76,820 research outputs found
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
Seeding with Costly Network Information
We study the task of selecting nodes in a social network of size , to
seed a diffusion with maximum expected spread size, under the independent
cascade model with cascade probability . Most of the previous work on this
problem (known as influence maximization) focuses on efficient algorithms to
approximate the optimal seed set with provable guarantees, given the knowledge
of the entire network. However, in practice, obtaining full knowledge of the
network is very costly. To address this gap, we first study the achievable
guarantees using influence samples. We provide an approximation
algorithm with a tight (1-1/e){\mbox{OPT}}-\epsilon n guarantee, using
influence samples and show that this dependence on
is asymptotically optimal. We then propose a probing algorithm that queries
edges from the graph and use them to find a seed set with the
same almost tight approximation guarantee. We also provide a matching (up to
logarithmic factors) lower-bound on the required number of edges. To address
the dependence of our probing algorithm on the independent cascade probability
, we show that it is impossible to maintain the same approximation
guarantees by controlling the discrepancy between the probing and seeding
cascade probabilities. Instead, we propose to down-sample the probed edges to
match the seeding cascade probability, provided that it does not exceed that of
probing. Finally, we test our algorithms on real world data to quantify the
trade-off between the cost of obtaining more refined network information and
the benefit of the added information for guiding improved seeding strategies
A graph-based mathematical morphology reader
This survey paper aims at providing a "literary" anthology of mathematical
morphology on graphs. It describes in the English language many ideas stemming
from a large number of different papers, hence providing a unified view of an
active and diverse field of research
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