Design patterns capture the distilled experience of expert designers. The compositions of design patterns may reuse design experience and solve a set of problems. Design patterns and their compositions are usually modeled using UML. When a design pattern is applied or composed with other patterns, the pattern-related information may be lost because UML does not track this information. Thus, it is hard for a designer to identify a design pattern when it is applied or composed. The benefits of design patterns are compromised because the designers cannot communicate with each other in terms of the design patterns they use when the design patterns are applied or composed. In this paper, we present notations to explicitly represent each pattern in the applications and compositions of design patterns. The notations allow us to maintain pattern-related information. Thus, a design pattern is identifiable and traceable from its application and composition with others. Keywords Design pattern...