This brief presents a suite of computationally efficient methods for bounding trajectories of dynamical systems with multi-dimensional intervals, or 'boxes'. It explains the importance of bounding trajectories for evaluating the robustness of systems in the face of parametric uncertainty, and for verification or control synthesis problems with respect to safety and reachability properties. The methods presented make use of: interval analysis; monotonicity theory; contraction theory; and data-driven techniques that sample trajectories. The methods are implemented in an accompanying open-source Toolbox for Interval Reachability Analysis. This brief provides a tutorial description of each method, focusing on the requirements and trade-offs relevant to the user, requiring only basic background on dynamical systems. The second part of the brief describes applications of interval reachability analysis. This makes the brief of interest to a wide range of academic researchers, graduate students, and practising engineers in the field of control and verification.

Jean Meyer is an accomplished painter who has spent most of her adult life in Italy, but she grew up in a terraced suburban house in Wirral, within the sound of the great ships of Liverpool and a ferry crossing away from the club where four mop-topped musicians were preparing to take the world by storm. Through the gate is a beautifully evocative memoir of those years which has been written as an imaginary voyage around her childhood home, focusing in turn on the events associated with each part of the house and garden. "With the idea that people leave their joys and tragedies in the fabric of the rooms they have inhabited, I have divided the story into the rooms of the house, each acting as the catalyst for remembering the things that took place there."