The persistence landscape and some of its properties

Persistence landscapes map persistence diagrams into a function space, which may often be taken to be a Banach space or even a Hilbert space. In the latter case, it is a feature map and there is an associated kernel. The main advantage of this summary is that it allows one to apply tools from statistics and machine learning. Furthermore, the mapping from persistence diagrams to persistence landscapes is stable and invertible. We introduce a weighted version of the persistence landscape and define a one-parameter family of Poisson-weighted persistence landscape kernels that may be useful for learning. We also demonstrate some additional properties of the persistence landscape. First, the persistence landscape may be viewed as a tropical rational function. Second, in many cases it is possible to exactly reconstruct all of the component persistence diagrams from an average persistence landscape. It follows that the persistence landscape kernel is characteristic for certain generic empirical measures. Finally, the persistence landscape distance may be arbitrarily small compared to the interleaving distance.Comment: 18 pages, to appear in the Proceedings of the 2018 Abel Symposiu

Uric acid level and the presence of metabolic syndrome: experiences from Vojvodina Region in Serbia

Introduction: Uric acid level (UAL) might represent an indirect marker of metabolic syndrome (MS). Study investigates differences in UAL in the overall study group and in separate groups of normal weight, overweight and obese subjects, regarding the presence of MS. Materials and Methods: Cross sectional study included 1333 participants. Anthropometrical measurements and relevant blood analysis were performed. For diagnosis of MS we used NCEP ATP III criteria. Results: 50.64% of the participants have fulfilled criteria for MS diagnosis. In the overall study group, participants with MS were older (

Contrôle de la phase relative d'impulsions harmoniques à une échelle de temps attoseconde

Nous démontrons la possibilité de générer quatre impulsions harmoniques bloquées en phase séparées temporellement, que nous caractérisons par interférométrie fréquentielle. Les spectres présentent alors une sensibilité extrême au déphasage entre les deux couples d'impulsions qui interfèrent. Nous montrons qu'un contrôle de cette phase relative peut être fait à une échelle attoseconde (1as=10$^{-18}$ s). La résolution spectrale et la haute sensibilité de cette technique pourraient être utilisées pour des mesures de haute précision en spectroscopie et interférométrie.

Computed stereo lensless X-ray imaging

International audienceRecovering the three-dimensional (3D) properties of artificial or biological systems using low X-ray doses is challenging as most techniques are based on computing hundreds of two-dimensional (2D) projections. The requirement for a low X-ray dose also prevents single-shot 3D imaging using ultrafast X-ray sources. Here we show that computed stereo vision concepts can be applied to X-rays. Stereo vision is important in the field of machine vision and robotics. We reconstruct two X-ray stereo views from coherent diffraction patterns and compute a nanoscale 3D representation of the sample from disparity maps. Similarly to brain perception, computed stereo vision algorithms use constraints. We demonstrate that phase-contrast images relax the disparity constraints, allowing occulted features to be revealed. We also show that by using nanoparticles as labels we can extend the applicability of the technique to complex samples. Computed stereo X-ray imaging will find application at X-ray free-electron lasers, synchrotrons and laser-based sources, and in industrial and medical 3D diagnosis method

Generation of high harmonics and attosecond pulses with ultrashort laser pulse filaments and conical waves

Results illustrating the nonlinear dynamics of ultrashort laser pulse filamentation in gases are presented, with particular emphasis on the filament properties useful for developing attosecond light sources. Two aspects of ultrashort pulse filaments are specifically discussed: (i) numerical simulation results on pulse self-compression by filamentation in a gas cell filled with noble gas. Measurements of high harmonics generated by the pulse extracted from the filament allows for the detection of intensity spikes and subcycle pulses generated within the filament. (ii) Simulation results on the spontaneous formation of conical wavepackets during filamentation in gases, which in turn can be used as efficient driving pulses for the generation of high harmonics and isolated attosecond pulses