Finite state machine based SDL

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A non-commutative Priestley duality

We prove that the category of left-handed strongly distributive skew lattices with zero and proper homomorphisms is dually equivalent to a category of sheaves over local Priestley spaces. Our result thus provides a non-commutative version of classical Priestley duality for distributive lattices and generalizes the recent development of Stone duality for skew Boolean algebras. From the point of view of skew lattices, Leech showed early on that any strongly distributive skew lattice can be embedded in the skew lattice of partial functions on some set with the operations being given by restriction and so-called override. Our duality shows that there is a canonical choice for this embedding. Conversely, from the point of view of sheaves over Boolean spaces, our results show that skew lattices correspond to Priestley orders on these spaces and that skew lattice structures are naturally appropriate in any setting involving sheaves over Priestley spaces.Comment: 20 page

Value of time, schedule delay and reliability - estimates based on choice behaviour of Dutch commuters facing congestion

This paper presents the results of a large stated choice experiment among Dutch commuters facing congestion. The experiment consisted of a fractional factorial design with 15 different attributes, three alternatives were car specific and the other was always public transport. Various model specifications have been estimated on the collected choice data allowing us to analyse choice behaviour of road users and determine their values of time, schedule delay (both late and early) and reliability (or uncertainty). In this paper we present the estimates of the best-fitting discrete choice models and interpret the results.

Kerr black hole lensing for generic observers in the strong deflection limit

We generalize our previous work on gravitational lensing by a Kerr black hole in the strong deflection limit, removing the restriction to observers on the equatorial plane. Starting from the Schwarzschild solution and adding corrections up to the second order in the black hole spin, we perform a complete analytical study of the lens equation for relativistic images created by photons passing very close to a Kerr black hole. We find out that, to the lowest order, all observables (including shape and shift of the black hole shadow, caustic drift and size, images position and magnification) depend on the projection of the spin on a plane orthogonal to the line of sight. In order to break the degeneracy between the black hole spin and its inclination relative to the observer, it is necessary to push the expansion to higher orders. In terms of future VLBI observations, this implies that very accurate measures are needed to determine these two parameters separately.Comment: 17 pages, 4 figures, one section added, to appear on Physical Review

Testing the validity of the ray-tracing code GYOTO

In the next few years, the near-infrared interferometer GRAVITY will be able to observe the Galactic center. Astrometric data will be obtained with an anticipated accuracy of 10 $\mu$as. To analyze these future data, we have developed a code called GYOTO to compute orbits and images. We want to assess the validity and accuracy of GYOTO in a variety of contexts, in particular for stellar astrometry in the Galactic center. Furthermore, we want to tackle and complete a study made on the astrometric displacements that are due to lensing effects of a star of the central parsec with GYOTO. We first validate GYOTO in the weak-deflection limit (WDL) by studying primary caustics and primary critical curves obtained for a Kerr black hole. We compare GYOTO results to available analytical approximations and estimate GYOTO errors using an intrinsic estimator. In the strong-deflection limit (SDL), we choose to compare null geodesics computed by GYOTO and the ray-tracing code named Geokerr. Finally, we use GYOTO to estimate the apparent displacements of a star for different angles from Sagittarius A* (Sgr A*). We have demonstrated that GYOTO is accurate to a very high level, orders of magnitude better than the GRAVITY requirements. GYOTO is also valid in weak- and strong-deflection regimes and for very long integrations. At the astrometric precision that GRAVITY is aiming for, lensing effects must always be taken into account when fitting stellar orbits in the central parsec of the Galaxy.Comment: 11 pages, 12 figure

Message sequence chart specifications with cross verification

Current software specification verification methods are usually performed within the context of the specification method. There is little cross verification, pitting one type of specification against another, taking place. The most common techniques involve syntax checks across specifications or doing specification transformations and running verification within the new context. Since viewpoints of a system are different even within programming teams we concentrate on producing an efficient way to run cross verification on specifications, particularly specifications written with Message Sequence Charts and State Transition Diagrams.;In this work an algorithm is proposed in which all conditional MSCs are transformed into an algebraic representations, Message Flow Graphs and by stepwise refinement, a Global State Transition Graph is created. This GSTG has all the properties of a State Transition Diagram and therefore can be analyzed in conjunction with the original STD

Economic Analysis and Statistical Disclosure Limitation

This paper explores the consequences for economic research of methods used by data publishers to protect the privacy of their respondents. We review the concept of statistical disclosure limitation for an audience of economists who may be unfamiliar with these methods. We characterize what it means for statistical disclosure limitation to be ignorable. When it is not ignorable, we consider the effects of statistical disclosure limitation for a variety of research designs common in applied economic research. Because statistical agencies do not always report the methods they use to protect confidentiality, we also characterize settings in which statistical disclosure limitation methods are discoverable; that is, they can be learned from the released data. We conclude with advice for researchers, journal editors, and statistical agencies