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Can Zhang

Publications and source records attributed to Can Zhang.

At least 55 records · Page 3Linked to original sources

A Fast Observability for Diffusion Equations in $\mathbb R^N$

Given an equidistributed set in the whole Euclidean space, we have established in [1] that there exists a constant positive $C$ such that the observability inequality of diffusion equations holds for all $T\in]0,1[$, with an observability cost being of the form $Ce^{C/T}$. In this paper, for any small constant $\varepsilon>0$, we prove that there exists a nontrivial equidistributed set (in the sense that whose complementary set is unbounded), so that the above observability cost can be improved to a fast form of $Ce^{\varepsilon/T}$ for certain constant $C>0$. The proof is based on the strategy used in [1], as well as an interpolation inequality for gradients of solutions to elliptic equations obtained recently in [2].

math.AP↗

Signatures of Majorana Bound States in the Diffraction Patterns of Extended Superconductor-Topological Insulator-Superconductor Josephson Junctions

In an extended superconductor-topological insulator-superconductor (S-TI-S) Josephson junction in a magnetic field, localized Majorana bound states (MBS) are predicted to exist at the cores of Josephson vortices where the local phase difference across the junction is an odd-multiple of $π$. These states contribute a supercurrent with a $4π$-periodic current-phase relation (CPR) that adds to the conventional $2π$-periodic sinusoidal CPR. In this work, we present a comprehensive experimental study of the critical current vs. applied magnetic field diffraction patterns of lateral Nb-Bi$_2$Se$_3$-Nb Josephson junctions. We compare our observations to a model of the Josephson dynamics in the S-TI-S junction system to explore what feature of MBS are, or are not, exhibited in these junctions. Consistent with the model, we find several distinct deviations from a Fraunhofer diffraction pattern that is expected for a uniform sin$(ϕ)$ CPR. In particular, we observe abrupt changes in the diffraction pattern at applied magnetic fields in which the current-carrying localized MBS are expected to enter the junction, and a lifting of the odd-numbered nodes consistent with a $4π$-periodic sin$(ϕ/2)$-component in the CPR. We also see that although the even-numbered nodes often remain fully-formed, we sometimes see deviations that are consistent with quasiparticle-induced fluctuations in the parity of the MBS pairs that encodes quantum information.

cond-mat.supr-con↗

Quantitative uniqueness estimates for stochastic parabolic equations on the whole Euclidean space

In this paper, a quantitative estimate of unique continuation for the stochastic heat equation with bounded potentials on the whole Euclidean space is established. This paper generalizes the earlier results in [29] and [17] from a bounded domain to an unbounded one. The proof is based on the locally parabolic-type frequency function method. An observability estimate from measurable sets in time for the same equation is also derived.

math.AP↗

The exponential turnpike property for periodic linear quadratic optimal control problems in infinite dimension

In this paper, we establish an exponential periodic turnpike property for linear quadratic optimal control problems governed by periodic systems in infinite dimension. We show that the optimal trajectory converges exponentially to a periodic orbit when the time horizon tends to infinity. Similar results are obtained for the optimal control and adjoint state. Our proof is based on the large time behavior of solutions of operator differential Riccati equations with periodic coefficients.

math.OC↗

MLP-AMDC: An MLP Architecture for Adaptive-Mask-based Dual-Camera snapshot hyperspectral imaging

Coded Aperture Snapshot Spectral Imaging (CASSI) system has great advantages over traditional methods in dynamically acquiring Hyper-Spectral Image (HSI), but there are the following problems. 1) Traditional mask relies on random patterns or analytical design, both of which limit the performance improvement of CASSI. 2) Existing high-quality reconstruction algorithms are slow in reconstruction and can only reconstruct scene information offline. To address the above two problems, this paper designs the AMDC-CASSI system, introducing RGB camera with CASSI based on Adaptive-Mask as multimodal input to improve the reconstruction quality. The existing SOTA reconstruction schemes are based on transformer, but the operation of self-attention pulls down the operation efficiency of the network. In order to improve the inference speed of the reconstruction network, this paper proposes An MLP Architecture for Adaptive-Mask-based Dual-Camera (MLP-AMDC) to replace the transformer structure of the network. Numerous experiments have shown that MLP performs no less well than transformer-based structures for HSI reconstruction, while MLP greatly improves the network inference speed and has less number of parameters and operations, our method has a 8 db improvement over SOTA and at least a 5-fold improvement in reconstruction speed. (https://github.com/caizeyu1992/MLP-AMDC.)

eess.IV↗

GeT: Generative Target Structure Debiasing for Domain Adaptation

Domain adaptation (DA) aims to transfer knowledge from a fully labeled source to a scarcely labeled or totally unlabeled target under domain shift. Recently, semi-supervised learning-based (SSL) techniques that leverage pseudo labeling have been increasingly used in DA. Despite the competitive performance, these pseudo labeling methods rely heavily on the source domain to generate pseudo labels for the target domain and therefore still suffer considerably from source data bias. Moreover, class distribution bias in the target domain is also often ignored in the pseudo label generation and thus leading to further deterioration of performance. In this paper, we propose GeT that learns a non-bias target embedding distribution with high quality pseudo labels. Specifically, we formulate an online target generative classifier to induce the target distribution into distinctive Gaussian components weighted by their class priors to mitigate source data bias and enhance target class discriminability. We further propose a structure similarity regularization framework to alleviate target class distribution bias and further improve target class discriminability. Experimental results show that our proposed GeT is effective and achieves consistent improvements under various DA settings with and without class distribution bias. Our code is available at: https://lulusindazc.github.io/getproject/.

cs.CV↗

Improving Scene Graph Generation with Superpixel-Based Interaction Learning

Recent advances in Scene Graph Generation (SGG) typically model the relationships among entities utilizing box-level features from pre-defined detectors. We argue that an overlooked problem in SGG is the coarse-grained interactions between boxes, which inadequately capture contextual semantics for relationship modeling, practically limiting the development of the field. In this paper, we take the initiative to explore and propose a generic paradigm termed Superpixel-based Interaction Learning (SIL) to remedy coarse-grained interactions at the box level. It allows us to model fine-grained interactions at the superpixel level in SGG. Specifically, (i) we treat a scene as a set of points and cluster them into superpixels representing sub-regions of the scene. (ii) We explore intra-entity and cross-entity interactions among the superpixels to enrich fine-grained interactions between entities at an earlier stage. Extensive experiments on two challenging benchmarks (Visual Genome and Open Image V6) prove that our SIL enables fine-grained interaction at the superpixel level above previous box-level methods, and significantly outperforms previous state-of-the-art methods across all metrics. More encouragingly, the proposed method can be applied to boost the performance of existing box-level approaches in a plug-and-play fashion. In particular, SIL brings an average improvement of 2.0% mR (even up to 3.4%) of baselines for the PredCls task on Visual Genome, which facilitates its integration into any existing box-level method.

cs.CV↗

3D Boson representation of affine Yangian of ${\mathfrak{gl}}(1)$ and 3D cut-and-join operators

We have constructed 3D Bosons. In this paper, we show the 3D Bosonic Fock space, which is isomorphic to the vector space of 3D Young diagrams as graded vector spaces. We use 3D Bosons to represent the generators of the affine Yangian of ${\mathfrak{gl}}(1)$ and define the 3D cut-and-join operators. Then we discuss the 3D Boson representation of $W$-operators in matrix models.

math-ph↗

Observability Inequality from Measurable Sets and the Stackelberg-Nash Game Problem for Degenerate Parabolic Equations

In this study, we employ the established Carleman estimates and propagation estimates of smallness from measurable sets for real analytic functions, along with the telescoping series method, to establish an observability inequality for the degenerate parabolic equation over measurable subsets in the time-space domain. As a direct application, we formulate a captivating Stackelberg-Nash game problem and provide a proof of the existence of its equilibrium. Additionally, we characterize the set of Stackelberg-Nash equilibria and delve into the analysis of a norm optimal control problem.

math.OC↗

Cross-Modality Time-Variant Relation Learning for Generating Dynamic Scene Graphs

Dynamic scene graphs generated from video clips could help enhance the semantic visual understanding in a wide range of challenging tasks such as environmental perception, autonomous navigation, and task planning of self-driving vehicles and mobile robots. In the process of temporal and spatial modeling during dynamic scene graph generation, it is particularly intractable to learn time-variant relations in dynamic scene graphs among frames. In this paper, we propose a Time-variant Relation-aware TRansformer (TR$^2$), which aims to model the temporal change of relations in dynamic scene graphs. Explicitly, we leverage the difference of text embeddings of prompted sentences about relation labels as the supervision signal for relations. In this way, cross-modality feature guidance is realized for the learning of time-variant relations. Implicitly, we design a relation feature fusion module with a transformer and an additional message token that describes the difference between adjacent frames. Extensive experiments on the Action Genome dataset prove that our TR$^2$ can effectively model the time-variant relations. TR$^2$ significantly outperforms previous state-of-the-art methods under two different settings by 2.1% and 2.6% respectively.

cs.CV↗

Jack polynomials, $\hbar$-dependent KP hierarchy and affine Yangian of ${\mathfrak{gl}}(1)$

In this paper, we discuss the relations between the Jack polynomials, $\hbar$-dependent KP hierarchy and affine Yangian of ${\mathfrak{gl}}(1)$. We find that $α=\hbar^2$ and $h_1=\hbar, \ h_2=-\hbar^{-1}$, where $α$ is the parameter in Jack polynomials, and $h_1,\ h_2$ are the parameters in affine Yangian of ${\mathfrak{gl}}(1)$. Then the vertex operators which are in Jack polynomials are the same with that in $\hbar$-KP hierarchy, and the Jack polynomials can be used to describe the tau functions of the $\hbar$-KP hierarchy.

nlin.SI↗

Deep Motion Prior for Weakly-Supervised Temporal Action Localization

Weakly-Supervised Temporal Action Localization (WSTAL) aims to localize actions in untrimmed videos with only video-level labels. Currently, most state-of-the-art WSTAL methods follow a Multi-Instance Learning (MIL) pipeline: producing snippet-level predictions first and then aggregating to the video-level prediction. However, we argue that existing methods have overlooked two important drawbacks: 1) inadequate use of motion information and 2) the incompatibility of prevailing cross-entropy training loss. In this paper, we analyze that the motion cues behind the optical flow features are complementary informative. Inspired by this, we propose to build a context-dependent motion prior, termed as motionness. Specifically, a motion graph is introduced to model motionness based on the local motion carrier (e.g., optical flow). In addition, to highlight more informative video snippets, a motion-guided loss is proposed to modulate the network training conditioned on motionness scores. Extensive ablation studies confirm that motionness efficaciously models action-of-interest, and the motion-guided loss leads to more accurate results. Besides, our motion-guided loss is a plug-and-play loss function and is applicable with existing WSTAL methods. Without loss of generality, based on the standard MIL pipeline, our method achieves new state-of-the-art performance on three challenging benchmarks, including THUMOS'14, ActivityNet v1.2 and v1.3.

cs.CV↗

LocVTP: Video-Text Pre-training for Temporal Localization

Video-Text Pre-training (VTP) aims to learn transferable representations for various downstream tasks from large-scale web videos. To date, almost all existing VTP methods are limited to retrieval-based downstream tasks, e.g., video retrieval, whereas their transfer potentials on localization-based tasks, e.g., temporal grounding, are under-explored. In this paper, we experimentally analyze and demonstrate the incompatibility of current VTP methods with localization tasks, and propose a novel Localization-oriented Video-Text Pre-training framework, dubbed as LocVTP. Specifically, we perform the fine-grained contrastive alignment as a complement to the coarse-grained one by a clip-word correspondence discovery scheme. To further enhance the temporal reasoning ability of the learned feature, we propose a context projection head and a temporal aware contrastive loss to perceive the contextual relationships. Extensive experiments on four downstream tasks across six datasets demonstrate that our LocVTP achieves state-of-the-art performance on both retrieval-based and localization-based tasks. Furthermore, we conduct comprehensive ablation studies and thorough analyses to explore the optimum model designs and training strategies.

cs.CV↗

CA-UDA: Class-Aware Unsupervised Domain Adaptation with Optimal Assignment and Pseudo-Label Refinement

Recent works on unsupervised domain adaptation (UDA) focus on the selection of good pseudo-labels as surrogates for the missing labels in the target data. However, source domain bias that deteriorates the pseudo-labels can still exist since the shared network of the source and target domains are typically used for the pseudo-label selections. The suboptimal feature space source-to-target domain alignment can also result in unsatisfactory performance. In this paper, we propose CA-UDA to improve the quality of the pseudo-labels and UDA results with optimal assignment, a pseudo-label refinement strategy and class-aware domain alignment. We use an auxiliary network to mitigate the source domain bias for pseudo-label refinement. Our intuition is that the underlying semantics in the target domain can be fully exploited to help refine the pseudo-labels that are inferred from the source features under domain shift. Furthermore, our optimal assignment can optimally align features in the source-to-target domains and our class-aware domain alignment can simultaneously close the domain gap while preserving the classification decision boundaries. Extensive experiments on several benchmark datasets show that our method can achieve state-of-the-art performance in the image classification task.

cs.CV↗

On Pursuit of Designing Multi-modal Transformer for Video Grounding

Video grounding aims to localize the temporal segment corresponding to a sentence query from an untrimmed video. Almost all existing video grounding methods fall into two frameworks: 1) Top-down model: It predefines a set of segment candidates and then conducts segment classification and regression. 2) Bottom-up model: It directly predicts frame-wise probabilities of the referential segment boundaries. However, all these methods are not end-to-end, i.e., they always rely on some time-consuming post-processing steps to refine predictions. To this end, we reformulate video grounding as a set prediction task and propose a novel end-to-end multi-modal Transformer model, dubbed as GTR. Specifically, GTR has two encoders for video and language encoding, and a cross-modal decoder for grounding prediction. To facilitate the end-to-end training, we use a Cubic Embedding layer to transform the raw videos into a set of visual tokens. To better fuse these two modalities in the decoder, we design a new Multi-head Cross-Modal Attention. The whole GTR is optimized via a Many-to-One matching loss. Furthermore, we conduct comprehensive studies to investigate different model design choices. Extensive results on three benchmarks have validated the superiority of GTR. All three typical GTR variants achieve record-breaking performance on all datasets and metrics, with several times faster inference speed.

cs.CV↗

SpatioTemporal Focus for Skeleton-based Action Recognition

Graph convolutional networks (GCNs) are widely adopted in skeleton-based action recognition due to their powerful ability to model data topology. We argue that the performance of recent proposed skeleton-based action recognition methods is limited by the following factors. First, the predefined graph structures are shared throughout the network, lacking the flexibility and capacity to model the multi-grain semantic information. Second, the relations among the global joints are not fully exploited by the graph local convolution, which may lose the implicit joint relevance. For instance, actions such as running and waving are performed by the co-movement of body parts and joints, e.g., legs and arms, however, they are located far away in physical connection. Inspired by the recent attention mechanism, we propose a multi-grain contextual focus module, termed MCF, to capture the action associated relation information from the body joints and parts. As a result, more explainable representations for different skeleton action sequences can be obtained by MCF. In this study, we follow the common practice that the dense sample strategy of the input skeleton sequences is adopted and this brings much redundancy since number of instances has nothing to do with actions. To reduce the redundancy, a temporal discrimination focus module, termed TDF, is developed to capture the local sensitive points of the temporal dynamics. MCF and TDF are integrated into the standard GCN network to form a unified architecture, named STF-Net. It is noted that STF-Net provides the capability to capture robust movement patterns from these skeleton topology structures, based on multi-grain context aggregation and temporal dependency. Extensive experimental results show that our STF-Net significantly achieves state-of-the-art results on three challenging benchmarks NTU RGB+D 60, NTU RGB+D 120, and Kinetics-skeleton.

cs.CV↗

Unsupervised Pre-training for Temporal Action Localization Tasks

Unsupervised video representation learning has made remarkable achievements in recent years. However, most existing methods are designed and optimized for video classification. These pre-trained models can be sub-optimal for temporal localization tasks due to the inherent discrepancy between video-level classification and clip-level localization. To bridge this gap, we make the first attempt to propose a self-supervised pretext task, coined as Pseudo Action Localization (PAL) to Unsupervisedly Pre-train feature encoders for Temporal Action Localization tasks (UP-TAL). Specifically, we first randomly select temporal regions, each of which contains multiple clips, from one video as pseudo actions and then paste them onto different temporal positions of the other two videos. The pretext task is to align the features of pasted pseudo action regions from two synthetic videos and maximize the agreement between them. Compared to the existing unsupervised video representation learning approaches, our PAL adapts better to downstream TAL tasks by introducing a temporal equivariant contrastive learning paradigm in a temporally dense and scale-aware manner. Extensive experiments show that PAL can utilize large-scale unlabeled video data to significantly boost the performance of existing TAL methods. Our codes and models will be made publicly available at https://github.com/zhang-can/UP-TAL.

cs.CV↗

Quantitative unique continuation for parabolic equations with Neumann boundary conditions

In this paper, we establish a globally quantitative estimate of unique continuation at one time point for solutions of parabolic equations with Neumann boundary conditions in bounded domains. Our proof is mainly based on Carleman commutator estimates and a global frequency function argument, which is motivated from a recent work [5]. As an application, we obtain an observability inequality from measurable sets in time for all solutions of the above equations.

math.AP↗