The branching structure of diffusion-limited aggregates

I analyze the topological structures generated by diffusion-limited aggregation (DLA), using the recently developed "branched growth model". The computed bifurcation number B for DLA in two dimensions is B ~ 4.9, in good agreement with the numerically obtained result of B ~ 5.2. In high dimensions, B -> 3.12; the bifurcation ratio is thus a decreasing function of dimensionality. This analysis also determines the scaling properties of the ramification matrix, which describes the hierarchy of branches.Comment: 6 pages, 1 figure, Euro-LaTeX styl

The homotopy theory of dg-categories and derived Morita theory

The main purpose of this work is the study of the homotopy theory of dg-categories up to quasi-equivalences. Our main result provides a natural description of the mapping spaces between two dg-categories $C$ and $D$ in terms of the nerve of a certain category of $(C,D)$-bimodules. We also prove that the homotopy category $Ho(dg-Cat)$ is cartesian closed (i.e. possesses internal Hom's relative to the tensor product). We use these two results in order to prove a derived version of Morita theory, describing the morphisms between dg-categories of modules over two dg-categories $C$ and $D$ as the dg-category of $(C,D)$-bi-modules. Finally, we give three applications of our results. The first one expresses Hochschild cohomology as endomorphisms of the identity functor, as well as higher homotopy groups of the \emph{classifying space of dg-categories} (i.e. the nerve of the category of dg-categories and quasi-equivalences between them). The second application is the existence of a good theory of localization for dg-categories, defined in terms of a natural universal property. Our last application states that the dg-category of (continuous) morphisms between the dg-categories of quasi-coherent (resp. perfect) complexes on two schemes (resp. smooth and proper schemes) is quasi-equivalent to the dg-category of quasi-coherent complexes (resp. perfect) on their product.Comment: 50 pages. Few mistakes corrected, and some references added. Thm. 8.15 is new. Minor corrections. Final version, to appear in Inventione

Combination of linear classifiers using score function -- analysis of possible combination strategies

In this work, we addressed the issue of combining linear classifiers using their score functions. The value of the scoring function depends on the distance from the decision boundary. Two score functions have been tested and four different combination strategies were investigated. During the experimental study, the proposed approach was applied to the heterogeneous ensemble and it was compared to two reference methods -- majority voting and model averaging respectively. The comparison was made in terms of seven different quality criteria. The result shows that combination strategies based on simple average, and trimmed average are the best combination strategies of the geometrical combination

The reaction Δ+N→N+N+ϕ\Delta+N\to N+N+\phi in ion-ion collisions

We study the threshold $\phi$-meson production in the process $\Delta+N\to N+N+\phi$, which appears as a possible important mechanism in high energy nuclei-nuclei collisions. The isotopic invariance of the strong interaction and the selection rules due to P-parity and total angular momentum result in a general and model independent parametrization of the spin structure of the matrix element in terms of three partial amplitudes. In the framework of one-pion exchange model these amplitudes can be derived in terms of the two threshold partial amplitudes for the process $\pi+N\to N+\phi$. We predict the ratio of cross sections for $\phi-$meson production in $pp$- and $\Delta N$-collisions and the polarization properties of the $\phi$-meson, in $\Delta+N\to N+N+\phi$, as a function of a single parameter, which characterizes the relative role of transversal and longitudinal $\phi$-meson polarizations in the process $\pi+N\to N+\phi$.Comment: 10 pages 3 figure

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

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.

Bose-Einstein Correlations of Three Charged Pions in Hadronic Z^0 Decays

Bose-Einstein Correlations (BEC) of three identical charged pions were studied in 4 x 10^6 hadronic Z^0 decays recorded with the OPAL detector at LEP. The genuine three-pion correlations, corrected for the Coulomb effect, were separated from the known two-pion correlations by a new subtraction procedure. A significant genuine three-pion BEC enhancement near threshold was observed having an emitter source radius of r_3 = 0.580 +/- 0.004 (stat.) +/- 0.029 (syst.) fm and a strength of \lambda_3 = 0.504 +/- 0.010 (stat.) +/- 0.041 (syst.). The Coulomb correction was found to increase the \lambda_3 value by \~9% and to reduce r_3 by ~6%. The measured \lambda_3 corresponds to a value of 0.707 +/- 0.014 (stat.) +/- 0.078 (syst.) when one takes into account the three-pion sample purity. A relation between the two-pion and the three-pion source parameters is discussed.Comment: 19 pages, LaTeX, 5 eps figures included, accepted by Eur. Phys. J.

A Measurement of Rb using a Double Tagging Method

The fraction of Z to bbbar events in hadronic Z decays has been measured by the OPAL experiment using the data collected at LEP between 1992 and 1995. The Z to bbbar decays were tagged using displaced secondary vertices, and high momentum electrons and muons. Systematic uncertainties were reduced by measuring the b-tagging efficiency using a double tagging technique. Efficiency correlations between opposite hemispheres of an event are small, and are well understood through comparisons between real and simulated data samples. A value of Rb = 0.2178 +- 0.0011 +- 0.0013 was obtained, where the first error is statistical and the second systematic. The uncertainty on Rc, the fraction of Z to ccbar events in hadronic Z decays, is not included in the errors. The dependence on Rc is Delta(Rb)/Rb = -0.056*Delta(Rc)/Rc where Delta(Rc) is the deviation of Rc from the value 0.172 predicted by the Standard Model. The result for Rb agrees with the value of 0.2155 +- 0.0003 predicted by the Standard Model.Comment: 42 pages, LaTeX, 14 eps figures included, submitted to European Physical Journal