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

Coil conversion to β-strand induced by dimerisation

Most molecular processes in living organisms rely on protein–protein interactions, many of which are mediated by β-sheet interfaces; this study investigates the formation of β-sheet interfaces through the conversion of coils into β-strands. Following an exhaustive search in the Protein Data Bank, the corresponding structural dimorphic fragments were extracted, characterised and analysed. Their short strand lengths and specific amino acid profiles indicate that dimorphic β-strand interfaces are likely to be less stable than standard ones and could even convert to coil interfaces if their environment changes. Moreover, the construction of a simple classifier able to discriminate between the sequences of dimorphic and standard β-strand interfaces suggests that the nature of those dimorphic sequences could be predicted, providing a novel means of identifying proteins capable of forming dimers

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

Environmental Exposures and Invasive Meningococcal Disease: An Evaluation of Effects on Varying Time Scales

Invasive meningococcal disease (IMD) is an important cause of meningitis and bacteremia worldwide. Seasonal variation in IMD incidence has long been recognized, but mechanisms responsible for this phenomenon remain poorly understood. The authors sought to evaluate the effect of environmental factors on IMD risk in Philadelphia, Pennsylvania, a major urban center. Associations between monthly weather patterns and IMD incidence were evaluated using multivariable Poisson regression models controlling for seasonal oscillation. Short-term weather effects were identified using a case-crossover approach. Both study designs control for seasonal factors that might otherwise confound the relation between environment and IMD. Incidence displayed significant wintertime seasonality (for oscillation, P < 0.001), and Poisson regression identified elevated monthly risk with increasing relative humidity (per 1% increase, incidence rate ratio = 1.04, 95% confidence interval: 1.004, 1.08). Case-crossover methods identified an inverse relation between ultraviolet B radiation index 1–4 days prior to onset and disease risk (odds ratio = 0.54, 95% confidence interval: 0.34, 0.85). Extended periods of high humidity and acute changes in ambient ultraviolet B radiation predict IMD occurrence in Philadelphia. The latter effect may be due to decreased pathogen survival or virulence and may explain the wintertime seasonality of IMD in temperate regions of North America

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

Search for New Physics with Jets and Missing Transverse Momentum in pp collisions at sqrt(s) = 7 TeV

A search for new physics is presented based on an event signature of at least three jets accompanied by large missing transverse momentum, using a data sample corresponding to an integrated luminosity of 36 inverse picobarns collected in proton--proton collisions at sqrt(s)=7 TeV with the CMS detector at the LHC. No excess of events is observed above the expected standard model backgrounds, which are all estimated from the data. Exclusion limits are presented for the constrained minimal supersymmetric extension of the standard model. Cross section limits are also presented using simplified models with new particles decaying to an undetected particle and one or two jets

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

Measurement of the t t-bar production cross section in the dilepton channel in pp collisions at sqrt(s) = 7 TeV

The t t-bar production cross section (sigma[t t-bar]) is measured in proton-proton collisions at sqrt(s) = 7 TeV in data collected by the CMS experiment, corresponding to an integrated luminosity of 2.3 inverse femtobarns. The measurement is performed in events with two leptons (electrons or muons) in the final state, at least two jets identified as jets originating from b quarks, and the presence of an imbalance in transverse momentum. The measured value of sigma[t t-bar] for a top-quark mass of 172.5 GeV is 161.9 +/- 2.5 (stat.) +5.1/-5.0 (syst.) +/- 3.6(lumi.) pb, consistent with the prediction of the standard model.Comment: Replaced with published version. Included journal reference and DO