1,084 research outputs found
Linear convergence of accelerated conditional gradient algorithms in spaces of measures
A class of generalized conditional gradient algorithms for the solution of
optimization problem in spaces of Radon measures is presented. The method
iteratively inserts additional Dirac-delta functions and optimizes the
corresponding coefficients. Under general assumptions, a sub-linear
rate in the objective functional is obtained, which is sharp
in most cases. To improve efficiency, one can fully resolve the
finite-dimensional subproblems occurring in each iteration of the method. We
provide an analysis for the resulting procedure: under a structural assumption
on the optimal solution, a linear convergence rate is
obtained locally.Comment: 30 pages, 7 figure
Burgers Turbulence
The last decades witnessed a renewal of interest in the Burgers equation.
Much activities focused on extensions of the original one-dimensional
pressureless model introduced in the thirties by the Dutch scientist J.M.
Burgers, and more precisely on the problem of Burgers turbulence, that is the
study of the solutions to the one- or multi-dimensional Burgers equation with
random initial conditions or random forcing. Such work was frequently motivated
by new emerging applications of Burgers model to statistical physics,
cosmology, and fluid dynamics. Also Burgers turbulence appeared as one of the
simplest instances of a nonlinear system out of equilibrium. The study of
random Lagrangian systems, of stochastic partial differential equations and
their invariant measures, the theory of dynamical systems, the applications of
field theory to the understanding of dissipative anomalies and of multiscaling
in hydrodynamic turbulence have benefited significantly from progress in
Burgers turbulence. The aim of this review is to give a unified view of
selected work stemming from these rather diverse disciplines.Comment: Review Article, 49 pages, 43 figure
On the Exploitation of Admittance Measurements for Wired Network Topology Derivation
The knowledge of the topology of a wired network is often of fundamental
importance. For instance, in the context of Power Line Communications (PLC)
networks it is helpful to implement data routing strategies, while in power
distribution networks and Smart Micro Grids (SMG) it is required for grid
monitoring and for power flow management. In this paper, we use the
transmission line theory to shed new light and to show how the topological
properties of a wired network can be found exploiting admittance measurements
at the nodes. An analytic proof is reported to show that the derivation of the
topology can be done in complex networks under certain assumptions. We also
analyze the effect of the network background noise on admittance measurements.
In this respect, we propose a topology derivation algorithm that works in the
presence of noise. We finally analyze the performance of the algorithm using
values that are typical of power line distribution networks.Comment: A version of this manuscript has been submitted to the IEEE
Transactions on Instrumentation and Measurement for possible publication. The
paper consists of 8 pages, 11 figures, 1 tabl
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