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All optical systems, which involve the collimation of a reflected, transmitted or scattered wave subsequent to tight focusing, are subject to two kinds of deviations. One is the wavefront curvature due to inaccurate focal placement of the…

We consider the inverse problem for countable, locally finite electrical networks with edge weights in an arbitrary field. The electrical inverse problem seeks to determine the weights of the edges knowing only the potential and current…

The inverse problem of diffraction theory in essence amounts to the reconstruction of the atomic positions of a solid from its diffraction image. From a mathematical perspective, this is a notoriously difficult problem, even in the…

Using diffusion priors to solve inverse problems in imaging have significantly matured over the years. In this chapter, we review the various different approaches that were proposed over the years. We categorize the approaches into the more…

Photochromic diarylethene is known to exhibit reversible photoisomerization under irradiation with ultraviolet (UV) and visible light. Besides reversible optical properties upon light irradiation, a variety of discontinuous morphological…

Two different versions of an optical theorem for a scattering body embedded inside a lossy background medium are derived in this paper. The corresponding fundamental upper bounds on absorption are then obtained in closed form by elementary…

Using the complexity equals action proposal we study holographic complexity for hyperscaling violating theories in the presence of a finite cutoff that, in turns, requires to obtain all counter terms needed to have finite boundary energy…

Score-based diffusion models are a recently developed framework for posterior sampling in Bayesian inverse problems with a state-of-the-art performance for severely ill-posed problems by leveraging a powerful prior distribution learned from…

We have considered a stationary outflowing envelope from the star accelerated by the radiative force in arbitrary optical depth case. Introduced approximations provide satisfactory description of the behavior of the matter flux with…

With a Bayesian approach, the linear optics correction algorithm for storage rings is revisited. Starting from the Bayes' theorem, a complete linear optics model is simplified as "likelihood functions" and "prior probability distributions".…

One-dimensional optical waveguiding is revisited using the electromagnetic deduction of Fresnel formulas relating the incident, reflected, and transmitted waves on the abrupt interface between two different optical media. Throughout the…

Recently dictionary screening has been proposed as an effective way to improve the computational efficiency of solving the lasso problem, which is one of the most commonly used method for learning sparse representations. To address today's…

A method for detecting and approximating fault lines or surfaces, respectively, or decision curves in two and three dimensions with guaranteed accuracy is presented. Reformulated as a classification problem, our method starts from a set of…

Scarf's lemma is one of the fundamental results in combinatorics, originally introduced to study the core of an N-person game. Over the last four decades, the usefulness of Scarf's lemma has been demonstrated in several important…

While scattered light conveys most of the information we perceive, scattering may also distort that information before it reaches our detectors. The problem is acute in many applications, such as in high-resolution microscopy of biological…

We develop a cut finite element method (CutFEM) for convection-diffusion problems posed on mixed-dimensional domains, i.e., unions of manifolds of different dimensions arranged in a hierarchical structure where lower-dimensional components…

A general framework for determining fundamental bounds in nanophotonics is introduced in this paper. The theory is based on convex optimization of dual problems constructed from operators generated by electromagnetic integral equations. The…

Optical forces have been fruitfully applied in a broad variety of areas that not only span the traditional scientific fields such as physics, chemistry, and biology, but also in more applied fields. It is customary and useful to split the…

Various imaging techniques have significantly enhanced our ability to visualize objects embedded within complex media such as biological tissues, fog, atmosphere, or various turbid media. Optical imaging, in particular, offers multiple…

Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…