Replica Symmetry Breaking in Compressive Sensing

For noisy compressive sensing systems, the asymptotic distortion with respect to an arbitrary distortion function is determined when a general class of least-square based reconstruction schemes is employed. The sampling matrix is considered to belong to a large ensemble of random matrices including i.i.d. and projector matrices, and the source vector is assumed to be i.i.d. with a desired distribution. We take a statistical mechanical approach by representing the asymptotic distortion as a macroscopic parameter of a spin glass and employing the replica method for the large-system analysis. In contrast to earlier studies, we evaluate the general replica ansatz which includes the RS ansatz as well as RSB. The generality of the solution enables us to study the impact of symmetry breaking. Our numerical investigations depict that for the reconstruction scheme with the "zero-norm" penalty function, the RS fails to predict the asymptotic distortion for relatively large compression rates; however, the one-step RSB ansatz gives a valid prediction of the performance within a larger regime of compression rates.Comment: 7 pages, 3 figures, presented at ITA 201

Web Service Retrieval by Structured Models

Much of the information available on theWorldWideWeb cannot effectively be found by the help of search engines because the information is dynamically generated on a user’s request.This applies to online decision support services as well as Deep Web information. We present in this paper a retrieval system that uses a variant of structured modeling to describe such information services, and similarity of models for retrieval. The computational complexity of the similarity problem is discussed, and graph algorithms for retrieval on repositories of service descriptions are introduced. We show how bounds for combinatorial optimization problems can provide filter algorithms in a retrieval context. We report about an evaluation of the retrieval system in a classroom experiment and give computational results on a benchmark library.Economics ;