Random variables with completely independent subcollections

AbstractWe investigate the algebra and geometry of the independence conditions on discrete random variables in which we consider a collection of random variables and study the condition of independence of some subcollections. We interpret independence conditions as an ideal of algebraic relations. After a change of variables, this ideal is generated by generalized 2×2 minors of multi-way tables and linear forms. In particular, let Δ be a simplicial complex on some random variables and A be the table corresponding to the product of those random variables. If A is Δ-independent table then A can be written as the entrywise sum AI+A0 where AI is a completely independent table and A0 is identically 0 in its Δ-margins.We compute the isolated components of the original ideal, showing that there is only one component that could correspond to probability distributions, and relate the algebra and geometry of the main component to that of the Segre embedding. If Δ has fewer than three facets, we are able to compute generators for the main component, show that it is Cohen–Macaulay, and give a full primary decomposition of the original ideal

Measurements of Flavour Dependent Fragmentation Functions in Z^0 -> qq(bar) Events

Fragmentation functions for charged particles in Z -> qq(bar) events have been measured for bottom (b), charm (c) and light (uds) quarks as well as for all flavours together. The results are based on data recorded between 1990 and 1995 using the OPAL detector at LEP. Event samples with different flavour compositions were formed using reconstructed D* mesons and secondary vertices. The \xi_p = ln(1/x_E) distributions and the position of their maxima \xi_max are also presented separately for uds, c and b quark events. The fragmentation function for b quarks is significantly softer than for uds quarks.Comment: 29 pages, LaTeX, 5 eps figures (and colour figs) included, submitted to Eur. Phys. J.

CHEK2 1100delC in patients with metachronous cancers of the breast and the colorectum

BACKGROUND: Development of multiple primary tumors is a hallmark of hereditary cancer. At least 1/10 of breast cancers and colorectal cancers occur because of heredity and recently the cell cycle kinase 2, CHEK2 1100delC allele has been identified at a particularly high frequency in families with hereditary breast and colorectal cancer. METHODS: We utilized the Southern Sweden population-based cancer registry to identify women with double primary breast and colorectal cancer and sequenced tumor material in order to assess the contribution of the CHEK2 1100delC to the development of such metachronous tumors. RESULTS: Among the 75 patients successfully analyzed, 2 (2.5%) carried the CHEK2 1100delC allele. which was not significantly different (p = 0.26) from the 1% (3/300) carriers identified in the control group. CONCLUSION: In summary, our data suggest that the CHEK2 1100delC is not a major cause of double primary breast and colorectal cancer in Sweden, which suggests that this patient group should not routinely be screened for the CHEK2 1100delC variant

Commissioning of the CMS High Level Trigger

The CMS experiment will collect data from the proton-proton collisions delivered by the Large Hadron Collider (LHC) at a centre-of-mass energy up to 14 TeV. The CMS trigger system is designed to cope with unprecedented luminosities and LHC bunch-crossing rates up to 40 MHz. The unique CMS trigger architecture only employs two trigger levels. The Level-1 trigger is implemented using custom electronics, while the High Level Trigger (HLT) is based on software algorithms running on a large cluster of commercial processors, the Event Filter Farm. We present the major functionalities of the CMS High Level Trigger system as of the starting of LHC beams operations in September 2008. The validation of the HLT system in the online environment with Monte Carlo simulated data and its commissioning during cosmic rays data taking campaigns are discussed in detail. We conclude with the description of the HLT operations with the first circulating LHC beams before the incident occurred the 19th September 2008

Bose-Einstein Correlations in e+e- to W+W- at 172 and 183 GeV

Bose-Einstein correlations between like-charge pions are studied in hadronic final states produced by e+e- annihilations at center-of-mass energies of 172 and 183 GeV. Three event samples are studied, each dominated by one of the processes W+W- to qqlnu, W+W- to qqqq, or (Z/g)* to qq. After demonstrating the existence of Bose-Einstein correlations in W decays, an attempt is made to determine Bose-Einstein correlations for pions originating from the same W boson and from different W bosons, as well as for pions from (Z/g)* to qq events. The following results are obtained for the individual chaoticity parameters lambda assuming a common source radius R: lambda_same = 0.63 +- 0.19 +- 0.14, lambda_diff = 0.22 +- 0.53 +- 0.14, lambda_Z = 0.47 +- 0.11 +- 0.08, R = 0.92 +- 0.09 +- 0.09. In each case, the first error is statistical and the second is systematic. At the current level of statistical precision it is not established whether Bose-Einstein correlations, between pions from different W bosons exist or not.Comment: 24 pages, LaTeX, including 6 eps figures, submitted to European Physical Journal

W+W- production and triple gauge boson couplings at LEP energies up to 183 GeV

A study of W-pair production in e+e- annihilations at Lep2 is presented, based on 877 W+W- candidates corresponding to an integrated luminosity of 57 pb-1 at sqrt(s) = 183 GeV. Assuming that the angular distributions of the W-pair production and decay, as well as their branching fractions, are described by the Standard Model, the W-pair production cross-section is measured to be 15.43 +- 0.61 (stat.) +- 0.26 (syst.) pb. Assuming lepton universality and combining with our results from lower centre-of-mass energies, the W branching fraction to hadrons is determined to be 67.9 +- 1.2 (stat.) +- 0.5 (syst.)%. The number of W-pair candidates and the angular distributions for each final state (qqlnu,qqqq,lnulnu) are used to determine the triple gauge boson couplings. After combining these values with our results from lower centre-of-mass energies we obtain D(kappa_g)=0.11+0.52-0.37, D(g^z_1)=0.01+0.13-0.12 and lambda=-0.10+0.13-0.12, where the errors include both statistical and systematic uncertainties and each coupling is determined setting the other two couplings to the Standard Model value. The fraction of W bosons produced with a longitudinal polarisation is measured to be 0.242+-0.091(stat.)+-0.023(syst.). All these measurements are consistent with the Standard Model expectations.Comment: 48 pages, LaTeX, including 13 eps or ps figures, submitted to European Physical Journal

Determination of alpha_s using Jet Rates at LEP with the OPAL detector

Hadronic events produced in e+e- collisions by the LEP collider and recorded by the OPAL detector were used to form distributions based on the number of reconstructed jets. The data were collected between 1995 and 2000 and correspond to energies of 91 GeV, 130-136 GeV and 161-209 GeV. The jet rates were determined using four different jet-finding algorithms (Cone, JADE, Durham and Cambridge). The differential two-jet rate and the average jet rate with the Durham and Cambridge algorithms were used to measure alpha(s) in the LEP energy range by fitting an expression in which order alpah_2s calculations were matched to a NLLA prediction and fitted to the data. Combining the measurements at different centre-of-mass energies, the value of alpha_s (Mz) was determined to be alpha(s)(Mz)=0.1177+-0.0006(stat.)+-0.0012$(expt.)+-0.0010(had.)+-0.0032(theo.) \.Comment: 40 pages, 17 figures, Submitted to Euro. Phys. J.

Search for Neutral Higgs Bosons in e+e- Collisions at sqrt(s) ~189GeV

A search for neutral Higgs bosons has been performed with the OPAL detector at LEP, using approximately 170 pb-1 of e+e- collision data collected at sqrt(s)~189GeV. Searches have been performed for the Standard Model (SM) process e+e- to H0Z0 and the MSSM processes e+e- to H0Z0, A0h0. The searches are sensitive to the b b-bar and tau antitau decay modes of the Higgs bosons, and also to the MSSM decay mode h0 to A0A0. OPAL search results at lower centre-of-mass energies have been incorporated in the limits we set, which are valid at the 95% confidence level. For the SM Higgs boson, we obtain a lower mass bound of 91.0 GeV. In the MSSM, our limits are mh>74.8GeV and mA>76.5GeV, assuming tan(beta)>1, that the mixing of the scalar top quarks is either zero or maximal, and that the soft SUSY-breaking masses are 1 TeV. For the case of zero scalar top mixing, we exclude values of tan(beta) between 0.72 and 2.19.Comment: 38 pages, 15 figures, submitted Euro. Phys. J.