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In der folgenden Arbeit werden Eigenschaften von Verzweigungsprozessen in zufälliger Umgebung (engl. branching processes in random environment, kurz BPREs) untersucht. Das Modell geht auf Smith (1969) und Athreya (1971) zurück. Ein BPRE ist ein einfaches mathematisches Modell für die Entwicklung einer Population von apomiktischen (d.h. sich ungeschlechtlich fortpflanzenden) Individuen in diskreter Zeit, wobei die Umgebungsbedingungen einen Einfluß auf den Fortpflanzungserfolg der Individuen haben. Dabei wird angenommen, dass die Umgebungsbedingungen in den einzelnen Generationen zufällig sind, und zwar unabhängig und identisch verteilt von Generation zu Generation. Man denke z.B. an eine Population von Pflanzen mit einem einjährigen Zyklus, die in jedem Jahr anderen Witterungsbedingungen ausgesetzt sind, wobei angenommen wird, dass diese sich unabhängig und identisch verteilt ändern. In Kapitel 1 wird eines der wichtigsten Hilfsmittel zur Beschreibung von BPREs, die sogenannte zugehörige Irrfahrt, eingeführt und die Klassifizierung von BPREs beschrieben. In Kapitel 2 werden bekannte Resultate, insbesondere zu kritischen, schwach subkritischen und stark subkritischen Verzweigungsprozessen, wiederholt. In Kapitel 3 wird der sogenannte intermediär subkritische Fall behandelt. Mithilfe von funktionalen Grenzwertsätzen für bedingte Irrfahrten wird die genaue Asymptotik der Überlebenswahrscheinlichkeit des Prozesses, die bereits in Vatutin (2004) bewiesen wurde, unter etwas allgemeineren Voraussetzungen gezeigt. Anschließend wird untersucht, wie häufig der Prozess, bedingt auf Überleben, nur noch aus einem Individuum besteht. Im letzten Teil des Kapitels wird ein funktionaler Grenzwertsatz für die zugehörige Irrfahrt, bedingt aufs Überleben des Prozesses, gezeigt. Diese konvergiert, richtig skaliert, gegen einen Levy-Prozess, der darauf bedingt ist, sein Minimum am Ende anzunehmen. In Kapitel 4 werden große Abweichungen von BPREs untersucht. Die Ratenfunktion des BPRE wird sowohl für den Fall mindestens geometrisch schnell abfallender Tails, als auch für den Fall von Nachkommenverteilungen mit schweren Tails bestimmt. Wie sich herausstellt, hängt die Ratenfunktion von der Ratenfunktion der zugehörigen Irrfahrt, der exponentiellen Abfallrate der Überlebenswahrscheinlichkeit sowie, bei Nachkommenverteilungen mit schweren Tails, auch von den Tails derselben ab. In der Ratenfunktion spiegeln sich die wahrscheinlichsten Wege, um Ereignisse der großen Abweichungen zu realisieren, wider, was in Kapitel 4.3 beschrieben wird. In Kapitel 4.4 wird im speziellen Fall von Nachkommenverteilungen mit gebrochen-linearer Erzeugendenfunktion die Ratenfunktion für Ereignisse bestimmt, bei denen ein superkritischer BPRE überlebt, aber klein im Vergleich zum Erwartungswert bleibt. In Kapitel 4.5 werden die großen Abweichungen, bedingt auf die Umgebung untersucht (engl. quenched). In diesem Fall können unwahrscheinliche Ereignisse nur über den Verzweigungsmechanismus und nicht mehr über eine außergewöhnliche Umgebung realisiert werden. Zum Abschluss der Dissertation werden Verzweigungsprozesse in zufälliger Umgebung, bedingt auf Überle-ben, simuliert. Dazu wird eine Konstruktion nach Geiger (1999) angewendet. Diese erlaubt es, Galton-Watson Bäume in variierender Umgebung, bedingt auf Überleben, entlang einer Ahnenlinie zu konstruieren. Der Fall geometrischer Nachkommenverteilungen, auf den wir uns in Kapitel 5 beschränken, erlaubt die explizite Berechnung der benötigten Verteilungen. Als Anwendung des Grenzwertsatzes aus Kapitel 3.1 können nun intermediär subkritische Verzweigungsprozesse, bedingt auf Überleben, wie folgt simuliert werden: Zunächst wird die Umgebung zufällig bestimmt, und zwar als Irrfahrt, bedingt darauf ihr Minimum am Ende anzunehmen. Anschließend wird, der Geiger-Konstruktion folgend, ein Verzweigungsprozess in dieser Umgebung, bedingt auf Überleben, simuliert. Zum Abschluss wird in einem kurzen Ausblick auf aktuelle Forschung verwiesen. Im Anhang befinden sich einige technische Resultate.
Brecht - Galileo
(2010)
This is the age of doubt, says Brecht's Galileo, the 17th century scientist. "It ain't necessarily so," says Gershwin's Sportin' Life of the 1930ies. "De t'ings dat yo li'ble / to read in de Bible / it ain't necessarily so. / Now I takes dat gospel / whenever it's pos'ble / but wid a grain of salt."
Condensing phenomena for systems biology, ecology and sociology present in real life different complex behaviors. Based on local interaction between agents, we present another result of the Energy-based model presented by [20]. We involve an additional condition providing the total condensing (also called consensus) of a discrete positive measure. Key words: Condensing; consensus; random move; self-organizing groups; collective intelligence; stochastic modeling. AMS Subject Classifications: 81T80; 93A30; 37M05; 68U20
We examined financial literacy among the young using the most recent wave of the 1997 National Longitudinal Survey of Youth. We showed that financial literacy is low; fewer than one-third of young adults possess basic knowledge of interest rates, inflation, and risk diversification. Financial literacy was strongly related to sociodemographic characteristics and family financial sophistication. Specifically, a college-educated male whose parents had stocks and retirement savings was about 45 percentage points more likely to know about risk diversification than a female with less than a high school education whose parents were not wealthy. These findings have implications for consumer policy. JEL Classification: D91
How ordinary consumers make complex economic decisions: financial literacy and retirement readiness
(2010)
This paper explores who is financially literate, whether people accurately perceive their own economic decision-making skills, and where these skills come from. Self-assessed and objective measures of financial literacy can be linked to consumers’ efforts to plan for retirement in the American Life Panel, and causal relationships with retirement planning examined by exploiting information about respondent financial knowledge acquired in school. Results show that those with more advanced financial knowledge are those more likely to be retirement-ready.
Introduction: Hypothermia improves survival and neurological recovery after cardiac arrest. Pro-inflammatory cytokines have been implicated in focal cerebral ischemia/reperfusion in-jury. It is unknown whether cardiac arrest also triggers the release of cerebral inflammatory molecules, and whether therapeutic hypothermia alters this inflammatory response. This study sought to examine whether hypothermia or the combination of hypothermia with anes-thetic postconditioning with sevoflurane affect cerebral inflammatory response after cardio-pulmonary resuscitation. Methods: Thirty pigs (28 - 34kg) were subjected to cardiac arrest following temporary coro-nary artery occlusion. After 7 minutes of ventricular fibrillation and 2 minutes of basic life support, advanced cardiac life support was started according to the current AHA guidelines. Return of spontaneous circulation was achieved in 21 animals who were randomized to ei-ther normothermia at 38degreesC, hypothermia at 33degreesC or hypothermia at 33degreesC combined with se-voflurane (each group: n = 7) for 24 hours. The effects of hypothermia and the combination of hypothermia with sevoflurane on cerebral inflammatory response after cardiopulmonary resuscitation were studied using tissue samples from the cerebral cortex of pigs euthanized after 24 hours and employing quantitative RT-PCR and ELISA techniques. Results: Global cerebral ischemia following resuscitation resulted in significant upregulation of cerebral tissue inflammatory cytokine mRNA expression (mean +/- SD; interleukin (IL)-1beta 8.7 +/- 4.0, IL-6 4.3 +/- 2.6, IL-10 2.5 +/- 1.6, tumor necrosis factor (TNF)alpha 2.8 +/- 1.8, intercellular adhesion molecule-1 (ICAM-1) 4.0 +/- 1.9-fold compared with sham control) and IL-1beta protein concentration (1.9 +/- 0.6-fold compared with sham control). Hypothermia was associated with a significant (P <0.05 versus normothermia) reduction in cerebral inflammatory cytokine mRNA expression (IL-1beta 1.7 +/- 1.0, IL-6 2.2 +/- 1.1, IL-10 0.8 +/- 0.4, TNFalpha 1.1 +/- 0.6, ICAM-1 1.9 +/- 0.7-fold compared with sham control). These results were also confirmed for IL-1beta on protein level. Experimental settings employing hypothermia in combination with sevoflurane showed that the volatile anesthetic did not confer additional anti-inflammatory effects com-pared with hypothermia alone. Conclusions: Mild therapeutic hypothermia resulted in decreased expression of typical ce-rebral inflammatory mediators after cardiopulmonary resuscitation. This may confer, at least in part, neuroprotection following global cerebral ischemia and resuscitation.
The purpose of this essay is to assess the automatic exchange of information as described in EU Directive 2003/48 of 3 June 2003 on taxation of savings income in the form of interest payments with regard to the fundamental right of the individual to a private life, to banking secrecy and the freedoms on which the European internal market is based. The assessment reveals the conflicts of interests and values involved in the holding by banks (particularly those offering private banking services) of increasingly extensive, detailed and intimate information about their clients and in the automatic processing of that information by ever more powerful and sophisticated systems. Banking secrecy plays an essential role in protecting clients against the dangers which the disclosure of such information without their permission might produce. Banking secrecy exists not only in Luxembourg but also in many other European countries, and in Germany and France in particular it is not very different from the system applying in Luxembourg. While the French and German tax authorities do have some investigative powers not enjoyed by their Luxembourg counterparts, those powers are strictly circumscribed and cannot rely on the electronic exchange of information set out in EU Directive 2003/48/EC. While banking secrecy is totally incompatible with the electronic exchange of information, the core question is whether the latter can be reconciled with the respect for private life. In a Europe that sets itself up as the cradle of human rights, the general and en-masse exchange of private information cannot provide adequate and sufficient guarantees that the information exchanged will not be misused. The amount of interference in private life is clearly out of proportion to the public interest involved and is contrary to sub-section 2, article 8 of the European Convention for the Protection of Human Rights and Fundamental Freedoms and to articles 7 and 8 of the Charter of Fundamental Rights of the European Union. Since the automatic exchange of information at least potentially risks restricting the free flow of capital among Member States and discouraging the use of transborder banking services, its compliance with the fundamental principles of the internal market also needs to be closely examined. The restrictions imposed by such exchange very probably go beyond the limits within which the free movement of capital and services is possible. The European Court of Justice has found that there is no proportionality if the measures supposedly undertaken in the general interest are actually based on a general presumption of tax evasion or tax fraud. However, it would be true to say that the ECJ does not always examine the tax restrictions placed on the free movement of capital particularly thoroughly to ensure that they are necessary or proportionate. The economic effectiveness of the automatic exchange of information is far from being proved and involves significant cost to the banks providing the information and to the tax authorities using it. To date the system does not appear to have produced any significant new tax revenue nor does it prevent the continuing outflow of capital from Europe. Yet withholding at source, which respects individual and economic freedoms, does generate tax revenue that is cost-free to the State. Exchange of information on request in justified cases using the OECD Tax Convention on Income and Capital model does also fight tax fraud while at the same time providing citizens with the guarantees required to ensure their private lives are respected. A combination of these two systems - withholding at source and exchange of information on request in justified cases - would create the proper balance between the public and private interest that the automatic exchange of information cannot provide.