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In this paper, an orthogonal mode decomposition method is proposed to decompose ffnite length real signals on both the real and imaginary axes of the complex plane. The interpolation function space of ffnite length discrete signal is…

Spherical harmonics (SH) have been extensively used as a basis for analyzing the morphology of particles in granular mechanics. The use of SH is facilitated by mapping the particle coordinates onto a unit sphere, in practice often a…

Effective methods are introduced for testing zero-dimensionality of varieties at a point. The motivation of this paper is to compute and analyze deformations of isolated hypersurface singularities. As an application, methods for computing…

Based on the interaction between different spatial modes, semiconductor Bragg-reflection waveguides provide a highly functional platform for non-linear optics. Therefore, the control and engineering of the properties of each spatial mode is…

The surface errors of freeform surfaces reflect the manufacturing complexities and significantly impact the feasibility of processing designed optical systems. With multiple degrees of freedom, freeform surfaces pose challenges in surface…

This paper proposes a simple approach to derive efficient error bounds for learning multiple components with sparsity-inducing regularization. We show that for such regularization schemes, known decompositions of the Rademacher complexity…

Optical approaches for wavefront shaping traditionally rely on phase modulation through holographic techniques. Shaping the phase determines a wave's diffraction and hence its intensity distribution in space. We instead show that shaping…

There are a variety of industrial products that possess periodic textures or surfaces, such as carbon fiber textiles and display panels. Traditional image-based quality inspection methods for these products require identifying the periodic…

While approaches to model the progression of fracture have received significant attention, methods to find the solution to the associated nonlinear equations have not. In general, nonlinear solution methods and optimization methods have a…

In this paper we propose a general algorithmic framework for first-order methods in optimization in a broad sense, including minimization problems, saddle-point problems and variational inequalities. This framework allows to obtain many…

The paper presents the results from a multi-year effort to develop and validate image processing methods for selecting the best physical models based on solar image observations. The approach consists of selecting the physical models based…

This chapter provides various perspective on an important challenge in data assimilation: model error. While the overall goal is to understand the implication of model error of any type in data assimilation, we emphasize on the effect of…

In this article, we show that Fourier eigenmeasures supported on spheres with radii given by a locally finite sequence, which we call $k$-spherical measures, correspond to Fourier series exhibiting a modular-type transformation behaviour…

We proposed the method of the optical fiber modal decomposition of the radiation propagating in a multimode optical fiber with a step like refractive index profile. The field distribution at the output end of the fiber was used. The method…

Alternating patterns of small and large amplitude oscillations occur in a wide variety of physical, chemical, biological and engineering systems. These mixed-mode oscillations (MMOs) are often found in systems with multiple time scales.…

Modal expansion is an attractive technique for solving electromagnetic scattering problems. With the one set of resonator modes, calculated once and for all, any configuration of near-field or far-field sources can be obtained almost…

The growing availability of sensors within semiconductor manufacturing processes makes it feasible to detect defective wafers with data-driven models. Without directly measuring the quality of semiconductor devices, they capture the…

For over a century diffraction theory has been thought to limit the resolution of focusing and imaging in the optical domain. The size of the smallest spot achievable is inversely proportional to the range of spatial wavevectors available.…

In this paper we study the problem of computing wavelet coefficients of compactly supported functions from their Fourier samples. For this, we use the recently introduced framework of generalized sampling. Our first result demonstrates that…

A method evaluating the sensitivity of a given parameter to topological changes is proposed within the method of moments paradigm. The basis functions are used as degrees of freedom which, when compared to the classical pixeling technique,…