Enumerating Abelian Returns to Prefixes of Sturmian Words

We follow the works of Puzynina and Zamboni, and Rigo et al. on abelian returns in Sturmian words. We determine the cardinality of the set $\mathcal{APR}_u$ of abelian returns of all prefixes of a Sturmian word $u$ in terms of the coefficients of the continued fraction of the slope, dependingly on the intercept. We provide a simple algorithm for finding the set $\mathcal{APR}_u$ and we determine it for the characteristic Sturmian words.Comment: 19page

Update on the ICUD-SIU consultation on multi-parametric magnetic resonance imaging in localised prostate cancer

Introduction: Prostate cancer (PCa) imaging is a rapidly evolving field. Dramatic improvements in prostate MRI during the last decade will probably change the accuracy of diagnosis. This chapter reviews recent current evidence about MRI diagnostic performance and impact on PCa management. Materials and methods: The International Consultation on Urological Diseases nominated a committee to review the literature on prostate MRI. A search of the PubMed database was conducted to identify articles focussed on MP-MRI detection and staging protocols, reporting and scoring systems, the role of MP-MRI in diagnosing PCa prior to biopsy, in active surveillance, in focal therapy and in detecting local recurrence after treatment. Results: Differences in opinion were reported in the use of the strength of magnets [1.5 Tesla (T) vs. 3T] and coils. More agreement was found regarding the choice of pulse sequences; diffusion-weighted MRI (DW-MRI), dynamic contrast-enhanced MRI (DCE MRI), and/or MR spectroscopy imaging (MRSI) are recommended in addition to conventional T2-weighted anatomical sequences. In 2015, the Prostate Imaging Reporting and Data System (PI-RADS version 2) was described to standardize image acquisition and interpretation. MP-MRI improves detection of clinically significant PCa (csPCa) in the repeat biopsy setting or before the confirmatory biopsy in patients considering active surveillance. It is useful to guide focal treatment and to detect local recurrences after treatment. Its role in biopsy-naive patients or during the course of active surveillance remains debated. Conclusion: MP-MRI is increasingly used to improve detection of csPCa and for the selection of a suitable therapeutic approach

Sudden To Adiabatic Transition in Beta Decay

We discuss effects in beta decays at very low beta energies, of the order of the kinetic energies of atomic electrons. As the beta energy is lowered the atomic response changes from sudden to adiabatic. As a consequence, the beta decay rate increases slightly and the ejection of atomic electrons (shake off) and subsequent production of X rays is turned off. We estimate the transition energy and the change in decay rate. The rate increase is largest in heavy atoms, which have a small Q value in their decay. The X ray switch-off is independent of Q value.Comment: 6 pages LaTe

The Scattering Approach to the Casimir Force

We present the scattering approach which is nowadays the best tool for describing the Casimir force in realistic experimental configurations. After reminders on the simple geometries of 1d space and specular scatterers in 3d space, we discuss the case of stationary arbitrarily shaped mirrors in electromagnetic vacuum. We then review specific calculations based on the scattering approach, dealing for example with the forces or torques between nanostructured surfaces and with the force between a plane and a sphere. In these various cases, we account for the material dependence of the forces, and show that the geometry dependence goes beyond the trivial {\it Proximity Force Approximation} often used for discussing experiments.Comment: Proceedings of the QFEXT'09 conference (Oklahoma, 2009

Sealed operation, and circulation and purification of gas in the HARPO TPC

HARPO is a time projection chamber (TPC) demonstrator of a gamma-ray telescope and polarimeter in the MeV-GeV range, for a future space mission. We present the evolution of the TPC performance over a five month sealed-mode operation, by the analysis of cosmic-ray data, followed by the fast and complete recovery of the initial gas properties using a lightweight gas circulation and purification system.Comment: Proceedings_MPGD2015, EPJ Web of Conference

Traversable Wormholes in Geometries of Charged Shells

We construct a static axisymmetric wormhole from the gravitational field of two charged shells which are kept in equilibrium by their electromagnetic repulsion. For large separations the exterior tends to the Majumdar-Papapetrou spacetime of two charged particles. The interior of the wormhole is a Reissner-Nordstr\"om black hole matching to the two shells. The wormhole is traversable and connects to the same asymptotics without violation of energy conditions. However, every point in the Majumdar-Papapetrou region lies on a closed timelike curve.Comment: 9 pages, LaTeX, 1 figur

Casimir interaction between plane and spherical metallic surfaces

We give an exact series expansion of the Casimir force between plane and spherical metallic surfaces in the non trivial situation where the sphere radius $R$, the plane-sphere distance $L$ and the plasma wavelength $\lambda_\P$ have arbitrary relative values. We then present numerical evaluation of this expansion for not too small values of $L/R$. For metallic nanospheres where $R, L$ and $\lambda_\P$ have comparable values, we interpret our results in terms of a correlation between the effects of geometry beyond the proximity force approximation (PFA) and of finite reflectivity due to material properties. We also discuss the interest of our results for the current Casimir experiments performed with spheres of large radius $R\gg L$.Comment: 4 pages, new presentation (highlighting the novelty of the results) and added references. To appear in Physical Review Letter

Painting Many Pasts: Synthesizing Time Lapse Videos of Paintings

We introduce a new video synthesis task: synthesizing time lapse videos depicting how a given painting might have been created. Artists paint using unique combinations of brushes, strokes, and colors. There are often many possible ways to create a given painting. Our goal is to learn to capture this rich range of possibilities. Creating distributions of long-term videos is a challenge for learning-based video synthesis methods. We present a probabilistic model that, given a single image of a completed painting, recurrently synthesizes steps of the painting process. We implement this model as a convolutional neural network, and introduce a novel training scheme to enable learning from a limited dataset of painting time lapses. We demonstrate that this model can be used to sample many time steps, enabling long-term stochastic video synthesis. We evaluate our method on digital and watercolor paintings collected from video websites, and show that human raters find our synthetic videos to be similar to time lapse videos produced by real artists. Our code is available at https://xamyzhao.github.io/timecraft.Comment: 10 pages, CVPR 202