669 research outputs found
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 and in
terms of the nerve of a certain category of -bimodules. We also prove
that the homotopy category 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 and as the
dg-category of -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 in ion-ion collisions
We study the threshold -meson production in the process , 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 . We predict the
ratio of cross sections for meson production in - and -collisions and the polarization properties of the -meson, in
, as a function of a single parameter, which
characterizes the relative role of transversal and longitudinal -meson
polarizations in the process .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.
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