Bregman distances and Chebyshev sets

A closed set of a Euclidean space is said to be Chebyshev if every point in the space has one and only one closest point in the set. Although the situation is not settled in infinite-dimensional Hilbert spaces, in 1932 Bunt showed that in Euclidean spaces a closed set is Chebyshev if and only if the set is convex. In this paper, from the more general perspective of Bregman distances, we show that if every point in the space has a unique nearest point in a closed set, then the set is convex. We provide two approaches: one is by nonsmooth analysis; the other by maximal monotone operator theory. Subdifferentiability properties of Bregman nearest distance functions are also given

Adaptive Control of Space Robot Manipulators with Task Space Base on Neural Network

As are considered, the body posture is controlled and position cannot control, space manipulator system model is difficult to be set up because of disturbance and model uncertainty. An adaptive control strategy based on neural network is put forward. Neural network on-line modeling technology is used to approximate the system uncertain model, and the strategy avoids solving the inverse Jacobi matrix, neural network approximation error and external bounded disturbance are eliminated by variable structure control controller. Inverse dynamic model of the control strategy does not need to be estimated, also do not need to take the training process, globally asymptotically stable of the closed-loop system is proved based on the lyapunov theory. The simulation results show that the designed controller can achieve high control precision has the important value of engineering application

Federated Multi-View Synthesizing for Metaverse

The metaverse is expected to provide immersive entertainment, education, and business applications. However, virtual reality (VR) transmission over wireless networks is data- and computation-intensive, making it critical to introduce novel solutions that meet stringent quality-of-service requirements. With recent advances in edge intelligence and deep learning, we have developed a novel multi-view synthesizing framework that can efficiently provide computation, storage, and communication resources for wireless content delivery in the metaverse. We propose a three-dimensional (3D)-aware generative model that uses collections of single-view images. These single-view images are transmitted to a group of users with overlapping fields of view, which avoids massive content transmission compared to transmitting tiles or whole 3D models. We then present a federated learning approach to guarantee an efficient learning process. The training performance can be improved by characterizing the vertical and horizontal data samples with a large latent feature space, while low-latency communication can be achieved with a reduced number of transmitted parameters during federated learning. We also propose a federated transfer learning framework to enable fast domain adaptation to different target domains. Simulation results have demonstrated the effectiveness of our proposed federated multi-view synthesizing framework for VR content delivery

Optimal Policies for Selling New and Remanufactured Products

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/138248/1/poms12724.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/138248/2/poms12724-sup-0001-Supinfo.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/138248/3/poms12724_am.pd