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Methods. We performed measurements of the \MgII, \MgI, \FeIIa, \FeIIb, and \FeIIc\ spectral lines present in the spectra of the selected sample to determine the EW and velocity of the flows observed in the star-forming galaxies. Subsequently, we conducted $10^7$ bootstrap simulations using Spearman's rank correlation coefficient ($\rho_s$) to explore correlations with galaxy properties. Furthermore, we calculated the covering factor, gas density, and optical depth for the measured \ion{Fe}{II} doublets. Results. Our analysis revealed strong correlations between the EW of \ion{Mg}{II} lines and both $M_{*}$ ($\rho_s=0.43$, 4.5$\sigma$) and SFR ($\rho_s=0.42$, 4.4$\sigma$). For the \ion{Fe}{II} lines, we observed strong correlations between the EW and SFR ($\rho_s\sim0.65$, $>3.9\sigma$), with a weaker correlation for $M_{*}$ ($\rho_s\sim0.35$, $>1.9\sigma$). No notable correlations were found between velocity measurements of \ion{Mg}{II} line and $M_{*}$, SFR, or sSFR of the objects ($\rho_s\sim0.1)$. However, a negative strong correlation was found between the velocity of the \ion{Fe}{II} lines and the SFR of the galaxies ($\rho_s\sim-0.45$, $\sim3\sigma$). Our results align with previous studies but studying FIR-selected objects. Finally, we detected a candidate \textit{loitering outflow}, a recently discovered subtype of FeLoBAL quasar, at redshift of $z=1.4399$, exhibiting emission in \ion{C}{III}] and low line velocities ($|v|\lesssim$ 200 km/s)., Comment: 25 pages, 31 figures

Heart diseases are the main international cause of human defunction. According to the WHO, nearly 18 million people decease each year because of heart diseases. Also considering the increase of medical data, much pressure is put on the health industry to develop systems for early and accurate heart disease recognition. In this work, an automatic cardiac pathology recognition system based on a novel deep learning framework is proposed, which analyses in real-time echocardiography video sequences. The system works in two stages. The first one transforms the data included in a database of echocardiography sequences into a machine-learning-compatible collection of annotated images which can be used in the training stage of any kind of machine learning-based framework, and more specifically with deep learning. This includes the use of the Higher Order Dynamic Mode Decomposition (HODMD) algorithm, for the first time to the authors' knowledge, for both data augmentation and feature extraction in the medical field. The second stage is focused on building and training a Vision Transformer (ViT), barely explored in the related literature. The ViT is adapted for an effective training from scratch, even with small datasets. The designed neural network analyses images from an echocardiography sequence to predict the heart state. The results obtained show the superiority of the proposed system and the efficacy of the HODMD algorithm, even outperforming pretrained Convolutional Neural Networks (CNNs), which are so far the method of choice in the literature.

Convection-permitting models (CPMs) enable the representation of meteorological variables at horizontal high resolution spatial scales (higher than 4 km), where convection plays a significant role. Physical schemes need to be evaluated considering factors in the studied region such as orography and climate variability. This study investigates the sensitivity of the WRF model as CPM to the use of different physics schemes on Andalusia, a complex orography region in southern Iberian Peninsula (IP). A set of 1-year WRF simulations was completed based on two one-way nested domains: the parent domain (d01) spanning the entire IP with 5 km spatial resolution and the nested domain (d02) for the region of Andalusia at 1 km of spatial resolution. 12 physic schemes were examined from combinations of microphysics (MP) schemes including THOMPSON, WRF single moment 6-class (WSM6), and WRF single moment 7-class (WSM7), and different options for the convection in d01, the Grell 3D (G3), Grell-Freitas (GF), Kain-Fritsch (KF), and deactivated cumulus parameterization (OFF). The simulated precipitation and 2-m temperature for the year 2018, a very wet year, were compared with observational datasets to determine the optimal WRF configuration, including point-to-point and station-point comparisons at different time aggregations. In general, greater differences were shown when comparing the results of convection schemes in d01. Simulations completed with GF or OFF presented better performance compared to the reference datasets. Concerning the MP, although THOMPSON showed a better fit in high mountain areas, it generally presents a worse agreement with the reference datasets. In terms of temperature, the results were very similar and, therefore, the selection of the best configuration was based mainly on the precipitation results with the WSM7-GF scheme being suitable for Andalusia region.

The formation redshift and abundance of the first stars and galaxies is highly sensitive to the build up of low mass dark matter halos as well as astrophysical feedback effects which modulate star formation in these low mass halos. The 21-cm signal at cosmic dawn will depend strongly on the formation of these first luminous sources and thus can be used to constrain unknown astrophysical and dark matter properties in the early universe. In this paper, we explore how well we could measure properties of dark matter using the 21-cm power spectrum at $z>10$, given unconstrained astrophysical parameters. We create a generalizable form of the dark matter halo mass function for models with damped and/or oscillatory linear power spectra, finding a single "smooth-k" window function which describes a broad range of models including CDM. We use this to make forecasts for structure formation using the Effective Theory of Structure Formation (ETHOS) framework to explore a broad parameter space of dark matter models. We make predictions for the 21-cm power spectrum observed by HERA varying both cosmological ETHOS parameters as well as astrophysical parameters. Using a Markov Chain Monte Carlo forecast we find that the ETHOS dark matter parameters are degenerate with astrophysical parameters linked to star formation in low mass dark matter halos but not with X-ray heating produced by the first generation of stars. After marginalizing over uncertainties in astrophysical parameters we demonstrate that with just 540 days of HERA observations it should be possible to distinguish between CDM and a broad range of dark matter models with suppression at wavenumbers $k\lesssim 200\,h$Mpc$^{-1}$ assuming a moderate noise level. These results demonstrate the potential of 21-cm observations to constrain the matter power spectrum on scales smaller than current probes., Comment: 13 pages, 9 figures, submitted to PRD

Surface stiffnesses engender steady patterns of Faraday waves (FWs), so called hydrodynamic crystals as correspond to ordered wave lattices made of discrete subharmonics under monochromatic driving. Mastering rules are both inertia-imposed parametric resonance for frequency-halving together with rigidity-driven nonlinearity for wavefield self-focusing. They harness the discretization needed for coherent FW-packets to localize in space and time. Collective lattice excitations are observed as dispersionless propagating dislocations that lead periodic modulations arising from explicit symmetry breaking. In a field theory perspective, a halving genesis for the collective distorting modes is revealed as the natural pathway for hydrodynamic crystal melting.

The main purpose of this paper is to study both the underdamped and the overdamped dynamics of the nonlinear Helmholtz oscillator with a fractional order damping. For that purpose, we use the Grunwald-Letnikov fractional derivative algorithm in order to get the numerical simulations. Here, we investigate the effect of taking the fractional derivative in the dissipative term in function of the parameter a. Our main findings show that the trajectories can remain inside the well or can escape from it depending on a which plays the role of a control parameter. Besides, the parameter a is also relevant for the creation or destruction of chaotic motions. On the other hand, the study of the escape times of the particles from the well, as a result of variations of the initial conditions and the undergoing force F, is reported by the use of visualization techniques such as basins of attraction and bifurcation diagrams, showing a good agreement with previous results. Finally, the study of the escape times versus the fractional parameter a shows an exponential decay which goes to zero when a is larger than one. All the results have been carried out for weak damping where chaotic motions can take place in the non-fractional case and also for a stronger damping (overdamped case), where the influence of the fractional term plays a crucial role to enhance chaotic motions. We expect that these results can be of interest in the field of fractional calculus and its applications.

Most of the observed galaxies cannot be resolved into individual stars and are studied through their integrated spectrum using simple stellar populations (SSPs) models, with stellar libraries being a key ingredient in building them. Spectroscopic observations are increasingly being directed towards the near-infrared (NIR), where much is yet to be explored. SSPs in the NIR are still limited, and there are inconsistencies between different sets of models. One of the ways to minimize this problem is to have reliable NIR stellar libraries. The main goal of this work is to present SMARTY (mileS Moderate resolution neAr-infRared sTellar librarY) a ~0.9-2.4$\mu$m stellar spectral library composed of 31 stars observed with the Gemini Near-IR Spectrograph (GNIRS) at the 8.1m Gemini North telescope and make it available to the community. The stars were chosen from the SMARTY library, for which the atmospheric parameters are reliable (and well tested), to populate different regions of the Hertzsprung-Russell (HR) diagram. Furthermore, five of these stars have NIR spectra available that we use to assess the quality of SMARTY. The remaining 26 stars are presented for the first time in the NIR. We compared the observed SMARTY spectra with synthetic and interpolated spectra, finding a mean difference of ~20% in the equivalent widths and ~1% in the overall continuum shape in both sets of comparisons. We computed the spectrophotometric broadband magnitudes and colours and compared them with the 2MASS ones, resulting in mean differences up to 0.07 and 0.10mag in magnitudes and colours, respectively. In general, a small difference was noted between the SMARTY spectra corrected using the continuum from the interpolated and the theoretical stars.

We introduce a surveillance strategy specifically designed for urban areas to enhance preparedness and response to disease outbreaks by leveraging the unique characteristics of human behavior within urban contexts. By integrating data on individual residences and travel patterns, we construct a Mixing matrix that facilitates the identification of critical pathways that ease pathogen transmission across urban landscapes enabling targeted testing strategies. Our approach not only enhances public health systems' ability to provide early epidemiological alerts but also underscores the variability in strategy effectiveness based on urban layout. We prove the feasibility of our mobility-informed policies by mapping essential mobility flows to major transit stations, showing that few resources focused on specific stations yields a more effective surveillance than non-targeted approaches. This study emphasizes the critical role of integrating human behavioral patterns into epidemic management strategies to improve the preparedness and resilience of major cities against future outbreaks., Comment: 12 pages, 5 figures. Supplementary Material: 5 pages, 5 figures, 1 table

This study delves into the intricate kinematic behavior of ionized gas within IZw18, a galaxy known for its remarkably low metallicity and proximity. Leveraging data from MEGARA/GTC, we meticulously analyzed the galaxy's structure and dynamics using H{\alpha} line profiles. Employing single and double Gaussian component fittings, we generated detailed maps of luminosity, velocity, and velocity dispersion across both the main body (MB) and Halo regions. By extracting integrated spectra from various galactic zones, we enhanced the signal-to-noise (S/N) ratio. In the MB, a clear rotational pattern emerged, supplemented by a more intricate kinematic structure from the double-component fitting, notably featuring a broad component with a FWHM nearing 2000 km/s. This broad component, exhibiting wide spatial extension, hints at a high-energy outflow and suggests non-localized sources of significant kinetic energy. The considerable velocity disparities between narrow and broad components imply potential spatial segregation, possibly due to dense gas near the kinematic origin acting as a momentum-reflection 'wall'. Examining the halos, the NE Halo appears tranquil with low velocity dispersions, while the SW Halo displays higher velocities and complex kinematics, indicative of varied dynamic interactions. The presence of the broad component throughout the MB and the intricate kinematics across all regions suggests widespread and subtle turbulent motion. This nuanced understanding of IZw18's kinematic behavior, elucidating the interplay of gas components and internal structures, enriches our comprehension of dynamics in blue compact dwarf galaxies. It holds promise for shedding light on early galaxy formation and the complex kinematics inherent to such environments.

Methods.We applied distinct selection criteria to attain an SFG sample with minimal AGN contamination. Multiple approaches were used to estimate the intrinsic extinction, SFR and gas-phase metallicity for the SFGs. In conjunction with findings in the literature, we examined the correlation between SFRs and stellar masses ($M_*$), as well as the metallicity evolution depending on $M_*$. Finally, the 3D relationship between $M_*$, SFR and metallicity, is also studied.} Results. From the initial spectroscopic sample of 409 FIR-selected objects from the Lockman--SpReSO catalogue, 69 (17\%) AGNs have been identified and excluded, which is nearly double the percentage found in local studies, leaving a sample of 340 SFGs. The analysis of the $M_*$--SFR relationship revealed that Lockman--SpReSO IR-selected SFGs show signs of evolution at redshifts $z>0.4$, shifting above the main sequence, with a mean value of $\sim0.4$ dex. They are located within the starburst galaxy region since 78\% of the galaxies fall into this category. In addition, no evident flattening was found in the relation to specific SFR with redshift for $\log M_* (M_\odot) \gtrsim 10.5$. In line with the $M_*$--metallicity relation (MZR) outcomes published in previous studies for optically selected SFGs, however, during the analysis of the MZR, it was found that IR-selected SFGs exhibit lower metallicities than those anticipated on the basis of their $M_*$ and redshift. During the investigation of the 3D $M_*$--SFR--metallicity relation (FP), it was established that the research sample is consistent with relations in the existing literature, with an average scatter of $\sim0.2$ dex. However, a re-calibration of the FP when using the SFR obtained from the IR luminosity is required and, in this case, no attenuation in the correlation for $\log M_* (M_\odot) \gtrsim 10.5$ is observed., Comment: 21 pages, 17 figures, accepted in A&A

We analyze the nonlinear Helmholtz oscillator in the presence of fractional damping, a characteristic feature in several physical situations. In our specific scenario, as well as in the non-fractional case, for large enough excitation amplitudes, all initial conditions are escaping from the potential well. To address this, we incorporate the phase control technique into a parametric term, a feature commonly encountered in real-world situations. In the non-fractional case it has been shown that, a phase difference of {\phi_{OPT}} \simeq {\pi}, is the optimal value to avoid the escapes of the particles from the potential well. Here, our investigation focuses on understanding when particles escape, considering both the phase difference {\phi} and the fractional parameter {\alpha} as control parameters. Our findings unveil the robustness of phase control, as evidenced by the consistent oscillation of the optimal {\phi} value around its non-fractional counterpart when varying the fractional parameter. Additionally, our results underscore the pivotal role of the fractional parameter in governing the proportion of bounded particles, even when utilizing the optimal phase.

Accurate quantification of Gross Primary Production (GPP) is crucial for understanding terrestrial carbon dynamics. It represents the largest atmosphere-to-land CO$_2$ flux, especially significant for forests. Eddy Covariance (EC) measurements are widely used for ecosystem-scale GPP quantification but are globally sparse. In areas lacking local EC measurements, remote sensing (RS) data are typically utilised to estimate GPP after statistically relating them to in-situ data. Deep learning offers novel perspectives, and the potential of recurrent neural network architectures for estimating daily GPP remains underexplored. This study presents a comparative analysis of three architectures: Recurrent Neural Networks (RNNs), Gated Recurrent Units (GRUs), and Long-Short Term Memory (LSTMs). Our findings reveal comparable performance across all models for full-year and growing season predictions. Notably, LSTMs outperform in predicting climate-induced GPP extremes. Furthermore, our analysis highlights the importance of incorporating radiation and RS inputs (optical, temperature, and radar) for accurate GPP predictions, particularly during climate extremes., Comment: Accepted at IGARSS24

Let's imagine that in a few years generative AI has changed software development dramatically, taking charge of most of the programming tasks. Let's also assume that extended reality devices became ubiquitous, being the preferred interface for interacting with computers. This paper proposes how this situation would impact IDEs, by exploring how the development process would be affected, and analyzing which tools would be needed for supporting developers.

Preceding a core-collapse supernova, various processes produce an increasing amount of neutrinos of all flavors characterized by mounting energies from the interior of massive stars. Among them, the electron antineutrinos are potentially detectable by terrestrial neutrino experiments such as KamLAND and Super-Kamiokande via inverse beta decay interactions. Once these pre-supernova neutrinos are observed, an early warning of the upcoming core-collapse supernova can be provided. In light of this, KamLAND and Super-Kamiokande, both located in the Kamioka mine in Japan, have been monitoring pre-supernova neutrinos since 2015 and 2021, respectively. Recently, we performed a joint study between KamLAND and Super-Kamiokande on pre-supernova neutrino detection. A pre-supernova alert system combining the KamLAND detector and the Super-Kamiokande detector was developed and put into operation, which can provide a supernova alert to the astrophysics community. Fully leveraging the complementary properties of these two detectors, the combined alert is expected to resolve a pre-supernova neutrino signal from a 15 M$_{\odot}$ star within 510 pc of the Earth, at a significance level corresponding to a false alarm rate of no more than 1 per century. For a Betelgeuse-like model with optimistic parameters, it can provide early warnings up to 12 hours in advance., Comment: Resubmitted to ApJ. 22 pages, 16 figures, for more information about the combined pre-supernova alert system, see https://www.lowbg.org/presnalarm/

A classical inequality by Gr\"unbaum provides a sharp lower bound for the ratio $\mathrm{vol}(K^{-})/\mathrm{vol}(K)$, where $K^{-}$ denotes the intersection of a convex body with non-empty interior $K\subset\mathbb{R}^n$ with a halfspace bounded by a hyperplane $H$ passing through the centroid $\mathrm{g}(K)$ of $K$. In this paper we extend this result to the case in which the hyperplane $H$ passes by any of the points lying in a whole uniparametric family of $r$-powered centroids associated to $K$ (depending on a real parameter $r\geq0$), by proving a more general functional result on concave functions. The latter result further connects (and allows one to recover) various inequalities involving the centroid, such as a classical inequality (due to Minkowski and Radon) that relates the distance of $\mathrm{g}(K)$ to a supporting hyperplane of $K$, or a result for volume sections of convex bodies proven independently by Makai Jr. & Martini and Fradelizi.

In this paper, we prove that flat free boundaries of solutions to inhomogeneous one-phase Stefan problem are $C^{1,\alpha}$.

We investigate the synchronization between two neurons using the stochastic version of the map-based Chialvo model. To simulate non-identical neurons, a mismatch is introduced in one of the main parameters of the model. Subsequently, the synchronization of the neurons is studied as a function of this mismatch, the noise introduced in the stochastic model, and the coupling strength between the neurons. We propose the simplest neuron network for study, as its analysis is more straightforward and does not compromise generality. Within this network, two nonidentical neuron maps are electrically coupled. In order to understand if specific behaviors affect the global behavior of the system, we consider different cases related to the behavior of the neurons (chaotic or periodic). Furthermore, we study how variations in model parameters affect the firing frequency in all cases. Additionally, we consider that the two neurons have both excitatory and inhibitory couplings. Consequently, we identify critical values of noise and mismatch for achieving satisfactory synchronization between the neurons in both cases. Finally, we conjecture that the results are of a general nature and are applicable to different neuron models.

We apply the in-in formalism to address the question of whether the size of the one-loop spectrum of curvature fluctuations in ultra-slow-roll inflation models designed for producing a large population of primordial black holes implies a breakdown of perturbation theory. We consider a simplified piece-wise description of inflation, in which the ultra-slow-roll phase is preceded and followed by slow-roll phases linked by transitional periods. We work in the $\delta\phi$-gauge, including all relevant cubic and quartic interactions and the necessary counterterms to renormalize the ultraviolet divergences, regularized by a cutoff. The ratio of the one-loop to the tree-level contributions to the spectrum of curvature perturbations is controlled by the duration of the ultra-slow-roll phase and of the transitions. Our results indicate that perturbation theory does not necessarily break in well-known models proposed to account for all the dark matter in the form of primordial black holes., Comment: Accepted in JCAP

We consider the damped nonlinear Schr\''{o}dinger equation with saturation: i.e., the complex evolution equation contains in its left hand side, besides the potential term $V(x)u,$ a nonlinear term of the form $\mathrm{i}\mu u(t,x)/|u(t,x)|$ for a given parameter $\mu >0$ (arising in optical applications on non-Kerr-like fibers). In the right hand side we assume a given forcing term $f(t,x).$ The important new difficulty, in contrast to previous results in the literature, comes from the fact that the spatial domain is assumed to be unbounded. We start by proving the existence and uniqueness of weak and strong solutions according the regularity of the data of the problem. The existence of solutions with a lower regularity is also obtained by working with a sequence of spaces verifying the Radon-Nikod\'{y}m property. Concerning the asymptotic behavior for large times we prove a strong stabilization result. For instance, in the one dimensional case we prove that there is extinction in finite time of the solutions under the mere assumption that the $L^\infty$-norm of the forcing term $f(t,x)$ becomes less than $\mu$ after a finite time. This presents some analogies with the so called feedback \textit{bang-bang controls} $v$ (here $v=-\mathrm{i}\mu u/|u|+f).$

At the current pace of technological advancements, Generative AI models, including both Large Language Models and Large Multi-modal Models, are becoming integral to the developer workspace. However, challenges emerge due to the 'black box' nature of many of these models, where the processes behind their outputs are not transparent. This position paper advocates for a 'white box' approach to these generative models, emphasizing the necessity of transparency and understanding in AI-generated code to match the proficiency levels of human developers and better enable software maintenance and evolution. We outline a research agenda aimed at investigating the alignment between AI-generated code and developer skills, highlighting the importance of responsibility, security, legal compliance, creativity, and social value in software development. The proposed research questions explore the potential of white-box methodologies to ensure that software remains an inspectable, adaptable, and trustworthy asset in the face of rapid AI integration, setting a course for research that could shape the role of code proficiency into 2030 and beyond., Comment: submitted to Software Engineering 2030

surfQuake is a new software designed to streamline the estimation of seismic source parameters. Its comprehensive set of toolboxes automate the determination of seismic arrival times, event association and locations, moment magnitude from P- or S- wave displacement spectra and moment tensor inversions within a Bayesian framework. surfQuake is programmed in Python 3 and offers the users the possibility of three programming levels for flexibility and customization. The core library allows users to integrate the core of surfQuake into their preexisting scripts, giving advanced users full control, while the Command Line Interface gives users access to an upper layer that simplifies the use of the core. Alternatively, surfQuake core is wrapped by a Graphical User Interface (GUI) and connected to a SQLite database making it accessible to users with little coding experience. The software has been fully tested with an earthquake cluster of more than 2000 events, that occurred in central Pyrenees in 2021-22. The source parameters retrieved from the cluster and the basic statistics associated with them are displayed using the surfQuake database toolbox. Additionally, we offer a web tutorial with the documentation of surfQuake and a set of usage examples for the three programming levels., Comment: 32 pages, 7 figures

In this paper, we study different types of phase space structures which appear in the context of relativistic chaotic scattering. By using the relativistic version of the H\'{e}non-Heiles Hamiltonian, we numerically study the topology of different kind of exit basins and compare it with the case of low velocities in which the Newtonian version of the system is valid. Specifically, we numerically study the escapes in the phase space, in the energy plane and also in the $\beta$ plane which richly characterize the dynamics of the system. In all cases, fractal structures are present, and the escaping dynamics is characterized. Besides, in every case a scaling law is numerically obtained in which the percentage of the trapped trajectories as a function of the relativistic parameter $\beta$ and the energy is obtained. Our work could be useful in the context of charged particles which eventually can be trapped in the magnetosphere, where the analysis of these structures can be relevant.

In this proceedings a solution of the target-rapidity Balitsky-Kovchegov (BK) equation is presented considering the complete impact-parameter dependence, including the orientation of the dipole with respect to the impact-parameter vector. The target-rapidity formulation of the BK equation introduces non-locality in rapidity. Three different prescriptions are considered to take into account the rapidities preceding the initial condition. The solutions are used to compute the structure functions of the proton and the diffractive photo- and electro-production of J/{\psi} off protons. The predictions agree well with HERA data, confirming that the target-rapidity Balitsky-Kovchegov equation with the full impact-parameter dependence is a viable tool to study the small Bjorken-x limit of perturbative QCD at current facilities like RHIC and LHC as well as in future colliders like the EIC., Comment: 1st International Workshop on the physics of Ultra Peripheral Collisions (UPC 2023)

In this paper, we investigate a two-dimensional photonic array featuring a circular shape and an alternating gain and loss pattern. Our analysis revolves around determining the presence and resilience of optical ring modes with varying vorticity values. This investigation is conducted with respect to both the array's length and the strength of the non-Hermitian parameter. For larger values of array's length, we observe a reduction in the stability domain as the non-Hermitian parameter increases. Interestingly, upon an increasing of vorticity of the optical modes full stability windows emerge for shorter lattice sizes regime.

In studies of quantum squeezing, the emphasis is typically placed more on specific squeezed states and their evolution rather than on the dynamical operations that could simultaneously squeeze a broader range of quantum states, regardless of their initial configuration. We explore new developments in this area, facilitated by gently acting external fields which might induce squeezing of the canonical observables $q$ and $p$ in charged particles. The extensive research in this field has yielded many valuable insights, raising the question of whether there is still room for significant new contributions to our understanding. Nonetheless, we present some exactly solvable instances of this problem, observed in symmetric evolution intervals. These intervals allow for the explicit determination of the temporal dependence of external fields necessary to generate the required evolution operators. Our findings are linked with a straightforward application of Toeplitz matrices, offering a more accessible description of the problem compared to the frequently employed Ermakov-Milne invariants., Comment: arXiv admin note: text overlap with arXiv:1704.05840

The possibility that quantum geometry effects may alleviate the apparent tensions existing at large angular scales in the observations of the Cosmic Microwave Background explains the increasing interest in considering primordial perturbations within the framework of Loop Quantum Cosmology. In this framework, a number of approximations have been suggested to simplify the study of perturbations and derive analytic expressions for the power spectra. This study requires a new choice of vacuum state that takes into account the preinflationary background geometry, choice for which we adopt the so-called NO-AHD prescription. Here, we apply the aforementioned approximations to the investigation of scalar perturbations. We discuss two approaches to the quantization of perturbations in Loop Quantum Cosmology, namely the hybrid and the dressed metric approaches. We improve previous approximations by including slow-roll corrections in the inflationary era. Moreover, for the first time in the literature of the NO-AHD prescription, we compute numerically the primordial power spectra for the two considered approaches, and show that the analytic estimations are remarkably accurate for all observable modes. We also discuss the similarities and differences between the spectra obtained with those two approaches., Comment: 13 pages, 4 figures

The flux of ultra-high energy cosmic rays reaching Earth above the ankle energy (5 EeV) can be described as a mixture of nuclei injected by extragalactic sources with very hard spectra and a low rigidity cutoff. Extragalactic magnetic fields existing between the Earth and the closest sources can affect the observed CR spectrum by reducing the flux of low-rigidity particles reaching Earth. We perform a combined fit of the spectrum and distributions of depth of shower maximum measured with the Pierre Auger Observatory including the effect of this magnetic horizon in the propagation of UHECRs in the intergalactic space. We find that, within a specific range of the various experimental and phenomenological systematics, the magnetic horizon effect can be relevant for turbulent magnetic field strengths in the local neighbourhood of order $B_{\rm rms}\simeq (50-100)\,{\rm nG}\,(20\rm{Mpc}/{d_{\rm s})( 100\,\rm{kpc}/L_{\rm coh}})^{1/2}$, with $d_{\rm s}$ the typical intersource separation and $L_{\rm coh}$ the magnetic field coherence length. When this is the case, the inferred slope of the source spectrum becomes softer and can be closer to the expectations of diffusive shock acceleration, i.e., $\propto E^{-2}$. An additional cosmic-ray population with higher source density and softer spectra, presumably also extragalactic and dominating the cosmic-ray flux at EeV energies, is also required to reproduce the overall spectrum and composition results for all energies down to 0.6~EeV., Comment: Matches published version