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Institute
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- Physik (60)
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- Biowissenschaften (55)
- Geowissenschaften (45)
- Center for Financial Studies (CFS) (37)
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- E-Finance Lab e.V. (21)
- Extern (19)
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."
Background: To evaluate the effectivity of fractionated radiotherapy in adolescent and adult patients with pineal parenchymal tumors (PPT). Methods: Between 1982 and 2003, 14 patients with PPTs were treated with fractionated radiotherapy. 4 patients had a pineocytoma (PC), one a PPT with intermediate differentiation (PPTID) and 9 patients a pineoblastoma (PB), 2 of which were recurrences. All patients underwent radiotherapy to the primary tumor site with a median total dose of 54 Gy. In 9 patients with primary PB treatment included whole brain irradiation (3 patients) or irradiation of the craniospinal axis (6 patients) with a median total dose of 35 Gy. Results: Median follow-up was 123 months in the PC patients and 109 months in the patients with primary PB. 7 patients were free from relapse at the end of follow-up. One PC patient died from spinal seeding. Among 5 PB patients treated with radiotherapy without chemotherapy, 3 developed local or spinal tumor recurrence. Both patients treated for PB recurrences died. The patient with PPTID is free of disease 7 years after radiotherapy. Conclusion: Local radiotherapy seems to be effective in patients with PC and some PPTIDs. Diagnosis and treatment of patients with more aggressive variants of PPTIDs as well as treatment of PB need to be further improved, since local and spinal failure even despite craniospinal irradiation (CSI) is common. As PPT are very rare tumors, treatment within multi-institutional trials remains necessary.
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.