Cramer-Rao Bound for Sparse Signals Fitting the Low-Rank Model with Small Number of Parameters

In this paper, we consider signals with a low-rank covariance matrix which reside in a low-dimensional subspace and can be written in terms of a finite (small) number of parameters. Although such signals do not necessarily have a sparse representation in a finite basis, they possess a sparse structure which makes it possible to recover the signal from compressed measurements. We study the statistical performance bound for parameter estimation in the low-rank signal model from compressed measurements. Specifically, we derive the Cramer-Rao bound (CRB) for a generic low-rank model and we show that the number of compressed samples needs to be larger than the number of sources for the existence of an unbiased estimator with finite estimation variance. We further consider the applications to direction-of-arrival (DOA) and spectral estimation which fit into the low-rank signal model. We also investigate the effect of compression on the CRB by considering numerical examples of the DOA estimation scenario, and show how the CRB increases by increasing the compression or equivalently reducing the number of compressed samples.Comment: 14 pages, 1 figure, Submitted to IEEE Signal Processing Letters on December 201

Convergence of optimal control problems governed by second kind parabolic variational inequalities

We consider a family of optimal control problems where the control variable is given by a boundary condition of Neumann type. This family is governed by parabolic variational inequalities of the second kind. We prove the strong convergence of the optimal controls and state systems associated to this family to a similar optimal control problem. This work solves the open problem left by the authors in IFIP TC7 CSMO2011

Electron-electron and spin-orbit interactions in armchair graphene ribbons

The effects of intrinsic spin-orbit and Coulomb interactions on low-energy properties of finite width graphene armchair ribbons are studied by means of a Dirac Hamiltonian. It is shown that metallic states subsist in the presence of intrinsic spin-orbit interactions as spin-filtered edge states, in contrast with the insulating behavior predicted for graphene planes. A charge-gap opens due to Coulomb interactions in neutral ribbons, that vanishes as $\Delta\sim 1/W$, with a gapless spin sector. Weak intrinsic spin-orbit interactions do not change the insulating behavior. Explicit expressions for the width-dependent gap and various correlation functions are presented.Comment: Will appear in PR

Identifying psychological and socio-economic factors affecting motorcycle helmet use

Sixty percent of motorcyclist fatalities in traffic accidents of Iran are due to head injuries, but helmet use is low, despite it being a legal requirement. This study used face-to-face interviews to investigate the factors associated with helmet use among motorcycle riders in Mashhad city, the second largest city in Iran. Principal Component Analysis (PCA) and Confirmatory Factor Analysis (CFA) were used for data reduction and identification of consistent features of the data. Ordered and multinomial logit analyses were used to quantify the influences on helmet use and non-use. The data show that 47% of the sample used a helmet use, but a substantial proportion of these did not wear their helmet properly. In addition, 5% of motorcyclists believed that helmets reduced their safety. Norms, attitudes toward helmet use, risky traffic behavior and awareness of traffic rules were found to be the key determinants of helmet use, but perceptions of enforcement lacked influence. Duration of daily motorcycle trips, riding experience and type of job also affected helmet use. Results indicate that motorcyclist training, safety courses for offending motorcyclists and social programs to improve social norms and attitudes regarding helmet use are warranted, as are more effective law enforcement techniques, in order to increase proper use of helmets in Iranian motorcyclists. In addition, special safety courses should be considered for motorcyclists who have committed traffic violations

SWKB and proper quantization conditions for translationally shape invariant potentials

Using a recently proposed classification for the primary translationally shape invariant potentials, we show that the exact quantization rule formulated by Ma and Xu is equivalent to the supersymmetric JWKB quantization condition. The energy levels for the two considered categories of shaped invariant potentials are also derived