"Optimal power flow (OPF) is an important problem for power generation and it is in general non-convex. With the employment of renewable energy, it will be desirable if OPF can be solved very efficiently so its solution can be used in real time. With some special network structure, e.g. trees, the problem has been shown to have a zero duality gap and the convex dual problem yields the optimal solution. In this paper, we propose a primal and a dual algorithm to coordinate the smaller subproblems decomposed from the convexified OPF. We can arrange the subproblems to be solved sequentially and cumulatively in a central node or solved in parallel in distributed nodes. We test the algorithms on IEEE radial distribution test feeders, some random tree-structured networks, and the IEEE transmission system benchmarks. Simulation results show that the computation time can be improved dramatically with our algorithms over the centralized approach of solving the problem without decomposition, especially in tree-structured problems. The computation time grows linearly with the problem size with the cumulative approach while the distributed one can have size-independent computation time."

“Nobody’s original,” Cope says. “We are what we eat, and in music, we are what we hear. What we do is look through history and listen to music. Everybody copies from everybody. The skill is in how large a fragment you choose to copy and how elegantly you can put them together.”

"Music composition used to be a pen and paper activity. These these days music is often composed with the aid of computer software, even to the point where the computer compose parts of the score autonomously. The composition of most styles of music is governed by rules. We show that by approaching the automation, analysis and verification of composition as a knowledge representation task and formalising these rules in a suitable logical language, powerful and expressive intelligent composition tools can be easily built. …"

"SuperCollider is an environment and programming language for real time audio synthesis and algorithmic composition. It provides an interpreted object-oriented language which functions as a network client to a state of the art, realtime sound synthesis server.

SuperCollider was written by James McCartney over a period of many years, and is now an open source (GPL) project maintained and developed by various people. It is used by musicians, scientists, and artists working with sound. For some background, see SuperCollider described by Wikipedia."

"In 1787, Mozart wrote the measures and instructions for a musical composition dice game. The idea is to cut and paste pre-written measures of music together to create a Minuet.

This site is an implementation of such a game. The music and table of rules for this game appear to have been published anonymously in 1787, and interestingly, the table of rules for this Minuet is identical to Mozart's. However, it is not clear who the composer of these measures is."

IKEA 2007 catalog normalized