22,431 research outputs found
Second look at the spread of epidemics on networks
In an important paper, M.E.J. Newman claimed that a general network-based
stochastic Susceptible-Infectious-Removed (SIR) epidemic model is isomorphic to
a bond percolation model, where the bonds are the edges of the contact network
and the bond occupation probability is equal to the marginal probability of
transmission from an infected node to a susceptible neighbor. In this paper, we
show that this isomorphism is incorrect and define a semi-directed random
network we call the epidemic percolation network that is exactly isomorphic to
the SIR epidemic model in any finite population. In the limit of a large
population, (i) the distribution of (self-limited) outbreak sizes is identical
to the size distribution of (small) out-components, (ii) the epidemic threshold
corresponds to the phase transition where a giant strongly-connected component
appears, (iii) the probability of a large epidemic is equal to the probability
that an initial infection occurs in the giant in-component, and (iv) the
relative final size of an epidemic is equal to the proportion of the network
contained in the giant out-component. For the SIR model considered by Newman,
we show that the epidemic percolation network predicts the same mean outbreak
size below the epidemic threshold, the same epidemic threshold, and the same
final size of an epidemic as the bond percolation model. However, the bond
percolation model fails to predict the correct outbreak size distribution and
probability of an epidemic when there is a nondegenerate infectious period
distribution. We confirm our findings by comparing predictions from percolation
networks and bond percolation models to the results of simulations. In an
appendix, we show that an isomorphism to an epidemic percolation network can be
defined for any time-homogeneous stochastic SIR model.Comment: 29 pages, 5 figure
Blowup of Jang's equation at outermost marginally trapped surfaces
The aim of this paper is to collect some facts about the blowup of Jang's
equation. First, we discuss how to construct solutions that blow up at an
outermost MOTS. Second, we exclude the possibility that there are extra blowup
surfaces in data sets with non-positive mean curvature. Then we investigate the
rate of convergence of the blowup to a cylinder near a strictly stable MOTS and
show exponential convergence near a strictly stable MOTS.Comment: 15 pages. This revision corrects some typo
Residue currents associated with weakly holomorphic functions
We construct Coleff-Herrera products and Bochner-Martinelli type residue
currents associated with a tuple of weakly holomorphic functions, and show
that these currents satisfy basic properties from the (strongly) holomorphic
case, as the transformation law, the Poincar\'e-Lelong formula and the
equivalence of the Coleff-Herrera product and the Bochner-Martinelli type
residue current associated with when defines a complete intersection.Comment: 28 pages. Updated with some corrections from the revision process. In
particular, corrected and clarified some things in Section 5 and 6 regarding
products of weakly holomorphic functions and currents, and the definition of
the Bochner-Martinelli type current
Non-adiabatic holonomic quantum computation
We develop a non-adiabatic generalization of holonomic quantum computation in
which high-speed universal quantum gates can be realized by using non-Abelian
geometric phases. We show how a set of non-adiabatic holonomic one- and
two-qubit gates can be implemented by utilizing optical transitions in a
generic three-level configuration. Our scheme opens up for universal
holonomic quantum computation on qubits characterized by short coherence times.Comment: Some changes, journal reference adde
Delocalization power of global unitary operations on quantum information
We investigate how originally localized two pieces of quantum information
represented by a tensor product of two unknown qudit states are delocalized by
performing two-qudit global unitary operations. To characterize the
delocalization power of global unitary operations on quantum information, we
analyze the necessary and sufficient condition to deterministically relocalize
one of the two pieces of quantum information to its original Hilbert space by
using only LOCC. We prove that this LOCC one-piece relocalization is possible
if and only if the global unitary operation is local unitary equivalent to a
controlled-unitary operation. The delocalization power and the entangling power
characterize different non-local properties of global unitary operations.Comment: 14 pages, 1 figur
A detailed study of quasinormal frequencies of the Kerr black hole
We compute the quasinormal frequencies of the Kerr black hole using a
continued fraction method. The continued fraction method first proposed by
Leaver is still the only known method stable and accurate for the numerical
determination of the Kerr quasinormal frequencies. We numerically obtain not
only the slowly but also the rapidly damped quasinormal frequencies and analyze
the peculiar behavior of these frequencies at the Kerr limit. We also calculate
the algebraically special frequency first identified by Chandrasekhar and
confirm that it coincide with the quasinormal frequency only at the
Schwarzschild limit.Comment: REVTEX, 15 pages, 7 eps figure
Revival of quantum correlations without system-environment back-action
Revivals of quantum correlations have often been explained in terms of
back-action on quantum systems by their quantum environment(s). Here we
consider a system of two independently evolving qubits, each locally
interacting with a classical random external field. The environments of the
qubits are also independent, and there is no back-action on the qubits.
Nevertheless, entanglement, quantum discord and classical correlations between
the two qubits may revive in this model. We explain the revivals in terms of
correlations in a classical-quantum state of the environments and the qubits.
Although classical states cannot store entanglement on their own, they can play
a role in storing and reviving entanglement. It is important to know how the
absence of back-action, or modelling an environment as classical, affects the
kind of system time evolutions one is able to describe. We find a class of
global time evolutions where back-action is absent and for which there is no
loss of generality in modelling the environment as classical. Finally, we show
that the revivals can be connected with the increase of a parameter used to
quantify non-Markovianity of the single-qubit dynamics.Comment: 8 pages, 4 figures; this version to appear in Phys. Rev.
Energy dependence of transverse mass spectra of kaons produced in p+p and p+pbar interactions.A compilation
The data on m_T spectra of K0S K+ and K- mesons produced in all inelastic p+p
and p+pbar interactions in the energy range sqrt(s)NN=4.7-1800GeV are compiled
and analyzed. The spectra are parameterized by a single exponential function,
dN/(m_T*dm_T)=C exp(-m_T/T), and the inverse slope parameter T is the main
object of study. The T parameter is found to be similar for K0S, K+ and K-
mesons. It increases monotonically with collision energy from T~30MeV at
sqrt(s)NN=4.7GeV to T~220MeV at sqrt(s)NN=1800GeV. The T parameter measured in
p+p and p+pbar interactions is significantly lower than the corresponding
parameter obtained for central Pb+Pb collisions at all studied energies. Also
the shape of the energy dependence of is different for central Pb+Pb
collisions and p+p(pbar) interactions.Comment: more differential analysis adde
Decay widths of large-spin mesons from the non-critical string/gauge duality
In this paper, we use the non-critical string/gauge duality to calculate the
decay widths of large-spin mesons. Since it is believed that the string theory
of QCD is not a ten dimensional theory, we expect that the non-critical
versions of ten dimensional black hole backgrounds lead to better results than
the critical ones. For this purpose we concentrate on the confining theories
and consider two different six dimensional black hole backgrounds. We choose
the near extremal AdS6 model and the near extremal KM model to compute the
decay widths of large-spin mesons. Then, we present our results from these two
non-critical backgrounds and compare them together with those from the critical
models and experimental data.Comment: 21 pages and 3 figure
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