A rational conjugate gradient method for linear ill-conditioned problems

We consider linear ill-conditioned operator equations in a Hilbert space setting. Motivated by the aggregation method, we consider approximate solutions constructed from linear combinations of Tikhonov regularization, which amounts to finding solutions in a rational Krylov space. By mixing these with usual Krylov spaces, we consider least-squares problem in these mixed rational spaces. Applying the Arnoldi method leads to a sparse, pentadiagonal representation of the forward operator, and we introduce the Lanczos method for solving the least-squares problem by factorizing this matrix. Finally, we present an equivalent conjugate-gradient-type method that does not rely on explicit orthogonalization but uses short-term recursions and Tikhonov regularization in each second step. We illustrate the convergence and regularization properties by some numerical examples

General regularization in covariate shift adaptation

Sample reweighting is one of the most widely used methods for correcting the error of least squares learning algorithms in reproducing kernel Hilbert spaces (RKHS), that is caused by future data distributions that are different from the training data distribution. In practical situations, the sample weights are determined by values of the estimated Radon-Nikod\'ym derivative, of the future data distribution w.r.t.~the training data distribution. In this work, we review known error bounds for reweighted kernel regression in RKHS and obtain, by combination, novel results. We show under weak smoothness conditions, that the amount of samples, needed to achieve the same order of accuracy as in the standard supervised learning without differences in data distributions, is smaller than proven by state-of-the-art analyses

Philosophische Hermeneutik in der Kultur- und Sozialanthropologie

Die vorliegende Arbeit versucht der Frage nachzugehen inwiefern die philosophische Hermeneutik, wie sie von Gadamer in seinem Hauptwerk Wahrheit und Methode entworfen wurde, in der Kultur- und Sozialanthropologie rezipiert wurde und ob eine weitere Rezeption sinnvoll ist. In der theoretischen Ausführung wird zuerst wird auf die Formierung der Geisteswissenschaften Bezug genommen, um die Problematik der wissenschaftlichen Methode(n), die eine zentrale Rolle in der Arbeit Gadamers spielt auszubreiten. Darauf folgt eine ausführliche Beleuchtung des Begriffs Hermeneutik. Eine kurzen Darlegung der Geschichte der Hermeneutik wird für einen historischen Kontext entworfen. Insbesondere die Hermeneutik Heideggers, auf die ein Großteil der Hermeneutik Gadamers aufbaut wird besprochen. Die Rezeption von Gadamer orientiert sich an den Begriffen: Historismus, Vorurteil, Horizont, Wirkungsgeschichte, wirkungsgeschichtliches Bewusstsein, Wachsamkeit, Tradition, Klassik, Anwendung, Relativismus und Sprache. Die Analyse der Rezeption in der Kultur- und Sozialanthropologie erfolgt auf dreifache Weise. Zuerst wird der Kernbegriff des Fachs: Kultur – kritisch betrachtet und für eine Nutzbarmachung im Gadamerschen Kontext ausgeführt. Anschließend wird eine notwendige Abgrenzung zu Clifford Geertz vorgenommen, da dieser seine Arbeitsweise selbst als hermeneutisch bezeichnet und sich daraus in der Kultur- und Sozialanthropologie eine nahezu synonyme Verwendung der Geertzschen Arbeit und Hermeneutik ergeben hat, die aus Sicht dieser Arbeit problematisch ist. In der abschließenden Spurensuche wird versucht einige Überschneidungen Gadamers in der rezenten Kultur- und Sozialanthropologie exemplarisch darzustellen. Dies wird anhand von Texten von Kirsten Hastrup, Peter Hervik und Marit Melhuus vorgenommen. Das Fazit versucht einen Ausblick für eine weitere Auseinandersetzung mit Gadamer, vor allem im Kontext der anthropologischen Epistemologie, zu geben.The paper attempts to explore the question to what extent the philosophical hermeneutics designed by Gadamer in his Wahrheit und Methode, was received in cultural and social anthropology, and in how far a further reception would be fruitful. At first, in this theoretical text, the formation of the humanities is being examined in reference to the problems of scientific method, which plays a central role in the work of Gadamer. This is followed by a detailed clarification of the term hermeneutics. A brief description of the history of hermeneutics is created to shape a historical context. In particular the hermeneutics of Heidegger, who was an important base for Gadamer‘s thoughts on hermeneutics is discussed. The reception of Gadamer is based on the concepts: „Historismus“, „Vorurteil“, „Horizont“, „Wirkungsgeschichte“, „wirkungsgeschichtliches Bewusstsein“, „Wachsamkeit“, „Tradition“, „Klassik“, „Anwendung“, „Relativismus“ and „Sprache“. The analysis of Gadamer's reception in the field of Anthropology is done in three different, yet connected, ways. First, the core concept of the science – culture – is being scrutinized and critically developed for a utilization in the reception of Gadamer. Then, a necessary distinction from Clifford Geertz has to be made, since he called his interpretative approach himself a hermeneutic one. In consequence Geertz‘s approach and hermeneutics are used virtually synonymous in anthropology, which is problematic from the perspective of this paper. In the final chapter called „Spurensuche“ traces of hermeneutics in the Gadamerian sense are being tracked down in current anthropological texts. This is work is being exemplified by three texts namely by Kirsten Hastrup, Peter and Marit Hervik Melhuus. The conclusion attempts an outlook for a further discussion of Gadamer especially in the context of anthropological epistemology

Lyrical Strains: 1820-1920

Following John Stuart Mill, one important strain of contemporary scholarship has understood lyric poetry to convey the voice of an "overheard" subject who expresses private thoughts and emotions, either to herself or to an unavailable other. This work thus assumes, with Mill, that the lyric speaker is a model liberal subject (self-enclosed, self-reliant, self-possessed) and that lyric poetry merely communicates this subject's natural, preexisting interiority. "Lyrical Strains: 1820-1920," however, argues that lyric poetry does not merely reflect liberal subjectivity but also helps to construct it, fashioning what it means to be a self in the nineteenth century. Furthermore, because this was a dynamic, historically contingent process rather than a static given, lyric was constantly in crisis, bearing the strains of trying to create an unchanging, universal ideal of selfhood. By examining poetic efforts to fashion the self while assuming its stable existence, I demonstrate that lyric engenders its own impossibility. In chapters pairing Henry Wadsworth Longfellow and Stephen Crane, Walt Whitman and Edwin Arlington Robinson, Frances Sargent Osgood and Edna St. Vincent Millay, and George Moses Horton and Paul Laurence Dunbar, this project offers an insight into both genealogies of the modern self and an anticipation of its deconstruction.Doctor of Philosoph

Quantum extension of European option pricing based on the Ornstein-Uhlenbeck process

In this work we propose a option pricing model based on the Ornstein-Uhlenbeck process. It is a new look at the Black-Scholes formula which is based on the quantum game theory. We show the differences between a classical look which is price changing by a Wiener process and the pricing is supported by a quantum model

On regularized Radon-Nikodym differentiation

We discuss the problem of estimating Radon-Nikodym derivatives. This problem appears in various applications, such as covariate shift adaptation, likelihood-ratio testing, mutual information estimation, and conditional probability estimation. To address the above problem, we employ the general regularization scheme in reproducing kernel Hilbert spaces. The convergence rate of the corresponding regularized algorithm is established by taking into account both the smoothness of the derivative and the capacity of the space in which it is estimated. This is done in terms of general source conditions and the regularized Christoffel functions. We also find that the reconstruction of Radon-Nikodym derivatives at any particular point can be done with high order of accuracy. Our theoretical results are illustrated by numerical simulations.Comment: arXiv admin note: text overlap with arXiv:2307.1150