Sylow's theorem for Moufang loops

For finite Moufang loops, we prove an analog of the first Sylow theorem giving a criterion of the existence of a p-Sylow subloop. We also find the maximal order of p-subloops in the Moufang loops that do not possess p-Sylow subloops.Comment: 21 page

Using diffusion MRI to discriminate areas of cortical grey matter

Cortical area parcellation is a challenging problem that is often approached by combining structural imaging (e.g., quantitative T1, diffusion-based connectivity) with functional imaging (e.g., task activations, topological mapping, resting state correlations). Diffusion MRI (dMRI) has been widely adopted to analyse white matter microstructure, but scarcely used to distinguish grey matter regions because of the reduced anisotropy there. Nevertheless, differences in the texture of the cortical 'fabric' have long been mapped by histologists to distinguish cortical areas. Reliable area-specific contrast in the dMRI signal has previously been demonstrated in selected occipital and sensorimotor areas. We expand upon these findings by testing several diffusion-based feature sets in a series of classification tasks. Using Human Connectome Project (HCP) 3T datasets and a supervised learning approach, we demonstrate that diffusion MRI is sensitive to architectonic differences between a large number of different cortical areas defined in the HCP parcellation. By employing a surface-based cortical imaging pipeline, which defines diffusion features relative to local cortical surface orientation, we show that we can differentiate areas from their neighbours with higher accuracy than when using only fractional anisotropy or mean diffusivity. The results suggest that grey matter diffusion may provide a new, independent source of information for dividing up the cortex

A Web-Based Flexible Communication System in Radiology

A web-based system for rapid multidirectional communication has been created in the Radiology department at San Francisco General Hospital. The system allows messaging among radiology attendings, residents, and technologists, as well as other members of the hospital community, such as Emergency Department physicians and nurses. Instead of being tied to a particular workflow, this system provides a flexible communication infrastructure which can be easily adapted for different functions and user roles. The system has so far been configured to successfully support the standard “wet reading” workflow, to support marking and tracking of critical results, as well as multiple educational and quality improvement workflows. In the 19 months of operation, the system has gained over 1,800 users (virtually all providers at our institution), it has been accessed by radiologists over 39,000 times and by non-radiologists over 34,000 times. It has become an integral part of the radiology department operations and non-radiology clinical workflows. Unlike most existing softwares, our system is not a task-specific application, but a multipurpose communication system. It is able to effectively accommodate multiple workflows and user roles through configuration (without additional programming). This flexibility has helped this system to be rapidly and widely adopted within our enterprise. The extended reach of the system enables improved monitoring and documentation of workflows, helping with management decision making, and quality assurance. We report a successful radiology communication system based on the principles of flexibility and inclusiveness of users inside and outside the radiology department