Inpainting of Cyclic Data using First and Second Order Differences

Cyclic data arise in various image and signal processing applications such as interferometric synthetic aperture radar, electroencephalogram data analysis, and color image restoration in HSV or LCh spaces. In this paper we introduce a variational inpainting model for cyclic data which utilizes our definition of absolute cyclic second order differences. Based on analytical expressions for the proximal mappings of these differences we propose a cyclic proximal point algorithm (CPPA) for minimizing the corresponding functional. We choose appropriate cycles to implement this algorithm in an efficient way. We further introduce a simple strategy to initialize the unknown inpainting region. Numerical results both for synthetic and real-world data demonstrate the performance of our algorithm.Comment: accepted Converence Paper at EMMCVPR'1

A Second Order TV-type Approach for Inpainting and Denoising Higher Dimensional Combined Cyclic and Vector Space Data

In this paper we consider denoising and inpainting problems for higher dimensional combined cyclic and linear space valued data. These kind of data appear when dealing with nonlinear color spaces such as HSV, and they can be obtained by changing the space domain of, e.g., an optical flow field to polar coordinates. For such nonlinear data spaces, we develop algorithms for the solution of the corresponding second order total variation (TV) type problems for denoising, inpainting as well as the combination of both. We provide a convergence analysis and we apply the algorithms to concrete problems.Comment: revised submitted versio

Precise Radial Velocities of Giant Stars VII. Occurrence Rate of Giant Extrasolar Planets as a Function of Mass and Metallicity

(abridged) We have obtained precise radial velocities for a sample of 373 G and K type giants at Lick Observatory regularly over more than 12 years. Planets have been identified around 15 giant stars; an additional 20 giant stars host planet candidates. We investigate the occurrence rate of substellar companions around giant stars as a function of stellar mass and metallicity. We probe the stellar mass range from about 1 to beyond 3 M_Sun, which is not being explored by main-sequence samples. We fit the giant planet occurrence rate as a function of stellar mass and metallicity with a Gaussian and an exponential distribution, respectively. We find strong evidence for a planet-metallicity correlation among the secure planet hosts of our giant star sample, in agreement with the one for main-sequence stars. However, the planet-metallicity correlation is absent for our sample of planet candidates, raising the suspicion that a good fraction of them might indeed not be planets. Consistent with the results obtained by Johnson for subgiants, the giant planet occurrence rate increases in the stellar mass interval from 1 to 1.9 M_Sun. However, there is a maximum at a stellar mass of 1.9 +0.1/-0.5 M_Sun, and the occurrence rate drops rapidly for masses larger than 2.5-3.0 M_Sun. We do not find any planets around stars more massive than 2.7 M_Sun, although there are 113 stars with masses between 2.7 and 5 M_Sun in our sample (corresponding to a giant planet occurrence rate < 1.6% at 68.3% confidence in that stellar mass bin). We also show that this result is not a selection effect related to the planet detectability being a function of the stellar mass. We conclude that giant planet formation or inward migration is suppressed around higher mass stars, possibly because of faster disk depletion coupled with a longer migration timescale.Comment: 13 pages plus long table appendix, accepted by A&

Are membranes non-apoptotic compartments for apoptotic caspases

Critical mediators of apoptotic cell death are caspases, a highly specialized class of Cys-proteases that cleave substrates after Asp residues. Under normal conditions, caspases are cytosolic proteins. After their activation, they cleave a large number of cytosolic proteins and execute apoptosis (Figure 1, left). However, in addition to their well-studied role in apoptosis, caspases also have many non-apoptotic functions [1, 2]. It is not very well understood how cells escape the potential harmful action of caspases when they perform nonapoptotic functions. In our recent work, we now show that epithelial cells may prevent apoptosis by sequestration of caspases at the plasma membrane, specifically the basal side of the plasma membrane, for non-apoptotic functions [3]

A Second Order Non-Smooth Variational Model for Restoring Manifold-Valued Images

We introduce a new non-smooth variational model for the restoration of manifold-valued data which includes second order differences in the regularization term. While such models were successfully applied for real-valued images, we introduce the second order difference and the corresponding variational models for manifold data, which up to now only existed for cyclic data. The approach requires a combination of techniques from numerical analysis, convex optimization and differential geometry. First, we establish a suitable definition of absolute second order differences for signals and images with values in a manifold. Employing this definition, we introduce a variational denoising model based on first and second order differences in the manifold setup. In order to minimize the corresponding functional, we develop an algorithm using an inexact cyclic proximal point algorithm. We propose an efficient strategy for the computation of the corresponding proximal mappings in symmetric spaces utilizing the machinery of Jacobi fields. For the n-sphere and the manifold of symmetric positive definite matrices, we demonstrate the performance of our algorithm in practice. We prove the convergence of the proposed exact and inexact variant of the cyclic proximal point algorithm in Hadamard spaces. These results which are of interest on its own include, e.g., the manifold of symmetric positive definite matrices

Second Order Differences of Cyclic Data and Applications in Variational Denoising

In many image and signal processing applications, as interferometric synthetic aperture radar (SAR), electroencephalogram (EEG) data analysis or color image restoration in HSV or LCh spaces the data has its range on the one-dimensional sphere $\mathbb S^1$. Although the minimization of total variation (TV) regularized functionals is among the most popular methods for edge-preserving image restoration such methods were only very recently applied to cyclic structures. However, as for Euclidean data, TV regularized variational methods suffer from the so called staircasing effect. This effect can be avoided by involving higher order derivatives into the functional. This is the first paper which uses higher order differences of cyclic data in regularization terms of energy functionals for image restoration. We introduce absolute higher order differences for $\mathbb S^1$-valued data in a sound way which is independent of the chosen representation system on the circle. Our absolute cyclic first order difference is just the geodesic distance between points. Similar to the geodesic distances the absolute cyclic second order differences have only values in [0,{\pi}]. We update the cyclic variational TV approach by our new cyclic second order differences. To minimize the corresponding functional we apply a cyclic proximal point method which was recently successfully proposed for Hadamard manifolds. Choosing appropriate cycles this algorithm can be implemented in an efficient way. The main steps require the evaluation of proximal mappings of our cyclic differences for which we provide analytical expressions. Under certain conditions we prove the convergence of our algorithm. Various numerical examples with artificial as well as real-world data demonstrate the advantageous performance of our algorithm.Comment: 32 pages, 16 figures, shortened version of submitted manuscrip

Imposing a unilateral carbon constraint on European energy-intensive industries and its impact on their international competitiveness - data & analysis

This paper investigates the implications of EU climate change policy for energy intensive industries. Specifically, it calculates, for a range of energy-intensive processes and products, the product price increases that would be required to maintain unit profits at present levels, based on likely values of allowance prices in the European Union Emissions Trading Scheme up to 2020. For most of the energy- and carbon-intensive products considered here, an allowance price of €20 per tonne of carbon dioxide would require price increases of between 0.1 to 5% to maintain profits, assuming full pass-through of the allowance price along the value chain. Doubling the allowance price to €40/tonne would double the required increase. The activities that risk being most challenged by the carbon constraint appear to be container glass production using virgin inputs, primary aluminium production, primary steel production based on the basic oxygen furnace process, and some basic chemicals production. However, the analysis has also shown that for many of these cases alternative production processes exist, based on recycled inputs, for example. The cement sector, although very energy- and carbon-intensive, is relatively little exposed to international competition. Indeed, the paper also investigates in how far it would be possible for the affected activities to pass through cost increases to their clients, by analysing their exposure to domestic and international competition. It concludes that the sectors analysed are typically relatively highly concentrated (sometimes even at the world level) and form parts of vertically integrated and locally-clustered value chains. This tends to increase market entry and exit barriers and, thus, to reduce the risk of large output losses and delocalisation.climate change, competitiveness, energy-intensive industries, emissions trading