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As an alternative to the popular parametrisations of the dark energy equation of state, we construct a quintessence model where the scalar field has a linear dependence on the number of e-folds. Constraints on more complex models are typically limited by the degeneracies that increase with the number of parameters. The proposed parametrisation conveniently constrains the evolution of the dark energy equation of state as it allows for a wide variety of time evolutions. We also consider a non-minimal coupling to cold dark matter. We fit the model with Planck and KiDS observational data. The CMB favours a non-vanishing coupling with energy transfer from dark energy to dark matter. Conversely, gravitational weak lensing measurements slightly favour energy transfer from dark matter to dark energy, with a substantial departure of the dark energy equation of state from -1.

Several types of sensors have been available in off-the-shelf mobile devices, including motion, magnetic, vision, acoustic, and location sensors. This paper focuses on the fusion of the data acquired from motion and magnetic sensors, i.e., accelerometer, gyroscope and magnetometer sensors, for the recognition of Activities of Daily Living (ADL) using pattern recognition techniques. The system developed in this study includes data acquisition, data processing, data fusion, and artificial intelligence methods. Artificial Neural Networks (ANN) are included in artificial intelligence methods, which are used in this study for the recognition of ADL. The purpose of this study is the creation of a new method using ANN for the identification of ADL, comparing three types of ANN, in order to achieve results with a reliable accuracy. The best accuracy was obtained with Deep Learning, which, after the application of the L2 regularization and normalization techniques on the sensors data, reports an accuracy of 89.51%.

A well-known problem of the $\Lambda$CDM model is the tension between the relatively high level of clustering, as quantified by the parameter $\sigma_8$, found in cosmic microwave background experiments and the smaller one obtained from large-scale observations in the late Universe. In this paper we show that coupled quintessence, i.e. a single dark energy scalar field conformally coupled to dark matter through a constant coupling, can solve this problem if the background is taken to be identical to the $\Lambda$CDM one. We show that two competing effects arise. On one hand, the additional scalar force is attractive, and is therefore expected to increase the clustering. On the other, in order to obtain the same background as $\Lambda$CDM, coupled quintessence must have a smaller amount of dark matter near the present epoch. We show that the second effect is dominating today and leads to an overall slower growth. Comparing to redshift distortion data, we find that coupled quintessence with $\Lambda$CDM background solves the tension between early and late clustering. We find for the coupling $\beta$ and for $\sigma_8$ the best fit values $|\beta| = 0.079^{+ 0.059}_{- 0.067}$ and $\sigma_8 = 0.818^{+0.115}_{-0.088}$. These values also fit the lensing data from the KiDS-450 survey. We also estimate that the future missions SKA and Euclid will constrain $\beta$ with an error of $\pm\, 1.5\times10^{-3}$ and for $\sigma_8$ of $\pm \,1.8\times10^{-3}$ at $1\sigma$ level.

In this study, we meticulously construct a 3-form Lagrangian designed to mimic the dynamics of both dust matter in the past and dark energy driving the acceleration in the present era. A dynamical systems approach is used to investigate the underlying behavior of the cosmological background. By investigating the influence of the potential slope and initial conditions on the dynamical solutions, we identify distinct viable scenarios capable of replicating a De Sitter universe in the present epoch. An intriguing aspect of the model is the existence of solutions describing multiple inflationary phases in which the 3-form self-interacting potential decays rapidly.

We generalize E. Verlinde's entropic gravity reasoning to a phase-space noncommutativity set-up. This allow us to impose a bound on the product of the noncommutative parameters based on the Equivalence Principle. The key feature of our analysis is an effective Planck's constant that naturally arises when accounting for the noncommutative features of the phase-space.

We are studying the fundamental tools for a quantum calculus based on the Tsallis $q$-exponential In particular we are looking at $q$-Fock spaces, structural identities, as well as rational functions in this context.

We address the question of the appearence of ordinary quantum mechanics in the context of noncommutative quantum mechanics. We obtain the noncommutative extension of the Hu-Paz-Zhang master equation for a Brownian particle linearly coupled to a bath of harmonic oscillators. We consider the particular case of an Ohmic regime.

We review the construction of the path integral and the corresponding effective action for the Regge formulation of General Relativity under the assumption that the short-distance structure of the spacetime is not a smooth 4-manifold, but a picewise linear manifold based on a triangulation of a smooth 4-manifold. We point out that the exponentially damped 4-volume path-integral measure does not give a finite path integral, although it can be used for the construction of the perturbative effective action. We modify the 4-volume measure by multiplying it by an inverse power of the product of the edge-lengths such that the new measure gives a finite path integral while it retains all the nice features of the unmodified measure.

Forecast constraints for a Symmetric Teleparallel Gravity model with a $\Lambda$CDM background are made using forthcoming ground and space based gravitational waves observatories. A Bayesian analysis resorting to generated mock catalogs shows that LIGO is not expected to be able to distinguish this model from $\Lambda$CDM, while both LISA and the ET will, with the ET outperforming LISA. We also show that low redshift events are favored in order to improve the quality of the constrains.