Problems associated with m-ary trees have been studied by computer scientists and combinatorialists. It is well known that a simple generalization of the Catalan numbers counts the number of m-ary trees on n nodes. In this paper we consider τm, n, the number of m-ary search trees on n keys, a quantity that arises in studying the space of m-ary search trees under the uniform probability model. We prove an exact formula for τm, n, both by analytic and by combinatorial means. We use uniform local approximations for sums of i.i.d. random variables to study the asymptotic development of τm, n for fixed m as n→∞.

The Turán Number T(n, k, r) is the smallest possible number of edges in a k-graph of ordern such that every set of r vertices contains an edge. The limit

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exists, but there is no pair (k, r) with r>k[ges ]3 for which this function could be determined as yet. We give a constructive proof of the upper bound

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for every k and r with r[ges ]k[ges ]2. In the case k=6, r=11 we improve this result, refuting thereby a conjecture of Turán.

Software packages developed for visualising time-varying timbres, findingparameter settings for modelling acoustic instrument tones, and forsynthesising timbres are described. The sndan package, written in C for Unix machines, provides spectrum analysis, pitch tracking, spectrumdisplay, parameter modification, and additive synthesis. Other programsthat estimate the best possible parameters for recreating acoustic soundsusing techniques such as multiple FM and wavetable synthesis and extendednonlinear/filter synthesis are outlined. Hybrid instruments created byfashioning sounds out of the recombined spectral characteristics of two ormore very different tones are also presented.

Evolution in musical notation has been tied to the development of music theory and performance.

Clustering of a translation memory is proposed to make the retrieval of similar translation examples from a translation memory more efficient, while a second contribution is a metric of text similarity which is based on both surface structure and content. Tests on the two proposed techniques are run on part of the CELEX database. The results reported indicate that the clustering of the translation memory results in a significant gain in the retrieval response time, while the deterioration in the retrieval accuracy can be considered to be negligible. The text similarity metric proposed is evaluated by a human expert and found to be compatible with the human perception of text similarity.

In this article, and within the context of sound art as a basis for artistic freedom in experimental music and art, the development of pendulum-based sculptural instruments and an improvisational form of video called ‘percussive video’ are described. Methods used to produce time-based public art events are also outlined, and their effectiveness in directing social change at the local level is discussed.

Case systems abound in natural language processing. Almost any attempt to recognize and uniformly represent relationships within a clause – a unit at the centre of any linguistic system that goes beyond word level statistics – must be based on semantic roles drawn from a small, closed set. The set of roles describing relationships between a verb and its arguments within a clause is a case system. What is required of such a case system? How does a natural language practitioner build a system that is complete and detailed yet practical and natural? This paper chronicles the construction of a case system from its origin in English marker words to its successful application in the analysis of English text.

The maximal zero-free intervals for chromatic polynomials of graphs are precisely (−∞, 0), (0, 1), (1, 32/27]. We also investigate the distribution of zeros of chromatic polynomials in various classes of graphs closed under minors. For example, the zeros of chromatic polynomials of graphs of tree-width at most k consist of 0, 1 and a dense subset of the interval (32/27, k].

A graph G is called an H-type graph for some graph H if there is a mapping from V(G) to V(H) preserving edges. In this paper, we shall prove that: (1) every triangle-free graph G of order n with χ(G)[les ]3 and δ(G)>n/3 is of Fd-type for some d[ges ]1, where Fd is a certain d-regular triangle-free Hamiltonian Cayley graph of order 3d−1, (2) every triangle-free graph G of order n with χ(G)[ges ]4 and δ(G)>n/3 contains the Mycielski graph (see Figure 2) as a subgraph.

The cyclic tour property has previously been an equality for the expected time to complete a tour, compared with that for the reverse tour, for reversible Markov chains. We give a simple bijection to show that the equality can be extended to the distributions involved. The bijection is based on rotation of circular words.

We study the fraction of time that a Markov chain spends in a given subset of states. We give an exponential bound on the probability that it exceeds its expectation by a constant factor. Our bound depends on the mixing properties of the chain, and is asymptotically optimal for a certain class of Markov chains. It beats the best previously known results in this direction. We present an application to the leader election problem.

This paper presents a new and self-contained proof of a result characterizing objects isomorphic in the free symmetric monoidal closed category, i.e., objects isomorphic in every symmetric monoidal closed category. This characterization is given by a finitely axiomatizable and decidable equational calculus, which differs from the calculus that axiomatizes all arithmetical equalities in the language with 1, product and exponentiation by lacking 1c=1 and (a · b)c=ac · bc (the latter calculus characterizes objects isomorphic in the free cartesian closed category). Nevertheless, this calculus is complete for a certain arithmetical interpretation, and its arithmetical completeness plays an essential role in the proof given here of its completeness with respect to symmetric monoidal closed isomorphisms.

This paper studies the properties of the subnets of a proof-net for first-order Multiplicative Linear Logic without propositional constants (MLL−), extended with the rule of Mix: from [vdash ]Γ and [vdash ]Δ infer [vdash ]Γ, Δ. Asperti's correctness criterion and its interpretation in terms of concurrent processes are extended to the first-order case. The notions of kingdom and empire of a formula are extended from MLL− to MLL−+MIX. A new proof of the sequentialization theorem is given. As a corollary, a system of proof-nets is given for De Paiva and Hyland's Full Intuitionistic Linear Logic with Mix; this result gives a general method for translating Abramsky-style term assignments into proof-nets, and vice versa.

This paper reviews Machine Learning (ML), and extends and complements previous work (Kocabas, 1991; Kalkanis and Conroy, 1991). Although this paper focuses on inductive learning, it at least touches on a great many aspects of ML in general. In addition, incremental induction is also reviewed. Therefore, a general review of ML is presented, but specific detail which has been covered previously is omitted, although other relevant references are noted, and later material is commented upon.

‘Uncertainty reasoning” refers in a general way to problems discussed by that subset of the AI community interested in representing and reasoning with knowledge that cannot be expressed as certainties. The range of problems discussed runs the gamut from fundamental philosophical inquiry into the nature of uncertainty and how (if at all) it can be measured and modelled, to practical performance issues arising from the (automatic) construction of real-world models and making inferences from such models.