If G is a word hyperbolic group of cohomological dimension 2, then every subgroup of G of type FP2 is also word hyperbolic. Isoperimetric inequalities are denned for groups of type FP2 and it is shown that the linear isoperimetric inequality in this generalized context is equivalent to word hyperbolicity. A sufficient condition for hyperbolicity of a general graph is given along with an applica...

— We provide new arguments to see topological Kac-Moody groups as generalized semisimple groups over local fields: they are products of topologically simple groups and their Iwahori subgroups are the normalizers of the pro-p Sylow subgroups. We use a dynamical characterization of parabolic subgroups to prove that some countable Kac-Moody groups with Fuchsian buildings are not linear. We show fo...

We investigate subgroups of the group PLo(I) of piecewise-linear, orientation-preserving homeomorphisms of the unit interval with finitely many breaks in slope, under the operation of composition, and also subgroups of generalized Thompson groups Fn. We find geometric criteria determining the derived length of any such group, and use this criteria to produce a geometric classification of the so...

There are several procedures for fitting generalized additive models, i.e. multivariate regression models for an exponential family response where the influence of each single covariates is assumed to have unknown, potentially non-linear shape. Simulated data is used to compare a smoothing parameter optimization approach for selection of smoothness and covariate, a stepwise approach, a mixed mo...

A tight-binding procedure is presented for fitting electronic band structures of crystals. It is based on a fully automated method of determining all possible independent matrix elements for arbitrary crystal structures. A fit, using this method, for the band structure of hexagonal close-packed Tc is more than an order of magnitude better than previous fits. A practical procedure for optimizing...

This is a summary on verbal subgroups in the groups T(∞, K) and UT(∞, K) of infinite dimensional triangular and unitriangular matrices over a field K, |K| > 2. The characterization of the lattices of verbal subgroups in these groups is presented, and the width of verbal subgroups generated by non-commutators, powers and (generalized) Engel words is given [2, 3, 4]. The groups T(∞, K) and UT(∞, ...

Geometric methods proposed by Stallings [13] 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, 5, 9, 10, 16]. In the present paper we employ the generalized Stallings’ folding method developed in [11] to introduce a procedure, which given a subgroup H of a free product of finite...

We investigate subgroups of the group PLo(I) of piecewise-linear, orientation-preserving homeomorphisms of the unit interval with finitely many breaks in slope, under the operation of composition, and also subgroups of generalized Thompson groups Fn. We find geometric criteria determining the derived length of any such group, and use this criteria to produce a geometric classification of the so...

Generalized additive models are an effective regression tool, popular in the statistics literature, that provides an automatic extension of traditional linear models to nonlinear systems. We present a distributed algorithm for fitting generalized additive models, based on the alternating direction method of multipliers (ADMM). In our algorithm the component functions of the model are fit indepe...

The lognormal distribution is commonly used to model certain types of data that arise in several fields of engineering as, for example, different types of lifetime data or coefficients of wear and friction. However, a generalized form of the lognormal distribution can be used to provide better fits for many types of experimental or observational data. In this paper, a Bayesian analysis of a gen...