Given a real-analytic manifold M , a compact connected Lie group G and a principal G-bundle P → M , there is a canonical ‘generalized measure’ on the space A/G of smooth connections on P modulo gauge transformations. This allows one to define a Hilbert space L2(A/G). Here we construct a set of vectors spanning L2(A/G). These vectors are described in terms of ‘spin networks’: graphs φ embedded i...

Frank Harary in his article [2] was the first to speak of combinatorial diseases (actually, he spoke of graphical diseases). His original diseases were the four-colour disease, the hamiltonian disease and the reconstruction disease. Shortly thereafter, Read and Corneil [9] have discussed the graph isomorphism disease, and somewhat later, Huang, Kotzig and Rosa [4] spoke of a labelling disease. ...

This paper aims to address the solution for the Subtask 1 of Shared Task on transliterated search,a task in FIRE ’14. The task addresses the problem of data containing English words and transliterated words of Indian languages in English.The task calls for language identification and subsequent back transliteration into the native Indian scripts.The system proposed herewith implements Language ...

Change labelling is a fundamental challenge in software evolution. Certain kinds of changes can be labeled based on directly measurable characteristics. Labels for other kinds of changes, such as changes causing subsequent fixes, need to be estimated retrospectively. In this article we present a weight-based approach for identifying potential causes for events of interest based on a cause-fix g...

A graph G on m edges is considered graceful if there is a labelling f of the vertices of G with distinct integers in the set {0, 1, . . . ,m} such that the induced edge labelling g defined by g(uv) = |f(u) − f(v)| is a bijection to {1, . . . ,m}. We here consider some relaxations of these conditions as applied to tree labellings: 1. Edge-relaxed graceful labellings, in which repeated edge label...

Given a real-analytic manifold M, a compact connected Lie group G and a principal G-bundle P ! M, there is a canonicaìgeneralized measure' on the space A=G of smooth connections on P modulo gauge transformations. This allows one to deene a Hilbert space L 2 (A=G). Here we construct a set of vectors spanning L 2 (A=G). These vectors are described in terms of`spin networks': graphs embedded in M,...

Expressive tools work primarily on the problem of the clarity and style of expression of models in some underlying theory. There is a structure among mathematics, a theory of the world (e.g. music), expressive constructs with their own structure, the applied theory, and models of some real entity. Lewin’s transformational networks are expressive tools of great currency in music theory. We gener...

Graph-theoretic structures are an obvious means to reason about systems of asynchronous processes. Their dynamic behaviour can be simulated by applying productions of a graph grammar. The present paper is motivated by looking for a formal method that is able to describe the behaviour of systems of processes that share data structures. We generalize the categorical graph-grammar approach by labe...

Compared to tree grammars, graph grammars have stronger generative capacity over structures. Based on an edge replacement grammar, in this paper we propose to use a synchronous graph-to-string grammar for statistical machine translation. The graph we use is directly converted from a dependency tree by labelling edges. We build our translation model in the log-linear framework with standard feat...

We consider two infinite games, played on a countable graph G given with an integer vertex labelling. One player seeks to construct a ray (a one-way infinite path) in G, so that the ray’s labels dominate or elude domination by an integer sequence being constructed by another player. For each game, we give a structural characterization of the graphs on which one player or the other can win, prov...