arXiv subjects
Publications and source records attributed to Geng Chen.
In this paper, we prove the singularity formation for Poiseuille laminar flow of full Ericksen-Leslie system modeling nematic liquid crystal flows in dimension two. The singularity is due to the geometric effect at the origin.
In this paper, we study the Lipschitz continuous dependence of conservative Hölder continuous weak solutions to a variational wave system derived from a model for nematic liquid crystals. Since the solution of this system generally forms finite time cusp singularity, the solution flow is not Lipschitz continuous under the Sobolev metric used in the existence and uniqueness theory. We establish a Finsler type optimal transport metric, and show the Lipschitz continuous dependence of solution on the initial data under this metric. This kind of Finsler type optimal transport metrics was first established in [A. Bressan and G. Chen, Arch. Ration. Mech. Anal. 226(3) (2017), 1303-1343] for the scalar variational wave equation. This equation can be used to describe the unit direction n of mean orientation of nematic liquid crystals, when n is restricted on a circle. The model considered in this paper describes the propagation of n without this restriction, i.e. n takes any value on the unite sphere. So we need to consider a wave system instead of a scalar equation.
The precision of quantum metrology is widely believed to be restricted by the Heisenberg limit, corresponding to a root mean square error that is inversely proportional to the number of independent processes probed in an experiment, N. In the past, some proposals have challenged this belief, for example using non-linear interactions among the probes. However, these proposals turned out to still obey the Heisenberg limit with respect to other relevant resources, such as the total energy of the probes. Here, we present a photonic implementation of a quantum metrology protocol surpassing the Heisenberg limit by probing two groups of independent processes in a superposition of two alternative causal orders. Each process creates a phase space displacement, and our setup is able to estimate a geometric phase associated to two sets of N displacements with an error that falls quadratically with N. Our results only require a single-photon probe with an initial energy that is independent of N. Using a superposition of causal orders outperforms every setup where the displacements are probed in a definite order. Our experiment features the demonstration of indefinite causal order in a continuous-variable system, and opens up the experimental investigation of quantum metrology setups boosted by indefinite causal order.
We present the first comprehensive video polyp segmentation (VPS) study in the deep learning era. Over the years, developments in VPS are not moving forward with ease due to the lack of large-scale fine-grained segmentation annotations. To address this issue, we first introduce a high-quality frame-by-frame annotated VPS dataset, named SUN-SEG, which contains 158,690 colonoscopy frames from the well-known SUN-database. We provide additional annotations with diverse types, i.e., attribute, object mask, boundary, scribble, and polygon. Second, we design a simple but efficient baseline, dubbed PNS+, consisting of a global encoder, a local encoder, and normalized self-attention (NS) blocks. The global and local encoders receive an anchor frame and multiple successive frames to extract long-term and short-term spatial-temporal representations, which are then progressively updated by two NS blocks. Extensive experiments show that PNS+ achieves the best performance and real-time inference speed (170fps), making it a promising solution for the VPS task. Third, we extensively evaluate 13 representative polyp/object segmentation models on our SUN-SEG dataset and provide attribute-based comparisons. Finally, we discuss several open issues and suggest possible research directions for the VPS community.
Camouflaged object detection (COD) aims to identify the objects that conceal themselves in natural scenes. Accurate COD suffers from a number of challenges associated with low boundary contrast and the large variation of object appearances, e.g., object size and shape. To address these challenges, we propose a novel Context-aware Cross-level Fusion Network (C2F-Net), which fuses context-aware cross-level features for accurately identifying camouflaged objects. Specifically, we compute informative attention coefficients from multi-level features with our Attention-induced Cross-level Fusion Module (ACFM), which further integrates the features under the guidance of attention coefficients. We then propose a Dual-branch Global Context Module (DGCM) to refine the fused features for informative feature representations by exploiting rich global context information. Multiple ACFMs and DGCMs are integrated in a cascaded manner for generating a coarse prediction from high-level features. The coarse prediction acts as an attention map to refine the low-level features before passing them to our Camouflage Inference Module (CIM) to generate the final prediction. We perform extensive experiments on three widely used benchmark datasets and compare C2F-Net with state-of-the-art (SOTA) models. The results show that C2F-Net is an effective COD model and outperforms SOTA models remarkably. Further, an evaluation on polyp segmentation datasets demonstrates the promising potentials of our C2F-Net in COD downstream applications. Our code is publicly available at: https://github.com/Ben57882/C2FNet-TSCVT.
Accelerated multi-modal magnetic resonance (MR) imaging is a new and effective solution for fast MR imaging, providing superior performance in restoring the target modality from its undersampled counterpart with guidance from an auxiliary modality. However, existing works simply combine the auxiliary modality as prior information, lacking in-depth investigations on the potential mechanisms for fusing different modalities. Further, they usually rely on the convolutional neural networks (CNNs), which is limited by the intrinsic locality in capturing the long-distance dependency. To this end, we propose a multi-modal transformer (MTrans), which is capable of transferring multi-scale features from the target modality to the auxiliary modality, for accelerated MR imaging. To capture deep multi-modal information, our MTrans utilizes an improved multi-head attention mechanism, named cross attention module, which absorbs features from the auxiliary modality that contribute to the target modality. Our framework provides three appealing benefits: (i) Our MTrans use an improved transformers for multi-modal MR imaging, affording more global information compared with existing CNN-based methods. (ii) A new cross attention module is proposed to exploit the useful information in each modality at different scales. The small patch in the target modality aims to keep more fine details, the large patch in the auxiliary modality aims to obtain high-level context features from the larger region and supplement the target modality effectively. (iii) We evaluate MTrans with various accelerated multi-modal MR imaging tasks, e.g., MR image reconstruction and super-resolution, where MTrans outperforms state-of-the-art methods on fastMRI and real-world clinical datasets.
Predictive learning ideally builds the world model of physical processes in one or more given environments. Typical setups assume that we can collect data from all environments at all times. In practice, however, different prediction tasks may arrive sequentially so that the environments may change persistently throughout the training procedure. Can we develop predictive learning algorithms that can deal with more realistic, non-stationary physical environments? In this paper, we study a new continual learning problem in the context of video prediction, and observe that most existing methods suffer from severe catastrophic forgetting in this setup. To tackle this problem, we propose the continual predictive learning (CPL) approach, which learns a mixture world model via predictive experience replay and performs test-time adaptation with non-parametric task inference. We construct two new benchmarks based on RoboNet and KTH, in which different tasks correspond to different physical robotic environments or human actions. Our approach is shown to effectively mitigate forgetting and remarkably outperform the naïve combinations of previous art in video prediction and continual learning.
We consider the Poiseuille flow of nematic liquid crystals via the full Ericksen-Leslie model. The model is described by a coupled system consisting of a heat equation and a quasilinear wave equation. In this paper, we will construct an example with a finite time cusp singularity due to the quasilinearity of the wave equation, extended from an earlier result on a special case.
Salient object detection (SOD) on RGB and depth images has attracted more and more research interests, due to its effectiveness and the fact that depth cues can now be conveniently captured. Existing RGB-D SOD models usually adopt different fusion strategies to learn a shared representation from the two modalities (\ie, RGB and depth), while few methods explicitly consider how to preserve modality-specific characteristics. In this study, we propose a novel framework, termed SPNet} (Specificity-preserving network), which benefits SOD performance by exploring both the shared information and modality-specific properties (\eg, specificity). Specifically, we propose to adopt two modality-specific networks and a shared learning network to generate individual and shared saliency prediction maps, respectively. To effectively fuse cross-modal features in the shared learning network, we propose a cross-enhanced integration module (CIM) and then propagate the fused feature to the next layer for integrating cross-level information. Moreover, to capture rich complementary multi-modal information for boosting the SOD performance, we propose a multi-modal feature aggregation (MFA) module to integrate the modality-specific features from each individual decoder into the shared decoder. By using a skip connection, the hierarchical features between the encoder and decoder layers can be fully combined. Extensive experiments demonstrate that our~\ours~outperforms cutting-edge approaches on six popular RGB-D SOD and three camouflaged object detection benchmarks. The project is publicly available at: https://github.com/taozh2017/SPNet.
We are concerned with the inviscid limit of the Navier-Stokes equations to the Euler equations for barotropic compressible fluids in $\mathbb{R}^3$. When the viscosity coefficients obey a lower power-law of the density (i.e., $ρ^δ$ with $0<δ<1$), we identify a quasi-symmetric hyperbolic--singular elliptic coupled structure of the Navier-Stokes equations to control the behavior of the velocity of the fluids near the vacuum. Then this structure is employed to prove that there exists a unique regular solution to the corresponding Cauchy problem with arbitrarily large initial data and far-field vacuum, whose life span is uniformly positive in the vanishing viscosity limit. Some uniform estimates on both the local sound speed and the velocity in $H^3(\mathbb{R}^3)$ with respect to the viscosity coefficients are also obtained, which lead to the strong convergence of the regular solutions of the Navier-Stokes equations with finite mass and energy to the corresponding regular solutions of the Euler equations in $L^{\infty}([0, T]; H^{s}_{\rm loc}(\mathbb{R}^3))$ for any $s\in [2, 3)$. As a consequence, we show that, for both viscous and inviscid flows, it is impossible that the $L^\infty$ norm of any global regular solution with vacuum decays to zero asymptotically, as $t$ tends to infinity. Our framework developed here is applicable to the same problem for the other physical dimensions via some minor modifications.
We are concerned with the formation of singularities and the existence of global continuous solutions of the Cauchy problem for the one-dimensional non-isentropic Euler equations for compressible fluids. For the isentropic Euler equations, we pinpoint a necessary and sufficient condition for the formation of singularities of solutions with large initial data that allow a far-field vacuum -- there exists a compression in the initial data. For the non-isentropic Euler equations, we identify a sufficient condition for the formation of singularities of solutions with large initial data that allow a far-field vacuum -- there exists a strong compression in the initial data. Furthermore, we identify two new phenomena -- decompression and de-rarefaction -- for the non-isentropic Euler flows, different from the isentropic flows, via constructing two respective solutions. For the decompression phenomenon, we construct a first global continuous non-isentropic solution, even though initial data contain a weak compression, by solving an inverse Goursat problem, so that the solution is smooth, except on several characteristic curves across which the solution has a weak discontinuity (i.e., only Lipschitz continuity). For the de-rarefaction phenomenon, we construct a continuous non-isentropic solution whose initial data contain isentropic rarefactions (i.e., without compression) and a locally stationary varying entropy profile, for which the solution still forms a shock wave in a finite time.
We propose a novel Synergistic Attention Network (SA-Net) to address the light field salient object detection by establishing a synergistic effect between multi-modal features with advanced attention mechanisms. Our SA-Net exploits the rich information of focal stacks via 3D convolutional neural networks, decodes the high-level features of multi-modal light field data with two cascaded synergistic attention modules, and predicts the saliency map using an effective feature fusion module in a progressive manner. Extensive experiments on three widely-used benchmark datasets show that our SA-Net outperforms 28 state-of-the-art models, sufficiently demonstrating its effectiveness and superiority. Our code is available at https://github.com/PanoAsh/SA-Net.
Genuine multipartite entanglement represents the strongest type of entanglement, which is an essential resource for quantum information processing. Standard methods to detect genuine multipartite entanglement, e.g., entanglement witnesses, state tomography, or quantum state verification, require full knowledge of the Hilbert space dimension and precise calibration of measurement devices, which are usually difficult to acquire in an experiment. The most radical way to overcome these problems is to detect entanglement solely based on the Bell-like correlations of measurement outcomes collected in the experiment, namely, device-independently (DI). However, it is difficult to certify genuine entanglement of practical multipartite states in this way, and even more difficult to quantify it, due to the difficulty to identify optimal multipartite Bell inequalities and protocols tolerant to state impurity. In this work, we explore a general and robust DI method which can be applied to various realistic multipartite quantum state in arbitrary finite dimension, while merely relying on bipartite Bell inequalities. Our method allows us both to certify the presence of genuine multipartite entanglement and to quantify it. Several important classes of entangled states are tested with this method, leading to the detection of genuinely entangled states. We also certify genuine multipartite entanglement in weakly-entangled GHZ states, thus showing that the method applies equally well to less standard states.
Camouflaged object detection (COD) is a challenging task due to the low boundary contrast between the object and its surroundings. In addition, the appearance of camouflaged objects varies significantly, e.g., object size and shape, aggravating the difficulties of accurate COD. In this paper, we propose a novel Context-aware Cross-level Fusion Network (C2F-Net) to address the challenging COD task. Specifically, we propose an Attention-induced Cross-level Fusion Module (ACFM) to integrate the multi-level features with informative attention coefficients. The fused features are then fed to the proposed Dual-branch Global Context Module (DGCM), which yields multi-scale feature representations for exploiting rich global context information. In C2F-Net, the two modules are conducted on high-level features using a cascaded manner. Extensive experiments on three widely used benchmark datasets demonstrate that our C2F-Net is an effective COD model and outperforms state-of-the-art models remarkably. Our code is publicly available at: https://github.com/thograce/C2FNet.
Existing video polyp segmentation (VPS) models typically employ convolutional neural networks (CNNs) to extract features. However, due to their limited receptive fields, CNNs can not fully exploit the global temporal and spatial information in successive video frames, resulting in false-positive segmentation results. In this paper, we propose the novel PNS-Net (Progressively Normalized Self-attention Network), which can efficiently learn representations from polyp videos with real-time speed (~140fps) on a single RTX 2080 GPU and no post-processing. Our PNS-Net is based solely on a basic normalized self-attention block, equipping with recurrence and CNNs entirely. Experiments on challenging VPS datasets demonstrate that the proposed PNS-Net achieves state-of-the-art performance. We also conduct extensive experiments to study the effectiveness of the channel split, soft-attention, and progressive learning strategy. We find that our PNS-Net works well under different settings, making it a promising solution to the VPS task.
Magnetic resonance (MR) image acquisition is an inherently prolonged process, whose acceleration by obtaining multiple undersampled images simultaneously through parallel imaging has always been the subject of research. In this paper, we propose the Dual-Octave Convolution (Dual-OctConv), which is capable of learning multi-scale spatial-frequency features from both real and imaginary components, for fast parallel MR image reconstruction. By reformulating the complex operations using octave convolutions, our model shows a strong ability to capture richer representations of MR images, while at the same time greatly reducing the spatial redundancy. More specifically, the input feature maps and convolutional kernels are first split into two components (i.e., real and imaginary), which are then divided into four groups according to their spatial frequencies. Then, our Dual-OctConv conducts intra-group information updating and inter-group information exchange to aggregate the contextual information across different groups. Our framework provides two appealing benefits: (i) it encourages interactions between real and imaginary components at various spatial frequencies to achieve richer representational capacity, and (ii) it enlarges the receptive field by learning multiple spatial-frequency features of both the real and imaginary components. We evaluate the performance of the proposed model on the acceleration of multi-coil MR image reconstruction. Extensive experiments are conducted on an {in vivo} knee dataset under different undersampling patterns and acceleration factors. The experimental results demonstrate the superiority of our model in accelerated parallel MR image reconstruction. Our code is available at: github.com/chunmeifeng/Dual-OctConv.
In optical metrological protocols to measure physical quantities, it is, in principle, always beneficial to increase photon number to improve measurement precision. However, practical constraints prevent arbitrary increase of n due to the imperfections of a practical detector, especially when the detector response is dominated by saturation effect. In this work, we show that a modified weak measurement protocol, namely, biased weak measurement significantly improves the precision of optical metrology in the presence of saturation effect. This method detects an ultra-small fraction of photons while maintains considerable amount of metrological information. The biased pre-coupling leads to an additional reduction of photons in the post-selection and generates an extinction point in the spectrum distribution, which is extremely sensitive to the estimated parameter and difficult to be saturated. Therefore, the Fisher information can be persistently enhanced by increasing the photon number. In our magnetic-sensing experiment, biased weak measurement achieves precision approximately one order of magnitude better than those of previously used methods. The proposed method can be applied in various optical measurement schemes to circumvent detector saturation effect with low-cost apparatuses.
Saliency detection based on the complementary information from RGB images and depth maps has recently gained great popularity. In this paper, we propose Complementary Attention and Adaptive Integration Network (CAAI-Net), a novel RGB-D saliency detection model that integrates complementary attention based feature concentration and adaptive cross-modal feature fusion into a unified framework for accurate saliency detection. Specifically, we propose a context-aware complementary attention (CCA) module, which consists of a feature interaction component, a complementary attention component, and a global-context component. The CCA module first utilizes the feature interaction component to extract rich local context features. The resulting features are then fed into the complementary attention component, which employs the complementary attention generated from adjacent levels to guide the attention at the current layer so that the mutual background disturbances are suppressed and the network focuses more on the areas with salient objects. Finally, we utilize a specially-designed adaptive feature integration (AFI) module, which sufficiently considers the low-quality issue of depth maps, to aggregate the RGB and depth features in an adaptive manner. Extensive experiments on six challenging benchmark datasets demonstrate that CAAI-Net is an effective saliency detection model and outperforms nine state-of-the-art models in terms of four widely-used metrics. In addition, extensive ablation studies confirm the effectiveness of the proposed CCA and AFI modules.