79,665 research outputs found
Influence of initiators on the tipping point in the extended Watts model
In this paper, we study how the influence of initiators (seeds) affects the
tipping point of information cascades in networks. We consider an extended
version of the Watts model, in which each node is either active (i.e., having
adopted an innovation) or inactive. In this extended model, the adoption
threshold, defined as the fraction of active neighbors required for an inactive
node to become active, depends on whether the node is a seed neighbor (i.e.,
connected to one or more initiators) or an ordinary node (i.e., not connected
to any initiators). Using the tree approximation on random graphs, we determine
the tipping point, at which the fraction of active nodes in the final state
increases discontinuously with an increasing seed fraction. The occurrence of a
tipping point and the scale of cascades depend on two factors: whether a giant
component of seed neighbors is formed when the seed fraction is large enough to
trigger cascades among seed neighbors, and whether the giant component of
ordinary nodes is maintained when newly activated nodes trigger further
activations among ordinary nodes. The coexistence of two giant components
suggests that a tipping point can appear twice. We present an example
demonstrating the existence of two tipping points when there is a gap between
the adoption thresholds of seed neighbors and ordinary nodes. Monte Carlo
simulations clearly show that the first cascade, occurring at a small tipping
point, occurs in the giant component of seed neighbors, while the second
cascade, occurring at a larger tipping point, extends into the giant component
of ordinary nodes.Comment: 10 pages, 5 figure
Maximizing Spectral Flux from Self-Seeding Hard X-ray FELs
Fully coherent x-rays can be generated by self-seeding x-ray free-electron
lasers (XFELs). Self-seeding by a forward Bragg diffraction (FBD) monochromator
has been recently proposed [1] and demonstrated [2]. Characteristic time To of
FBD determines the power, spectral, and time characteristics of the FBD seed
[3]. Here we show that for a given electron bunch with duration sigma_e the
spectral flux of the self-seeding XFEL can be maximized, and the spectral
bandwidth can be respectively minimized by choosing To ~ sigma_e/pi and by
optimizing the electron bunch delay tau_e. The choices of To and tau_e are not
unique. In all cases, the maximum value of the spectral flux and the minimum
bandwidth are primarily determined by sigma_e. Two-color seeding takes place To
>> sigma_e/\pi. The studies are performed, for a Gaussian electron bunch
distribution with the parameters, close to those used in the short-bunch
(sigma_e ~ 5 fs) and long-bunch (sigma_e ~ 20 fs) operation modes of the LCLS
XFEL
Pattern vectors from algebraic graph theory
Graphstructures have proven computationally cumbersome for pattern analysis. The reason for this is that, before graphs can be converted to pattern vectors, correspondences must be established between the nodes of structures which are potentially of different size. To overcome this problem, in this paper, we turn to the spectral decomposition of the Laplacian matrix. We show how the elements of the spectral matrix for the Laplacian can be used to construct symmetric polynomials that are permutation invariants. The coefficients of these polynomials can be used as graph features which can be encoded in a vectorial manner. We extend this representation to graphs in which there are unary attributes on the nodes and binary attributes on the edges by using the spectral decomposition of a Hermitian property matrix that can be viewed as a complex analogue of the Laplacian. To embed the graphs in a pattern space, we explore whether the vectors of invariants can be embedded in a low- dimensional space using a number of alternative strategies, including principal components analysis ( PCA), multidimensional scaling ( MDS), and locality preserving projection ( LPP). Experimentally, we demonstrate that the embeddings result in well- defined graph clusters. Our experiments with the spectral representation involve both synthetic and real- world data. The experiments with synthetic data demonstrate that the distances between spectral feature vectors can be used to discriminate between graphs on the basis of their structure. The real- world experiments show that the method can be used to locate clusters of graphs
Seeding for pervasively overlapping communities
In some social and biological networks, the majority of nodes belong to
multiple communities. It has recently been shown that a number of the
algorithms that are designed to detect overlapping communities do not perform
well in such highly overlapping settings. Here, we consider one class of these
algorithms, those which optimize a local fitness measure, typically by using a
greedy heuristic to expand a seed into a community. We perform synthetic
benchmarks which indicate that an appropriate seeding strategy becomes
increasingly important as the extent of community overlap increases. We find
that distinct cliques provide the best seeds. We find further support for this
seeding strategy with benchmarks on a Facebook network and the yeast
interactome.Comment: 8 Page
- …