Generic scale of the "scale-free" growing networks

We show that the connectivity distributions $P(k,t)$ of scale-free growing networks ($t$ is the network size) have the generic scale -- the cut-off at $k_{cut} \sim t^\beta$. The scaling exponent $\beta$ is related to the exponent $\gamma$ of the connectivity distribution, $\beta=1/(\gamma-1)$. We propose the simplest model of scale-free growing networks and obtain the exact form of its connectivity distribution for any size of the network. We demonstrate that the trace of the initial conditions -- a hump at $k_h \sim k_{cut} \sim t^\beta$ -- may be found for any network size. We also show that there exists a natural boundary for the observation of the scale-free networks and explain why so few scale-free networks are observed in Nature.Comment: 4 pages revtex, 3 figure

Growing Scale-Free Networks with Small World Behavior

In the context of growing networks, we introduce a simple dynamical model that unifies the generic features of real networks: scale-free distribution of degree and the small world effect. While the average shortest path length increases logartihmically as in random networks, the clustering coefficient assumes a large value independent of system size. We derive expressions for the clustering coefficient in two limiting cases: random (C ~ (ln N)^2 / N) and highly clustered (C = 5/6) scale-free networks.Comment: 4 pages, 4 figure

Interface Depinning in the Absence of External Driving Force

We study the pinning-depinning phase transition of interfaces in the quenched Kardar-Parisi-Zhang model as the external driving force $F$ goes towards zero. For a fixed value of the driving force we induce depinning by increasing the nonlinear term coefficient $\lambda$, which is related to lateral growth, up to a critical threshold. We focus on the case in which there is no external force applied (F=0) and find that, contrary to a simple scaling prediction, there is a finite value of $\lambda$ that makes the interface to become depinned. The critical exponents at the transition are consistent with directed percolation depinning. Our results are relevant for paper wetting experiments, in which an interface gets moving with no external driving force.Comment: 4 pages, 3 figures included, uses epsf. Submitted to PR

Highly clustered scale-free networks

We propose a model for growing networks based on a finite memory of the nodes. The model shows stylized features of real-world networks: power law distribution of degree, linear preferential attachment of new links and a negative correlation between the age of a node and its link attachment rate. Notably, the degree distribution is conserved even though only the most recently grown part of the network is considered. This feature is relevant because real-world networks truncated in the same way exhibit a power-law distribution in the degree. As the network grows, the clustering reaches an asymptotic value larger than for regular lattices of the same average connectivity. These high-clustering scale-free networks indicate that memory effects could be crucial for a correct description of the dynamics of growing networks.Comment: 6 pages, 4 figure

Growing dynamics of Internet providers

In this paper we present a model for the growth and evolution of Internet providers. The model reproduces the data observed for the Internet connection as probed by tracing routes from different computers. This problem represents a paramount case of study for growth processes in general, but can also help in the understanding the properties of the Internet. Our main result is that this network can be reproduced by a self-organized interaction between users and providers that can rearrange in time. This model can then be considered as a prototype model for the class of phenomena of aggregation processes in social networks

Heuristic Segmentation of a Nonstationary Time Series

Many phenomena, both natural and human-influenced, give rise to signals whose statistical properties change under time translation, i.e., are nonstationary. For some practical purposes, a nonstationary time series can be seen as a concatenation of stationary segments. Using a segmentation algorithm, it has been reported that for heart beat data and Internet traffic fluctuations--the distribution of durations of these stationary segments decays with a power law tail. A potential technical difficulty that has not been thoroughly investigated is that a nonstationary time series with a (scale-free) power law distribution of stationary segments is harder to segment than other nonstationary time series because of the wider range of possible segment sizes. Here, we investigate the validity of a heuristic segmentation algorithm recently proposed by Bernaola-Galvan et al. by systematically analyzing surrogate time series with different statistical properties. We find that if a given nonstationary time series has stationary periods whose size is distributed as a power law, the algorithm can split the time series into a set of stationary segments with the correct statistical properties. We also find that the estimated power law exponent of the distribution of stationary-segment sizes is affected by (i) the minimum segment size, and (ii) the ratio of the standard deviation of the mean values of the segments, and the standard deviation of the fluctuations within a segment. Furthermore, we determine that the performance of the algorithm is generally not affected by uncorrelated noise spikes or by weak long-range temporal correlations of the fluctuations within segments.Comment: 23 pages, 14 figure

Measurement of the partial widths of the Z into up- and down-type quarks

Using the entire OPAL LEP1 on-peak Z hadronic decay sample, Z -> qbarq gamma decays were selected by tagging hadronic final states with isolated photon candidates in the electromagnetic calorimeter. Combining the measured rates of Z -> qbarq gamma decays with the total rate of hadronic Z decays permits the simultaneous determination of the widths of the Z into up- and down-type quarks. The values obtained, with total errors, were Gamma u = 300 ^{+19}_{-18} MeV and Gamma d = 381 ^{+12}_{-12} MeV. The results are in good agreement with the Standard Model expectation.Comment: 22 pages, 5 figures, Submitted to Phys. Letts.

Search for R-Parity Violating Decays of Scalar Fermions at LEP

A search for pair-produced scalar fermions under the assumption that R-parity is not conserved has been performed using data collected with the OPAL detector at LEP. The data samples analysed correspond to an integrated luminosity of about 610 pb-1 collected at centre-of-mass energies of sqrt(s) 189-209 GeV. An important consequence of R-parity violation is that the lightest supersymmetric particle is expected to be unstable. Searches of R-parity violating decays of charged sleptons, sneutrinos and squarks have been performed under the assumptions that the lightest supersymmetric particle decays promptly and that only one of the R-parity violating couplings is dominant for each of the decay modes considered. Such processes would yield final states consisting of leptons, jets, or both with or without missing energy. No significant single-like excess of events has been observed with respect to the Standard Model expectations. Limits on the production cross- section of scalar fermions in R-parity violating scenarios are obtained. Constraints on the supersymmetric particle masses are also presented in an R-parity violating framework analogous to the Constrained Minimal Supersymmetric Standard Model.Comment: 51 pages, 24 figures, Submitted to Eur. Phys. J.

Measurement of Rb in e+e- Collisions at 182 - 209 GeV

Measurements of Rb, the ratio of the bbbar cross-section to the qqbar cross- section in e+e- collisions, are presented. The data were collected by the OPAL experiment at LEP at centre-of-mass energies between 182 GeV and 209 GeV. Lepton, lifetime and event shape information is used to tag events containing b quarks with high efficiency. The data are compatible with the Standard Model expectation. The mean ratio of the eight measurements reported here to the Standard Model prediction is 1.055+-0.031+-0.037, where the first error is statistical and the second systematic.Comment: 21 pages, 5 figures, Submitted to Phys. Letts

Search for the standard model Higgs boson decaying into two photons in pp collisions at sqrt(s)=7 TeV

A search for a Higgs boson decaying into two photons is described. The analysis is performed using a dataset recorded by the CMS experiment at the LHC from pp collisions at a centre-of-mass energy of 7 TeV, which corresponds to an integrated luminosity of 4.8 inverse femtobarns. Limits are set on the cross section of the standard model Higgs boson decaying to two photons. The expected exclusion limit at 95% confidence level is between 1.4 and 2.4 times the standard model cross section in the mass range between 110 and 150 GeV. The analysis of the data excludes, at 95% confidence level, the standard model Higgs boson decaying into two photons in the mass range 128 to 132 GeV. The largest excess of events above the expected standard model background is observed for a Higgs boson mass hypothesis of 124 GeV with a local significance of 3.1 sigma. The global significance of observing an excess with a local significance greater than 3.1 sigma anywhere in the search range 110-150 GeV is estimated to be 1.8 sigma. More data are required to ascertain the origin of this excess.Comment: Submitted to Physics Letters