Prototypes for automated spatial layout in architecture focus on approaches, which define occupiable space as an orthogonal 2D-grid and use algorithms to allocate each rectangle of the grid to a particular function. However, these approaches are limiting the design to orthogonal spatial layouts. Based on SAT solving techniques, the prototype presented in this paper proposes a methodology for au...

A neuj method for digital line differential protection is presented. The protection compares the time function and the orthogonal function of the symmetrical positive-sequence component at the input and output o f a transmission line. From these values the magnitude of the differential current is evaluated. The time function is calculated according to the SD4c algorithm and the orthogonal funct...

It has been observed from image denoising experiments that translation invariant (TI) wavelet transforms often outperform orthogonal wavelet transforms. This paper compares the two transforms from the viewpoint of approximation theory, extending previous results based on Haar wavelets. The advantages of the TI expansion over orthogonal expansion are twofold: the TI expansion produces smaller ap...

A class of simple Jacobi-type algorithms for non-orthogonal matrix joint diagonalization based on the LU or QR factorization is introduced. By appropriate parametrization of the underlying manifolds, i.e. using triangular and orthogonal Jacobi matrices we replace a high dimensional minimization problem by a sequence of simple one dimensional minimization problems. In addition, a new scale-invar...

We develop a climatological model for the Arctic ionosphere based on more than one solar cycle of data (2010–2021) rate change total electron content index (ROTI) maps from International GNSS Service (IGS). The IGS ROTI are daily averaged in magnetic latitude and local time coordinates. To model, decomposed into base functions coefficients using empirical orthogonal function (EOF) method. EOF m...