In radiation therapy, the fractionation schedule, i.e. the total number of treatment days and the dose delivered per day, plays an important role in treatment outcome. In the first part of the talk, we analyze the effect of tumor repopulation on the optimal fractionation scheme. We find that due to accelerated repopulation, larger dose fractions are suggested later in the treatment to compensate for the increased tumor proliferation. In the second part of the talk, we briefly describe how substantial reduction in normal tissue dose can result by exploiting tumor shrinkage via an optimal design of multi-stage treatments.
Doubly logarithmic factors are usually ignored, often an artifact of analysis, and always less than 5. This talk explores the attempts of a handful of researchers at removing a doubly logarithmic factor, and why in the end, this log log factor is unavoidable.
More specifically, I will discuss the problem of sampling from distributions to find the one with the largest mean. This can be mathematically modeled as a multi-armed bandit problem in which each distribution is associated with an arm. Finding the arm with the largest mean is often referred to as the ‘best arm’ problem. In the ‘best arm’ framework, procedures must succeed with ‘uniformly small probability of error’, meaning they must automatically adjust sampling to match the perceived hardness of the problem in order to guarantee success in the most adverse settings. I will present a new algorithm for the best arm problem, called PRISM. While PRISM has linear sample complexity for a wide range of problems (an improvement over the state of the art), PRISM has an additional doubly logarithmic factor in general. Lastly, relying on a result from the statistic literature in the 60’s, I will explain why in general this doubly logarithmic dependance cannot be removed.
Discovery Building, Orchard View Room
Jagdish Ramakrishnan, Matt Malloy