We present a study and application of quasi-stationarity of electroencephalogram for intraoperative neurophysiological monitoring (IONM) and an application of Chebyshev time windowing for preconditioning SSEP trials to retain the morphological characteristics of somatosensory evoked potentials (SSEP). This preconditioning was followed by the application of a principal component analysis (PCA)-b...

An infinite Markov system {f0, f1, . . . } of C2 functions on [a, b] has dense span in C[a, b] if and only if there is an unbounded Bernstein inequality on every subinterval of [a, b]. That is if and only if, for each [α, β] ⊂ [a, b] and γ > 0, we can find g ∈ span{f0, f1, . . . } with ‖g′‖[α,β] > γ‖g‖[a,b]. This is proved under the assumption (f1/f0)′ does not vanish on (a, b). Extension to hi...

To every subspace arrangement X we will associate symmetric functions P[X] and H[X]. These symmetric functions encode the Hilbert series and the minimal projective resolution of the product ideal associated to the subspace arrangement. They can be defined for discrete polymatroids as well. The invariant H[X] specializes to the Tutte polynomial T [X]. Billera, Jia and Reiner recently introduced ...

A discrete-time variable structure controller for aircraft elevator control using the method for control of plants with finite zeros in canonical subspace is proposed in this paper. First, a discrete mathematical model of the system over canonical space, using the delta transform, is given. Then, decomposition of the canonical space to subspaces with and without control is carried out by introd...

A visualization of three-dimensional incompressible flows by divergence-free quasi-twodimensional projections of the velocity field onto three coordinate planes is revisited. An alternative and more general way to compute the projections is proposed. The approach is based on the Chorin projection combined with a SIMPLE-like iteration. Compared to the previous methodology based on divergence-fre...

The boundary integral method is an efficient approach for solving time-harmonic acoustic obstacle scattering problems. The main computational task is the evaluation of an oscillatory boundary integral at each discretization point of the boundary. This paper presents a new fast algorithm for this task in two dimensions. This algorithm is built on top of directional low-rank approximations of the...

The optical behaviour of the (human) cornea is often characterized with the Zernike-coefficients derived via the Zernike-transform of its optical power map. In this paper, a radial transform based on the Chebyshev-polynomials of the second kind is suggested for a surface-based, rather than an optical power map based representation of the cornea. This transform is well-suited for providing compa...

IDR(s) is one of the most efficient methods for solving large sparse nonsymmetric linear systems of equations. We present two useful extensions of IDR(s), namely a flexible variant and a multi-shift variant. The algorithms exploit the underlying Hessenberg decomposition computed by IDR(s) to generate basis vectors for the Krylov subspace. The approximate solution vectors are computed using a Qu...

We study the problem of reconstructing a sparse polynomial in a basis of Chebyshev polynomials (Chebyshev basis in short) from given samples on a Chebyshev grid of [−1, 1]. A polynomial is called M -sparse in a Chebyshev basis, if it can be represented by a linear combination of M Chebyshev polynomials. For a polynomial with known and unknown Chebyshev sparsity, respectively, we present efficie...