Class numbers of multinorm-one tori

We present a formula for the class number of a multinorm one torus $T_{L/k}$ associated to any \'etale algebra $L$ over a global field $k$. This is deduced from a formula for analogues of invariants introduced by T.~Ono, which are interpreted as a generalization of Gauss genus theory. This paper includes the variants of Ono's invariant for arbitrary $S$-ideal class numbers and the narrow version, generalizing results of Katayama, Morishita, Sasaki and Ono.Comment: 21 pages; comments welcom

NOMAD: Non-locking, stOchastic Multi-machine algorithm for Asynchronous and Decentralized matrix completion

We develop an efficient parallel distributed algorithm for matrix completion, named NOMAD (Non-locking, stOchastic Multi-machine algorithm for Asynchronous and Decentralized matrix completion). NOMAD is a decentralized algorithm with non-blocking communication between processors. One of the key features of NOMAD is that the ownership of a variable is asynchronously transferred between processors in a decentralized fashion. As a consequence it is a lock-free parallel algorithm. In spite of being an asynchronous algorithm, the variable updates of NOMAD are serializable, that is, there is an equivalent update ordering in a serial implementation. NOMAD outperforms synchronous algorithms which require explicit bulk synchronization after every iteration: our extensive empirical evaluation shows that not only does our algorithm perform well in distributed setting on commodity hardware, but also outperforms state-of-the-art algorithms on a HPC cluster both in multi-core and distributed memory settings

Camouflaged Image Synthesis Is All You Need to Boost Camouflaged Detection

Camouflaged objects that blend into natural scenes pose significant challenges for deep-learning models to detect and synthesize. While camouflaged object detection is a crucial task in computer vision with diverse real-world applications, this research topic has been constrained by limited data availability. We propose a framework for synthesizing camouflage data to enhance the detection of camouflaged objects in natural scenes. Our approach employs a generative model to produce realistic camouflage images, which can be used to train existing object detection models. Specifically, we use a camouflage environment generator supervised by a camouflage distribution classifier to synthesize the camouflage images, which are then fed into our generator to expand the dataset. Our framework outperforms the current state-of-the-art method on three datasets (COD10k, CAMO, and CHAMELEON), demonstrating its effectiveness in improving camouflaged object detection. This approach can serve as a plug-and-play data generation and augmentation module for existing camouflaged object detection tasks and provides a novel way to introduce more diversity and distributions into current camouflage datasets

Predictive Effects of the Quality of Online Peer-Feedback Provided and Received on Primary School Students' Quality of Question-Generation

[[abstract]]The research objectives of this study were to examine the individual and combined predictive effects of the quality of online peer-feedback provided and received on primary school students’ quality of question-generation. A correlational study was adopted, and performance data from 213 fifth-grade students engaged in online question-generation and peer assessment for six weeks were analysed using hierarchical multiple regression, with the dependent variable of scores on question-generation and independent variables of scores on peer-feedback provided and received. The results from the two-step hierarchical regression analysis indicated that the quality of peer-feedback provided and received, respectively, predicted students’ quality of question-generation. Furthermore, the results from the three-step hierarchical regression analysis showed that the quality of peer-feedback provided and received in combination also predicted students’ quality of question-generation. Details of the significance of this study are provided, as well as suggestions for instructional implementations.[[notice]]補正完