Let A be a real symmetric matrix of size N such that the number of non-zero entries in each row is polylogarithmic in N and the positions and the values of these entries are specified by an efficiently computable function. We consider the problem of estimating an arbitrary diagonal entry (Am) j j of the matrix Am up to an error of ε bm, where b is an a priori given upper bound on the norm of A ...

The Capon beamformer has better resolution and much better interference rejection capability than the standard (data-independent) beamformer, provided that the array steering vector corresponding to the signal of interest (SOI) is accurately known. However, whenever the knowledge of the SOI steering vector is imprecise (as is often the case in practice), the performance of the Capon beamformer ...

The Quantum Unique Ergodicity (QUE) conjecture of RudnickSarnak is that every eigenfunction φn of the Laplacian on a manifold with uniformly-hyperbolic geodesic flow becomes equidistributed in the semiclassical limit (eigenvalue En → ∞), that is, ‘strong scars’ are absent. We study numerically the rate of equidistribution for a uniformly-hyperbolic Sinai-type planar Euclidean billiard with Diri...

Adaptive beamforming suffers from performance degradation in the presence of mismatch between the actual and presumed array steering vector of the desired signal. This idea enlightens us, so we propose a subspace approach to adaptive beamforming that is robust to array errors based on minimizing MUSIC output power. The proposed method involves two steps, the first step is to estimate the actual...

We shall show that any two quadrangulations on the sphere with n vertices can be transformed into each other by at most 6n− 32 diagonal slides and rotations, up to homeomorphism, if n ≥ 9.