Monodromy eigenvalues and zeta functions with differential forms

For a complex polynomial or analytic function f, one has been studying intensively its so-called local zeta functions or complex powers; these are integrals of |f|^{2s}w considered as functions in s, where the w are differential forms with compact support. There is a strong correspondence between their poles and the eigenvalues of the local monodromy of f. In particular Barlet showed that each monodromy eigenvalue of f is of the form exp(a2i\pi), where a is such a pole. We prove an analogous result for similar p-adic complex powers, called Igusa (local) zeta functions, but mainly for the related algebro-geometric topological and motivic zeta functions.Comment: To appear in Advances in Mathematics. 17 page

Improved binomial charts for monitoring high-quality processes

For processes concerning attribute data with (very) small failure rate p, often negative binomial control charts are used. The decision whether to stop or continue is made each time r failures have occurred, for some r≥1. Finding the optimal r for detecting a given increase of p first requires alignment of the charts in terms of in-control behavior. In the present paper binomial charts are subjected to this same requirement. Subsequent study reveals that the resulting charts are quite attractive in several aspects, such as detection power. For the case of unknown p, an estimated version of the chart is derived and studied

"Freedom of Movement within 'Fortress Europe'"

Introduction. Much attention has been focused on those seeking to enter ‘fortress Europe’ ­ whether the concept is understood to refer only to the EU Schengen countries or to include non-EU Schengen countries, the United Kingdom and Ireland, or the countries which joined the Union in May 2004. Yet internal mobility within ‘fortress Europe’ is at least as worthy of consideration. The rise of freedom of movement rights in Europe ­ now codified with the legal category of European Union citizenship ­ represents a startling reversal of the historical tradition of state sovereignty. States have historically been defined in terms of insiders (citizens) and outsiders (foreigners). The new supranational rights supersede this traditional distinction by reducing or even removing the ability of European states to discriminate between their own citizens and those of other EU member states. Borders within the European Union still matter, but the remaining barriers to freedom of movement within ‘fortress Europe’ are practical rather than legal, and even they are rapidly disappearing. Exceptions to the European free movement regime still exist ­ such as the case of individuals deemed to pose a significant threat to public health or public security. But the rights of free movement have now been extended to virtually all European citizens, even though there will be a phase-in period for workers from most of the new accession states. By contrast, third-country nationals ­ citizens neither of the host state (first country) nor of another EU member state (second country) but of a non-EU state ­ continue to be denied freedom of movement rights within the Union, despite the efforts of the Commission and some national governments to extend them the same rights as those enjoyed by EU citizens. Exceptions to Schengen also continue to exist, as with special events such as the European soccer cup, for which Portugal in 2004 (just as Belgium and the Netherlands in 2000) was granted a temporary exemption on the requirement to abstain from checking the identification of individuals crossing Portuguese borders. On the whole, however, the picture that emerges for freedom of movement within Europe is one of a continent in which Europeans can move about freely, and in which state borders (though clearly not the borders between ‘fortress Europe’ and the rest of the world!) have lost most of the significance they once possessed. This paper lays out the development of the Schengen system and places it within the context of European Union citizenship

Misspecification in mixed-model based association analysis

Additive genetic variance in natural populations is commonly estimated using mixed models, in which the covariance of the genetic effects is modeled by a genetic similarity matrix derived from a dense set of markers. An important but usually implicit assumption is that the presence of any non-additive genetic effect only increases the residual variance, and does not affect estimates of additive genetic variance. Here we show that this is only true for panels of unrelated individuals. In case there is genetic relatedness, the combination of population structure and epistatic interactions can lead to inflated estimates of additive genetic variance

Control charts for health care monitoring under intermittent out-of-control behavior

Health care monitoring typically concerns attribute data with very low failure rates. Efficient control charts then signal if the waiting time till r (e.g. r≤5) failures is too small. An interesting alternative is the MAX-chart, which signals if all the associated r waiting times for a single failure are sufficiently small. In comparing these choices, the usual change point set-up has been used, in which going Out-of-Control (OoC) means that the failure rate suddenly jumps up and then stays at this higher level. However, another situation of interest is intermittent OoC behavior. In industrial settings, an OoC process can be adjusted to return to In-Control (IC), but with health care monitoring this usually is no option and stretches of OoC and IC behavior may alternate. Comparison of such intermittent alternatives to the change point situation shows that the former can be characterized as tail alternatives, in the sense that the difference w.r.t. the IC-distribution becomes more concentrated in the lower tail. This suggests to generalize the MAX-chart as follows: now signal if all but 1 (or 2) out of r individual waiting times are too small. A numerical study shows that this approach indeed works well