Uniqueness of iterative positive solutions for the singular infinite-point p-Laplacian fractional differential system via sequential technique

By sequential techniques and mixed monotone operator, the uniqueness of positive solution for singular p-Laplacian fractional differential system with infinite-point boundary conditions is obtained. Green's function is derived, and some useful properties of Green' function are obtained. Based on these new properties, the existence of unique positive solutions is established, moreover, an iterative sequence and a convergence rate are given, which are important for practical application, and an example is given to demonstrate the validity of our main results

Existence of multiple positive solutions for a class of infinite-point singular p-Laplacian fractional differential equation with singular source terms

Based on properties of Green’s function and by Avery–Peterson fixed point theorem, the existence of multiple positive solutions are obtained for singular p-Laplacian fractional differential equation with infinite-point boundary conditions, and an example is given to demonstrate the validity of our main results

DoSTra: Discovering common behaviors of objects using the duration of staying on each location of trajectories

Since semantic trajectories can discover more semantic meanings of a user\u27s interests without geographic restrictions, research on semantic trajectories has attracted a lot of attentions in recent years. Most existing work discover the similar behavior of moving objects through analysis of their semantic trajectory pattern, that is, sequences of locations. However, this kind of trajectories without considering the duration of staying on a location limits wild applications. For example, Tom and Anne have a common pattern of Home→Restaurant → Company → Restaurant, but they are not similar, since Tom works at Restaurant, sends snack to someone at Company and return to Restaurant while Anne has breakfast at Restaurant, works at Company and has lunch at Restaurant. If we consider duration of staying on each location we can easily to differentiate their behaviors. In this paper, we propose a novel approach for discovering common behaviors by considering the duration of staying on each location of trajectories (DoSTra). Our approach can be used to detect the group that has similar lifestyle, habit or behavior patterns and predict the future locations of moving objects. We evaluate the experiment based on synthetic dataset, which demonstrates the high effectiveness and efficiency of the proposed method

PDPP:Projected Diffusion for Procedure Planning in Instructional Videos

In this paper, we study the problem of procedure planning in instructional videos, which aims to make goal-directed plans given the current visual observations in unstructured real-life videos. Previous works cast this problem as a sequence planning problem and leverage either heavy intermediate visual observations or natural language instructions as supervision, resulting in complex learning schemes and expensive annotation costs. In contrast, we treat this problem as a distribution fitting problem. In this sense, we model the whole intermediate action sequence distribution with a diffusion model (PDPP), and thus transform the planning problem to a sampling process from this distribution. In addition, we remove the expensive intermediate supervision, and simply use task labels from instructional videos as supervision instead. Our model is a U-Net based diffusion model, which directly samples action sequences from the learned distribution with the given start and end observations. Furthermore, we apply an efficient projection method to provide accurate conditional guides for our model during the learning and sampling process. Experiments on three datasets with different scales show that our PDPP model can achieve the state-of-the-art performance on multiple metrics, even without the task supervision. Code and trained models are available at https://github.com/MCG-NJU/PDPP.Comment: Accepted as a highlight paper at CVPR 202

StageInteractor: Query-based Object Detector with Cross-stage Interaction

Previous object detectors make predictions based on dense grid points or numerous preset anchors. Most of these detectors are trained with one-to-many label assignment strategies. On the contrary, recent query-based object detectors depend on a sparse set of learnable queries and a series of decoder layers. The one-to-one label assignment is independently applied on each layer for the deep supervision during training. Despite the great success of query-based object detection, however, this one-to-one label assignment strategy demands the detectors to have strong fine-grained discrimination and modeling capacity. To solve the above problems, in this paper, we propose a new query-based object detector with cross-stage interaction, coined as StageInteractor. During the forward propagation, we come up with an efficient way to improve this modeling ability by reusing dynamic operators with lightweight adapters. As for the label assignment, a cross-stage label assigner is applied subsequent to the one-to-one label assignment. With this assigner, the training target class labels are gathered across stages and then reallocated to proper predictions at each decoder layer. On MS COCO benchmark, our model improves the baseline by 2.2 AP, and achieves 44.8 AP with ResNet-50 as backbone, 100 queries and 12 training epochs. With longer training time and 300 queries, StageInteractor achieves 51.1 AP and 52.2 AP with ResNeXt-101-DCN and Swin-S, respectively

Memory-and-Anticipation Transformer for Online Action Understanding

Most existing forecasting systems are memory-based methods, which attempt to mimic human forecasting ability by employing various memory mechanisms and have progressed in temporal modeling for memory dependency. Nevertheless, an obvious weakness of this paradigm is that it can only model limited historical dependence and can not transcend the past. In this paper, we rethink the temporal dependence of event evolution and propose a novel memory-anticipation-based paradigm to model an entire temporal structure, including the past, present, and future. Based on this idea, we present Memory-and-Anticipation Transformer (MAT), a memory-anticipation-based approach, to address the online action detection and anticipation tasks. In addition, owing to the inherent superiority of MAT, it can process online action detection and anticipation tasks in a unified manner. The proposed MAT model is tested on four challenging benchmarks TVSeries, THUMOS'14, HDD, and EPIC-Kitchens-100, for online action detection and anticipation tasks, and it significantly outperforms all existing methods. Code is available at https://github.com/Echo0125/Memory-and-Anticipation-Transformer.Comment: ICCV 2023 Camera Read