19,301 research outputs found
Bourgain-Brezis-Mironescu formula for magnetic operators
We prove a Brezis-Bourgain-Mironescu type formula for a class of nonlocal
magnetic spaces, which builds a bridge between a fractional magnetic operator
recently introduced and the classical theory.Comment: revised versio
Pair of pants decomposition of 4-manifolds
Using tropical geometry, Mikhalkin has proved that every smooth complex
hypersurface in decomposes into pairs of pants: a pair of
pants is a real compact -manifold with cornered boundary obtained by
removing an open regular neighborhood of generic hyperplanes from
. As is well-known, every compact surface of genus decomposes into pairs of pants, and it is now natural to investigate this
construction in dimension 4. Which smooth closed 4-manifolds decompose into
pairs of pants? We address this problem here and construct many examples: we
prove in particular that every finitely presented group is the fundamental
group of a 4-manifold that decomposes into pairs of pants.Comment: 41 pages, 25 figures; exposition has been improved; the proof of
Theorem 2 was incorrect, and it has been fixed. Accepted for publications in
Algebr. Geom. Topo
Spectral radius, index estimates for Schrodinger operators and geometric applications
In this paper we study the existence of a first zero and the oscillatory
behavior of solutions of the ordinary differential equation ,
where are functions arising from geometry. In particular, we introduce a
new technique to estimate the distance between two consecutive zeros. These
results are applied in the setting of complete Riemannian manifolds: in
particular, we prove index bounds for certain Schr\"odinger operators, and an
estimate of the growth of the spectral radius of the Laplacian outside compact
sets when the volume growth is faster than exponential. Applications to the
geometry of complete minimal hypersurfaces of Euclidean space, to minimal
surfaces and to the Yamabe problem are discussed.Comment: 48 page
Some generalizations of Calabi compactness theorem
In this paper we obtain generalized Calabi-type compactness criteria for
complete Riemannian manifolds that allow the presence of negative amounts of
Ricci curvature. These, in turn, can be rephrased as new conditions for the
positivity, for the existence of a first zero and for the
nonoscillatory-oscillatory behaviour of a solution of ,
subjected to the initial condition , . A unified approach for
this ODE, based on the notion of critical curve, is presented. With the aid of
suitable examples, we show that our new criteria are sharp and, even for , in borderline cases they improve on previous works of Calabi, Hille-Nehari
and Moore.Comment: 20 pages, submitte
Do Linguistic Style and Readability of Scientific Abstracts affect their Virality?
Reactions to textual content posted in an online social network show
different dynamics depending on the linguistic style and readability of the
submitted content. Do similar dynamics exist for responses to scientific
articles? Our intuition, supported by previous research, suggests that the
success of a scientific article depends on its content, rather than on its
linguistic style. In this article, we examine a corpus of scientific abstracts
and three forms of associated reactions: article downloads, citations, and
bookmarks. Through a class-based psycholinguistic analysis and readability
indices tests, we show that certain stylistic and readability features of
abstracts clearly concur in determining the success and viral capability of a
scientific article.Comment: Proceedings of the Sixth International AAAI Conference on Weblogs and
Social Media (ICWSM 2012), 4-8 June 2012, Dublin, Irelan
Minimal two-sphere model of the generation of fluid flow at low Reynolds numbers
Locomotion and generation of flow at low Reynolds number are subject to
severe limitations due to the irrelevance of inertia: the "scallop theorem"
requires that the system have at least two degrees of freedom, which move in
non-reciprocal fashion, i.e. breaking time-reversal symmetry. We show here that
a minimal model consisting of just two spheres driven by harmonic potentials is
capable of generating flow. In this pump system the two degrees of freedom are
the mean and relative positions of the two spheres. We have performed and
compared analytical predictions, numerical simulation and experiments, showing
that a time-reversible drive is sufficient to induce flow.Comment: 5 pages, 3 figures, revised version, corrected typo
Influence of homology and node-age on the growth of protein-protein interaction networks
Proteins participating in a protein-protein interaction network can be
grouped into homology classes following their common ancestry. Proteins added
to the network correspond to genes added to the classes, so that the dynamics
of the two objects are intrinsically linked. Here, we first introduce a
statistical model describing the joint growth of the network and the
partitioning of nodes into classes, which is studied through a combined
mean-field and simulation approach. We then employ this unified framework to
address the specific issue of the age dependence of protein interactions,
through the definition of three different node wiring/divergence schemes.
Comparison with empirical data indicates that an age-dependent divergence move
is necessary in order to reproduce the basic topological observables together
with the age correlation between interacting nodes visible in empirical data.
We also discuss the possibility of nontrivial joint partition/topology
observables.Comment: 14 pages, 7 figures [accepted for publication in PRE
- …