An explicit candidate for the set of Steinitz classes of tame Galois extensions with fixed Galois group of odd order

Given a finite group G and a number field k, a well-known conjecture asserts that the set R_t(k,G) of Steinitz classes of tame G-Galois extensions of k is a subgroup of the ideal class group of k. In this paper we investigate an explicit candidate for R_t(k,G), when G is of odd order. More precisely, we define a subgroup W(k,G) of the class group of k and we prove that R_t(k,G) is contained in W(k,G). We show that equality holds for all groups of odd order for which a description of R_t(k,G) is known so far. Furthermore, by refining techniques introduced in arXiv:0910.5080v1, we use the Shafarevich-Weil Theorem in cohomological class field theory, to construct some tame Galois extensions with given Steinitz class. In particular, this allows us to prove the equality R_t(k,G)=W(k,G) when G is a group of order dividing l^4, where l is an odd prime.Comment: 25 page

Control of Energy Storage Device for Rail Vehicles

This master thesis has been done in Berlin at Daimler Chrysler. It is concerned with technological research and development for electrical engine. This thesis treats to evaluate what margins can be achieved by using energy storage system on rail vehicle. Energy storage devices, like accumulator, flywheels or capacitors are currently under consideration by the rail vehicle industry. The expected benefit introducing storage systems is not only reduced energy consumption but also advantages concerning reduced line peak loads, network stabilisation, improved driving performance. These devices are able to store kinetic energy during the brake time and feed it back during acceleration or during max power demand. The work is divided into two steps: - A simulation model of the vehicle’s drive and energy storage system has to be set up using ”Matlab”. Multi-objective optimisation has to be applied using, e.g., non-linear programming or evolutionary strategies. The results, at this stage, are optimised cycles for the storage operation depending on given sets of track profiles and driving cycles. These results are not necessarily already under control laws. The problem of reduced run-time information is also not considered at this stage. - During the second step, the results of step one must lead to a control law for the energy storage device that is suitable for run-time implementation and that is able to deal with the mentioned reduced information. General control design principles should be derived. It should be evaluated, what margins can be achieved compared with those of step one. Simple control laws should be specified for following next controller implementation. The proposal of the research work is to determine a control law that permits to utilise in optimal way the energy storage device in such way to centre the prefixed objective, like reduced energy consumption, advantages concerning reduced line peak loads, network stabilisation, improved driving performance. All this without knowing in advances the characteristic of the route, the brake and acceleration moment. The control law must be set up in Real-time context

Il problema della classificazione delle estensioni locali: le estensioni di grado p^2 di Qp.

Il corpo della tesi, che e` preceduto da una rapida panoramica sulle tecniche e gli strumenti utilizzati, si compone di due parti. All'esposizione della classificazione delle estensioni di grado p dei p-adici (sono risultati gia` noti), segue una seconda parte nella quale si espongono alcuni piccoli risultati originali volti a classificare le estensioni di grado p^2, almeno nei casi piu` semplici. Vengono trattati il caso di estensioni normali e il caso di estensioni con p coniugati ed una sottoestensione di grado p comune fra di essi. Infine, si propongono alcune tecniche eleganti e piu` sofisticate di classificazione legate alla teoria dei corpi di classe

FreeREA: Training-Free Evolution-based Architecture Search

In the last decade, most research in Machine Learning contributed to the improvement of existing models, with the aim of increasing the performance of neural networks for the solution of a variety of different tasks. However, such advancements often come at the cost of an increase of model memory and computational requirements. This represents a significant limitation for the deployability of research output in realistic settings, where the cost, the energy consumption, and the complexity of the framework play a crucial role. To solve this issue, the designer should search for models that maximise the performance while limiting its footprint. Typical approaches to reach this goal rely either on manual procedures, which cannot guarantee the optimality of the final design, or upon Neural Architecture Search algorithms to automatise the process, at the expenses of extremely high computational time. This paper provides a solution for the fast identification of a neural network that maximises the model accuracy while preserving size and computational constraints typical of tiny devices. Our approach, named FreeREA, is a custom cell-based evolution NAS algorithm that exploits an optimised combination of training-free metrics to rank architectures during the search, thus without need of model training. Our experiments, carried out on the common benchmarks NAS-Bench-101 and NATS-Bench, demonstrate that i) FreeREA is the first method able to provide very accurate models in minutes of search time; ii) it outperforms State of the Art training-based and training-free techniques in all the datasets and benchmarks considered, and iii) it can easily generalise to constrained scenarios, representing a competitive solution for fast Neural Architecture Search in generic constrained applications.Comment: 16 pages, 4 figurre