Cyclic homogeneous Riemannian manifolds

In spin geometry, traceless cyclic homogeneous Riemannian manifolds equipped with a homogeneous spin structure can be viewed as the simplest manifolds after Riemannian symmetric spin spaces. In this paper, we give some characterizations and properties of cyclic and traceless cyclic homogeneous Riemannian manifolds and we obtain the classification of simply-connected cyclic homogeneous Riemannian manifolds of dimension less than or equal to four. We also present a wide list of examples of non-compact irreducible Riemannian $3$-symmetric spaces admitting cyclic metrics and give the expression of these metrics

Singular random matrix decompositions: distributions.

Assuming that Y has a singular matrix variate elliptically contoured distribution with respect to the Hausdorff measure, the distributions of several matrices associated to QR, modified QR, SV and Polar decompositions of matrix Y are determined, for central and non-central, non-singular and singular cases, as well as their relationship to the Wishart and Pseudo-Wishart generalized singular and non-singular distributions. We present a particular example for the Karhunen-Lòeve decomposition. Some of these results are also applied to two particular subfamilies of elliptical distributions, the singular matrix variate normal distribution and the singular matrix variate symmetric Pearson type VII distribution

Homogeneous spin Riemannian manifolds with the simplest Dirac operator

We show the existence of nonsymmetric homogeneous spin Riemannian manifolds whose Dirac operator is like that on a Riemannian symmetric spin space. Such manifolds are exactly the homogeneous spin Riemannian manifolds $(M,g)$ which are traceless cyclic with respect to some quotient expression $M=G/K$ and reductive decomposition $\mathfrak{g} = \mathfrak{k} \oplus \mathfrak{m}$. Using transversally symmetric fibrations of noncompact type, we give a list of them

Singular random matrix decompositions: Jacobians.

For a singular random matrix Y, we find the Jacobians associated with the following decompositions; QR, Polar, Singular Value (SVD), L'U, L'DM and modified QR (QDR). Similarly, we find the Jacobinas of the following decompositions: Spectral, Cholesky's, L'DL and symmetric non-negative definite square root, of the cross-product matrix S = Y'Y

Highly-complex optical signal generation using electro-optical systems with non-linear, non-invertible transmission functions

We present a scheme whereby a static non-linear, non-invertible transmission function performed by the electro-optic Mach-Zehnder modulator produces highly complex optical chaos. The scheme allows the deterministic transformation of low-dimensional band-limited chaotic signals into much higher-dimensional structures with broadband spectra and without using any delay elements or feedback. Standard benchmark tests show that all the considered complexity indices are highly increased due to this transformation in a controlled fashion. This mechanism allows the design of simple optoelectronic delayed oscillators with extremely complex chaotic output.Comment: 4 pages, 5 figures. To appear in Applied Physics Letters (August 2012

Strategic Wage Setting and Coordination Frictions with Multiple Applications

We examine wage competition in a model where identical workers choose the number of jobs to apply for and identical firms simultaneously post a wage. The Nash equilibrium of this game exhibits the following properties: (i) an equilibrium where workers apply for just one job exhibits unemployment and absence of wage dispersion; (ii) an equilibrium where workers apply for two or for more (but not for all) jobs always exhibits wage dispersion and, typically, unemployment; (iii) the equilibrium wage distribution with a higher vacancy-to-unemployment ratio first-order stochastically dominates the wage distribution with a lower level of labor market tightness; (iv) the average wage is non-monotonic in the number of applications; (v) the equilibrium number of applications is non-monotonic in the vacancy-to-unemployment ratio; (vi) a minimum wage increase can be welfare improving because it compresses the wage distribution and reduces the congestion effects caused by the socially excessive number of applications; and (vii) the only way to obtain efficiency is to impose a mandatory wage that eliminates wage dispersion altogether.wage setting, unemployment, minimum wage, Nash equilibrium

SINGULAR RANDOM MATRIX DECOMPOSITIONS: DISTRIBUTIONS.

Assuming that Y has a singular matrix variate elliptically contoured distribution with respect to the Hausdorff measure, the distributions of several matrices associated to QR, modified QR, SV and Polar decompositions of matrix Y are determined, for central and non-central, non-singular and singular cases, as well as their relationship to the Wishart and Pseudo-Wishart generalized singular and non-singular distributions. We present a particular example for the Karhunen-Lòeve decomposition. Some of these results are also applied to two particular subfamilies of elliptical distributions, the singular matrix variate normal distribution and the singular matrix variate symmetric Pearson type VII distribution.