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We study spinning particle/defect geometries in the context of AdS$_3$/CFT$_2$. These solutions lie below the BTZ threshold, and can be obtained from identifications of AdS$_3$. We construct the Feynman propagator by solving the bulk equation of motion in the spinning particle geometry, summing over the modes of the fields and passing to the boundary. The quantization of the scalar fields becomes challenging when confined to the regions that are causally well-behaved. If the region containing closed timelike curves (CTCs) is included, the normalization of the scalar fields enjoys an analytical simplification and the propagator can be expressed as an infinite sum over image geodesics. In the dual CFT$_2$, the propagator can be recast as the HHLL four-point function, where by taking into account the $PSL (2,\mathbb{Z})$ modular images, we recover the bulk computation. We comment on the casual behavior of bulk geometries associated with single-trace operators of spin scaling with the central charge below the BTZ threshold., Comment: 24 pages, 1 figure; comments welcome! v2: 26 pages, 2 figures, improved various discussions, added references, corrected minor typos v3: clarifications regarding boundary conditions added

In this paper we are concerned with restricted additive Schwarz with local impedance transformation conditions for a family of Helmholtz problems in two dimensions. These problems are discretized by the finite element method with conforming nodal finite elements. We design and analyze a new adaptive coarse space for this kind of restricted additive Schwarz method. This coarse space is spanned by some eigenvalue functions of local generalized eigenvalue problems, which are defined by weighted positive semi-definite bilinear forms on subspaces consisting of local discrete Helmholtz-harmonic functions from impedance boundary data. We proved that a two-level hybrid Schwarz preconditioner with the proposed coarse space possesses uniformly convergence independent of the mesh size, the subdomain size and the wave numbers under suitable assumptions. We also introduce an economic coarse space to avoid solving generalized eigenvalue problems. Numerical experiments confirm the theoretical results.

Multi-scale features are essential for dense prediction tasks, such as object detection, instance segmentation, and semantic segmentation. The prevailing methods usually utilize a classification backbone to extract multi-scale features and then fuse these features using a lightweight module (e.g., the fusion module in FPN and BiFPN, two typical object detection methods). However, as these methods allocate most computational resources to the classification backbone, the multi-scale feature fusion in these methods is delayed, which may lead to inadequate feature fusion. While some methods perform feature fusion from early stages, they either fail to fully leverage high-level features to guide low-level feature learning or have complex structures, resulting in sub-optimal performance. We propose a streamlined cascade encoder-decoder network, dubbed CEDNet, tailored for dense \mbox{prediction} tasks. All stages in CEDNet share the same encoder-decoder structure and perform multi-scale feature fusion within the decoder. A hallmark of CEDNet is its ability to incorporate high-level features from early stages to guide low-level feature learning in subsequent stages, thereby enhancing the effectiveness of multi-scale feature fusion. We explored three well-known encoder-decoder structures: Hourglass, UNet, and FPN. When integrated into CEDNet, they performed much better than traditional methods that use a pre-designed classification backbone combined with a lightweight fusion module. Extensive experiments on object detection, instance segmentation, and semantic segmentation demonstrated the effectiveness of our method. The code is available at https://github.com/zhanggang001/CEDNet., Comment: Technical report; Code: https://github.com/zhanggang001/CEDNet

The goal of this paper is to extract the visual-language correspondence from a pre-trained text-to-image diffusion model, in the form of segmentation map, i.e., simultaneously generating images and segmentation masks for the corresponding visual entities described in the text prompt. We make the following contributions: (i) we pair the existing Stable Diffusion model with a novel grounding module, that can be trained to align the visual and textual embedding space of the diffusion model with only a small number of object categories; (ii) we establish an automatic pipeline for constructing a dataset, that consists of {image, segmentation mask, text prompt} triplets, to train the proposed grounding module; (iii) we evaluate the performance of open-vocabulary grounding on images generated from the text-to-image diffusion model and show that the module can well segment the objects of categories beyond seen ones at training time; (iv) we adopt the augmented diffusion model to build a synthetic semantic segmentation dataset, and show that, training a standard segmentation model on such dataset demonstrates competitive performance on the zero-shot segmentation(ZS3) benchmark, which opens up new opportunities for adopting the powerful diffusion model for discriminative tasks.

\emph{Noisy trapdoor claw-free function} (NTCF) as a powerful post-quantum cryptographic tool can efficiently constrain actions of untrusted quantum devices. However, the original NTCF is essentially \emph{2-to-1} one-way function (NTCF$^1_2$). In this work, we attempt to further extend the NTCF$^1_2$ to achieve \emph{many-to-one} trapdoor claw-free functions with polynomial bounded preimage size. Specifically, we focus on a significant extrapolation of NTCF$^1_2$ by drawing on extrapolated dihedral cosets, thereby giving a model of NTCF$^1_{\kappa}$ where $\kappa$ is a polynomial integer. Then, we present an efficient construction of NTCF$^1_{\kappa}$ assuming \emph{quantum hardness of the learning with errors (LWE)} problem. We point out that NTCF can be used to bridge the LWE and the dihedral coset problem (DCP). By leveraging NTCF$^1_2$ (resp. NTCF$^1_{\kappa}$), our work reveals a new quantum reduction path from the LWE problem to the DCP (resp. extrapolated DCP). Finally, we demonstrate the NTCF$^1_{\kappa}$ can naturally be reduced to the NTCF$^1_2$, thereby achieving the same application for proving the quantumness., Comment: 34 pages, 7 figures

Existing models on super-resolution often specialized for one scale, fundamentally limiting their use in practical scenarios. In this paper, we aim to develop a general plugin that can be inserted into existing super-resolution models, conveniently augmenting their ability towards Arbitrary Resolution Image Scaling, thus termed ARIS. We make the following contributions: (i) we propose a transformer-based plugin module, which uses spatial coordinates as query, iteratively attend the low-resolution image feature through cross-attention, and output visual feature for the queried spatial location, resembling an implicit representation for images; (ii) we introduce a novel self-supervised training scheme, that exploits consistency constraints to effectively augment the model's ability for upsampling images towards unseen scales, i.e. ground-truth high-resolution images are not available; (iii) without loss of generality, we inject the proposed ARIS plugin module into several existing models, namely, IPT, SwinIR, and HAT, showing that the resulting models can not only maintain their original performance on fixed scale factor but also extrapolate to unseen scales, substantially outperforming existing any-scale super-resolution models on standard benchmarks, e.g. Urban100, DIV2K, etc.

We study the Feynman propagator of free scalar fields in $AdS_3$ with a conical defect. The propagator is built by solving the bulk equation of motion, summing over the modes of the field, and taking the boundary limit. We then perform several consistency checks. In the dual CFT, the operator responsible for the defect creates a highly excited state. We consider the exchange of the Virasoro identity block in the heavy-light limit to obtain an expression for the propagator sensitive to the mass of the defect. In $AdS_3/\mathbb{Z}_n$, we treat the propagator by the method of images and in the geodesic approximation. More generally, we argue that long-range correlations of the scalar are suppressed as the defect becomes more massive: we find a continuous phase transition in the correlator at the BTZ threshold and examine its critical behavior. Finally, we apply our results to holographic entanglement entropy using an analogy between our scalars and replica twist fields., Comment: 33 pages, 5 figures, JHEP style. v2: Section 4 was rewritten: an error was corrected that arose from using an approximation that did not apply. The crossing relations are now verified to all orders and do not present a puzzle any longer. The conclusions are updated based on the new calculations. Figures and references added. v3: Number of typos reduced. Supersedes the published version