Automorphism Group of Certain Power Graphs of Finite Groups

The power graph $\mathcal{P}(G)$ of a group $G$ is the graphwith group elements as vertex set and two elements areadjacent if one is a power of the other. The aim of this paper is to compute the automorphism group of the power graph of several well-known and important classes of finite groups

Brain MR imaging segmentation using convolutional auto encoder network for PET attenuation correction

The final authenticated version is available online at https://doi.org/10.1007/978-3-030-55190-2_32© Springer Nature Switzerland AG 2021. Magnetic resonance (MR) image segmentation is one of the most robust MR based attenuation correction methods which have been adopted in clinical routine for positron emission tomography (PET) quantification. However, the segmentation of the brain into different tissue classes is a challenging process due to the similarity between bone and air signal intensity values. The aim of this work is to study the feasibility of deep learning to improve the brain segmentation with the application of data augmentation. A deep convolutional auto encoder network is applied to segment the brain into three tissue classes: air, soft tissue, and bone. The dice similarity coefficients of air, soft tissue, and bone tissues are 0.96 ± 0.01, 0.86 ± 0.02, and 0.63 ± 0.06 respectively. Despite the small datasets used in this work, the results are promising and show the feasibility of deep learning with data augmentation to perform accurate segmentation