Lectures on Duflo isomorphisms in Lie algebra and complex geometry

International audienceDuflo isomorphism first appeared in Lie theory and representation theory. It is an isomorphism between invariant polynomials of a Lie algebra and the center of its universal enveloping algebra, generalizing the pioneering work of Harish-Chandra on semi-simple Lie algebras. Later on, Duflo’s result was refound by Kontsevich in the framework of deformation quantization, who also observed that there is a similar isomorphism between Dolbeault cohomology of holomorphic polyvector fields on a complex manifold and its Hochschild cohomology. The present book, which arose from a series of lectures by the first author at ETH, derives these two isomorphisms from a Duflo-type result for Q-manifolds.All notions mentioned above are introduced and explained in the book, the only prerequisites being basic linear algebra and differential geometry. In addition to standard notions such as Lie (super)algebras, complex manifolds, Hochschild and Chevalley–Eilenberg cohomologies, spectral sequences, Atiyah and Todd classes, the graphical calculus introduced by Kontsevich in his seminal work on deformation quantization is addressed in details.The book is well-suited for graduate students in mathematics and mathematical physics as well as for researchers working in Lie theory, algebraic geometry and deformation theory

Quantum Hypergraph States

We introduce a class of multiqubit quantum states which generalizes graph states. These states correspond to an underlying mathematical hypergraph, i.e. a graph where edges connecting more than two vertices are considered. We derive a generalised stabilizer formalism to describe this class of states. We introduce the notion of k-uniformity and show that this gives rise to classes of states which are inequivalent under the action of the local Pauli group. Finally we disclose a one-to-one correspondence with states employed in quantum algorithms, such as Deutsch-Jozsa's and Grover's.Comment: 9+5 pages, 5 figures, 1 table, published versio

Boundary fluxes for non-local diffusion

We study a nonlocal diffusion operator in a bounded smooth domain prescribing the flux through the boundary. This problem may be seen as a generalization of the usual Neumann problem for the heat equation. First, we prove existence, uniqueness and a comparison principle. Next, we study the behavior of solutions for some prescribed boundary data including blowing up ones. Finally, we look at a nonlinear flux boundary condition

Mars Observer Radar Altimeter Radiometer (MORAR)

The Mars Observer Project will permit the advancement of the state of the topographic and hypsometric knowledge of Mars to a level of 10 m or better over the surface of the planet Mars, the measurement of microwave surface brightness temperature of Mars with an accuracy of 15 to 20 K over 24 hours, and the measurement, globally, of surface returned power related to radar cross section with an accuracy of 1 dB and a repeatability of .5 dB. The MORAR Hardware Development, Ground Data Processing, and the Mission Operations will allow the accomplishment of these scientific objectives to define globally the topography of Mars at sufficient vertical resolution and spatial scale to address both large-scale geophysical and small-scale geologic problems, and to obtain global surface electrical and scattering properties of the upper several centimeters of the Martian surface for assessment of the composition, physical state, and volatile distribution of the surface

Advances in Feature Selection with Mutual Information

The selection of features that are relevant for a prediction or classification problem is an important problem in many domains involving high-dimensional data. Selecting features helps fighting the curse of dimensionality, improving the performances of prediction or classification methods, and interpreting the application. In a nonlinear context, the mutual information is widely used as relevance criterion for features and sets of features. Nevertheless, it suffers from at least three major limitations: mutual information estimators depend on smoothing parameters, there is no theoretically justified stopping criterion in the feature selection greedy procedure, and the estimation itself suffers from the curse of dimensionality. This chapter shows how to deal with these problems. The two first ones are addressed by using resampling techniques that provide a statistical basis to select the estimator parameters and to stop the search procedure. The third one is addressed by modifying the mutual information criterion into a measure of how features are complementary (and not only informative) for the problem at hand

Identification of Showers with Cores Outside the ARGO-YBJ Detector

In any EAS array, the rejection of events with shower cores outside the detector boundaries is of great importance. A large difference between the true and the reconstructed shower core positions may lead to a systematic miscalculation of some shower characteristics. Moreover, an accurate determination of the shower core position for selected internal events is important to reconstruct the primary direction using conical fits to the shower front, improving the detector angular resolution, or to performe an efficient gamma/hadron discrimination. In this paper we present a procedure able to identify and reject showers with cores outside the ARGO-YBJ carpet boundaries. A comparison of the results for gamma and proton induced showers is reported.Comment: 4 pages, to be published in the Proceedings of the 28th International Cosmic Ray Conference (Tsukuba, Japan 2003

The PS 10 MHz High Level RF System Upgrade

In view of the upgrade of the injectors for the High Luminosity LHC, significantly higher bunch intensity is required for LHC-type beams. In this context an upgrade of the main accelerating RF system of the Proton Synchrotron (PS) is necessary, aiming at reducing the cavity impedance which is the source of longitudinal coupled-bunch oscillations. These instabilities pose as a major limitation for the increase of the beam intensity as planned after LS2. The 10 MHz RF system consists in 11 ferrite loaded cavities, driven by tube-based power amplifiers for reasons of radiation hardness. The cavity-amplifier system is equipped with a wide-band feedback that reduces the beam induced voltage. A further reduction of the beam loading is foreseen by upgrading the feedback system, which can be reasonably achieved by increasing the loop gain of the existing amplification chain. This paper describes the progress of the design of the upgraded feedback system and shows the results of the tests on the new amplifier prototype, installed in the PS during the 2015-16 technical stop. It also reports the first results of its performance with beam, observed in the beginning of the 2016 run

Modeling and Detection of Hotspot in Shaded Photovoltaic Cells

In this paper, we address the problem of modeling the thermal behavior of photovoltaic (PV) cells undergoing a hotspot condition. In case of shading, PV cells may experience a dramatic temperature increase, with consequent reduction of the provided power. Our model has been validated against experimental data, and has highlighted a counter-intuitive PV cell behavior, that should be considered to improve the energy efficiency of PV arrays. Then, we propose a hotspot detection scheme, enabling to identify the PV module that is under hotspot condition. Such a scheme can be used to avoid the permanent damage of the cells under hotspot, thus their drawback on the power efficiency of the entire PV system