R package flexmix provides flexible modelling of finite mixtures of regression models using the EM algorithm. Several new features of the software such as fixed and nested varying effects for mixtures of generalized linear models and multinomial regression for a-priori probabilities given concomitant variables are introduced. The use of the software in addition to model selection is demonstrate...

Complexes constructed from chains of p-subgroups of a group G provide valuable tools in group theory, for the understanding of p-local structure, in algebraic topology, for the study of classifying spaces and mod-p group cohomology through homology decompositions, and in modular representation theory, where the Lefschetz module associated to the complex of all nonidentity p-subgroups can be reg...

In this paper we enumerate fuzzy subgroups, up to a natural equivalence, of some finite abelian p-groups of rank two where p is any prime number. After obtaining the number of maximal chains of subgroups, we count fuzzy subgroups using inductive arguments. The number of such fuzzy subgroups forms a polynomial in p with pleasing combinatorial coefficients. By exploiting the order, we label the s...

We study subgroups Γ in Aff(N) = N ⋊ Aut(N) acting properly discontinuously and cocompactly on N . Here N is a simply connected, connected real nilpotent Lie group of finite dimension n. This situation is a natural generalization of the so-called affine crystallographic groups. We prove that for all dimensions 1 ≤ n ≤ 5 the generalized Auslander conjecture holds, i.e., that such subgroups are v...

Geometric methods proposed by Stallings [17] for treating finitely generated subgroups of free groups were successfully used to solve a wide collection of decision problems for free groups and their subgroups [1, 6, 10, 11, 15, 16, 20]. In the present paper we employ the generalized Stallings’ folding method developed in [12] to introduce a procedure, which given a subgroup H of a free product ...

In this paper we provide explicit formulas for the number of elements/subgroups/cyclic subgroups of a given order and for the total number of subgroups/cyclic subgroups in a finite Hamiltonian group. The coverings with three proper subgroups and the principal series of such a group are also counted. Finally, we give a complete description of the lattice of characteristic subgroups of a finite H...

In this work, we present a generalized method for analysis of data series based on shape constraint spline fitting which constitutes the first step towards a statistically optimal method for qualitative analysis of trends. The presented method is based on a branch-and-bound (B&B) algorithm which is applied for globally optimal fitting of a spline function subject to shape constraints. More spec...