In der vorliegenden Arbeit wird die Wiederkehr im Phasenraum ausgenutzt. Dabei werden drei Hauptresultate besprochen. 1. Die Wiederkehr erlaubt die Vorhersagbarkeit des Systems zu quantifizieren. 2. Die Wiederkehr enthaelt (unter bestimmten Voraussetzungen) sämtliche relevante Information über die Dynamik im Phasenraum 3. Die Wiederkehr erlaubt die Erzeugung dynamischer Ersatzdaten. / Recurrence plots, a rather promising tool of data analysis, have been introduced by Eckman et al. in 1987. They visualise recurrences in phase space and give an overview about the system's dynamics. Two features have made the method rather popular. Firstly they are rather simple to compute and secondly they are putatively easy to interpret. However, the straightforward interpretation of recurrence plots for some systems yields rather surprising results. For example indications of low dimensional chaos have been reported for stock marked data, based on recurrence plots. In this work we exploit recurrences or ``naturally occurring analogues'' as they were termed by E. Lorenz, to obtain three key results. One of which is that the most striking structures which are found in recurrence plots are hinged to the correlation entropy and the correlation dimension of the underlying system. Even though an eventual embedding changes the structures in recurrence plots considerably these dynamical invariants can be estimated independently of the special parameters used for the computation. The second key result is that the attractor can be reconstructed from the recurrence plot. This means that it contains all topological information of the system under question in the limit of long time series. The graphical representation of the recurrences can also help to develop new algorithms and exploit specific structures. This feature has helped to obtain the third key result of this study. Based on recurrences to points which have the same ``recurrence structure'', it is possible to generate surrogates of the system which capture all relevant dynamical characteristics, such as entropies, dimensions and characteristic frequencies of the system. These so generated surrogates are shadowed by a trajectory of the system which starts at different initial conditions than the time series in question. They can be used then to test for complex synchronisation.

Die tägliche Erfahrung zeigt uns, daß bei vielen physikalischen Systemen kleine Änderungen in den Anfangsbedingungen auch zu kleinen Änderungen im Verhalten des Systems führen. Wenn man z.B. das Steuerrad beim Auto fahren nur ein wenig zur Seite dreht, unterscheidet sich die Richtung des Wagens auch nur wenig von der ursprünglichen Richtung. Aber es gibt auch Situationen, für die das Gegenteil dieser Regel zutrifft. Die Folge von Kopf und Zahl, die wir erhalten, wenn wir eine Münze werfen, zeigt ein irreguläres oder chaotisches Zeitverhalten, da winzig kleine Änderungen in den Anfangsbedingungen, die z.B. durch leichte Drehung der Hand hervorgebracht werden, zu vollkommen verschiedenen Resultaten führen. In den letzten Jahren hat man sehr viele nichtlineare Systeme mit schnellen Rechnern untersucht und festgestellt, daß eine sensitive Abhängigkeit von den Anfangsbedingungen, die zu einem chaotischen Verhalten führt, keinesfalls die Ausnahme darstellt, sondern eine typische Eigenschaft vieler Systeme ist. Obwohl chaotische Systeme kleinen Änderungen in den Anfangsbedingungen gegenüber sehr empfindlich reagieren, können sie synchronisieren wenn sie durch eine gemeinsame äußere Kraft getrieben werden, oder wenn sie miteinander gekoppelt sind. Das heißt, sie vergessen ihre Anfangsbedingungen und passen ihre Rhythmen aneinander. Diese Eigenschaft chaotischer Systeme hat viele Anwendungen, wie z.B. das Design von Kommunikationsgeräte und die verschlüsselte Übertragung von Mitteilungen. Abgesehen davon, findet man Synchronisation in natürlichen Systemen, wie z.B. das Herz-Atmungssystem, raumverteilte ökologische Systeme, die Magnetoenzephalographische Aktivität von Parkinson Patienten, etc. In solchen komplexen Systemen ist es nicht trivial Synchronisation zu detektieren und zu quantifizieren. Daher ist es notwendig, besondere mathematische Methoden zu entwickeln, die diese Aufgabe erledigen. Das ist das Ziel dieser Arbeit. Basierend auf dergrundlegenden Idee von Rekurrenzen (Wiederkehr) von Trajektorien dynamischer Systeme, sind verschiedene Maße entwickelt worden, die Synchronisation in chaotischen und komplexen Systemen detektieren. Das Wiederkehr von Trajektorien erlaubt uns Vorhersagen über den zukünftigen Zustand eines Systems zu treffen. Wenn man diese Eigenschaft der Wiederkehr von zwei interagierenden Systemen vergleicht, kann man Schlüsse über ihre dynamische Anpassung oder Synchronisation ziehen. Ein wichtiger Vorteil der Rekurrenzmaße für Synchronisation ist die Robustheit gegen Rauschen und Instationariät. Das erlaubt eine Synchronisationsanalyse in Systemen durchzuführen, die bisher nicht darauf untersucht werden konnten. / This work deals with the connection between two basic phenomena in Nonlinear Dynamics: synchronization of chaotic systems and recurrences in phase space. Synchronization takes place when two or more systems adapt (synchronize) some characteristic of their respective motions, due to an interaction between the systems or to a common external forcing. The appearence of synchronized dynamics in chaotic systems is rather universal but not trivial. In some sense, the possibility that two chaotic systems synchronize is counterintuitive: chaotic systems are characterized by the sensitivity ti different initial conditions. Hence, two identical chaotic systems starting at two slightly different initial conditions evolve in a different manner, and after a certain time, they become uncorrelated. Therefore, at a first glance, it does not seem to be plausible that two chaotic systems are able to synchronize. But as we will see later, synchronization of chaotic systems has been demonstrated. On one hand it is important to investigate the conditions under which synchronization of chaotic systems occurs, and on the other hand, to develop tests for the detection of synchronization. In this work, I have concentrated on the second task for the cases of phase synchronization (PS) and generalized synchronization (GS). Several measures have been proposed so far for the detection of PS and GS. However, difficulties arise with the detection of synchronization in systems subjected to rather large amounts of noise and/or instationarities, which are common when analyzing experimental data. The new measures proposed in the course of this thesis are rather robust with respect to these effects. They hence allow to be applied to data, which have evaded synchronization analysis so far. The proposed tests for synchronization in this work are based on the fundamental property of recurrences in phase space.

The treatment of rectal cancer is complex and comprises: diagnostic measures; different preoperative treatments; a multitude of surgical and technical choices; possibilities of postoperative treatments and postoperative care and follow up. In this thesis, some aspects of this complex paradigm have been further investigated. One of the most feared complications after rectal cancer surgery is anastomotic leakage. The risk of anastomotic leakage is affected by non-influenceable factors related to the tumour and the patient. In the first paper, the risk of anastomotic leakage in relation to a surgical instrument, the circular stapler, was investigated. The risk of leakage was 7% or 11%, depending on the choice of instrument. In the second paper, a long-term evaluation of survival and local recurrence rates in the Swedish Rectal Cancer Trial was made. Randomisation was to either preoperative radiotherapy followed by surgery or surgery alone. After 13 years median follow-up, survival was 38% in the radiotherapy group and 30% in the surgery alone group. Differences in local recurrence rates were seen in all stages. Most rectal cancer operations carry a high risk of morbidity and mortality. For early stage cancers, a local procedure may be sufficient and in the third paper, population-based results of local excision of rectal cancer were explored. In stage I, cancer specific survival was the same after local excision as after major resection, but the relative survival was lower. The risk of local recurrence was higher after local excision than after resections. In the fourth paper, differences in survival rates in the Nordic countries and Scotland were investigated. The relative excess risk of death was highest in Denmark, but only in the first 90 postoperative days. Through applying already existing knowledge and successively introducing new treatments, the results for rectal cancer treatment will be further improved.

Inguinal hernia repair is the most common operation in general surgery. Its main challenge is to achieve low recurrence rates. With the introduction of mesh implants, first in open and later in laparoscopic repair, recurrence rates have decreased substantially. Therefore, the focus has been shifted from clinical outcome, such as recurrence, towards patient-experienced endpoints, such as chronic pain. In order to compare the results of open and laparoscopic hernia repair, a randomised multicentre trial - the Swedish Multicentre trial of Inguinal hernia repair by Laparoscopy (SMIL) - was designed by a study group from 11 hospitals. Between November 1996 and August 2000, 1512 men aged 30-70 years with a primary inguinal hernia were randomised to either laparoscopic (TEP, Totally ExtraPeritoneal) or open (Lichtenstein) repair. The primary endpoint was recurrence at five years. Secondary endpoints were short-term results, frequency of chronic pain and a cost analysis including complications and recurrences up to five years after surgery. In total, 1370 patients, 665 in the TEP and 705 in the Lichtenstein group, underwent operation. With 94% of operated patients available for follow-up after 5.1 years, the recurrence rate was 3.5% in the TEP and 1.2% in the Lichtenstein group. Postoperative pain was lower in the TEP group up to 12 weeks after operation, resulting in five days less sick leave and 11 days shorter time to full recovery. Patients in the TEP group had a slightly increased risk of major complications. Chronic pain was reported by 9-11% of patients in the TEP and 19-25% in the Lichtenstein group at the different follow-up points. Hospital costs for TEP were higher than for Lichtenstein, while community costs were lower due to shorter sick leave. By avoiding disposable laparoscopic equipment, the cost for TEP would be almost equal compared with Lichtenstein. In conclusion, both TEP and Lichtenstein repair have advantages and disadvantages for the patient. Depending on local resources and expertise both methods can be used and recommended for primary inguinal hernia repair.

Aberrant promoter methylation is known to silence tumor-suppressor genes in prostate cancer. Using a quantitative real-time PCR assay(MethyLight), I determined promoter methylation levels of APC, RASSF1A, CYP26A1 and TBX15 in 219 radical prostatectomies diagnosed between 1998-2001, examined their correlation with clinicopathological follow-up data including Gleason Pattern(GP), Gleason Score(GS) and pathological stage, and explored their potential in predicting biochemical recurrence(BR) using univariate and multivariate analyses. I demonstrated that methylation status of all four genes could accurately differentiate normal from cancerous tissues. Quantitative methylation levels of APC and TBX15 correlated strongly with GP, GS, and pathological stage. Both APC and TBX15 methylation levels could significantly predict BR in univariate analysis(p-value=0.028 and 0.003, respectively). The methylation profiles of APC and TBX15 combined could discriminate patients into high, intermediate, and low risk groups of BR(p-value=0.005). My project demonstrated that quantitative increase in promoter methylation levels of APC and TBX15 were associated with PCa progression.

Aberrant promoter methylation is known to silence tumor-suppressor genes in prostate cancer. Using a quantitative real-time PCR assay(MethyLight), I determined promoter methylation levels of APC, RASSF1A, CYP26A1 and TBX15 in 219 radical prostatectomies diagnosed between 1998-2001, examined their correlation with clinicopathological follow-up data including Gleason Pattern(GP), Gleason Score(GS) and pathological stage, and explored their potential in predicting biochemical recurrence(BR) using univariate and multivariate analyses. I demonstrated that methylation status of all four genes could accurately differentiate normal from cancerous tissues. Quantitative methylation levels of APC and TBX15 correlated strongly with GP, GS, and pathological stage. Both APC and TBX15 methylation levels could significantly predict BR in univariate analysis(p-value=0.028 and 0.003, respectively). The methylation profiles of APC and TBX15 combined could discriminate patients into high, intermediate, and low risk groups of BR(p-value=0.005). My project demonstrated that quantitative increase in promoter methylation levels of APC and TBX15 were associated with PCa progression.

This thesis addresses two interpretative questions concerning the philosophy of Friedrich Nietzsche. The first is to ascertain the primary objection that Nietzsche has to a morality that he describes as decadent. The conclusion reached is that Nietzsche’s objection to decadent morality is based on the harm it does to a class of “higher” individuals who have valuable work to perform in achieving a desirable future for humanity. The second question is to determine the manner in which Nietzsche’s own values are to be understood based on the skepticism he expresses concerning the objectivity of value. The conclusion reached is that Nietzsche’s values are objects of the same analysis he applies to human values generally. The values Nietzsche endorses, including the valuing of “higher” individuals, are to be understood as symptoms of a particular physiology and its relationship to living.

There are many parallels and points of similarity between the themes of the play Waiting for Godot by Samuel Beckett and the themes explored by Friedrich Nietzsche. This essay examines the play in light of some of Nietzsche’s key concepts, such as the Will to Power, the Übermensch or Overman, the Eternal Recurrence, as well as the aesthetic conception of existence. The essay argues that while Waiting for Godot shares many of the premises and conclusions of Nietzsche’s philosophy, the play can also be interpreted as a critique of the same. The play presents a post-religious world marked by pessimism and resignation rather than affirmation and Nietzschean amor fati. The characters are as far removed from the heroic Overman ideal as can be imagined, unable to harness the Will to Power, which is absent or distorted or even unknowable. Communication is fraught with difficulty and uncertainty. The dynamic of the Eternal Recurrence is present but rather than being affirmed it is a source of crushing boredom, tediousness and existential angst. The characters are unable to embrace the Eternal Recurrence and are in a continual state of mental flight from its implications. They suffer from a vague recollection of the past while projecting their hopes into the future in order to diminish the unbearable suffering of the existing present, or state of perpetual becoming. Beckett can thus be said to be offering a satirical critique of the concept of salvation, both in its traditional religious sense as well as in the sense implied by Nietzsche’s concept of the Eternal Recurrence. However, Beckett does offer a sense of hope by suggesting, paradoxically, that the abandonment of hope of salvation may lead to a sort of salvation of resignation.

The aim of this essay is to discuss the meaning of the human and its possible overcoming in Friedrich Nietzsche’s doctrine of the eternal recurrence of the same, with Martin Heidegger’s readings of Nietzsche as point of departure. According to Heidegger, Nietzsche’s doctrine of the eternal recurrence of the same represents the end of occidental metaphysical thinking. The thought concludes a thinking of being as the presence of beings, where the original question of being was never developed out of its own ground. But at the heart of this interpretation, often considered “violent”, lies the question of whether man is able to think being out of his finitude. This is the question I will unfold, through a reading of Nietzsche’s thought of the eternal recurrence of the same, as it is presented in his Thus spoke Zarathustra, as an attempt to think beings in their being beyond a “humanization” of them, expressed in transcendental aims, purposes and categories. This attempt, I argue, is essentially bound up with a comportment toward the human self as the finite and the corporal. In this sense the human being in its finitude and corporeality is thefocus and the basis for the search for “the overman”. But this focus on man, as he who can overcome himself, is at the same time a focus that canbe said to lead man away from himself, in not asking the deeper question about what it means to be this human being. I will furthermore consider the tragic as the theme where this question of the overcoming of the human comes to the fore; the dionysic-tragic reveals both a view of man as the being that is mastered by the abyss that underlies this world, and therefore mastered by his finitude - and as the being who can master this same abyss, in thinking it as one with the human self. The purpose is not to take a position for or against Heidegger’s reading, but to develop a discussion between Heidegger and Nietzsche about the human self as always being both the closed and the open, and about the ways in which human thinking can approach this.

The doctrine of eternal recurrence is not only an aspect of Nietzsche&rsquo / s philosophy, but a notion that structures the base of his philosophy. The doctrine is analyzed by many interpreters in various ways. The cosmological and the ethical-existential approaches to the doctrine are at the very base wrong. The doctrine&rsquo / s impact cannot be adequately understood in these terms. Besides, the doctrine of eternal recurrence has multiple problems within it, problems which can be solved if the doctrine is understood and analyzed properly. In this thesis it was suggested, following Lawrence J. Hatab and Pierre Klossowski, that the doctrine should be read in terms of mimetic literality. And in this way the reading and the understanding of the doctrine lead the self to a dissolution which solves many of the problems within the doctrine.