In the group testing problem, the goal is to identify a subset of defective items within a larger set of items based on tests whose outcomes indicate whether any defective item is present. This problem is relevant in areas such as medical testing, DNA sequencing, and communications. In this paper, we study a doubly-regular design in which the number of tests-per-item and the number of items-per-test are fixed. We analyze the performance of this test design alongside the Definite Defectives (DD) decoding algorithm in several settings, namely, (i) the sub-linear regime$k=o(n)$with exact recovery, (ii) the linear regime$k=\Theta (n)$with approximate recovery, and (iii) the size-constrained setting, where the number of items per test is constrained. Under setting (i), we show that our design together with the DD algorithm, matches an existing achievability result for the DD algorithm with the near-constant tests-per-item design, which is known to be asymptotically optimal in broad scaling regimes. Under setting (ii), we provide novel approximate recovery bounds that complement a hardness result regarding exact recovery. Lastly, under setting (iii), we improve on the best known upper and lower bounds in scaling regimes where the maximum test size grows with the total number of items.

Recent research works have pointed out that the synthesized images by StyleGAN contain prominent circular artifacts which severely degrade the quality of generated images. In this work, we provide a systematic investigation on how those circular artifacts are formed by studying the functionalities of different modules that are used in the Style-GAN architecture. We present both analysis of the StyleGAN mechanism and extensive experiments to verify our claims. The key modules of StyleGAN that promote such undesired artifacts are highlighted based on the analysis. Besides, we propose a simple yet effective solution to remove the prominent circular artifacts for StyleGAN, by applying a simple but efficient pixel-instance normalization layer. The improved StyleGAN model trained via our proposed approach successfully prevents the appearance of circular artifacts in the generated images.