2,020 research outputs found
Stability of graph communities across time scales
The complexity of biological, social and engineering networks makes it
desirable to find natural partitions into communities that can act as
simplified descriptions and provide insight into the structure and function of
the overall system. Although community detection methods abound, there is a
lack of consensus on how to quantify and rank the quality of partitions. We
show here that the quality of a partition can be measured in terms of its
stability, defined in terms of the clustered autocovariance of a Markov process
taking place on the graph. Because the stability has an intrinsic dependence on
time scales of the graph, it allows us to compare and rank partitions at each
time and also to establish the time spans over which partitions are optimal.
Hence the Markov time acts effectively as an intrinsic resolution parameter
that establishes a hierarchy of increasingly coarser clusterings. Within our
framework we can then provide a unifying view of several standard partitioning
measures: modularity and normalized cut size can be interpreted as one-step
time measures, whereas Fiedler's spectral clustering emerges at long times. We
apply our method to characterize the relevance and persistence of partitions
over time for constructive and real networks, including hierarchical graphs and
social networks. We also obtain reduced descriptions for atomic level protein
structures over different time scales.Comment: submitted; updated bibliography from v
A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments
The computational study of chemical reactions in complex, wet environments is
critical for applications in many fields. It is often essential to study
chemical reactions in the presence of applied electrochemical potentials,
taking into account the non-trivial electrostatic screening coming from the
solvent and the electrolytes. As a consequence the electrostatic potential has
to be found by solving the generalized Poisson and the Poisson-Boltzmann
equation for neutral and ionic solutions, respectively. In the present work
solvers for both problems have been developed. A preconditioned conjugate
gradient method has been implemented to the generalized Poisson equation and
the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the
minimization problem with some ten iterations of a ordinary Poisson equation
solver. In addition, a self-consistent procedure enables us to solve the
non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy
and parallel efficiency, and allow for the treatment of different boundary
conditions, as for example surface systems. The solver has been integrated into
the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be
released as an independent program, suitable for integration in other codes
Variational bound on energy dissipation in turbulent shear flow
We present numerical solutions to the extended Doering-Constantin variational
principle for upper bounds on the energy dissipation rate in plane Couette
flow, bridging the entire range from low to asymptotically high Reynolds
numbers. Our variational bound exhibits structure, namely a pronounced minimum
at intermediate Reynolds numbers, and recovers the Busse bound in the
asymptotic regime. The most notable feature is a bifurcation of the minimizing
wavenumbers, giving rise to simple scaling of the optimized variational
parameters, and of the upper bound, with the Reynolds number.Comment: 4 pages, RevTeX, 5 postscript figures are available as one .tar.gz
file from [email protected]
Negative Quasi-Probability as a Resource for Quantum Computation
A central problem in quantum information is to determine the minimal physical
resources that are required for quantum computational speedup and, in
particular, for fault-tolerant quantum computation. We establish a remarkable
connection between the potential for quantum speed-up and the onset of negative
values in a distinguished quasi-probability representation, a discrete analog
of the Wigner function for quantum systems of odd dimension. This connection
allows us to resolve an open question on the existence of bound states for
magic-state distillation: we prove that there exist mixed states outside the
convex hull of stabilizer states that cannot be distilled to non-stabilizer
target states using stabilizer operations. We also provide an efficient
simulation protocol for Clifford circuits that extends to a large class of
mixed states, including bound universal states.Comment: 15 pages v4: This is a major revision. In particular, we have added a
new section detailing an explicit extension of the Gottesman-Knill simulation
protocol to deal with positively represented states and measurement (even
when these are non-stabilizer). This paper also includes significant
elaboration on the two main results of the previous versio
High Frequency Cluster Radio Galaxies: Luminosity Functions and Implications for SZE Selected Cluster Samples
We study the overdensity of point sources in the direction of X-ray-selected
galaxy clusters from the Meta-Catalog of X-ray detected Clusters of galaxies
(MCXC; ) at South Pole Telescope (SPT) and Sydney
University Molonglo Sky Survey (SUMSS) frequencies. Flux densities at 95, 150
and 220 GHz are extracted from the 2500 deg SPT-SZ survey maps at the
locations of SUMSS sources, producing a multi-frequency catalog of radio
galaxies. In the direction of massive galaxy clusters, the radio galaxy flux
densities at 95 and 150 GHz are biased low by the cluster Sunyaev-Zel'dovich
Effect (SZE) signal, which is negative at these frequencies. We employ a
cluster SZE model to remove the expected flux bias and then study these
corrected source catalogs. We find that the high frequency radio galaxies are
centrally concentrated within the clusters and that their luminosity functions
(LFs) exhibit amplitudes that are characteristically an order of magnitude
lower than the cluster LF at 843 MHz. We use the 150 GHz LF to estimate the
impact of cluster radio galaxies on an SPT-SZ like survey. The radio galaxy
flux typically produces a small bias on the SZE signal and has negligible
impact on the observed scatter in the SZE mass-observable relation. If we
assume there is no redshift evolution in the radio galaxy LF then
percent of the clusters would be lost from the sample. Allowing for redshift
evolution of the form increases the incompleteness to
percent. Improved constraints on the evolution of the cluster radio galaxy LF
require a larger cluster sample extending to higher redshift.Comment: Submitted to MNRA
Scalability of quantum computation with addressable optical lattices
We make a detailed analysis of error mechanisms, gate fidelity, and
scalability of proposals for quantum computation with neutral atoms in
addressable (large lattice constant) optical lattices. We have identified
possible limits to the size of quantum computations, arising in 3D optical
lattices from current limitations on the ability to perform single qubit gates
in parallel and in 2D lattices from constraints on laser power. Our results
suggest that 3D arrays as large as 100 x 100 x 100 sites (i.e.,
qubits) may be achievable, provided two-qubit gates can be performed with
sufficiently high precision and degree of parallelizability. Parallelizability
of long range interaction-based two-qubit gates is qualitatively compared to
that of collisional gates. Different methods of performing single qubit gates
are compared, and a lower bound of is determined on the
error rate for the error mechanisms affecting Cs in a blue-detuned
lattice with Raman transition-based single qubit gates, given reasonable limits
on experimental parameters.Comment: 17 pages, 5 figures. Accepted for publication in Physical Review
Magnetic fields and Sunyaev-Zel'dovich effect in galaxy clusters
In this work we study the contribution of magnetic fields to the Sunyaev
Zeldovich (SZ) effect in the intracluster medium. In particular we calculate
the SZ angular power spectrum and the central temperature decrement. The effect
of magnetic fields is included in the hydrostatic equilibrium equation by
splitting the Lorentz force into two terms one being the force due to magnetic
pressure which acts outwards and the other being magnetic tension which acts
inwards. A perturbative approach is adopted to solve for the gas density
profile for weak magnetic fields (< 4 micro G}). This leads to an enhancement
of the gas density in the central regions for nearly radial magnetic field
configurations. Previous works had considered the force due to magnetic
pressure alone which is the case only for a special set of field
configurations. However, we see that there exists possible sets of
configurations of ICM magnetic fields where the force due to magnetic tension
will dominate. Subsequently, this effect is extrapolated for typical field
strengths (~ 10 micro G) and scaling arguments are used to estimate the angular
power due to secondary anisotropies at cluster scales. In particular we find
that it is possible to explain the excess power reported by CMB experiments
like CBI, BIMA, ACBAR at l > 2000 with sigma_8 ~ 0.8 (WMAP 5 year data) for
typical cluster magnetic fields. In addition we also see that the magnetic
field effect on the SZ temperature decrement is more pronounced for low mass
clusters ( ~ 2 keV). Future SZ detections of low mass clusters at few arc
second resolution will be able to probe this effect more precisely. Thus, it
will be instructive to explore the implications of this model in greater detail
in future works.Comment: 20 pages, 8 figure
Detection of Enhancement in Number Densities of Background Galaxies due to Magnification by Massive Galaxy Clusters
We present a detection of the enhancement in the number densities of
background galaxies induced from lensing magnification and use it to test the
Sunyaev-Zel'dovich effect (SZE) inferred masses in a sample of 19 galaxy
clusters with median redshift selected from the South Pole
Telescope SPT-SZ survey. Two background galaxy populations are selected for
this study through their photometric colours; they have median redshifts
(low- background) and
(high- background). Stacking these
populations, we detect the magnification bias effect at and
for the low- and high- backgrounds, respectively. We fit NFW
models simultaneously to all observed magnification bias profiles to estimate
the multiplicative factor that describes the ratio of the weak lensing
mass to the mass inferred from the SZE observable-mass relation. We further
quantify systematic uncertainties in resulting from the photometric
noise and bias, the cluster galaxy contamination and the estimations of the
background properties. The resulting for the combined background
populations with uncertainties is
, indicating good consistency
between the lensing and the SZE-inferred masses. We use our best-fit to
predict the weak lensing shear profiles and compare these predictions with
observations, showing agreement between the magnification and shear mass
constraints. This work demonstrates the promise of using the magnification as a
complementary method to estimate cluster masses in large surveys.Comment: 16 pages, 10 figures, accepted for publication in MNRA
First-order nature of the ferromagnetic phase transition in (La-Ca)MnO_3 near optimal doping
Neutron scattering has been used to study the nature of the ferromagnetic
transition in single crystals of La_0.7Ca_0.3MnO_3 and La_0.8Ca_0.2MnO_3, and
polycrystalline samples of La_0.67Ca_0.33MnO_3 and La_5/8Ca_3/8MnO_3 where the
naturally occurring O-16 can be replaced with the O-18 isotope. Small angle
neutron scattering on the x=0.3 single crystal reveals a discontinuous change
in the scattering at the Curie temperature for wave vectors below ~0.065 A^-1.
Strong relaxation effects are observed for this domain scattering, for the
magnetic order parameter, and for the quasielastic scattering, demonstrating
that the transition is not continuous in nature. There is a large oxygen
isotope effect observed for the T_C in the polycrystalline samples. For the
optimally doped x=3/8 sample we observed T_C(O-16)=266.5 K and T_C(O-18)=261.5
K at 90% O-18 substitution. The temperature dependence of the spin-wave
stiffness is found to be identical for the two samples despite changes in T_C.
Hence, T_C is not solely determined by the magnetic subsystem, but instead the
ferromagnetic phase is truncated by the formation of polarons which cause an
abrupt transition to the paramagnetic, insulating state. Application of
uniaxial stress in the x=0.3 single crystal sharply enhances the polaron
scattering at room temperature. Measurements of the phonon density-of-states
show only modest differences above and below T_C and between the two different
isotopic samples.Comment: 13 pages, 16 figures, submitted to Phys. Rev.
The Rest-Frame Submillimeter Spectrum of High-Redshift, Dusty, Star-Forming Galaxies
We present the average rest-frame spectrum of high-redshift dusty,
star-forming galaxies from 250-770GHz. This spectrum was constructed by
stacking ALMA 3mm spectra of 22 such sources discovered by the South Pole
Telescope and spanning z=2.0-5.7. In addition to multiple bright spectral
features of 12CO, [CI], and H2O, we also detect several faint transitions of
13CO, HCN, HNC, HCO+, and CN, and use the observed line strengths to
characterize the typical properties of the interstellar medium of these
high-redshift starburst galaxies. We find that the 13CO brightness in these
objects is comparable to that of the only other z>2 star-forming galaxy in
which 13CO has been observed. We show that the emission from the high-critical
density molecules HCN, HNC, HCO+, and CN is consistent with a warm, dense
medium with T_kin ~ 55K and n_H2 >~ 10^5.5 cm^-3. High molecular hydrogen
densities are required to reproduce the observed line ratios, and we
demonstrate that alternatives to purely collisional excitation are unlikely to
be significant for the bulk of these systems. We quantify the average emission
from several species with no individually detected transitions, and find
emission from the hydride CH and the linear molecule CCH for the first time at
high redshift, indicating that these molecules may be powerful probes of
interstellar chemistry in high-redshift systems. These observations represent
the first constraints on many molecular species with rest-frame transitions
from 0.4-1.2mm in star-forming systems at high redshift, and will be invaluable
in making effective use of ALMA in full science operations.Comment: 19 pages, 10 figures (2 in appendices); accepted for publication in
Ap
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