PMLAB: An scripting environment for process mining

In a decade of process mining research, several algorithms have been proposed to solve particular process mining tasks. At the same pace, tools have appeared both in the academic and the commercial domains. These tools have enabled the use of process mining practices to a rather limited extent. In this paper we advocate for a change in the mentality: process mining may be an exploratory discipline, and PMLAB - a Python-based scripting environment supporting this - is proposed. This demo presents the main features of the PMLAB environment.Peer ReviewedPostprint (published version

Time--space harmonic polynomials relative to a L\'{e}vy process

In this work, we give a closed form and a recurrence relation for a family of time--space harmonic polynomials relative to a L\'{e}vy process. We also state the relationship with the Kailath--Segall (orthogonal) polynomials associated to the process.Comment: Published in at http://dx.doi.org/10.3150/07-BEJ6173 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

El Món de les variables sense moments finits de tots els ordres: de la paradoxa de Sant Petersburg als processos de Lévy

Les variables aleatòries sense moments de tots els ordres no són actualment una patologia, sinó que ocupen una posició central en la teoria de la probabilitat. Des de la paradoxa de Sant Petersburg, de començaments del segle xviii, fins a les distribucions estables no gaussianes i als vols de Lévy, s'ha desenvolupat una teoria plena de bellesa, de la qual us pretenem presentar alguns aspectes en aquest article. Acabem amb unes aplicacions a distintes situacions, entre aquestes una nova mirada a la vella paradoxa de Sant Petersburg, i una descripció de l'evolució de la temperatura de la Terra en els darrers 250.000 anys, com a tast de la seva importància en la modelització matemàtica de la realitat.Random variables without finite moments of all orders are not at present a pathology, but a central subject in probability theory. From the Saint Petersburg paradox, dated at the beginning of the eighteenth century, until the non-Gaussian stable distributions and Lévy flights, a very beautiful theory has been developed, at which, in this paper, we will take a quick glance. We will finish with some applications to different situations as a taste of the importance of this theory in mathematical modelling. Specifically, we will consider asset prices modelling, the study of earthquakes, a new view to the classical Saint Petersburg paradox, and finally the evolution of the mean temperature in the North Atlantic sea over the last 250,000 years

Incertesa i probabilitat : un passeig per algunes paradoxes i problemes clàssics de la teoria de la probabilitat

Els humans sempre han temut la incertesa que governa les seves vides. En aquest treball, fem la descripció d'un passeig amable per les nostres reaccions davant de l'aleatorietat, des dels vells temps passatsquan va ser divinitzada , fins a la matematització que representa la teoria de la probabilitat, que, segons Laplace, no és més que el bon sentit reduït al càlcul. Considerarem algunes preguntes que ja apareixen a la correspondència entre Pascal i Fermat, en el naixement de la teoria, així com alguns dels problemes clàssics, com el famós problema de les tres portes, l'aposta a la martingala o el passeig aleatori amb barreres, seleccionats entre l'immens número de sorprenents resultats i paradoxes d'aquesta teoria.The humans always have feared the uncertainty that directs their lives. In this paper, we describe a kind walk along our behavior in front of randomness, from the old times, when it was divinized, until the present mathematical treatment with the Theory of Probability, that, as Laplace wrote, is only the common sense reduced to calculus.We will consider the first questions that appear in the correspondence among Pascal and Fermat, at the dawn of the Theory, and also some of the most classical problems, as for instance the martingale betting, and the random walk between barriers, selected in the so rich and enormous set of surprising results and paradoxes of this Theory