Two-Point Correlation Functions and Universality for the Zeros of Systems of SO(n+1)-invariant Gaussian Random Polynomials

We study the two-point correlation functions for the zeroes of systems of $SO(n+1)$-invariant Gaussian random polynomials on $\mathbb{RP}^n$ and systems of ${\rm isom}(\mathbb{R}^n)$-invariant Gaussian analytic functions. Our result reflects the same "repelling," "neutral," and "attracting" short-distance asymptotic behavior, depending on the dimension, as was discovered in the complex case by Bleher, Shiffman, and Zelditch. For systems of the ${\rm isom}(\mathbb{R}^n)$-invariant Gaussian analytic functions we also obtain a fast decay of correlations at long distances. We then prove that the correlation function for the ${\rm isom}(\mathbb{R}^n)$-invariant Gaussian analytic functions is "universal," describing the scaling limit of the correlation function for the restriction of systems of the $SO(k+1)$-invariant Gaussian random polynomials to any $n$-dimensional $C^2$ submanifold $M \subset \mathbb{RP}^k$. This provides a real counterpart to the universality results that were proved in the complex case by Bleher, Shiffman, and Zelditch. (Our techniques also apply to the complex case, proving a special case of the universality results of Bleher, Shiffman, and Zelditch.)Comment: 28 pages, 1 figure. To appear in International Mathematics Research Notices (IMRN

TIMSS und PISA - Chancen eines neuen Anfangs in Bildungspolitik, -planung, -verwaltung und Unterricht. Endlich ein Schock mit Folgen?

Der Tenor des Beitrags ist durch die Einschätzung bestimmt, dass mit TIMSS und PISA ein qualitativer Sprung in der international vergleichenden Schulforschung gelungen ist. Auf dieser Basis werden im einleitenden Kapitel die Chancen erörtert, aus der in diesen Projekten empirisch begründeten Kritik des deutschen Bildungssystems konsensfähige Maßnahmen zu dessen Weiterentwicklung abzuleiten. Unter diesem Aspekt wird die Kritik am Föderalismus im Bildungssystem zusammen mit einigen einschlägigen Befunden zum Bundesländervergleich in PISA thematisiert; die Entwicklung der Bildungsforschung selbst wird als wichtige Rahmenbedingung im Prozess der Umsetzung von Forschungsergebnissen in praktische Veränderungen bewertet. Im zweiten Kapitel werden die in den öffentlichen Reaktionen auf die aktuellen Schulleistungsstudien geäußerten Reformvorschläge unter der Fragestellung diskutiert, welche Veränderungen angesichts einer Vielfalt in sich komplexer Anforderungen vorrangig sein sollten. Kapitel 3 befasst sich mit Forschungsergebnissen zur Bedeutung der Schularten im gegliederten System für die Lenkung von Schülerströmen - explizit nach den Kriterien Befähigung und Vorwissen, in Deutschland aber stärker als in den meisten anderen PISA-Teilnehmerstaaten verbunden mit Statusmerkmalen der Herkunftsfamilie, die maßgeblich an der Entwicklung von Befähigung und Wissen beteiligt ist. Im abschließenden Kapitel 4 werden Resultate von PISA zur in Deutschland besonders häufigen Verzögerung von Schullaufbahnen referiert und mit Ergebnissen anderer Projekte konfrontiert, die eine weniger rigorose Bewertung nahe legen. Die zweifellos zu kritisierende Häufigkeit von Verzögerungen z.B. durch Klassenwiederholungen erscheint vor diesem Hintergrund eher als Folge des Fehlens praktikabler Alternativen zur Förderung von Schülern mit gravierenden Leistungsschwächen. (DIPF/Orig.

The Global Effort to Eradicate Rinderpest

During the past 70 years, concerted efforts by the national veterinary services of affected countries from Senegal to China and Russia to South Africa—aided by international organizations—have brought the once-dreaded rinderpest virus to the point of extinction. In the near future, we can expect to see a global declaration of freedom from rinderpest, the first time this has been achieved for a livestock disease. The devastation wrought by rinderpest stimulated the founding of veterinary schools in many countries, and provided the basis for the development of the veterinary profession. The legacy of control programs in the past 20 years includes vaccine innovations and the development of new epidemiological and surveillance tools that are based on participatory techniques. Additionally, the benefits derived from eradication are many, ranging from increased confidence in livestock-based agriculture to increased food security, protected rural livelihoods, technically more proficient veterinary services, an opening of trade into lucrative markets in the Middle East, and the safeguarding of Africa’s wildlife heritage from a serious threat to its dwindling populations. As for the financial benefits of rinderpest eradication, describing them is constrained because of a general lack of studies on the subject, and the fact that programs covering multiple issues often did not clearly discern the rinderpest problem. This analysis attempts to present lessons learned from the experience gained in eradicating rinderpest, and explores the socioeconomic gains made as a result

Gender differences in the choice of advanced and basic courses in senior high school

Die vorliegende Untersuchung stützt sich auf Erhebungen der Bundesländer über die Wahlen von Leistungs- und Grundkursen sowie auf Informationen auf einer Schülerbefragung zur Bewertung von Aspekten des Kurssystems, die im Rahmen einer internationalen Untersuchung zum mathematisch- naturwissenschaftlichen Unterricht durchgeführt wurde. Auf der Grundlage dieser Daten werden Unterschiede und Gemeinsamkeiten im Kurswahlverhalten der Geschlechter erörtert. Fokus der abschließenden Diskussion ist der Kontrast zwischen geschlechtsspezifischem Kurswahlverhalten einerseits und dem in den vergangenen Jahrzehnten zu beobachtenden Prozeß der Angleichung der formalen Bildungskarrieren beider Geschlechter andererseits. (DIPF/Orig.)The study presented is based on statistics provided by the Laender Ministries of Education regarding curricular options of senior high school students in choosing advanced and basic courses. In addition, information gained from an international survey on students\u27 opinions concerning, among other things, the quality of the advanced courses they had taken is utilized for a broader interpretation of the observed gender differences in curricular options. The concluding discussion focusses on the contrast between gender-specific curricular options and the process of an equalization of male and female formal educational careers that has been observed during the last three decades. (DIPF/Orig.

Tessellations and Pattern Formation in Plant Growth and Development

The shoot apical meristem (SAM) is a dome-shaped collection of cells at the apex of growing plants from which all above-ground tissue ultimately derives. In Arabidopsis thaliana (thale cress), a small flowering weed of the Brassicaceae family (related to mustard and cabbage), the SAM typically contains some three to five hundred cells that range from five to ten microns in diameter. These cells are organized into several distinct zones that maintain their topological and functional relationships throughout the life of the plant. As the plant grows, organs (primordia) form on its surface flanks in a phyllotactic pattern that develop into new shoots, leaves, and flowers. Cross-sections through the meristem reveal a pattern of polygonal tessellation that is suggestive of Voronoi diagrams derived from the centroids of cellular nuclei. In this chapter we explore some of the properties of these patterns within the meristem and explore the applicability of simple, standard mathematical models of their geometry.Comment: Originally presented at: "The World is a Jigsaw: Tessellations in the Sciences," Lorentz Center, Leiden, The Netherlands, March 200

Condition-specific outcome measures for low back pain: Part I: Validation

A literature review of the nine most widely used, condition-specific, self-administered assessment questionnaires for low back pain has been undertaken. General and historic aspects, reliability, responsiveness and minimum clinically important difference, external validity, floor and ceiling effects and available languages were analysed for the nine most-used outcome tools. When considering which condition-specific measure to employ, the present overview on assessment tools should provide the necessary information to define the technical aspects of the nine questionnaires. These criteria, however, are only part of the consideration. In part II the construction of these scales in relationship to the measurement domains will be evaluate