Hamilton-Jacobi Reachability Analysis (HJRA) google
Hamilton-Jacobi (HJ) reachability analysis is an important formal verification method for guaranteeing performance and safety properties of dynamical systems; it has been applied to many small-scale systems in the past decade. Its advantages include compatibility with general nonlinear system dynamics, formal treatment of bounded disturbances, and the availability of well-developed numerical tools. The main challenge is addressing its exponential computational complexity with respect to the number of state variables. In this tutorial, we present an overview of basic HJ reachability theory and provide instructions for using the most recent numerical tools, including an efficient GPU-parallelized implementation of a Level Set Toolbox for computing reachable sets. In addition, we review some of the current work in high-dimensional HJ reachability to show how the dimensionality challenge can be alleviated via various general theoretical and application-specific insights. …

Partial Robust M Regression google
If an appropriate
weighting scheme is chosen, partial M-estimators become entirely robust to any type of
outlying points, and are called Partial Robust M-estimators. It is shown that partial robust
M-regression outperforms existing methods for robust PLS regression in terms of statistical
precision and computational speed, while keeping good robustness properties. …


Mesa google
Mesa is a highly scalable analytic data warehousing system that stores critical measurement data related to Google’s Internet advertising business. Mesa is designed to satisfy a complex and challenging set of user and systems requirements, including near real-time data ingestion and queryability, as well as high availability, reliability, fault tolerance, and scalability for large data and query volumes. Specifically, Mesa handles petabytes of data, processes millions of row updates per second, and serves billions of queries that fetch trillions of rows per day. Mesa is geo-replicated across multiple datacenters and provides consistent and repeatable query answers at low latency, even when an entire datacenter fails. …

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