Crossed products and entropy of automorphisms

Let A be an exact C^*-algebra, let G be a locally compact group, and let (A,G,\alpha) be a C*-dynamical system. Each automorphism \alpha_g induces a spatial automorphism Ad_{\lamba_g} on the reduced crossed product A\times_\alpha G. In this paper we examine the question, first raised by E. Stormer, of when the topological entropies of \alpha_g and Ad_{\alpha_g} coincide. This had been answered by N. Brown for the particular case of discrete abelian groups. Using different methods, we extend his result to a wider class of groups called locally [FIA]^-. This class includes all abelian groups, both discrete and continuous, as well as all compact groups.Comment: A few corrections suggested by the referee. To appear in Journal of Functional Analysi

The role of oxygen vacancies on the structure and the density of states of iron doped zirconia

In this paper we study, both with theoretical and experimental approach, the effect of iron doping in zirconia. Combining density functional theory (DFT) simulations with the experimental characterization of thin films, we show that iron is in the Fe3+ oxidation state and accordingly that the films are rich in oxygen vacancies (VO). VO favor the formation of the tetragonal phase in doped zirconia (ZrO2:Fe) and affect the density of state at the Fermi level as well as the local magnetization of Fe atoms. We also show that the Fe(2p) and Fe(3p) energy levels can be used as a marker for the presence of vacancies in the doped system. In particular the computed position of the Fe(3p) peak is strongly sensitive to the VO to Fe atoms ratio. A comparison of the theoretical and experimental Fe(3p) peak position suggests that in our films this ratio is close to 0.5. Besides the interest in the material by itself, ZrO2:Fe constitutes a test case for the application of DFT on transition metals embedded in oxides. In ZrO2:Fe the inclusion of the Hubbard U correction significantly changes the electronic properties of the system. However the inclusion of this correction, at least for the value U = 3.3 eV chosen in the present work, worsen the agreement with the measured photo-emission valence band spectra.Comment: 24 pages, 8 figure

Lagrangian versus Quantization

We discuss examples of systems which can be quantized consistently, although they do not admit a Lagrangian description.Comment: 8 pages, no figures; small corrections, references adde

A path integral leading to higher-order Lagrangians

We consider a simple modification of standard phase-space path integrals and show that it leads in configuration space to Lagrangians depending also on accelerations.Comment: 6 page

Simultaneous in vivo positron emission tomography and magnetic resonance imaging

Positron emission tomography (PET) and magnetic resonance imaging (MRI) are widely used in vivo imaging technologies with both clinical and biomedical research applications. The strengths of MRI include high-resolution, high-contrast morphologic imaging of soft tissues; the ability to image physiologic parameters such as diffusion and changes in oxygenation level resulting from neuronal stimulation; and the measurement of metabolites using chemical shift imaging. PET images the distribution of biologically targeted radiotracers with high sensitivity, but images generally lack anatomic context and are of lower spatial resolution. Integration of these technologies permits the acquisition of temporally correlated data showing the distribution of PET radiotracers and MRI contrast agents or MR-detectable metabolites, with registration to the underlying anatomy. An MRI-compatible PET scanner has been built for biomedical research applications that allows data from both modalities to be acquired simultaneously. Experiments demonstrate no effect of the MRI system on the spatial resolution of the PET system and <10% reduction in the fraction of radioactive decay events detected by the PET scanner inside the MRI. The signal-to-noise ratio and uniformity of the MR images, with the exception of one particular pulse sequence, were little affected by the presence of the PET scanner. In vivo simultaneous PET and MRI studies were performed in mice. Proof-of-principle in vivo MR spectroscopy and functional MRI experiments were also demonstrated with the combined scanner

Anonymized Counting of Nonstationary Wi-Fi Devices When Monitoring Crowds

Pedestrian dynamics are nowadays commonly analyzed by leveraging Wi-Fi signals sent by devices that people carry with them and captured by an infrastructure of Wi-Fi scanners. Emitting such signals is not a feature for devices of only passersby, but also for printers, smart TVs, and other devices that exhibit a stationary behavior over time, which eventually end up affecting pedestrian crowd measurements. In this paper we propose a system that accurately counts nonstationary devices sensed by scanners, separately from stationary devices, using no information other than the Wi-Fi signals captured by each scanner in isolation. As counting involves dealing with privacy-sensitive detections of people's devices, the system discards any data in the clear immediately after sensing, later working on encrypted data that it cannot decrypt in the process. The only information made available in the clear is the intended output, i.e. statistical counts of Wi-Fi devices. Our approach relies on an object, which we call comb, that maintains, under encryption, a representation of the frequency of occurrence of devices over time. Applying this comb on the detections made by a scanner enables the calculation of the separate counts. We implement the system and feed it with data from a large open-air festival, showing that accurate anonymized counting of nonstationary Wi-Fi devices is possible when dealing with real-world detections.</p