We present an online algorithm for detecting changes in computer network activity. Anomalous activity in IT systems often appear as changes in network topology as edges evolve in a dynamic graph; identifying these behavioral changes can be a challenging task. We propose a method that uses principles of Hyperdimensional Computing to encode graphs to a real valued space where anomalies are easily identifiable. With reasonable assumptions of the baseline edge generating process, our approach operates in real time and can produce an anomaly score primitive for one sample independently of all others. This score lends itself easily to an online Bayesian confidence estimate in constant memory, which is essential for real-world applications where networks are extremely large and interpretable predictions are needed in real time. We demonstrate the effectiveness of our approach on both synthetic and real-world datasets.

Analysis of stability and stabilizability of switched linear systems is a well-researched topic. This article pursues a polar coordinate approach which offers a convenient framework to analyze second-order continuous time switched linear systems. We elaborate on the analytic utility of polar coordinates and present necessary and sufficient conditions under which a stabilizing switched control law can be constructed. Implications of polar coordinate analysis for switched linear systems include sensitivity analysis of switching control laws and the design of oscillators.