Slide 1More formally: DefinitionsStructure illustrationDefinitions, cont’dVector space illustrationDefinitions - 3Definitions - 45 S FormalismsMore formally: Definitions•Definition: A stream is a sequence whose codomain is 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.Structure illustrationImagesAudio filesBooksCollectionincludesincludesincludesA very simple structure. How might it be enhanced? How would an index be included? What substructures might be added? What are the G, L,F, V, E parts of this example?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 illustrateVector 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.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.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 ck2 x … x cknj. 1<= k1 < k2 < … < knj<= n, which specifies the communities involved in the relationship and ij is an
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