Personal Data Security: Divergent Standards in the European Union and the United States

This Note argues that the U.S. Government should discontinue all attempts to establish EES as the de facto encryption standard in the United States because the economic disadvantages associated with widespread implementation of EES outweigh the advantages this advanced data security system provides. Part I discusses the EU\u27s legislative efforts to ensure personal data security and analyzes the evolution of encryption technology in the United States. Part II examines the methods employed by the U.S. Government to establish EES as the de facto U.S. encryption standard. Part III argues that the U.S. Government should terminate its effort to establish EES as the de facto U.S. encryption standard and institute an alternative standard that ensures continued U.S. participation in the international marketplace

Non-linear Group Actions with Polynomial Invariant Rings and a Structure Theorem for Modular Galois Extensions

Let $G$ be a finite $p$-group and $k$ a field of characteristic $p>0$. We show that $G$ has a \emph{non-linear} faithful action on a polynomial ring $U$ of dimension $n=\mathrm{log}_p(|G|)$ such that the invariant ring $U^G$ is also polynomial. This contrasts with the case of \emph{linear and graded} group actions with polynomial rings of invariants, where the classical theorem of Chevalley-Shephard-Todd and Serre requires $G$ to be generated by pseudo-reflections. Our result is part of a general theory of "trace surjective $G$-algebras", which, in the case of $p$-groups, coincide with the Galois ring-extensions in the sense of \cite{chr}. We consider the \emph{dehomogenized symmetric algebra} $D_k$, a polynomial ring with non-linear $G$-action, containing $U$ as a retract and we show that $D_k^G$ is a polynomial ring. Thus $U$ turns out to be \emph{universal} in the sense that every trace surjective $G$-algebra can be constructed from $U$ by "forming quotients and extending invariants". As a consequence we obtain a general structure theorem for Galois-extensions with given $p$-group as Galois group and any prescribed commutative $k$-algebra $R$ as invariant ring. This is a generalization of the Artin-Schreier-Witt theory of modular Galois field extensions of degree $p^s$.Comment: 20 page

A geometric characterization of the classical Lie algebras

A nonzero element x in a Lie algebra g over a field F with Lie product [ , ] is called a extremal element if [x, [x, g]] is contained in Fx. Long root elements in classical Lie algebras are examples of extremal elements. Arjeh Cohen et al. initiated the investigation of Lie algebras generated by extremal elements in order to provide a geometric characterization of the classical Lie algebras generated by their long root el- ements. He and Gabor Ivanyos studied the so-called extremal geometry with as points the 1-dimensional subspaces of g generated by extremal elements of g and as lines the 2-dimensional subspaces of g all whose nonzero vectors are extremal. For simple finite dimensional g this geometry turns out to be a root shadow space of a spherical building. In this paper we show that the isomorphism type of g is determined by its extremal geometry, provided the building has rank at least 3

Large deviations for sums defined on a Galton-Watson process

In this paper we study the large deviation behavior of sums of i.i.d. random variables X_i defined on a supercritical Galton-Watson process Z. We assume the finiteness of the moments EX_1^2 and EZ_1log Z_1. The underlying interplay of the partial sums of the X_i and the lower deviation probabilities of Z is clarified. Here we heavily use lower deviation probability results on Z we recently published in [FW06]

Trimmed trees and embedded particle systems

In a supercritical branching particle system, the trimmed tree consists of those particles which have descendants at all times. We develop this concept in the superprocess setting. For a class of continuous superprocesses with Feller underlying motion on compact spaces, we identify the trimmed tree, which turns out to be a binary splitting particle system with a new underlying motion that is a compensated h-transform of the old one. We show how trimmed trees may be estimated from above by embedded binary branching particle systems.Comment: Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/00911790400000009

Renormalization analysis of catalytic Wright-Fisher diffusions

Recently, several authors have studied maps where a function, describing the local diffusion matrix of a diffusion process with a linear drift towards an attraction point, is mapped into the average of that function with respect to the unique invariant measure of the diffusion process, as a function of the attraction point. Such mappings arise in the analysis of infinite systems of diffusions indexed by the hierarchical group, with a linear attractive interaction between the components. In this context, the mappings are called renormalization transformations. We consider such maps for catalytic Wright-Fisher diffusions. These are diffusions on the unit square where the first component (the catalyst) performs an autonomous Wright-Fisher diffusion, while the second component (the reactant) performs a Wright-Fisher diffusion with a rate depending on the first component through a catalyzing function. We determine the limit of rescaled iterates of renormalization transformations acting on the diffusion matrices of such catalytic Wright-Fisher diffusions.Comment: 65 pages, 3 figure

Estimating Lyapunov exponents in billiards

Dynamical billiards are paradigmatic examples of chaotic Hamiltonian dynamical systems with widespread applications in physics. We study how well their Lyapunov exponent, characterizing the chaotic dynamics, and its dependence on external parameters can be estimated from phase space volume arguments, with emphasis on billiards with mixed regular and chaotic phase spaces. We show that in the very diverse billiards considered here the leading contribution to the Lyapunov exponent is inversely proportional to the chaotic phase space volume, and subsequently discuss the generality of this relationship. We also extend the well established formalism by Dellago, Posch, and Hoover to calculate the Lyapunov exponents of billiards to include external magnetic fields and provide a software implementation of it

The Effects of Social and Labour Market Policies of EU-countries on the Socio-Economic Integration of First and Second Generation Immigrants from Different Countries of Origin

In this article, we analyse four different dimensions of socio-economic integration of 1st and 2nd generation immigrants into the labour markets of 13 EU countries and we assess, taking into account a number of individual characteristics, the effects of the countries of origin and the countries of destination on this integration. We find that participation in the labour market, unemployment, occupational status and the chances of reaching the upper middle-class are different, although inter-related, dimensions of the socio-economic integration of immigrants and they work differently for men and women. In the countries of destination, the level of employment protection legislation and the conservative welfare regime affect this integration negatively. Most indicators of national policies aimed at the integration of immigrants have no effects on the socio-economic integration of immigrants. Furthermore, we find a number of origin effects which continue to have an impact on 2nd generation immigrants. Political stability and political freedom in origin countries have positive and negative effects on socio-economic integration. The emigration rate of the origin countries has a negative effect. The higher levels of socio-economic integration amongst immigrants from other EU-countries demonstrates the functioning of the European Union as an integrated labour market .Controlling for individual religious affiliation turns out to be very useful, since we find a number of negative effects of being a Muslim, among both men and women. While individual education is an important predictor of immigrants' labour market outcomes, our findings indicate lower returns on this education in terms of occupational status, indicating a ceiling effect for highly-educated 2nd generation immigrants who cannot translate their qualifications into high-status jobs to the same extent as their native peers.immigration, integration, labour market, European Union, social policy

Statistics of Extreme Waves in Random Media

Waves traveling through random media exhibit random focusing that leads to extremely high wave intensities even in the absence of nonlinearities. Although such extreme events are present in a wide variety of physical systems and the statistics of the highest waves is important for their analysis and forecast, it remains poorly understood in particular in the regime where the waves are highest. We suggest a new approach that greatly simplifies the mathematical analysis and calculate the scaling and the distribution of the highest waves valid for a wide range of parameters