In this paper, we present a novel bilinear invariant representation for multimedia information classification and retrieval. We introduce the concept of kernel space from functional analysis to show that null space invariants are only the special case when the transformation is linear. Subsequently, we derive the exact invariant basis for one of the important applications for kernel space: bili...

We discuss the relation of a certain type of generalized Lyapunov equations to Gramians of stochastic and bilinear systems together with the corresponding energy functionals. While Gramians and energy functionals of stochastic linear systems show a strong correspondence to the analogous objects for deterministic linear systems, the relation of Gramians and energy functionals for bilinear system...

The field of two-dimensional filters and their design methods have been approached by many researchers, for more than three decades (Lim, 1990; Lu & Antoniou, 1992). A commonly-used design technique for 2D filters is to start from a specified 1D prototype filter and transform its transfer function using various frequency mappings in order to obtain a 2D filter with a desired frequency response....

Introduction. During the last 3 years the present author made a series of works [1, 2, 3, 4, 5, 8, 6, 7, 9] dedicated to the study of the unusual spectral properties of low-dimensional continuous and discrete (difference) Schrodinger Operators. Some of these works were done in collaboration with A.Veselov, I.Taimanov and I.Dynnikov. First, let me briefly describe the list of problems discussed ...

A new method for aligning families of two-dimensional polyacrylamide gel electrophoresis (2D-PAGE) images arising in proteomics studies is presented. Forward piecewise bilinear transformations are used to determine an ideal gel and to obtain an initial alignment of the family of gels to this ideal gel. Both the ideal landmarks and the coefficients defining the transformations are obtained by so...

We present a systematic approach to the construction of Miura transformations for discrete Painlevé equations. Our method is based on the bilinear formalism and we start with the expression of the nonlinear discrete equation in terms of τ-functions. Elimination of τ-functions from the resulting system leads to another nonlinear equation, which is a " modified " version of the original equation....

A new method for aligning families of two-dimensional polyacrylamide gel electrophoresis (2D-PAGE) images arising in proteomics studies is presented. Forward piecewise bilinear transformations are used to determine an ideal gel and to obtain an initial alignment of the family of gels to this ideal gel. Both the ideal landmarks and the coefficients defining the transformations are obtained by so...

In this paper, we construct a Darboux transformation and the related Backlund for super-symmetric Sawada-Kotera (SSK) equation. The associated nonlinear superposition formula is ...