Networks for Nonlinear Diffusion Problems in Imaging

A multitude of imaging and vision tasks have seen recently a major transformation by deep learning methods and in particular by the application of convolutional neural networks. These methods achieve impressive results, even for applications where it is not apparent that convolutions are suited to capture the underlying physics. In this work we develop a network architecture based on nonlinear diffusion processes, named DiffNet. By design, we obtain a nonlinear network architecture that is well suited for diffusion related problems in imaging. Furthermore, the performed updates are explicit, by which we obtain better interpretability and generalisability compared to classical convolutional neural network architectures. The performance of DiffNet tested on the inverse problem of nonlinear diffusion with the Perona-Malik filter on the STL-10 image dataset. We obtain competitive results to the established U-Net architecture, with a fraction of parameters and necessary training data

From Short-Term to Long-Term Orientation - Political Economy of the Policy Reform Process

Despite the fact that policymakers often have a short-term horizon and prefer discretionary over rule bound policy, one can observe policy reform with a focus on rules and long-term orientation. Sometimes reforms are driven by crisis, sometimes they are pursued in times of relative prosperity. The paper analyses reform processes theoretically under the assumption of imperfect knowledge. After the introduction, the second section of the paper shows that rule bound policy encourages a long-term orientation of policymakers, resulting in higher economic dynamics as compared with discretionary policy. In the third section, the political economy of the reform process, i.e. replacing discretionary by rule-bound policy, is analysed in an evolutionary setting. The basic hypothesis is that a policy reform is triggered in a feedback-process determined by four key factors: (1) an emerging shadow economy and growing corruption, (2) external, in particular international pressure, (3) increasing knowledge of policymakers with respect to the effectiveness of policy paradigms and (4) improved economic knowledge of the public. In a fourth section, we draw conclusions and present some preliminary empirical evidence.Dynamic Learning Process, Long-Term-Orientation, Rules, Consistency, Political Business Cycles, Policy Reform

A Pragmatic Reading of Friedman's Methodological Essay and What It Tells Us for the Discussion of ABMs

The issues of empirical calibration of parameter values and functional relationships describing the interactions between the various actors plays an important role in agent based modelling. Agent-based models range from purely theoretical exercises focussing on the patterns in the dynamics of interactions processes to modelling frameworks which are oriented closely at the replication of empirical cases. ABMs are classified in terms of their generality and their use of empirical data. In the literature the recommendation can be found to aim at maximizing both criteria by building so-called 'abductive models'. This is almost the direct opposite of Milton Friedman's famous and provocative methodological credo 'the more significant a theory, the more unrealistic the assumptions'. Most methodologists and philosophers of science have harshly criticised Friedman's essay as inconsistent, wrong and misleading. By presenting arguments for a pragmatic reinterpretation of Friedman's essay, we will show why most of the philosophical critique misses the point. We claim that good simulations have to rely on assumptions, which are adequate for the purpose in hand and those are not necessarily the descriptively accurate ones.Methodology, Agent-Based Modelling, Assumptions, Calibration

Hypervelocity stars in the Gaia era: Runaway B stars beyond the velocity limit of classical ejection mechanisms

Young massive stars in the halo are assumed to be runaway stars from the Galactic disk. Possible ejection scenarios are binary supernova ejections (BSE) or dynamical ejections from star clusters (DE). Hypervelocity stars (HVSs) are extreme runaway stars that are potentially unbound from the Galaxy. Powerful acceleration mechanisms such as the tidal disruption of a binary system by a supermassive black hole (SMBH) are required to produce them. Therefore, HVSs are believed to originate in the Galactic center (GC), the only place known to host an SMBH. The second Gaia data release (DR2) offers the opportunity of studying HVSs in an unprecedented manner. We revisit some of the most interesting high-velocity stars, that is, 15 stars for which proper motions with the Hubble Space Telescope were obtained in the pre-Gaia era, to unravel their origin. By carrying out kinematic analyses based on revised spectrophotometric distances and proper motions from Gaia DR2, kinematic properties were obtained that help constrain the spatial origins of these stars. Stars that were previously considered (un)bound remain (un)bound in Galactic potentials favored by Gaia DR2 astrometry. For nine stars (five candidate HVSs plus all four radial velocity outliers), the GC can be ruled out as spatial origin at least at $2\sigma$ confidence level, suggesting that a large portion of the known HVSs are disk runaway stars launched close to or beyond Galactic escape velocities. The fastest star in the sample, HVS3, is confirmed to originate in the Large Magellanic Cloud. Because the ejection velocities of five of our non-GC stars are close to or above the upper limits predicted for BSE and DE, another powerful dynamical ejection mechanism (e.g., involving massive perturbers such as intermediate-mass black holes) is likely to operate in addition to the three classical scenarios mentioned above.Comment: Accepted for publication in A&A (Astronomy and Astrophysics