Critical random graphs: limiting constructions and distributional properties

We consider the Erdos-Renyi random graph G(n,p) inside the critical window, where p = 1/n + lambda * n^{-4/3} for some lambda in R. We proved in a previous paper (arXiv:0903.4730) that considering the connected components of G(n,p) as a sequence of metric spaces with the graph distance rescaled by n^{-1/3} and letting n go to infinity yields a non-trivial sequence of limit metric spaces C = (C_1, C_2, ...). These limit metric spaces can be constructed from certain random real trees with vertex-identifications. For a single such metric space, we give here two equivalent constructions, both of which are in terms of more standard probabilistic objects. The first is a global construction using Dirichlet random variables and Aldous' Brownian continuum random tree. The second is a recursive construction from an inhomogeneous Poisson point process on R_+. These constructions allow us to characterize the distributions of the masses and lengths in the constituent parts of a limit component when it is decomposed according to its cycle structure. In particular, this strengthens results of Luczak, Pittel and Wierman by providing precise distributional convergence for the lengths of paths between kernel vertices and the length of a shortest cycle, within any fixed limit component.Comment: 30 pages, 4 figure

Critical random graphs : limiting constructions and distributional properties

We consider the Erdos-Renyi random graph G(n, p) inside the critical window, where p = 1/n + lambda n(-4/3) for some lambda is an element of R. We proved in Addario-Berry et al. [2009+] that considering the connected components of G(n, p) as a sequence of metric spaces with the graph distance rescaled by n(-1/3) and letting n -> infinity yields a non-trivial sequence of limit metric spaces C = (C-1, C-2,...). These limit metric spaces can be constructed from certain random real trees with vertex-identifications. For a single such metric space, we give here two equivalent constructions, both of which are in terms of more standard probabilistic objects. The first is a global construction using Dirichlet random variables and Aldous' Brownian continuum random tree. The second is a recursive construction from an inhomogeneous Poisson point process on R+. These constructions allow us to characterize the distributions of the masses and lengths in the constituent parts of a limit component when it is decomposed according to its cycle structure. In particular, this strengthens results of Luczak et al. [1994] by providing precise distributional convergence for the lengths of paths between kernel vertices and the length of a shortest cycle, within any fixed limit component

Presencia de Bryopsida fértil en los niveles Westfalianos del subgrup Itararé, Cuenca de Paraná, Brasil

The bryophyte fossils are rare, mainly in Paleozoic sedimentary rocks in spite of being present since the Silurian Period. In the Division Bryophyta, the fossils that belong to the Class Bryopsida are recognized since the Carboniferous, but they are extremely scarce. They are plentiful only in Permian sediments, in the Petchora, Kuznetsk and Russian Platform basins, also in Antarctica, Karoo basin (the last in South Africa) and India. Identified at the genus Dwykea, gametophyte specimens bearing pleurocarpous sporophyte were recovered from the lowermost levels of Itararé Subgroup, near Campinas city, S. Paulo State. These fossils correspond to the first register of bryophyte female gametophyte for the Carboniferous Period. The microflora in association with these fossils allow correlations of these levels to the Palynozone Ahrensisporites cristatus of Westphalian age. Related to proglacial sediments, they may correspond to a tundra vegetation covering the Northeastern border of Paraná Basin, during the Westphalian.Los fósiles atribuidos a briófitos son escasos, principalmente en rocas paleozoicas a pesar de ser registrados desde el Silúrico. Para la División Bryophyta, los fósiles correspondientes a la Clase Bryopsida comienzan a ser encontrados a partir del Carbonífero, aunque son bastante escasos. Registros más abundantes son conocidos para el Pérmico en rocas de las cuencas de Petchora, Kuznetsk y en la Plataforma Rusa, así como en la Antártica, en la Cuenca del Karoo (África del Sur) e India. Especímenes de gametófitos con esporofitos pleurocárpicos del género Dwykea fueron colectados en los niveles inferiores del Subgrupo Itararé, próximos a la ciudad de Campinas, Estado de S. Paulo. Estos fósiles corresponden al primer registro para el periodo Carbonífero de gametofitos femeninos fértiles. La microflora asociada a los fósiles de Dwykea permite establecer correlaciones con la Palinozona Ahrensisporites cristatus de edad westfaliana. Además los niveles donde fueron colectados los ejemplares de Dwykea corresponden a sedimentos proglaciales, que son interpretados como una vegetación de tundra que habitaba en el margen noreste de la Cuenca del Paraná, durante el Westfaliano

Search for the standard model Higgs boson in the H to ZZ to 2l 2nu channel in pp collisions at sqrt(s) = 7 TeV

A search for the standard model Higgs boson in the H to ZZ to 2l 2nu decay channel, where l = e or mu, in pp collisions at a center-of-mass energy of 7 TeV is presented. The data were collected at the LHC, with the CMS detector, and correspond to an integrated luminosity of 4.6 inverse femtobarns. No significant excess is observed above the background expectation, and upper limits are set on the Higgs boson production cross section. The presence of the standard model Higgs boson with a mass in the 270-440 GeV range is excluded at 95% confidence level.Comment: Submitted to JHE

Long and short paths in uniform random recursive dags

In a uniform random recursive k-dag, there is a root, 0, and each node in turn, from 1 to n, chooses k uniform random parents from among the nodes of smaller index. If S_n is the shortest path distance from node n to the root, then we determine the constant \sigma such that S_n/log(n) tends to \sigma in probability as n tends to infinity. We also show that max_{1 \le i \le n} S_i/log(n) tends to \sigma in probability.Comment: 16 page

Combined search for the quarks of a sequential fourth generation

Results are presented from a search for a fourth generation of quarks produced singly or in pairs in a data set corresponding to an integrated luminosity of 5 inverse femtobarns recorded by the CMS experiment at the LHC in 2011. A novel strategy has been developed for a combined search for quarks of the up and down type in decay channels with at least one isolated muon or electron. Limits on the mass of the fourth-generation quarks and the relevant Cabibbo-Kobayashi-Maskawa matrix elements are derived in the context of a simple extension of the standard model with a sequential fourth generation of fermions. The existence of mass-degenerate fourth-generation quarks with masses below 685 GeV is excluded at 95% confidence level for minimal off-diagonal mixing between the third- and the fourth-generation quarks. With a mass difference of 25 GeV between the quark masses, the obtained limit on the masses of the fourth-generation quarks shifts by about +/- 20 GeV. These results significantly reduce the allowed parameter space for a fourth generation of fermions.Comment: Replaced with published version. Added journal reference and DO

Performance of CMS muon reconstruction in pp collision events at sqrt(s) = 7 TeV

The performance of muon reconstruction, identification, and triggering in CMS has been studied using 40 inverse picobarns of data collected in pp collisions at sqrt(s) = 7 TeV at the LHC in 2010. A few benchmark sets of selection criteria covering a wide range of physics analysis needs have been examined. For all considered selections, the efficiency to reconstruct and identify a muon with a transverse momentum pT larger than a few GeV is above 95% over the whole region of pseudorapidity covered by the CMS muon system, abs(eta) < 2.4, while the probability to misidentify a hadron as a muon is well below 1%. The efficiency to trigger on single muons with pT above a few GeV is higher than 90% over the full eta range, and typically substantially better. The overall momentum scale is measured to a precision of 0.2% with muons from Z decays. The transverse momentum resolution varies from 1% to 6% depending on pseudorapidity for muons with pT below 100 GeV and, using cosmic rays, it is shown to be better than 10% in the central region up to pT = 1 TeV. Observed distributions of all quantities are well reproduced by the Monte Carlo simulation.Comment: Replaced with published version. Added journal reference and DO

Performance of CMS muon reconstruction in pp collision events at sqrt(s) = 7 TeV

The performance of muon reconstruction, identification, and triggering in CMS has been studied using 40 inverse picobarns of data collected in pp collisions at sqrt(s) = 7 TeV at the LHC in 2010. A few benchmark sets of selection criteria covering a wide range of physics analysis needs have been examined. For all considered selections, the efficiency to reconstruct and identify a muon with a transverse momentum pT larger than a few GeV is above 95% over the whole region of pseudorapidity covered by the CMS muon system, abs(eta) < 2.4, while the probability to misidentify a hadron as a muon is well below 1%. The efficiency to trigger on single muons with pT above a few GeV is higher than 90% over the full eta range, and typically substantially better. The overall momentum scale is measured to a precision of 0.2% with muons from Z decays. The transverse momentum resolution varies from 1% to 6% depending on pseudorapidity for muons with pT below 100 GeV and, using cosmic rays, it is shown to be better than 10% in the central region up to pT = 1 TeV. Observed distributions of all quantities are well reproduced by the Monte Carlo simulation.Comment: Replaced with published version. Added journal reference and DO

Measurement of the t-channel single top quark production cross section in pp collisions at √s =7 TeV

Peer reviewe

Measurement of the sum ofWW and WZ production with W+dijet events in pp collisions at √ s = 7 TeV

A measurement of the inclusive WW+WZ diboson production cross section in proton–proton collisions is reported, based on events containing a leptonically decaying √W boson and exactly two jets. The data sample, collected at s = 7 TeV with the CMS detector at the LHC, corresponds to an integrated luminosity of 5.0 fb−1. The measured value of the sum of the inclusive WW and WZ cross sections is σ(pp → WW + WZ) = 68.9 ± 8.7 (stat.) ± 9.7 (syst.) ± 1.5 (lum.) pb, consistent with the standard model prediction of 65.6±2.2 pb. This is the first measurement of WW+WZ production in pp collisions using this signature. No evidence for anomalous triple gauge couplings is found and upper limits are set on their magnitudes