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This article presents an arithmetic, called superposition relaxation, for bracketing the graph of a multivariate factorable function on a compact domain between a pair of underestimating and overestimating functions that are both separable.…
A method is given that "inverts" a logic grammar and displays it from the point of view of the logical form, rather than from that of the word string. LR-compiling techniques are used to allow a recursive-descent generation algorithm to…
We apply the Lie algebraic method to reflecting optical systems with plane-symmetric freeform mirrors. Using analytical ray-tracing equations we construct an optical map. The expansion of this map gives us the aberration coefficients in…
In extending results from Lie to Leibniz algebras, it is helpful to have techniques which translate results from the former to the latter without having to repeat the (perhaps modified) arguments. Such a technique is developed in this work,…
In this paper, we propose an extension to the Propagator algorithm for source bearing estimation by performing root decomposition which eliminates the need for spectral search over angles. Further the propagator spatial spectrum is reused…
Numerical modeling of electromagnetic waves is an important tool for understanding the interaction of light and matter, and lies at the core of computational electromagnetics. Traditional approaches to injecting and evolving electromagnetic…
Based on the property that solving the system of linear matrix equations via the column space and the row space projections boils down to an approximation in the least squares error sense, a formulation for learning the weight matrices of…
Similarly to the standard effective range expansion that is done near the threshold energy, we obtain a generalized power-series expansion of the multi-channel Jost-matrix that can be done near an arbitrary point on the Riemann surface of…
Cooperative Greedy Pursuit Strategies are considered for approximating a signal partition subjected to a global constraint on sparsity. The approach aims at producing a high quality sparse approximation of the whole signal, using highly…
We present a simple analytical method to solve master equations for finite temperatures and any initial conditions, which consists in the expansion of the density operator into normal modes. These modes and the expansion coefficients are…
This paper shows that the plane wave expansion can be a useful tool in obtaining analytical solutions to infinite integrals over spherical Bessel functions and the derivation of identites for these functions. The integrals are often used in…
As it stands, density matrix purification is a powerful tool for linear scaling electronic structure calculations. The convergence is rapid and depends only weakly on the band gap. However, as will be shown in this paper, there is room for…
This paper presents a comprehensive survey of methods which can be utilized to search for solutions to systems of nonlinear equations (SNEs). Our objectives with this survey are to synthesize pertinent literature in this field by presenting…
We introduce the notion of extended affine Lie superalgebras and investigate the properties of their root systems. Extended affine Lie algebras, invariant affine reflection algebras, finite dimensional basic classical simple Lie…
We describe an algorithm for fast multiplication of skew polynomials. It is based on fast modular multiplication of such skew polynomials, for which we give an algorithm relying on evaluation and interpolation on normal bases. Our…
A new analytical method of performing ERBL evolution is described. The main goal is to develop an approach that works for distribution amplitudes that do not vanish at the end points, for which the standard method of expansion in Gegenbauer…
Taylor expansions of analytic functions are considered with respect to two points. Cauchy-type formulas are given for coefficients and remainders in the expansions, and the regions of convergence are indicated. It is explained how these…
In this paper we present seven techniques that everybody should know to improve example-based single image super resolution (SR): 1) augmentation of data, 2) use of large dictionaries with efficient search structures, 3) cascading, 4) image…
Algorithms are described that help with obtaining a classification of the semisimple subalgebras of a given semisimple Lie algebra, up to linear equivalence. The algorithms have been used to obtain classifications of the semisimple…
Models trained on semantically related datasets and tasks exhibit comparable inter-sample relations within their latent spaces. We investigate in this study the aggregation of such latent spaces to create a unified space encompassing the…