Time dependent couplings in the dark sector: from background evolution to nonlinear structure formation

We present a complete numerical study of cosmological models with a time dependent coupling between the dark energy component driving the present accelerated expansion of the Universe and the Cold Dark Matter (CDM) fluid. Depending on the functional form of the coupling strength, these models show a range of possible intermediate behaviors between the standard LCDM background evolution and the widely studied case of interacting dark energy models with a constant coupling. These different background evolutions play a crucial role in the growth of cosmic structures, and determine strikingly different effects of the coupling on the internal dynamics of nonlinear objects. By means of a suitable modification of the cosmological N-body code GADGET-2 we have performed a series of high-resolution N-body simulations of structure formation in the context of interacting dark energy models with variable couplings. Depending on the type of background evolution, the halo density profiles are found to be either less or more concentrated with respect to LCDM, contrarily to what happens for constant coupling models where concentrations can only decrease. However, for some specific choice of the interaction function the reduction of halo concentrations can be larger than in constant coupling scenarios. In general, we find that time dependent interactions between dark energy and CDM can in some cases determine stronger effects on structure formation as compared to the constant coupling case, with a significantly weaker impact on the background evolution of the Universe, and might therefore provide a more viable possibility to alleviate the tensions between observations and the LCDM model on small scales than the constant coupling scenario. [Abridged]Comment: 27 pages, 17 figures, 3 tables. Minor revisions. MNRAS accepte

The nonlinear evolution of large scale structures in Growing Neutrino cosmologies

We present the results of the first N-body simulations of the Growing Neutrino scenario, as recently discussed in Baldi et al. (2011). Our results have shown for the first time how neutrino lumps forming in the context of Growing Neutrino cosmologies are expected to pulsate as a consequence of the rapid oscillations of the dark energy scalar field. We have also computed for the first time a realistic statistical distribution of neutrino halos and determined their impact on the underlying Cold Dark Matter structures.Comment: 4 pages, 2 Figures. To appear in the Proceedings Volume of the Conference "Advances in computational astrophysics", Cefalu' (Italy), 13-17 June 201

The new class of FR0 radio galaxies

Are the FRI and FRII radio galaxies representative of the radio-loud (RL) AGN population in the local Universe? Recent studies on the local low-luminosity radio sources cast lights on an emerging population of compact radio galaxies which lack extended radio emission. In a pilot JVLA project, we study the high-resolution images of a small but representative sample of this population. The radio maps reveal compact unresolved or slightly resolved radio structures on a scale of 1-3 kpc. We find that these RL AGN live in red massive early-type galaxies, with large black hole masses ($\gtrsim$10$^{8}$ M$_{\odot}$), and spectroscopically classified as Low Excitation Galaxies, all characteristics typical of FRI radio galaxies which they also share the same nuclear luminosity with. However, they are more core dominated (by a factor of $\sim$30) than FRIs and show a clear deficit of extended radio emission. We call these sources 'FR0' to emphasize their lack of prominent extended radio emission. A posteriori, other compact radio sources found in the literature fulfill the requirements for a FR0 classification. Hence, the emerging FR0 population appears to be the dominant radio class of the local Universe. Considering their properties we speculate on their possible origins and the possible cosmological scenarios they imply.Comment: 5 pages, 3 figures. Submitted for publication in Astronomische Nachrichten. Contribution to the proceedings of the 5th Workshop on CSS and GPS radio sources, held in Rimini (Italy) in May 201

Periodic solutions of forced Kirchhoff equations

We consider Kirchhoff equations for vibrating bodies in any dimension in presence of a time-periodic external forcing with period 2pi/omega and amplitude epsilon, both for Dirichlet and for space-periodic boundary conditions. We prove existence, regularity and local uniqueness of time-periodic solutions of period 2pi/omega and order epsilon, by means of a Nash-Moser iteration scheme. The results hold for parameters (omega, epsilon) in Cantor sets having measure asymptotically full as epsilon tends to 0. (What's new in version 2: the case of finite-order Sobolev regularity, the case of space-periodic boundary conditions, a different iteration scheme in the proof, some references).Comment: 23 page

Early massive clusters and the bouncing coupled dark energy

The abundance of the most massive objects in the Universe at different epochs is a very sensitive probe of the cosmic background evolution and of the growth history of density perturbations, and could provide a powerful tool to distinguish between a cosmological constant and a dynamical dark energy field. In particular, the recent detection of very massive clusters of galaxies at high redshifts has attracted significant interest as a possible indication of a failure of the standard LCDM model. Several attempts have been made in order to explain such detections in the context of non-Gaussian scenarios or interacting dark energy models, showing that both these alternative cosmologies predict an enhanced number density of massive clusters at high redshifts, possibly alleviating the tension. However, all the models proposed so far also overpredict the abundance of massive clusters at the present epoch, and are therefore in contrast with observational bounds on the low-redshift halo mass function. In this paper we present for the first time a new class of interacting dark energy models that simultaneously account for an enhanced number density of massive clusters at high redshifts and for both the standard cluster abundance at the present time and the standard power spectrum normalization at CMB. The key feature of this new class of models is the "bounce" of the dark energy scalar field on the cosmological constant barrier at relatively recent epochs. We present the background and linear perturbations evolution of the model, showing that the standard amplitude of density perturbations is recovered both at CMB and at the present time, and we demonstrate by means of large N-body simulations that our scenario predicts an enhanced number of massive clusters at high redshifts without affecting the present halo abundance. (Abridged)Comment: 11 pages, 6 figures, 2 tables. Minor changes, references added. Accepted for publication in MNRA

Logics of variable inclusion and the lattice of consequence relations

In this paper, firstly, we determine the number of sublogics of variable inclusion of an arbitrary finitary logic L with partition function. Then, we investigate their position into the lattice of consequence relations over the language of L.Comment: arXiv admin note: text overlap with arXiv:1804.08897, arXiv:1809.0676

On L\'evy's Brownian motion indexed by the elements of compact groups

We investigate positive definiteness of the Brownian kernel K(x,y)=1/2(d(x,x_0) + d(y,x_0) - d(x,y)) on a compact group G and in particular for G=SO(n).Comment: Accepted for publication. 10 page

Temporal evolution of generalization during learning in linear networks

We study generalization in a simple framework of feedforward linear networks with n inputs and n outputs, trained from examples by gradient descent on the usual quadratic error function. We derive analytical results on the behavior of the validation function corresponding to the LMS error function calculated on a set of validation patterns. We show that the behavior of the validation function depends critically on the initial conditions and on the characteristics of the noise. Under certain simple assumptions, if the initial weights are sufficiently small, the validation function has a unique minimum corresponding to an optimal stopping time for training for which simple bounds can be calculated. There exists also situations where the validation function can have more complicated and somewhat unexpected behavior such as multiple local minima (at most n) of variable depth and long but finite plateau effects. Additional results and possible extensions are briefly discussed

Neural Networks for Fingerprint Recognition

After collecting a data base of fingerprint images, we design a neural network algorithm for fingerprint recognition. When presented with a pair of fingerprint images, the algorithm outputs an estimate of the probability that the two images originate from the same finger. In one experiment, the neural network is trained using a few hundred pairs of images and its performance is subsequently tested using several thousand pairs of images originated from a subset of the database corresponding to 20 individuals. The error rate currently achieved is less than 0.5%. Additional results, extensions, and possible applications are also briefly discussed