Independent subspace anlaysis (ISA) is a linear modelbased method which generalizes independent component analysis (ICA) by incorporating the invariant feature subspace into multidimensional ICA. In this paper we apply ISA to the problem of gene expression data analysis and show the useful behavior of the independent subspaces of gene expression data in the task of gene clustering and gene-gene...

We prove that a locally finitely dimensional shiftinvariant linear space of distributions must be a linear subspace of some shift-invariant space generated by finitely many compactly supported distributions. If the locally finitely dimensional shiftinvariant space is a subspace of the Hölder continuous space C or the fractional Sobolev space L , then the superspace can be chosen to be C or L , ...

This paper provides a comprehensive framework for the state-space approach to Boolean networks. First, it surveys the authors' recent work on the topic: Using semitensor product of matrices and the matrix expression of logic, the logical dynamic equations of Boolean (control) networks can be converted into standard discrete-time dynamics. To use the state-space approach, the state space and its...

Given a square matrix A, the inverse subspace problem is concerned with determining a closest matrix to A with a prescribed invariant subspace. When A is Hermitian, the closest matrix may be required to be Hermitian. We measure distance in the Frobenius norm and discuss applications to Krylov subspace methods for the solution of large-scale linear systems of equations and eigenvalue problems as...

Finite codimensional invariant subspaces in the abstract Hardy space defined by a unique representing measure on a uniform algebra are described. Mathematics Subject Classification: Primary 47B48

In this article we present a new method for visual face tracking that is carried out in wavelet subspace. Firstly, a wavelet representation for the face template is created, which spans a low dimensional subspace of the image space. The wavelet representation of the face is a point in this wavelet subspace. The video sequence frames in which the face is tracked are orthogonally projected into t...

In this paper, we introduce subspace-frequently hypercyclic operators. We show that these operators are subspace-hypercyclic and there are subspace-hypercyclic  operators that are not subspace-frequently hypercyclic. There is a criterion like to subspace-hypercyclicity criterion that implies subspace-frequent hypercyclicity and if an operator $T$ satisfies this criterion, then $Toplus T$ is sub...

We present a parallel data-driven strategy to identify finite-dimensional functional spaces invariant under the Koopman operator associated an unknown dynamical system. build on Symmetric Subspace Decomposition (SSD) algorithm, centralized method that mild conditions data sampling provably finds maximal Koopman-invariant subspace and all eigenfunctions in arbitrary space. A network of processor...

We study the following question: suppose that A and B are two algebras of complex n×n matrices such that the ring commutator [A, B] = AB−BA is “small” for each A ∈ A and B ∈ B. Does this imply that A and B have a common non-trivial invariant subspace? This question is motivated by a series of papers studying the structure of “almost-commutative” algebras and, more generally, semigroups. A simpl...

The invariant subspace problem relative to a von Neumann algebra M ⊆ B(H) asks whether every operator T ∈ M has a proper, nontrivial invariant subspace H0 ⊆ H such that the orthogonal projection p onto H0 is an element of M; equivalently, it asks whether there is a projection p ∈ M, p / ∈ {0, 1}, such that Tp = pTp. Even when M is a II1–factor, this invariant subspace problem remains open. In t...