Fast Fourier Optimization: Sparsity Matters

Many interesting and fundamentally practical optimization problems, ranging from optics, to signal processing, to radar and acoustics, involve constraints on the Fourier transform of a function. It is well-known that the {\em fast Fourier transform} (fft) is a recursive algorithm that can dramatically improve the efficiency for computing the discrete Fourier transform. However, because it is recursive, it is difficult to embed into a linear optimization problem. In this paper, we explain the main idea behind the fast Fourier transform and show how to adapt it in such a manner as to make it encodable as constraints in an optimization problem. We demonstrate a real-world problem from the field of high-contrast imaging. On this problem, dramatic improvements are translated to an ability to solve problems with a much finer grid of discretized points. As we shall show, in general, the "fast Fourier" version of the optimization constraints produces a larger but sparser constraint matrix and therefore one can think of the fast Fourier transform as a method of sparsifying the constraints in an optimization problem, which is usually a good thing.Comment: 16 pages, 8 figure

Multidisciplinary team in cancer management

The multidisciplinary team (MDT) is defined as a group of people of different healthcare disciplines, which meets together at a given time to discuss a given patient; each of them is able to contribute independently to the diagnostic and treatment decision about the patient. In general, surgeon, radiologist and medical oncology dignify the core member of the team. The concept of MDT was formally introduced into UK practice during the 1990s. A major impetus was given by the publication of the Calman-Hine report in 1995 and the consequent drive to ensure that all patients with cancer, no matter where they might live, and to whom they might have been referred, would have equal access to a high and uniform standard of care. Theoretically, MDT working should ensure an effective coordination, the best quality as well as a good continuity of patient care by bringing together key professionals with all necessary knowledge, skills and experience. The recent institution of Virtual Multidisciplinary Teem (vMDT) has been introduced to resolve the economical and organisational problems of MDT. MDT work is widely accepted in many other countries, e.g. USA, Australia and some countries in Europe, all of which have comparable initiatives to those listed above. © 2014 Springer International Publishing Switzerland. All rights reserved