Sturmfels offered 100 Swiss Francs in 2005 to a conjecture, which deals with a special case of the maximum likelihood estimation for a latent class model. This paper confirms the conjecture positively. Mathematics Subject Classification (2000). Primary 65H10; Secondary 62P10, 62F30.

A university-based digital education developer was asked for help in creating some training by the Australian research branch of a multinational telecommunications innovator. The subject matter was an in-house methodology for use by engineers taking the role of project manager in research projects. The initial purpose was to encourage its uptake, but further exploration revealed wider needs. So...

The lattice of the set partitions of [n] ordered by refinement is studied. Suppose r partitions p1, . . . , pr are chosen independently and uniformly at random. The probability that the coarsest refinement of all pi ’s is the finest partition {1}, . . . , {n} is shown to approach 0 for r = 2, and 1 for r ≥ 3. The probability that the finest coarsening of all pi ’s is the one-block partition is ...

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Gödel’s second incompleteness theorem is proved for Herbrand consistency of some arithmetical theories with bounded induction, by using a technique of logarithmic shrinking the witnesses of bounded formulas, due to Z. Adamowicz [Herbrand consistency and bounded arithmetic, Fundamenta Mathematicae 171 (2002) 279–292]. In that paper, it was shown that one cannot always shrink the witness of a bou...

In this paper we present a new, practical algorithm for solving the subgroup conjugacy problem in the general linear group. Mathematics Subject Classification: 20-04, 20H30. 1 Introductory Material This paper presents a new algorithm to solve a subcase of the following: Problem. Given two groups G,H ≤ K, determine whether there exists a k ∈ K such that G = H. If so, return one such k. This prob...

Björner and Wachs generalized the definition of shellability by dropping the assumption of purity; they also introduced the h-triangle, a doubly-indexed generalization of the h-vector which is combinatorially significant for nonpure shellable complexes. Stanley subsequently defined a nonpure simplicial complex to be sequentially Cohen-Macaulay if it satisfies algebraic conditions that generaliz...

In this paper we study the irregularities of distribution of subsets relative to higher dimensional arithmetic progressions. In particular we give one-sided estimate of the discrepancies of subsets of d-dimensional cubes, i.e. we show that these discrepancies have both large positive and small negative values. 2000 Mathematics Subject Classification: Primary 11K38

Invariant correlation functions for SO(1, N ) hyperbolic sigma-models are investigated. The existence of a large N asymptotic expansion is proven on finite lattices of dimension d ≥ 2. The unique saddle point configuration is characterized by a negative gap vanishing at least like 1/V with the volume. Technical difficulties compared to the compact case are bypassed using horospherical coordinat...