arXiv subjects

Yucheng Wang

Publications and source records attributed to Yucheng Wang.

At least 109 records · Page 6Linked to original sources

arXiv2024

Nonlinear stability and transition threshold for the planar helical flow

In this paper, we study the nonlinear stability for the 3-D planar helical flow $(δ^2\sin(m_0 y),δ^2\cos(m_0 y),0)$ on torus $\mathbb{T}^3=\{(x_1,x_2,y)\big|x_1,x_2\in \mathbb{T}_{2π}, y\in \mathbb{T}_{2πδ}, δ\geq1\}$ for high Reynolds number $Re$. We prove that if the initial velocity $U_0$ satisfies $$ \left\|U_0-(δ^2\sin(m_0 y),δ^2\cos(m_0 y),0)\right\|_{X_0}\leq c_0 Re^{-7/4} $$ for some $c_0>0$ independent of $Re$, then the solution of 3-D incompressible Navier-Stokes equation is global in time and does not transit away from the planar helical flow. Here $δ>1, m_0=δ^{-1}$ and the norm $\|\cdot\|_{X_0}$ is defined in (1.8). This is a nonlinear stability result for 3-D non-shear flow and the transition threshold is less than $7/4$.

math.AP↗

arXiv2024

Knowledge Transfer with Simulated Inter-Image Erasing for Weakly Supervised Semantic Segmentation

Though adversarial erasing has prevailed in weakly supervised semantic segmentation to help activate integral object regions, existing approaches still suffer from the dilemma of under-activation and over-expansion due to the difficulty in determining when to stop erasing. In this paper, we propose a \textbf{K}nowledge \textbf{T}ransfer with \textbf{S}imulated Inter-Image \textbf{E}rasing (KTSE) approach for weakly supervised semantic segmentation to alleviate the above problem. In contrast to existing erasing-based methods that remove the discriminative part for more object discovery, we propose a simulated inter-image erasing scenario to weaken the original activation by introducing extra object information. Then, object knowledge is transferred from the anchor image to the consequent less activated localization map to strengthen network localization ability. Considering the adopted bidirectional alignment will also weaken the anchor image activation if appropriate constraints are missing, we propose a self-supervised regularization module to maintain the reliable activation in discriminative regions and improve the inter-class object boundary recognition for complex images with multiple categories of objects. In addition, we resort to intra-image erasing and propose a multi-granularity alignment module to gently enlarge the object activation to boost the object knowledge transfer. Extensive experiments and ablation studies on PASCAL VOC 2012 and COCO datasets demonstrate the superiority of our proposed approach. Source codes and models are available at https://github.com/NUST-Machine-Intelligence-Laboratory/KTSE.

cs.CV↗

arXiv2024

Foster Adaptivity and Balance in Learning with Noisy Labels

Label noise is ubiquitous in real-world scenarios, posing a practical challenge to supervised models due to its effect in hurting the generalization performance of deep neural networks. Existing methods primarily employ the sample selection paradigm and usually rely on dataset-dependent prior knowledge (\eg, a pre-defined threshold) to cope with label noise, inevitably degrading the adaptivity. Moreover, existing methods tend to neglect the class balance in selecting samples, leading to biased model performance. To this end, we propose a simple yet effective approach named \textbf{SED} to deal with label noise in a \textbf{S}elf-adaptiv\textbf{E} and class-balance\textbf{D} manner. Specifically, we first design a novel sample selection strategy to empower self-adaptivity and class balance when identifying clean and noisy data. A mean-teacher model is then employed to correct labels of noisy samples. Subsequently, we propose a self-adaptive and class-balanced sample re-weighting mechanism to assign different weights to detected noisy samples. Finally, we additionally employ consistency regularization on selected clean samples to improve model generalization performance. Extensive experimental results on synthetic and real-world datasets demonstrate the effectiveness and superiority of our proposed method. The source code has been made available at https://github.com/NUST-Machine-Intelligence-Laboratory/SED.

cs.CV↗

arXiv2024

Level spacing distribution of localized phases induced by quasiperiodic potentials

Level statistics is a crucial tool in the exploration of localization physics. The level spacing distribution of the disordered localized phase follows Poisson statistics, and many studies naturally apply it to the quasiperiodic localized phase. Here we analytically obtain the level spacing distribution of the quasiperiodic localized phase, and find that it deviates from Poisson statistics. Moreover, based on this level statistics, we derive the ratio of adjacent gaps and find that for a single sample, it is a $δ$ function, which is in excellent agreement with numerical studies. Additionally, unlike disordered systems, in quasiperiodic systems, there are variations in the level spacing distribution across different regions of the spectrum, and increasing the size and increasing the sample are non-equivalent. Our findings carry significant implications for the reevaluation of level statistics in quasiperiodic systems and a profound understanding of the distinct effects of quasiperiodic potentials and disorder induced localization.

cond-mat.dis-nn↗

arXiv2024

Normed modules and The Stieltjes integrations of functions defined on finite-dimensional algebras

We define integrals for functions on finite-dimensional algebras, adapting methods from Leinster's research. This paper discusses the relationships between the integrals of functions defined on subsets $\mathbb{I}_1 \subseteq {\mathitΛ}_1$ and $\mathbb{I}_2 \subseteq {\mathitΛ}_2$ of two finite-dimensional algebras, under the influence of a mapping $ω$, which can be an injection or a bijection. We explore four specific cases: $\bullet$ $ω$ as a monotone non-decreasing and right-continuous function; $\bullet$ $ω$ as an injective, absolutely continuous function; $\bullet$ $ω$ as a bijection; $\bullet$ and $ω$ as the identity on $\mathbb{R}$. These scenarios correspond to the frameworks of Lebesgue-Stieltjes integration, Riemann-Stieltjes integration, substitution rules for Lebesgue integrals, and traditional Lebesgue or Riemann integration, respectively.

math.CA↗

arXiv2024

Dissipation induced extended-localized transition

Mobility edge (ME), representing the critical energy that distinguishes between extended and localized states, is a key concept in understanding the transition between extended (metallic) and localized (insulating) states in disordered and quasiperiodic systems. Here we explore the impact of dissipation on a quasiperiodic system featuring MEs by calculating steady-state density matrix and analyzing quench dynamics with sudden introduction of dissipation, and demonstrate that dissipation can lead the system into specific states predominantly characterized by either extended or localized states, irrespective of the initial state. Our results establish the use of dissipation as a new avenue for inducing transitions between extended and localized states, and for manipulating dynamic behaviors of particles.

cond-mat.dis-nn↗

arXiv2024

Local existence of classical solution to the chemotaxis-shallow water system with vacuum in $\mathbb{R}^2$

In this paper, we consider the chemotaxis-shallow water system in $\mathbb{R}^2$. We establish the local existence of classical solution without assuming the initial height is small or has a small perturbation near a constant. The far field behavior of the height is a constant which could be either vacuum or non-vacuum. The initial data is allowed vacuum and the spatial measure of the set of vacuum can be arbitrarily large.

math.AP↗

arXiv2024

On Robustness and Generalization of ML-Based Congestion Predictors to Valid and Imperceptible Perturbations

There is substantial interest in the use of machine learning (ML)-based techniques throughout the electronic computer-aided design (CAD) flow, particularly methods based on deep learning. However, while deep learning methods have achieved state-of-the-art performance in several applications, recent work has demonstrated that neural networks are generally vulnerable to small, carefully chosen perturbations of their input (e.g. a single pixel change in an image). In this work, we investigate robustness in the context of ML-based EDA tools -- particularly for congestion prediction. As far as we are aware, we are the first to explore this concept in the context of ML-based EDA. We first describe a novel notion of imperceptibility designed specifically for VLSI layout problems defined on netlists and cell placements. Our definition of imperceptibility is characterized by a guarantee that a perturbation to a layout will not alter its global routing. We then demonstrate that state-of-the-art CNN and GNN-based congestion models exhibit brittleness to imperceptible perturbations. Namely, we show that when a small number of cells (e.g. 1%-5% of cells) have their positions shifted such that a measure of global congestion is guaranteed to remain unaffected (e.g. 1% of the design adversarially shifted by 0.001% of the layout space results in a predicted decrease in congestion of up to 90%, while no change in congestion is implied by the perturbation). In other words, the quality of a predictor can be made arbitrarily poor (i.e. can be made to predict that a design is "congestion-free") for an arbitrary input layout. Next, we describe a simple technique to train predictors that improves robustness to these perturbations. Our work indicates that CAD engineers should be cautious when integrating neural network-based mechanisms in EDA flows to ensure robust and high-quality results.

cs.LG↗

arXiv2024

Graph-Aware Contrasting for Multivariate Time-Series Classification

Contrastive learning, as a self-supervised learning paradigm, becomes popular for Multivariate Time-Series (MTS) classification. It ensures the consistency across different views of unlabeled samples and then learns effective representations for these samples. Existing contrastive learning methods mainly focus on achieving temporal consistency with temporal augmentation and contrasting techniques, aiming to preserve temporal patterns against perturbations for MTS data. However, they overlook spatial consistency that requires the stability of individual sensors and their correlations. As MTS data typically originate from multiple sensors, ensuring spatial consistency becomes essential for the overall performance of contrastive learning on MTS data. Thus, we propose Graph-Aware Contrasting for spatial consistency across MTS data. Specifically, we propose graph augmentations including node and edge augmentations to preserve the stability of sensors and their correlations, followed by graph contrasting with both node- and graph-level contrasting to extract robust sensor- and global-level features. We further introduce multi-window temporal contrasting to ensure temporal consistency in the data for each sensor. Extensive experiments demonstrate that our proposed method achieves state-of-the-art performance on various MTS classification tasks. The code is available at https://github.com/Frank-Wang-oss/TS-GAC.

cs.LG↗

arXiv2024

Fully-Connected Spatial-Temporal Graph for Multivariate Time-Series Data

Multivariate Time-Series (MTS) data is crucial in various application fields. With its sequential and multi-source (multiple sensors) properties, MTS data inherently exhibits Spatial-Temporal (ST) dependencies, involving temporal correlations between timestamps and spatial correlations between sensors in each timestamp. To effectively leverage this information, Graph Neural Network-based methods (GNNs) have been widely adopted. However, existing approaches separately capture spatial dependency and temporal dependency and fail to capture the correlations between Different sEnsors at Different Timestamps (DEDT). Overlooking such correlations hinders the comprehensive modelling of ST dependencies within MTS data, thus restricting existing GNNs from learning effective representations. To address this limitation, we propose a novel method called Fully-Connected Spatial-Temporal Graph Neural Network (FC-STGNN), including two key components namely FC graph construction and FC graph convolution. For graph construction, we design a decay graph to connect sensors across all timestamps based on their temporal distances, enabling us to fully model the ST dependencies by considering the correlations between DEDT. Further, we devise FC graph convolution with a moving-pooling GNN layer to effectively capture the ST dependencies for learning effective representations. Extensive experiments show the effectiveness of FC-STGNN on multiple MTS datasets compared to SOTA methods. The code is available at https://github.com/Frank-Wang-oss/FCSTGNN.

cs.LG↗

arXiv2023

SEA++: Multi-Graph-based High-Order Sensor Alignment for Multivariate Time-Series Unsupervised Domain Adaptation

Unsupervised Domain Adaptation (UDA) methods have been successful in reducing label dependency by minimizing the domain discrepancy between a labeled source domain and an unlabeled target domain. However, these methods face challenges when dealing with Multivariate Time-Series (MTS) data. MTS data typically consist of multiple sensors, each with its own unique distribution. This characteristic makes it hard to adapt existing UDA methods, which mainly focus on aligning global features while overlooking the distribution discrepancies at the sensor level, to reduce domain discrepancies for MTS data. To address this issue, a practical domain adaptation scenario is formulated as Multivariate Time-Series Unsupervised Domain Adaptation (MTS-UDA). In this paper, we propose SEnsor Alignment (SEA) for MTS-UDA, aiming to reduce domain discrepancy at both the local and global sensor levels. At the local sensor level, we design endo-feature alignment, which aligns sensor features and their correlations across domains. To reduce domain discrepancy at the global sensor level, we design exo-feature alignment that enforces restrictions on global sensor features. We further extend SEA to SEA++ by enhancing the endo-feature alignment. Particularly, we incorporate multi-graph-based high-order alignment for both sensor features and their correlations. Extensive empirical results have demonstrated the state-of-the-art performance of our SEA and SEA++ on public MTS datasets for MTS-UDA.

cs.LG↗

arXiv2023

Accelerating Relaxation Dynamics in Open Quantum System with Liouvillian Skin Effect

We investigate a non-Hermitian model featuring non-reciprocal gradient hoppings. Through an in-depth analysis of the Liouvillian spectrum and dynamics, we confirm the emergence of the Liouvillian skin effect resulting from the non-reciprocal nature of hoppings in this model. Furthermore, we observe that the presence of gradient hopping strength leads to an accelerated relaxation time for the system. Through numerical investigations of the Liouvillian gap, relaxation time, and steady-state localization length, we discover that the relaxation time in this model cannot be explained by the currently established relationship associated with the Liouvillian skin effect. This discrepancy highlights the need for further exploration and theoretical advancements to fully comprehend the intricate mechanisms underlying quantum relaxation processes. Motivated by these findings, we propose a theoretical approach to realize this non-Hermitian model in an atomic system with a sideband structure by employing adiabatic elimination technique. These results contribute to our deeper comprehension of quantum relaxation dynamics and provide theoretical backing for the development of techniques aimed at controlling quantum relaxation processes.

quant-ph↗

arXiv2023

Two dimensional vertex-decorated Lieb lattice with exact mobility edges and robust flat bands

The mobility edge (ME) that marks the energy separating extended and localized states is a central concept in understanding the metal-insulator transition induced by disordered or quasiperiodic potentials. MEs have been extensively studied in three dimensional disorder systems and one-dimensional quasiperiodic systems. However, the studies of MEs in two dimensional (2D) systems are rare. Here we propose a class of 2D vertex-decorated Lieb lattice models with quasiperiodic potentials only acting on the vertices of a (extended) Lieb lattice. By mapping these models to the 2D Aubry-André model, we obtain exact expressions of MEs and the localization lengths of localized states, and further demonstrate that the flat bands remain unaffected by the quasiperiodic potentials. Finally, we propose a highly feasible scheme to experimentally realize our model in a quantum dot array. Our results open the door to studying and realizing exact MEs and robust flat bands in 2D systems.

cond-mat.dis-nn↗

arXiv2023

Observing Quantum Synchronization of a Single Trapped-Ion Qubit

Synchronizing a few-level quantum system is of fundamental importance to understanding synchronization in deep quantum regime. Whether a two-level system, the smallest quantum system, can be synchronized has been theoretically debated for the past several years. Here, for the first time, we demonstrate that a qubit can indeed be synchronized to an external driving signal by using a trapped-ion system. By engineering fully controllable gain and damping processes, an ion qubit is synchronized to oscillate at the same frequency as the driving signal and lock in phase. We systematically investigate the parameter regions of synchronization and observe characteristic features of the Arnold tongue. Our measurements agree remarkably well with numerical simulations based on recent theory on qubit synchronization. By synchronizing the basic unit of quantum information, our research opens up the possibility of applying quantum synchronization to large-scale quantum networks.

quant-ph↗

arXiv2023

Combinatorial Properties for a Class of Simplicial Complexes Extended from Pseudo-fractal Scale-free Web

Simplicial complexes are a popular tool used to model higher-order interactions between elements of complex social and biological systems. In this paper, we study some combinatorial aspects of a class of simplicial complexes created by a graph product, which is an extension of the pseudo-fractal scale-free web. We determine explicitly the independence number, the domination number, and the chromatic number. Moreover, we derive closed-form expressions for the number of acyclic orientations, the number of root-connected acyclic orientations, the number of spanning trees, as well as the number of perfect matchings for some particular cases.

math.CO↗

arXiv2022

Mobility edges and critical regions in periodically kicked incommensurate optical Raman lattice

Conventionally the mobility edge (ME) separating extended states from localized ones is a central concept in understanding Anderson localization transition. The critical state, being delocalized and non-ergodic, is a third type of fundamental state that is different from both the extended and localized states. Here we study the localization phenomena in a one dimensional periodically kicked quasiperiodic optical Raman lattice by using fractal dimensions. We show a rich phase diagram including the pure extended, critical and localized phases in the high frequency regime, the MEs separating the critical regions from the extended (localized) regions, and the coexisting phase of extended, critical and localized regions with increasing the kicked period. We also find the fragility of phase boundaries, which are more susceptible to the dynamical kick, and the phenomenon of the reentrant localization transition. Finally, we demonstrate how the studied model can be realized based on current cold atom experiments and how to detect the rich physics by the expansion dynamics. Our results provide insight into studying and detecting the novel critical phases, MEs, coexisting quantum phases, and some other physics phenomena in the periodically kicked systems.

cond-mat.dis-nn↗

arXiv2022

Non-Hermitian boundary spectral winding

Spectral winding of complex eigenenergies represents a topological aspect unique in non-Hermitian systems, which vanishes in one-dimensional (1D) systems under the open boundary conditions (OBC). In this work, we discover a boundary spectral winding in two-dimensional non-Hermitian systems under the OBC, originating from the interplay between Hermitian boundary localization and non-Hermitian non-reciprocal pumping. Such a nontrivial boundary topology is demonstrated in a non-Hermitian breathing Kagome model with a triangle geometry, whose 1D boundary mimics a 1D non-Hermitian system under the periodic boundary conditions with nontrivial spectral winding. In a trapezoidal geometry, such a boundary spectral winding can even co-exist with corner accumulation of edge states, instead of extended ones along 1D boundary of a triangle geometry. An OBC type of hybrid skin-topological effect may also emerge in a trapezoidal geometry, provided the boundary spectral winding completely vanishes. By studying the Green's function, we unveil that the boundary spectral winding can be detected from a topological response of the system to a local driving field, offering a realistic method to extract the nontrivial boundary topology for experimental studies.

cond-mat.mes-hall↗

arXiv2022

Manipulating non-Hermitian skin effect via electric fields

In non-Hermitian systems, the phenomenon that the bulk-band eigenstates are accumulated at the boundaries of the systems under open boundary conditions is called non-Hermitian skin effect (NHSE), which is one of the most iconic and important features of a non-Hermitian system. In this work, we investigate the fate of NHSE in the presence of electric fields by analytically calculating the dynamical evolution of an initial bulk state and numerically computing the spectral winding number, the distributions of eigenstates, as well as the dynamical evolutions. We show abundant manipulation effects of dc and ac fields on the NHSE, and that the physical mechanism behind these effects is the interplay between the Stark localization, dynamic localization and the NHSE. In addition, the finite size analysis of the non-Hermitian system with a pure dc field shows the phenomenon of size-dependent NHSE. We further propose a scheme to realize the discussed model based on an electronic circuit. The results will help to deepen the understanding of NHSE and its manipulation.

quant-ph↗