Search Results
Adaptive smoothing of digital images: The R package adimpro
2007, Polzehl, J., Tabelow, K.
Digital imaging has become omnipresent in the past years with a bulk of applications ranging from medical imaging to photography. When pushing the limits of resolution and sensitivity noise has ever been a major issue. However, commonly used non-adaptive filters can do noise reduction at the cost of a reduced effective spatial resolution only. Here we present a new package adimpro for R, which implements the propagationseparation approach by (Polzehl arid Spokoiriy 2006) for smoothing digital images. This method naturally adapts to different structures of different size in the image and thus avoids oversmoothing edges and fine structures. We extend the method for imaging data with spatial correlation. Furthermore we show how the estimation of the dependence between variance and mean value can be included. We illustrate the use of the package through some examples.
Analysis and Quantum Theory
2005, Derezinski, Jan, Solovej, Jan-Philip
The MFO-Workshop 0538 Analysis and Quantum Theory focussed on problems in mathematical physics, especially those connected to quantum field theory. Several theoretical physicists introduced a mostly mathematically oriented audience to topics in theoretical physics such as perturbative quantum field theory and fractional quantum Hall effect, thus bridging the gap between theoretical physics and mathematics. Apart from these reviews, a selection of research reports on recent results in mathematical physics was presented.
Algebraic Groups
2007, Jantzen, Jens Carsten, Rouquier, Raphael
The workshop dealt with a broad range of topics from the structure theory and the representation theory of algebraic groups (in the widest sense). There was emphasis on the following areas: structure and classification of wonderful varieties, finite reductive groups and character sheaves, quantum cohomology of homogeneous varieties, representation categories and their connections to orbits and flag varieties.
Mini-Workshop: Theory and Numerics of Fluid-Solid Interaction
2007, Rannacher, Rolf, Turek, Stefan
This volume contains the abstracts of a series of talks given at a mini-workshop in Oberwolfach on the theory and numerics of continuum mechanical fluid-solid/structure interaction. The characteristics of these coupled multi-field problems are that the displacement of the solid/structure has a direct influence on the surrounding flow and vice versa. This interaction is generally nonlinear making the modeling complicated. The mathematical analysis concentrates on the well-posedness of the models in order to provide a rigorous explanation of fundamental experiments. Various competing numerical approaches are discussed based on different variational formulations and mainly using finite element methods.
Statistical methods for the qualitative assessment of dynamic models with time delay (R package qualV)
2007, Jachner, S., Van Den Boogaart, K.G., Petzoldt, T.
Results of ecological models differ, to some extent, more from measured data than from empirical knowledge. Existing techniques for validation based on quantitative assessments sometimes cause an underestimation of the performance of models due to time shifts, accelerations and delays or systematic differences between measurement and simulation. However, for the application of such models it is often more important to reproduce essential patterns instead of seemingly exact numerical values. This paper presents techniques to identify patterns and numerical methods to measure the consistency of patterns between observations and model results. An orthogonal set of deviance measures for absolute, relative and ordinal scale was compiled to provide informations about the type of difference. Furthermore, two different approaches accounting for time shifts were presented. The first one transforms the time to take time delays and speed differences into account. The second one describes known qualitative criteria dividing time series into interval units in accordance to their main features. The methods differ in their basic concepts and in the form of the resulting criteria. Both approaches and the deviance measures discussed are implemented in an R package. All methods are demonstrated by means of water quality measurements and simulation data. The proposed quality criteria allow to recognize systematic differences and time shifts between time series and to conclude about the quantitative and qualitative similarity of patterns.
Algebraic K-Theory
2006, Huber-Klawitter, Annette, Jannsen, Uwe, Levine, Marc
This is the report on the Oberwolfach workshop Algebraic KTheory, held in July 2006. The talks covered mainly topics from Algebraic Geometry and Number Theory in connection with K-Theory. Special emphasis was placed on motivic cohomology and motivic homotopy of general schemes.
Mini-Workshop: Statistical Methods for Inverse Problems
2006, Reiß, Markus
Inverse problems appear naturally in a broad range of applications. Numerical analysis and statistics have – often independently – developed methods for regularisation and inversion. The aim of this mini-workshop is to bring together these methods and to consider their use in applications, with a focus on mathematical finance.
Algebraic K-Theory and Motivic Cohomology
2009, Huber-Klawitter, Annette, Jannsen, Uwe, Levine, Marc
Algebraic K-theory and the related motivic cohomology are a systematic way of producing invariants for algebraic or geometric structures. Its definition and methods are taken from algebraic topology, but it has also proved particularly fruitful for problems of algebraic geometry, number theory or quadratic forms. 19 one-hour talks presented a wide range of results on K-theory itself and applications. We had a lively evening session trading questions and discussing open problems.
Mini-Workshop: The Pisot Conjecture - From Substitution Dynamical Systems to Rauzy Fractals and Meyer Sets
2009, Damanik, David, Lenz, Daniel
This mini-workshop brought together researchers with diverse backgrounds and a common interest in facets of the Pisot conjecture, which relates certain properties of a substitution to dynamical properties of the associated subshift.