Category Theory and Model-Driven Engineering: From Formal Semantics to Design Patterns and Beyond

There is a hidden intrigue in the title. CT is one of the most abstract mathematical disciplines, sometimes nicknamed "abstract nonsense". MDE is a recent trend in software development, industrially supported by standards, tools, and the status of a new "silver bullet". Surprisingly, categorical patterns turn out to be directly applicable to mathematical modeling of structures appearing in everyday MDE practice. Model merging, transformation, synchronization, and other important model management scenarios can be seen as executions of categorical specifications. Moreover, the paper aims to elucidate a claim that relationships between CT and MDE are more complex and richer than is normally assumed for "applied mathematics". CT provides a toolbox of design patterns and structural principles of real practical value for MDE. We will present examples of how an elementary categorical arrangement of a model management scenario reveals deficiencies in the architecture of modern tools automating the scenario.Comment: In Proceedings ACCAT 2012, arXiv:1208.430

Efficient out-coupling of high-purity single photons from a coherent quantum dot in a photonic-crystal cavity

We demonstrate a single-photon collection efficiency of $(44.3\pm2.1)\%$ from a quantum dot in a low-Q mode of a photonic-crystal cavity with a single-photon purity of $g^{(2)}(0)=(4\pm5)\%$ recorded above the saturation power. The high efficiency is directly confirmed by detecting up to $962\pm46$ kilocounts per second on a single-photon detector on another quantum dot coupled to the cavity mode. The high collection efficiency is found to be broadband, as is explained by detailed numerical simulations. Cavity-enhanced efficient excitation of quantum dots is obtained through phonon-mediated excitation and under these conditions, single-photon indistinguishability measurements reveal long coherence times reaching $0.77\pm0.19$ ns in a weak-excitation regime. Our work demonstrates that photonic crystals provide a very promising platform for highly integrated generation of coherent single photons including the efficient out-coupling of the photons from the photonic chip.Comment: 13 pages, 8 figures, submitte