Quantum and random walks as universal generators of probability distributions

Quantum walks and random walks bear similarities and divergences. One of the most remarkable disparities affects the probability of finding the particle at a given location: typically, almost a flat function in the first case and a bell-shaped one in the second case. Here I show how one can impose any desired stochastic behavior (compatible with the continuity equation for the probability function) on both systems by the appropriate choice of time- and site-dependent coins. This implies, in particular, that one can devise quantum walks that show diffusive spreading without loosing coherence, as well as random walks that exhibit the characteristic fast propagation of a quantum particle driven by a Hadamard coin.Comment: 8 pages, 2 figures; revised and enlarged versio

Two-Player Reachability-Price Games on Single-Clock Timed Automata

We study two player reachability-price games on single-clock timed automata. The problem is as follows: given a state of the automaton, determine whether the first player can guarantee reaching one of the designated goal locations. If a goal location can be reached then we also want to compute the optimum price of doing so. Our contribution is twofold. First, we develop a theory of cost functions, which provide a comprehensive methodology for the analysis of this problem. This theory allows us to establish our second contribution, an EXPTIME algorithm for computing the optimum reachability price, which improves the existing 3EXPTIME upper bound.Comment: In Proceedings QAPL 2011, arXiv:1107.074

LTL Parameter Synthesis of Parametric Timed Automata

The parameter synthesis problem for parametric timed automata is undecidable in general even for very simple reachability properties. In this paper we introduce restrictions on parameter valuations under which the parameter synthesis problem is decidable for LTL properties. The investigated bounded integer parameter synthesis problem could be solved using an explicit enumeration of all possible parameter valuations. We propose an alternative symbolic zone-based method for this problem which results in a faster computation. Our technique extends the ideas of the automata-based approach to LTL model checking of timed automata. To justify the usefulness of our approach, we provide experimental evaluation and compare our method with explicit enumeration technique.Comment: 23 pages, extended versio

Interplate seismicity at the CRISP site: the 2002 Osa earthquake sequence

The Costa Rica Seismogenesis Project (CRISP) is designed to explore the processes involved in the nucleation of large interplate earthquakes in erosional subduction zones. On 16 June 2002 a magnitude Mw=6.4 earthquake and its aftershocks may have nucleated at the subduction thrust to be penetrated and sampled by CRISP, ~40 km west of Osa Peninsula. Global event locations present uncertainties too large to prove that the event actually occurred at a location and depth reachable by riser drilling. We have compiled a database including foreshocks, the main shock, and ~400 aftershocks, with phase arrival times from all the seismological networks that recorded the 2002 Osa sequence locally. This includes a temporal network of ocean-bottom hydrophones (OBH) that happened to be installed close to the area at the time of the earthquake. The coverage increase provided by the OBH network allow us to better constrain the event relocations, and to further analyze the seismicity in the vicinity of Osa for the six months during which they were deployed. Moreover, we undertook teleseismic waveform inversion to provide additional constraints for the centroid depth of the 2002 Osa earthquake, allowing further study of the focal mechanism. Along the Costa Rican seismogenic zone, the 2002 Osa sequence is the most recent. It nucleated in the SE region of the forearc where this erosional margin is underthrust by a seamount covered ocean plate. A Mw=6.9 earthquake sequence occurred in 1999, co-located with a subducted ridge and associated seamounts. The Osa mainshock and first hours of aftershocks began in the CRISP area, ~30 km seaward of the 1999 sequence. In the following two weeks, subsequent aftershocks migrated into the 1999 aftershock area and also clustered in an area updip from it. The Osa updip seismicity apparently occurred where interplate temperatures are ~100°C or less. In this study, we present the relocation of the 2002 Osa earthquake sequence and background seismicity using different techniques and a moment tensor inversion for the mainshock, and discuss the corresponding uncertainties, in an effort to provide further evidence that the planned Phase B of CRISP will be successful in drilling the seismogenic coupling zone