Coordinate-Descent Adaptation over Hamiltonian Multi-Agent Networks

The incremental least-mean-square (ILMS) algorithm is a useful method to perform distributed adaptation and learning in Hamiltonian networks. To implement the ILMS algorithm, each node needs to receive the local estimate of the previous node on the cycle path to update its own local estimate. However, in some practical situations, perfect data exchange may not be possible among the nodes. In this paper, we develop a new version of ILMS algorithm, wherein in its adaptation step, only a random subset of the coordinates of update vector is available. We draw a comparison between the proposed coordinate-descent incremental LMS (CD-ILMS) algorithm and the ILMS algorithm in terms of convergence rate and computational complexity. Employing the energy conservation relation approach, we derive closed-form expressions to describe the learning curves in terms of excess mean-square-error (EMSE) and mean-square deviation (MSD). We show that, the CD-ILMS algorithm has the same steady-state error performance compared with the ILMS algorithm. However, the CD-ILMS algorithm has a faster convergence rate. Numerical examples are given to verify the efficiency of the CD-ILMS algorithm and the accuracy of theoretical analysis.

Robust Distributed Kalman Filtering: On the Choice of the Local Tolerance

We propose a distributed Kalman filter for a sensor network under model uncertainty. The distributed scheme is characterized by two communication stages in each time step: in the first stage, the local units exchange their observations and then they can compute their local estimate; in the final stage, the local units exchange their local estimate and compute the final estimate using a diffusion scheme. Each local estimate is computed in order to be optimal according to the least favorable model belonging to a prescribed local ambiguity set. The latter is a ball, in the Kullback–Liebler topology, about the corresponding nominal local model. We propose a strategy to compute the radius, called local tolerance, for each local ambiguity set in the sensor network, rather than keep it constant across the network. Finally, some numerical examples show the effectiveness of the proposed scheme.

Local estimate on convexity radius and decay of injectivity radius in a Riemannian manifold

In this paper, we prove the following pointwise and curvature-free estimates on convexity radius, injectivity radius and local behavior of geodesics in a complete Riemannian manifold [Formula: see text]: (1) the convexity radius of [Formula: see text], [Formula: see text], where [Formula: see text] is the injectivity radius of [Formula: see text] and [Formula: see text] is the focal radius of open ball centered at [Formula: see text] with radius [Formula: see text]; (2) for any two points [Formula: see text] in [Formula: see text], [Formula: see text] where [Formula: see text] is the conjugate radius of [Formula: see text]; (3) for any [Formula: see text], any (not necessarily minimizing) geodesic in [Formula: see text] has length [Formula: see text]. We also clarify two different concepts on convexity radius and give examples to illustrate that the one more frequently used in literature is not continuous.

Gas Seepage along the Edge of the Aquitaine Shelf (France): Origin and Local Fluxes

During the scientific expedition GAZCOGNE2 at the Bay of Biscay nine gas seeps were sampled for the first time and their flux was measured using an in situ pressure-preservation sampler (PEGAZ, ©IFREMER). Overall, three sites were investigated to determine the nature and the origin of the gases bubbling at the seafloor and forming acoustic plumes into the water column, as this was the question raised from the first geologic study of the area. This has guided our study and accordingly corresponds to the main purpose of the present article. Thus, the molecular and isotopic (δD and δ13C) analyses revealed that the gas seeps were primarily composed of methane. Both methane and ethane are of microbial origin, and the former has been generated by microbial reduction of carbon dioxide. Heavier hydrocarbons accounted for less than 0.06% mol of the total amount. Despite the microbial origin of methane, the samples exhibit subtle differences with respect to the δ13CCH4 values, which varied between −72.7 and −66.1‰. It has been suggested that such a discrepancy was predominantly governed by the occurrence of anaerobic methane oxidation. The PEGAZ sampler also enabled us to estimate the local gas fluxes from the sampled streams. The resulting values are extremely heterogeneous between seeps, ranging from 35 to 368 mLn·min−1. Assuming a steady discharge, the mean calculated methane emission for the nine seeps is of 38 kmol·yr−1. Considering the extent of the seep area, this very local estimate suggests that the Aquitaine Shelf is a very appropriate place to study methane discharge and its fate on continental shelves.

Imaging cosmic polarization rotation

We introduce a method to isolate the contribution of parity-violating modes to the peak constrained correlation function. This method can be used as a local estimate of polarization rotation. We test this method using simulations and by applying it to Planck maps [P. A. R. Ade et al., arXiv:1502.01589 astro.ph.co]. We obtain a constraint on the monopole of the polarization rotation angle [Formula: see text].