Related papers: Tilings by translation
We show that there is only one Hilbert space of entire functions that is invariant under the action of naturally defined weighted translations.
We count tilings of a rectangle of integer sides m-1 and n-1 by a special set of tiles. The result is obtained fron the study of the kernel of the adjacency matrix of an n x n rectangular graph of Z x Z.
In this paper, we propose a new metric for Machine Translation (MT) evaluation, based on bi-directional entailment. We show that machine generated translation can be evaluated by determining paraphrasing with a reference translation…
We introduce an elementary transformation called flips on tilings by squares and triangles and conjecture that it connects any two tilings of the same region of the Euclidean plane.
This note is the written version of conversations with young colleagues on unofficial history, general ideas, unexpected facts and open problems concerning tilting theory.
These informal notes briefly discuss some basic topics in harmonic analysis along the lines of convolutions and Fourier transforms.
In continuation of Part I, we study translative integral formulas for certain translation invariant functionals, which are defined on general convex bodies. Again, we consider local extensions and use these to show that the translative…
We survey some results on toric topology.
We investigated singular points of translation surfaces under the linearly independent condition. In this paper, as completion, we investigate singular points of translation surfaces under the linearly dependent condition, using the…
As a result of the rapid changes in information and communication technology (ICT), the world has become a small village where people from all over the world connect with each other in dialogue and communication via the Internet. Also,…
This paper examines the existence and region of convergence of Fourier transform of the functions of bicomplex variables with the help of projection on its idempotent components as auxiliary complex planes. Several basic properties of this…
With the help of a simple model, we analyze Scanning Tunneling Microscopy images of simple and double moir\'e patterns resulting from misoriented bi- and tri-layers graphene stacks. It is found that the model reproduces surprisingly well…
In digital signal processing time-frequency transforms are used to analyze time-varying signals with respect to their spectral contents over time. Apart from the commonly used short-time Fourier transform, other methods exist in literature,…
Cross-lingual alignment, the meaningful similarity of representations across languages in multilingual language models, has been an active field of research in recent years. We survey the literature of techniques to improve cross-lingual…
Given a finite collection of two-dimensional tile types, the field of study concerned with covering the plane with tiles of these types exclusively has a long history, having enjoyed great prominence in the last six to seven decades. Much…
Machine translation (MT) technology has facilitated our daily tasks by providing accessible shortcuts for gathering, elaborating and communicating information. However, it can suffer from biases that harm users and society at large. As a…
In this note, we describe an interpretation of the (continuous) Fourier transform from the perspective of the Chinese Remainder Theorem. Some related issues, including a new derivation of Poisson summation formula, are discussed.
This is a survey of the use of Fourier analysis in additive combinatorics, with a particular focus on situations where it cannot be straightforwardly applied, but needs to be generalized first. Sometimes very satisfactory generalizations…
This paper surveys hyperinterpolation, a quadrature-based approximation scheme. We cover classical results, provide examples on several domains, review recent progress on relaxed quadrature exactness, introduce methodological variants, and…
Is there a fixed dimension $n$ such that translational tiling of $\mathbb{Z}^n$ with a monotile is undecidable? Several recent results support a positive answer to this question. Greenfeld and Tao disprove the periodic tiling conjecture by…