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Synchronization – the adjustment of rhythms among coupled self-oscillatory systems – is a fascinating dynamical phenomenon found in many biological, social, and technical systems.
The present thesis deals with synchronization in finite ensembles of weakly coupled self-sustained oscillators with distributed frequencies.
The standard model for the description of this collective phenomenon is the Kuramoto model – partly due to its analytical tractability in the thermodynamic limit of infinitely many oscillators. Similar to a phase transition in the thermodynamic limit, an order parameter indicates the transition from incoherence to a partially synchronized state. In the latter, a part of the oscillators rotates at a common frequency. In the finite case, fluctuations occur, originating from the quenched noise of the finite natural frequency sample.
We study intermediate ensembles of a few hundred oscillators in which fluctuations are comparably strong but which also allow for a comparison to frequency distributions in the infinite limit.
First, we define an alternative order parameter for the indication of a collective mode in the finite case. Then we test the dependence of the degree of synchronization and the mean rotation frequency of the collective mode on different characteristics for different coupling strengths.
We find, first numerically, that the degree of synchronization depends strongly on the form (quantified by kurtosis) of the natural frequency sample and the rotation frequency of the collective mode depends on the asymmetry (quantified by skewness) of the sample. Both findings are verified in the infinite limit.
With these findings, we better understand and generalize observations of other authors. A bit aside of the general line of thoughts, we find an analytical expression for the volume contraction in phase space.
The second part of this thesis concentrates on an ordering effect of the finite-size fluctuations. In the infinite limit, the oscillators are separated into coherent and incoherent thus ordered and disordered oscillators. In finite ensembles, finite-size fluctuations can generate additional order among the asynchronous oscillators. The basic principle – noise-induced synchronization – is known from several recent papers. Among coupled oscillators, phases are pushed together by the order parameter fluctuations, as we on the one hand show directly and on the other hand quantify with a synchronization measure from directed statistics between pairs of passive oscillators.
We determine the dependence of this synchronization measure from the ratio of pairwise natural frequency difference and variance of the order parameter fluctuations. We find a good agreement with a simple analytical model, in which we replace the deterministic fluctuations of the order parameter by white noise.
Supercritical Kuramoto oscillators with distributed frequencies can be separated into two disjoint groups: an ordered one locked to the mean field, and a disordered one consisting of effectively decoupled oscillators-at least so in the thermodynamic limit. In finite ensembles, in contrast, such clear separation fails: The mean field fluctuates due to finite-size effects and thereby induces order in the disordered group. This publication demonstrates this effect, similar to noise-induced synchronization, in a purely deterministic system. We start by modeling the situation as a stationary mean field with additional white noise acting on a pair of unlocked Kuramoto oscillators. An analytical expression shows that the cross-correlation between the two increases with decreasing ratio of natural frequency difference and noise intensity. In a deterministic finite Kuramoto model, the strength of the mean-field fluctuations is inextricably linked to the typical natural frequency difference. Therefore, we let a fluctuating mean field, generated by a finite ensemble of active oscillators, act on pairs of passive oscillators with a microscopic natural frequency difference between which we then measure the cross-correlation, at both super- and subcritical coupling.
We present an alternative approach to finite-size effects around the synchronization transition in the standard Kuramoto model. Our main focus lies on the conditions under which a collective oscillatory mode is well defined. For this purpose, the minimal value of the amplitude of the complex Kuramoto order parameter appears as a proper indicator. The dependence of this minimum on coupling strength varies due to sampling variations and correlates with the sample kurtosis of the natural frequency distribution. The skewness of the frequency sample determines the frequency of the resulting collective mode. The effects of kurtosis and skewness hold in the thermodynamic limit of infinite ensembles. We prove this by integrating a self-consistency equation for the complex Kuramoto order parameter for two families of distributions with controlled kurtosis and skewness, respectively.
Remembering is more than an activation of a memory trace. As retrieval cues are often not uniquely related to one specific memory, cognitive control should come into play to guide selective memory retrieval by focusing on relevant while ignoring irrelevant information. Here, we investigated, by means of EEG and fMRI, how the memory system deals with retrieval interference arising when retrieval cues are associated with two material types (faces and spatial positions), but only one is task-relevant. The topography of slow EEG potentials and the fMRI BOLD signal in posterior storage areas indicated that in such situations not only the relevant but also the irrelevant material becomes activated. This results in retrieval interference that triggers control processes mediated by the medial and lateral PFC, which are presumably involved in biasing target representations by boosting the task-relevant material. Moreover, memory-based conflict was found to be dissociable from response conflict that arises when the relevant and irrelevant materials imply different responses. The two types of conflict show different activations in the medial frontal cortex, supporting the claim of domain-specific prefrontal control systems.
We investigate the vibrational relaxation of a Morse oscillator, nonlinearly coupled to a finite-dimensional bath of harmonic oscillators at zero temperature, using two different approaches: Reduced dynamics with the help of the Lindblad formalism of reduced density matrix theory in combination with Fermi's Golden Rule, and exact dynamics (within the chosen model). with the multiconfiguration time-dependent Hartree (MCTDH) method. Two different models have been constructed, the situation where the bath spectrum is exactly resonant with the anharmonic oscillator transition frequencies, and the case for which the subsystem is slightly off-resonant with the environment. At short times, reduced dynamics calculations describe the relaxation process qualitatively well but fail to reproduce recurrences observed with MCTDH for longer times. Lifetimes of all the vibrational levels of the Morse oscillator have been calculated, and both Lindblad and MCTDH. results show the same dependence of the lifetimes on the initial vibrational state quantum number. A prediction, which should be generic for adsorbate systems is a striking, sharp increase of lifetimes of the subsystem vibrational levels close to the dissociation This is contradictory with harmonic/linear extrapolation laws, which predict a monotonic decrease of the lifetime with initial vibrational quantum number.
Reflexion ist eine Schlüsselkategorie für die professionelle Entwicklung von Lehrkräften, welche als Ausbildungsziel in den Bildungsstandards für die Lehrkräftebildung verankert ist. Eine Verstetigung universitär geprägter Forschung und Modellierung in der praxisnahen Anwendung im schulischen Kontext bietet Potentiale nachhaltiger Professionalisierung. Die Stärkung reflexionsbezogener Kompetenzen durch Empirie und Anwendung scheint eine phasenübergreifende Herausforderung der Lehrkräftebildung zu sein, die es zu bewältigen gilt. Ziele des Tagungsbandes Reflexion in der Lehrkräftebildung sind eine theoretische Schärfung des Konzeptes „Reflexive Professionalisierung“ und der Austausch über Fragen der Einbettung wirksamer reflexionsbezogener Lerngelegenheiten in die Lehrkräftebildung. Forschende und Lehrende der‚ drei Phasen (Studium, Referendariat sowie Fort- und Weiterbildung) der Lehrkräftebildung stellen Lehrkonzepte und Forschungsprojekte zum Thema Reflexion in der Lehrkräftebildung vor und diskutieren diese. Gemeinsam mit Teilnehmenden aller Phasen und von verschiedenen Standorten der Lehrkräftebildung werden zukünftige Herausforderungen identifiziert und Lösungsansätze herausgearbeitet.
Fontanes Medien
(2023)
Theodor Fontane war, im durchaus modernen Sinne, ein Medienarbeiter: Als Presse-Agent in London lernte er die innovativste Presselandschaft seiner Zeit kennen; als Redakteur in Berlin leistete er journalistische Kärrnerarbeit; er schrieb Kritiken über das Theater, die bildende Kunst und die Literatur – und auch seine Romane wie seine Reisebücher sind stets Medienprodukte, als Serien in in Zeitungen und Zeitschriften platziert, bevor sie auf dem Buchmarkt erschienen.
Der vorliegende Band dokumentiert die Ergebnisse eines internationalen Kongresses, veranstaltet 2019 vom Theodor-Fontane-Archiv in Potsdam. Die ebenso rasante wie umfassende Medialisierung und Vernetzung der Gesellschaft im Laufe des 19. Jahrhunderts wird dabei als produktive Voraussetzung der schriftstellerischen Tätigkeit Fontanes begriffen. Eingebettet in ein weit verzweigtes Netz der Korrespondenz und der postalischen Textzirkulation, vertraut mit den Routinen und Publika der periodischen Massenpresse, für die er sein Leben lang schrieb, und auf vielfältige Weise geprägt von der visuellen Kultur seiner Zeit wird Theodor Fontane als gleichermaßen journalistisch versierter wie ästhetisch sensibler Grenzgänger erkennbar.
Übungsbuch zur Stochastik
(2023)
Dieses Buch stellt Übungen zu den Grundbegriffen und Grundsätzen der Stochastik und ihre Lösungen zur Verfügung. So wie man Tonleitern in der Musik trainiert, so berechnet man Übungsaufgaben in der Mathematik. In diesem Sinne soll dieses Übungsbuch vor allem als Vorlage dienen für das eigenständige, eigenverantwortliche Lernen und Üben.
Die Schönheit und Einzigartigkeit der Wahrscheinlichkeitstheorie besteht darin, dass sie eine Vielzahl von realen Phänomenen modellieren kann. Daher findet man hier Aufgaben mit Verbindungen zur Geometrie, zu Glücksspielen, zur Versicherungsmathematik, zur Demographie und vielen anderen Themen.
Aim
Although research and clinical definitions of psychotherapeutic competence have been proposed, less is known about the layperson perspective. The aim was to explore the views of individuals with different levels of psychotherapy experience regarding what-in their views-constitutes a competent therapist.
Method
In an online survey, 375 persons (64% female, mean age 33.24 years) with no experience, with professional experience, or with personal pre-experience with psychotherapy participated. To provide low-threshold questions, we first presented two qualitative items (i.e. "In your opinion, what makes a good/competent psychotherapist?"; "How do you recognize that a psychotherapist is not competent?") and analysed them using inductive content analysis techniques (Mayring, 2014). Then, we gave participants a 16-item questionnaire including items from previous surveys and from the literature and analysed them descriptively.
Results
Work-relatedprinciples, professionalism, personalitycharacteristics, caringcommunication, empathy and understandingwere important categories of competence. Concerning the quantitative questions, most participants agreed with items indicating that a therapist should be open, listen well, show empathy and behave responsibly.
Conclusion
Investigating layperson perspectives suggested that effective and professional interpersonal behaviour of therapists plays a central role in the public's perception of psychotherapy.
Aim
Although research and clinical definitions of psychotherapeutic competence have been proposed, less is known about the layperson perspective. The aim was to explore the views of individuals with different levels of psychotherapy experience regarding what-in their views-constitutes a competent therapist.
Method
In an online survey, 375 persons (64% female, mean age 33.24 years) with no experience, with professional experience, or with personal pre-experience with psychotherapy participated. To provide low-threshold questions, we first presented two qualitative items (i.e. "In your opinion, what makes a good/competent psychotherapist?"; "How do you recognize that a psychotherapist is not competent?") and analysed them using inductive content analysis techniques (Mayring, 2014). Then, we gave participants a 16-item questionnaire including items from previous surveys and from the literature and analysed them descriptively.
Results
Work-relatedprinciples, professionalism, personalitycharacteristics, caringcommunication, empathy and understandingwere important categories of competence. Concerning the quantitative questions, most participants agreed with items indicating that a therapist should be open, listen well, show empathy and behave responsibly.
Conclusion
Investigating layperson perspectives suggested that effective and professional interpersonal behaviour of therapists plays a central role in the public's perception of psychotherapy.