Related papers: Algebraic theory of phase retrieval
Reasoning-Intensive Retrieval (RIR) targets retrieval settings where relevance is mediated by latent inferential links between a query and supporting evidence, rather than semantic similarity. Motivated by the emergent reasoning abilities…
Constraints imposed directly on accelerations of the system leading to the relation of constants of motion with appropriate local projectors occurring in the derived equations are considered. In this way a generalization of the Noether's…
The aim of this article is to give a rather extensive, and yet nontechnical, account of the birth of the regularity theory for generalized minimal surfaces, of its various ramifications along the decades, of the most recent developments,…
Information Retriever (IR) aims to find the relevant documents (e.g. snippets, passages, and articles) to a given query at large scale. IR plays an important role in many tasks such as open domain question answering and dialogue systems,…
A new method for phase recovery from a single two-beam interferogram is presented. Conventional approaches, relying on trigonometric inversion followed by phase unfolding and unwrapping, are hindered by discontinuities typically addressed…
In this chapter, we survey some recent developments in the field of geophysical inversion. We aim to provide an accessible general introduction to the breadth of current research, rather than focussing in depth on particular topics. In…
The most recent wave of applications of logic to operator algebras is a young and rapidly developing field. This is a snapshot of the current state of the art.
Phase recovery (PR) refers to calculating the phase of the light field from its intensity measurements. As exemplified from quantitative phase imaging and coherent diffraction imaging to adaptive optics, PR is essential for reconstructing…
These lecture notes provide a relatively self-contained introduction to field theoretic methods employed in the study of classical and quantum phase transitions.
We demonstrate by means of a simple example that the arbitrariness of defining a phase from an aperiodic signal is not just an academic problem, but is more serious and fundamental. Decomposition of the signal into components with positive…
Continued fractions have a long history in number theory, especially in the area of Diophantine approximation. The aim of this expository paper is to survey the main results on the theory of $p$--adic continued fractions, i.e. continued…
The purpose of this note is to give a number of open problems on matching theory and their relation to the well-known results in this area. We also give a linear analogue of the acyclic matchings.
This is a survey article on some recent developments in the arithmetic theory of linear algebraic groups over higher-dimensional fields, written for the Notices of the AMS.
In this exposition, I discuss several developments in the theory of vertex operator algebras, and I include motivation for the definition.
The purpose of this informal article is to introduce the reader to some of the objects and methods of the theory of p-adic representations. My hope is that students and mathematicians who are new to the subject will find it useful as a…
The purpose of this report is a study of the algebraic approach possibilities to reconstruct images. This approach is reduced to solution of the large system of linear algebraic equations. We also point out some possible further…
In this paper we discuss the basic problems of algorithmic algebraic number theory. The emphasis is on aspects that are of interest from a purely mathematical point of view, and practical issues are largely disregarded. We describe what has…
The present paper is mainly a survey of our work arXiv:0708.4221 and arXiv:0808.2440 but it also contains the announcement of some new results. Its main purpose is to present an accessible introduction to a technique allowing efficient…
The goal of this article is to invite the reader to get to know and to get involved into higher Teichm\"uller theory by describing some of its many facets.
In this work we consider the problem of reconstruction of a signal from the magnitude of its Fourier transform, also known as phase retrieval. The problem arises in many areas of astronomy, crystallography, optics, and coherent diffraction…