In this research paper, nonlinear digital filters based on weak superposition of binary output of rotation invariant Boolean filters (operating on the binary signals obtained by threshold decomposition of digital signal) are proposed. Also, quadratic filters based on Toeplitz weight matrix are proposed and are related to "correlation filters".

In this research paper, threshold decomposition property (arising in the case of rank order order filters) is generalized to bipolar signals. By associating a square "threshold matrix" with a digital signal, its linear algebraic properties are investigated. Also, most general class of nonlinear filters for which the weak superposition property (based on threshold decomposition) holds (in the spirit of rank order filters) are identified. Partition theoretic interpretation of threshold decomposition is explored. It is reasoned that columnwise Boolean median filtering leads to faster implementation of median filter.

In this research paper, we show that the convergence theorem of Hopfield neural network hods true without the condition that the diagonal elements must be non-negative (using epsilon perturbation of diagonal elements). More general version of this result is also proved. It is also shown that the eigenvalue vector of a symmetric matrix and the diagonal element vector are related through a linear system of equations with the coefficient matrix being a doubly stochastic matrix. Also, Perturbation analysis of Hopfield neural network is discussed.

In this research paper, the problem of characterization of corner positive matrices ( an open research problem ) is addressed. Based on optimization of energy function associated with Hopfield Neural Network, an algorithmic approach to determine the corner positive definiteness of a symmetric matrix is proposed. It is reasoned that the problem addressed is an NP hard problem.