On linear order and computation : The expressiveness of interactive computations on linear orders and computations indexed by ordinals

We solve the Dynamic Ehrenfeucht-Fra\"iss\'e Game on linear orders for both players, yielding a normal form for quantifier-rank equivalence classes of linear orders in first-order logic, infinitary logic, and generalized-infinitary logics with linearly ordered clocks. We show that Scott Sentences can be manipulated quickly, classified into local information, and consistency can be decided effectively in the length of the Scott Sentence. We describe a finite set of linked automata moving continuously on a linear order. Running them on ordinals, we compute the ordinal truth predicate and compute truth in the constructible universe of set-theory. Among the corollaries are a study of semi-models as efficient database of both model-theoretic and formulaic information, and a new proof of the atomicity of the Boolean algebra of sentences consistent with the theory of linear order -- i.e., that the finitely axiomatized theories of linear order are dense.

Recommendation of Multimedia Objects Using Metadata and Link Analysis

We investigate methods for recommending multimedia items suitable for an online multimedia sharing community and introduce a novel algorithm called UserRank for ranking multimedia items based on link analysis. We also take the initiative of applying EigenRumor from the domain of blogosphere to multimedia. Furthermore, we present a strategy for making personalized recommendation that combines UserRank with collaborative filtering. We evaluate our method with an informal user study and show that results obtained are promising.