We study the subgroup structure, Hecke algebras, quasi-regular representations, and asymptotic properties of some fractal groups of branch type. We introduce parabolic subgroups, show that they are weakly maximal, and that the corresponding quasi-regular representations are irreducible. These (infinite-dimensional) representations are approximated by finite-dimensional quasi-regular representat...

In order to be able to draw inferences about real world phenomena from a representation expressed in a digital computer, it is essential that the representation should have a rigorously correct algebraic structure. It is also desirable that the underlying algebra be familiar, and provide a close modelling of those phenomena. The fundamental problem addressed in this paper is that, since compute...

In order to deal with infinite regular trees (or other pointed graph structures) efficiently, we give new algorithms to store such structures. The trees are stored in such a way that their representation is unique and shares substructures as much as possible. This maximal sharing allows substantial memory gain and speed up over previous techniques. For example, equality testing becomes constant...

People find it difficult to create and maintain abstractions. We often deal with abstract tasks by using notations that make the structure of the abstraction visible. Programming-by-example (PBE) systems sometimes make it more difficult to create abstractions. The user has to second-guess the results of the inference algorithm and sometimes cannot see any visual representation of the inferred r...

It is well known that for irreducible, square-integrable representations of a locally compact group, there exist so-called admissible vectors which allow the construction of generalized continuous wavelet transforms. In this paper we discuss when the irreducibility requirement can be dropped, using a connection between generalized wavelet transforms and Plancherel theory. For unimodular groups ...

We provide a dual representation of quasi-convex maps π : LF → LG , between two locally convex lattices of random variables, in terms of conditional expectations. This generalizes the dual representation of quasi-convex real valued functions π : LF → R and the dual representation of conditional convex maps π : LF → LG . These results were inspired by the theory of dynamic measurements of risk a...

Reverse subdivision aims at constructing a coarser representation of an object given by a fine polygon mesh. In this paper, we first derive a mask for reverse Loop subdivision that can be applied to both regular and extraordinary vertices. The mask is parameterized, and thus can also be used in reversing variants of Loop subdivision, such as those proposed by Warren and Litke. We apply this mas...

A subset of the vertex set of a graph G, S ⊆ V (G), is a (k, τ)-regular set if it induces a k-regular subgraph of G and every vertex not in the subset has τ neighbors in it. This paper is a contribution to the given problem of existence of (k, τ)-regular sets associated with all distinct eigenvalues of integral strongly regular graphs. The minimal idempotents of the Bose-Mesner algebra of stron...

We survey the relationships between two-weight linear [n, k] codes over GF(q), projective (n, k, /»„ /»,) sets in PG(£— \,q), and certain strongly regular graphs. We also describe and tabulate essentially all the known examples.

A graph is subeulerian if it is spanned by an eulerian supergraph. Boesch, Suffel and Tindell have characterized the class of subeulerian graphs and determined the minimum number of additional lines required to make a subeulerian graph eulerian. In this paper, we consider the related notion of a subsemi-eulerian graph, i.e. a graph which is spanned by a supergraph having an open trail containin...