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

Generalized Teacher Forcing for Learning Chaotic Dynamics

Chaotic dynamical systems (DS) are ubiquitous in nature and society. Often we are interested in reconstructing such systems from observed time series for prediction or mechanistic insight, where by reconstruction we mean learning geometrical and invariant temporal properties of the system in question (like attractors). However, training reconstruction algorithms like recurrent neural networks (RNNs) on such systems by gradient-descent based techniques faces severe challenges. This is mainly due to exploding gradients caused by the exponential divergence of trajectories in chaotic systems. Moreover, for (scientific) interpretability we wish to have as low dimensional reconstructions as possible, preferably in a model which is mathematically tractable. Here we report that a surprisingly simple modification of teacher forcing leads to provably strictly all-time bounded gradients in training on chaotic systems, and, when paired with a simple architectural rearrangement of a tractable RNN design, piecewise-linear RNNs (PLRNNs), allows for faithful reconstruction in spaces of at most the dimensionality of the observed system. We show on several DS that with these amendments we can reconstruct DS better than current SOTA algorithms, in much lower dimensions. Performance differences were particularly compelling on real world data with which most other methods severely struggled. This work thus led to a simple yet powerful DS reconstruction algorithm which is highly interpretable at the same time.Comment: Published in the Proceedings of the 40th International Conference on Machine Learning (ICML 2023

Einfluss einer Belastung mit bodenbürtigen Schaderregern auf bunt- und weißblühende Erbsen in einem Gefäßversuch

Generally, purple-flowered peas are assumed to be less susceptible to soilborne pests. The above- and belowground biomass yield of one purple-flowered and one white-flowered pea were compared on three soils with and without soil fatigue. Both peas showed lower above- and belowground biomass yield on soil fatigue soils than on unstressed soils. The aboveground yield´s decrease of the purple-flowered pea was higher than for white-flowered pea on two of the three soils. Hence, purple-flowered peas are generally not less susceptible to soilborne pests than white-flowered peas

Timing is Money - Evaluating the Effects of Early Availability of Feature Films via Video on Demand

Based on survey data from 489 German potential Video On Demand users this research explores effects of early movie availability on consumers’ utility, their willingness to pay, and copyright violations. Using a triangulation approach, we employed adaptive conjoint analysis and contingent valuation methodologies. Our results show substantially increased utility levels and greater willingness to pay for Video On Demand services that offer movies simultaneously with or shortly before the first official theatrical release. Our findings bear similarities to results from experiments on hyperbolic discounting, a concept from the field of behavioral economics. Diverging from classic microeconomic theory, immediate consumption seems to be valued irrationally high. This effect is even stronger for copyright violators. Implications both for future academic research and for the motion picture industry are drawn

Combined schemes for signature and encryption: The public-key and the identity-based setting

Consider a scenario in which parties use a public-key encryption scheme and a signature scheme with a single public key/private key pair-so the private key sk is used for both signing and decrypting. Such a simultaneous use of a key is in general considered poor cryptographic practice, but from an efficiency point of view looks attractive. We offer security notions to analyze such violations of key separation. For both the identity-and the non-identity-based setting, we show that-although being insecure in general-for schemes of interest the resulting combined scheme can offer strong security guarantees.First and last author were supported by the Spanish Ministerio de Economía y Competitividad through the project grant MTM-2012-15167