Related papers: Patch frequencies in Penrose rhombic tilings
We find an explicit matrix model computing the refined topological vertex, starting from its representation in terms of plane partitions. We then find the spectral curve of that matrix model, and thus the mirror symmetry of the refined…
Normal thermal fluctuations of the cell membrane have been studied extensively using high resolution microscopy and focused light, particularly at the peripheral regions of a cell. We use a single probe particle attached non-specifically to…
We set up the theory for a distributed algorithm for computing persistent homology. For this purpose we develop linear algebra of persistence modules. We present bases of persistence modules, and give motivation as for the advantages of…
Random matrix theory (RMT) provides a framework to study the spectral fluctuations in physical systems. RMT is capable of making predictions for the fluctuations only after the removal of the secular properties of the spectrum. Spectral…
In this work a robust clustering algorithm for stationary time series is proposed. The algorithm is based on the use of estimated spectral densities, which are considered as functional data, as the basic characteristic of stationary time…
For a large class of tilings, including those which are obtained by the generalized dual method from regular grids, it is shown that their algebra is stably isomorphic to a crossed product with $\Z^d$. Penrose tilings belong to this class.…
We compute the number of rhombus tilings of a hexagon with side lengths N,M,N,N,M,N, with N and M having the same parity, which contain a particular rhombus next to the center of the hexagon. The special case N=M of one of our results…
Persistent homology is a popular computational tool for analyzing the topology of point clouds, such as the presence of loops or voids. However, many real-world datasets with low intrinsic dimensionality reside in an ambient space of much…
We derive new explicit expressions for the components of Moore-Penrose inverses of symmetric difference matrices. These generalized inverses are applied in a new regularization approach for scattered data interpolation based on partial…
A new algorithm for estimating the time-varying frequency of a noiseless sinusoidal signal is considered. It is assumed that the amplitude and frequency of the sinusoidal signal are unknown functions of time, but are solutions of linear…
Transformer-based PDE surrogates achieve remarkable performance but face two key challenges: fixed patch sizes cause systematic error accumulation at harmonic frequencies, and computational costs remain inflexible regardless of problem…
We advocate a simple multipole expansion of the polarisation density matrix. The resulting multipoles appear as successive moments of the Stokes variables and can be obtained from feasible measurements. In terms of these multipoles, we…
We present a geometrical description of new canonical $d$-dimensional codimension one quasiperiodic tilings based on generalized Fibonacci sequences. These tilings are made up of rhombi in 2d and rhombohedra in 3d as the usual Penrose and…
This paper presents an algorithm for computing the contraction of two-dimensional tensor networks on a square lattice; and we combine it with solving congruence equations to compute the exact enumeration (including weighted enumeration) of…
We establish a connection between gaps problems in Diophantine approximation and the frequency spectrum of patches in cut and project sets with special windows. Our theorems provide bounds for the number of distinct frequencies of patches…
A separated net is a set of points which is relatively dense and uniformly discrete (another name for a Delone set). We are dealing with tilings and separated nets in Euclidean spaces and with the question whether a given separated net is…
Mining and exploring databases should provide users with knowledge and new insights. Tiles of data strive to unveil true underlying structure and distinguish valuable information from various kinds of noise. We propose a novel Boolean…
Finding coarse representations of large graphs is an important computational problem in the fields of scientific computing, large scale graph partitioning, and the reduction of geometric meshes. Of particular interest in all of these fields…
Two-dimensional thin plates are widely used in many aerospace and automotive applications. Among many methods for the attenuation of vibration of these mechanical structures, piezoelectric shunt damping is a promising way. It enables a…
We propose a two-step pulse observation method to enhance frequency stability for coherent population trapping (CPT) atomic clocks. The proposed method is a Raman-Ramsey scheme with low light intensity at resonance observation, and provides…