Probing dynamical spacetimes with gravitational waves

This decade will see the first direct detections of gravitational waves by observatories such as Advanced LIGO and Virgo. Among the prime sources are coalescences of binary neutron stars and black holes, which are ideal probes of dynamical spacetime. This will herald a new era in the empirical study of gravitation. For the first time, we will have access to the genuinely strong-field dynamics, where low-energy imprints of quantum gravity may well show up. In addition, we will be able to search for effects which might only make their presence known at large distance scales, such as the ones that gravitational waves must traverse in going from source to observer. Finally, coalescing binaries can be used as cosmic distance markers, to study the large-scale structure and evolution of the Universe. With the advanced detector era fast approaching, concrete data analysis algorithms are being developed to look for deviations from general relativity in signals from coalescing binaries, taking into account the noisy detector output as well as the expectation that most sources will be near the threshold of detectability. Similarly, several practical methods have been proposed to use them for cosmology. We explain the state of the art, including the obstacles that still need to be overcome in order to make optimal use of the signals that will be detected. Although the emphasis will be on second-generation observatories, we will also discuss some of the science that could be done with future third-generation ground-based facilities such as Einstein Telescope, as well as with space-based detectors.Comment: 38 pages, 9 figures. Book chapter for the Springer Handbook of Spacetime (Springer Verlag, to appear in 2013

On the Complexity and Approximation of Binary Evidence in Lifted Inference

Lifted inference algorithms exploit symmetries in probabilistic models to speed up inference. They show impressive performance when calculating unconditional probabilities in relational models, but often resort to non-lifted inference when computing conditional probabilities. The reason is that conditioning on evidence breaks many of the model's symmetries, which can preempt standard lifting techniques. Recent theoretical results show, for example, that conditioning on evidence which corresponds to binary relations is #P-hard, suggesting that no lifting is to be expected in the worst case. In this paper, we balance this negative result by identifying the Boolean rank of the evidence as a key parameter for characterizing the complexity of conditioning in lifted inference. In particular, we show that conditioning on binary evidence with bounded Boolean rank is efficient. This opens up the possibility of approximating evidence by a low-rank Boolean matrix factorization, which we investigate both theoretically and empirically.Comment: To appear in Advances in Neural Information Processing Systems 26 (NIPS), Lake Tahoe, USA, December 201