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Rong Yuan

Publications and source records attributed to Rong Yuan.

12 recordsLinked to original sources

OMUDA: Omni-level Masking for Unsupervised Domain Adaptation in Semantic Segmentation

Unsupervised domain adaptation (UDA) enables semantic segmentation models to generalize from a labeled source domain to an unlabeled target domain. However, existing UDA methods still struggle to bridge the domain gap due to cross-domain contextual ambiguity, inconsistent feature representations, and class-wise pseudo-label noise. To address these challenges, we propose Omni-level Masking for Unsupervised Domain Adaptation (OMUDA), a unified framework that introduces hierarchical masking strategies across distinct representation levels. Specifically, OMUDA comprises: 1) a Context-Aware Masking (CAM) strategy that adaptively distinguishes foreground from background to balance global context and local details; 2) a Feature Distillation Masking (FDM) strategy that enhances robust and consistent feature learning through knowledge transfer from pre-trained models; and 3) a Class Decoupling Masking (CDM) strategy that mitigates the impact of noisy pseudo-labels by explicitly modeling class-wise uncertainty. This hierarchical masking paradigm effectively reduces the domain shift at the contextual, representational, and categorical levels, providing a unified solution beyond existing approaches. Extensive experiments on multiple challenging cross-domain semantic segmentation benchmarks validate the effectiveness of OMUDA. Notably, on the SYNTHIA->Cityscapes and GTA5->Cityscapes tasks, OMUDA can be seamlessly integrated into existing UDA methods and consistently achieving state-of-the-art results with an average improvement of 7%.

cs.CV

Double variational principle for mean dimension of $\mathbb{Z}^{K}$-actions

In this paper, we introduce mean dimension and rate distortion dimension for $\mathbb{Z}^{k}$-actions dynamical system $(\mathcal{X},\mathbb{Z}^k,T)$. Suppose $(\mathcal{X},\mathbb{Z}^k,T)$ has the marker property. Taking these two variables, the metric $d$ on $\mathcal{X}$ and $\mathbb{Z}^{k}$-invariant measure $μ$, into consideration, a minimax-type variational principle for mean dimension of $\mathbb{Z}^{k}$-actions is established. This result extends the double variational principle obtained recently by Lindenstrauss and Tsukamoto \cite{LT19} from $\mathbb{Z}$-actions dynamical systems to $\mathbb{Z}^{k}$-actions dynamical systems.

math.DS

Spreading speeds of a nonlocal diffusion model with free boundaries in the time almost periodic media

In this paper, we mainly investigate the spreading dynamics of a nonlocal diffusion KPP model with free boundaries which is firstly explored in time almost periodic media. As the spreading occurs, the long-run dynamics are obtained. Especially, when the threshold condition for the kernel function is satisfied, applying the novel positive time almost periodic function, we accurately express the unique asymptotic spreading speed of the free boundary problem.

math.AP

Persistence of solutions in a nonlocal predator-prey system with a shifting habitat

In this paper, we mainly study the propagation properties of a nonlocal dispersal predator-prey system in a shifting environment. It is known that Choi et al. [J. Differ. Equ. 302 (2021), pp. 807-853] studied the persistence or extinction of the prey and the predator separately in various moving frames. In particular, they achieved a complete picture in the local diffusion case. However, the question of the persistence of the prey and the predator in some intermediate moving frames in the nonlocal diffusion case is left open in Choi et al.'s paper. By using some prior estimates, the Arzela-Ascoli theorem and a diagonal extraction process, we can extend and improve the main results of Choi et al. to achieve a complete picture in the nonlocal diffusion case.

math.AP

Traveling Wave in a Ratio-dependent Holling-Tanner System with Nonlocal Diffusion and Strong Allee Effect

In this paper, a ratio-dependent Holling-Tanner system with nonlocal diffusion is taken into account, where the prey is subject to a strong Allee effect. To be special, by applying Schauder's fixed point theorem and iterative technique, we provide a general theory on the existence of traveling waves for such system. Then appropriate upper and lower solutions and a novel sequence, similar to squeeze method, are constructed to demonstrate the existence of traveling waves for c>c*. Moreover, the existence of traveling wave for c=c* is also established by spreading speed theory and comparison principle. Finally, the nonexistence of traveling waves for c<c* is investigated, and the minimal wave speed then is determined.

math.AP

Traveling Waves of Modified Leslie-Gower Predator-prey Systems

The spreading phenomena in modified Leslie-Gower reaction-diffusion predator-prey systems are the topic of this paper. We mainly study the existence of two different types of traveling waves. Be specific, with the aid of the upper and lower solutions method, we establish the existence of traveling wave connecting the prey-present state and the coexistence state or the prey-present state and the prey-free state by constructing different and appropriate Lyapunov functions. Moreover, for traveling wave connecting the prey-present state and the prey-free state, we gain more monotonicity information on wave profile based on the asymptotic behavior at negative infinite. Finally, our results are applied to modified Leslie-Gower system with Holling II type or Lotka-Volterra type, and then a novel Lyapunov function is constructed for the latter, which further enhances our results. Meanwhile, some numerical simulations are carried to support our results.

math.AP

A sufficient condition on successful invasion by the predator

In this paper, we provide a sufficient condition on successful invasion by the predator. Specially, we obtain the persistence of traveling wave solutions of predator-prey system, in which the predator can survive without the predation of the prey. This proof heavily depends on comparison principle of scalar monostable equation, the rescaling method and phase-plane analysis.

math.AP

Existence and Stability of Random Transition Waves for Nonautonomous Fisher-KPP Equations with Nonlocal Diffusion

In this paper, we study the existence and stability of random transition waves for time heterogeneous Fisher-KPP Equations with nonlocal diffusion. More specifically, we consider general time heterogeneities both for the nonlocal diffusion kernel and the reaction term. We use the comparison principle of the scalar equation and the method of upper and lower solutions to investigate the existence of random transition wave solution when the wave speed is large enough. In addition, we show the stability of random transition fronts for non-autonomous Fisher-KPP equations with nonlocal diffusion.

math.AP

The odd-even effect of mosaic modulation period of quasi-periodic hopping on the Anderson localization in a one-dimensional lattice model

In this study, we investigate Anderson localization in a one-dimensional lattice with a mosaic off-diagonal quasiperiodic hopping. Our findings reveal that the localization behavior of zero-energy states is highly dependent on the parity of the mosaic modulation period, denoted as $\kappa$. Specifically, when $\kappa$ is an odd integer, there is no Anderson localization transition even for large quasiperiodic hopping strengths, and the zero-energy state remains in a critical state. On the other hand, for an even $\kappa$ and a generic quasiperiodic hopping, the zero-energy state becomes a localized edge state at either the left or right end of the system. Additionally, we observe that the geometric mean value of the energy spectrum is equal to the constant hopping for an even $\kappa$, while for an odd $\kappa$, it is equal to the geometric mean value of the hopping. This odd-even effect of the mosaic period also extends to other eigenstates near zero energy. More specifically, for an odd $\kappa$, there exists an energy window in which the eigenstates remain critical even for strong quasiperiodic hopping. In contrast, for an even $\kappa$, an Anderson localization transition occurs as the hopping strength increases. Furthermore, we are able to accurately determine the Lyapunov exponent $\gamma(E)$ and the mobility edges $E_c$. By analyzing the Lyapunov exponent, we identify critical regions in the hopping-energy parameter planes. Additionally, as the energy approaches the mobility edges, we observe a critical index of localization length of $\nu=1$. Finally, we demonstrate that different systems can be characterized by their Lyapunov exponent $\gamma(E)$ and Avila's acceleration $\omega(E)$.

cond-mat.dis-nn

Small Boxes Big Data: A Deep Learning Approach to Optimize Variable Sized Bin Packing

Bin Packing problems have been widely studied because of their broad applications in different domains. Known as a set of NP-hard problems, they have different vari- ations and many heuristics have been proposed for obtaining approximate solutions. Specifically, for the 1D variable sized bin packing problem, the two key sets of optimization heuristics are the bin assignment and the bin allocation. Usually the performance of a single static optimization heuristic can not beat that of a dynamic one which is tailored for each bin packing instance. Building such an adaptive system requires modeling the relationship between bin features and packing perform profiles. The primary drawbacks of traditional AI machine learnings for this task are the natural limitations of feature engineering, such as the curse of dimensionality and feature selection quality. We introduce a deep learning approach to overcome the drawbacks by applying a large training data set, auto feature selection and fast, accurate labeling. We show in this paper how to build such a system by both theoretical formulation and engineering practices. Our prediction system achieves up to 89% training accuracy and 72% validation accuracy to select the best heuristic that can generate a better quality bin packing solution.

cs.LG

Massera Type Theorem for Abstract Functional Differential Equations

The paper is concerned with conditions for the existence of almost periodic solutions of the following abstract functional differential equation $ \dot u(t) = Au(t) + [{\cal B}u](t) +f(t), $ where $A$ is a closed operator in a Banach space $\X$, $\cal B$ is a general bounded linear operator in the function space of all $\X$-valued bounded and uniformly continuous functions that satisfies a so-called {\it autonomous} condition. We develop a general procedure to carry out the decomposition that does not need the well-posedness of the equations. The obtained conditions are of Massera type, which are stated in terms of spectral conditions of the operator ${\cal A}+{\cal B}$ and the spectrum of $f$. Moreover, we give conditions for the equation not to have quasi-periodic solutions with different structures of spectrum. The obtained results extend previous ones.

math.FA