Let Γ be a torsion-free cocompact lattice in Aut(T1) × Aut(T2), where T1, T2 are trees whose vertices all have degree at least three. The group H2(Γ,Z) is determined explicitly in terms of an associated 2-dimensional tiling system. It follows that under appropriate conditions the crossed product C∗algebra A associated with the action of Γ on the boundary of T1 ×T2 satisfies rankK0(A) = 2 · rank...

It is shown that each element σ in the normalizer of the automorphism group Aut(G) of a simple graph G with labeled vertex set V is an Aut(G) invariant isomorphism between G and the graph obtained from G by the σ permutation of V—i.e., σ is a hidden permutation symmetry of G. A simple example illustrates the theory and the applied notion of system robustness for reconfiguration under symmetry c...

In this report we present a mathematical analysis of a simple model of a cortical column. We first recall some known biological facts about cortical columns. We then present a mathematical model of such a column, developed by a number of people including Lopes Da Silva, Jansen, Rit. Finally we analyze some aspects of its behaviour in the framework of the theory of dynamical systems using bifurc...

Much less known, however, is that there is a description of Aut(G), the automorphism group of G. The first compete characterization that we are aware of is contained in a paper by Ranum [1] near the turn of the last century. Beyond this, however, there are few other expositions. Our goal is to fill this gap, thereby providing a much needed accessible and modern treatment. Our characterization o...

The purpose of this study was the exploration of attitudes toward disabled brothers/sisters in 140 typically developed siblings (13-18 years) with brothers or sisters with Down syndrome (DS), autism (AUT), or intellectual disability (ID). Results showed that siblings of brothers/sisters with DS thought that they could “be entered into the world of work” and “achieve personal autonomy”; siblings...

Let M be a Kobayashi-hyperbolic 2-dimensional complex manifold and Aut(M) the group of holomorphic automorphisms of M . We showed earlier that if dimAut(M) = 3, then Aut(M)-orbits are closed submanifolds in M of (real) codimension 1 or 2. In this paper we classify all connected Kobayashi-hyperbolic 2-dimensional manifolds with 3-dimensional automorphism groups in the case when every orbit has c...

The existence of an extremal self-dual binary linear code C of length 72 is a long-standing open problem. We continue the investigation of its automorphism group: looking at the combination of the subcodes xed by di erent involutions and doing a computer calculation with Magma, we prove that Aut(C) is not isomorphic to the elementary abelian group of order 8. Combining this with the known resul...

A technique is described that produces symmetric drawings of a graph G in the plane. The method requries that G have a non-trivial automorphism group Aut(G), and that a non-trivial symmetry g ∈ Aut(G) has been selected in some way. The technique is found to be very effective in practice. It forms a part of the Groups & Graphs** software package. 1. Symmetric Cycles Let G be a connected undirect...

Let D be a domain (a connected open set) in C, n ≥ 2. Denote by Aut(D) the group of holomorphic automorphisms of D; that is, Aut(D) is the group under composition of all biholomorphic self-maps of D. If D is bounded or, more generally, Kobayashi-hyperbolic, then the group Aut(D) with the topology of uniform convergence on compact subsets of D is in fact a finitedimensional Lie group (see [Ko])....