Log Skeletons: A Classification Approach to Process Discovery

To test the effectiveness of process discovery algorithms, a Process Discovery Contest (PDC) has been set up. This PDC uses a classification approach to measure this effectiveness: The better the discovered model can classify whether or not a new trace conforms to the event log, the better the discovery algorithm is supposed to be. Unfortunately, even the state-of-the-art fully-automated discovery algorithms score poorly on this classification. Even the best of these algorithms, the Inductive Miner, scored only 147 correct classified traces out of 200 traces on the PDC of 2017. This paper introduces the rule-based log skeleton model, which is closely related to the Declare constraint model, together with a way to classify traces using this model. This classification using log skeletons is shown to score better on the PDC of 2017 than state-of-the-art discovery algorithms: 194 out of 200. As a result, one can argue that the fully-automated algorithm to construct (or: discover) a log skeleton from an event log outperforms existing state-of-the-art fully-automated discovery algorithms.Comment: 16 pages with 9 figures, followed by an appendix of 14 pages with 17 figure

de Broglie-Proca and Bopp-Podolsky massive photon gases in cosmology

We investigate the influence of massive photons on the evolution of the expanding universe. Two particular models for generalized electrodynamics are considered, namely de Broglie-Proca and Bopp-Podolsky electrodynamics. We obtain the equation of state (EOS) $P=P(\varepsilon)$ for each case using dispersion relations derived from both theories. The EOS are inputted into the Friedmann equations of a homogeneous and isotropic space-time to determine the cosmic scale factor $a(t)$. It is shown that the photon non-null mass does not significantly alter the result $a\propto t^{1/2}$ valid for a massless photon gas; this is true either in de Broglie-Proca's case (where the photon mass $m$ is extremely small) or in Bopp-Podolsky theory (for which $m$ is extremely large).Comment: 8 pages, 2 figures; v2 matches the published versio

Measuring stellar differential rotation with high-precision space-borne photometry

We introduce a method of measuring a lower limit to the amplitude of surface differential rotation from high-precision, evenly sampled photometric time series. It is applied to main-sequence late-type stars whose optical flux modulation is dominated by starspots. An autocorrelation of the time series was used to select stars that allow an accurate determination of starspot rotation periods. A simple two-spot model was applied together with a Bayesian information criterion to preliminarily select intervals of the time series showing evidence of differential rotation with starspots of almost constant area. Finally, the significance of the differential rotation detection and a measurement of its amplitude and uncertainty were obtained by an a posteriori Bayesian analysis based on a Monte Carlo Markov Chain approach. We applied our method to the Sun and eight other stars for which previous spot modelling had been performed to compare our results with previous ones. We find that autocorrelation is a simple method for selecting stars with a coherent rotational signal that is a prerequisite for successfully measuring differential rotation through spot modelling. For a proper Monte Carlo Markov Chain analysis, it is necessary to take the strong correlations among different parameters that exist in spot modelling into account. For the planet-hosting star Kepler-30, we derive a lower limit to the relative amplitude of the differential rotation of \Delta P / P = 0.0523 \pm 0.0016. We confirm that the Sun as a star in the optical passband is not suitable for measuring differential rotation owing to the rapid evolution of its photospheric active regions. In general, our method performs well in comparison to more sophisticated and time-consuming approaches.Comment: Accepted to Astronomy and Astrophysics, 15 pages, 13 figures, 4 tables and an Appendi

Bopp-Podolsky black holes and the no-hair theorem

Bopp-Podolsky electrodynamics is generalized to curved space-times. The equations of motion are written for the case of static spherically symmetric black holes and their exterior solutions are analyzed using Bekenstein's method. It is shown the solutions split-up into two parts, namely a non-homogeneous (asymptotically massless) regime and a homogeneous (asymptotically massive) sector which is null outside the event horizon. In addition, in the simplest approach to Bopp-Podolsky black holes, the non-homogeneous solutions are found to be Maxwell's solutions leading to a Reissner-Nordstr\"om black hole. It is also demonstrated that the only exterior solution consistent with the weak and null energy conditions is the Maxwell's one. Thus, in light of energy conditions, it is concluded that only Maxwell modes propagate outside the horizon and, therefore, the no-hair theorem is satisfied in the case of Bopp-Podolsky fields in spherically symmetric space-times.Comment: 9 pages, updated to match published versio

Lithium and magnetic fields in giants. HD 232862 : a magnetic and lithium-rich giant star

We report the detection of an unusually high lithium content in HD 232862, a field giant classified as a G8II star, and hosting a magnetic field. With the spectropolarimeters ESPaDOnS at CFHT and NARVAL at TBL, we have collected high resolution and high signal-to-noise spectra of three giants : HD 232862, KU Peg and HD 21018. From spectral synthesis we have inferred stellar parameters and measured lithium abundances that we have compared to predictions from evolutionary models. We have also analysed Stokes V signatures, looking for a magnetic field on these giants. HD 232862, presents a very high abundance of lithium (ALi = 2.45 +/- 0.25 dex), far in excess of the theoretically value expected at this spectral type and for this luminosity class (i.e, G8II). The evolutionary stage of HD 232862 has been precised, and it suggests a mass in the lower part of the [1.0 Msun ; 3.5 Msun ] mass interval, likely 1.5 to 2.0 solar mass, at the bottom of the Red Giant Branch. Besides, a time variable Stokes V signature has been detected in the data of HD 232862 and KU Peg, pointing to the presence of a magnetic field at the surface of these two rapidly rotating active stars.Comment: 11 pages, 9 figures ; accepted by Astronomy and Astrophysic