1,628 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
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
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
Representations of p-brane topological charge algebras
The known extended algebras associated with p-branes are shown to be
generated as topological charge algebras of the standard p-brane actions. A
representation of the charges in terms of superspace forms is constructed. The
charges are shown to be the same in standard/extended superspace formulations
of the action.Comment: 22 pages. Typos fixed, refs added. Minor additions to comments
sectio
The Non-Trapping Degree of Scattering
We consider classical potential scattering. If no orbit is trapped at energy
E, the Hamiltonian dynamics defines an integer-valued topological degree. This
can be calculated explicitly and be used for symbolic dynamics of
multi-obstacle scattering.
If the potential is bounded, then in the non-trapping case the boundary of
Hill's Region is empty or homeomorphic to a sphere.
We consider classical potential scattering. If at energy E no orbit is
trapped, the Hamiltonian dynamics defines an integer-valued topological degree
deg(E) < 2. This is calculated explicitly for all potentials, and exactly the
integers < 2 are shown to occur for suitable potentials.
The non-trapping condition is restrictive in the sense that for a bounded
potential it is shown to imply that the boundary of Hill's Region in
configuration space is either empty or homeomorphic to a sphere.
However, in many situations one can decompose a potential into a sum of
non-trapping potentials with non-trivial degree and embed symbolic dynamics of
multi-obstacle scattering. This comprises a large number of earlier results,
obtained by different authors on multi-obstacle scattering.Comment: 25 pages, 1 figure Revised and enlarged version, containing more
detailed proofs and remark
Homological algebra for osp(1/2n)
We discuss several topics of homological algebra for the Lie superalgebra
osp(1|2n). First we focus on Bott-Kostant cohomology, which yields classical
results although the cohomology is not given by the kernel of the Kostant
quabla operator. Based on this cohomology we can derive strong
Bernstein-Gelfand-Gelfand resolutions for finite dimensional osp(1|2n)-modules.
Then we state the Bott-Borel-Weil theorem which follows immediately from the
Bott-Kostant cohomology by using the Peter-Weyl theorem for osp(1|2n). Finally
we calculate the projective dimension of irreducible and Verma modules in the
category O
Nestin in immature embryonic neurons affects axon growth cone morphology and Semaphorin3a sensitivity
Correct wiring in the neocortex requires that responses to an individual guidance cue vary among neurons in the same location, and within the same neuron over time. Nestin is an atypical intermediate filament expressed strongly in neural progenitors and is thus used widely as a progenitor marker. Here we show a subpopulation of embryonic cortical neurons that transiently express nestin in their axons. Nestin expression is thus not restricted to neural progenitors, but persists for 2–3 d at lower levels in newborn neurons. We found that nestin-expressing neurons have smaller growth cones, suggesting that nestin affects cytoskeletal dynamics. Nestin, unlike other intermediate filament subtypes, regulates cdk5 kinase by binding the cdk5 activator p35. Cdk5 activity is induced by the repulsive guidance cue Semaphorin3a (Sema3a), leading to axonal growth cone collapse in vitro. Therefore, we tested whether nestin-expressing neurons showed altered responses to Sema3a. We find that nestin-expressing newborn neurons are more sensitive to Sema3a in a roscovitine-sensitive manner, whereas nestin knockdown results in lowered sensitivity to Sema3a. We propose that nestin functions in immature neurons to modulate cdk5 downstream of the Sema3a response. Thus, the transient expression of nestin could allow temporal and/or spatial modulation of a neuron’s response to Sema3a, particularly during early axon guidance
Putting String/Fivebrane Duality to the Test
According to string/fivebrane duality, the Green-Schwarz factorization of the
spacetime anomaly polynomial into means that just
as is the anomaly polynomial of the string worldsheet so
should be the anomaly polynomial of the fivebrane worldvolume. To test
this idea we perform a fivebrane calculation of and find perfect
agreement with the string one--loop result.Comment: 14 pages, CERN TH-6614/92, CTP-TAMU 60/9
Representation theory of finite W algebras
In this paper we study the finitely generated algebras underlying
algebras. These so called 'finite algebras' are constructed as Poisson
reductions of Kirillov Poisson structures on simple Lie algebras. The
inequivalent reductions are labeled by the inequivalent embeddings of
into the simple Lie algebra in question. For arbitrary embeddings a coordinate
free formula for the reduced Poisson structure is derived. We also prove that
any finite algebra can be embedded into the Kirillov Poisson algebra of a
(semi)simple Lie algebra (generalized Miura map). Furthermore it is shown that
generalized finite Toda systems are reductions of a system describing a free
particle moving on a group manifold and that they have finite symmetry. In
the second part we BRST quantize the finite algebras. The BRST cohomology
is calculated using a spectral sequence (which is different from the one used
by Feigin and Frenkel). This allows us to quantize all finite algebras in
one stroke. Explicit results for and are given. In the last part
of the paper we study the representation theory of finite algebras. It is
shown, using a quantum version of the generalized Miura transformation, that
the representations of finite algebras can be constructed from the
representations of a certain Lie subalgebra of the original simple Lie algebra.
As a byproduct of this we are able to construct the Fock realizations of
arbitrary finite algebras.Comment: 62 pages, THU-92/32, ITFA-28-9
Linking and causality in globally hyperbolic spacetimes
The linking number is defined if link components are zero homologous.
Our affine linking invariant generalizes to the case of linked
submanifolds with arbitrary homology classes. We apply to the study of
causality in Lorentz manifolds. Let be a spacelike Cauchy surface in a
globally hyperbolic spacetime . The spherical cotangent bundle
is identified with the space of all null geodesics in
Hence the set of null geodesics passing through a point gives an
embedded -sphere in called the sky of Low observed
that if the link is nontrivial, then are causally
related. This motivated the problem (communicated by Penrose) on the Arnold's
1998 problem list to apply link theory to the study of causality. The spheres
are isotopic to fibers of They are nonzero
homologous and is undefined when is closed, while is well defined. Moreover, if is not an
odd-dimensional rational homology sphere. We give a formula for the increment
of \alk under passages through Arnold dangerous tangencies. If is
such that takes values in and is conformal to having all
the timelike sectional curvatures nonnegative, then are causally
related if and only if . We show that in
nonrefocussing are causally unrelated iff can be deformed
to a pair of -fibers of by an isotopy through skies. Low
showed that if (\ss, g) is refocussing, then is compact. We show that the
universal cover of is also compact.Comment: We added: Theorem 11.5 saying that a Cauchy surface in a refocussing
space time has finite pi_1; changed Theorem 7.5 to be in terms of conformal
classes of Lorentz metrics and did a few more changes. 45 pages, 3 figures. A
part of the paper (several results of sections 4,5,6,9,10) is an extension
and development of our work math.GT/0207219 in the context of Lorentzian
geometry. The results of sections 7,8,11,12 and Appendix B are ne
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