5,114 research outputs found
Re-Examination of Possible Bimodality of GALLEX Solar Neutrino Data
The histogram formed from published capture-rate measurements for the GALLEX
solar neutrino experiment is bimodal, showing two distinct peaks. On the other
hand, the histogram formed from published measurements derived from the similar
GNO experiment is unimodal, showing only one peak. However, the two experiments
differ in run durations: GALLEX runs are either three weeks or four weeks
(approximately) in duration, whereas GNO runs are all about four weeks in
duration. When we form 3-week and 4-week subsets of the GALLEX data, we find
that the relevant histograms are unimodal. The upper peak arises mainly from
the 3-week runs, and the lower peak from the 4-week runs. The 4-week subset of
the GALLEX dataset is found to be similar to the GNO dataset. A recent
re-analysis of GALLEX data leads to a unimodal histogram.Comment: 14 pages, 8 figure
A network approach to topic models
One of the main computational and scientific challenges in the modern age is
to extract useful information from unstructured texts. Topic models are one
popular machine-learning approach which infers the latent topical structure of
a collection of documents. Despite their success --- in particular of its most
widely used variant called Latent Dirichlet Allocation (LDA) --- and numerous
applications in sociology, history, and linguistics, topic models are known to
suffer from severe conceptual and practical problems, e.g. a lack of
justification for the Bayesian priors, discrepancies with statistical
properties of real texts, and the inability to properly choose the number of
topics. Here we obtain a fresh view on the problem of identifying topical
structures by relating it to the problem of finding communities in complex
networks. This is achieved by representing text corpora as bipartite networks
of documents and words. By adapting existing community-detection methods --
using a stochastic block model (SBM) with non-parametric priors -- we obtain a
more versatile and principled framework for topic modeling (e.g., it
automatically detects the number of topics and hierarchically clusters both the
words and documents). The analysis of artificial and real corpora demonstrates
that our SBM approach leads to better topic models than LDA in terms of
statistical model selection. More importantly, our work shows how to formally
relate methods from community detection and topic modeling, opening the
possibility of cross-fertilization between these two fields.Comment: 22 pages, 10 figures, code available at https://topsbm.github.io
Sampling motif-constrained ensembles of networks
The statistical significance of network properties is conditioned on null
models which satisfy spec- ified properties but that are otherwise random.
Exponential random graph models are a principled theoretical framework to
generate such constrained ensembles, but which often fail in practice, either
due to model inconsistency, or due to the impossibility to sample networks from
them. These problems affect the important case of networks with prescribed
clustering coefficient or number of small connected subgraphs (motifs). In this
paper we use the Wang-Landau method to obtain a multicanonical sampling that
overcomes both these problems. We sample, in polynomial time, net- works with
arbitrary degree sequences from ensembles with imposed motifs counts. Applying
this method to social networks, we investigate the relation between
transitivity and homophily, and we quantify the correlation between different
types of motifs, finding that single motifs can explain up to 60% of the
variation of motif profiles.Comment: Updated version, as published in the journal. 7 pages, 5 figures, one
Supplemental Materia
Torus invariant divisors
Using the language of polyhedral divisors and divisorial fans we describe
invariant divisors on normal varieties X which admit an effective codimension
one torus action. In this picture X is given by a divisorial fan on a smooth
projective curve Y. Cartier divisors on X can be described by piecewise affine
functions h on the divisorial fan S whereas Weil divisors correspond to certain
zero and one dimensional faces of it. Furthermore we provide descriptions of
the divisor class group and the canonical divisor. Global sections of line
bundles O(D_h) will be determined by a subset of a weight polytope associated
to h, and global sections of specific line bundles on the underlying curve Y.Comment: 16 pages; 5 pictures; small changes in the layout, further typos
remove
String junctions revisited
Recent measurements at the LHC have revealed heavy-flavour baryon fractions much larger than those observed at LEP, with e.g., Îc+/D0 and Îb0/B0 reaching ⌠0.5 at low pâ„. One scenario that has been at least partly successful in predicting observed trends is QCD colour reconnections with string junctions. In previous work, however, the limit of a low-pâ„ heavy quark was not well defined. We reconsider the string equations of motion for junction systems in this limit, and find that the junction effectively becomes bound to the heavy quark, a scenario we refer to as a âpearl on a stringâ. We extend string-junction fragmentation in Pythia with a dedicated modelling of this limit for both light- and heavy-quark âpearlsâ
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