Real-time image-guided treatment of mobile tumors in proton therapy by a library of treatment plans: a simulation study.

Purpose: To improve target coverage and reduce the dose in the surrounding organs-at-risks (OARs), we developed an image-guided treatment method based on a precomputed library of treatment plans controlled and delivered in real-time.

Methods: A library of treatment plans is constructed by optimizing a plan for each breathing phase of a four dimensional computed tomography (4DCT). Treatments are delivered by simulation on a continuous sequence of synthetic computed tomographies (CTs) generated from real magnetic resonance imaging (MRI) sequences.

Extended Formulations for Order Polytopes through Network Flows.

Mathematical psychology has a long tradition of modeling probabilistic choice via distribution-free random utility models and associated random preference models. For such models, the predicted choice probabilities often form a bounded and convex polyhedral set, or polytope. Polyhedral combinatorics have thus played a key role in studying the mathematical structure of these models.

Accelerated multiplicative updates and hierarchical ALS algorithms for nonnegative matrix factorization.

Nonnegative matrix factorization (NMF) is a data analysis technique used in a great variety of applications such as text mining, image processing, hyperspectral data analysis, computational biology, and clustering. In this letter, we consider two well-known algorithms designed to solve NMF problems: the multiplicative updates of Lee and Seung and the hierarchical alternating least squares of Cichocki et al. We propose a simple way to significantly accelerate these schemes, based on a careful analysis of the computational cost needed at each iteration, while preserving their convergence properties.