We propose to deploy limits that arise from different tests of the Pauli Exclusion Principle in order: i) to provide theories of quantum gravity with an experimental guidance; ii) to distinguish among the plethora of possible models the ones that are already ruled out by current data; iii) to direct future attempts to be in accordance with experimental constraints. We firstly review experimental bounds on nuclear processes forbidden by the Pauli Exclusion Principle, which have been derived by several experimental collaborations making use of different detector materials. Distinct features of the experimental devices entail sensitivities on the constraints hitherto achieved that may differ one another by several orders of magnitude. We show that with choices of these limits, renown examples of flat noncommutative space-time instantiations of quantum gravity can be heavily constrained, and eventually ruled out. We devote particular attention to the analysis of theκ-Minkowski and θ-Minkowski noncommutative spacetimes. These are deeply connected to some scenarios in string theory, loop quantum gravity and noncommutative geometry. We emphasize that the severe constraints on these quantum spacetimes, although cannot rule out theories of top-down quantum gravity to whom are connected in various way, provide a powerful limitations of those models that it will make sense to focus on in the future.

Symmetry is a common geometric feature in human-made objects. Urban objects are no exception and are guided by bilateral or radial symmetry. Symmetry has been used as a feature for object detection in images, although in many cases, the objects are not acquired in their entirety, so the symmetry detection is greatly complicated or not applicable. The same problem occurs in point clouds, Mobile Laser Scanning (MLS) technology allows acquiring 3D urban environments in precise and fast way and allows mapping the elements of the urban scene. Urban objects, although symmetrical, are often acquired partially.

This work studies the occlusions of urban objects and the relationship with the symmetry and the MLS acquisition trajectory. In the case of vehicles, objects with bilateral symmetry, a new automatic method is presented to correct the occlusions in vehicles by reflecting the point cloud with respect to the symmetry axis of the vehicle. The proposed method consists of three phases: (1) a quasi-axis symmetry is generated in the partially acquired object, (2) the point cloud is reflected, and (3) the input point cloud and the reflected point cloud are registered using the ICP algorithm. The method has been tested on data acquired with Terrestrial Laser Scanning to quantify the registration error and MLS for evaluation the results on large urban scenes.

One of the main questions of fundamental physics is the problem of the asymmetry matter/antimatter in the universe and the action of gravity on antimatter. Tests on antimatter gravity have currently a limited precision, with the sign of gravity acceleration not yet known experimentally. Ambitious projects are developed at CERN facilities to produce low energy antihydrogen with the aim of measuring the free fall of antihydrogen atoms. Among them, the GBAR experiment (Gravitational Behaviour of Antihydrogen at Rest) aims at measuring the gravity acceleration of antihydrogen atoms during a free fall in Earth’s gravitational field. The simulation of the free-fall chamber includes the Monte-Carlo generation of trajectories and the statistical analysis. A precision of the measurement beyond the % level is confirmed by taking into account the experimental design. We also propose a new method using quantum reflection of antiatoms above a reflecting mirror followed by a classical free fall; the quantum interference pattern obtained at detection improves the accuracy of the experiment by approximately 3 orders of magnitude.

In general, a mathematical model that contains many linear/nonlinear differential equations, describing a phenomenon, does not have an explicit hierarchy of system variables. That is, the identification of the fast variables and the slow variables of the system is not explicitly clear. The decomposition of a system into fast and slow subsystems is usually based on intuitive ideas and knowledge of the mathematical model being investigated. In this study, we apply the singular perturbed vector field (SPVF) method to the COVID-19 mathematical model to expose the hierarchy of the model. This decomposition enables us to rewrite the model in new coordinates in the form of fast and slow subsystems and, hence, to investigate only the fast subsystem with different asymptotic methods. In addition, this decomposition enables us to investigate the stability analysis of the model, which is important in the case of COVID-19. We found the stable equilibrium points of the mathematical model and compared the results of the model with those reported by the Chinese authorities and found a fit of approximately 96%.

It is shown that the two component Fermi or Bose many-body Hamiltonian, such as the two-orbit fermion pairing and two-site Bose-Hubbard model with arbitrary finite higher order terms can always be solved exactly by using Bethe ansatz vector construction based on the permutation of two components of bosons or fermions involved. As examples of the solution, the extended one-dimensional dimer Bose -Hubbard model with multi-body interactions and the mean-fifield plus orbit-dependent non-separable pairing model with two non-degenerate j-orbits are demonstrated with the eigenstates and the eigen-energy and the related Bethe ansatz equations. It is shown that the main feature of the solutions lies in the fact that the Bethe ansatz vectors can be expressed in terms of binomials of the boson or fermion operators times the related symmetric functions. As the consequence, two-component quantum many-body systems , such as the extended Lipkin-Meshkov-Glick model with higher-order interactions, can be solved in a similar way.