"The main research theme in this proposal is non-parametric anomaly (novelty) detection in multidimensional distributed networks. First, we will address the centralized version of anomaly detection. We will reformulate this abstract problem in a topological hypothesis testing framework that is directly applicable to bio-medical applications. The research will focus on algorithm design, performance assessment and uncertainty management. As part of this quest, we will investigate other closely related topics such as manifold learning, intrinsic dimension estimation, robust level set estimation and annotated ranking of measurements. Next, we will consider the anomaly detection problem in a more ambitious and practical setting, namely under distributed, constantly changing and complex network conditions. Using tools from information theory and differential geometry, we will study the fundamental performance bounds on anomaly detection in such settings. Given these bounds and our novel topological framework, we will address the design and employment of such networks using concepts from compressed sensing, active learning, sequential experiment design and modern sampling techniques. Finally, we will analyze the data and measurements using spatio-temporal graphical models and state of the art message passing methods."