arXiv subjects

Yulin Zhao

Publications and source records attributed to Yulin Zhao.

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 \'{A}lvarez 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

Focus-then-Context: Subject-Centric Progressive Visual Token Reduction for Vision-Language Models

Vision-Language Models (VLMs) face a bottleneck of prohibitive computational costs arising from massive visual token sequences during inference. Existing vision token reduction methods alleviate this burden, but they unintentionally preserve the isolated visual subject strictly aligned with the user's query, which fails to substantially explore salient subjects and their contextual relationships. In this paper, we propose SPpruner, a subject-centric progressive reduction paradigm that emulates the \textit{Focus-then-Context} mechanism of the human visual perception system. Specifically, we first construct a focus identification module to explicitly model the interplay between visual saliency and semantic relevance. Herein, it can excavate the comprehensive visual subject spectrum to ensure a high-fidelity representation of visual input. Subsequently, a context-aware structural scanning module is developed to aggregate contextual cues from neighboring regions. As such, it can effectively restore global relational dependencies to uphold the structural integrity of the preserved subjects. Extensive experiments demonstrate that our paradigm consistently outperforms SOTA methods, achieving up to 2.53 times speedup with only 22.2% of visual tokens retained in Qwen2.5-VL and a 67% FLOPs reduction on LLaVA with a negligible 0.6% accuracy drop.

cs.CV↗

arXiv2025

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↗

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 Poincar\'{e} 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

Towards Effective and General Graph Unlearning via Mutual Evolution

With the rapid advancement of AI applications, the growing needs for data privacy and model robustness have highlighted the importance of machine unlearning, especially in thriving graph-based scenarios. However, most existing graph unlearning strategies primarily rely on well-designed architectures or manual process, rendering them less user-friendly and posing challenges in terms of deployment efficiency. Furthermore, striking a balance between unlearning performance and framework generalization is also a pivotal concern. To address the above issues, we propose \underline{\textbf{M}}utual \underline{\textbf{E}}volution \underline{\textbf{G}}raph \underline{\textbf{U}}nlearning (MEGU), a new mutual evolution paradigm that simultaneously evolves the predictive and unlearning capacities of graph unlearning. By incorporating aforementioned two components, MEGU ensures complementary optimization in a unified training framework that aligns with the prediction and unlearning requirements. Extensive experiments on 9 graph benchmark datasets demonstrate the superior performance of MEGU in addressing unlearning requirements at the feature, node, and edge levels. Specifically, MEGU achieves average performance improvements of 2.7\%, 2.5\%, and 3.2\% across these three levels of unlearning tasks when compared to state-of-the-art baselines. Furthermore, MEGU exhibits satisfactory training efficiency, reducing time and space overhead by an average of 159.8x and 9.6x, respectively, in comparison to retraining GNN from scratch.

cs.LG↗

arXiv2022

Efficient Training of the Memristive Deep Belief Net Immune to Non-Idealities of the Synaptic Devices

The tunability of conductance states of various emerging non-volatile memristive devices emulates the plasticity of biological synapses, making it promising in the hardware realization of large-scale neuromorphic systems. The inference of the neural network can be greatly accelerated by the vector-matrix multiplication (VMM) performed within a crossbar array of memristive devices in one step. Nevertheless, the implementation of the VMM needs complex peripheral circuits and the complexity further increases since non-idealities of memristive devices prevent precise conductance tuning (especially for the online training) and largely degrade the performance of the deep neural networks (DNNs). Here, we present an efficient online training method of the memristive deep belief net (DBN). The proposed memristive DBN uses stochastically binarized activations, reducing the complexity of peripheral circuits, and uses the contrastive divergence (CD) based gradient descent learning algorithm. The analog VMM and digital CD are performed separately in a mixed-signal hardware arrangement, making the memristive DBN high immune to non-idealities of synaptic devices. The number of write operations on memristive devices is reduced by two orders of magnitude. The recognition accuracy of 95%~97% can be achieved for the MNIST dataset using pulsed synaptic behaviors of various memristive synaptic devices.

eess.SP↗

arXiv2021

The Relation between Morphological Asymmetry and Nuclear Activity in Low-redshift Galaxies

The morphology of galaxies reflects their assembly history and ongoing dynamical perturbations from the environment. Analyzing i-band images from the Pan-STARRS1 Survey, we study the optical morphological asymmetry of the host galaxies of a large, well-defined sample of nearby active galactic nuclei (AGNs) to investigate the role of mergers and interactions in triggering nuclear activity. The AGNs, comprising 245 type 1 and 4514 type 2 objects, are compared with 4537 star-forming galaxies matched in redshift and stellar mass. We develop a comprehensive masking strategy to isolate the emission of the target from foreground stars and other contaminating sources, all the while retaining projected companions of comparable brightness that may be major mergers. Among three variants of nonparametric indices, both the popular CAS asymmetry parameter and the outer asymmetry parameter (A_outer) yield robust measures of morphological distortion for star-forming galaxies and type 2 AGNs, while only A_outer is effective for type 1 AGNs. The shape asymmetry, by comparison, is affected more adversely by background noise. Asymmetry indices > 0.4 effectively trace systems that are candidate ongoing mergers. Contrary to theoretical expectations, galaxy interactions and mergers are not the main drivers of nuclear activity, at least not in our sample of low-redshift, relatively low-luminosity AGNs, whose host galaxies are significantly less asymmetric than the control sample of star-forming galaxies. Moreover, type 2 AGNs are morphologically indistinguishable from their type 1 counterparts. The level of AGN activity does not correlate with asymmetry, not even among the major merger candidates. As a by-product, we find, consistent with previous studies, that the average asymmetry of star-forming galaxies increases above the main sequence, although not all major mergers exhibit enhanced star formation.

astro-ph.GA↗

arXiv2021

The Diverse Morphology, Stellar Population, and Black Hole Scaling Relations of the Host Galaxies of Nearby Quasars

We present rest-frame $B$ and $I$ imaging of 35 low-redshift ($z < 0.5$) Palomar-Green quasars using the Hubble Space Telescope Wide Field Camera 3. We perform multi-component two-dimensional image decomposition to separate the host galaxy from its bright active nucleus, characterize its morphology, and measure its photometric properties. Special care is devoted to quantifying the structural parameters of the galaxy bulge, determine its $B-I$ color, and estimate its stellar mass. Roughly half of the sample, comprising the less luminous ($L_{5100} \lesssim 10^{45}\,\mathrm{erg\,s^{-1}}$) but most high Eddington ratio quasars, reside in disk galaxies that are often barred and possess pseudo bulges. The large stellar masses, large effective radii, and faint surface brightnesses suggest that the host galaxies of the most luminous quasars are mostly ellipticals. Major mergers constitute only a minority ($\lesssim 20\%$) of our sample. Our quasar sample roughly obeys the scaling relations between black hole mass and host galaxy (bulge, core, total) stellar mass. Hosts with black holes more massive than $\sim 10^8\,M_\odot$ behave similarly to classical bulges and early-type galaxies, while those with less massive black holes, particular the narrow-line Seyfert 1s, are consistent with pseudo bulges in late-type galaxies. The host galaxy bulges, irrespective of whether they are classical or pseudo, follow the relatively tight inverse relation between effective radius and mean effective surface brightness of inactive classical bulges and ellipticals. We argue that pseudo bulges experience recent or ongoing nuclear star formation.

astro-ph.GA↗

arXiv2021

The necessary and sufficient conditions for the real Jacobian conjecture

The real Jacobian conjecture claims that if $F=\left(f^1,\ldots,f^n\right):\mathbb{R}^n\rightarrow \mathbb{R}^n$ is a polynomial map such that $\det DF$ is nowhere zero, then $F$ is a global injective. The first part is to study the two-dimensional real Jacobian conjecture via the method of the qualitative theory of dynamical systems. By Bendixson compactification, an induced polynomial differential system can be obtained from the Hamiltonian system associated to polynomial map $F$. We prove that the following statements are equivalent: (A) $F$ is a global injective; (B) the origin of induced system is a center; (C) the origin of induced system is a monodromic singular point; (D) the origin of induced system has no hyperbolic sectors; (E) induced system has a $C^k$ first integral with an isolated minimun at the origin and $k\in\mathbb{N}^{+}\cup\{\infty\}$. Moreover, applying the above results we present a necessary and sufficient condition for the validity of the two-dimensional real Jacobian conjecture, which is an algebraic criterion. By definition a criterion function, $F$ is a global injective if and only if the limit of criterion function is infinite as $\left|x\right|+\left|y\right|$ tends to infinity. This algebraic criterion improves the main result of Braun et al [J. Differential Equations {\bf 260} (2016) 5250-5258]. In the second part, the necessary and sufficient conditions on the $n$-dimensional real Jacobian conjecture is obtained. Using the tool from the nonlinear functional analysis, $F$ is a global injective if and only if $\parallel F\left(\mathbf{x}\right)\parallel$ approaches to infinite as $\parallel\mathbf{x}\parallel\rightarrow\infty$, which is a generalization of the above algebraic criterion. As an application, we give an alternate proof of the Cima's result on the $n$-dimensional real Jacobian conjecture [Nonlinear Anal. {\bf 26} (1996) 877-885].

math.DS↗

arXiv2019

The Role of Major Mergers and Nuclear Star Formation in Nearby Obscured Quasars

We investigate the triggering mechanism and the structural properties of obscured luminous active galactic nuclei from a detailed study of the rest-frame $B$ and $I$ HST images of 29 nearby ($z\approx 0.04-0.4$) optically selected type 2 quasars. Morphological classification reveals that only a minority (34%) of the hosts are mergers or interacting galaxies. More than half (55%) of the hosts contain regular disks, and a substantial fraction (38%), in fact, are disk-dominated ($B/T\lesssim 0.2$) late-type galaxies with low Sersic indices ($n < 2$), which is characteristic of pseudo bulges. The prevalence of bars in the spiral host galaxies may be sufficient to supply the modest fuel requirements needed to power the nuclear activity in these systems. Nuclear star formation seems to be ubiquitous in the central regions, leading to positive color gradients within the bulges and enhancements in the central surface brightness of most systems.

astro-ph.GA↗

arXiv2019

Kinematics of the Broad-line Region of 3C 273 from a Ten-year Reverberation Mapping Campaign

Despite many decades of study, the kinematics of the broad-line region of 3C~273 are still poorly understood. We report a new, high signal-to-noise, reverberation mapping campaign carried out from November 2008 to March 2018 that allows the determination of time lags between emission lines and the variable continuum with high precision. The time lag of variations in H$β$ relative to those of the 5100 Angstrom continuum is $146.8_{-12.1}^{+8.3}$ days in the rest frame, which agrees very well with the Paschen-$α$ region measured by the GRAVITY at The Very Large Telescope Interferometer. The time lag of the H$γ$ emission line is found to be nearly the same as for H$β$. The lag of the Fe II emission is $322.0_{-57.9}^{+55.5}$ days, longer by a factor of $\sim$2 than that of the Balmer lines. The velocity-resolved lag measurements of the H$β$ line show a complex structure which can be possibly explained by a rotation-dominated disk with some inflowing radial velocity in the H$β$-emitting region. Taking the virial factor of $f_{\rm BLR} = 1.3$, we derive a BH mass of $M_{\bullet} = 4.1_{-0.4}^{+0.3} \times 10^8 M_{\odot}$ and an accretion rate of $9.3\,L_{\rm Edd}\,c^{-2}$ from the H$β$ line. The decomposition of its $HST$ images yields a host stellar mass of $M_* = 10^{11.3 \pm 0.7} M_\odot$, and a ratio of $M_{\bullet}/M_*\approx 2.0\times 10^{-3}$ in agreement with the Magorrian relation. In the near future, it is expected to compare the geometrically-thick BLR discovered by the GRAVITY in 3C 273 with its spatially-resolved torus in order to understand the potential connection between the BLR and the torus.

astro-ph.GA↗

arXiv2018

Four limit cycles in a predator-prey system of Leslie type with generalized Holling type III functional response

This paper, as a complement to the works by Hsu et al [SIAM. J. Appl. Math. 55 (1995)] and Huang et al [J. Differential Equations 257 (2014)], aims to examine the Hopf bifurcation and global dynamics of a predator-prey model of Leslie type with generalized Holling type III functional response for the two cases: (A) when it has a unique non-degenerate positive equilibrium; (B) when it has three distinct positive equilibria. For each case, the type and stability of each equilibrium, Hopf bifurcation at each weak focus, and the number and distribution of limit cycles in the first quadrant are studied. It is shown that every equilibrium is not a center. For the case (A), $i$ limit cycle(s) can appear near the unique positive equilibrium, $i=1, \cdots, 4$. For $i=3$ or $4$, the model has two stable limit cycles, which gives a positive answer to the open problem proposed by Coleman [Differential equations model,1983]: finding at least two ecologically stable cycles in any natural (or laboratory) predator-prey system. For the case (B), one positive equilibrium is a saddle and the others are both anti-saddle. If one of the two anti-saddles is weak focus and the other is not, then the order of the weak focus is at most $3$. If both anti-saddles are weak foci, then they are unstable weak foci of order one. Moreover, one limit cycle can bifurcate from each of them simultaneously. Numerical simulations demonstrate that there is also a big stable limit cycle enclosing these two limit cycles. Our results indicate that the maximum number of limit cycles in the model of this kind is at least $4$, which improves the preceding results that this number is at least $2$.

math.DS↗

arXiv2018

Hopf cyclicity and global dynamics for a predator-prey system of Leslie type with simplified Holling type IV functional response

This paper is concerned with a predator-prey model of Leslie type with simplified Holling type IV functional response, provided that it has either a unique non-degenerate positive equilibrium or three distinct positive equilibria. The type and stability of each equilibrium, Hopf cyclicity of each weak focus, and the number and distribution of limit cycles in the first quadrant are studied. It is shown that every equilibrium cannot be a center. If system has a unique positive equilibrium which is a weak focus, then its order is at most $2$ and it has Hopf cyclicity $2$. Moreover, some sufficient conditions for the global stability of the unique equilibrium are established by applying Dulac's criterion and constructing the Liapunov function. If system has three distinct positive equilibria, then one of them is a saddle and the others are both anti-saddles. For two anti-saddles, we prove that the Hopf cyclicity for positive equilibrium with smaller abscissa (resp. bigger abscissa) is $2$ (resp. $1$). Furthermore, if both anti-saddle positive equilibria are weak foci, then they are unstable multiple foci with multiplicity one. Moreover, one limit cycle can bifurcate from each of them simultaneously. Numerical simulations demonstrate that there is a big stable limit cycle enclosing these two small limit cycles.

math.DS↗

arXiv2016

On the cyclicity of the period annulus of quadratic Hamiltonian triangle vector field

This paper is concerned with the cyclicity of the period annulus of quadratic Hamiltonian triangle vector field under quadratic perturbations. This problem has been studied by Iliev (J. Differential Equations {\bf 128}(1996)), based on the displacement function obtained by Żoładek (J. Differential Equations {\bf 109}(1994)). Recently, P. Mardešić etc. (J. Dynamical and Control Systems {\bf 17}(2011)) studied unfoldings of the Hamiltonian triangle within quadratic vector fields. It turned out that the displacement function is not precise of the form given by Żoładek. Using the corrected form of the displacement function obtained by P. Mardešić etc, it is proved in this paper that the cyclicity of the period annulus under quadratic perturbations is equal to three.

math.CA↗

arXiv2016

Bifurcation analysis and global dynamics of a mathematical model of antibiotic resistance in hospitals

Antibiotic-resistant bacteria has posed a grave threat to public health by causing a number of nosocomial infections in hospitals. Mathematical models have been used to study the transmission of antibiotic-resistant bacteria within a hospital and the measures to control antibiotic resistance in nosocomial pathogens. Studies presented in \cite{LBL,LB} have shown great value in understanding the transmission of antibiotic-resistant bacteria in a hospital. However, their results are limited to numerical simulations of a few different scenarios without analytical analysis of the models in all biologically feasible parameter regions. Bifurcation analysis and identification of the global stability conditions are necessary to assess the interventions which are proposed to limit nosocomial infection and stem the spread of antibiotic-resistant bacteria. In this paper we study the global dynamics of the mathematical model of antibiotic resistance in hospitals in \cite{LBL,LB}. The invasion reproduction number $\mathcal R_{ar}$ of antibiotic-resistant bacteria is introduced. We give the relationship of $\mathcal R_{ar}$ and two control reproduction numbers of sensitive bacteria and resistant bacteria ($\mathcal R_{sc}$ and $\mathcal R_{rc}$). More importantly, we prove that a backward bifurcation may occur at $\mathcal R_{ar}=1$ when the model includes superinfection which is not mentioned in \cite{LB}. That is, there exists a new threshold $\mathcal R_{ar}^c$, and if $\mathcal R_{ar}^c<\mathcal R_{ar}<1$, then the system can have two interior equilibria and it supports an interesting bistable phenomenon. This provides critical information on controlling the antibiotic-resistance in a hospital.

q-bio.PE↗

arXiv2016

On the number of limit cycles for a class of discontinuous quadratic differential systems

The present paper is devoted to the study of the maximum number of limit cycles bifurcated from the periodic orbits of the quadratic isochronous center $\dot{x}=-y+\frac{16}{3}x^{2}-\frac{4}{3}y^{2},\dot{y}=x+\frac{8}{3}xy$ by the averaging method of first order, when it is perturbed inside a class of discontinuous quadratic polynomial differential systems. The \emph{Chebyshev criterion} is used to show that this maximum number is 5 and can be realizable. The result and that in paper \cite{LC} completely answer the questions left in the paper \cite{LM}.

math.CA↗

arXiv2014

Abelian integrals and limit cycles for a class of cubic polynomial vector fields of Lotka-Volterra type with a rational first integral of degree 2

In this paper, we study the number of limit cycles which bifurcate from the periodic orbits of cubic polynomial vector fields of Lotka-Volterra type having a rational first integral of degree 2, under polynomial perturbations of degree $n$. The analysis is carried out by estimating the number of zeros of the corresponding Abelian integrals. Moreover, using \emph{Chebyshev criterion}, we show that the sharp upper bound for the number of zeros of the Abelian integrals defined on each period annulus is 3 for $n=3$. The simultaneous bifurcation and distribution of limit cycles for the system with two period annuli under cubic polynomial perturbations are considered. All configurations $(u,v)$ with $0\leq u, v\leq 3, u+v\leq5$ are realizable.

math.DS↗

arXiv2014

Which factor dominates the industry evolution? A synergy analysis based on China's ICT industry

Industry evolution caused by various reasons, among which technology progress driving industry development has been approved, but with the new trend of industry convergence, inter-industry convergence also plays an increasing important role. This paper plans to probe the industry synergetic evolution mechanism based on industry convergence and technology progress. Firstly, we use self-organization method and Haken Model to establish synergetic evolution equations, select technology progress and industry convergence as the key variables of industry evolution system; then use patent licensing data of china's listed ICT companies to measure industry convergence rate and apply DEA Malmquist index method to calculate technology progress level; furthermore apply simultaneous equation estimation method to investigate the synergetic industry evolution process. From 2002 to 2012, China's ICT industry develops rapidly; it has the most obvious convergence and powerful technology progress compared with other industries. We choose china's listed ICT industry to make empirical analysis. Our main findings are: a) technology progress is the order parameter which dominates industry system evolution. Moreover, industry convergence is the control parameter which is influenced by technology progress; b) Development of technology progress is the core factor for causing evolution of industry system, and industry convergence is the outcome of technology progress; c) Especially, it is important that the dominated role of technology progress will be sustained, even though in the environment of convergence, companies also need focus on self-innovation, rather than only adapt to the new industry evolution trend.

physics.soc-ph↗