相关论文: Modified strip projection method

Projectivity and injectivity are fundamental notions in category theory. We consider natural weakenings termed semiprojectivity and semiinjectivity, and study these concepts in different categories. For example, in the category of metric…

Quasicrystals are fascinating structures, characterized by strong positional order but lacking the periodicity of a crystal. In colloidal systems, quasicrystals are typically predicted for particles with complex or highly specific…

Strip packing is a classical packing problem, where the goal is to pack a set of rectangular objects into a strip of a given width, while minimizing the total height of the packing. The problem has multiple applications, e.g. in scheduling…

SpectralNet is a graph clustering method that uses neural network to find an embedding that separates the data. So far it was only used with $k$-nn graphs, which are usually constructed using a distance metric (e.g., Euclidean distance).…

Crystal Structure Prediction (CSP) remains a fundamental challenge with significant implications for the development of new materials and the advancement of various scientific disciplines. Recent developments have shown that generative…

Let $G=(V, E)$ be a planar graph and let $\mathcal{C}$ be a partition of $V$. We refer to the graphs induced by the vertex sets in $\mathcal{C}$ as Clusters. Let $D_{\mathcal C}$ be an arrangement of disks with a bijection between the disks…

This paper continues our study of quasicrystals initiated in Part I. We propose a general mechanism for constructing quasicrystals, existing globally in time, in spatially-extended systems (partial differential equations with Euclidean…

Single cluster covering approach provides a plausible mechanism for the formation and stability of octagonal and decagonal quasiperiodic structures. For dodecagonal quasiperiodic pattern such a single cluster covering scheme is still…

We evaluate the optical gap and Stokes shift of several candidate 1 nm silicon nanocrystal structures using density functional and quantum Monte Carlo (QMC) methods. We find that the combination of absorption gap calculations and Stokes…

X-ray and Sunyaev-Zeldovich effect observations can be combined to measure the distance to clusters of galaxies. If the intracluster gas distribution is not spherical, but elongated by a factor of Z along the line of sight, the inferred…

We briefly review the diffraction of quasicrystals and then give an elementary alternative proof of the diffraction formula for regular cut-and-project sets, which is based on Bochner's theorem from Fourier analysis. This clarifies a common…

In projective clustering we are given a set of n points in $R^d$ and wish to cluster them to a set $S$ of $k$ linear subspaces in $R^d$ according to some given distance function. An $\eps$-coreset for this problem is a weighted (scaled)…

Quasicrystals have a higher degree of rotational and point-reflection symmetry than conventional crystals. As a result, quasicrystalline heterostructures fabricated from dielectric materials with micrometer-scale features exhibit…

In the graph clustering problem with a planted solution, the input is a graph on $n$ vertices partitioned into $k$ clusters, and the task is to infer the clusters from graph structure. A standard assumption is that clusters induce…

Mining dense quasi-cliques is a well-known clustering task with applications ranging from social networks over collaboration graphs to document analysis. Recent work has extended this task to multiple graphs; i.e. the goal is to find groups…

We report a novel kind of dodecagonal quasicrystal that has so far never been observed, nor theoretically predicted. It is composed of axially stacked hexagonal particle layers, with 12-fold rotational symmetry induced by 30 degrees…

The quasi-unit cell picture describes the atomic structure of quasicrystals in terms of a single, repeating cluster which overlaps neighbors according to specific overlap rules. In this paper, we discuss the precise relationship between a…

Semidefinite programming (SDP) is a powerful tool for tackling a wide range of computationally hard problems such as clustering. Despite the high accuracy, semidefinite programs are often too slow in practice with poor scalability on large…

We present a novel quantitative scheme of cluster classification based on the morphological properties that are manifested in X-ray images. We use a conventional radial surface brightness concentration parameter (c_{SB}) as defined…

We interpret experimentally known B-Mg-Ru crystals as quasicrystal approximants. These approximant structures imply a deterministic decoration of tiles by atoms that can be extended quasiperiodically. Experimentally observed structural…