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5 S Formalisms

5 S Formalisms. More formally: Definitions. Definition: A stream is a sequence whose codomain is a non empty set.

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5 S Formalisms

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  1. 5 S Formalisms

  2. More formally: Definitions • Definition: A stream is a sequence whose codomainis a non empty set. • Definition: A structure is a tuple (G, L, F) where G = (V,E) is a directed graph with vertex set V and edge set E, L is a set of label values, and F is a labeling function. F : (V ∪ E ) → L. See http://www.mathsisfun.com/sets/domain-range-codomain.html for a nice description of domain, range, codomain if you need it.

  3. Structure illustration What are the G, L,F, V, E parts of this example? Collection includes includes includes Books Audio files Images A very simple structure. How might it be enhanced? How would an index be included? What substructures might be added?

  4. Definitions, cont’d • Definition: A space is a measurable space, measure space, probability space, vector space, topological space, or metric space • A vector space is a representation for the set of elements in a collection. The vector representing each element is a set of characteristics held by that element and both connecting that element to others that are similar and distinguishing it from those that are different. • We will do an exercise to illustrate

  5. Vector space illustration • Consider a car. What are the characteristics that you associate with a car? If you want to compare one car to another, what characteristics would you choose? • Make a vector of those characteristics. • Then, fill in the vector for several specific cars.

  6. Definitions - 3 • Definition: A scenario is a sequence of related transition events (e1, e2, …, en) on state set S such that ek = (sk, sk+1,) for 1 <= k <= n. • More easily visualized, a scenario is a path in a directed graph, G = (S, ∑e), where vertices correspond to states in the state set S and directed edges are equivalent to events in a set of events, ∑e, and correspond to transitions between states. • Scenarios must be implemented to make a working system.

  7. Definitions - 4 • Definition: A society is a tuple (C,R) where • C = (c1, c2, …, cn) is a set of conceptual communities, each community referring to a set of individuals of the same class or type (e.g. actors, activities, components, hardware, software, data); • R = (r1, r2, …, rm) is a set of relationships, each relationship being a tuple rj = (ej, ij) where ej is a Cartesian product ck1 x ck2x … x cknj. 1<= k1 < k2 < … < knj<= n, which specifies the communities involved in the relationship and ij is an activity.

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