $\mathbb R^{k+1}\times Z$. We show that there exists $C(n,ε)>0$ and $β(n,ε)>0$, independent of the volume, so that for any disjoint collection $\big\{B_{r_i}(x_i):x_i\in \mathcal S_{ε,\,βr_i}^k(X)\cap B_1, \,r_i\le 1\big\}$, the packing estimate $\sum r_i^k\le C$ holds. Consequently, we obtain the Hausdorff measure estimates $\mathcal H^k(\mathcal S^k_ε(X)\cap B_1)\le C$ and $\mathcal H^n\big(B_r (\mathcal S^k_{ε,\,r}(X))\cap B_1(p)\big)\leq C\,r^{n-k}$. This answers an open question asked by Kapovitch and Lytchak. We also show that the $k$-singular set $\mathcal S^k(X)=\underset{ε>0}\cup\left(\underset{r>0}\cap\mathcal S^k_{ε,\,r}\right)$ is $k$-rectifiable and construct examples to show that such a structure is sharp. For instance, in the $k=1$ case we can build for any closed set $T\subseteq \mathbb S^1$ and $ε>0$ a space $Y\in\text{Alex}^3(0)$ with $\mathcal S^{1}_ε(Y)=ϕ(T)$, where $ϕ\colon\mathbb S^1\to Y$ is a bi-Lipschitz embedding. Taking $T$ to be a Cantor set it gives rise to an example where the singular set is a $1$-rectifiable, $1$-Cantor set with positive $1$-Hausdorff measure.

math.DG↗

arXiv2019

Lipschitz-Volume Rigidity and Globalization

Let $X$ and $Y$ be length metric spaces. Let $\mathcal H^n$ denote the $n$-dimensional Hausdorff measure. The Lipschitz-Volume Rigidity is a property that if there exists a 1-Lipschitz map $f\colon X\to Y$ and $0<\mathcal H^n(X)=\mathcal H^n(f(X))<\infty$, then $f$ preserves the length of path. This property holds for smooth manifolds but doesn't hold for all singular spaces. We survey the Lipschitz-Volume Rigidity Theorems on singular spaces with lower curvature bounds and discuss some related open problems.

math.DG↗

arXiv2019

Maltese cross coupling to individual cold atoms in free space

We report on the simultaneous observation from four directions of the fluorescence of single $^{87}$Rb atoms trapped at the common focus of four high numerical aperture (${\rm NA}=0.5$) aspheric lenses. We use an interferometrically-guided pick-and-place technique to precisely and stably position the lenses along the four cardinal directions with their foci at a single central point. The geometry gives right angle access to a single quantum emitter, and will enable new trapping, excitation, and collection methods. The fluorescence signals indicate both sub-Poissonian atom number statistics and photon anti-bunching, showing suitability for cold atom quantum optics.

physics.atom-ph↗

arXiv2019

Co-optimization of Speed and Gearshift Control for Battery Electric Vehicles Using Preview Information

This paper addresses the co-optimization of speed and gearshift control for battery electric vehicles using short-range traffic information. To achieve greater electric motor efficiency, a multi-speed transmission is employed, whose control involves discrete-valued gearshift signals. To overcome the computational difficulties in solving the integrated speed-and-gearshift optimal control problem that involves both continuous and discrete-valued optimization variables, we propose a hierarchical procedure to decompose the integrated hybrid problem into purely continuous and discrete sub-problems, each of which can be efficiently solved. We show, by simulations in various driving scenarios, that the co-optimization of speed and gearshift control using our proposed hierarchical procedure can achieve greater energy efficiency than other typical approaches.

eess.SY↗

arXiv2019

Decision making in dynamic and interactive environments based on cognitive hierarchy theory, Bayesian inference, and predictive control

In this paper, we describe an integrated framework for autonomous decision making in a dynamic and interactive environment. We model the interactions between the ego agent and its operating environment as a two-player dynamic game, and integrate cognitive behavioral models, Bayesian inference, and receding-horizon optimal control to define a dynamically-evolving decision strategy for the ego agent. Simulation examples representing autonomous vehicle control in three traffic scenarios where the autonomous ego vehicle interacts with a human-driven vehicle are reported.

cs.AI↗