More than 14 million new cases of cancer are diagnosed globally each year, with approximately 50% of all cancer patients receiving radiation therapy during the course of their disease. Advanced technology using a multi-leaf collimator can deliver non-uniform radiation doses that best conform to the tumor shape while sparing the surrounding normal tissues. Combinatorically, selecting beam angles is computationally taxing and remains a major challenge. Consequently, clinical systems opt to use preselected angles without integrating a combinatorial computational engine within the fluence map optimization process.In this paper, we offer a mixed integer quadratic programming optimization approach to simultaneously determine optimal beam angles and fluence maps. For computational efficiency, a dynamic restricted branch-and-price method is derived to solve these large-scale patient instances. Clinical analyses of prostate and head-and-neck cancer patient cases show that our approach yields treatment plans that are far superior to current best practice in the clinical environment. Specifically, the resulting plans achieve better conformity and homogeneity to the tumor while reducing radiation exposure to the critical structures. Computationally, besides drastically reducing the solution time, the dynamic restricted branch-and-price method provides an additional bonus: every node consists of only a relatively small number of beam variables in the branch-and-bound framework. This implies that in the middle of the solution process, a feasible and clinically acceptable treatment plan is available, and can be obtained by taking a few branching steps on the beam variables that are in the active set.

In our increasingly connected digital world, many sensors are connected to each other. Each sensor provides several features and data from those features. As a result, the data sets created from Internet of Things (IoT) applications can consist of hundreds or even thousands of dimensions. Even though the dimensionality is high in these data sets, the actual rank is mostly low because of the high correlations between these dimensions. As a result, subspace analysis and subspace tracking are useful methods of capturing low-dimensional structures from high-frequency, high-dimensional data. In streaming data, a substantial change in the subspace can indicate an anomaly. In this paper, we introduce several measures for detecting changes in the subspace that we use in our anomaly and degradation detection methods. We also present the results of applying our methods to simulated and real-world data sets. These methods have been implemented in an event stream processing platform.