An optimal algorithm to generate tilings

局部生成密铺：偶双色Wang瓦片集

Local generation of tilings: the even bicolor Wang tilesets

本文应用局部生成密铺技术，通过引入描述子移位局部生成密铺过程的定义，对所有满足每块瓦片颜色数均为偶数的双色Wang瓦片集进行了分类。

作为迭代函数系统的帽形多kite（hat polykite）

The hat polykite as an Iterated Function System

本研究将著名的非周期帽形铺砌对应到重叠迭代函数系统，通过研究分量一致收敛的无穷迭代函数系统序列，为帽形铺砌的非完美替换系统提供了理论建模。

周期平铺猜想的若干变体

Some variants of the periodic tiling conjecture

本文针对周期平铺猜想提出并证明三个变体，包括将常值右端替换为零、在Z²中考虑整值周期右端以及保持示性函数的多重平铺情形，从而得到相关整数平铺与多重平铺的可判定性。

Ergodic Dynamics in Sigma-Delta Quantization: Tiling Invariant Sets and Spectral Analysis of Error

This paper has two themes that are intertwined: The first is the dynamics of certain piecewise affine maps on the Euclidean space that arise from a class of analog-to-digital conversion methods called Sigma-Delta quantization. The second is the analysis of reconstruction error associated to each such method. Sigma-Delta quantization generates approximate representations of functions by sequences that lie in a restricted set of discrete values. These are special sequences in that their local averages track the function values closely, thus enabling simple convolutional reconstruction. In this p…