Computational and Theoretical Aspects of \u3cem\u3eN\u3c/em\u3e-E.C. Graphs

We consider graphs with the n-existentially closed adjacency property. For a positive integer n, a graph is n-existentially closed (or n-e.c.) if for all disjoint sets of vertices A and B with \A∪ B\ = n (one of A or B can be empty), there is a vertex 2 not in A∪B joined to each vertex of A and no vertex of B. Although the n-e.c. property is straightforward to define, it is not obvious from the definition that graphs with the property exist. In 1963, Erdos and Rényi gave a non-explicit, randomized construction of such graphs. Until recently, only a few explicit families of n-e.c. graphs were known such as Paley graphs. Furthermore, n-e.c. graphs of minimum order have received much attention due to Erdos’ conjecture 011 the asymptotic order of these graphs. The exact minimum orders are only known for n = 1 and n = 2. We provide a survey of properties and examples of n-e.c. graphs. Using a computer search, a new example of a 3-e.c. graph of order 30 is presented. Previously, no known 3-e.c. graph was known to exist of that order. We give a new randomized construction of n-e.c. vertex-transitive graphs, exploiting Cayley graphs. The construction uses only elementary probability and group theory

Entity Ranking on Graphs: Studies on Expert Finding

Todays web search engines try to offer services for finding various information in addition to simple web pages, like showing locations or answering simple fact queries. Understanding the association of named entities and documents is one of the key steps towards such semantic search tasks. This paper addresses the ranking of entities and models it in a graph-based relevance propagation framework. In particular we study the problem of expert finding as an example of an entity ranking task. Entity containment graphs are introduced that represent the relationship between text fragments on the one hand and their contained entities on the other hand. The paper shows how these graphs can be used to propagate relevance information from the pre-ranked text fragments to their entities. We use this propagation framework to model existing approaches to expert finding based on the entity's indegree and extend them by recursive relevance propagation based on a probabilistic random walk over the entity containment graphs. Experiments on the TREC expert search task compare the retrieval performance of the different graph and propagation models

Timbre space as synthesis space: towards a navigation based approach to timbre specification

Much research into timbre, its perception and classification over the last forty years has modelled timbre as an n-dimensional co-ordinate space or timbre space, whose axes are measurable acoustical quantities (variously, spectral density, simultaneity of partial onsets etc). Typically, these spaces have been constructed from data generated from similarity/dissimilarity listening tests, using multidimensional scaling (MDS) analysis techniques. Our current research is the computer assisted synthesis of new timbres using a timbre space search strategy, in which a previously constructed simple timbre space is used as a search space by an algorithm designed to synthesize desired new timbres steered by iterative user input. The success of such an algorithm clearly depends on establishing suitable mapping between its quantifiable features and its perceptual features. We therefore present here, firstly, some of the findings of a series of listening tests aimed at establishing the perceptual topography and granularity of a simple, predefined timbre space, and secondly, the results of preliminary tests of two search strategies designed to navigate this space. The behaviour of these strategies in a circumscribed space of this kind, together with the corresponding user experience is intended to provide a baseline to applications in a more complex space