War pact model of shrinking networks.

Many real systems can be described by a set of interacting entities forming a complex network. To some surprise, these have been shown to share a number of structural properties regardless of their type or origin. It is thus of vital importance to design simple and intuitive models that can explain their intrinsic structure and dynamics. These can, for instance, be used to study networks analytically or to construct networks not observed in real life. Most models proposed in the literature are of two types. A model can be either static, where edges are added between a fixed set of nodes according to some predefined rule, or evolving, where the number of nodes or edges increases over time. However, some real networks do not grow but rather shrink, meaning that the number of nodes or edges decreases over time. We here propose a simple model of shrinking networks called the war pact model. We show that networks generated in such a way exhibit common structural properties of real networks. Furthermore, compared to classical models, these resemble international trade, correlates of war, Bitcoin transactions and other networks more closely. Network shrinking may therefore represent a reasonable explanation of the evolution of some networks and greater emphasis should be put on such models in the future.

Monolithically integrated heterodyne optical phase-lock loop with RF XOR phase detector.

We present results for an heterodyne optical phase-lock loop (OPLL), monolithically integrated on InP with external phase detector and loop filter, which phase locks the integrated laser to an external source, for offset frequencies tuneable between 0.6 GHz and 6.1 GHz. The integrated semiconductor laser emits at 1553 nm with 1.1 MHz linewidth, while the external laser has a linewidth less than 150 kHz. To achieve high quality phase locking with lasers of these linewidths, the loop delay has been made less than 1.8 ns. Monolithic integration reduces the optical path delay between the laser and photodiode to less than 20 ps. The electronic part of the OPLL was implemented using a custom-designed feedback circuit with a propagation delay of ~1 ns and an open-loop bandwidth greater than 1 GHz. The heterodyne signal between the locked slave laser and master laser has phase noise below -90 dBc/Hz for frequency offsets greater than 20 kHz and a phase error variance in 10 GHz bandwidth of 0.04 rad2.