arXiv subjects

Jianfeng Huang

Publications and source records attributed to Jianfeng Huang.

At least 19 recordsLinked to original sources

arXiv2026

On the Number of Limit Cycles in Generalized Abel Equations with Coefficients Having the Chebyshev Property

This paper concerns the maximum number of limit cycles of generalized Abel differential equations $dx/dt = A(t)x^p + B(t)x^q$, where $A$ and $B$ belong to the linear span of a family of functions having the Chebyshev property. Motivated by a recent open problem posed by Huang et al. (Nonlinearity, 2026), we investigate whether this maximum number can be bounded in terms of $p$, $q$, and the structure of the family. Under some natural hypotheses and by means of first- and second-order analyses using Melnikov functions, we provide lower bounds for this maximum number. In contrast to previous work, no specific form for the coefficients is assumed. We then apply these estimates to Abel equations with trigonometric polynomial, polynomial, and hyperbolic coefficients. In the trigonometric polynomial case, we reestablish the results of Álvarez et al. (J. Math. Anal. Appl., 2008) and Huang et al. (SIAM J. Appl. Dyn. Syst., 2020), while in the polynomial case, we improve the classical lower bound given by Lins-Neto.

math.DS↗

arXiv2026

Bifurcation of limit cycles in a class of piecewise smooth generalized Abel equations with two asymmetric zones

This paper studies the number of limit cycles, known as the Smale-Pugh problem, for the generalized Abel equation \begin{align*} \frac{dx}{dθ}=A(θ)x^p+B(θ)x^q, \end{align*} where $A$ and $B$ are are piecewise trigonometrical polynomials of degree $ m $ with two zones $0\leqθ<θ_1$ and $θ_1\leqθ\leq2π$. By means of the first and second order analysis using the Melnikov theory and applying the new Chebyshev criterion that established by \cite{HLZ2023}, we estimate the maximum number of positive and negative limit cycles that such equations can have, and reveal how this maximum number, denoted by $H_{θ_1}(m)$, is affected by the location of the separation line $θ=θ_1$. For the equation of classical Abel type, our result not only includes the estimates provided in the recent paper (Huang et al., SIAM J. Appl. Dyn. Syst., 2020), i.e., $H_{2π}(m)\geq 4m-2$ for $θ_1=2π$, but also shows that the equation in the discontinuous case can possess more than two times as many limit cycles as in the continuous case. More accurately, $H_π(m)\geq 8m+2$ and $H_{θ_1}(m)\geq 14m-6$ for $θ_1\in (0,π)\cup (π,2π)$.

math.CA↗

arXiv2026

A Chebyshev criterion for at most two non-zero limit cycles in Abel equations

In this paper, we investigate the maximum number of limit cycles of the reduced Abel equation $\dot{x}=A(t)x^{3}+B(t)x^{2}$ on an interval $[0,T]$. The Smale-Pugh problem asks whether this maximum number is bounded in terms of a given class of coefficients. We establish for the first time a Chebyshev criterion, providing a positive answer to the problem when this class spanned by an extended Chebyshev system (ET-system) $\mathcal{F}=\{f_{0},f_{1},f_{2}\}$ on $[0,T)$ with $f_{0}\not=0$. As an application, we prove that the equation has at most three limit cycles (including $x=0$) when the coefficients $A$ and $B$ are both linear trigonometric functions or quadratic polynomials. This reestablishes the result of Yu et al. (J. Differ. Equ., 2024) and improves the work of Bravo et al. (Disc. Cont. Dyn. Syst., 2015 \& J. Differ. Equ., 2024). We also obtain the same maximum number of limit cycles for the equation with trinomial coefficients.

math.CA↗

arXiv2025

A proximal algorithm incorporating difference of convex functions optimization for solving a class of single-ratio fractional programming

In this paper, we consider a class of single-ratio fractional minimization problems, where both the numerator and denominator of the objective are convex functions satisfying positive homogeneity. Many nonsmooth optimization problems on the sphere that are commonly encountered in application scenarios across different scientific fields can be converted into this equivalent fractional programming. We derive local and global optimality conditions of the problem and subsequently propose a proximal-subgradient-difference of convex functions algorithm (PS-DCA) to compute its critical points. When the DCA step is removed, PS-DCA reduces to the proximal-subgradient algorithm (PSA). Under mild assumptions regarding the algorithm parameters, it is shown that any accumulation point of the sequence produced by PS-DCA or PSA is a critical point of the problem. Moreover, for a typical class of generalized graph Fourier mode problems, we establish global convergence of the entire sequence generated by PS-DCA or PSA. Numerical experiments conducted on computing the generalized graph Fourier modes demonstrate that, compared to proximal gradient-type algorithms, PS-DCA integrates difference of convex functions (d.c.) optimization, rendering it less sensitive to initial points and preventing the sequence it generates from being trapped in low-quality local minimizers.

math.OC↗

arXiv2025

LSM-OPD: Boosting Scan in LSM-Trees by Enabling Direct Computing on Compressed Data

Scan-based operations, such as backstage compaction and value filtering, have emerged as the main bottleneck for LSM-Trees in supporting contemporary data-intensive applications. For slower external storage devices, such as HDD and SATA SSD, the scan performance is primarily limited by the I/O bandwidth (i.e., I/O bound) due to the substantial read/write amplifications in LSM-Trees. Recent adoption of high-performance storage devices, such as NVMe SSD, has transformed the main limitation to be compute-bound, emerging the impact of computational resource consumption caused by inefficient compactions and filtering. However, when the value size increases, the bottleneck for scan performance in fast devices gradually shifts towards the I/O bandwidth as well, and the overall throughput across all types of devices undergo a dramatic reduction. This paper addresses the core issues by proposing LSM-OPD, a Log-S tructured M erge-O rder- Preserving Dictionary encoding scheme that enables direct computing on compressed data within LSM-Trees. It first enables key-value-separated data flushing to disk in a densely encoded columnar layout, ideally with few bytes for a large string value (e.g., 1024 bytes), thereby significantly alleviating the frequent I/O requests caused by intensive scans. Then, it is capable of offloading the costly scan-based operations on large values, including compaction and value filtering, to lightweight dictionaries due to the order-preserving property. And SIMD-based vectorization can now be employed to maximize the evaluating performance on modern multi-core processors, further breaking the compute-bound limitations in LSM-trees. Extensive experiments demonstrate the superior efficiency of LSM-OPD in processing various workloads that involve intensive scan-based operations on diverse modern storage devices.

cs.DB↗

arXiv2025

Unsupervised Multi-modal Feature Alignment for Time Series Representation Learning

In recent times, the field of unsupervised representation learning (URL) for time series data has garnered significant interest due to its remarkable adaptability across diverse downstream applications. Unsupervised learning goals differ from downstream tasks, making it tricky to ensure downstream task utility by focusing only on temporal feature characterization. Researchers have proposed multiple transformations to extract discriminative patterns implied in informative time series, trying to fill the gap. Despite the introduction of a variety of feature engineering techniques, e.g. spectral domain, wavelet transformed features, features in image form and symbolic features etc. the utilization of intricate feature fusion methods and dependence on heterogeneous features during inference hampers the scalability of the solutions. To address this, our study introduces an innovative approach that focuses on aligning and binding time series representations encoded from different modalities, inspired by spectral graph theory, thereby guiding the neural encoder to uncover latent pattern associations among these multi-modal features. In contrast to conventional methods that fuse features from multiple modalities, our proposed approach simplifies the neural architecture by retaining a single time series encoder, consequently leading to preserved scalability. We further demonstrate and prove mechanisms for the encoder to maintain better inductive bias. In our experimental evaluation, we validated the proposed method on a diverse set of time series datasets from various domains. Our approach outperforms existing state-of-the-art URL methods across diverse downstream tasks.

cs.LG↗

arXiv2024

On the study of the limit cycles for a class of population models with time-varying factors

In this paper, we study a class of population models with time-varying factors, represented by one-dimensional piecewise smooth autonomous differential equations. We provide several derivative formulas in "discrete" form for the Poincaré map of such equations, and establish a criterion for the existence of limit cycles. These two tools, together with the known ones, are then combined in a preliminary procedure that can provide a simple and unified way to analyze the equations. As an application, we prove that a general model of single species with seasonal constant-yield harvesting can only possess at most two limit cycles, which improves the work of Xiao in 2016. We also apply our results to a general model described by the Abel equations with periodic step function coefficients, showing that its maximum number of limit cycles, is three. Finally, a population suppression model for mosquitos considered by Yu and Li in 2020 and Zheng et al. in 2021 is studied using our approach.

math.CA↗

arXiv2024

Unsupervised Industrial Anomaly Detection via Pattern Generative and Contrastive Networks

It is hard to collect enough flaw images for training deep learning network in industrial production. Therefore, existing industrial anomaly detection methods prefer to use CNN-based unsupervised detection and localization network to achieve this task. However, these methods always fail when there are varieties happened in new signals since traditional end-to-end networks suffer barriers of fitting nonlinear model in high-dimensional space. Moreover, they have a memory library by clustering the feature of normal images essentially, which cause it is not robust to texture change. To this end, we propose the Vision Transformer based (VIT-based) unsupervised anomaly detection network. It utilizes a hierarchical task learning and human experience to enhance its interpretability. Our network consists of pattern generation and comparison networks. Pattern generation network uses two VIT-based encoder modules to extract the feature of two consecutive image patches, then uses VIT-based decoder module to learn the human designed style of these features and predict the third image patch. After this, we use the Siamese-based network to compute the similarity of the generation image patch and original image patch. Finally, we refine the anomaly localization by the bi-directional inference strategy. Comparison experiments on public dataset MVTec dataset show our method achieves 99.8% AUC, which surpasses previous state-of-the-art methods. In addition, we give a qualitative illustration on our own leather and cloth datasets. The accurate segment results strongly prove the accuracy of our method in anomaly detection.

cs.CV↗

arXiv2023

QUEST: An Efficient Query Evaluation Scheme Towards Scan-Intensive Cross-Model Analysis

Modern data-driven applications require that databases support fast cross-model analytical queries. Achieving fast analytical queries in a database system is challenging since they are usually scan-intensive (i.e., they need to intensively scan over a large number of records) which results in huge I/O and memory costs. And it becomes tougher when the analytical queries are cross-model. It is hard to accelerate cross-model analytical queries in existing databases due to the lack of appropriate storage layout and efficient query processing techniques. In this paper, we present QUEST (QUery Evaluation Scheme Towards scan-intensive cross-model analysis) to push scan-intensive queries down to unified columnar storage layout and seamlessly deliver payloads across different data models. QUEST employs a columnar data layout to unify the representation of multi-model data. Then, a novel index structure named Skip-Tree is developed for QUEST to enable the query evaluation more efficient. With the help of two pairwise bitset-based operations coupled with Skip-Tree, the scan of most irrelevant instances can be pruned so as to avoid the giant intermediate result, thus reducing query response latency and saving the computational resources significantly when evaluating scan-intensive cross-model analysis. The proposed methods are implemented on an open-source platform. Through comprehensive theoretical analysis and extensive experiments, we demonstrate that QUEST improves the performance by 3.7x - 178.2x compared to state-of-the-art multi-model databases when evaluating scan-intensive cross-model analytical queries.

cs.DB↗

arXiv2023

Maximum number of limit cycles for Abel equation having coefficients with linear trigonometric functions

This paper devotes to the study of the classical Abel equation $\frac{dx}{dt}=g(t)x^{3}+f(t)x^{2}$, where $g(t)$ and $f(t)$ are trigonometric polynomials of degree $m\geq1$. We are interested in the problem that whether there is a uniform upper bound for the number of limit cycles of the equation with respect to $m$, which is known as the famous Smale-Pugh problem. In this work we generalize an idea from the recent paper (Yu, Chen and Liu, arXiv:$2304.13528$, $2023$) and give a new criterion to estimate the maximum multiplicity of limit cycles of the above Abel equations. By virtue of this criterion and the previous results given by {Á}lvarez et al. and Bravo et al., we completely solve the simplest case of the Smale-Pugh problem, i.e., the case when $g(t)$ and $f(t)$ are linear trigonometric, and obtain that the maximum number of limit cycles, is three.

math.CA↗

arXiv2023

Smoothing algorithms for nonsmooth and nonconvex minimization over the stiefel manifold

We consider a class of nonsmooth and nonconvex optimization problems over the Stiefel manifold where the objective function is the summation of a nonconvex smooth function and a nonsmooth Lipschitz continuous convex function composed with an linear mapping. We propose three numerical algorithms for solving this problem, by combining smoothing methods and some existing algorithms for smooth optimization over the Stiefel manifold. In particular, we approximate the aforementioned nonsmooth convex function by its Moreau envelope in our smoothing methods, and prove that the Moreau envelope has many favorable properties. Thanks to this and the scheme for updating the smoothing parameter, we show that any accumulation point of the solution sequence generated by the proposed algorithms is a stationary point of the original optimization problem. Numerical experiments on building graph Fourier basis are conducted to demonstrate the efficiency of the proposed algorithms.

math.OC↗

arXiv2022

An unsupervised approach for semantic place annotation of trajectories based on the prior probability

Semantic place annotation can provide individual semantics, which can be of great help in the field of trajectory data mining. Most existing methods rely on annotated or external data and require retraining following a change of region, thus preventing their large-scale applications. Herein, we propose an unsupervised method denoted as UPAPP for the semantic place annotation of trajectories using spatiotemporal information. The Bayesian Criterion is specifically employed to decompose the spatiotemporal probability of the candidate place into spatial probability, duration probability, and visiting time probability. Spatial information in ROI and POI data is subsequently adopted to calculate the spatial probability. In terms of the temporal probabilities, the Term Frequency Inverse Document Frequency weighting algorithm is used to count the potential visits to different place types in the trajectories, and generates the prior probabilities of the visiting time and duration. The spatiotemporal probability of the candidate place is then combined with the importance of the place category to annotate the visited places. Validation with a trajectory dataset collected by 709 volunteers in Beijing showed that our method achieved an overall and average accuracy of 0.712 and 0.720, respectively, indicating that the visited places can be annotated accurately without any external data.

cs.LG↗

arXiv2020

Appearance-Invariant 6-DoF Visual Localization using Generative Adversarial Networks

We propose a novel visual localization network when outside environment has changed such as different illumination, weather and season. The visual localization network is composed of a feature extraction network and pose regression network. The feature extraction network is made up of an encoder network based on the Generative Adversarial Network CycleGAN, which can capture intrinsic appearance-invariant feature maps from unpaired samples of different weathers and seasons. With such an invariant feature, we use a 6-DoF pose regression network to tackle long-term visual localization in the presence of outdoor illumination, weather and season changes. A variety of challenging datasets for place recognition and localization are used to prove our visual localization network, and the results show that our method outperforms state-of-the-art methods in the scenarios with various environment changes.

cs.CV↗

arXiv2020

A new Chebyshev criterion and its application to planar differential systems

This paper establishes a new Chebyshev criterion for some family of integrals. By virtue of this criterion we obtain several new Chebyshev families. With the help of these new families we can answer the conjecture posed by Gasull et al in 2015. %[J. Differential Equations, 258 (2015), 3286--3303]. Their applications to other two planar differential systems also show that our approach is simpler and in a unified way to handle many kinds of planar differential systems for estimating the number of limit cycles bifurcating from period annulus.

math.CA↗

arXiv2019

How Old Are You? Face Age Translation with Identity Preservation Using GANs

We present a novel framework to generate images of different age while preserving identity information, which is known as face aging. Different from most recent popular face aging networks utilizing Generative Adversarial Networks(GANs) application, our approach do not simply transfer a young face to an old one. Instead, we employ the edge map as intermediate representations, firstly edge maps of young faces are extracted, a CycleGAN-based network is adopted to transfer them into edge maps of old faces, then another pix2pixHD-based network is adopted to transfer the synthesized edge maps, concatenated with identity information, into old faces. In this way, our method can generate more realistic transfered images, simultaneously ensuring that face identity information be preserved well, and the apparent age of the generated image be accurately appropriate. Experimental results demonstrate that our method is feasible for face age translation.

cs.CV↗

arXiv2019

Graph Fourier Transform Based on $\ell_1$ Norm Variation Minimization

The definition of the graph Fourier transform is a fundamental issue in graph signal processing. Conventional graph Fourier transform is defined through the eigenvectors of the graph Laplacian matrix, which minimize the $\ell_2$ norm signal variation. However, the computation of Laplacian eigenvectors is expensive when the graph is large. In this paper, we propose an alternative definition of graph Fourier transform based on the $\ell_1$ norm variation minimization. We obtain a necessary condition satisfied by the $\ell_1$ Fourier basis, and provide a fast greedy algorithm to approximate the $\ell_1$ Fourier basis. Numerical experiments show the effectiveness of the greedy algorithm. Moreover, the Fourier transform under the greedy basis demonstrates a similar rate of decay to that of Laplacian basis for simulated or real signals.

cs.IT↗

arXiv2019

Deep Global-Relative Networks for End-to-End 6-DoF Visual Localization and Odometry

Although a wide variety of deep neural networks for robust Visual Odometry (VO) can be found in the literature, they are still unable to solve the drift problem in long-term robot navigation. Thus, this paper aims to propose novel deep end-to-end networks for long-term 6-DoF VO task. It mainly fuses relative and global networks based on Recurrent Convolutional Neural Networks (RCNNs) to improve the monocular localization accuracy. Indeed, the relative sub-networks are implemented to smooth the VO trajectory, while global subnetworks are designed to avoid drift problem. All the parameters are jointly optimized using Cross Transformation Constraints (CTC), which represents temporal geometric consistency of the consecutive frames, and Mean Square Error (MSE) between the predicted pose and ground truth. The experimental results on both indoor and outdoor datasets show that our method outperforms other state-of-the-art learning-based VO methods in terms of pose accuracy.

cs.CV↗

arXiv2017

Limit cycles of planar system defined by the sum of two quasi-homogeneous vecter fields

In this paper we consider the limit cycles of the planar system $$\frac{d}{dt}(x,y)=\mathbf X_n+\mathbf X_m, $$ where $\mathbf X_n$ and $\mathbf X_m$ are quasi-homogeneous vector fields of degree $n$ and $m$ respectively. We prove that under a new hypothesis, the maximal number of limit cycles of the system is $1$. We also show that our result can be applied to some systems when the previous results are invalid. The proof is based on the investigations for the Abel equation and the generalized-polar equation associated with the system, respectively. Usually these two kinds of equations need to be dealt with separately, and for both equations, an efficient approach to estimate the number of periodic solutions is constructing suitable auxiliary functions. In the present paper we develop a formula on the divergence, which allows us to construct an auxiliary function of one equation with the auxiliary function of the other equation, and vice versa.

math.CA↗