Modulus Structure Theory

Abstract

This chapter introduces a new concept called the modulus structure. The modulus structure is a powerful tool to describe the characteristics of stochastic models. It can be determined in many ways and we introduce three of them here, namely, the modulus structure of expanded and compressed sequences; the modulus structure of sequence alignment; and the modulus structure of sequence mutation. Similar to the ordinary binary operators used in set theory, we can also define the corresponding binary operators between any pair of modes such as intersection, union, subtraction and symmetric subtraction. The order relation is also defined. We then discuss the properties of order relation and the binary operations. The modulus structure is important in the SPA and SMA, and the usefulness of modulus structure is shown in the next two chapters