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I have highlighted four portfolio companies (CSK, Interpore, Possis Medical, and Charles & Colvard) with P/Es signi cantly higher than the portfolio average and the small-cap indexes Conversely, it appears that only one portfolio company (Acambis ADR) does not have positive earnings for the prior 12-month period (this company s P/E ratio is listed as , which in this case denotes a negative number) Given that CAM considers itself a value-driven rm, I would inquire about these stocks At this point, we can start to include aspects of the other portfolio analysis we have already performed We had previously determined that the CAM small-cap value portfolio is concentrated mainly in three broad sectors (cyclical, nancials, and health care) The health care sector is traditionally considered to be more growth oriented than value oriented because the companies tend to have higher valuation ratios associated with their higher growth rates.

s 4 and 5, as well as 8 and 9, point toward improving computation of the distribution of the maximum on the basis of special properties of the process, such as the regularity of the paths and the domain In 8 one pro ts from the implicit formula for the density of the distribution of the maximum that has been proved in 7 to study second-order approximation of the tails of the distribution as the level u tends to + , as done in Adler and Taylor s recent book (2007) by other methods The direct method employed here is also suited to obtaining nonasymptotic results 10 contains a short account of limit theorems when the time domain grows to in nity, including the Volkonskii Rozanov theorem on the asymptotic Poisson character of the stream of up-crossings for one-parameter stationary Gaussian processes under an appropriate normalization.

This implies that the distribution of the maximum, after re-scaling, converges to a Gumbel distribution Section 102 establishes a central limit theorem for nonlinear functionals of Gaussian process, which applies to the limit behavior of the number of crossings In 11 we describe the modeling of the surface of the sea using Gaussian random elds Some geometric characteristics of waves, such as length of crests and velocities of contours, are introduced The Rice formula is used to deduce from the directional spectrum of the sea, some properties of the distribution of these characteristics Some non-Gaussian generalizations are proposed in Section 115 In 12 we study random systems of equations over the reals, having more than one unknown.

Because the CAM portfolio has about a quarter.

For polynomial systems, the rst signi cant results on the number of roots were published in the 1990s, starting with the Shub Smale theorem (1993), which gives a simple, elegant formula for the expectation of the number of roots This is a fascinating subject in which the main questions remain unanswered What can one say about the probability distribution of the number of solutions, and how does it depend on the probability law of the coef cients What is the probability of having no solution What can one say about the distribution of the roots in space, and how can this help to solve the system numerically How do all these things behave as the number of unknowns grows inde nitely What about the same questions for undetermined systems And so on.

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Answering some of these natural questions would imply at the same time making progress in key problems in numerical analysis and algorithmic complexity as well as in other areas The content of the chapter is extremely modest with respect to the aforementioned questions, and it is our hope that it may stimulate other people to work on the numerous problems arising in this eld 13 is on condition numbers Roughly speaking, the condition number of a problem measures the dif culty of the problem to be solved by any algorithm Of course, there are many measures of this sort The standard procedure is to give a metric on the space of problems and de ne the condition number of a problem as the inverse of its distance to the set of ill-posed problems, possibly with some additional normalization.

In this chapter we consider the simplest situation, in which a problem is a square system of linear equations and the set of ill-posed problems is the set of systems in which the matrix of coef cients is noninvertible..