3,969 research outputs found
Constraining Sub-Parsec Binary Supermassive Black Holes in Quasars with Multi-Epoch Spectroscopy. II. The Population with Kinematically Offset Broad Balmer Emission Lines
A small fraction of quasars have long been known to show bulk velocity
offsets in the broad Balmer lines with respect to the systemic redshift of the
host galaxy. Models to explain these offsets usually invoke broad-line region
gas kinematics/asymmetry around single black holes (BHs), orbital motion of
massive (~sub-pc) binary black holes (BBHs), or recoil BHs, but single-epoch
spectra are unable to distinguish between these scenarios. The line-of-sight
(LOS) radial velocity (RV) shifts from long-term spectroscopic monitoring can
be used to test the BBH hypothesis. We have selected a sample of 399 quasars
with offset broad H-beta lines from the SDSS DR7 quasar catalog, and have
conducted second-epoch optical spectroscopy for 50 of them. Combined with the
existing SDSS spectra, the new observations enable us to constrain the LOS RV
shifts of broad H-beta lines with a rest-frame baseline of a few years to
nearly a decade. Using cross-correlation analysis, we detect significant (99%
confidence) radial accelerations in the broad H-beta lines in 24 of the 50
objects. We suggest that 9 of the 24 detections are sub-pc BBH candidates,
which show consistent velocity shifts independently measured from a second
broad line (either H-alpha or Mg II) without significant changes in the
broad-line profiles. Combining the results on the general quasar population
studied in Paper I, we find a tentative anti-correlation between the velocity
offset in the first-epoch spectrum and the average acceleration between two
epochs, which could be explained by orbital phase modulation when the time
separation between two epochs is a non-negligible fraction of the orbital
period of the motion causing the line displacement. We discuss the implications
of our results for the identification of sub-pc BBH candidates in offset-line
quasars and for the constraints on their frequency and orbital parameters.
[Abridged]Comment: 23 pages, 18 figures, ApJ in pres
The aggregation-diffusion equation with the intermediate exponent
We consider a Keller-Segel model with non-linear porous medium type diffusion
and nonlocal attractive power law interaction, focusing on potentials that are
less singular than Newtonian interaction. Here, the nonlinear diffusion is
chosen to be in which case the steady states
are compactly supported. We analyse under which conditions on the initial data
the regime that attractive forces are stronger than diffusion occurs and
classify the global existence and finite time blow-up of solutions. It is shown
that there is a threshold value which is characterized by the optimal constant
of a variant of Hardy-Littlewood-Sobolev inequality such that the solution will
exist globally if the initial data is below the threshold, while the solution
blows up in finite time when the initial data is above the threshold
Federated Learning via Indirect Server-Client Communications
Federated Learning (FL) is a communication-efficient and privacy-preserving
distributed machine learning framework that has gained a significant amount of
research attention recently. Despite the different forms of FL algorithms
(e.g., synchronous FL, asynchronous FL) and the underlying optimization
methods, nearly all existing works implicitly assumed the existence of a
communication infrastructure that facilitates the direct communication between
the server and the clients for the model data exchange. This assumption,
however, does not hold in many real-world applications that can benefit from
distributed learning but lack a proper communication infrastructure (e.g.,
smart sensing in remote areas). In this paper, we propose a novel FL framework,
named FedEx (short for FL via Model Express Delivery), that utilizes mobile
transporters (e.g., Unmanned Aerial Vehicles) to establish indirect
communication channels between the server and the clients. Two algorithms,
called FedEx-Sync and FedEx-Async, are developed depending on whether the
transporters adopt a synchronized or an asynchronized schedule. Even though the
indirect communications introduce heterogeneous delays to clients for both the
global model dissemination and the local model collection, we prove the
convergence of both versions of FedEx. The convergence analysis subsequently
sheds lights on how to assign clients to different transporters and design the
routes among the clients. The performance of FedEx is evaluated through
experiments in a simulated network on two public datasets.Comment: 6 page
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