A number of machine translation systems based on the learning algorithms are presented. These methods acquire translation rules from pairs of similar sentences in a bilingual text corpora. This means that it is difficult for the systems to acquire the translation rules from sparse data. As a result, these methods require large amounts of training data in order to acquire high-quality translatio...

Chain rules for Tsallis type entropies are proven, as including the famous pseudoadditivity in nonextensive statistics as a special case. They give important relations between Tsallis conditional entropy and Tsallis joint entropy. Moreover the subadditivity of Tsallis type entropies is shown for the correlated two random variables in the case of q ≥ 1 with the help of the generalized Shannon in...

Chain rules are maximally chaotic CA rules that can be constructed at random to provide a huge number of encryption keys — where the the CA is run backwards to encrypt, forwards to decrypt. The methods are based on the reverse algorithm and the Z-parameter [5]. 1 The CA reverse algorithm and basins of attraction In the simplest cellular automata [4], each cell in a ring of cells updates its val...

Discovering association rules and association rules change (ARC) from existing large databases is an important problem. This paper presents an approach based on multi-hash chain structures to mine association rules change from large database with shorter transactions. In most existing algorithms of association rules change, the mining procedure is divided into two phases, first, association rul...

Consider a finite irreducible Markov chain with transition matrix M = (pij). Fixing a target distribution τ , we study a family of optimal stopping rules from the singleton distributions to τ . We show that this family of rules is dual to a family of (not necessarily optimal) rules on the reverse chain from the singleton distributions to a related distribution α̂ called the τ -contrast distribut...