542 research outputs found
Cooperative Convex Optimization in Networked Systems: Augmented Lagrangian Algorithms with Directed Gossip Communication
We study distributed optimization in networked systems, where nodes cooperate
to find the optimal quantity of common interest, x=x^\star. The objective
function of the corresponding optimization problem is the sum of private (known
only by a node,) convex, nodes' objectives and each node imposes a private
convex constraint on the allowed values of x. We solve this problem for generic
connected network topologies with asymmetric random link failures with a novel
distributed, decentralized algorithm. We refer to this algorithm as AL-G
(augmented Lagrangian gossiping,) and to its variants as AL-MG (augmented
Lagrangian multi neighbor gossiping) and AL-BG (augmented Lagrangian broadcast
gossiping.) The AL-G algorithm is based on the augmented Lagrangian dual
function. Dual variables are updated by the standard method of multipliers, at
a slow time scale. To update the primal variables, we propose a novel,
Gauss-Seidel type, randomized algorithm, at a fast time scale. AL-G uses
unidirectional gossip communication, only between immediate neighbors in the
network and is resilient to random link failures. For networks with reliable
communication (i.e., no failures,) the simplified, AL-BG (augmented Lagrangian
broadcast gossiping) algorithm reduces communication, computation and data
storage cost. We prove convergence for all proposed algorithms and demonstrate
by simulations the effectiveness on two applications: l_1-regularized logistic
regression for classification and cooperative spectrum sensing for cognitive
radio networks.Comment: 28 pages, journal; revise
Large Deviations Performance of Consensus+Innovations Distributed Detection with Non-Gaussian Observations
We establish the large deviations asymptotic performance (error exponent) of
consensus+innovations distributed detection over random networks with generic
(non-Gaussian) sensor observations. At each time instant, sensors 1) combine
theirs with the decision variables of their neighbors (consensus) and 2)
assimilate their new observations (innovations). This paper shows for general
non-Gaussian distributions that consensus+innovations distributed detection
exhibits a phase transition behavior with respect to the network degree of
connectivity. Above a threshold, distributed is as good as centralized, with
the same optimal asymptotic detection performance, but, below the threshold,
distributed detection is suboptimal with respect to centralized detection. We
determine this threshold and quantify the performance loss below threshold.
Finally, we show the dependence of the threshold and performance on the
distribution of the observations: distributed detectors over the same random
network, but with different observations' distributions, for example, Gaussian,
Laplace, or quantized, may have different asymptotic performance, even when the
corresponding centralized detectors have the same asymptotic performance.Comment: 30 pages, journal, submitted Nov 17, 2011; revised Apr 3, 201
Distributed Detection over Random Networks: Large Deviations Performance Analysis
We study the large deviations performance, i.e., the exponential decay rate
of the error probability, of distributed detection algorithms over random
networks. At each time step each sensor: 1) averages its decision variable
with the neighbors' decision variables; and 2) accounts on-the-fly for its new
observation. We show that distributed detection exhibits a "phase change"
behavior. When the rate of network information flow (the speed of averaging) is
above a threshold, then distributed detection is asymptotically equivalent to
the optimal centralized detection, i.e., the exponential decay rate of the
error probability for distributed detection equals the Chernoff information.
When the rate of information flow is below a threshold, distributed detection
achieves only a fraction of the Chernoff information rate; we quantify this
achievable rate as a function of the network rate of information flow.
Simulation examples demonstrate our theoretical findings on the behavior of
distributed detection over random networks.Comment: 30 pages, journal, submitted on December 3rd, 201
The formation of massive, quiescent galaxies at cosmic noon
The cosmic noon (z~1.5-3) marked a period of vigorous star formation for most
galaxies. However, about a third of the more massive galaxies at those times
were quiescent in the sense that their observed stellar populations are
inconsistent with rapid star formation. The reduced star formation activity is
often attributed to gaseous outflows driven by feedback from supermassive black
holes, but the impact of black hole feedback on galaxies in the young Universe
is not yet definitively established. We analyze the origin of quiescent
galaxies with the help of ultra-high resolution, cosmological simulations that
include feedback from stars but do not model the uncertain consequences of
black hole feedback. We show that dark matter halos with specific accretion
rates below ~0.25-0.4 per Gyr preferentially host galaxies with reduced star
formation rates and red broad-band colors. The fraction of such halos in large
dark matter only simulations matches the observed fraction of massive quiescent
galaxies (~10^10-10^11 Msun). This strongly suggests that halo accretion rate
is the key parameter determining which massive galaxies at z~1.5-3 become
quiescent. Empirical models that connect galaxy and halo evolution, such as
halo occupation distribution or abundance matching models, assume a tight link
between galaxy properties and the masses of their parent halos. These models
will benefit from adding the specific accretion rate of halos as a second model
parameter.Comment: 5 pages, 5 figures, to appear in MNRAS Letter
Galactic r-process enrichment by neutron star mergers in cosmological simulations of a Milky Way-mass galaxy
We quantify the stellar abundances of neutron-rich r-process nuclei in
cosmological zoom-in simulations of a Milky Way-mass galaxy from the Feedback
In Realistic Environments project. The galaxy is enriched with r-process
elements by binary neutron star (NS) mergers and with iron and other metals by
supernovae. These calculations include key hydrodynamic mixing processes not
present in standard semi-analytic chemical evolution models, such as galactic
winds and hydrodynamic flows associated with structure formation. We explore a
range of models for the rate and delay time of NS mergers, intended to roughly
bracket the wide range of models consistent with current observational
constraints. We show that NS mergers can produce [r-process/Fe] abundance
ratios and scatter that appear reasonably consistent with observational
constraints. At low metallicity, [Fe/H]<-2, we predict there is a wide range of
stellar r-process abundance ratios, with both supersolar and subsolar
abundances. Low-metallicity stars or stars that are outliers in their r-process
abundance ratios are, on average, formed at high redshift and located at large
galactocentric radius. Because NS mergers are rare, our results are not fully
converged with respect to resolution, particularly at low metallicity. However,
the uncertain rate and delay time distribution of NS mergers introduces an
uncertainty in the r-process abundances comparable to that due to finite
numerical resolution. Overall, our results are consistent with NS mergers being
the source of most of the r-process nuclei in the Universe.Comment: Accepted for publication in MNRAS, 10 pages and 4 figures. Revised
version: minor change
Giant clumps in the FIRE simulations: a case study of a massive high-redshift galaxy
The morphology of massive star-forming galaxies at high redshift is often
dominated by giant clumps of mass ~10^8-10^9 Msun and size ~100-1000 pc.
Previous studies have proposed that giant clumps might have an important role
in the evolution of their host galaxy, particularly in building the central
bulge. However, this depends on whether clumps live long enough to migrate from
their original location in the disc or whether they get disrupted by their own
stellar feedback before reaching the centre of the galaxy. We use cosmological
hydrodynamical simulations from the FIRE (Feedback in Realistic Environments)
project that implement explicit treatments of stellar feedback and ISM physics
to study the properties of these clumps. We follow the evolution of giant
clumps in a massive (stellar mass ~10^10.8 Msun at z=1), discy, gas-rich galaxy
from redshift z>2 to z=1. Even though the clumpy phase of this galaxy lasts
over a gigayear, individual gas clumps are short-lived, with mean lifetime of
massive clumps of ~20 Myr. During that time, they turn between 0.1% and 20% of
their gas into stars before being disrupted, similar to local GMCs. Clumps with
M>10^7 Msun account for ~20% of the total star formation in the galaxy during
the clumpy phase, producing ~10^10 Msun of stars. We do not find evidence for
net inward migration of clumps within the galaxy. The number of giant clumps
and their mass decrease at lower redshifts, following the decrease in the
overall gas fraction and star-formation rate.Comment: 20 pages, 19 figures; revised version, accepted for publication in
MNRA
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