The homology of path spaces and Floer homology with conormal boundary conditions

We define the Floer complex for Hamiltonian orbits on the cotangent bundle of a compact manifold satisfying non-local conormal boundary conditions. We prove that the homology of this chain complex is isomorphic to the singular homology of the natural path space associated to the boundary conditions.Comment: 25 pages, final versio

Breast cancer mass detection in dce-mri using deep-learning features followed by discrimination of infiltrative vs. in situ carcinoma through a machine-learning approach

Breast cancer is the leading cause of cancer deaths worldwide in women. This aggressive tumor can be categorized into two main groups-in situ and infiltrative, with the latter being the most common malignant lesions. The current use of magnetic resonance imaging (MRI) was shown to provide the highest sensitivity in the detection and discrimination between benign vs. malignant lesions, when interpreted by expert radiologists. In this article, we present the prototype of a computer-aided detection/diagnosis (CAD) system that could provide valuable assistance to radiologists for discrimination between in situ and infiltrating tumors. The system consists of two main processing levels-(1) localization of possibly tumoral regions of interest (ROIs) through an iterative procedure based on intensity values (ROI Hunter), followed by a deep-feature extraction and classification method for false-positive rejection; and (2) characterization of the selected ROIs and discrimination between in situ and invasive tumor, consisting of Radiomics feature extraction and classification through a machine-learning algorithm. The CAD system was developed and evaluated using a DCE-MRI image database, containing at least one confirmed mass per image, as diagnosed by an expert radiologist. When evaluating the accuracy of the ROI Hunter procedure with respect to the radiologist-drawn boundaries, sensitivity to mass detection was found to be 75%. The AUC of the ROC curve for discrimination between in situ and infiltrative tumors was 0.70

Detectability of large-scale counter-rotating stellar disks in galaxies with integral-field spectroscopy

In recent years integral-field spectroscopic surveys have revealed that the presence of kinematically decoupled stellar components is not a rare phenomenon in nearby galaxies. However, complete statistics are still lacking because they depend on the detection limit of these objects. We investigate the kinematic signatures of two large-scale counter-rotating stellar disks in mock integral-field spectroscopic data to address their detection limits as a function of the galaxy properties and instrumental setup. We built a set of mock data of two large-scale counter-rotating stellar disks as if they were observed with the Multi-Unit Spectroscopic Explorer (MUSE). We accounted for different photometric, kinematic, and stellar population properties of the two counter-rotating components as a function of galaxy inclination. We extracted the stellar kinematics in the wavelength region of the calcium triplet absorption lines by adopting a Gauss-Hermite (GH) parameterization of the line-of-sight velocity distribution (LOSVD). We confirm that the strongest signature of the presence of two counter-rotating stellar disks is the symmetric double peak in the velocity dispersion map, already known as the $2\sigma$ feature. The size, shape, and slope of the 2$\sigma$ peak strongly depend on the velocity separation and relative light contribution of the two counter-rotating stellar disks. When the $2\sigma$ peak is difficult to detect due to the low signal-to-noise ratio of the data, the large-scale structure in the $h_3$ map can be used as a diagnostic for strong and weak counter-rotation. The counter-rotating kinematic signatures become fainter at lower viewing angles as an effect of the smaller projected velocity separation between the two counter-rotating components. We confirm that the observed frequency of $2\sigma$ galaxies represents only a lower limit of the stellar counter-rotation phenomenon.Comment: Accepted for publication in Astronomy & Astrophysics. 17 pages, 11 figures, 2 table

Bifurcation of critical points along gap-continuous families of subspaces

We consider the restriction of twice differentiable functionals on a Hilbert space to families of subspaces that vary continuously with respect to the gap metric. We study bifurcation of branches of critical points along these families, and apply our results to semilinear systems of ordinary differential equations

Searching for nuclear stellar discs in simulations of star cluster mergers

The nuclei of galaxies often host small stellar discs with scalelengths of a few tens of parsecs and luminosities up to 107 L�. To investigate the formation and properties of nuclear stellar discs (NSDs), we look for their presence in a set of N-body simulations studying the dissipationless merging of multiple star clusters in galactic nuclei. A few tens of star clusters with sizes and masses comparable to those of globular clusters observed in the Milky Way are accreted on to a pre-existing nuclear stellar component: either a massive super star cluster or a rapidly rotating, compact disc with a scalelength of a few parsecs, mimicking the variety of observed nuclear structures. Images and kinematic maps of the simulation time-steps are then built and analysed as if they were real and at the distance of the Virgo cluster. We use the Scorza–Bender method to search for the presence of disc structures via photometric decomposition. In one case, the merger remnant has all the observed photometric and kinematic properties of NSDs observed in real galaxies. This shows that current observations are consistent with most of the NSD mass being assembled from the migration and accretion of star clusters into the galactic centre. In the other simulation instead, we detect an elongated structure from the unsharp masked image, that does not develop the photometric or kinematic signature of an NSD. Thus, in the context of searches for a disc structure, the Scorza–Bender method is a robust and necessary tool

Data processing on simulated data for SHARK-NIR

A robust post processing technique is mandatory to analyse the coronagraphic high contrast imaging data. Angular Differential Imaging (ADI) and Principal Component Analysis (PCA) are the most used approaches to suppress the quasi-static structure in the Point Spread Function (PSF) in order to revealing planets at different separations from the host star. The focus of this work is to apply these two data reduction techniques to obtain the best limit detection for each coronagraphic setting that has been simulated for the SHARK-NIR, a coronagraphic camera that will be implemented at the Large Binocular Telescope (LBT). We investigated different seeing conditions ($0.4"-1"$) for stellar magnitude ranging from R=6 to R=14, with particular care in finding the best compromise between quasi-static speckle subtraction and planet detection.Comment: 9 pages, 8 figures, proceeding for the fifth Adaptive Optics for Extremely Large Telescopes (AO4ELT5) meeting in 201

HE-LHC: The High-Energy Large Hadron Collider – Future Circular Collider Conceptual Design Report Volume 4

In response to the 2013 Update of the European Strategy for Particle Physics (EPPSU), the Future Circular Collider (FCC) study was launched as a world-wide international collaboration hosted by CERN. The FCC study covered an energy-frontier hadron collider (FCC-hh), a highest-luminosity high-energy lepton collider (FCC-ee), the corresponding 100 km tunnel infrastructure, as well as the physics opportunities of these two colliders, and a high-energy LHC, based on FCC-hh technology. This document constitutes the third volume of the FCC Conceptual Design Report, devoted to the hadron collider FCC-hh. It summarizes the FCC-hh physics discovery opportunities, presents the FCC-hh accelerator design, performance reach, and staged operation plan, discusses the underlying technologies, the civil engineering and technical infrastructure, and also sketches a possible implementation. Combining ingredients from the Large Hadron Collider (LHC), the high-luminosity LHC upgrade and adding novel technologies and approaches, the FCC-hh design aims at significantly extending the energy frontier to 100 TeV. Its unprecedented centre-of-mass collision energy will make the FCC-hh a unique instrument to explore physics beyond the Standard Model, offering great direct sensitivity to new physics and discoveries