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 $\mathbb{CP}^{n+1}$ decomposes into pairs of pants: a pair of pants is a real compact $2n$-manifold with cornered boundary obtained by removing an open regular neighborhood of $n+2$ generic hyperplanes from $\mathbb{CP}^n$. As is well-known, every compact surface of genus $g\geqslant 2$ 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 $(vz')'+Avz = 0$, where $A,v$ 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 $g(t)$ of $g"+Kg=0$, subjected to the initial condition $g(0)=0$, $g'(0)=1$. 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 $K\ge 0$, 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