7,322 research outputs found
Probing the topological properties of complex networks modeling short written texts
In recent years, graph theory has been widely employed to probe several
language properties. More specifically, the so-called word adjacency model has
been proven useful for tackling several practical problems, especially those
relying on textual stylistic analysis. The most common approach to treat texts
as networks has simply considered either large pieces of texts or entire books.
This approach has certainly worked well -- many informative discoveries have
been made this way -- but it raises an uncomfortable question: could there be
important topological patterns in small pieces of texts? To address this
problem, the topological properties of subtexts sampled from entire books was
probed. Statistical analyzes performed on a dataset comprising 50 novels
revealed that most of the traditional topological measurements are stable for
short subtexts. When the performance of the authorship recognition task was
analyzed, it was found that a proper sampling yields a discriminability similar
to the one found with full texts. Surprisingly, the support vector machine
classification based on the characterization of short texts outperformed the
one performed with entire books. These findings suggest that a local
topological analysis of large documents might improve its global
characterization. Most importantly, it was verified, as a proof of principle,
that short texts can be analyzed with the methods and concepts of complex
networks. As a consequence, the techniques described here can be extended in a
straightforward fashion to analyze texts as time-varying complex networks
Finitary languages
The class of omega-regular languages provides a robust specification language
in verification. Every omega-regular condition can be decomposed into a safety
part and a liveness part. The liveness part ensures that something good happens
"eventually". Finitary liveness was proposed by Alur and Henzinger as a
stronger formulation of liveness. It requires that there exists an unknown,
fixed bound b such that something good happens within b transitions. In this
work we consider automata with finitary acceptance conditions defined by
finitary Buchi, parity and Streett languages. We study languages expressible by
such automata: we give their topological complexity and present a
regular-expression characterization. We compare the expressive power of
finitary automata and give optimal algorithms for classical decisions
questions. We show that the finitary languages are Sigma 2-complete; we present
a complete picture of the expressive power of various classes of automata with
finitary and infinitary acceptance conditions; we show that the languages
defined by finitary parity automata exactly characterize the star-free fragment
of omega B-regular languages; and we show that emptiness is NLOGSPACE-complete
and universality as well as language inclusion are PSPACE-complete for finitary
parity and Streett automata
The Levi-Civita spacetime as a limiting case of the Gamma spacetime
It is shown that the Levi-Civita metric can be obtained from a family of the
Weyl metric, the Gamma metric, by taking the limit when the length of its
Newtonian image source tends to infinity. In this process a relationship
appears between two fundamental parameters of both metrics.Comment: LaTeX2e 17 page
Effect of edge removal on topological and functional robustness of complex networks
We study the robustness of complex networks subject to edge removal. Several
network models and removing strategies are simulated. Rather than the existence
of the giant component, we use total connectedness as the criterion of
breakdown. The network topologies are introduced a simple traffic dynamics and
the total connectedness is interpreted not only in the sense of topology but
also in the sense of function. We define the topological robustness and the
functional robustness, investigate their combined effect and compare their
relative importance to each other. The results of our study provide an
alternative view of the overall robustness and highlight efficient ways to
improve the robustness of the network models.Comment: 21 pages, 9 figure
Homotopy limits of model categories and more general homotopy theories
Generalizing a definition of homotopy fiber products of model categories, we
give a definition of the homotopy limit of a diagram of left Quillen functors
between model categories. As has been previously shown for homotopy fiber
products, we prove that such a homotopy limit does in fact correspond to the
usual homotopy limit, when we work in a more general model for homotopy
theories in which they can be regarded as objects of a model category.Comment: 10 pages; a few minor changes made. arXiv admin note: text overlap
with arXiv:0811.317
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