In the paper, we investigate a one-to-one correspondence between n-dimensional observables and spectral resolutions with values in kind of lexicographic form quantum structures like perfect MV-algebras or effect algebras. The multidimensional version this problem is more complicated than one-dimensional one because if our algebraic structure k-perfect for k>1, then even two-dimensional case hav...

In this work, we investigate the transfer of some homological properties from a ring $R$ to its amalgamated duplication along some ideal $I$ of $R$ $Rbowtie I$, and then generate new and original families of rings with these properties.

We present three novel methods of compactly storing very large n-gram language models. These methods use substantially less space than all known approaches and allow n-gram probabilities or counts to be retrieved in constant time, at speeds comparable to modern language modeling toolkits. Our basic approach generates an explicit minimal perfect hash function, that maps all n-grams in a model to...

1991 Mathematics Subject Classi cation: 11A25, 11Y70 Let 0(n) = n and m(n) = ( m 1(n)), where m 1 and is the sum-of-divisors function. We say that n is (m; k)perfect if m(n) = kn. We have tabulated all (2; k)-perfect numbers up to 109 and all (3; k)and (4; k)-perfect numbers up to 2 108. These tables have suggested several conjectures, some of which we prove here. We ask in particular: For any ...

Given a one-factorization F of the complete bipartite graph Kn,n, let pf(F) denote the number of Hamiltonian cycles obtained by taking pairwise unions of perfect matchings in F . Let pf(n) be the maximum of pf(F) over all one-factorizations F of Kn,n. In this work we prove that pf(n) > n2/4, for all n > 2. 1 Perfect one-factorizations A one-factorization of a graph G is a partition of its set o...

In this paper we propose a new method of compactly storing n-gram language models called Minimal Perfect Hash Rank (MPHR) that uses significantly less space than all known approaches. It requires O(n) construction time and allows for O(1) random access of probability values or frequency counts associated with n-grams. We make use of minimal perfect hashing to store fingerprints of n-grams in an...

The recent availability of large collections of text such as the Google 1T 5-gram corpus (Brants and Franz, 2006) and the Gigaword corpus of newswire (Graff, 2003) have made it possible to build language models that incorporate counts of billions of n-grams. This paper proposes two new methods of efficiently storing large language models that allow O(1) random access and use significantly less ...

We propose a succinct randomized language model which employs a perfect hash function to encode fingerprints of n-grams and their associated probabilities, backoff weights, or other parameters. The scheme can represent any standard n-gram model and is easily combined with existing model reduction techniques such as entropy-pruning. We demonstrate the space-savings of the scheme via machine tran...

Properties of nonlinear perfect binary codes are investigated and several new constructions of perfect codes are derived from these properties. An upper bound on the cardinality of the intersection of two perfect codes of length n is presented, and perfect codes whose intersection attains the upper bound are constructed for all n. As an immediate consequence of the proof of the upper bound we o...