Sharp comparison and maximum principles via horizontal normal mapping in the Heisenberg group

In this paper we solve a problem raised by Gutiérrez and Montanari about comparison principles for H−convex functions on subdomains of Heisenberg groups. Our approach is based on the notion of the sub-Riemannian horizontal normal mapping and uses degree theory for set-valued maps. The statement of the comparison principle combined with a Harnack inequality is applied to prove the Aleksandrov-type maximum principle, describing the correct boundary behavior of continuous H−convex functions vanishing at the boundary of horizontally bounded subdomains of Heisenberg groups. This result answers a question by Garofalo and Tournier. The sharpness of our results are illustrated by examples.

Scientific drilling projects in ancient lakes: Integrating geological and biological histories

Sedimentary sequences in ancient or long-lived lakes can reach several thousands of meters in thickness and often provide an unrivalled perspective of the lake's regional climatic, environmental, and biological history. Over the last few years, deep-drilling projects in ancient lakes became increasingly multi- and interdisciplinary, as, among others, seismological, sedimentological, biogeochemical, climatic, environmental, paleontological, and evolutionary information can be obtained from sediment cores. However, these multi- and interdisciplinary projects pose several challenges. The scientists involved typically approach problems from different scientific perspectives and backgrounds, and setting up the program requires clear communication and the alignment of interests. One of the most challenging tasks, besides the actual drilling operation, is to link diverse datasets with varying resolution, data quality, and age uncertainties to answer interdisciplinary questions synthetically and coherently. These problems are especially relevant when secondary data, i.e., datasets obtained independently of the drilling operation, are incorporated in analyses. Nonetheless, the inclusion of secondary information, such as isotopic data from fossils found in outcrops or genetic data from extant species, may help to achieve synthetic answers. Recent technological and methodological advances in paleolimnology are likely to increase the possibilities of integrating secondary information. Some of the new approaches have started to revolutionize scientific drilling in ancient lakes, but at the same time, they also add a new layer of complexity to the generation and analysis of sediment-core data. The enhanced opportunities presented by new scientific approaches to study the paleolimnological history of these lakes, therefore, come at the expense of higher logistic, communication, and analytical efforts. Here we review types of data that can be obtained in ancient lake drilling projects and the analytical approaches that can be applied to empirically and statistically link diverse datasets to create an integrative perspective on geological and biological data. In doing so, we highlight strengths and potential weaknesses of new methods and analyses, and provide recommendations for future interdisciplinary deep-drilling projects.

Beyond a logic of effectiveness: Horizontal coordination, democratic legitimacy and accountability

Horizontal coordination, where actors join together to accomplish a common task, has been applauded for its output legitimacy. However, such processes often face challenges due to opposition from local actors who raise concerns about democratic legitimacy and accountability. Moving beyond a logic of effectiveness, we aim to show how and why other forms of legitimacy such as input and throughput dimensions also affect horizontal coordination, in addition to output criteria. Beyond the assumed positive relationship between coordination and effectiveness, we additionally expect horizontal coordination to be (a) impeded by local actors' fear of losing democratic legitimacy; and (b) fostered by accountability in terms of the steering capacity of the state. A comparative case study analysis of water supply structures at the regional level in Switzerland shows, in contrast to our expectation, that effectiveness has mixed impacts on horizontal coordination. Rather than being solely a positive factor for horizontal coordination, certain output criteria such as financial redistribution are found to be a key hindrance. We also find that democratic legitimacy may, indeed, impede horizontal coordination whereas increased accountability positively affects such coordination.