Learning Theory Estimates via Integral Operators and Their Approximations

The regression problem in learning theory is investigated with least square Tikhonov regularization schemes in reproducing kernel Hilbert spaces (RKHS). We follow our previous work and apply the sampling operator to the error analysis in both the RKHS norm and the L² norm. The tool for estimating the sample error is a Bennet inequality for random variables with values in Hilbert spaces. By taking the Hilbert space to be the one consisting of Hilbert-Schmidt operators in the RKHS, we improve the error bounds in the L² metric, motivated by an idea of Caponnetto and de Vito. The error bounds we derive in the RKHS norm, together with a Tsybakov function we discuss here, yield interesting applications to the error analysis of the (binary) classification problem, since the RKHS metric controls the one for the uniform convergence.     

OR and the challenge to improve the NHS: modelling for insight and improvement in in-patient flows

This paper considers efforts to improve in-patient flows, a particularly urgent issue in the National Health Service (NHS). The context is described and related to reasons why OR has been making relatively little contribution. The paper argues that large complex models may often be unnecessary and even get in the way of providing clear insight and guidance for problem owners. The importance of understanding the generic working of systems to lead to improvement, and the limitations of simply describing them, is stressed. It is demonstrated that some very simple models can be of significant practical value in understanding and managing complex systems, changing mindsets and driving collection and use of operationally valuable data. Recommendations for more effective engagement with the NHS are offered.     

Improved tabu search algorithm for the handling of route duration constraints in vehicle routing problems with time windows

This note introduces a refinement to a previously proposed tabu search algorithm for vehicle routing problems with time windows. This refinement yields new best known solutions on a set of benchmark instances of the multi-depot, the periodic and the site-dependent vehicle routing problems with time windows.     

Weak-mixing implies sensitive dependence

Let X be a metric space, B the σ-algebra of Borel subsets of X, and μ a probability measure on (X,B). In this note, for a measure-preserving map T (respectively a measure-preserving semi-flow φ) on (X,B,μ), we prove that if suppμ=X, and T (respectively φ) is weak-mixing, then T (respectively φ) has sensitive dependence.     

A Higher-Dimensional Version of the Brody Reparametrization Lemma

We prove a generalization of the Brody reparametrization lemma.__________Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 10, pp. 1369 – 1377, October, 2004.     

A Note on the Linearity of Real-valued Functions with Respect to Suitable Metrics

In this paper we prove that for every real-valued Morse function φ on a smooth closed manifold ℳ and every neighborhood U of its critical points a suitable Riemannian metric μ _U exists such that φ is linear outside U