16,089 research outputs found

### Diffusion Strategies Outperform Consensus Strategies for Distributed Estimation over Adaptive Networks

Adaptive networks consist of a collection of nodes with adaptation and
learning abilities. The nodes interact with each other on a local level and
diffuse information across the network to solve estimation and inference tasks
in a distributed manner. In this work, we compare the mean-square performance
of two main strategies for distributed estimation over networks: consensus
strategies and diffusion strategies. The analysis in the paper confirms that
under constant step-sizes, diffusion strategies allow information to diffuse
more thoroughly through the network and this property has a favorable effect on
the evolution of the network: diffusion networks are shown to converge faster
and reach lower mean-square deviation than consensus networks, and their
mean-square stability is insensitive to the choice of the combination weights.
In contrast, and surprisingly, it is shown that consensus networks can become
unstable even if all the individual nodes are stable and able to solve the
estimation task on their own. When this occurs, cooperation over the network
leads to a catastrophic failure of the estimation task. This phenomenon does
not occur for diffusion networks: we show that stability of the individual
nodes always ensures stability of the diffusion network irrespective of the
combination topology. Simulation results support the theoretical findings.Comment: 37 pages, 7 figures, To appear in IEEE Transactions on Signal
Processing, 201

### On the Influence of Informed Agents on Learning and Adaptation over Networks

Adaptive networks consist of a collection of agents with adaptation and
learning abilities. The agents interact with each other on a local level and
diffuse information across the network through their collaborations. In this
work, we consider two types of agents: informed agents and uninformed agents.
The former receive new data regularly and perform consultation and in-network
tasks, while the latter do not collect data and only participate in the
consultation tasks. We examine the performance of adaptive networks as a
function of the proportion of informed agents and their distribution in space.
The results reveal some interesting and surprising trade-offs between
convergence rate and mean-square performance. In particular, among other
results, it is shown that the performance of adaptive networks does not
necessarily improve with a larger proportion of informed agents. Instead, it is
established that the larger the proportion of informed agents is, the faster
the convergence rate of the network becomes albeit at the expense of some
deterioration in mean-square performance. The results further establish that
uninformed agents play an important role in determining the steady-state
performance of the network, and that it is preferable to keep some of the
highly connected agents uninformed. The arguments reveal an important interplay
among three factors: the number and distribution of informed agents in the
network, the convergence rate of the learning process, and the estimation
accuracy in steady-state. Expressions that quantify these relations are
derived, and simulations are included to support the theoretical findings. We
further apply the results to two models that are widely used to represent
behavior over complex networks, namely, the Erdos-Renyi and scale-free models.Comment: 35 pages, 8 figure

### Reprocessed emission from warped accretion discs induced by the Bardeen-Petterson effect

The broad Balmer emission-line profiles resulting from the reprocessing of
UV/X-ray radiation from a warped accretion disc induced by the
Bardeen-Petterson effect are studied. We adopt a thin warped disc geometry and
a central ring-like illuminating source in our model. We compute the
steady-state shape of the warped disc numerically, and then use it in the
calculation of the line profile. We find that, from the outer radius to the
inner radius of the disc, the warp is twisted by an angle of $\sim\pi$ before
being flattened efficiently into the equatorial plane. The profiles obtained
depend weakly on the illuminating source radius in the range from $3r_{g}$ to
$10r_g$, but depend strongly on this radius when it approaches the marginally
stable orbit of an extreme Kerr black hole. Double- or triplet-peaked line
profiles are present in most cases when the illuminating source radius is low.
The triplet-peaked line profiles observed from the Sloan Digital Sky Survey may
be a {"}signature" of a warped disc.Comment: 8 pages, 6 figures, typos corrected, matches version to appear in
MNRA

### Competing electronic orders on Kagome lattices at van Hove filling

The electronic orders in Hubbard models on a Kagome lattice at van Hove
filling are of intense current interest and debate. We study this issue using
the singular-mode functional renormalization group theory. We discover a rich
variety of electronic instabilities under short range interactions. With
increasing on-site repulsion $U$, the system develops successively
ferromagnetism, intra unit-cell antiferromagnetism, and charge bond order. With
nearest-neighbor Coulomb interaction $V$ alone (U=0), the system develops
intra-unit-cell charge density wave order for small $V$, s-wave
superconductivity for moderate $V$, and the charge density wave order appears
again for even larger $V$. With both $U$ and $V$, we also find spin bond order
and chiral $d_{x^2 - y^2} + i d_{xy}$ superconductivity in some particular
regimes of the phase diagram. We find that the s-wave superconductivity is a
result of charge density wave fluctuations and the squared logarithmic
divergence in the pairing susceptibility. On the other hand, the d-wave
superconductivity follows from bond order fluctuations that avoid the matrix
element effect. The phase diagram is vastly different from that in honeycomb
lattices because of the geometrical frustration in the Kagome lattice.Comment: 8 pages with 9 color figure

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