Higher dimensional cluster combinatorics and representation theory

Higher Auslander algebras were introduced by Iyama generalizing classical concepts from representation theory of finite dimensional algebras. Recently these higher analogues of classical representation theory have been increasingly studied. Cyclic polytopes are classical objects of study in convex geometry. In particular, their triangulations have been studied with a view towards generalizing the rich combinatorial structure of triangulations of polygons. In this paper, we demonstrate a connection between these two seemingly unrelated subjects. We study triangulations of even-dimensional cyclic polytopes and tilting modules for higher Auslander algebras of linearly oriented type A which are summands of the cluster tilting module. We show that such tilting modules correspond bijectively to triangulations. Moreover mutations of tilting modules correspond to bistellar flips of triangulations. For any d-representation finite algebra we introduce a certain d-dimensional cluster category and study its cluster tilting objects. For higher Auslander algebras of linearly oriented type A we obtain a similar correspondence between cluster tilting objects and triangulations of a certain cyclic polytope. Finally we study certain functions on generalized laminations in cyclic polytopes, and show that they satisfy analogues of tropical cluster exchange relations. Moreover we observe that the terms of these exchange relations are closely related to the terms occuring in the mutation of cluster tilting objects.Comment: 41 pages. v4: minor corrections throughout the pape

Was bringen Stiftungsuniversitäten und der Rückzug des Staates aus der Detailsteuerung? : Vortrag von Thomas Oppermann am 30. Mai 2007 an der Johann Wolfgang Goethe-Universität Frankfurt am Main (Extrakt einer frei gehaltenen Rede)

* Warum Stiftungen? Es geht nicht um Stiftung an sich, sondern die Stiftung ist Mittel zum Zweck. Die Beamtenuniversität, die Universität als Staatsbetrieb, muss von der staatlichen Umklammerung gelöst werden, wenn sich die Hochschule qualitativ weiterentwickeln soll. Der Staat klammert, aber umgekehrt ist die Universität auch auf den Staat fixiert. Diese Staatsfixierung behindert ein Innovationsklima. Sie schützt Mittelmaß. Sie begründet hierarchische, bürokratisch ausgestaltbare Beziehungen. Die Hochschule ist am Ende eine nachgeordnete Behörde: Die deutsche Universität ist überbürokratisiert und unterfinanziert. Sie ist fixiert auf den armen Staat und ignoriert die reiche Gesellschaft, genauer: Sie ist fixiert auf den finanziell armen, aber stets regelungsbereiten Staat und sie ignoriert die ideell und materiell reiche Gesellschaft. * Die Zielsetzung ist Entstaatlichung, nicht Privatisierung. * Die Stiftungsuniversität ermöglicht die Entstaatlichung, Autonomie und gesellschaftliche Verankerung der Hochschule. * Die Stiftungsuniversität erhöht die Entscheidungsfreiheit und die Entscheidungsfreude der Universität. * Die Stiftung als Rechtsform einer Universität eignet sich, um den Dualismus aus staatlicher Umklammerung und staatlicher Fixierung der Hochschulen zu ersetzen durch ein Dreieck Staat – Hochschule – Gesellschaft. * Die Stiftungsuniversität ermöglicht einen höheren Identifikationsgrad der Hochschulmitglieder und der Gesellschaft mit der Hochschule. * Die Stiftungsuniversität soll dazu beitragen, die privaten Mittel für Hochschulen zu erhöhen

High Resolution X-Ray CT for Advanced Electronics Packaging

Advanced electronics packaging is a challenge for non-destructive Testing (NDT). More, smaller and mostly hidden interconnects dominate modern electronics components and systems. To solve the demands of customers to get products with a high functionality by low volume, weight and price (e.g. mobile phones, personal medical monitoring systems) often the designers use System-in-Package solutions (SiP). The non-destructive testing of such devices is a big challenge (see [1]). So our paper will impart fundamentals and applications for non-destructive evaluation of inner structures of electronics packaging for quality assurance and reliability investigations. The main NDE methods for electronics packaging are scanning acoustic microscopy and X-ray macrostructure analysis like X-ray radiography and X-ray computed tomography (CT) (see [2] & [3]). Our presentation will focus on X-ray nano focus computed tomography as a method for component development, process development and reliability research. We will discuss the potentials and the limits of X-ray NDE techniques, illustrated by crack observation in solder joints, evaluation of micro vias in PCBs and interposers and the investigation of a complex SiP like a USB memory device. We will show tomography results with voxel sizes less than 800nm. To reach these results we developed special techniques to prepare the samples for high resolution CTs. Figure 1 shows the tool, a prepared specimen and a high resolution CT result picture

Wireless location technologies and applications

[No abstract available

Do Tratado de Nice de 2001 à Convenção para a Constituição Européia 2002/2003: rumo a uma Ordem Constitucional na Europa?

No período que se estende entre a promulgação do Tratado de Nice de 2001 e a concretização do alargamento da União Européia em maio de 2004, de quinze para vinte e cinco Estados-Membros, a elaboração de um projeto legível e factível de uma Constituição Européia se constitui uma tarefa inevitável. Seguindo a esteira de resultados da Convenção Européia de Direitos Fundamentais de 2000, o Conselho da UE lança uma segunda Convenção dos Estados-Membros, a qual, até a segunda metade de 2003, deve apresentar o projeto de um Tratado Constitucional para a Comunidade. Paralelamente, uma Convenção Parlamentar do governo alemão decide sobre o referido projeto. O presente artigo descreve o percurso em direção a uma nova rodada de trabalhos em Bruxelas, sua formação e os resultados da Convenção até final de 2002, bem como contribui para o debate do tema da Constituição Européia até então desenvolvido no contexto europeu

The XENON100 exclusion limit without considering Leff as a nuisance parameter

In 2011, the XENON100 experiment has set unprecedented constraints on dark matter-nucleon interactions, excluding dark matter candidates with masses down to 6 GeV if the corresponding cross section is larger than 10^{-39} cm^2. The dependence of the exclusion limit in terms of the scintillation efficiency (Leff) has been debated at length. To overcome possible criticisms XENON100 performed an analysis in which Leff was considered as a nuisance parameter and its uncertainties were profiled out by using a Gaussian likelihood in which the mean value corresponds to the best fit Leff value smoothly extrapolated to zero below 3 keVnr. Although such a method seems fairly robust, it does not account for more extreme types of extrapolation nor does it enable to anticipate on how much the exclusion limit would vary if new data were to support a flat behaviour for Leff below 3 keVnr, for example. Yet, such a question is crucial for light dark matter models which are close to the published XENON100 limit. To answer this issue, we use a maximum Likelihood ratio analysis, as done by the XENON100 collaboration, but do not consider Leff as a nuisance parameter. Instead, Leff is obtained directly from the fits to the data. This enables us to define frequentist confidence intervals by marginalising over Leff.Comment: 10 pages;, 9 figures; references adde

Combined transarterial chemoembolization and arterial administration of Bletilla striata in treatment of liver tumor in rats

AIM: To evaluate and compare the effect of combined transarterial chemoembolization (TACE) and arterial administration of Bletilla striata (a Chinese traditional medicine against liver tumor) versus TACE alone for the treatment of hepatocellular carcinoma (HCC) in ACI rats. METHODS: Subcapsular implantation of a solid Morris hepatoma 3 924A (2 mm3) in the liver was carried out in 30 male ACI rats. Tumor volume (V1) was measured by magnetic resonance imaging (MRI) on day 13 after implantation. The following different agents of interventional treatment were injected after retrograde catheterization via gastroduodenal artery (on day 14), namely, (A) TACE (0.1 mg mitomycin + 0.1 ml Lipiodol) + Bletilla striata (1.0 mg) (n=10); (B) TACE + Bletilla striata (1.0 mg) + ligation of hepatic artery (n=10), (C) TACE alone (control group, n=10). Tumor volume (V2) was assessed by MRI (on day 13 after treatment) and the tumor growth ratio (V2/V1) was calculated. RESULTS: The mean tumor volume before (V1) and after (V2) treatment was 0.0355 cm3 and 0.2248 cm3 in group A, 0.0374 cm3 and 0.0573 cm3 in group B, 0.0380 cm3 and 0.3674 cm3 in group C, respectively. The mean ratio (V2/V1) was 6.2791 in group A, 1.5324 in group B and 9.1382 in group C. Compared with the control group (group C), group B showed significant inhibition of tumor growth (P0.05). None of the animals died during implantation or in the postoperative period. CONCLUSION: Combination of TACE and arterial administration of Bletilla striata plus ligation of hepatic artery is more effective than TACE alone in the treatment of HCC in rats

Triangulations of cyclic polytopes

We give a new description of the combinatorics of triangulations of even-dimensional cyclic polytopes, and of their bistellar flips. We show that the tropical exchange relation governing the number of intersections between diagonals of a polygon and a lamination (which generalizes to arbitrary surfaces) can also be generalized in a different way, to the setting of higher dimensional cyclic polytopes