This paper proposes the use of subspace tracking algorithms for performing MIMO channel estimation at millimeter wave (mmWave) frequencies. Using a subspace approach, we develop a protocol enabling the estimation of the right (resp. left) singular vectors at the transmitter (resp. receiver) side; then, we adapt the projection approximation subspace tracking with deflation (PASTd) and the orthog...

In this paper, we use free field realisations of the A-type principal, or Casimir, WN algebras to derive explicit formulae for singular vectors in Fock modules. These singular vectors are constructed by applying screening operators to Fock module highest weight vectors. The action of the screening operators is then explicitly evaluated in terms of Jack symmetric functions and their skew analogu...

Recall this theorem from last time. Theorem 1 (Singular Value Decomposition and best rank-k-approximation) An m × n real matrix has t ≤ min {m,n} nonnegative real numbers σ1, σ2, . . . , σt (called singular values) and two sets of unit vectors U = {u1, u2, . . . , ut} which are in <m and V = v1, v2, . . . , vt ∈ <n (all vectors are column vectors) where U, V are orthogonormal sets and ui M = σi...

The theory of diophantine approximation studies how well x = (x1, . . . , xn) ∈ R can be approximated by (p1/q1, . . . , pn/qn) ∈ Q of a given ‘complexity’, where this complexity is usually measured by the quantity lcm(q1, . . . , qn). Thus one is interested in minimizing the difference, in a suitable sense, between qx and a vector p, where p ∈ Z and q ∈ N, with a given upper bound on q. Often ...

In 1998 the Adapted Ordering Method was developed for the representation theory of the superconformal algebras in two dimensions. It allows: to determine maximal dimensions for a given type of space of singular vectors, to identify all singular vectors by only a few coefficients, to spot subsingular vectors and to set the basis for constructing embedding diagrams. In this article we present the...

Some stochastic evolutions of conformal maps can be described by SLE and may be linked to conformal field theory via stochastic differential equations and singular vectors in highest-weight modules of the Virasoro algebra. Here we discuss how this may be extended to superconformal maps of N = 1 superspace with links to superconformal field theory and singular vectors of the N = 1 superconformal...

The principal component analysis (PCA) faces the problem of high computation complexity and inaccurate estimated covariance matrix from training face images for face recognition. The expressive feature face recognition algorithm (EFFRA) is proposed. In EFFRA, the subspace basic vector extracted by PCA is substituted by the right singular vectors of training images, so that the transformation fr...

Mobile Ad-hoc Networks (MANETs) by contrast of other networks have more vulnerability because of having nature properties such as dynamic topology and no infrastructure. Therefore, a considerable challenge for these networks, is a method expansion that to be able to specify anomalies with high accuracy at network dynamic topology alternation. In this paper, two methods proposed for dynamic anom...

Given a matrix A, it can be shown that there is a vector z ∈ 0, 1 for which |Az|/|Z| ≥ |A|2/C log(n) (a0/1 sum of columns of A which witnesses its large spectral norm) for instance by discretizing the top singular vector of A and taking a dyadic expansion. We give a simple geometric proof of this fact by relating it to the Euclidean diameter of a polytope, and obtain a sharp bound of |Az| ≥ 2|A...

The dynamics of the growth of linear disturbances to a chaotic basic state is analyzed in an asymptotic model of weakly nonlinear, baroclinic wave-mean interaction. In this model, an ordinary differential equation for the wave amplitude is coupled to a partial differential equation for the zonal flow correction. The leading Lyapunov vector is nearly parallel to the leading Floquet vector φ1 of ...