NR-SLAM: Non-Rigid Monocular SLAM

In this paper we present NR-SLAM, a novel non-rigid monocular SLAM system founded on the combination of a Dynamic Deformation Graph with a Visco-Elastic deformation model. The former enables our system to represent the dynamics of the deforming environment as the camera explores, while the later allows us to model general deformations in a simple way. The presented system is able to automatically initialize and extend a map modeled by a sparse point cloud in deforming environments, that is refined with a sliding-window Deformable Bundle Adjustment. This map serves as base for the estimation of the camera motion and deformation and enables us to represent arbitrary surface topologies, overcoming the limitations of previous methods. To assess the performance of our system in challenging deforming scenarios, we evaluate it in several representative medical datasets. In our experiments, NR-SLAM outperforms previous deformable SLAM systems, achieving millimeter reconstruction accuracy and bringing automated medical intervention closer. For the benefit of the community, we make the source code public.Comment: 12 pages, 7 figures, submited to the IEEE Transactions on Robotics (T-RO

Hierarchical Merger of Primordial Black Holes in Dwarf Galaxies

We study the merger history of primordial black holes (PBHs) in a scenario where they represent the dominant dark matter component of a typical dwarf galaxies' core. We investigate the possibility of a sequence of collisions resulting in a hierarchical merger of black holes and look at the final mass spectrum in such {\it clusters}, which initially present a monochromatic (single-mass) PBH population. Our study shows that the merging process results in the transfer of about $40\%$ of the total mass of the core to the merger products regardless of the initial mass of PBHs, with about $5\%$ of energy radiated out in the form of gravitational waves. We find that, in the lighter mass limit, black holes up to eight times more massive than the original population can be formed within a Hubble time.Comment: 17 pages, 3 figures, updated reference

Fluctuations and response in a non-equilibrium micron-sized system

The linear response of non-equilibrium systems with Markovian dynamics satisfies a generalized fluctuation-dissipation relation derived from time symmetry and antisymmetry properties of the fluctuations. The relation involves the sum of two correlation functions of the observable of interest: one with the entropy excess and the second with the excess of dynamical activity with respect to the unperturbed process, without recourse to anything but the dynamics of the system. We illustrate this approach in the experimental determination of the linear response of the potential energy of a Brownian particle in a toroidal optical trap. The overdamped particle motion is effectively confined to a circle, undergoing a periodic potential and driven out of equilibrium by a non-conservative force. Independent direct and indirect measurements of the linear response around a non-equilibrium steady state are performed in this simple experimental system. The same ideas are applicable to the measurement of the response of more general non-equilibrium micron-sized systems immersed in Newtonian fluids either in stationary or non-stationary states and possibly including inertial degrees of freedom.Comment: 12 pages, submitted to J. Stat. Mech., revised versio