4.1 Eigenvalues and Optimization I cannot believe that I have managed to teach three lectures on spectral graph theory without giving the characterization of eigenvalues as solutions to optimization problems. It is one of the most useful ways of understanding eigenvalues of symmetric matrices. To begin, let A be a symmetric matrix with eigenvalues α1 ≥ α2 ≥ · · · ≥ αn, and corresponding orthono...

Introduction. In this paper we shall be concerned with the structure of the rational representation of certain sets of matrices, to which we give the name generalized Fischer sets. If K is any field, any fixed automorphism of K, and A any matrix with elements in K, we use the notation A* for the 0-automorph of A ; that is, the matrix obtained from A by subjecting each of its elements to the...

Innate airway hyperresponsiveness (AHR) is well modeled by two strains of rat, the hyperresponsive Fischer 344 rat and the normoresponsive Lewis rat. Arginase has been implicated in AHR associated with allergic asthma models. We addressed the role of arginase in innate AHR using the Fischer-Lewis model. In vivo arginase inhibition with N(ω)-hydroxy-nor-arginine (nor-NOHA) was evaluated on metha...

Die Moving-Window-Technologie ist eine Rahmenmethode zur Beschreibung der Verteilung von räumlich verteilten Objekten in der Landschaft. Über die Größe und Form des Analysefensters ist der Generalisierungsgrad skalierbar. An Beispieldaten aus dem Atlas für Farnund Blütenpflanzen Ostdeutschlands werden darauf basierende Methoden zur Generalisierung und Disaggregation im Vergleich mit konventione...

Economic policy was used actively in most countries to curb the economic downturn. Substantial resources were deployed in the form of stimulus packages and measures to prevent financial market collapse. Nonetheless, unemployment in the OECD area rose by 15 million in the first year after the outbreak of the crisis. The downturn also led to a sharp fall in tax revenues. Budget deficits ballooned...

The concept of runs, i.e. maximal periodicity or maximal occurrence of repetitions, coined by Iliopoulos et al. [10] when analysing Fibanacci words, has been introduced to represent in a succinct manner all occurrences of repetitions in a word. It is known that there are only O(n) many of them in a word of length n from Kolpakov and Kucherov [11] who proved it in a non-constructive manner. The ...