1,298 research outputs found
Adapting Search Theory to Networks
The CSE is interested in the general problem of locating objects in networks. Because of their exposure to search theory, the problem they brought to the workshop was phrased in terms of adapting search theory to networks. Thus, the first step was the introduction of an already existing healthy literature on searching graphs.
T. D. Parsons, who was then at Pennsylvania State University, was approached in 1977 by some local spelunkers who asked his aid in optimizing a search for someone lost in a cave in Pennsylvania. Parsons quickly formulated the problem as a search problem in a graph. Subsequent papers led to two divergent problems. One problem dealt with searching under assumptions of fairly extensive information, while the other problem dealt with searching under assumptions of essentially zero information. These two topics are developed in the next two sections
Complexity of weakly null sequences
We introduce an ordinal index which measures the complexity of a weakly null
sequence, and show that a construction due to J. Schreier can be iterated to
produce for each alpha < omega_1, a weakly null sequence (x^{alpha}_n)_n in
C(omega^{omega^{alpha}})) with complexity alpha. As in the Schreier example
each of these is a sequence of indicator functions which is a suppression-1
unconditional basic sequence. These sequences are used to construct
Tsirelson-like spaces of large index. We also show that this new ordinal index
is related to the Lavrentiev index of a Baire-1 function and use the index to
sharpen some results of Alspach and Odell on averaging weakly null sequences
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