18,918 research outputs found
Sterile neutrino Dark Matter production from scalar decay in a thermal bath
We calculate the production rate of singlet fermions from the decay of
neutral or charged scalar fields in a hot plasma. We find that there are
considerable thermal corrections when the temperature of the plasma exceeds the
mass of the decaying scalar. We give analytic expressions for the
temperature-corrected production rates in the regime where the decay products
are relativistic. We also study the regime of non-relativistic decay products
numerically. Our results can be used to determine the abundance and momentum
distribution of Dark Matter particles produced in scalar decays. The inclusion
of thermal corrections helps to improve predictions for the free streaming of
the Dark Matter particles, which is crucial to test the compatibility of a
given model with cosmic structure formation. With some modifications, our
results may be generalised to the production of other Dark Matter candidates in
scalar decays.Comment: This version matches the one published in JHEP. 44 pages, 10 figure
TPA: Fast, Scalable, and Accurate Method for Approximate Random Walk with Restart on Billion Scale Graphs
Given a large graph, how can we determine similarity between nodes in a fast
and accurate way? Random walk with restart (RWR) is a popular measure for this
purpose and has been exploited in numerous data mining applications including
ranking, anomaly detection, link prediction, and community detection. However,
previous methods for computing exact RWR require prohibitive storage sizes and
computational costs, and alternative methods which avoid such costs by
computing approximate RWR have limited accuracy. In this paper, we propose TPA,
a fast, scalable, and highly accurate method for computing approximate RWR on
large graphs. TPA exploits two important properties in RWR: 1) nodes close to a
seed node are likely to be revisited in following steps due to block-wise
structure of many real-world graphs, and 2) RWR scores of nodes which reside
far from the seed node are proportional to their PageRank scores. Based on
these two properties, TPA divides approximate RWR problem into two subproblems
called neighbor approximation and stranger approximation. In the neighbor
approximation, TPA estimates RWR scores of nodes close to the seed based on
scores of few early steps from the seed. In the stranger approximation, TPA
estimates RWR scores for nodes far from the seed using their PageRank. The
stranger and neighbor approximations are conducted in the preprocessing phase
and the online phase, respectively. Through extensive experiments, we show that
TPA requires up to 3.5x less time with up to 40x less memory space than other
state-of-the-art methods for the preprocessing phase. In the online phase, TPA
computes approximate RWR up to 30x faster than existing methods while
maintaining high accuracy.Comment: 12pages, 10 figure
Fast and Accurate Random Walk with Restart on Dynamic Graphs with Guarantees
Given a time-evolving graph, how can we track similarity between nodes in a
fast and accurate way, with theoretical guarantees on the convergence and the
error? Random Walk with Restart (RWR) is a popular measure to estimate the
similarity between nodes and has been exploited in numerous applications. Many
real-world graphs are dynamic with frequent insertion/deletion of edges; thus,
tracking RWR scores on dynamic graphs in an efficient way has aroused much
interest among data mining researchers. Recently, dynamic RWR models based on
the propagation of scores across a given graph have been proposed, and have
succeeded in outperforming previous other approaches to compute RWR
dynamically. However, those models fail to guarantee exactness and convergence
time for updating RWR in a generalized form. In this paper, we propose OSP, a
fast and accurate algorithm for computing dynamic RWR with insertion/deletion
of nodes/edges in a directed/undirected graph. When the graph is updated, OSP
first calculates offset scores around the modified edges, propagates the offset
scores across the updated graph, and then merges them with the current RWR
scores to get updated RWR scores. We prove the exactness of OSP and introduce
OSP-T, a version of OSP which regulates a trade-off between accuracy and
computation time by using error tolerance {\epsilon}. Given restart probability
c, OSP-T guarantees to return RWR scores with O ({\epsilon} /c ) error in O
(log ({\epsilon}/2)/log(1-c)) iterations. Through extensive experiments, we
show that OSP tracks RWR exactly up to 4605x faster than existing static RWR
method on dynamic graphs, and OSP-T requires up to 15x less time with 730x
lower L1 norm error and 3.3x lower rank error than other state-of-the-art
dynamic RWR methods.Comment: 10 pages, 8 figure
Attractor scenarios and superluminal signals in k-essence cosmology
Cosmological scenarios with k-essence are invoked in order to explain the
observed late-time acceleration of the universe. These scenarios avoid the need
for fine-tuned initial conditions (the "coincidence problem") because of the
attractor-like dynamics of the k-essence field \phi. It was recently shown that
all k-essence scenarios with Lagrangians p=L(X)/\phi^2, necessarily involve an
epoch where perturbations of \phi propagate faster than light (the "no-go
theorem"). We carry out a comprehensive study of attractor-like cosmological
solutions ("trackers") involving a k-essence scalar field \phi and another
matter component. The result of this study is a complete classification of
k-essence Lagrangians that admit asymptotically stable tracking solutions,
among all Lagrangians of the form p=K(\phi)L(X) . Using this classification, we
select the class of models that describe the late-time acceleration and avoid
the coincidence problem through the tracking mechanism. An analogous "no-go
theorem" still holds for this class of models, indicating the existence of a
superluminal epoch. In the context of k-essence cosmology, the superluminal
epoch does not lead to causality violations. We discuss the implications of
superluminal signal propagation for possible causality violations in
Lorentz-invariant field theories.Comment: 27 pages, RevTeX4. Minor cosmetic changes, references adde
The electromagnetic form factors of the proton in the timelike region
The reactions ppbar -> e+e- and e+e- -> ppbar are analyzed in the
near-threshold region. Specific emphasis is put on the role played by the
interaction in the initial- or final antinucleon-nucleon state which is taken
into account rigorously. For that purpose a recently published NNbar potential
derived within chiral effective field theory and fitted to results of a new
partial-wave analysis of ppbar scattering data is employed. Our results provide
strong support for the conjecture that the pronounced energy dependence of the
e+e- ppbar cross section, seen in pertinent experiments, is primarily due
to the ppbar interaction. Predictions for the proton electromagnetic form
factors G_E and G_M in the timelike region, close to the NNbar threshold, and
for spin-dependent observables are presented. The steep rise of the effective
form factor for energies close to the ppbar threshold is explained solely in
terms of the ppbar interaction. The corresponding experimental information is
quantitatively described by our calculation.Comment: 14 pages, 11 figure
VoG: Summarizing and Understanding Large Graphs
How can we succinctly describe a million-node graph with a few simple
sentences? How can we measure the "importance" of a set of discovered subgraphs
in a large graph? These are exactly the problems we focus on. Our main ideas
are to construct a "vocabulary" of subgraph-types that often occur in real
graphs (e.g., stars, cliques, chains), and from a set of subgraphs, find the
most succinct description of a graph in terms of this vocabulary. We measure
success in a well-founded way by means of the Minimum Description Length (MDL)
principle: a subgraph is included in the summary if it decreases the total
description length of the graph.
Our contributions are three-fold: (a) formulation: we provide a principled
encoding scheme to choose vocabulary subgraphs; (b) algorithm: we develop
\method, an efficient method to minimize the description cost, and (c)
applicability: we report experimental results on multi-million-edge real
graphs, including Flickr and the Notre Dame web graph.Comment: SIAM International Conference on Data Mining (SDM) 201
{VoG}: {Summarizing} and Understanding Large Graphs
How can we succinctly describe a million-node graph with a few simple sentences? How can we measure the "importance" of a set of discovered subgraphs in a large graph? These are exactly the problems we focus on. Our main ideas are to construct a "vocabulary" of subgraph-types that often occur in real graphs (e.g., stars, cliques, chains), and from a set of subgraphs, find the most succinct description of a graph in terms of this vocabulary. We measure success in a well-founded way by means of the Minimum Description Length (MDL) principle: a subgraph is included in the summary if it decreases the total description length of the graph. Our contributions are three-fold: (a) formulation: we provide a principled encoding scheme to choose vocabulary subgraphs; (b) algorithm: we develop \method, an efficient method to minimize the description cost, and (c) applicability: we report experimental results on multi-million-edge real graphs, including Flickr and the Notre Dame web graph
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