Spin-structures and 2-fold coverings

Gonçalves, Daciberg Lima; Hayat, Claude; Mello, Maria Hermínia de Paula Leite

doi:10.5269/bspm.v23i1-2.7451

Cited by 2 publications

(2 citation statements)

References 2 publications

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“…The World Wide Web (WWW) is the location of various human actions that are of interest to many physicists because of the plethora of available data 1,2,3,4,5,6,7,8,9,10 and the complexity of phenomena taking place in techno-social networks. An example is the bursty nature of human activities in cyberspace (emails, web-browsing) considered by Barabási 11,12 to be a consequence of decisionbased queuing processes.…”

Section: Introductionmentioning

confidence: 99%

Flow of Emotional Messages in Artificial Social Networks

Chmiel

Hołyst

2010

Int. J. Mod. Phys. C

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Models of message flows in an artificial group of users communicating via the Internet are introduced and investigated using numerical simulations. We assumed that messages possess an emotional character with a positive valence and that the willingness to send the next affective message to a given person increases with the number of messages received from this person. As a result, the weights of links between group members evolve over time. Memory effects are introduced, taking into account that the preferential selection of message receivers depends on the communication intensity during the recent period only. We also model the phenomenon of secondary social sharing when the reception of an emotional e-mail triggers the distribution of several emotional e-mails to other people.

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Section: Introductionmentioning

confidence: 99%

Flow of Emotional Messages in Artificial Social Networks

Chmiel

Hołyst

2010

Int. J. Mod. Phys. C

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“…One motivation to study special 2-fold coverings is that they can be considered as Spin-structures associated to an oriented 2-vector bundle over F g with even Chern class q = 2c; see Milnor [12] and the article by the last three authors [7]. When this oriented 2-vector bundle is the tangent bundle and F g is orientable, Atiyah [2], Birman and Craggs [3] and Johnson [9,10] studied the Torelli subgroup of the mapping class group of the surface F g .…”

Section: Introductionmentioning

confidence: 99%

A classification of special 2–fold coverings

Bauval¹,

Gonçalves²,

Hayat³

et al. 2008

Geometry and Topology Monographs

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Starting with an SO(2)-principal fibration over a closed oriented surface F g , g ≥ 1, a 2-fold covering of the total space is said to be special when the monodromy sends the fiber SO(2) ∼ S 1 to the nontrivial element of Z 2 . Adapting D Johnson's method [11], we define an action of Sp(Z 2 , 2g), the group of symplectic isomorphisms of (H 1 (F g ; Z 2 ), .), on the set of special 2-fold coverings which has two orbits, one with 2 g−1 (2 g + 1) elements and one with 2 g−1 (2 g − 1) elements. These two orbits are obtained by considering Arf-invariants and some congruence of the derived matrices coming from Fox Calculus. Sp(Z 2 , 2g) is described as the union of conjugacy classes of two subgroups, each of them fixing a special 2-fold covering. Generators of these two subgroups are made explicit.

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Spin-structures and 2-fold coverings

Cited by 2 publications

References 2 publications

Flow of Emotional Messages in Artificial Social Networks

Flow of Emotional Messages in Artificial Social Networks

A classification of special 2–fold coverings

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