Strange nonchaotic attractors typically appear in quasiperiodically driven nonlinear systems. Two methods of their characterization are proposed. The first one is based on the bifurcation analysis of the systems, resulting from periodic approximations of the quasiperiodic forcing. Second, we propose to characterize their strangeness by calculating a phase sensitivity exponent, that measures the...

Consider the n-dimensional vector y = Xβ+ ǫ, where β ∈ R has only k nonzero entries and ǫ ∈ R is a Gaussian noise. This can be viewed as a linear system with sparsity constraints, corrupted by noise. We find a non-asymptotic upper bound on the probability that the optimal decoder for β declares a wrong sparsity pattern, given any generic perturbation matrix X . In the case when X is randomly dr...

We consider the random Gibbs field formalism for the ferromagnetic ID dichotomous random-field Ising model as the simplest example of a quenched disordered system. We prove that for nonzero temperatures the Gibbs state is unique for any realization of the external field. Then we prove that as T-* 0, the Gibbs state converges to a limit, a ground state, for almost all realizations of the externa...

The problem of detecting and locating multiple scatterers in multibaseline Synthetic Aperture Radar (SAR) tomography, starting from compressive measurements and applying support detection techniques, is addressed. Different approaches based on the detection of the support set of the unknown sparse vector, that is, of the position of the nonzero elements in the unknown sparse vector, are analyze...

A low-complexity recursive procedure is presented for model selection and minimum mean squared error (MMSE) estimation in linear regression. Emphasis is given to the case of a sparse parameter vector and fewer observations than unknown parameters. A Gaussian mixture is chosen as the prior on the unknown parameter vector. The algorithm returns both a set of high posterior probability models and ...

The capability of nodes to broadcast their message to the entire wireless network when nodes employ cooperation is considered. We employ an asymptotic analysis using an extended random network setting and show that the broadcast performance strongly depends on the path loss exponent of the medium. In particular, as the size of the random network grows, the probability of broadcast in a one-dime...

We obtain the exact asymptotic result for the disorder-averaged probability distribution function for a random walk in a biased Sinai model and show that it is characterized by a creeping behavior of the displacement moments with time, ∼t(μn), where μ<1 is dimensionless mean drift. We employ a method originated in quantum diffusion which is based on the exact mapping of the problem to an ...

This paper develops a theoretical framework based on Markov chains for the simple genetic algorithm (operators of reproduction, crossover, and mutation). We prove the existence of a unique stationary distribution for the Markov chain when mutation probability is used as a control parameter. We also show that there is a stationary distribution limit when the control parameter approaches zero. Fi...

It is shown that determining whether a quantum computation has a non-zero probability of accepting is at least as hard as the polynomial time hierarchy. This hardness result also applies to determining in general whether a given quantum basis state appears with nonzero amplitude in a superposition, or whether a given quantum bit has positive expectation value at the end of a quantum computation...

with initial conditions x−2, x−1, x0, y−2, y−1, and y0 are nonzero real numbers. Recently, there has been great interest in studying difference equation systems. One of the reasons for this is the necessity for some techniques that can be used in the investigation of equations arising in mathematical models describing real life situations in population biology, economics, probability theory, ge...