Paley-Wiener Theorem for Probabilistic Frames

The Paley-Wiener Theorem is a classical result about the stability of basis in Banach spaces claiming that if a sequence is close to a basis, then this sequence is a basis. Similar results are also extended to frames in Hilbert spaces. As the extension of finite frames for $\mathbb{R}^d$, probabilistic frames are probability measures on $\mathbb{R}^d$ with finite second moments and the support of which span $\mathbb{R}^d$. This paper generalizes the Paley-Wiener theorem to the probabilistic frame setting. We claim that if a probability measure is close to a probabilistic frame, then this probability measure is also a probabilistic frame

Rediscover Climate Change during Global Warming Slowdown via Wasserstein Stability Analysis

Climate change is one of the key topics in climate science. However, previous research has predominantly concentrated on changes in mean values, and few research examines changes in Probability Distribution Function (PDF). In this study, a novel method called Wasserstein Stability Analysis (WSA) is developed to identify PDF changes, especially the extreme event shift and non-linear physical value constraint variation in climate change. WSA is applied to 21st-century warming slowdown period and is compared with traditional mean-value trend analysis. The result indicates that despite no significant trend, the central-eastern Pacific experienced a decline in hot extremes and an increase in cold extremes, indicating a La Nina-like temperature shift. Further analysis at two Arctic locations suggests sea ice severely restricts the hot extremes of surface air temperature. This impact is diminishing as sea ice melts. Overall, based on detecting PDF changes, WSA is a useful method for re-discovering climate change.Comment: 12 pages, 4 figures, and 1 Algorith

Joint Resources and Workflow Scheduling in UAV-Enabled Wirelessly-Powered MEC for IoT Systems

This paper considers a UAV-enabled mobile edge computing (MEC) system, where a UAV first powers the Internet of things device (IoTD) by utilizing Wireless Power Transfer (WPT) technology. Then each IoTD sends the collected data to the UAV for processing by using the energy harvested from the UAV. In order to improve the energy efficiency of the UAV, we propose a new time division multiple access (TDMA) based workflow model, which allows parallel transmissions and executions in the UAV-assisted system. We aim to minimize the total energy consumption of the UAV by jointly optimizing the IoTDs association, computing resources allocation, UAV hovering time, wireless powering duration and the services sequence of the IoTDs. The formulated problem is a mixed-integer non-convex problem, which is very difficult to solve in general. We transform and relax it into a convex problem and apply flow-shop scheduling techniques to address it. Furthermore, an alternative algorithm is developed to set the initial point closer to the optimal solution. Simulation results show that the total energy consumption of the UAV can be effectively reduced by the proposed scheme compared with the conventional systems

A Task Allocation Algorithm for Profit Maximization in NFC-RAN

In this paper, we study a general Near-Far Computing Enhanced C-RAN (NFC-RAN), in which users can offload the tasks to the near edge cloud (NEC) or the far edge cloud (FEC).We aim to propose a profit-aware task allocation model by maximizing the profit of the edge cloud operators. We first prove that this problem can be transformed to a Multiple-Choice Multi-Dimensional 0-1 Knapsack Problem (MMKP), which is NP-hard. Then, we solve it by using a low complexity heuristic algorithm. The simulation results show that the proposed algorithm achieves a good tradeoff between the performance and the complexity compared with the benchmark algorithm

Review helps learn better: Temporal Supervised Knowledge Distillation

Reviewing plays an important role when learning knowledge. The knowledge acquisition at a certain time point may be strongly inspired with the help of previous experience. Thus the knowledge growing procedure should show strong relationship along the temporal dimension. In our research, we find that during the network training, the evolution of feature map follows temporal sequence property. A proper temporal supervision may further improve the network training performance. Inspired by this observation, we propose Temporal Supervised Knowledge Distillation (TSKD). Specifically, we extract the spatiotemporal features in the different training phases of student by convolutional Long Short-term memory network (Conv-LSTM). Then, we train the student net through a dynamic target, rather than static teacher network features. This process realizes the refinement of old knowledge in student network, and utilizes it to assist current learning. Extensive experiments verify the effectiveness and advantages of our method over existing knowledge distillation methods, including various network architectures and different tasks (image classification and object detection) .Comment: Under review in AAAI 202