Colloidal transport through optical tweezer arrays

Viscously damped particles driven past an evenly spaced array of potential energy wells or barriers may become kinetically locked in to the array, or else may escape from the array. The transition between locked-in and free-running states has been predicted to depend sensitively on the ratio between the particles' size and the separation between wells. This prediction is confirmed by measurements on monodisperse colloidal spheres driven through arrays of holographic optical traps.Comment: 4 pages, 4 figure

Point cloud discretization of Fokker-Planck operators for committor functions

The committor functions provide useful information to the understanding of transitions of a stochastic system between disjoint regions in phase space. In this work, we develop a point cloud discretization for Fokker-Planck operators to numerically calculate the committor function, with the assumption that the transition occurs on an intrinsically low-dimensional manifold in the ambient potentially high dimensional configurational space of the stochastic system. Numerical examples on model systems validate the effectiveness of the proposed method.Comment: 17 pages, 11 figure

Adversarial Training for Physics-Informed Neural Networks

Physics-informed neural networks have shown great promise in solving partial differential equations. However, due to insufficient robustness, vanilla PINNs often face challenges when solving complex PDEs, especially those involving multi-scale behaviors or solutions with sharp or oscillatory characteristics. To address these issues, based on the projected gradient descent adversarial attack, we proposed an adversarial training strategy for PINNs termed by AT-PINNs. AT-PINNs enhance the robustness of PINNs by fine-tuning the model with adversarial samples, which can accurately identify model failure locations and drive the model to focus on those regions during training. AT-PINNs can also perform inference with temporal causality by selecting the initial collocation points around temporal initial values. We implement AT-PINNs to the elliptic equation with multi-scale coefficients, Poisson equation with multi-peak solutions, Burgers equation with sharp solutions and the Allen-Cahn equation. The results demonstrate that AT-PINNs can effectively locate and reduce failure regions. Moreover, AT-PINNs are suitable for solving complex PDEs, since locating failure regions through adversarial attacks is independent of the size of failure regions or the complexity of the distribution

Implicit Anatomical Rendering for Medical Image Segmentation with Stochastic Experts

Integrating high-level semantically correlated contents and low-level anatomical features is of central importance in medical image segmentation. Towards this end, recent deep learning-based medical segmentation methods have shown great promise in better modeling such information. However, convolution operators for medical segmentation typically operate on regular grids, which inherently blur the high-frequency regions, i.e., boundary regions. In this work, we propose MORSE, a generic implicit neural rendering framework designed at an anatomical level to assist learning in medical image segmentation. Our method is motivated by the fact that implicit neural representation has been shown to be more effective in fitting complex signals and solving computer graphics problems than discrete grid-based representation. The core of our approach is to formulate medical image segmentation as a rendering problem in an end-to-end manner. Specifically, we continuously align the coarse segmentation prediction with the ambiguous coordinate-based point representations and aggregate these features to adaptively refine the boundary region. To parallelly optimize multi-scale pixel-level features, we leverage the idea from Mixture-of-Expert (MoE) to design and train our MORSE with a stochastic gating mechanism. Our experiments demonstrate that MORSE can work well with different medical segmentation backbones, consistently achieving competitive performance improvements in both 2D and 3D supervised medical segmentation methods. We also theoretically analyze the superiority of MORSE.Comment: Accepted at International Conference on Medical Image Computing and Computer-Assisted Intervention (MICCAI 2023

Self-positioning Point-based Transformer for Point Cloud Understanding

Transformers have shown superior performance on various computer vision tasks with their capabilities to capture long-range dependencies. Despite the success, it is challenging to directly apply Transformers on point clouds due to their quadratic cost in the number of points. In this paper, we present a Self-Positioning point-based Transformer (SPoTr), which is designed to capture both local and global shape contexts with reduced complexity. Specifically, this architecture consists of local self-attention and self-positioning point-based global cross-attention. The self-positioning points, adaptively located based on the input shape, consider both spatial and semantic information with disentangled attention to improve expressive power. With the self-positioning points, we propose a novel global cross-attention mechanism for point clouds, which improves the scalability of global self-attention by allowing the attention module to compute attention weights with only a small set of self-positioning points. Experiments show the effectiveness of SPoTr on three point cloud tasks such as shape classification, part segmentation, and scene segmentation. In particular, our proposed model achieves an accuracy gain of 2.6% over the previous best models on shape classification with ScanObjectNN. We also provide qualitative analyses to demonstrate the interpretability of self-positioning points. The code of SPoTr is available at https://github.com/mlvlab/SPoTr.Comment: Accepted paper at CVPR 202

Dual-Neighborhood Deep Fusion Network for Point Cloud Analysis

Recently, deep neural networks have made remarkable achievements in 3D point cloud classification. However, existing classification methods are mainly implemented on idealized point clouds and suffer heavy degradation of per-formance on non-idealized scenarios. To handle this prob-lem, a feature representation learning method, named Dual-Neighborhood Deep Fusion Network (DNDFN), is proposed to serve as an improved point cloud encoder for the task of non-idealized point cloud classification. DNDFN utilizes a trainable neighborhood learning method called TN-Learning to capture the global key neighborhood. Then, the global neighborhood is fused with the local neighbor-hood to help the network achieve more powerful reasoning ability. Besides, an Information Transfer Convolution (IT-Conv) is proposed for DNDFN to learn the edge infor-mation between point-pairs and benefits the feature transfer procedure. The transmission of information in IT-Conv is similar to the propagation of information in the graph which makes DNDFN closer to the human reasoning mode. Extensive experiments on existing benchmarks especially non-idealized datasets verify the effectiveness of DNDFN and DNDFN achieves the state of the arts.Comment: ICMEW202

Adaptive Channel Encoding Transformer for Point Cloud Analysis

Transformer plays an increasingly important role in various computer vision areas and remarkable achievements have also been made in point cloud analysis. Since they mainly focus on point-wise transformer, an adaptive channel encoding transformer is proposed in this paper. Specifically, a channel convolution called Transformer-Conv is designed to encode the channel. It can encode feature channels by capturing the potential relationship between coordinates and features. Compared with simply assigning attention weight to each channel, our method aims to encode the channel adaptively. In addition, our network adopts the neighborhood search method of low-level and high-level dual semantic receptive fields to improve the performance. Extensive experiments show that our method is superior to state-of-the-art point cloud classification and segmentation methods on three benchmark datasets.Comment: ICANN202

Revisiting Event Horizon Finders

Event horizons are the defining physical features of black hole spacetimes, and are of considerable interest in studying black hole dynamics. Here, we reconsider three techniques to localise event horizons in numerical spacetimes: integrating geodesics, integrating a surface, and integrating a level-set of surfaces over a volume. We implement the first two techniques and find that straightforward integration of geodesics backward in time to be most robust. We find that the exponential rate of approach of a null surface towards the event horizon of a spinning black hole equals the surface gravity of the black hole. In head-on mergers we are able to track quasi-normal ringing of the merged black hole through seven oscillations, covering a dynamic range of about 10^5. Both at late times (when the final black hole has settled down) and at early times (before the merger), the apparent horizon is found to be an excellent approximation of the event horizon. In the head-on binary black hole merger, only {\em some} of the future null generators of the horizon are found to start from past null infinity; the others approach the event horizons of the individual black holes at times far before merger.Comment: 30 pages, 15 figures, revision