As time goes by this page is getting longer as I update it when Google updates their algorithm and announces on their website. In looking over the history, it’s clear that this evolution has gone in fits and spurts but it also has been driving towards specific goals. What follows are the highlights to what Google have done for many years as we stand on the precipice of new change. By understanding where Google has been, we can see how this ever-growing company is aiming towards the elimination of irrelevant, though it still is a persistent problem and promoting social media in their SEO accountability. The applications demonstrate that the functional observer can significantly scale up our ability to explore otherwise inaccessible dynamical processes on complex networks.With the new changes expected in the algorithms of the Google search engine, it’s rather instructive to look back and see the history of these changes since Google first hit the scene in 1998. We apply the proposed methods to the detection of cyberattacks in power grids from limited phase measurement data and the inference of the prevalence rate of infection during an epidemic under limited testing conditions. Compared with the full-state observer, the proposed functional observer achieves the same estimation quality with substantially less sensing and fewer computational resources, making it suitable for large-scale networks. Here, we develop a graph-based theory of functional observability, which leads to highly scalable algorithms to 1) determine the minimal set of required sensors and 2) design the corresponding state observer of minimum order. To overcome the curse of dimensionality, we instead require the system to be functionally observable, meaning that a targeted subset of state variables can be reconstructed from the available measurements. Even if the system is in principle observable, high dimensionality poses fundamental limits on the computational tractability and performance of a full-state observer. In large-scale dynamical networks, it is often difficult or physically impossible to have enough sensor nodes to make the system fully observable. The quantitative understanding and precise control of complex dynamical systems can only be achieved by observing their internal states via measurement and/or estimation.

Astronomical algorithms 1998 pdf