Automated Detection of Coronal Loops using a Wavelet Transform Modulus Maxima Method

We propose and test a wavelet transform modulus maxima method for the au- tomated detection and extraction of coronal loops in extreme ultraviolet images of the solar corona. This method decomposes an image into a number of size scales and tracks enhanced power along each ridge corresponding to a coronal loop at each scale. We compare the results across scales and suggest the optimum set of parameters to maximise completeness while minimising detection of noise. For a test coronal image, we compare the global statistics (e.g., number of loops at each length) to previous automated coronal-loop detection algorithms

A multifractal random walk

We introduce a class of multifractal processes, referred to as Multifractal Random Walks (MRWs). To our knowledge, it is the first multifractal processes with continuous dilation invariance properties and stationary increments. MRWs are very attractive alternative processes to classical cascade-like multifractal models since they do not involve any particular scale ratio. The MRWs are indexed by few parameters that are shown to control in a very direct way the multifractal spectrum and the correlation structure of the increments. We briefly explain how, in the same way, one can build stationary multifractal processes or positive random measures.Comment: 5 pages, 4 figures, uses RevTe

The multi-fractal structure of contrast changes in natural images: from sharp edges to textures

We present a formalism that leads very naturally to a hierarchical description of the different contrast structures in images, providing precise definitions of sharp edges and other texture components. Within this formalism, we achieve a decomposition of pixels of the image in sets, the fractal components of the image, such that each set only contains points characterized by a fixed stregth of the singularity of the contrast gradient in its neighborhood. A crucial role in this description of images is played by the behavior of contrast differences under changes in scale. Contrary to naive scaling ideas where the image is thought to have uniform transformation properties \cite{Fie87}, each of these fractal components has its own transformation law and scaling exponents. A conjecture on their biological relevance is also given.Comment: 41 pages, 8 figures, LaTe

A flexible error estimate for the application of centre manifold theory

In applications of centre manifold theory we need more flexible error estimates than that provided by, for example, the Approximation Theorem 3 by Carr [4, 6]. Here we extend the theory to cover the case where the order of approximation in parameters and that in dynamical variables may be completely different. This allows, for example, the effective evaluation of low-dimensional dynamical models at finite parameter values

Wavelet Based Fractal Analysis of Airborne Pollen

The most abundant biological particles in the atmosphere are pollen grains and spores. Self protection of pollen allergy is possible through the information of future pollen contents in the air. In spite of the importance of airborne pol len concentration forecasting, it has not been possible to predict the pollen concentrations with great accuracy, and about 25% of the daily pollen forecasts have resulted in failures. Previous analysis of the dynamic characteristics of atmospheric pollen time series indicate that the system can be described by a low dimensional chaotic map. We apply the wavelet transform to study the multifractal characteristics of an a irborne pollen time series. We find the persistence behaviour associated to low pollen concentration values and to the most rare events of highest pollen co ncentration values. The information and the correlation dimensions correspond to a chaotic system showing loss of information with time evolution.Comment: 11 pages, 7 figure