Ran Wen | Search arXiv

arXiv2026

Idempotent-free non-solvable evolution algebras over $\mathbb{C}$

A recent conjecture states that a finite-dimensional complex evolution algebra is solvable if and only if it has no non-zero idempotents. We exhibit a three-dimensional counterexample over $\mathbb{C}$ whose isomorphism class already appears in the classification of three-dimensional complex evolution algebras. Since the conjecture is known in dimensions one and two, this counterexample has the smallest possible dimension. The algebra is defined over every field of characteristic different from $2$ and is the exceptional member of a one-parameter family of pairwise non-isomorphic non-solvable evolution algebras whose idempotents are determined explicitly. For the exceptional parameter, the derived series stabilises at a non-zero two-dimensional subalgebra whose only idempotent is zero. Direct sums with zero algebras give complex counterexamples in every dimension at least three. We also prove the conjectured equivalence whenever the stable term of the derived series is an evolution algebra.

math.RA↗

arXiv2019

Wider Channel Attention Network for Remote Sensing Image Super-resolution

Recently, deep convolutional neural networks (CNNs) have obtained promising results in image processing tasks including super-resolution (SR). However, most CNN-based SR methods treat low-resolution (LR) inputs and features equally across channels, rarely notice the loss of information flow caused by the activation function and fail to leverage the representation ability of CNNs. In this letter, we propose a novel single-image super-resolution (SISR) algorithm named Wider Channel Attention Network (WCAN) for remote sensing images. Firstly, the channel attention mechanism is used to adaptively recalibrate the importance of each channel at the middle of the wider attention block (WAB). Secondly, we propose the Local Memory Connection (LMC) to enhance the information flow. Finally, the features within each WAB are fused to take advantage of the network's representation capability and further improve information and gradient flow. Analytic experiments on a public remote sensing data set (UC Merced) show that our WCAN achieves better accuracy and visual improvements against most state-of-the-art methods.

cs.CV↗