We obtain a formula for the distribution of the first exit time of Brownian motion from a fundamental region associated with a finite reflection group. In the type A case it is closely related to a formula of de Bruijn and the exit probability is expressed as a Pfaffian. Our formula yields a generalisation of de Bruijn’s. We derive large and small time asymptotics, and formulas for expected fir...

A zeta function approach to the relation between the numbers of symmetry planes and axes of a polytope Abstract A derivation of the Cesàro-Fedorov relation from the Selberg trace formula on an orbifolded 2-sphere is elaborated and extended to higher dimensions using the known heat-kernel coefficients for manifolds with piecewise-linear boundaries. Several results are obtained that relate the co...

We study symmetries of feedforward networks in terms of their corresponding groups. We nd that these groups naturally act on and partition weight space into disjunct domains. We derive an algorithm to generate representative weight vectors in a fundamental domain. The analysis of the metric structure of the fundamental domain leads to improved evaluation procedures of learning results, such as ...

In this paper, we prove that the L combinatorial torsion of an amenable covering space can be approximated by the combinatorial torsions of a regular exhaustion. An ancillary theorem shows the L spectral density function of the combinatorial Laplacian on L-cochains on the covering space is approximated by the average spectral density functions of the combinatorial Laplacian on the cochains of t...

We show that, in perturbative string models where the source of CP violation is a complex vacuum expectation value (v.e.v.) for one or more compactification moduli, CP is conserved if a CP transformation acting on the modulus values is an element of a target-space (self-)duality group. Where the duality group is SL(2, Z) the result confirms a conjecture of Bailin et al. that CP is conserved for...

The goal of this article is to show that five explicitly given transformations, a rotation, two screw Heisenberg rotations, a vertical translation and an involution generate the Euclidean Picard modular groups with coefficient in the Euclidean ring of integers of a quadratic imaginary number field. We also obtain a presentation of the isotropy subgroup fixing infinity by analysis of the combina...

this research aims to compare the capabilities of a thesaurus and an ontology for representation of domain knowledge. this is the first to focus on the construction of an ontology in library and information science (lis), in the domain of indexing and in persian language. the research also develops the methodology of ontology construction by implementing domain analysis methodology. the present...

Bulk supergravity on a manifold with boundary must be supplemented by boundary conditions that preserve local supersymmetry. This “downstairs” picture has certain advantages over the equivalent “upstairs” picture, expressed in terms of orbifolds. In particular, Scherk-Schwarz supersymmetry breaking can be described much more simply in the downstairs picture. Nevertheless, physics on the fundame...