A BCI system, using orthogonalized EEG data sets and multiple multilayer neural networks (MLNNs) in a parallel form, is proposed. In order to emphasize feature of multi-channel EEG data, Gram-Schmidt orthogonalization has been applied. Since there are many channel orders to be orthogonalized, many kinds of orthogonalized data sets can be generated for the same EEG data set by changing the chann...

Two methods for solving the generalized Stokes problems that occur in viscous, incompressible ows are described and tested. Both are based on some type of linear algebraic orthogonaliza-tion process. The rst, EMGS, is a preconditioner derived from an incomplete Gram{Schmidt factorization, and it is proven to exist whenever the matrix being preconditioned can be factored using Gaussian eliminati...

Let μ be a probability measure on the real line with finite moments of all orders. Apply Gram-Schmidt orthogonalization process to the system {1, x, · · · , x, . . . } to get a sequence {Pn}∞n=0 of orthogonal polynomials with respect to μ. In this paper we explain a method of deriving a generating function ψ(t, x) for μ. The power series expansion of ψ(t, x) in t produces the explicit form of p...

Selected Common Threads and Root Concepts Linking Old to New Sandra L. Arlinghaus* and Joseph Kerski** Introduction In the twentieth century, much of mathematics experienced a well-known paradigm shift in moving from a focus on mathematical objects to a focus on transformations of objects. Thus, one sees, for example, linear algebra courses that focus on matrix vector products as linear transfo...

This paper presents a branch-and-lift algorithm for solving optimal control problems with smooth nonlinear dynamics and potentially nonconvex objective and constraint functionals to guaranteed global optimality. This algorithm features a direct sequential method and builds upon a generic, spatial branch-and-bound algorithm. A new operation, called lifting, is introduced, which refines the contr...

By the example of a mathematical model of a biochemical process, the structural instability of dynamical systems is studied by calculating the full spectrum of Lyapunov indices with the use of the generalized Benettin algorithm. For the reliability of the results obtained, the higher Lyapunov index determined with the orthogonalization of perturbation vectors by the Gram– Schmidt method is comp...

The Gram-Schmidt Process (GSP) is used to convert a non-orthogonal basis (a set of linearly independent vectors, matrices, etc) into an orthonormal basis (a set of orthogonal, unit-length vectors, bi or tri dimensional matrices). The process consists of taking each array and then subtracting the projections in common with the previous arrays. This paper introduces an enhanced version of the Gra...

We propose a 3-D sound reproduction system based on the boundary surface control principle (BoSC system) and evaluate its performance via demonstration and exhibition. The BoSC reproduction system, dome-shaped and constructed of wood, consists of 62 full-range loudspeakers and eight subwoofer loudspeakers. The BoSC recording system is designed from C80 fullerene consisting of 70 microphones of ...