Efficient Minimization of Decomposable Submodular Functions

Many combinatorial problems arising in machine learning can be reduced to the problem of minimizing a submodular function. Submodular functions are a natural discrete analog of convex functions, and can be minimized in strongly polynomial time. Unfortunately, state-of-the-art algorithms for general submodular minimization are intractable for larger problems. In this paper, we introduce a novel subclass of submodular minimization problems that we call decomposable. Decomposable submodular functions are those that can be represented as sums of concave functions applied to modular functions. We develop an algorithm, SLG, that can efficiently minimize decomposable submodular functions with tens of thousands of variables. Our algorithm exploits recent results in smoothed convex minimization. We apply SLG to synthetic benchmarks and a joint classification-and-segmentation task, and show that it outperforms the state-of-the-art general purpose submodular minimization algorithms by several orders of magnitude.Comment: Expanded version of paper for Neural Information Processing Systems 201

How Does EU Enlargement Affect Social Cohesion?

The enlargement of the European Union in May 2004 by ten new member states bear increasing challenges in creating social cohesion among its citizens and regions. Social cohesion is understood here in a broad sense as a coalescence of European societies in such a way that living conditions and quality of life of its citizens converge. This paper's empirical focus is on the two core life domains that are currently taking center stage in EU policy debates: (1) employment and working conditions and (2) economic resources and social exclusion. The analyses show that the 15 former member states are converging in terms of lliving and work-ing conditions and the situation has improved in all of these countries during the 1990s. With the enlargement the situation becomes more diverse in the enlarged EU. In particular the post-socialist countries have to make great efforts to catch up with their EU counterparts. We can identify three emerging clusters of countries that share empirically very similar living stan-dards. The first, wealthy cluster consists of the old northern European member states. The second, intermediary country group contains the most well-off accession countries and the old Mediterranean member countries with a lower living standard. The third, less developed clus-ter embraces new member states that were former post-communist countries.

A new method to suppress the bias in polarized intensity

Computing polarised intensities from noisy data in Stokes U and Q suffers from a positive bias that should be suppressed. To develop a correction method that, when applied to maps, should provide a distribution of polarised intensity that closely follows the signal from the source. We propose a new method to suppress the bias by estimating the polarisation angle of the source signal in a noisy environment with help of a modified median filter. We then determine the polarised intensity, including the noise, by projection of the observed values of Stokes U and Q onto the direction of this polarisation angle. We show that our new method represents the true signal very well. If the noise distribution in the maps of U and Q is Gaussian, then in the corrected map of polarised intensity it is also Gaussian. Smoothing to larger Gaussian beamsizes, to improve the signal-to-noise ratio, can be done directly with our method in the map of the polarised intensity. Our method also works in case of non-Gaussian noise distributions. The maps of the corrected polarised intensities and polarisation angles are reliable even in regions with weak signals and provide integrated flux densities and degrees of polarisation without the cumulative effect of the bias, which especially affects faint sources. Features at low intensity levels like 'depolarisation canals' are smoother than in the maps using the previous methods, which has broader implications, for example on the interpretation of interstellar turbulence.Comment: accepted for publication in Astronomy & Astrophysic

Operator scaled Wiener bridges

We introduce operator scaled Wiener bridges by incorporating a matrix scaling in the drift part of the SDE of a multidimensional Wiener bridge. A sufficient condition for the bridge property of the SDE solution is derived in terms of the eigenvalues of the scaling matrix. We analyze the asymptotic behavior of the bridges and briefly discuss the question whether the scaling matrix determines uniquely the law of the corresponding bridge.Comment: 21 page

The NOD3 software package: A graphical user interface-supported reduction package for single-dish radio continuum and polarisation observations

The venerable NOD2 data reduction software package for single-dish radio continuum observations, developed for use at the 100-m Effelsberg radio telescope, has been successfully applied over many decades. Modern computing facilities call for a new design. We aim to develop an interactive software tool with a graphical user interface (GUI) for the reduction of single-dish radio continuum maps. Special effort is given on the reduction of distortions along the scanning direction (scanning effects) by combining maps scanned in orthogonal directions or dual- or multiple-horn observations that need to be processed in a restoration procedure. The package should also process polarisation data and offer the possibility to include special tasks written by the individual user. Based on the ideas of the NOD2 package we developed NOD3, which includes all necessary tasks from the raw maps to the final maps in total intensity and linear polarisation. Furthermore, plot routines and several methods for map analysis are available. The NOD3 package is written in Python which allows to extend the package by additional tasks. The required data format for the input maps is FITS. NOD3 is a sophisticated tool to process and analyse maps from single-dish observations that are affected by 'scanning effects' due to clouds, receiver instabilities, or radio-frequency interference (RFI). The 'basket-weaving' tool combines orthogonally scanned maps to a final map that is almost free of scanning effects. The new restoration tool for dual-beam observations reduces the noise by a factor of about two compared to the NOD2 version. Combining single-dish with interferometer data in the map plane ensures the full recovery of the total flux density.Comment: 8 pages, 10 figures, Accepted for publication in A&