24,396 research outputs found
The Redner - Ben-Avraham - Kahng cluster system
We consider a coagulation model first introduced by Redner, Ben-Avraham and
Krapivsky in [Redner, Ben-Avraham, Kahng: Kinetics of 'cluster eating', J.
Phys. A: Math. Gen., 20 (1987), 1231-1238], the main feature of which is that
the reaction between a j-cluster and a k-cluster results in the creation of a
|j-k|-cluster, and not, as in Smoluchowski's model, of a (j+k)-cluster. In this
paper we prove existence and uniqueness of solutions under reasonably general
conditions on the coagulation coefficients, and we also establish
differenciability properties and continuous dependence of solutions. Some
interesting invariance properties are also proved. Finally, we study the
long-time behaviour of solutions, and also present a preliminary analysis of
their scaling behaviour.Comment: 24 pages. 2 figures. Dedicated to Carlos Rocha and Luis Magalhaes on
the occasion of their sixtieth birthday
The Redner - Ben-Avraham - Kahng coagulation system with constant coefficients: the finite dimensional case
We study the behaviour as of solutions to the
Redner--Ben-Avraham--Kahng coagulation system with positive and compactly
supported initial data, rigorously proving and slightly extending results
originally established in [4] by means of formal arguments.Comment: 13 pages, 1 figur
On time-varying collaboration networks
The patterns of scientific collaboration have been frequently investigated in
terms of complex networks without reference to time evolution. In the present
work, we derive collaborative networks (from the arXiv repository)
parameterized along time. By defining the concept of affine group, we identify
several interesting trends in scientific collaboration, including the fact that
the average size of the affine groups grows exponentially, while the number of
authors increases as a power law. We were therefore able to identify, through
extrapolation, the possible date when a single affine group is expected to
emerge. Characteristic collaboration patterns were identified for each
researcher, and their analysis revealed that larger affine groups tend to be
less stable
Three-feature model to reproduce the topology of citation networks and the effects from authors' visibility on their h-index
Various factors are believed to govern the selection of references in
citation networks, but a precise, quantitative determination of their
importance has remained elusive. In this paper, we show that three factors can
account for the referencing pattern of citation networks for two topics, namely
"graphenes" and "complex networks", thus allowing one to reproduce the
topological features of the networks built with papers being the nodes and the
edges established by citations. The most relevant factor was content
similarity, while the other two - in-degree (i.e. citation counts) and {age of
publication} had varying importance depending on the topic studied. This
dependence indicates that additional factors could play a role. Indeed, by
intuition one should expect the reputation (or visibility) of authors and/or
institutions to affect the referencing pattern, and this is only indirectly
considered via the in-degree that should correlate with such reputation.
Because information on reputation is not readily available, we simulated its
effect on artificial citation networks considering two communities with
distinct fitness (visibility) parameters. One community was assumed to have
twice the fitness value of the other, which amounts to a double probability for
a paper being cited. While the h-index for authors in the community with larger
fitness evolved with time with slightly higher values than for the control
network (no fitness considered), a drastic effect was noted for the community
with smaller fitness
Structure-semantics interplay in complex networks and its effects on the predictability of similarity in texts
There are different ways to define similarity for grouping similar texts into
clusters, as the concept of similarity may depend on the purpose of the task.
For instance, in topic extraction similar texts mean those within the same
semantic field, whereas in author recognition stylistic features should be
considered. In this study, we introduce ways to classify texts employing
concepts of complex networks, which may be able to capture syntactic, semantic
and even pragmatic features. The interplay between the various metrics of the
complex networks is analyzed with three applications, namely identification of
machine translation (MT) systems, evaluation of quality of machine translated
texts and authorship recognition. We shall show that topological features of
the networks representing texts can enhance the ability to identify MT systems
in particular cases. For evaluating the quality of MT texts, on the other hand,
high correlation was obtained with methods capable of capturing the semantics.
This was expected because the golden standards used are themselves based on
word co-occurrence. Notwithstanding, the Katz similarity, which involves
semantic and structure in the comparison of texts, achieved the highest
correlation with the NIST measurement, indicating that in some cases the
combination of both approaches can improve the ability to quantify quality in
MT. In authorship recognition, again the topological features were relevant in
some contexts, though for the books and authors analyzed good results were
obtained with semantic features as well. Because hybrid approaches encompassing
semantic and topological features have not been extensively used, we believe
that the methodology proposed here may be useful to enhance text classification
considerably, as it combines well-established strategies
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