A New Discontinuous Galerkin Finite Element Method for Directly Solving the Hamilton-Jacobi Equations

In this paper, we improve upon the discontinuous Galerkin (DG) method for Hamilton-Jacobi (HJ) equation with convex Hamiltonians in (Y. Cheng and C.-W. Shu, J. Comput. Phys. 223:398-415,2007) and develop a new DG method for directly solving the general HJ equations. The new method avoids the reconstruction of the solution across elements by utilizing the Roe speed at the cell interface. Besides, we propose an entropy fix by adding penalty terms proportional to the jump of the normal derivative of the numerical solution. The particular form of the entropy fix was inspired by the Harten and Hyman's entropy fix (A. Harten and J. M. Hyman. J. Comput. Phys. 50(2):235-269, 1983) for Roe scheme for the conservation laws. The resulting scheme is compact, simple to implement even on unstructured meshes, and is demonstrated to work for nonconvex Hamiltonians. Benchmark numerical experiments in one dimension and two dimensions are provided to validate the performance of the method

Entrepreneurs’ Activities on Social Media and Venture Financing

Social media has been an incredible platform for startups to develop meaningful connections with stakeholders and customers. We investigate ways in which entrepreneurs use social media to drive both the level of engagement for their startup and the subsequent level of venture financing. Our empirical analysis demonstrates how differences in entrepreneurs’ tweets—i.e., differences in the level informativity, persuasiveness, and transformativity—is associated with different levels of startup engagement and venture financing. We show differences in entrepreneurs’ activity with the social media platform—i.e., the number of tweets, the number of mentions of other accounts, and the number of retweets—further drives engagement and venture financing. We test our model by collecting an extensive dataset of over 7,000,000 tweets from entrepreneurs and startups that have been through accelerators. Results indicate associates between the social media activities of entrepreneurs, startup engagement, and venture financing

Delving into Discrete Normalizing Flows on SO(3) Manifold for Probabilistic Rotation Modeling

Normalizing flows (NFs) provide a powerful tool to construct an expressive distribution by a sequence of trackable transformations of a base distribution and form a probabilistic model of underlying data. Rotation, as an important quantity in computer vision, graphics, and robotics, can exhibit many ambiguities when occlusion and symmetry occur and thus demands such probabilistic models. Though much progress has been made for NFs in Euclidean space, there are no effective normalizing flows without discontinuity or many-to-one mapping tailored for SO(3) manifold. Given the unique non-Euclidean properties of the rotation manifold, adapting the existing NFs to SO(3) manifold is non-trivial. In this paper, we propose a novel normalizing flow on SO(3) by combining a Mobius transformation-based coupling layer and a quaternion affine transformation. With our proposed rotation normalizing flows, one can not only effectively express arbitrary distributions on SO(3), but also conditionally build the target distribution given input observations. Extensive experiments show that our rotation normalizing flows significantly outperform the baselines on both unconditional and conditional tasks.Comment: CVPR 202

A discontinuous Galerkin solver for front propagation

International audienceWe propose a new discontinuous Galerkin (DG) method based on [Cheng and Shu, JCP, 2007] to solve a class of Hamilton-Jacobi equations that arises from optimal control problems. These equations are connected to front propagation problems or minimal time problems with non isotropic dynamics. Several numerical experiments show the relevance of our method, in particular for front propagation

Deep Reflection Prior

Reflections are very common phenomena in our daily photography, which distract people's attention from the scene behind the glass. The problem of removing reflection artifacts is important but challenging due to its ill-posed nature. Recent learning-based approaches have demonstrated a significant improvement in removing reflections. However, these methods are limited as they require a large number of synthetic reflection/clean image pairs for supervision, at the risk of overfitting in the synthetic image domain. In this paper, we propose a learning-based approach that captures the reflection statistical prior for single image reflection removal. Our algorithm is driven by optimizing the target with joint constraints enhanced between multiple input images during the training stage, but is able to eliminate reflections only from a single input for evaluation. Our framework allows to predict both background and reflection via a one-branch deep neural network, which is implemented by the controllable latent code that indicates either the background or reflection output. We demonstrate superior performance over the state-of-the-art methods on a large range of real-world images. We further provide insightful analysis behind the learned latent code, which may inspire more future work

Liver Tumor Screening and Diagnosis in CT with Pixel-Lesion-Patient Network

Liver tumor segmentation and classification are important tasks in computer aided diagnosis. We aim to address three problems: liver tumor screening and preliminary diagnosis in non-contrast computed tomography (CT), and differential diagnosis in dynamic contrast-enhanced CT. A novel framework named Pixel-Lesion-pAtient Network (PLAN) is proposed. It uses a mask transformer to jointly segment and classify each lesion with improved anchor queries and a foreground-enhanced sampling loss. It also has an image-wise classifier to effectively aggregate global information and predict patient-level diagnosis. A large-scale multi-phase dataset is collected containing 939 tumor patients and 810 normal subjects. 4010 tumor instances of eight types are extensively annotated. On the non-contrast tumor screening task, PLAN achieves 95% and 96% in patient-level sensitivity and specificity. On contrast-enhanced CT, our lesion-level detection precision, recall, and classification accuracy are 92%, 89%, and 86%, outperforming widely used CNN and transformers for lesion segmentation. We also conduct a reader study on a holdout set of 250 cases. PLAN is on par with a senior human radiologist, showing the clinical significance of our results.Comment: MICCAI 2023, code: https://github.com/alibaba-damo-academy/pixel-lesion-patient-networ

Cluster-Induced Mask Transformers for Effective Opportunistic Gastric Cancer Screening on Non-contrast CT Scans

Gastric cancer is the third leading cause of cancer-related mortality worldwide, but no guideline-recommended screening test exists. Existing methods can be invasive, expensive, and lack sensitivity to identify early-stage gastric cancer. In this study, we explore the feasibility of using a deep learning approach on non-contrast CT scans for gastric cancer detection. We propose a novel cluster-induced Mask Transformer that jointly segments the tumor and classifies abnormality in a multi-task manner. Our model incorporates learnable clusters that encode the texture and shape prototypes of gastric cancer, utilizing self- and cross-attention to interact with convolutional features. In our experiments, the proposed method achieves a sensitivity of 85.0% and specificity of 92.6% for detecting gastric tumors on a hold-out test set consisting of 100 patients with cancer and 148 normal. In comparison, two radiologists have an average sensitivity of 73.5% and specificity of 84.3%. We also obtain a specificity of 97.7% on an external test set with 903 normal cases. Our approach performs comparably to established state-of-the-art gastric cancer screening tools like blood testing and endoscopy, while also being more sensitive in detecting early-stage cancer. This demonstrates the potential of our approach as a novel, non-invasive, low-cost, and accurate method for opportunistic gastric cancer screening.Comment: MICCAI 202