Viscosity approximation methods for nonexpansive mappings and monotone mappings

AbstractViscosity approximation methods for nonexpansive mappings are studied. Consider the iteration process {xn}, where x0∈C is arbitrary and xn+1=αnf(xn)+(1−αn)SPC(xn−λnAxn), f is a contraction on C, S is a nonexpansive self-mapping of a closed convex subset C of a Hilbert space H. It is shown that {xn} converges strongly to a common element of the set of fixed points of nonexpansive mapping and the set of solutions of the variational inequality for an inverse strongly-monotone mapping which solves some variational inequality

Finite-time stability and stabilization of nonlinear stochastic hybrid systems

AbstractThis paper deals with the problem of finite-time stability and stabilization of nonlinear Markovian switching stochastic systems which exist impulses at the switching instants. Using multiple Lyapunov function theory, a sufficient condition is established for finite-time stability of the underlying systems. Furthermore, based on the state partition of continuous parts of systems, a feedback controller is designed such that the corresponding impulsive stochastic closed-loop systems are finite-time stochastically stable. A numerical example is presented to illustrate the effectiveness of the proposed method

Demystifying Dependency Bugs in Deep Learning Stack

Deep learning (DL) applications, built upon a heterogeneous and complex DL stack (e.g., Nvidia GPU, Linux, CUDA driver, Python runtime, and TensorFlow), are subject to software and hardware dependencies across the DL stack. One challenge in dependency management across the entire engineering lifecycle is posed by the asynchronous and radical evolution and the complex version constraints among dependencies. Developers may introduce dependency bugs (DBs) in selecting, using and maintaining dependencies. However, the characteristics of DBs in DL stack is still under-investigated, hindering practical solutions to dependency management in DL stack. To bridge this gap, this paper presents the first comprehensive study to characterize symptoms, root causes and fix patterns of DBs across the whole DL stack with 446 DBs collected from StackOverflow posts and GitHub issues. For each DB, we first investigate the symptom as well as the lifecycle stage and dependency where the symptom is exposed. Then, we analyze the root cause as well as the lifecycle stage and dependency where the root cause is introduced. Finally, we explore the fix pattern and the knowledge sources that are used to fix it. Our findings from this study shed light on practical implications on dependency management

Content, Composition, and Biosynthesis of Anthocyanin in Fragaria Species: A Review

Anthocyanins are responsible for fruit coloration and are beneficial to human health. The fruits of cultivated strawberry (Fragaria ×ananassa) varieties are colorful, a trait that attracts consumers. The fruits of wild Fragaria species, close relatives of the cultivated strawberry, vary in color. In this review, we describe the content and composition of anthocyanins in cultivated and wild strawberry varieties. We also explore the biosynthetic pathway of anthocyanins, including their transcriptional regulation mechanisms. Additionally, we discuss the effect of environmental factors on anthocyanin accumulation. This review will inform further studies toward developing anthocyanin-rich strawberries via environmental control and exogenous application of compounds

Optical Orbital Angular Momentum Demultiplexing and Channel Equalization by Using Equalizing Dammann Vortex Grating

A novel equalizing Dammann vortex grating (EDVG) is proposed as orbital angular momentum (OAM) multiplexer to realize OAM signal demultiplexing and channel equalization. The EDVG is designed by suppressing odd diffraction orders and adjusting the grating structure. The light intensity of diffraction is subsequently distributed evenly in the diffraction orders, and the total diffraction efficiency can be improved from 53.22% to 82%. By using the EDVG, OAM demultiplexing and channel equalization can be realized. Numerical simulation shows that the bit error rate (BER) of each OAM channel can decrease to 10-4 when the bit SNR is 22 dB, and the intensity is distributed over the necessary order of diffraction evenly

ARU2-Net: A Deep Learning Approach for Global-Scale Oceanic Eddy Detection

Ocean eddies have a significant impact on marine ecosystems and the climate because they transport essential substances in the ocean. Detection of ocean eddies has become one of the most active topics in physical ocean research. In recent years, research based on deep learning has mainly focused on regional oceans, with small and specific data and relatively general detection results. This study processes the global eddy by pixel-by-pixel classification and generates a global eddy classification map with a resolution of 720 × 1440, which expands the data volume and improves the generality of the data. Moreover, a high-precision attention residual U 2 -Net model, referred to as ARU 2 -Net, is proposed, which is suitable for mining eddy surface features from sea level anomaly (SLA) and sea surface temperature (SST) data in the global ocean. ARU 2 -Net integrates the convolutional block attention module (CBAM). The channel attention of the CBAM module is used to learn the correlation features between the SST and SLA dual channels; the spatial attention mechanism of the CBAM module is used to learn the importance of the spatial location of the eddy, focusing on the locally important regions, which further improves the detection ability of ARU 2 -Net for eddies, and helps ARU 2 -Net to better identify the eddy categories. Finally, we demonstrate the effectiveness of our approach on the global eddy dataset, achieving a test performance of 94.926%, significantly exceeding previous detection in some areas