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 unavailable. Here we demonstrated that the ship tiling, one of the dodecagonal quasiperioidic structures, can be constructed from one single prototile with matching rules. A deflation procedure is devised by assigning proper orientations to the tiles present in the ship tiling including regular triangle, 30°-rhombus and square, and fourteen types of vertical configurations have been identified in the deflated pattern, which fulfill the closure condition under deflation and all result in a T-cluster centered at vertex. This result can facilitate the study of physical properties of dodecagonal quasicrystals.

We propose an intelligently structured receiver to achieve high-speed transmissions over optical code-division multiple access (OCDMA) networks. Employing spectral-amplitude coding (SAC) reduces multiuser interference (MUI) in OCDMA, but the network bit-rate is limited by phase-induced intensity noise (PIIN) coming from the incoherency of light sources. To mitigate PIIN, the receiver performs interference estimations and regenerations through consecutive stages. The MUI is removed by subtracting the estimated interference term from the received multiplexed signals. For PIIN variance, it is both dependent on and positively related to user number and bit-rate. Reducing the number of interference users allows the network to support transmissions with a higher speed under a given noise level. The proposed scheme has the advantages of all-optical signal processing and a compact structure. Additionally, the function of noise suppression is rarely studied in the existing MUI elimination schemes, such as serial interference cancellation (SIC) and parallel interference cancellation (PIC). The simulation results show the proposed receiver achieves significant increment in bit-rate than the conventional balanced detector in SAC–OCDMA networks.

The structural properties of a quasicrystal model with twelve-fold rotational symmetry are studied. We correct the errors in the self-similar transformation of the square-rhombus-hexagon tiling model proposed by Socolar. Based on the Stampfli-Ghler square-rhombus-triangle tiling model， the quasi-unit cell is successfully constructed， which can describe the dodecagonal quasiperiodic structure by the covering theory.

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An effective indexing scheme for clusters that enables fast structure comparison and congruence check is desperately desirable in the field of mathematics, artificial intelligence, materials science, etc. Here we introduce the concept of minimum vertex-type sequence for the indexing of clusters on square lattice, which contains a series of integers each labeling the vertex type of an atom. The minimum vertex-type sequence is orientation independent, and it builds a one-to-one correspondence with the cluster. By using minimum vertex-type sequence for structural comparison and congruence check, only one type of data is involved, and the largest amount of data to be compared is n pairs, n is the cluster size. In comparison with traditional coordinate-based methods and distance-matrix methods, the minimum vertex-type sequence indexing scheme has many other remarkable advantages. Furthermore, this indexing scheme can be easily generalized to clusters on other high-symmetry lattices. Our work can facilitate cluster indexing and searching in various situations, it may inspire the search of other practical indexing schemes for handling clusters of large sizes.

Two-dimensional lattices provide the arena for many physics problems of essential importance, a scale symmetry, which rarely exists as noticed by Galileo, in such lattices can help reveal the underlying physics. Here we report the discovery and proof of directional scaling symmetry for high symmetry 2D lattices, i.e., the square lattice, the equilateral triangular lattice and thus the honeycomb lattice, with aid of the function y = arcsin(sin(2πxn)), where the parameter x is either the platinum number or the silver number , which are related to the 12-fold and 8-fold quasiperiodic structures, respectively. The directions and scale factors for the symmetric scaling transformation are determined. The revealed scale symmetry may have a bearing on various physical problems modeled on 2D lattices, and the function adopted here can be used to generate quasiperiodic lattices with enumeration of lattice points. Our result is expected to initiate the search of directional scaling symmetry in more complicated geometries.

We present a cluster covering scheme to construct the two-dimensional octagonal quasilattice. A quasi-unit cell is successfully found which is a two-color cluster similar to the Gummelt's two-color decagon in five-fold quasilattice. The quasi-unit cells overlap each other following certain covering rules and thus lead to a perfect octagonal quasilattice.PACS: 61.44Br.

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