22,002 research outputs found
Learning Graphs from Linear Measurements: Fundamental Trade-offs and Applications
We consider a specific graph learning task: reconstructing a symmetric matrix that represents an underlying graph using linear measurements. We present a sparsity characterization for distributions of random graphs (that are allowed to contain high-degree nodes), based on which we study fundamental trade-offs between the number of measurements, the complexity of the graph class, and the probability of error. We first derive a necessary condition on the number of measurements. Then, by considering a three-stage recovery scheme, we give a sufficient condition for recovery. Furthermore, assuming the measurements are Gaussian IID, we prove upper and lower bounds on the (worst-case) sample complexity for both noisy and noiseless recovery. In the special cases of the uniform distribution on trees with n nodes and the Erdős-Rényi (n,p) class, the fundamental trade-offs are tight up to multiplicative factors with noiseless measurements. In addition, for practical applications, we design and implement a polynomial-time (in n ) algorithm based on the three-stage recovery scheme. Experiments show that the heuristic algorithm outperforms basis pursuit on star graphs. We apply the heuristic algorithm to learn admittance matrices in electric grids. Simulations for several canonical graph classes and IEEE power system test cases demonstrate the effectiveness and robustness of the proposed algorithm for parameter reconstruction
Cooperative Local Repair in Distributed Storage
Erasure-correcting codes, that support local repair of codeword symbols, have
attracted substantial attention recently for their application in distributed
storage systems. This paper investigates a generalization of the usual locally
repairable codes. In particular, this paper studies a class of codes with the
following property: any small set of codeword symbols can be reconstructed
(repaired) from a small number of other symbols. This is referred to as
cooperative local repair. The main contribution of this paper is bounds on the
trade-off of the minimum distance and the dimension of such codes, as well as
explicit constructions of families of codes that enable cooperative local
repair. Some other results regarding cooperative local repair are also
presented, including an analysis for the well-known Hadamard/Simplex codes.Comment: Fixed some minor issues in Theorem 1, EURASIP Journal on Advances in
Signal Processing, December 201
Multi-objective model for optimizing railway infrastructure asset renewal
Trabalho inspirado num problema real da empresa Infraestruturas de Portugal, EP.A multi-objective model for managing railway infrastructure asset renewal is presented. The model aims to optimize three objectives, while respecting operational constraints: levelling investment throughout multiple years, minimizing total cost and minimizing work start postponements. Its output is an optimized intervention schedule. The model is based on a case study from a Portuguese infrastructure management company, which specified the objectives and constraints, and reflects management practice on railway infrastructure. The results show that investment levelling greatly influences the other objectives and that total cost fluctuations may range from insignificant to important, depending on the condition of the infrastructure. The results structure is argued to be general and suggests a practical methodology for analysing trade-offs and selecting a solution for implementation.info:eu-repo/semantics/publishedVersio
On Fundamental Trade-offs of Device-to-Device Communications in Large Wireless Networks
This paper studies the gains, in terms of served requests, attainable through
out-of-band device-to-device (D2D) video exchanges in large cellular networks.
A stochastic framework, in which users are clustered to exchange videos, is
introduced, considering several aspects of this problem: the video-caching
policy, user matching for exchanges, aspects regarding scheduling and
transmissions. A family of \emph{admissible protocols} is introduced: in each
protocol the users are clustered by means of a hard-core point process and,
within the clusters, video exchanges take place. Two metrics, quantifying the
"local" and "global" fraction of video requests served through D2D are defined,
and relevant trade-off regions involving these metrics, as well as
quality-of-service constraints, are identified. A simple communication strategy
is proposed and analyzed, to obtain inner bounds to the trade-off regions, and
draw conclusions on the performance attainable through D2D. To this end, an
analysis of the time-varying interference that the nodes experience, and tight
approximations of its Laplace transform are derived.Comment: 33 pages, 9 figures. Updated version, to appear in IEEE Transactions
on Wireless Communication
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