3,577 research outputs found
The symplectic Deligne-Mumford stack associated to a stacky polytope
We discuss a symplectic counterpart of the theory of stacky fans. First, we
define a stacky polytope and construct the symplectic Deligne-Mumford stack
associated to the stacky polytope. Then we establish a relation between stacky
polytopes and stacky fans: the stack associated to a stacky polytope is
equivalent to the stack associated to a stacky fan if the stacky fan
corresponds to the stacky polytope.Comment: 20 pages; v2: To appear in Results in Mathematic
Uniqueness and examples of compact toric Sasaki-Einstein metrics
In [11] it was proved that, given a compact toric Sasaki manifold of positive
basic first Chern class and trivial first Chern class of the contact bundle,
one can find a deformed Sasaki structure on which a Sasaki-Einstein metric
exists. In the present paper we first prove the uniqueness of such Einstein
metrics on compact toric Sasaki manifolds modulo the action of the identity
component of the automorphism group for the transverse holomorphic structure,
and secondly remark that the result of [11] implies the existence of compatible
Einstein metrics on all compact Sasaki manifolds obtained from the toric
diagrams with any height, or equivalently on all compact toric Sasaki manifolds
whose cones have flat canonical bundle. We further show that there exists an
infinite family of inequivalent toric Sasaki-Einstein metrics on for each positive integer .Comment: Statements of the results are modifie
5-dimensional contact SO(3)-manifolds and Dehn twists
In this paper the 5-dimensional contact SO(3)-manifolds are classified up to
equivariant contactomorphisms. The construction of such manifolds with singular
orbits requires the use of generalized Dehn twists.
We show as an application that all simply connected 5-manifoldswith singular
orbits are realized by a Brieskorn manifold with exponents (k,2,2,2). The
standard contact structure on such a manifold gives right-handed Dehn twists,
and a second contact structure defined in the article gives left-handed twists.Comment: 16 pages, 1 figure; simplification of arguments by restricting
classification to coorientation preserving contactomorphism
Online Popularity and Topical Interests through the Lens of Instagram
Online socio-technical systems can be studied as proxy of the real world to
investigate human behavior and social interactions at scale. Here we focus on
Instagram, a media-sharing online platform whose popularity has been rising up
to gathering hundred millions users. Instagram exhibits a mixture of features
including social structure, social tagging and media sharing. The network of
social interactions among users models various dynamics including
follower/followee relations and users' communication by means of
posts/comments. Users can upload and tag media such as photos and pictures, and
they can "like" and comment each piece of information on the platform. In this
work we investigate three major aspects on our Instagram dataset: (i) the
structural characteristics of its network of heterogeneous interactions, to
unveil the emergence of self organization and topically-induced community
structure; (ii) the dynamics of content production and consumption, to
understand how global trends and popular users emerge; (iii) the behavior of
users labeling media with tags, to determine how they devote their attention
and to explore the variety of their topical interests. Our analysis provides
clues to understand human behavior dynamics on socio-technical systems,
specifically users and content popularity, the mechanisms of users'
interactions in online environments and how collective trends emerge from
individuals' topical interests.Comment: 11 pages, 11 figures, Proceedings of ACM Hypertext 201
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