We fix n and say a square in the two-dimensional grid indexed by (x, y) has color c if x+ y ≡ c (mod n). A ribbon tile of order-n is a connected polyomino containing exactly one square of each color. We show that the set of order-n ribbon tilings of a simply connected region R is in one-to-one correspondence with a set of height functions from the vertices of R to Zn satisfying certain differen...

The mapping between biological genotypes and phenotypes is central to the study of biological evolution. Here we introduce a rich, intuitive, and biologically realistic genotype-phenotype (GP) map, that serves as a model of self-assembling biological structures, such as protein complexes, and remains computationally and analytically tractable. Our GP map arises naturally from the self-assembly ...

managing the supply chain plays an important role in creating competitive advantages for companies. adequate information flow in supply chain is one of the most important issues in scm. therefore, using certain information systems can have a significant role in managing and integrating data and information within the supply chain. pharmaceutical supply chain is more complex than many other supp...

results our study showed that the sensitivity and specificity of taqman real time pcr was 96% and 95% respectively. these values were 89% and 90, 38% and 100%, 6% and 100% for pcr, culture and microscopy, respectively. conclusions our study showed that sensitivity of taqman real time pcr was higher that pcr, culture and microscopy but specificity of culture and microscopy was more than pcr and ...

This study develops virtual manipulative, polyominoes kits for junior high school students to explore polyominoes. The current work conducts a non-equivalent group pretest–post-test quasi-experimental design to compare the performance difference between using physical manipulatives and virtual manipulatives in finding the number of polyominoes. Sixty eighthgrade students from two different clas...

We establish a stronger symmetry between the numbers of northeast and southeast chains in the context of 01-fillings of moon polyominoes. Let M be a moon polyomino with n rows and m columns. Consider all the 01-fillings of M in which every row has at most one 1. We introduce four mixed statistics with respect to a bipartition of rows or columns of M. More precisely, let S ⊆ {1, 2, . . . , n} an...

The mapping between biological genotypes and phenotypes is central to the study of biological evolution. Here, we introduce a rich, intuitive and biologically realistic genotype-phenotype (GP) map that serves as a model of self-assembling biological structures, such as protein complexes, and remains computationally and analytically tractable. Our GP map arises naturally from the self-assembly o...

Harary’s generalized Tic-Tac-Toe is an achievement game for polyominoes, where two players alternately put a stone on a grid board, and the player who first achieves a given polyomino wins the game. It is known whether the first player has a winning strategy in the generalized Tic-Tac-Toe for almost all polyominoes except the one called Snaky. GTTT(p, q) is an extension of the generalized Tic-T...