21,657 research outputs found
Decomposition of Lagrangian classes on K3 surfaces
We study the decomposability of a Lagrangian homology class on a K3 surface into a sum of classes represented by special Lagrangian submanifolds, and develop criteria for it in terms of lattice theory. As a result, we prove the decomposability on an arbitrary K3 surface with respect to the Kähler classes in dense subsets of the Kähler cone. Using the same technique, we show that the Kähler classes on a K3 surface which admit a special Lagrangian fibration form a dense subset also. This implies that there are infinitely many special Lagrangian 3-tori in any log Calabi-Yau 3-fold.https://arxiv.org/abs/2001.00202Othe
Twitter in Academic Conferences: Usage, Networking and Participation over Time
Twitter is often referred to as a backchannel for conferences. While the main
conference takes place in a physical setting, attendees and virtual attendees
socialize, introduce new ideas or broadcast information by microblogging on
Twitter. In this paper we analyze the scholars' Twitter use in 16 Computer
Science conferences over a timespan of five years. Our primary finding is that
over the years there are increasing differences with respect to conversation
use and information use in Twitter. We studied the interaction network between
users to understand whether assumptions about the structure of the
conversations hold over time and between different types of interactions, such
as retweets, replies, and mentions. While `people come and people go', we want
to understand what keeps people stay with the conference on Twitter. By casting
the problem to a classification task, we find different factors that contribute
to the continuing participation of users to the online Twitter conference
activity. These results have implications for research communities to implement
strategies for continuous and active participation among members
Surface and Edge States in Topological Semi-metals
We study the topologically non-trivial semi-metals by means of the 6-band
Kane model. Existence of surface states is explicitly demonstrated by
calculating the LDOS on the material surface. In the strain free condition,
surface states are divided into two parts in the energy spectrum, one part is
in the direct gap, the other part including the crossing point of surface state
Dirac cone is submerged in the valence band. We also show how uni-axial strain
induces an insulating band gap and raises the crossing point from the valence
band into the band gap, making the system a true topological insulator. We
predict existence of helical edge states and spin Hall effect in the thin film
topological semi-metals, which could be tested with future experiment. Disorder
is found to significantly enhance the spin Hall effect in the valence band of
the thin films
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