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 $k$ 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