Digital Revolution

There are numerous collections of algorithms on the Internet. Places like AlgoWiki provide valuable service. Yet we feel that the Wiki model isn't the best way to present algorithms. Here's why. Wiki is designed not to credit authors. This is a huge dis-incentive, because very few people like to publish and perish. Rather, we believe that the library/arXiv model is superior in that it properly rewards outstanding authors with fame. There are various disadvantages using Wiki, like lack of personal style, lack of comprehensiveness due to low participation, and awkward search. These problems can be solved if the library model is implemented well. Details will be given once spectrum-dev is up and running.

Here we define a robust network to be a connected network that stays connected after a arbitrary link is removed. The minimal robust network connecting a set of nodes is a Hamiltonian cycle. Further, a robust network is called reduced if it can not stay robust after any link is removed. A robust network may contain multiple reduced robust networks. And reduced robust networks may be obtained by removing links from robust networks. It's a open problem to computationally characterize robust networks, and reduced robust networks. Not every robust network can be reduced to the minimal robust network because not every robust network contains a Hamiltonian cycle. It's another open problem to computationally find reduced robust networks contained in arbitrary robust networks.

Modern artificial intelligence rely on data fitting. For some, the approach seems shallow, for the result is a description that summarizes data, rather than a mechanism that generates them. The success of modern artificial intelligence requires a justification of data fitting in order to explain how a seemingly shallow method turns out to be highly efficient. One doesn't want to invoke the analogy of catching a baseball. Even if a baseball player has no idea of classical mechanics, the ball can be traced by following its trajectory. Data fitting is deeper than this. First it must be emphasized that data fitting is a essential tool even for hard sciences. Planck had no idea how to generate light quanta, but based on curve fitting derived with the quantum hypothesis, he successfully launched the quantum revolution. The beauty of his approach is the small number of parameters that can explain a host of radiation patterns. Although data fitting can not explain fundamental mechanisms, i...