1 - 10 of 10 Chapters
[Suppose we are given n balls colored with two colors. How many color-comparisons are needed to produce a ball of the majority color? The answer (first given by Saks and Werman) is M(n) = n−B(n), where B(n) is the number of 1’s in the binary representation of n. We consider in this paper several...
[This paper gives a broad overview of the area of searching with errors and the related field of error-correcting coding. In the vast literature regarding this problem, many papers simultaneously deal with various sorts of restrictions on the searching protocol. We partition this survey into...
[We discuss three types of inclusion matrices (subset, subspace and sequence). We exhibit their disjunct properties and their applications to error-correcting nonadaptive group testing. Under some limited conditions, these structures are optimal for their disjunct properties.]
[In designing an experiment, we often assume a model and then find a best design satisfying one or more optimal properties under the assumed model. This approach works well when we are absolutely sure about the assumed model that it will fit the experimental data adequately. In reality, we are...
[Topologies related to information divergence are introduced. The conditional limit theorem is taken as motivating example, and simplified proofs of the relevant theorems are given. Continuity properties of entropy and information divergence are discussed.]
[One of the distinguishing properties of the present scientific method is reproducibility. In one of its guises, probability theory is based on statistical reproduction, near certainty being obtained of truth of statements by averaging over long term to remove randomness occurring in individual...
[This lecture is intended to be an easily accessible first introduction to quantum information theory. The field is large and it is not completely covered even by the recent monograph . Therefore the simple topic of data compression is selected to present some ideas of the theory. Classical...
[Information theory is becoming more and more important for many fields. This is true for engineering- and technology-based areas but also for more theoretically oriented sciences such as probability and statistics.]
[Recently, many results on the computational complexity of sorting algorithms were obtained using Kolmogorov complexity (the incompressibility method). Especially, the usually hard average-case analysis is ammenable to this method. Here we survey such results about Bubblesort, Heapsort,...
[We survey some recent results concerning recognition problems. Recognition problems are special combinatorial search problems, where we need not find the hidden element x itself, just compute the value f(x) for a given function f. We mainly use the approaches of classical search theory and...
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