27,385 research outputs found
Sketch-based Influence Maximization and Computation: Scaling up with Guarantees
Propagation of contagion through networks is a fundamental process. It is
used to model the spread of information, influence, or a viral infection.
Diffusion patterns can be specified by a probabilistic model, such as
Independent Cascade (IC), or captured by a set of representative traces.
Basic computational problems in the study of diffusion are influence queries
(determining the potency of a specified seed set of nodes) and Influence
Maximization (identifying the most influential seed set of a given size).
Answering each influence query involves many edge traversals, and does not
scale when there are many queries on very large graphs. The gold standard for
Influence Maximization is the greedy algorithm, which iteratively adds to the
seed set a node maximizing the marginal gain in influence. Greedy has a
guaranteed approximation ratio of at least (1-1/e) and actually produces a
sequence of nodes, with each prefix having approximation guarantee with respect
to the same-size optimum. Since Greedy does not scale well beyond a few million
edges, for larger inputs one must currently use either heuristics or
alternative algorithms designed for a pre-specified small seed set size.
We develop a novel sketch-based design for influence computation. Our greedy
Sketch-based Influence Maximization (SKIM) algorithm scales to graphs with
billions of edges, with one to two orders of magnitude speedup over the best
greedy methods. It still has a guaranteed approximation ratio, and in practice
its quality nearly matches that of exact greedy. We also present influence
oracles, which use linear-time preprocessing to generate a small sketch for
each node, allowing the influence of any seed set to be quickly answered from
the sketches of its nodes.Comment: 10 pages, 5 figures. Appeared at the 23rd Conference on Information
and Knowledge Management (CIKM 2014) in Shanghai, Chin
Phase diagram of neutron star quark matter in nonlocal chiral models
We analyze the phase diagram of two-flavor quark matter under neutron star
constraints for a nonlocal covariant quark model within the mean field
approximation. Applications to cold compact stars are discussed.Comment: 3 pages, 1 figure, proceedings of the IV International Conference on
Quarks and Nuclear Physics (QNP06), Madrid, Spain, June 5-10, 2006. To appear
in Eur. Phys. J.
Construction of Simulation Wavefunctions for Aqueous Species: D3O+
This paper investigates Monte Carlo techniques for construction of compact
wavefunctions for the internal atomic motion of the D3O+ ion. The polarization
force field models of Stillinger, et al and of Ojamae, et al. were used.
Initial pair product wavefunctions were obtained from the asymptotic high
temperature many-body density matrix after contraction to atom pairs using
Metropolis Monte Carlo. Subsequent characterization shows these pair product
wavefunctions to be well optimized for atom pair correlations despite that fact
that the predicted zero point energies are too high. The pair product
wavefunctions are suitable to use within variational Monte Carlo, including
excited states, and density matrix Monte Carlo calculations. Together with the
pair product wavefunctions, the traditional variational theorem permits
identification of wavefunction features with significant potential for further
optimization. The most important explicit correlation variable found for the
D3O+ ion was the vector triple product {\bf r}({\bf
r}{\bf r}). Variational Monte Carlo with 9 of such
explicitly correlated functions yielded a ground state wavefunction with an
error of 5-6% in the zero point energy.Comment: 17 pages including 6 figures, typos correcte
Ill-posedness in the Einstein equations
It is shown that the formulation of the Einstein equations widely in use in
numerical relativity, namely, the standard ADM form, as well as some of its
variations (including the most recent conformally-decomposed version), suffers
from a certain but standard type of ill-posedness. Specifically, the norm of
the solution is not bounded by the norm of the initial data irrespective of the
data. A long-running numerical experiment is performed as well, showing that
the type of ill-posedness observed may not be serious in specific practical
applications, as is known from many numerical simulations.Comment: 13 pages, 3 figures, accepted for publication in Journal of
Mathematical Physics (to appear August 2000
Generalized gravity and the late-time cosmic acceleration
High-precision observational data have confirmed with startling evidence that
the Universe is currently undergoing a phase of accelerated expansion. This
phase, one of the most important and challenging current problems in cosmology,
represents a new imbalance in the governing gravitational equations.
Historically, physics has addressed such imbalances by either identifying
sources that were previously unaccounted for, or by altering the gravitational
theory. Several candidates, responsible for this expansion, have been proposed
in the literature, in particular, dark energy models and modified gravity
models, amongst others. Outstanding questions are related to the nature of this
so-called "dark energy" that is driving this acceleration, and whether it is
due to the vacuum energy or a dynamical field. On the other hand, the late-time
cosmic acceleration may be due to modifications of General Relativity. In this
work we explore a generalised modified gravity theory, namely
gravity, where is the Ricci scalar, is a scalar field, and is a
kinetic term. This theory contains a wide range of dark energy and modified
gravity models. We considered specific models and applications to the late-time
cosmic acceleration.Comment: 13 pages, 1 figure; slightly revised version, displayed name
corrected. arXiv admin note: text overlap with arXiv:1412.086
Dynamics of quartz tuning fork force sensors used in scanning probe microscopy
We have performed an experimental characterization of the dynamics of
oscillating quartz tuning forks which are being increasingly used in scanning
probe microscopy as force sensors. We show that tuning forks can be described
as a system of coupled oscillators. Nevertheless, this description requires the
knowledge of the elastic coupling constant between the prongs of the tuning
fork, which has not yet been measured. Therefore tuning forks have been usually
described within the single oscillator or the weakly coupled oscillators
approximation that neglects the coupling between the prongs. We propose three
different procedures to measure the elastic coupling constant: an
opto-mechanical method, a variation of the Cleveland method and a thermal noise
based method. We find that the coupling between the quartz tuning fork prongs
has a strong influence on the dynamics and the measured motion is in remarkable
agreement with a simple model of coupled harmonic oscillators. The precise
determination of the elastic coupling between the prongs of a tuning fork
allows to obtain a quantitative relation between the resonance frequency shift
and the force gradient acting at the free end of a tuning fork prong.Comment: 16 pages, 6 figures, 2 Table
Wave propagation in a fractional viscoelastic tissue model: Application to transluminal procedures
In this article, a wave propagation model is presented as the first step in the development of a new type of transluminal procedure for performing elastography. Elastography is a medical imaging modality for mapping the elastic properties of soft tissue. The wave propagation model is based on a Kelvin Voigt Fractional Derivative (KVFD) viscoelastic wave equation, and is numerically solved using a Finite Difference Time Domain (FDTD) method. Fractional rheological models, such as the KVFD, are particularly well suited to model the viscoelastic response of soft tissue in elastography. The transluminal procedure is based on the transmission and detection of shear waves through the luminal wall. Shear waves travelling through the tissue are perturbed after encountering areas of altered elasticity. These perturbations carry information of medical interest that can be extracted by solving the inverse problem. Scattering from prostate tumours is used as an example application to test the model. In silico results demonstrate that shear waves are satisfactorily transmitted through the luminal wall and that echoes, coming from reflected energy at the edges of an area of altered elasticity, which are feasibly detectable by using the transluminal approach. The model here presented provides a useful tool to establish the feasibility of transluminal procedures based on wave propagation and its interaction with the mechanical properties of the tissue outside the lumen
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