David M. Jackson

  • Dynamic contrast-enhanced MRI is now established as the methodology of choice for the assessment of tumor microcirculation in vivo. This is assisting clinical practitioners in the management of patients with solid tumors and is finding prominence in the assessment of tumor treatments, including anti-angiogenics, chemotherapy, and radiotherapy. In this book, targeted at both clinical practitioners and basic scientists, the principles of the methods, their practical implementation, and their application to specific tumor types are discussed by the leading authorities in the field today. The book will serve as an invaluable single-volume reference covering all the latest developments in contrast-enhanced oncological MRI.

  • This book provides an accessible introduction to knot theory, focussing on Vassiliev invariants, quantum knot invariants constructed via representations of quantum groups, and how these two apparently distinct theories come together through the Kontsevich invariant. Consisting of four parts, the book opens with an introduction to the fundamentals of knot theory, and to knot invariants such as the Jones polynomial. The second part introduces quantum invariants of knots, working constructively from first principles towards the construction of Reshetikhin-Turaev invariants and a description of how these arise through Drinfeld and Jimbo's quantum groups. Its third part offers an introduction to Vassiliev invariants, providing a careful account of how chord diagrams and Jacobi diagrams arise in the theory, and the role that Lie algebras play. The final part of the book introduces the Konstevich invariant. This is a universal quantum invariant and a universal Vassiliev invariant, and brings together these two seemingly different families of knot invariants. The book provides a detailed account of the construction of the Jones polynomial via the quantum groups attached to sl(2), the Vassiliev weight system arising from sl(2), and how these invariants come together through the Kontsevich invariant.