相关论文: Programming matrix optics into Mathematica
One approach to parametric and adaptive model reduction is via the interpolation of orthogonal bases, subspaces or positive definite system matrices. In all these cases, the sampled inputs stem from matrix sets that feature a geometric…
Semidefinite programming is a fundamental problem class in convex optimization, but despite recent advances in solvers, solving large-scale semidefinite programs remains challenging. Generally the matrix functions involved are spectral or…
We propose algorithms and software for computing projections onto the intersection of multiple convex and non-convex constraint sets. The software package, called SetIntersectionProjection, is intended for the regularization of inverse…
An optical neural network is proposed and demonstrated with programmable matrix transformation and nonlinear activation function of photodetection (square-law detection). Based on discrete phase-coherent spatial modes, the dimensionality of…
In the overview, a generic mathematical object (mapping) is introduced, and its relation to model physics parameterization is explained. Machine learning (ML) tools that can be used to emulate and/or approximate mappings are introduced.…
We apply matrix methods to arithmetic functions by associating matrices to the functions in a manner drawn from the theory of symmetric functions. Then we study the characteristic polynomials of the associated matrices.
In this paper, some real-world motivated examples are provided illustrating the power of linear algebra tools as the product of matrices, determinants, eigenvalues and eigenvectors. In this sense, some practical applications related to…
The algorithm for finding the optimal consistent approximation of an inconsistent pairwise comparisons matrix is based on a logarithmic transformation of a pairwise comparisons matrix into a vector space with the Euclidean metric.…
Optical logic gates are fundamental blocks of optical computing to accelerate information processing. While significant progress has been achieved in recent years, existing implementations typically rely on dedicated structures that are…
Computation, the use of a computer to solve, simulate, or visualize a physical problem, has revolutionized how physics research is done. Computation is used widely to model systems, to simulate experiments, and to analyze data. Yet, in most…
Modern applications of strong gravitational lensing require the ability to use precise and varied observational data to constrain complex lens models. I discuss two sets of computational methods for lensing calculations. The first is a new…
Over the last decade, it has been demonstrated that many systems in science and engineering can be modeled more accurately by fractional-order than integer-order derivatives, and many methods are developed to solve the problem of fractional…
Light is extensively used to steer the motion of atoms in free space, enabling cooling and trapping of matter waves through ponderomotive forces and Doppler-mediated photon scattering. Likewise, light interaction with free electrons has…
A procedure to obtain differentiation matrices is extended straightforwardly to yield new differentiation matrices useful to obtain derivatives of complex rational functions. Such matrices can be used to obtain numerical solutions of some…
The search for new control methods over light-matter interactions is one of the engines that advances fundamental physics and applied science alike. A specific class of light-matter interaction interfaces are setups coupling photons of…
Adaptive optics systems are usually prototyped in a convenient but slow language like MATLAB or Python, and then re-written from scratch using high-performance C/C++ to perform real-time control. This duplication of effort adds costs and…
These notes offer a unified introduction to spectral methods for the study of complex systems. They are intended as an operative manual rather than a theorem-proof textbook: the emphasis is on tools, identities, and perspectives that can be…
We prove that the inverse of a positive-definite matrix can be approximated by a weighted-sum of a small number of matrix exponentials. Combining this with a previous result [OSV12], we establish an equivalence between matrix inversion and…
Polynomial and rational functions are the number one choice when it comes to modeling of radial distortion of lenses. However, several extrapolation and numerical issues may arise while using these functions that have not been covered by…
Optical tweezers employing forces produced by light underpin important manipulation tools in many areas of applied and biological physics. Conventional optical tweezers are based on refractive optics, and they require excessive auxiliary…