1,989 research outputs found
Romantic Partnerships and the Dispersion of Social Ties: A Network Analysis of Relationship Status on Facebook
A crucial task in the analysis of on-line social-networking systems is to
identify important people --- those linked by strong social ties --- within an
individual's network neighborhood. Here we investigate this question for a
particular category of strong ties, those involving spouses or romantic
partners. We organize our analysis around a basic question: given all the
connections among a person's friends, can you recognize his or her romantic
partner from the network structure alone? Using data from a large sample of
Facebook users, we find that this task can be accomplished with high accuracy,
but doing so requires the development of a new measure of tie strength that we
term `dispersion' --- the extent to which two people's mutual friends are not
themselves well-connected. The results offer methods for identifying types of
structurally significant people in on-line applications, and suggest a
potential expansion of existing theories of tie strength.Comment: Proc. 17th ACM Conference on Computer Supported Cooperative Work and
Social Computing (CSCW), 201
Complex Line Bundles over Simplicial Complexes and their Applications
Discrete vector bundles are important in Physics and recently found
remarkable applications in Computer Graphics. This article approaches discrete
bundles from the viewpoint of Discrete Differential Geometry, including a
complete classification of discrete vector bundles over finite simplicial
complexes. In particular, we obtain a discrete analogue of a theorem of Andr\'e
Weil on the classification of hermitian line bundles. Moreover, we associate to
each discrete hermitian line bundle with curvature a unique piecewise-smooth
hermitian line bundle of piecewise constant curvature. This is then used to
define a discrete Dirichlet energy which generalizes the well-known cotangent
Laplace operator to discrete hermitian line bundles over Euclidean simplicial
manifolds of arbitrary dimension
Pattern equivariant functions and cohomology
The cohomology of a tiling or a point pattern has originally been defined via
the construction of the hull or the groupoid associated with the tiling or the
pattern. Here we present a construction which is more direct and therefore
easier accessible. It is based on generalizing the notion of equivariance from
lattices to point patterns of finite local complexity.Comment: 8 pages including 2 figure
A super-analogue of Kontsevich's theorem on graph homology
In this paper we will prove a super-analogue of a well-known result by
Kontsevich which states that the homology of a certain complex which is
generated by isomorphism classes of oriented graphs can be calculated as the
Lie algebra homology of an infinite-dimensional Lie algebra of symplectic
vector fields.Comment: 15 page
RationalMaps, a package for Macaulay2
This paper describes the RationalMaps package for Macaulay2. This package
provides functionality for computing several aspects of rational maps such as
whether a map is birational, or a closed embedding.Comment: 8 pages. The current version of the package (and other necessary
files) can be accessed at
https://github.com/Macaulay2/Workshop-2016-Utah/tree/master/RationalMap
The Role of the Honors College Dean in the Future of Honors Education
In this chapter, four honors deans reflect on the unique aspects of the honors dean\u27s role. The authors argue that by being responsive to the challenges, opportunities, and responsibilities they face daily, honors deans can enable honors to deliver on its promises to students and to serve the whole university community. Attentive to changing dynamics in honors education nationwide, the authors address how deans must confront myths about honors that bear the legacy of past realities while actively tending to justice in the admissions process, to recruiting and serving diverse populations, and to supporting an honors environment that addresses the needs of the whole student. Doing so, honors deans can be at the forefront of transforming higher education. The authors explore the honors dean’s transformative role of promoting interdisciplinarity, institutional nimbleness, and innovative approaches to fundraising, in addition to the imperative of developing powerful new strategies for telling the story of honors and the value it provides. The authors argue, finally, that honors deans have the critical task of leading honorably, which means that a modern concept of honor, focusing on justice, accessibility, well-being, and empowerment, should lie at the heart of every honors enterprise
Chern-Simons Theory on S^1-Bundles: Abelianisation and q-deformed Yang-Mills Theory
We study Chern-Simons theory on 3-manifolds that are circle-bundles over
2-dimensional surfaces and show that the method of Abelianisation,
previously employed for trivial bundles , can be adapted to
this case. This reduces the non-Abelian theory on to a 2-dimensional
Abelian theory on which we identify with q-deformed Yang-Mills theory,
as anticipated by Vafa et al. We compare and contrast our results with those
obtained by Beasley and Witten using the method of non-Abelian localisation,
and determine the surgery and framing presecription implicit in this path
integral evaluation. We also comment on the extension of these methods to BF
theory and other generalisations.Comment: 37 pages; v2: references adde
Remarks on Legendrian Self-Linking
The Thurston-Bennequin invariant provides one notion of self-linking for any
homologically-trivial Legendrian curve in a contact three-manifold. Here we
discuss related analytic notions of self-linking for Legendrian knots in
Euclidean space. Our definition is based upon a reformulation of the elementary
Gauss linking integral and is motivated by ideas from supersymmetric gauge
theory. We recover the Thurston-Bennequin invariant as a special case.Comment: 42 pages, many figures; v2: minor revisions, published versio
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