Josef Pochodzalla, Lech Mankiewicz, Murray Moinester, Gunther Piller , Andrzej Sandacz, Marc Vanderhaeghen Max-Planck-Institut für Kernphysik, 69029 Heidelberg, Germany Physics Department, Technical University Munich, D-85747 Garching, Germany School of Physics and Astronomy, R. and B. Sackler Faculty of Exact Sciences, Tel Aviv University, 69978 Ramat Aviv, Israel Soltan Institute for Nuclear ...

Graphical Abstract „The greatest scientific advance of the next decade will revolve around developing technologies that harmonize human progress with ecological integrity… The most important quality a mentor is to tailor guidance fit an individual's aspirations, acknowledging one size doesn't all.“ Find out more about Andreas Benjamin Schmidt in his Introducing… Profile.

Last time we defined the minimum distance λ1(L) of a lattice L, and showed that it is upper bounded by √ n · det(L)1/n (Minkowski’s theorem), but this bound is often very loose. Some natural computational questions are: given a lattice (specified by some arbitrary basis), can we compute its minimum distance? Can we find a vector that achieves this distance? Can we find good approximations to th...

We propose a feature extraction algorithm, based on the Hilbert–Schmidt independence criterion (HSIC) and the maximum dependence – minimum redundancy approach. Experiments with classification data sets demonstrate that suggested Hilbert–Schmidt component analysis (HSCA) algorithm in certain cases may be more efficient than other considered approaches.

2. Derivatives 10 2.1. Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2. Hasse-Schmidt derivatives ∂ z . . . . . . . . . . . . . . . . . . . . . 11 2.3. Hasse-Schmidt derivations in general . . . . . . . . . . . . . . . . . 18 2.4. Hasse-Schmidt derivations from A to B as algebra maps A→ B [[t]] 22 2.5. Extending Hasse-Schmidt derivations to localizations . ....

The behavior of the Hasse–Schmidt algebra under étale extension is used to show that the Hasse–Schmidt algebra of a smooth algebra of finite type over a field equals the ring of differential operators. These techniques show that the formation of Hasse–Schmidt derivations does not commute with localization, providing a counterexample to a question of Brown and Kuan; their conjecture is reformula...