Tame Class Field Theory for Global Function Fields

We give a function field specific, algebraic proof of the main results of class field theory for abelian extensions of degree coprime to the characteristic. By adapting some methods known for number fields and combining them in a new way, we obtain a different and much simplified proof, which builds directly on a standard basic knowledge of the theory of function fields. Our methods are explicit and constructive and thus relevant for algorithmic applications. We use generalized forms of the Tate-Lichtenbaum and Ate pairings, which are well-known in cryptography, as an important tool.Comment: 25 pages, to appear in Journal of Number Theor

Lower Bounds for the Complexity of the Voronoi Diagram of Polygonal Curves under the Discrete Frechet Distance

We give lower bounds for the combinatorial complexity of the Voronoi diagram of polygonal curves under the discrete Frechet distance. We show that the Voronoi diagram of n curves in R^d with k vertices each, has complexity Omega(n^{dk}) for dimension d=1,2 and Omega(n^{d(k-1)+2}) for d>2.Comment: 6 pages, 2 figure

Point compression for the trace zero subgroup over a small degree extension field

Using Semaev's summation polynomials, we derive a new equation for the $\mathbb{F}_q$-rational points of the trace zero variety of an elliptic curve defined over $\mathbb{F}_q$. Using this equation, we produce an optimal-size representation for such points. Our representation is compatible with scalar multiplication. We give a point compression algorithm to compute the representation and a decompression algorithm to recover the original point (up to some small ambiguity). The algorithms are efficient for trace zero varieties coming from small degree extension fields. We give explicit equations and discuss in detail the practically relevant cases of cubic and quintic field extensions.Comment: 23 pages, to appear in Designs, Codes and Cryptograph

Only in the Heat of the Moment? A Study of the Relationship between Weather and Mortality in Germany

In this study we analyze the relationship between heat events and mortality in Germany. The main research questions are: Does heat lead to rising mortality and if yes, are the effects persistent or compensated for in the near future? Furthermore, we consider differences between heat effects in urban and rural environments. Cause specific daily mortality and meteorological data is connected on the county level. We allow for static as well as dynamic relations between extreme temperatures and mortality and implement several panel data estimation approaches. We find that heat has a significant positive impact on mortality. The strongest effects can be measured on the day when heat occurs and the first week afterwards. The mortality increase ranges between 0.003 and 3.5 per 100,000 inhabitants depending on the particular death cause. We do not find a significant negative, and thus compensating impact in a medium term, which is in the contrary to the Harvesting Hypothesis. Using a value of statistical life approach we estimate that one additional hot day in Germany induces for the overall population a loss of m € 1,861. Moreover, the environment plays an important role. The heat induced increase in mortality is significantly higher in urban areas.Climate Change, Harvesting Hypothesis, Heat Waves, Mortality, Urban Heat Island effect

What about local climate governance? A review of promise and problems

A large proportion of greenhouse gas emissions is produced in urban areas, particularly in high income countries. Cities are also vulnerable to the impacts of climate change, and particularly so in developing countries. Therefore, local climate policies for mitigation and adaptation have to play an important role in any effective global climate protection strategy. Based upon a systematic literature review, this article gives a comprehensive overview of motivation and challenges for local climate governance. A large part of the literature focuses on mitigation and cities in industrialized countries. The review also includes the smaller and emerging body of literature on adaptation and cities in developing or industrializing countries. Motivations and challenges we find fall into broad categories like ‘economic’, ‘informational’, ‘institutional’, ‘liveability’ or ‘political/cultural’. We conclude that the mix of motivation and challenges is city-specific, and that the national framework conditions are important. It matters, whether cities engage in mitigation or adaptation policies, whether they are located in developing, industrializing or industrialized countries, and at which stage of climate policy-making cities are. For many cities, cost savings are a primary motivation for local mitigation policies, while perceived vulnerability and a commitment to development is the primary motivator for adaptation policies. The collective action problem of climate protection (also known as ‘Tragedy of the Commons’) and inappropriate legal frameworks are key barriers to mitigation policies. Challenges for adaptation include financial constraints, and a lack of expertise, cooperation, leadership and political support. Understanding their specific motivation and challenges may support cities in developing appropriate local climate action plans. Furthermore, the understanding of motivation and challenges can inform other policy levels that want to help realize the local climate protection potential.Climate policy, local authorities, cities, mitigation, adaptation, energy, local climate governance