11,572 research outputs found
Logarithmic forms and singular projective foliations
In this article we study polynomial logarithmic -forms on a projective
space and characterize those that define singular foliations of codimension
. Our main result is the algebraic proof of their infinitesimal stability
when with some extra degree assumptions. We determine new irreducible
components of the moduli space of codimension two singular projective
foliations of any degree, and we show that they are generically reduced in
their natural scheme structure. Our method is based on an explicit description
of the Zariski tangent space of the corresponding moduli space at a given
generic logarithmic form. Furthermore, we lay the groundwork for an extension
of our stability results to the general case .Comment: Version 3. 29 pages. Some grammar mistakes and typos were fixed. This
article will appear at Annales de l'Institut Fourie
Driving forces in researchers mobility
Starting from the dataset of the publication corpus of the APS during the
period 1955-2009, we reconstruct the individual researchers trajectories,
namely the list of the consecutive affiliations for each scholar. Crossing this
information with different geographic datasets we embed these trajectories in a
spatial framework. Using methods from network theory and complex systems
analysis we characterise these patterns in terms of topological network
properties and we analyse the dependence of an academic path across different
dimensions: the distance between two subsequent positions, the relative
importance of the institutions (in terms of number of publications) and some
socio-cultural traits. We show that distance is not always a good predictor for
the next affiliation while other factors like "the previous steps" of the
career of the researchers (in particular the first position) or the linguistic
and historical similarity between two countries can have an important impact.
Finally we show that the dataset exhibit a memory effect, hence the fate of a
career strongly depends from the first two affiliations
The role of homophily in the emergence of opinion controversies
Understanding the emergence of strong controversial issues in modern
societies is a key issue in opinion studies. A commonly diffused idea is the
fact that the increasing of homophily in social networks, due to the modern
ICT, can be a driving force for opinion polariation. In this paper we address
the problem with a modelling approach following three basic steps. We first
introduce a network morphogenesis model to reconstruct network structures where
homophily can be tuned with a parameter. We show that as homophily increases
the emergence of marked topological community structures in the networks
raises. Secondly, we perform an opinion dynamics process on homophily dependent
networks and we show that, contrary to the common idea, homophily helps
consensus formation. Finally, we introduce a tunable external media pressure
and we show that, actually, the combination of homophily and media makes the
media effect less effective and leads to strongly polarized opinion clusters.Comment: 24 pages, 10 figure
Can extremism guarantee pluralism?
Many models have been proposed to explain opinion formation in groups of
individuals; most of these models study opinion propagation as the interaction
between nodes/agents in a social network. Opinion formation is a complex
process and a realistic model should also take into account the important
feedbacks that the opinions of the agents have on the structure of the social
networks and on the characteristics of the opinion dynamics. In this paper we
will show that associating to different agents different kinds of
interconnections and different interacting behaviours can lead to interesting
scenarios, like the coexistence of several opinion clusters, namely pluralism.
In our model agents have opinions uniformly and continuously distributed
between two extremes. The social network is formed through a social aggregation
mechanism including the segregation process of the extremists that results in
many real communities. We show how this process affects the opinion dynamics in
the whole society. In the opinion evolution we consider the different
predisposition of single individuals to interact and to exchange opinion with
each other; we associate to each individual a different tolerance threshold,
depending on its own opinion: extremists are less willing to interact with
individuals with strongly different opinions and to change significantly their
ideas. A general result is obtained: when there is no interaction restriction,
the opinion always converges to uniformity, but the same is happening whenever
a strong segregation process of the extremists occurs. Only when extremists are
forming clusters but these clusters keep interacting with the rest of the
society, the survival of a wide opinion range is guaranteed.Comment: 20 pages, 10 figure
Structural and electronic transformation in low-angle twisted bilayer graphene
Experiments on bilayer graphene unveiled a fascinating realization of
stacking disorder where triangular domains with well-defined Bernal stacking
are delimited by a hexagonal network of strain solitons. Here we show by means
of numerical simulations that this is a consequence of a structural
transformation of the moir\'{e} pattern inherent of twisted bilayer graphene
taking place at twist angles below a crossover angle
. The transformation is governed by the interplay
between the interlayer van der Waals interaction and the in-plane strain field,
and is revealed by a change in the functional form of the twist energy density.
This transformation unveils an electronic regime characteristic of vanishing
twist angles in which the charge density converges, though not uniformly, to
that of ideal bilayer graphene with Bernal stacking. On the other hand, the
stacking domain boundaries form a distinct charge density pattern that provides
the STM signature of the hexagonal solitonic network.Comment: published version with supplementary materia
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