Characterizing the nature of Fossil Groups with XMM

We present an X-ray follow-up, based on XMM plus Chandra, of six Fossil Group (FG) candidates identified in our previous work using SDSS and RASS data. Four candidates (out of six) exhibit extended X-ray emission, confirming them as true FGs. For the other two groups, the RASS emission has its origin as either an optically dull/X-ray bright AGN, or the blending of distinct X-ray sources. Using SDSS-DR7 data, we confirm, for all groups, the presence of an r-band magnitude gap between the seed elliptical and the second-rank galaxy. However, the gap value depends, up to 0.5mag, on how one estimates the seed galaxy total flux, which is greatly underestimated when using SDSS (relative to Sersic) magnitudes. This implies that many FGs may be actually missed when using SDSS data, a fact that should be carefully taken into account when comparing the observed number densities of FGs to the expectations from cosmological simulations. The similarity in the properties of seed--FG and non-fossil ellipticals, found in our previous study, extends to the sample of X-ray confirmed FGs, indicating that bright ellipticals in FGs do not represent a distinct population of galaxies. For one system, we also find that the velocity distribution of faint galaxies is bimodal, possibly showing that the system formed through the merging of two groups. This undermines the idea that all selected FGs form a population of true fossils.Comment: 9 pages, 3 figures. Submitted 01/12/2011 to MNRAS, referee report received 21/02/2012, accepted 22/02/201

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

Semiclassical Series from Path Integrals

We derive the semiclassical series for the partition function in Quantum Statistical Mechanics (QSM) from its path integral representation. Each term of the series is obtained explicitly from the (real) minima of the classical action. The method yields a simple derivation of the exact result for the harmonic oscillator, and an accurate estimate of ground-state energy and specific heat for a single-well quartic anharmonic oscillator. As QSM can be regarded as finite temperature field theory at a point, we make use of Feynman diagrams to illustrate the non-perturbative character of the series: it contains all powers of $\hbar$ and graphs with any number of loops; the usual perturbative series corresponds to a subset of the diagrams of the semiclassical series. We comment on the application of our results to other potentials, to correlation functions and to field theories in higher dimensions.Comment: 18 pages, 4 figures. References update

Semiclassical Statistical Mechanics

We use a semiclassical approximation to derive the partition function for an arbitrary potential in one-dimensional Quantum Statistical Mechanics, which we view as an example of finite temperature scalar Field Theory at a point. We rely on Catastrophe Theory to analyze the pattern of extrema of the corresponding path-integral. We exhibit the propagator in the background of the different extrema and use it to compute the fluctuation determinant and to develop a (nonperturbative) semiclassical expansion which allows for the calculation of correlation functions. We discuss the examples of the single and double-well quartic anharmonic oscillators, and the implications of our results for higher dimensions.Comment: Invited talk at the La Plata meeting on `Trends in Theoretical Physics', La Plata, April, 1997; 14 pages + 5 ps figures. Some cosmetical modifications, and addition of some references which were missing in the previous versio