Partial reconstruction of the trajectories of a discretely observed branching diffusion with immigration and an application to inference

In this treatise we consider finite systems of branching particles where the particles move independently of each other according to d-dimensional diffusions. Particles are killed at a position dependent rate, leaving at their death position a random number of descendants according to a position dependent reproduction law. In addition particles immigrate at constant rate (one immigrant per immigration time). A process with above properties is called a branching diffusion withimmigration (BDI). In the first part we present the model in detail and discuss the properties of the BDI under our basic assumptions. In the second part we consider the problem of reconstruction of the trajectory of a BDI from discrete observations. We observe positions of the particles at discrete times; in particular we assume that we have no information about the pedigree of the particles. A natural question arises if we want to apply statistical procedures on the discrete observations: How can we find couples of particle positions which belong to the same particle? We give an easy to implement 'reconstruction scheme' which allows us to redraw or 'reconstruct' parts of the trajectory of the BDI with high accuracy. Moreover asymptotically the whole path can be reconstructed. Further we present simulations which show that our partial reconstruction rule is tractable in practice. In the third part we study how the partial reconstruction rule fits into statistical applications. As an extensive example we present a nonparametric estimator for the diffusion coefficient of a BDI where the particles move according to one-dimensional diffusions. This estimator is based on the Nadaraya-Watson estimator for the diffusion coefficient of one-dimensional diffusions and it uses the partial reconstruction rule developed in the second part above. We are able to prove a rate of convergence of this estimator and finally we present simulations which show that the estimator works well even if we leave our set of assumptions.

Transatlantic negotiations on "hell"?: W. E. B. Du Bois's visit to fascist Germany and Theodor W. Adorno's exile in the land of the culture industry

In 1936, the African-American intellectual W.E.B. Du Bois visited Nazi Germany for a period of five months. Two years later, the eleven-year-long American exile of the German philosopher Theodor W. Adorno began. From the latter’s perspective, the United States was the “home” of the Culture Industry. One intuitively assumes that these sojourns abroad must have amounted to “hell on earth” for both the civil rights activist W.E.B. Du Bois and the subtle intellectual Adorno. But was this really the case? Or did they perhaps arrive at totally different conclusions? This thesis deals with these questions and attempts to make sense of the experiences of both men. By way of a systematic and comparative analysis of published texts, hitherto unpublished documents and secondary literature, this dissertation first contextualizes Du Bois’s and Adorno’s transatlantic negotiations and then depicts them. The panoply of topics with which both men concerned themselves was diverse. In Du Bois’s case it encompassed Europe, science and technology, Wagner operas, the Olympics, industrial education, race relations, National Socialism and the German Africanist Diedrich Westermann. The opinion pieces which Du Bois wrote for the newspaper “Pittsburgh Courier” during his stay in Germany serve as a major source for this thesis. In his writings on America, Adorno concentrated on what he regarded as the universally victorious Enlightenment and the predominance of mass culture. This investigation also sheds light on the correspondences between the philosopher and Max Horkheimer, Thomas Mann, Walter Benjamin, Siegfried Kracauer and Oskar and Maria Wiesengrund. In these autobiographical texts, Adorno’s thoughts revolve around such diverse topics as the American landscape, his fears as German, Jew and Left-Hegelian as well as the loneliness of the refugee. This dissertation has to refute the intuitive assumption that Du Bois’s and Adorno’s experiences abroad were horrible events for them. Both men judged the foreign countries in which they were staying in an extremely differentiated and subtle manner. Du Bois, for example, was not racially discriminated against in Germany. He was also delighted by the country’s rich cultural offerings. Adorno, for his part, praised the U.S.’s humanity of everyday life and democratic spirit. In short: Although both men partly did have to deal with utterly negative experiences, the metaphor of “hell on earth” is simply untenable as an overall conclusion.