On the Free Boundary Problems for the Ideal Incompressible MHD Equations

We investigate the general plasma-vacuum interface problems for the ideal incompressible MHD equations with or without surface tension and prove their nonlinear local well-posedness in standard Sobolev spaces under either non-zero surface tension or the stability condition that the magnetic fields are everywhere non-collinear on the interface. In particular, the results show that both capillary forces and tangential magnetic fields can stabilize the motion of the plasma-vacuum interfaces. Moreover, the vanishing surface tension limit results are established under the Rayleigh-Taylor sign condition or the non-collinearity condition. All these results hold with no graph assumption on the free interface.Comment: arXiv admin note: text overlap with arXiv:2309.0353

Local Well-posedness of the Incompressible Current-Vortex Sheet Problems

We prove the local well-posedness of the incompressible current-vortex sheet problems in standard Sobolev spaces under the surface tension or the Syrovatskij condition, which shows that both capillary forces and large tangential magnetic fields can stabilize the motion of current-vortex sheets. Furthermore, under the Syrovatskij condition, the vanishing surface tension limit is established for the motion of current-vortex sheets. These results hold without assuming the interface separating the two plasmas being a graph

Plug-and-Play Methods Provably Converge with Properly Trained Denoisers

Plug-and-play (PnP) is a non-convex framework that integrates modern denoising priors, such as BM3D or deep learning-based denoisers, into ADMM or other proximal algorithms. An advantage of PnP is that one can use pre-trained denoisers when there is not sufficient data for end-to-end training. Although PnP has been recently studied extensively with great empirical success, theoretical analysis addressing even the most basic question of convergence has been insufficient. In this paper, we theoretically establish convergence of PnP-FBS and PnP-ADMM, without using diminishing stepsizes, under a certain Lipschitz condition on the denoisers. We then propose real spectral normalization, a technique for training deep learning-based denoisers to satisfy the proposed Lipschitz condition. Finally, we present experimental results validating the theory.Comment: Published in the International Conference on Machine Learning, 201

Measurement Axis Searching Model for Terrestrial Laser Scans Registration

Nowadays, terrestrial Lidar scans can cover rather a large area; the point densities are strongly varied because of the line-of-sight measurement principle in potential overlaps with scans taken from different viewpoints. Most of the traditional methods focus on registration algorithm and ignore searching model. Sometimes the traditional methods are directly used to align two point clouds; a large critically unsolved problem of the large biases will be created in areas distant from the overlaps while the local overlaps are often aligned well. So a novel measurement axis searching model (MASM) has been proposed in this paper. The method includes four steps: (1) the principal axis fitting, (2) the measurement axis generation, (3) low-high-precision search, and (4) result generation. The principal axis gives an orientation to the point cloud; the search scope is limited by the measurement axis. The point cloud orientation can be adjusted gradually until the achievement of the global optimum using low- and high-precision search. We perform some experiments with simulated point clouds and real terrestrial laser scans. The results of simulated point clouds have shown the processing steps of our method, and the results of real terrestrial laser scans have shown the sensitivity of the approach with respect to the indoor and outdoor scenes

Dynamic Causal Disentanglement Model for Dialogue Emotion Detection

Emotion detection is a critical technology extensively employed in diverse fields. While the incorporation of commonsense knowledge has proven beneficial for existing emotion detection methods, dialogue-based emotion detection encounters numerous difficulties and challenges due to human agency and the variability of dialogue content.In dialogues, human emotions tend to accumulate in bursts. However, they are often implicitly expressed. This implies that many genuine emotions remain concealed within a plethora of unrelated words and dialogues.In this paper, we propose a Dynamic Causal Disentanglement Model based on hidden variable separation, which is founded on the separation of hidden variables. This model effectively decomposes the content of dialogues and investigates the temporal accumulation of emotions, thereby enabling more precise emotion recognition. First, we introduce a novel Causal Directed Acyclic Graph (DAG) to establish the correlation between hidden emotional information and other observed elements. Subsequently, our approach utilizes pre-extracted personal attributes and utterance topics as guiding factors for the distribution of hidden variables, aiming to separate irrelevant ones. Specifically, we propose a dynamic temporal disentanglement model to infer the propagation of utterances and hidden variables, enabling the accumulation of emotion-related information throughout the conversation. To guide this disentanglement process, we leverage the ChatGPT-4.0 and LSTM networks to extract utterance topics and personal attributes as observed information.Finally, we test our approach on two popular datasets in dialogue emotion detection and relevant experimental results verified the model's superiority

Implicit Diffusion Models for Continuous Super-Resolution

Image super-resolution (SR) has attracted increasing attention due to its wide applications. However, current SR methods generally suffer from over-smoothing and artifacts, and most work only with fixed magnifications. This paper introduces an Implicit Diffusion Model (IDM) for high-fidelity continuous image super-resolution. IDM integrates an implicit neural representation and a denoising diffusion model in a unified end-to-end framework, where the implicit neural representation is adopted in the decoding process to learn continuous-resolution representation. Furthermore, we design a scale-controllable conditioning mechanism that consists of a low-resolution (LR) conditioning network and a scaling factor. The scaling factor regulates the resolution and accordingly modulates the proportion of the LR information and generated features in the final output, which enables the model to accommodate the continuous-resolution requirement. Extensive experiments validate the effectiveness of our IDM and demonstrate its superior performance over prior arts.Comment: 8 pages, 9 figures, published to CVPR202

IPDreamer: Appearance-Controllable 3D Object Generation with Image Prompts

Recent advances in text-to-3D generation have been remarkable, with methods such as DreamFusion leveraging large-scale text-to-image diffusion-based models to supervise 3D generation. These methods, including the variational score distillation proposed by ProlificDreamer, enable the synthesis of detailed and photorealistic textured meshes. However, the appearance of 3D objects generated by these methods is often random and uncontrollable, posing a challenge in achieving appearance-controllable 3D objects. To address this challenge, we introduce IPDreamer, a novel approach that incorporates image prompts to provide specific and comprehensive appearance information for 3D object generation. Our results demonstrate that IPDreamer effectively generates high-quality 3D objects that are consistent with both the provided text and image prompts, demonstrating its promising capability in appearance-controllable 3D object generation.Comment: 11 pages, 7 figure