Abstract. Wouldn’t it be nice to be able to conveniently use ordinary real number expressions within proof assistants? In this paper we outline how this can be done within a theorem proving framework. First, we formally establish upper and lower bounds for trigonometric and transcendental functions

This thesis discusses the use of the real numbers in theorem proving. Typically, theorem provers only support a few `discrete' datatypes such as the natural numbers. However the availability of the real numbers opens up many interesting and important application areas, such as the verification

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In this paper we develop some statistical theory for factor models of large dimensions. The focus is the determination of the number of factors, which is an unresolved issue in the rapidly growing literature on multifactor models. We propose a panel Cp criterion and show that the number of factors

The problem of multiprogram scheduling on a single processor is studied from the viewpoint...

Multimedia communication involving digital audio and/or digital video has rather strict delay requirements. A real-time channel is defined in this paper as a simplex connection between a source and a destination characterized by parameters representing the performance requirements of the client. A

Data augmentation and Gibbs sampling are two closely related, sampling-based approaches to the calculation of posterior moments. The fact that each produces a sample whose constituents are neither independent nor identically distributed complicates the assessment of convergence and numerical

We propose a method (the \Gap statistic") for estimating the number of clusters (groups) in a set of data. The technique uses the output of any clustering algorithm (e.g. k-means or hierarchical), comparing the change in within cluster dispersion to that expected under an appropriate reference

and Sturm sequences are given. Probabilistlc calculatton in real anthmetlc, prewously considered by Davis, is justified ngorously, but only in a special case. Theorems of elementary geometry can be proved much more efficiently by the techmques presented than by any known arttficml-mtelhgence approach