CFAR matched direction detector

In a previously published paper by Besson et al., we considered the problem of detecting a signal whose associated spatial signature is known to lie in a given linear subspace, in the presence of subspace interference and broadband noise of known level. We extend these results to the case of unknown noise level. More precisely, we derive the generalized-likelihood ratio test (GLRT) for this problem, which provides a constant false-alarm rate (CFAR) detector. It is shown that the GLRT involves the largest eigenvalue and the trace of complex Wishart matrices. The distribution of the GLRT is derived under the hypothesis. Numerical simulations illustrate its performance and provide a comparison with the GLRT when the noise level is known

Poisson-Dirichlet statistics for the extremes of a log-correlated Gaussian field

We study the statistics of the extremes of a discrete Gaussian field with logarithmic correlations at the level of the Gibbs measure. The model is defined on the periodic interval $[0,1]$, and its correlation structure is nonhierarchical. It is based on a model introduced by Bacry and Muzy [Comm. Math. Phys. 236 (2003) 449-475] (see also Barral and Mandelbrot [Probab. Theory Related Fields 124 (2002) 409-430]), and is similar to the logarithmic Random Energy Model studied by Carpentier and Le Doussal [Phys. Rev. E (3) 63 (2001) 026110] and more recently by Fyodorov and Bouchaud [J. Phys. A 41 (2008) 372001]. At low temperature, it is shown that the normalized covariance of two points sampled from the Gibbs measure is either $0$ or $1$. This is used to prove that the joint distribution of the Gibbs weights converges in a suitable sense to that of a Poisson-Dirichlet variable. In particular, this proves a conjecture of Carpentier and Le Doussal that the statistics of the extremes of the log-correlated field behave as those of i.i.d. Gaussian variables and of branching Brownian motion at the level of the Gibbs measure. The method of proof is robust and is adaptable to other log-correlated Gaussian fields.Comment: Published in at http://dx.doi.org/10.1214/13-AAP952 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Electrocarboxylation of chloroacetonitrile mediated by electrogenerated cobalt(I) phenanthroline

The electrocarboxylation of chloroacetonitrilemediated by [Co(II)(phen)3]2+ has been investigated. Cyclic voltammetry studies of [Co(II)(phen)3]2+ have shown that [Co(I)(phen)3]+, an 18 electron complex, activates chloroacetonitrile by an oxidative addition through the loss of a phenanthroline ligand to give [RCo(III)(phen)2Cl]+. The unstable one-electron-reduced complex underwent Co–C bond cleavage. In carbon dioxide saturated solution, CO2 insertion proceeds after reduction of the alkylcobalt complex. A catalytic current is observed which corresponds to the electrocarboxylation of chloroacetonitrile into cyanoacetic acid. Electrolyses confirmed the process and gave faradic yield of 62% in cyanoacetic acid at potentials that are about 0.3 V less cathodic than the one required for Ni(salen)

Matched direction detectors

In this paper, we address the problem of detecting a signal whose associated spatial signature is subject to uncertainties, in the presence of subspace interference and broadband noise, and using multiple snapshots from an array of sensors. To account for steering vector uncertainties, we assume that the spatial signature of interest lies in a given linear subspace H while its coordinates in this subspace are unknown. The generalized likelihood ratio test (GLRT) for the problem at hand is formulated. We show that the GLRT amounts to searching for the best direction in the subspace H after projecting out the interferences. The distribution of the GRLT under both hypotheses is derived and numerical simulations illustrate its performance

Uniqueness of large solutions

Given a nondecreasing nonlinearity $f$, we prove uniqueness of large solutions in the following two cases: the domain is the ball or the domain has nonnegative mean curvature and the nonlinearity is asymptotically convex

Matched direction detectors and estimators for array processing with subspace steering vector uncertainties

In this paper, we consider the problem of estimating and detecting a signal whose associated spatial signature is known to lie in a given linear subspace but whose coordinates in this subspace are otherwise unknown, in the presence of subspace interference and broad-band noise. This situation arises when, on one hand, there exist uncertainties about the steering vector but, on the other hand, some knowledge about the steering vector errors is available. First, we derive the maximum-likelihood estimator (MLE) for the problem and compute the corresponding Cramer-Rao bound. Next, the maximum-likelihood estimates are used to derive a generalized likelihood ratio test (GLRT). The GLRT is compared and contrasted with the standard matched subspace detectors. The performances of the estimators and detectors are illustrated by means of numerical simulations

Adaptive detection of a signal known only to lie on a line in a known subspace, when primary and secondary data are partially homogeneous

This paper deals with the problem of detecting a signal, known only to lie on a line in a subspace, in the presence of unknown noise, using multiple snapshots in the primary data. To account for uncertainties about a signal's signature, we assume that the steering vector belongs to a known linear subspace. Furthermore, we consider the partially homogeneous case, for which the covariance matrix of the primary and the secondary data have the same structure but possibly different levels. This provides an extension to the framework considered by Bose and Steinhardt. The natural invariances of the detection problem are studied, which leads to the derivation of the maximal invariant. Then, a detector is proposed that proceeds in two steps. First, assuming that the noise covariance matrix is known, the generalized-likelihood ratio test (GLRT) is formulated. Then, the noise covariance matrix is replaced by its sample estimate based on the secondary data to yield the final detector. The latter is compared with a similar detector that assumes the steering vector to be known

Linear stability of the 1D Saint-Venant equations and drag parameterizations

The stability of the homogeneous and steady flow based on the one-dimensional Saint-Venant equations for free surface and shallow water flows of constant slope is derived and displayed through graphs. With a suitable choice of units, the small and large drag limits, respectively, correspond to the small and large spatio-temporal scales of a linear system only controlled by the Froude number and two other dimensionless numbers associated with the bottom drag parameterization. Between the small drag limit, with the two families of marginal and non-dispersive shallow water waves, and the large drag limit, with the marginal and non-dispersive waves of the kinematic wave approximation, dispersive roll waves are detailed. These waves are damped or amplified, depending on the value of the three control parameters. The spatial generalized dispersion relations are also derived indicating that the roll-wave instability is of the convective type for all drag parameterizations

High-Reynolds shallow flow over an inclined sinusoidal bottom

An experimental study of a turbulent free-surface shallow flow over an inclined sinusoidal bottom with a fixed corrugation amplitude is presented. A parametric analysis is performed by varying both the inclination angle and the Reynolds number. We show that a “Pulse-Waves” regime, dominant for Reynolds smaller than 4 000, coexists with a “Roll-Waves” regime, which becomes dominant above this value. The relative energy of the waves is quantified in the parameter space. At Reynolds numbers larger than 8 000, these wave instabilities disappear