In this report we introduce and motivate the problem of reconstructing shapes from partial information. An appropriate mathematical abstraction capturing the notion of a shape in three-dimensional space is a two-dimensional manifold. The concept of the topological type of a manifold plays an important role in reconstruction, and we present a synopsis of the pertinent definitions and results. We...

3 Awareness and Knowledge 6 3.1 Awareness Structures by Fagin and Halpern (1988) . . . . . . . . . . . . . . . . . 6 3.2 An Impossibility Result on Unawareness in Kripke Frames . . . . . . . . . . . . . 15 3.3 Unawareness Frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.4 Unawareness Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.5...

Video synopsis is one of the popular research topics in the field of digital video and has broad application prospects. Current research of it focuses on the methods of generating video synopsis or studying to utilize optimization algorithms such as fuzzy theory,minimum sparse reconstruction, and genetic algorithm to optimize its computing steps. This paper mainly studies the object-based video...

The large volume of data streams poses unique space and time constraints on the computation process. Many query processing, database operations, and mining algorithms require efficient execution which can be difficult to achieve with a fast data stream. In many cases, it may be acceptable to generate approximate solutions for such problems. In recent years a number of synopsis structures have b...

Early approaches for computing duplicate-sensitive aggregates in sensor networks (e.g., in TAG) have used a tree topology, in order to conserve energy and to avoid double-counting sensor readings. However, a tree topology is not robust against node and communication failures that are common in sensor networks. Recent research has shown that for several duplicate-sensitive aggregates (e.g., Coun...