A Central Limit Theorem for intransitive dice

Intransive dice $D^{(1)}, \ldots, D^{(\ell)}$ are dice such that $D^{(1)}$ has advantage with respect to $D^{(2)}$, dice $D^{(2)}$ has advantage with respect to $D^{(3)}$ and so on, up to $D^{(\ell)}$, which has advantage over $D^{(1)}$. In this twofold work, we present: first, (deterministic) results on existence of general intransitive dice. Second and mainly, a central limit theorem for the vector of normalized victories of a die against the next one in the list when the faces of a die are i.i.d.\ random variables and all dice are independent, but different dice may have distinct distributions associated to, as well as they may have distinct number of faces. From this central limit theorem we derive a criteria to assure that the asymptotic probability of observing intransitive dice is null, which applies for many cases, including all continuous distributions and many discrete ones.Comment: 37 pages, 3 figure

Hemispheric asymmetries in the ionospheric response observed in the American sector during an intense geomagnetic storm

The main purpose of this investigation is to study the ionospheric F region response induced by the intense geomagnetic storm that occurred on 7-8 September 2002. The geomagnetic index Dst reached a minimum of -181 nT at 0100 UT on 8 September. In this study, we used observations from a chain of 12 GPS stations and another chain of 6 digital ionosonde stations. It should be mentioned that, soon after the sudden commencement (SC) at 1637 UT on 7 September, the TEC variations at midlatitude stations in both hemispheres showed an F region positive storm phase. However, during the recovery phase, a strong hemispheric asymmetry was observed in the ionospheric response. While a TID type soliton was observed to propagate in the Southern American sector, no TID activity was seen in the Northern American sector. Also, in the Southern Hemisphere, the TEC variations were less affected by the geomagnetic storm. The Northern Hemisphere observations showed a strong and long-lasting negative F region storm phase starting at about 1000 UT on 8 September (lasting for about 24 h). A perusal of TEC phase fluctuations and equatorial spread-F (ESF) ionospheric sounding data indicates that, on the disturbed night of 7-8 September, some stations showed the occurrence of ESF starting at about 0000 UT (2000 LT) on 8 September, whereas other stations showed that the ESF occurrence started much later, at about 0800 UT (0500 LT). This hemispheric asymmetric response of the ionospheric F region possibly indicates the presence of different mechanisms for the generation of ESF along the various latitudinal regions during the disturbed period.Facultad de Ciencias Astronómicas y Geofísica

Hemispheric asymmetries in the ionospheric response observed in the American sector during an intense geomagnetic storm

The main purpose of this investigation is to study the ionospheric F region response induced by the intense geomagnetic storm that occurred on 7-8 September 2002. The geomagnetic index Dst reached a minimum of -181 nT at 0100 UT on 8 September. In this study, we used observations from a chain of 12 GPS stations and another chain of 6 digital ionosonde stations. It should be mentioned that, soon after the sudden commencement (SC) at 1637 UT on 7 September, the TEC variations at midlatitude stations in both hemispheres showed an F region positive storm phase. However, during the recovery phase, a strong hemispheric asymmetry was observed in the ionospheric response. While a TID type soliton was observed to propagate in the Southern American sector, no TID activity was seen in the Northern American sector. Also, in the Southern Hemisphere, the TEC variations were less affected by the geomagnetic storm. The Northern Hemisphere observations showed a strong and long-lasting negative F region storm phase starting at about 1000 UT on 8 September (lasting for about 24 h). A perusal of TEC phase fluctuations and equatorial spread-F (ESF) ionospheric sounding data indicates that, on the disturbed night of 7-8 September, some stations showed the occurrence of ESF starting at about 0000 UT (2000 LT) on 8 September, whereas other stations showed that the ESF occurrence started much later, at about 0800 UT (0500 LT). This hemispheric asymmetric response of the ionospheric F region possibly indicates the presence of different mechanisms for the generation of ESF along the various latitudinal regions during the disturbed period.Facultad de Ciencias Astronómicas y Geofísica

Hemispheric asymmetries in the ionospheric response observed in the American sector during an intense geomagnetic storm

The main purpose of this investigation is to study the ionospheric F region response induced by the intense geomagnetic storm that occurred on 7-8 September 2002. The geomagnetic index Dst reached a minimum of -181 nT at 0100 UT on 8 September. In this study, we used observations from a chain of 12 GPS stations and another chain of 6 digital ionosonde stations. It should be mentioned that, soon after the sudden commencement (SC) at 1637 UT on 7 September, the TEC variations at midlatitude stations in both hemispheres showed an F region positive storm phase. However, during the recovery phase, a strong hemispheric asymmetry was observed in the ionospheric response. While a TID type soliton was observed to propagate in the Southern American sector, no TID activity was seen in the Northern American sector. Also, in the Southern Hemisphere, the TEC variations were less affected by the geomagnetic storm. The Northern Hemisphere observations showed a strong and long-lasting negative F region storm phase starting at about 1000 UT on 8 September (lasting for about 24 h). A perusal of TEC phase fluctuations and equatorial spread-F (ESF) ionospheric sounding data indicates that, on the disturbed night of 7-8 September, some stations showed the occurrence of ESF starting at about 0000 UT (2000 LT) on 8 September, whereas other stations showed that the ESF occurrence started much later, at about 0800 UT (0500 LT). This hemispheric asymmetric response of the ionospheric F region possibly indicates the presence of different mechanisms for the generation of ESF along the various latitudinal regions during the disturbed period.Facultad de Ciencias Astronómicas y Geofísica

Standalone vertex finding in the ATLAS muon spectrometer

A dedicated reconstruction algorithm to find decay vertices in the ATLAS muon spectrometer is presented. The algorithm searches the region just upstream of or inside the muon spectrometer volume for multi-particle vertices that originate from the decay of particles with long decay paths. The performance of the algorithm is evaluated using both a sample of simulated Higgs boson events, in which the Higgs boson decays to long-lived neutral particles that in turn decay to bbar b final states, and pp collision data at √s = 7 TeV collected with the ATLAS detector at the LHC during 2011