Related papers: Reflections on Tiles (in Self-Assembly)
We provide a proof of the Alpern multi-tower theorem for Z^d actions. We reformulate the theorem as a problem of measurably tiling orbits of a Z^d action by a collection of rectangles whose corresponding sides have no non-trivial common…
We present an extensive formulation of the inverse grating problem for exural waves, in which the energy of each diffracted mode is selected and the grating configuration is then obtained by solving a linear system of equations. The grating…
An integral self-affine tile is the solution of a set equation $\mathbf{A} \mathcal{T} = \bigcup_{d \in \mathcal{D}} (\mathcal{T} + d)$, where $\mathbf{A}$ is an $n \times n$ integer matrix and $\mathcal{D}$ is a finite subset of…
In this paper we compute the scaling functions of the effective central charges for various quantum integrable models in a deep ultraviolet region $R\to 0$ using two independent methods. One is based on the ``reflection amplitudes'' of the…
Generalized Additive Models (GAMs) are widely used explainable-by-design models in various applications. GAMs assume that the output can be represented as a sum of univariate functions, referred to as components. However, this assumption…
In this paper, we revisit the claim that many partition functions are invariant under reflecting temperatures to negative values (T-reflection). The goal of this paper is to demarcate which partition functions should be invariant under…
Let $A$ be a finite dimensional hereditary algebra over an algebraically closed field $k$, $T_2(A)=(\begin{array}{cc}A&0 A&A\end{array})$ be the triangular matrix algebra and $A^{(1)}=(\begin{array}{cc}A&0 DA&A\end{array})$ be the…
Symmetry is a ubiquitous and fundamental property in the visual world, serving as a critical cue for perception and structure interpretation. This paper investigates the detection of 3D reflection symmetry from a single RGB image, and…
Self-assembly is a fundamental process by which supramolecular species form spontaneously from their components. This process is ubiquitous throughout the life chemistry and is central to biological information processing. Algorithms for…
In [F. Caselli, Involutory reflection groups and their models, J. Algebra 24 (2010), 370--393] there is constructed a uniform Gelfand model for all non-exceptional irreducible complex reflection groups which are involutory. Such model can…
We present an efficient method for the design of anomalous reflectors for acoustic waves. The approach is based on the fact that the anomalous reflector is actually a diffraction grating in which the amplitude of all the modes is negligible…
We obtain structural results on translational tilings of periodic functions in $\mathbb{Z}^d$ by finite tiles. In particular, we show that any level one tiling of a periodic set in $\mathbb{Z}^2$ must be weakly periodic (the disjoint union…
The chapter contains a detailed presentation of the surface integral theory for modelling light diffraction by surface-relief diffraction gratings having a one-dimensional periodicity. Several different approaches are presented, leading…
We use a state-of-the-art optimization algorithm combined with a careful methodology to find optimal anti-reflective coatings. Our results show that ultra thin structures (less than $300 \,nm$ thick) outperform much thicker gradual patterns…
A tiling of the unit square is an MTP tiling if the smallest tile can tile all the other tiles. We look at the function $f(n)=\max \sum s_i$, where $s_i$ is the side length of the $i$th tile and the sum is taken over all MTP tilings with…
Step by step completion of a left-to-right tiling of a rectangular floor with tiles of a single shape starts from one edge of the floor, considers the possible ways of inserting a tile at the leftmost uncovered square, passes through a…
We demonstrate the capability of block-copolymer templating to tune the refractive indices of functional oxides over a broad range by structuring materials on the 20-1000 atoms scale, with simple one-pot synthesis. The presented method is…
In this paper, we prove that if a finite number of rectangles, every of which has at least one integer side, perfectly tile a big rectangle then there exists a strategy which reduces the number of these tiles (rectangles) without violating…
Reconfigurable reflectors have a significant potential in future telecommunication systems, and approaches to the design and realization of full and tunable reflection control are now actively studied. Reflectarrays, being the classical…
The Simplified Modal Method (SMM) provides a quick and intuitive way to analyze the performance of gratings of rectangular shapes. For non-rectangular shapes, a version of SMM has been developed, but it applies only to the Littrow-mounting…