8,018 research outputs found
Explaining Snapshots of Network Diffusions: Structural and Hardness Results
Much research has been done on studying the diffusion of ideas or
technologies on social networks including the \textit{Influence Maximization}
problem and many of its variations. Here, we investigate a type of inverse
problem. Given a snapshot of the diffusion process, we seek to understand if
the snapshot is feasible for a given dynamic, i.e., whether there is a limited
number of nodes whose initial adoption can result in the snapshot in finite
time. While similar questions have been considered for epidemic dynamics, here,
we consider this problem for variations of the deterministic Linear Threshold
Model, which is more appropriate for modeling strategic agents. Specifically,
we consider both sequential and simultaneous dynamics when deactivations are
allowed and when they are not. Even though we show hardness results for all
variations we consider, we show that the case of sequential dynamics with
deactivations allowed is significantly harder than all others. In contrast,
sequential dynamics make the problem trivial on cliques even though it's
complexity for simultaneous dynamics is unknown. We complement our hardness
results with structural insights that can help better understand diffusions of
social networks under various dynamics.Comment: 14 pages, 3 figure
Rouse Chains with Excluded Volume Interactions: Linear Viscoelasticity
Linear viscoelastic properties for a dilute polymer solution are predicted by
modeling the solution as a suspension of non-interacting bead-spring chains.
The present model, unlike the Rouse model, can describe the solution's
rheological behavior even when the solvent quality is good, since excluded
volume effects are explicitly taken into account through a narrow Gaussian
repulsive potential between pairs of beads in a bead-spring chain. The use of
the narrow Gaussian potential, which tends to the more commonly used
delta-function repulsive potential in the limit of a width parameter "d" going
to zero, enables the performance of Brownian dynamics simulations. The
simulations results, which describe the exact behavior of the model, indicate
that for chains of arbitrary but finite length, a delta-function potential
leads to equilibrium and zero shear rate properties which are identical to the
predictions of the Rouse model. On the other hand, a non-zero value of "d"
gives rise to a prediction of swelling at equilibrium, and an increase in zero
shear rate properties relative to their Rouse model values. The use of a
delta-function potential appears to be justified in the limit of infinite chain
length. The exact simulation results are compared with those obtained with an
approximate solution which is based on the assumption that the non-equilibrium
configurational distribution function is Gaussian. The Gaussian approximation
is shown to be exact to first order in the strength of excluded volume
interaction, and is found to be accurate above a threshold value of "d", for
given values of chain length and strength of excluded volume interaction.Comment: Revised version. Long chain limit analysis has been deleted. An
improved and corrected examination of the long chain limit will appear as a
separate posting. 32 pages, 9 postscript figures, LaTe
Prospects of Detecting Baryon and Quark Superfluidity from Cooling Neutron Stars
Baryon and quark superfluidity in the cooling of neutron stars are
investigated. Observations could constrain combinations of the neutron or
Lambda-hyperon pairing gaps and the star's mass. However, in a hybrid star with
a mixed phase of hadrons and quarks, quark gaps larger than a few tenths of an
MeV render quark matter virtually invisible for cooling. If the quark gap is
smaller, quark superfluidity could be important, but its effects will be nearly
impossible to distinguish from those of other baryonic constituents.Comment: 4 pages, 3 ps figures, uses RevTex(aps,prl). Submitted to Phys. Rev.
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Neutrino Emission from Goldstone Modes in Dense Quark Matter
We calculate neutrino emissivities from the decay and scattering of Goldstone
bosons in the color-flavor-locked (CFL) phase of quarks at high baryon density.
Interactions in the CFL phase are described by an effective low-energy theory.
For temperatures in the tens of keV range, relevant to the long-term cooling of
neutron stars, the emissivities involving Goldstone bosons dominate over those
involving quarks, because gaps in the CFL phase are MeV while the
masses of Goldstone modes are on the order of 10 MeV. For the same reason, the
specific heat of the CFL phase is also dominated by the Goldstone modes.
Notwithstanding this, both the emissivity and the specific heat from the
massive modes remain rather small, because of their extremely small number
densities. The values of the emissivity and the specific heat imply that the
timescale for the cooling of the CFL core in isolation is y,
which makes the CFL phase invisible as the exterior layers of normal matter
surrounding the core will continue to cool through significantly more rapid
processes. If the CFL phase appears during the evolution of a proto-neutron
star, neutrino interactions with Goldstone bosons are expected to be
significantly more important since temperatures are high enough (
MeV) to admit large number densities of Goldstone modes.Comment: 29 pages, no figures. slightly modified text, one new eqn. and new
refs. adde
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