1,720,958 research outputs found
Variational Source Conditions and Conditional Stability Estimates for Inverse Problems in PDEs
No full textSoftcover, 17x24Inverse Probleme befassen sich mit der Schätzung eines Parameters aus indirekten Messungen. Die Messung ist üblicherweise fehlerbehaftet während die Identifizierung des Parameters aus der Messung schlecht gestellt (d.h. unstetig) ist. Daher kommen zur Schätzung des Parameters Regularisierungsverfahren zum Einsatz, die diese Faktoren einbeziehen, um eine stabile Rekonstruktion zu erhalten. Um jedoch eine Abschätzung des Rekonstruktionsfehlers zu erhalten werden Zusatzannahmen an den zu Grunde liegenden Parameter benötigt. Diese werden üblicherweise in Form von sogenannten Variationellen Quellbedingungen formuliert. In dieser Doktorarbeit wird eine Strategie zur Verifizierung dieser Bedingungen entwickelt, die auf der Glattheit des Parameters und der Schlechtgestelltheit des Problems beruht; dabei wird ausgenutzt, dass letztere Ähnlichkeiten zu Stabilitätsabschätzungen aufweist. Anschließend wird diese Strategie eingesetzt um Variationelle Quellbedingungen für Probleme in der Parameteridentifikation, inversen Streutheorie sowie elektrischen Impedanztomographie nachzuweisen.In inverse problems one wants to find some parameter of interest which is not directly observable by indirect measurement. These measurements are usually noisy while the mapping of measurement to parameter is typically illposed (that is unstable). Therefore one applies regularization techniques that balance these two factors to find a stable approximation of the sought for parameter. However, in order to bound the reconstruction error, one needs additional information on the true parameter, which is nowadays typically formulated in terms of variational source conditions. In this thesis, we develop a general strategy to verify these conditions based on smoothness of the true parameter and the illposedness of the problem; the latter will be characterized by exploiting structural similarities to stability estimates. Following this, we apply our strategy to verify variational source conditions for parameter identification problems, inverse scattering and electrical impedance tomography
Variational source conditions and stability estimates for inverse electromagnetic medium scattering problems
No full textThis paper is concerned with the inverse problem to recover the scalar, complex-valued refractive index of a medium from measurements of scattered time-harmonic electromagnetic waves at a fixed frequency. The main results are two variational source conditions for near and far field data, which imply logarithmic rates of convergence of regularization methods, in particular Tikhonov regularization, as the noise level tends to 0. Moreover, these variational source conditions imply conditional stability estimates which improve and complement known stability estimates in the literature
Verification of a variational source condition for acoustic inverse medium scattering problems
No full textThis paper is concerned with the classical inverse scattering problem to recover the refractive index of a medium given near or far field measurements of scattered time-harmonic acoustic waves. It contains the first rigorous proof of (logarithmic) rates of convergence for Tikhonov regularization under Sobolev smoothness assumptions for the refractive index. This is achieved by combining two lines of research, conditional stability estimates via geometrical optics solutions and variational regularization theory
Characterizations of Variational Source Conditions, Converse Results, and Maxisets of Spectral Regularization Methods
No full textWe describe a general strategy for the verification of variational source condition by formulating two sufficient criteria describing the smoothness of the solution and the degree of illposedness of the forward operator in terms of a family of subspaces. For linear deterministic inverse problems we show that variational source conditions are necessary and sufficient for convergence rates of spectral regularization methods, which are slower than the square root of the noise level. A similar result is shown for linear inverse problems with white noise. In many cases variational source conditions can be characterized by Besov spaces. This is discussed for a number of prominent inverse problems
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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