Algebraic algorithms deal with numbers, vectors, matrices, polynomials, for-mal power series, exponential and differential polynomials, rational functions, algebraic sets, curves and surfaces. In this vast area, manipulation with matri-ces and polynomials is fundamental for modern computations

This is a preliminary version of a Chapter on Algebraic Algorithms in the up-

Anne SABOURIN Mélanges bayésiens de modèles d'extrêmes multivariés, Application à la prédétermination régionale des crues avec données incomplètes. Sous la direction de:

Abstract—The performance analysis of random vector chan-nels, particularly multiple-input-multiple-output (MIMO) chan-nels, has largely been established in the asymptotic regime of large channel dimensions, due to the analytical intractability of characterizing the exact distribution of the objective performance metrics. This paper exposes a new non-asymptotic framework that allows the characterization of many canonical MIMO system performance metrics to within a narrow interval under moderate-to-large channel dimensionality, provided that these metrics can be expressed as a separable function of the singular values of the matrix. The effectiveness of our framework is illustrated through two canonical examples. Specifically, we characterize the mutual information and power offset of random MIMO channels, as well as the minimum mean squared estimation error of MIMO channel inputs from the channel outputs. Our results lead to simple, informative, and reasonably accurate control of various performance metrics in the finite-dimensional regime, as corroborated by the numerical simulations. Our analysis frame-work is established via the concentration of spectral measure phenomenon for random matrices uncovered by Guionnet and Zeitouni, which arises in a variety of random matrix ensembles irrespective of the precise distributions of the matrix entries. Index Terms—MIMO, massive MIMO, confidence interval, concentration of spectral measure, random matrix theory, non-asymptotic analysis, mutual information, MMSE I.

We are surrounded by electronic devices that take advantage of wireless technologies, from our computer mice, which require little amounts of information, to our cellphones, which demand increasingly higher data rates. Until today, the coexistence of such a variety of services has been guaranteed by a fixed assignment of spectrum resources by regulatory agencies. This has resulted into a blind alley, as current wireless spectrum has become an expensive and a scarce resource. However, recent measurements in dense areas paint a very different picture: there is an actual underutilization of the spectrum by legacy sys-tems. Cognitive radio exhibits a tremendous promise for increasing the spectral efficiency for future wireless systems. Ideally, new secondary users would have a perfect panorama of the spectrum usage, and would opportunistically communicate over the available re-sources without degrading the primary systems. Yet in practice, monitoring the spectrum resources, detecting available resources for opportunistic communication, and transmit-ting over the resources are hard tasks. This thesis addresses the tasks of monitoring, de-

methods for phase retrieval

Caractérisation des problèmes conjoints de détection et d'estimation

de nationalité suisse et originaire de Zurich (ZH) et Lucerne (LU) acceptée sur proposition du jury:

Abstract. In this paper we design an econometric test for monotone comparative statics (MCS) often found in models with multiple equilibria. Our test exploits the observable implications of the MCS prediction: that the extreme (high and low) conditional quantiles of the dependent variable increase monotonically with the explanatory variable. The main contribution of the paper is to derive a likelihood-ratio test, which to the best of our knowledge, is the first econometric test of MCS proposed in the literature. The test is an asymptotic “chi-bar squared ” test for order restrictions on intermediate conditional quantiles. The key features of our approach are: (1) we do not need to estimate the underlying nonparametric model relating the dependent and explanatory variables to the latent disturbances; (2) we make few assumptions on the cardinality, location, or probabilities over equilibria. In particular, one can implement our test without assuming an equilibrium selection rule.

Abstract not found