We show that Kirchhoff ’s law of conservation holds for non-commutative graph flows if and only if the graph is planar. We generalize the theory of (Euclidean) lattices to infinite dimension and... Show moreWe show that Kirchhoff ’s law of conservation holds for non-commutative graph flows if and only if the graph is planar. We generalize the theory of (Euclidean) lattices to infinite dimension and consider the ring of algebraic integers as such a lattice. We compute some invariants using capacity theory and obtain a partial solution to the (algorithmic) closest vector problem. We generalize the results on (universally) graded rings by Lenstra and Silverberg. We study the special case of group rings, and show that under similar assumptions rings can be uniquely decomposed into a group ring in a maximal way. We give a functorial algorithm to compute roots of fractional ideals of orders in number rings. Show less
A cogent and comprehensive pathologic report is essential for optimal patient management, cancer staging, and prognostication. This article details the International Collaboration on Cancer... Show moreA cogent and comprehensive pathologic report is essential for optimal patient management, cancer staging, and prognostication. This article details the International Collaboration on Cancer Reporting (ICCR) process and the development of the vulval carcinoma reporting data set. It describes the "core" and "noncore" elements to be included in pathology reports for vulval carcinoma, inclusive of clinical, macroscopic, microscopic, and ancillary testing considerations. It provides definitions and commentary for the evidence and/or consensus-based deliberations for each element included in the data set. The commentary also discusses controversial issues, such as p16/human papillomavirus testing, tumor grading and measurements, as well as elements that show promise and warrant further evidence-based study. A summary and discussion of the updated vulval cancer staging system by the International Federation of Obstetricians and Gynaecologists (FIGO) in 2021 is also provided. We hope the widespread implementation of this data set will facilitate consistent and accurate reporting, data collection, comparison of epidemiological and pathologic parameters between different populations, facilitate research, and serve as a platform to improve patient outcomes. Show less
