Nonlinear dynamical systems possessing reflection symmetry have an invariant subspace in the phase space. The dynamics within the invariant subspace can be random or chaotic. As a system parameter changes, the motion transverse to the invariant subspace can lose stability, leading to on-off intermittency. Under certain conditions, the bursting behavior is symmetry breaking. We demonstrate the p...

Codes in finite projective spaces equipped with the subspace distance have been proposed for error control in random linear network coding. The resulting so-called Main Problem of Subspace Coding is to determine the maximum size Aq(v, d) of a code in PG(v−1,Fq) with minimum subspace distance d. Here we completely resolve this problem for d ≥ v − 1. For d = v − 2 we present some improved bounds ...

We derive multi-rank generalizations of the MVDR beamformer to separate an unknown signal of interest in the presence of interference and noise. The spatial signature of the signal is assumed to lie in a known linear subspace, but the orientation of the signal in that subspace is otherwise unknown. The unknown orientation may be fixed for a sequence of experimental realizations, in which case t...

High dimensional data, especially those emerging from genomics and proteomics studies, pose significant challenges to traditional classification algorithms because the performance of these algorithms may substantially deteriorate due to high dimensionality and existence of many noisy features in these data. To address these problems, pre-classification feature selection and aggregating algorith...

Fast estimation and tracking of the principal subspace of a sequence of random vectors is a classic problem, widely encountered in areas such as radar, sonar and speech processing, data compression, data filtering, parameter estimation, pattern recognition, neural analysis, wireless communications, to name just a few. Among the most robust algorithms for subspace tracking there are the so calle...

Using Joint Factor Analysis (JFA) supervector for subspace analysis has many problems, such as high processing complexity and over-fitting. We propose an analysis framework based on random subspace sampling to address these problems. In this framework, JFA supervectors are first partitioned equally and each partitioned subvector is projected on to a subspace by PCA. All projected subvectors are...

We consider estimating a random vector from its measurements in a fusion frame, in presence of noise and subspace erasures. A fusion frame is a collection of subspaces, for which the sum of the projection operators onto the subspaces is bounded below and above by constant multiples of the identity operator. We first consider the linear minimum mean-squared error (LMMSE) estimation of the random...

Codes in the projective space over a finite field, referred to as subspace codes, and in particular codes in the Grassmannian, referred to as constant-dimension codes (CDCs), have been proposed for error control in random network coding. In this paper, we first study the covering properties of CDCs. We determine some fundamental geometric properties of the Grassmannian. Using these properties, ...