Related papers: Programming matrix optics into Mathematica
Presentation of set matrices and demonstration of their efficiency as a tool using the path/cycle problem.
Optical computing systems provide an alternate hardware model which appears to be aligned with the demands of neural network workloads. However, the challenge of implementing energy efficient nonlinearities in optics -- a key requirement…
We consider the problem of matrix completion on an $n \times m$ matrix. We introduce the problem of Interpretable Matrix Completion that aims to provide meaningful insights for the low-rank matrix using side information. We show that the…
With this paper we bring about a discussion on the computing potential of complex optical networks and provide experimental demonstration that an optical fiber network can be used as an analog processor to calculate matrix inversion. A 3x3…
Lack of numerical precision in control software -- in particular, related to trajectory computation -- can lead to incorrect results with costly or even catastrophic consequences. Various tools have been proposed to analyze the precision of…
We employ neural networks to improve and speed up optical force calculations for dielectric particles. The network is first trained on a limited set of data obtained through accurate light scattering calculations, based on the Transition…
Mathematical models are used extensively for diverse tasks including analysis, optimization, and decision making. Frequently, those models are principled but imperfect representations of reality. This is either due to incomplete physical…
Mathematica is a powerful application package for doing mathematics and is used almost in all branches of science. It has widespread applications ranging from quantum computation, statistical analysis, number theory, zoology, astronomy, and…
In this study, the orthogonalization process for different inner products is applied to pairwise comparisons. Properties of consistent approximations of a given inconsistent pairwise comparisons matrix are examined. A method of a derivation…
In this article we show how to compute a matrix representation and the implicit equation by means of the method developed in [Botbol: arXiv:1007.3437], using the computer algebra system Macaulay2 \cite{M2}. As it is probably the most…
Matrices often represent important information in scientific applications and are involved in performing complex calculations. But systematically testing these applications is hard due to the oracle problem. Metamorphic testing is an…
We present an overview on the development and characterization of multiscale laser processing optics for versatile material modifications across more than six orders of magnitude. Starting with solutions for micromachining we present…
Performing linear operations using optical devices is a crucial building block in many fields ranging from telecommunication to optical analogue computation and machine learning. For many of these applications, key requirements are…
Ultrathin meta-optics offer unmatched, multifunctional control of light. Next-generation optical technologies, however, demand unprecedented performance. This will likely require design algorithms surpassing the capability of human…
A new technique for approximating the entire solution set for a nonlinear system of relations (nonlinear equations, inequalities, etc. involving algebraic, smooth, or even continuous functions) is presented. The technique is to first plot…
In this review, we present some advanced algorithms and programs used in our scientific school with short description of types of astrophysical systems, which we study. However, we discuss mainly mathematical methods, which may be applied…
The advent of transformation optics has lead to the initiation of designing devices and applications associated to electromagnetic wave propagation in anisotropic media. Here, a method is suggested using a coordinate transformation with…
Basic principles of mathematical modeling are reviewed in this book, with the focus on physics and its practical applications, and examples of selected mathematical methods are presented. Most of the models have been imported from physics…
For several years, students visit us on different occasions at the university. But how to bridge from the school curriculum to the contents of the university mathematics? And how to find a focal point at which an active contribute, despite…
Accurate and fast modeling of electric fields in layered structures have a great scientific and practical value. Prevalent method for that is transfer-matrix method. However, transfer matrix method is limited to infinite plane wave…