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We propose a scheme that generates period-doubled responses via periodically driving certain Hamiltonians hosting quantum many-body scars, akin to recent experimental observations in driven Rydberg atom arrays. Our construction takes advantage of an su(2) spectrum generating algebra associated with the static quantum-scarred Hamiltonian, which enacts a $\pi$-rotation within the scar subspace after one period of time evolution with appropriately chosen driving parameters. This yields period-doubled (subharmonic) responses in local observables for any choice of initial state residing in the scar subspace. The quasienergy spectrum features atypical $\pi$-paired eigenstates embedded in an otherwise fully thermal spectrum.The protocol requires neither a large driving frequency nor a large driving amplitude, and is thus distinct from the prethermalization physics in previous investigations of the driven PXP model. We demonstrate our scheme using several spin-1/2 and spin-1 quantum scarred models possessing an exact su(2) spectrum generating algebra, as well as a symmetry-deformed PXP model, where the su(2) algebra is only approximate. Our results extend the class of models hosting quantum many-body scars that can be leveraged to yield time-crystalline behaviors under periodic driving., Comment: 4.5+5 pages, 3 figures

This paper proposes a Robust and Efficient Memory Network, referred to as REMN, for studying semi-supervised video object segmentation (VOS). Memory-based methods have recently achieved outstanding VOS performance by performing non-local pixel-wise matching between the query and memory. However, these methods have two limitations. 1) Non-local matching could cause distractor objects in the background to be incorrectly segmented. 2) Memory features with high temporal redundancy consume significant computing resources. For limitation 1, we introduce a local attention mechanism that tackles the background distraction by enhancing the features of foreground objects with the previous mask. For limitation 2, we first adaptively decide whether to update the memory features depending on the variation of foreground objects to reduce temporal redundancy. Second, we employ a dynamic memory bank, which uses a lightweight and differentiable soft modulation gate to decide how many memory features need to be removed in the temporal dimension. Experiments demonstrate that our REMN achieves state-of-the-art results on DAVIS 2017, with a $\mathcal{J\&F}$ score of 86.3% and on YouTube-VOS 2018, with a $\mathcal{G}$ over mean of 85.5%. Furthermore, our network shows a high inference speed of 25+ FPS and uses relatively few computing resources., Comment: Accepted by ICME 2023. 6 pages, 6 figures

In the field of semi-supervised medical image segmentation, the shortage of labeled data is the fundamental problem. How to effectively learn image features from unlabeled images to improve segmentation accuracy is the main research direction in this field. Traditional self-training methods can partially solve the problem of insufficient labeled data by generating pseudo labels for iterative training. However, noise generated due to the model's uncertainty during training directly affects the segmentation results. Therefore, we added sample-level and pixel-level uncertainty to stabilize the training process based on the self-training framework. Specifically, we saved several moments of the model during pre-training, and used the difference between their predictions on unlabeled samples as the sample-level uncertainty estimate for that sample. Then, we gradually add unlabeled samples from easy to hard during training. At the same time, we added a decoder with different upsampling methods to the segmentation network and used the difference between the outputs of the two decoders as pixel-level uncertainty. In short, we selectively retrained unlabeled samples and assigned pixel-level uncertainty to pseudo labels to optimize the self-training process. We compared the segmentation results of our model with five semi-supervised approaches on the public 2017 ACDC dataset and 2018 Prostate dataset. Our proposed method achieves better segmentation performance on both datasets under the same settings, demonstrating its effectiveness, robustness, and potential transferability to other medical image segmentation tasks. Keywords: Medical image segmentation, semi-supervised learning, self-training, uncertainty estimation

The information diffusion performance of GCN and its variant models is limited by the adjacency matrix, which can lower their performance. Therefore, we introduce a new framework for graph convolutional networks called Hybrid Diffusion-based Graph Convolutional Network (HD-GCN) to address the limitations of information diffusion caused by the adjacency matrix. In the HD-GCN framework, we initially utilize diffusion maps to facilitate the diffusion of information among nodes that are adjacent to each other in the feature space. This allows for the diffusion of information between similar points that may not have an adjacent relationship. Next, we utilize graph convolution to further propagate information among adjacent nodes after the diffusion maps, thereby enabling the spread of information among similar nodes that are adjacent in the graph. Finally, we employ the diffusion distances obtained through the use of diffusion maps to regularize and constrain the predicted labels of training nodes. This regularization method is then applied to the HD-GCN training, resulting in a smoother classification surface. The model proposed in this paper effectively overcomes the limitations of information diffusion imposed only by the adjacency matrix. HD-GCN utilizes hybrid diffusion by combining information diffusion between neighborhood nodes in the feature space and adjacent nodes in the adjacency matrix. This method allows for more comprehensive information propagation among nodes, resulting in improved model performance. We evaluated the performance of DM-GCN on three well-known citation network datasets and the results showed that the proposed framework is more effective than several graph-based semi-supervised learning methods., Comment: 16 pages, 4 figures

We demonstrate slow dynamics and constrained motion of domain walls in one-dimensional (1D) interacting bosons with double-well dispersion. In the symmetry-broken regime, the domain-wall motion is ``fractonlike'' -- a single domain wall cannot move freely, while two nearby domain walls can move collectively. Consequently, we find an Ohmic-like linear response and a vanishing superfluid stiffness, which are atypical for a Bose condensate in a 1D translation invariant closed quantum system. Near Lifshitz quantum critical point, we obtain superfluid stiffness $\rho_s\sim T$ and sound velocity $v_s\sim T^{1/2}$, showing similar unconventional low-temperature slow dynamics to the symmetry-broken regime. Particularly, the superfluid stiffness suggests an order by disorder effect as $\rho_s$ increases with temperature. Our results pave the way for studying fractons in ultracold atom experiments., Comment: 7+6 pages, 3+1 figures. Published version

LiDAR and camera fusion techniques are promising for achieving 3D object detection in autonomous driving. Most multi-modal 3D object detection frameworks integrate semantic knowledge from 2D images into 3D LiDAR point clouds to enhance detection accuracy. Nevertheless, the restricted resolution of 2D feature maps impedes accurate re-projection and often induces a pronounced boundary-blurring effect, which is primarily attributed to erroneous semantic segmentation. To well handle this limitation, we propose a general multi-modal fusion framework Multi-Sem Fusion (MSF) to fuse the semantic information from both the 2D image and 3D points scene parsing results. Specifically, we employ 2D/3D semantic segmentation methods to generate the parsing results for 2D images and 3D point clouds. The 2D semantic information is further reprojected into the 3D point clouds with calibration parameters. To handle the misalignment between the 2D and 3D parsing results, we propose an Adaptive Attention-based Fusion (AAF) module to fuse them by learning an adaptive fusion score. Then the point cloud with the fused semantic label is sent to the following 3D object detectors. Furthermore, we propose a Deep Feature Fusion (DFF) module to aggregate deep features at different levels to boost the final detection performance. The effectiveness of the framework has been verified on two public large-scale 3D object detection benchmarks by comparing them with different baselines. The experimental results show that the proposed fusion strategies can significantly improve the detection performance compared to the methods using only point clouds and the methods using only 2D semantic information. Most importantly, the proposed approach significantly outperforms other approaches and sets state-of-the-art results on the nuScenes testing benchmark.

We systematically study emergent Kondo lattice models from magic-angle twisted bilayer graphene using the topological heavy fermion representation. At the commensurate fillings, we demonstrate a series of symmetric strongly correlated metallic states driven by the hybridization between a triangular lattice of $SU(8)$ local moments and delocalized fermions. In particular, a (fragile) topological Dirac Kondo semimetal can be realized, providing a potential explanation for the symmetry-preserving correlated state at $\nu=0$. We further investigate the stability of the Dirac Kondo semimetal by constructing a quantum phase diagram showing the interplay between Kondo hybridization and magnetic correlation. The destruction of Kondo hybridization suggests that the magic-angle twisted bilayer graphene may be on the verge of a solid-state quantum simulator for novel magnetic orders on a triangular lattice. Experimental implications are also discussed., Comment: 6+10 pages, 3+4 figures. Published version

The intensely studied measurement-induced entanglement phase transition has become a hallmark of non-unitary quantum many-body dynamics. Usually, such a transition only shows up at the level of each individual quantum trajectory, and is absent for the density matrix averaged over measurement outcomes. In this work, we introduce a class of adaptive random circuit models with feedback that exhibit transitions in both settings. After each measurement, a unitary operation is either applied or not depending on the measurement outcome, which steers the averaged density matrix towards a unique state above a certain measurement threshold. Interestingly, the transition for the density matrix and the entanglement transition in the individual quantum trajectory in general happen at \textit{different} critical measurement rates. We demonstrate that the former transition belongs to the parity-conserving universality class by an explicit mapping to a classical branching-annihilating random walk process., Comment: 4.5 pages,6 figures; 5 pages of supplemental material. [v2] Figures compressed to reduce file size. [v3] Reference added

In 1936, Krull asked if the integral closure of a primary ideal is still primary. Fifty years later, Huneke partially answered this question by giving a primary polynomial ideal whose integral closure is not primary in a regular local ring of characteristic $p=2$. We provide counterexamples to Krull's question regarding polynomial rings with any characteristics. We also find that the Jacobian ideal $J$ of the polynomial $f = x^6 + y^6 + x^4 z t + z^3$ given by Brian\c{c}on and Speder in 1975 is a counterexample to Krull's question. Let $V_1$ be the hypersurface defined by $f = 0$ and $V_2$ be its singular locus. Brian\c{c}on and Speder proved that Whitney equisingularity does not imply Zariski equisingularity by showing that the pair $(V_1 \setminus V_2,\ V_2)$ satisfies Whitney's conditions around the origin but fails Zariski's equisingular conditions. We discover that the pair $(V_1 \setminus V_2,\ V_2)$ fails Whitney's conditions at the variety of the embedded prime of the integral closure $\bar{J}$, which means that $V_1$ is not Whitney regular along $V_2$. Moreover, we also show that Whitney stratification of this hypersurface is different from the stratification of isosingular sets given by Hauenstein and Wampler, which is related to Thom-Boardman singularity., Comment: 10 pages, 6 figures

In this paper, a probabilistic interpretation for the viscosity solution of a parabolic partial differential equation is obtained by virtue of the solution of a class of quadratic backward stochastic differential equations (BSDEs, for short). Furthermore, we prove the convergence and the large deviation principle for the solution of this class of quadratic BSDEs, which is associated with a family of Markov processes with the diffusion coefficients that tend to be zero.

Quantum many-body scar states are special eigenstates of nonintegrable models with distinctive entanglement features that give rise to infinitely long-lived coherent dynamics under quantum quenches from certain initial states. We elaborate on a construction of quantum many-body scar states in which they emerge from Einstein-Podolsky-Rosen (EPR) states in systems with two layers, wherein the two layers are maximally entangled. We apply this construction to spin systems as well as systems of itinerant fermions and bosons and demonstrate how symmetries can be harnessed to enhance its versatility. We show that several well-known examples of quantum many-body scars, including the tower of states in the spin-1 XY model and the $\eta$-pairing states in the Fermi-Hubbard model, can be understood within this formalism. We also demonstrate how an {\it infinite} tower of many-body scar states can emerge in bilayer Bose-Hubbard models with charge conservation., Comment: 19 pages, 8 figures