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In this article, we propose the integration of the Holographic Multiple Input Multiple Output (HMIMO) as a transformative solution for next generation Non-Terrestrial Networks (NTNs), addressing key challenges, such as high hardware costs, launch expenses, and energy inefficiency. Traditional NTNs are constrained by the financial and operational limitations posed by bulky, costly antenna systems, alongside the complexities of maintaining effective communications in space. HMIMO offers a novel approach utilizing compact and lightweight arrays of densely packed radiating elements with real-time reconfiguration capabilities, thus, capable of optimizing system performance under dynamic conditions such as varying orbital dynamics and Doppler shifts. By replacing conventional antenna systems with HMIMO, the complexity and cost of satellite manufacturing and launch can be substantially reduced, enabling more streamlined and cost-effective satellite designs. This advancement holds significant potential to democratize space communications, making them accessible to a broader range of stakeholders, including smaller nations and commercial enterprises. Moreover, the inherent capabilities of HMIMO in enhancing energy efficiency, scalability, and adaptability position this technology as a key enabler of new use cases and sustainable satellite operations.

We study the performances of a world-wide network made by a European third-generation gravitational-wave (GW) detector, together with a 40-km Cosmic Explorer detector in the US, considering three scenarios for the European detector: (1) Einstein Telescope (ET) in its 10-km triangle configuration; (2) ET in its configuration featuring two 15-km L-shaped detectors in different sites, still taken to have all other ET characteristics (underground, and with each detector made of a high-frequency interferometer and a cryogenic low-frequency interferometer); (3) A single L-shaped underground interferometer with the ET amplitude spectral density, either with 15~km or with 20~km arm length. Overall, we find that, if a 2L configuration should be retained for ET, the network made by a single-L European underground detector together with CE-40km could already provide a very interesting intermediate step toward the construction of a full 2L+CE network, and is in any case superior to a 10-km triangle not inserted in an international network., Comment: 19 pages, 8 figures. arXiv admin note: text overlap with arXiv:2408.14946

At third-generation (3G) gravitational-wave detector networks, compact binaries coalescences produce a ``confusion noise'' due to unresolved sources and to the error in the reconstruction of resolved sources, that can degrade the sensitivity to cosmological backgrounds. We show how to characterize from first-principles this astrophysical confusion noise by reconstructing the resolved sources at a detector network, subtracting them from the data stream of each detector of the network, and then computing the correlation among detector pairs of these ``partially cleaned'' data streams that, beside instrumental noise, contain the unresolved sources and the error on the resolved sources. In a two-detector correlation, this residual astrophysical background then acts as an effective correlated noise. We point out that its effect, in the search for a cosmological background, must be evaluated by correlating two detectors with the filter function that optimizes the given cosmological search (and not the search for the astrophysical background itself) and therefore depends on the specific cosmological signal that we want to extract from the data. We show how to obtain search-independent upper bounds on the effect of this astrophysical confusion noise, and how to characterize its actual effect on a given cosmological search. We then apply this methodology to an example of a 3G network and, for a realistic population of mergers, we evaluate explicitly the upper bound on the effect of the astrophysical confusion noise, as well as its actual effect in the search of selected examples of power-law cosmological backgrounds and of backgrounds featuring broad peaks, as in phase transitions., Comment: 32 pages, 6 figures

We provide a detailed derivation of the spectral density of the stochastic background generated by the superposition of coalescing compact binaries. We show how the expression often used in the literature emerges from an average over the extrinsic parameters of the binaries (times of arrival, polarization angles, arrival directions and orbit inclinations) and how the Stokes parameters related to circular and linear polarization are set to zero by such averaging procedure. We then consider the effect of shot noise, i.e. the fact that for the superposition of a finite number of sources these averages are only approximate, and we show how it generates circular and linear polarizations (even for isotropic backgrounds) as well as spatial anisotropies, and we compute them explicitly for a realistic population of binary black holes and binary neutron stars., Comment: 21 pages, 2 figures

Machine learning (ML) has the potential to become an essential tool in supporting clinical decision-making processes, offering enhanced diagnostic capabilities and personalized treatment plans. However, outsourcing medical records to train ML models using patient data raises legal, privacy, and security concerns. Federated learning has emerged as a promising paradigm for collaborative ML, meeting healthcare institutions' requirements for robust models without sharing sensitive data and compromising patient privacy. This study proposes a novel method that combines federated learning (FL) and Graph Neural Networks (GNNs) to predict stroke severity using electroencephalography (EEG) signals across multiple medical institutions. Our approach enables multiple hospitals to jointly train a shared GNN model on their local EEG data without exchanging patient information. Specifically, we address a regression problem by predicting the National Institutes of Health Stroke Scale (NIHSS), a key indicator of stroke severity. The proposed model leverages a masked self-attention mechanism to capture salient brain connectivity patterns and employs EdgeSHAP to provide post-hoc explanations of the neurological states after a stroke. We evaluated our method on EEG recordings from four institutions, achieving a mean absolute error (MAE) of 3.23 in predicting NIHSS, close to the average error made by human experts (MAE $\approx$ 3.0). This demonstrates the method's effectiveness in providing accurate and explainable predictions while maintaining data privacy., Comment: 13 pages, 5 figures, Proceedings of the II edition of the Workshop on Unifying Representations in Neural Models (UniReps 2024)

Third-generation gravitational-wave detectors will observe up to millions of merging binary black holes. With such a vast dataset, stacking events into population analyses will arguably be more important than analyzing single sources. We present the first application of population-level Fisher-matrix forecasts tailored to third-generation gravitational-wave interferometers. We implement the formalism first derived by Gair et al. and explore how future experiments such as Einstein Telescope and Cosmic Explorer will constrain the distributions of black-hole masses, spins, and redshift. Third-generation detectors will be transformative, improving constraints on the population hyperparameters by several orders of magnitude compared to current data. At the same time, we highlight that a single third-generation observatory and a network of detectors will deliver qualitatively similar performances. Obtaining precise measurements of some population features (e.g. peaks in the mass spectrum) will require only a few months of observations while others (e.g. the fraction of binaries with aligned spins) will instead require years if not decades. We argue population forecasts of this kind should be featured in white papers and feasibility studies aimed at developing the science case of future gravitational-wave interferometers., Comment: 16 pages, 6 figures, 3 tables

After an acute stroke, accurately estimating stroke severity is crucial for healthcare professionals to effectively manage patient's treatment. Graph theory methods have shown that brain connectivity undergoes frequency-dependent reorganization post-stroke, adapting to new conditions. Traditional methods often rely on handcrafted features that may not capture the complexities of clinical phenomena. In this study, we propose a novel approach using Graph Neural Networks (GNNs) to predict stroke severity, as measured by the NIH Stroke Scale (NIHSS). We analyzed electroencephalography (EEG) recordings from 71 patients at the time of hospitalization. For each patient, we generated five graphs weighted by Lagged Linear Coherence (LLC) between signals from distinct Brodmann Areas, covering $\delta$ (2-4 Hz), $\theta$ (4-8 Hz), $\alpha_1$ (8-10.5 Hz), $\alpha_2$ (10.5-13 Hz), and $\beta_1$ (13-20 Hz) frequency bands. To emphasize key neurological connections and maintain sparsity, we applied a sparsification process based on structural and functional brain network properties. We then trained a graph attention model to predict the NIHSS. By examining its attention coefficients, our model reveals insights into brain reconfiguration, providing clinicians with a valuable tool for diagnosis, personalized treatment, and early intervention in neurorehabilitation., Comment: 7 pages, 7 figures

Recently, detailed studies have been made to compare the performance of the European next generation GW observatory Einstein Telescope (ET) in a single-site triangular configuration with the performance of a configuration featuring two L-shaped detectors in different sites, still taken to have all other ET characteristics except for the geometry, in particular, underground and composed of a low-frequency interferometer working at cryogenic temperatures and a high-frequency interferometer working at room temperature. Here we study a further possibility for a European network, made by a single L-shaped underground detector, like one of the detectors considered for the 2L version of ET, and a single third-generation 20-km L-shaped interferometer on the surface. We compare the performances of such a network to those of the triangle and of the 2L-underground ET configurations. We then examine the performance of an intercontinental network made by a 40-km CE in the US, together with any of these European networks., Comment: 36 pages, 14 figures

Gravitational-wave observations have the potential of allowing the identification of a population of merging primordial black-hole binaries. We provide an overview of the capabilities of present and future GW detectors, with a special emphasis on the perspective for observing quantities that are signatures of a primordial origin., Comment: To appear in the book "Primordial Black Holes", ed. Chris Byrnes, Gabriele Franciolini, Tomohiro Harada, Paolo Pani, Misao Sasaki; Springer (2024)

Joint gravitational-wave (GW) and $\gamma$-ray burst (GRB) observations are among the best prospects for standard siren cosmology. However, the strong selection effect for the coincident GRB detection, which is possible only for sources with small inclination angles, induces a systematic uncertainty that is currently not accounted for. We show that this severe source of bias can be removed by inferring the \emph{a priori} unknown electromagnetic detection probability directly from multimessenger data. This leads at the same time to an unbiased measurement of the Hubble constant, to constrain the properties of GRB emission, and to accurately measure the viewing angle of each source. Our inference scheme is applicable to real data already in the small-statistics regime, a scenario that might become reality in the near future. Additionally, we introduce a novel likelihood approximant for GW events which treats the dependence on distance and inclination as exact., Comment: 5+6 pages, 5 figures, v2: matches version to appear on PRL, added Sec. III.C and Fig 1 in Supplemental Material

Third-generation (3G) gravitational-wave detectors such as the Einstein Telescope (ET) will observe binary black hole (BBH) mergers at redshifts up to $z\sim 100$. However, an unequivocal determination of the origin of high-redshift sources will remain uncertain because of the low signal-to-noise ratio (S/N) and poor estimate of their luminosity distance. This study proposes a machine-learning approach to infer the origins of high-redshift BBHs. We specifically differentiate those arising from Population III (Pop. III) stars, which probably are the first progenitors of star-born BBH mergers in the Universe, and those originated from Population I-II (Pop. I-II) stars. We considered a wide range of models that encompass the current uncertainties on Pop. III BBH mergers. We then estimated the parameter errors of the detected sources with ET using the Fisher information-matrix formalism, followed by a classification using XGBoost, which is a machine-learning algorithm based on decision trees. For a set of mock observed BBHs, we provide the probability that they belong to the Pop. III class while considering the parameter errors of each source. In our fiducial model, we accurately identify $\gtrsim 10\%$ of the detected BBHs that originate from Pop. III stars with a precision $>90\%$. Our study demonstrates that machine-learning enables us to achieve some pivotal aspects of the ET science case by exploring the origin of individual high-redshift GW observations. We set the basis for further studies, which will integrate additional simulated populations and account for further uncertainties in the population modeling., Comment: Published in Astronomy & Astrophysics. 15 pages, 9 Figures and 6 tables. Comments are welcome

The Lunar Gravitational-wave Antenna (LGWA) is a proposed array of next-generation inertial sensors to monitor the response of the Moon to gravitational waves (GWs). Given the size of the Moon and the expected noise produced by the lunar seismic background, the LGWA would be able to observe GWs from about 1 mHz to 1 Hz. This would make the LGWA the missing link between space-borne detectors like LISA with peak sensitivities around a few millihertz and proposed future terrestrial detectors like Einstein Telescope or Cosmic Explorer. In this article, we provide a first comprehensive analysis of the LGWA science case including its multi-messenger aspects and lunar science with LGWA data. We also describe the scientific analyses of the Moon required to plan the LGWA mission.

With the growing number of gravitational-wave detections and the advent of large galaxy redshift surveys, a new era in cosmology is unfolding. This study explores the synergies between gravitational waves and galaxy surveys to jointly constrain cosmological and gravitational-wave population parameters. We introduce CHIMERA, a novel code for gravitational-wave cosmology combining information from the population properties of compact binary mergers and galaxy catalogs. We study constraints for scenarios representative of LIGO-Virgo-KAGRA O4 and O5 observing runs, assuming to have a complete catalog of potential host galaxies with either spectroscopic or photometric redshift measurements. We find that a percent-level measurement of $H_0$ could be achieved with the best 100 binary black holes in O5 using a spectroscopic galaxy catalog. In this case, the intrinsic correlation that exists between $H_0$ and the binary black hole population mass scales is broken. Instead, by using a photometric catalog the accuracy is degraded up to a factor of $\sim\! 9$, leaving a significant correlation between $H_0$ and the mass scales that must be carefully modeled to avoid bias. Interestingly, we find that using spectroscopic redshift measurements in the O4 configuration yields a better constraint on $H_0$ compared to the O5 configuration with photometric measurements. In view of the wealth of gravitational-wave data that will be available in the future, we argue the importance of obtaining spectroscopic galaxy catalogs to maximize the scientific return of gravitational-wave cosmology., Comment: 24 pages, 11 figures, 2 tables. Accepted for publication in ApJ. $\mathtt{CHIMERA}$ is available at https://github.com/CosmoStatGW/CHIMERA

The existence of merging black hole-neutron star (BHNS) binaries has been ascertained through the observation of their gravitational wave (GW) signals. However, to date, no definitive electromagnetic (EM) emission has been confidently associated with these mergers. Such an association could help unravel crucial information on these systems, for example, their BH spin distribution, the equation of state (EoS) of NS and the rate of heavy element production. We model the multi-messenger (MM) emission from BHNS mergers detectable during the fourth (O4) and fifth (O5) observing runs of the LIGO-Virgo-KAGRA GW detector network, in order to provide detailed predictions that can help enhance the effectiveness of observational efforts and extract the highest possible scientific information from such remarkable events. Our methodology is based on a population synthesis-approach, which includes the modelling of the signal-to-noise ratio of the GW signal in the detectors, the GW-inferred sky localization of the source, the kilonova (KN) optical and near-infrared light curves, the relativistic jet gamma-ray burst (GRB) prompt emission peak photon flux, and the GRB afterglow light curves in the radio, optical and X-ray bands. The resulting prospects for BHNS MM detections during O4 are not promising, with a GW detection rate of $15.0^{+15.4}_{-8.8}$ yr$^{-1}$, but joint MM rates of $\sim 10^{-1}$ yr$^{-1}$ for the KN and $\sim 10^{-2}$ yr$^{-1}$ for the jet-related emission. In O5 we find an overall increase in expected detection rates by around an order of magnitude, owing to both the enhanced sensitivity of the GW detector network, and the coming online of future EM facilities. Finally, we discuss direct searches for the GRB radio afterglow with large-field-of-view instruments as a new possible follow-up strategy in the context of ever-dimming prospects for KN detection., Comment: Submitted to A&A. 17 pages, 11 figures, 2 tables. Comments are welcome!

The emergence of Fifth-Generation (5G) communication networks has brought forth unprecedented connectivity with ultra-low latency, high data rates, and pervasive coverage. However, meeting the increasing demands of applications for seamless and high-quality communication, especially in rural areas, requires exploring innovative solutions that expand 5G beyond traditional terrestrial networks. Within the context of Non-Terrestrial Networks (NTNs), two promising technologies with vast potential are High Altitude Platforms (HAPs) and satellites. The combination of these two platforms is able to provide wide coverage and reliable communication in remote and inaccessible areas, and/or where terrestrial infrastructure is unavailable. This study evaluates the performance of the communication link between a Geostationary Equatorial Orbit (GEO) satellite and a HAP using the Internet of Drones Simulator (IoD-Sim), implemented in ns-3 and incorporating the 3GPP TR 38.811 channel model. The code base of IoD-Sim is extended to simulate HAPs, accounting for the Earths curvature in various geographic coordinate systems, and considering realistic mobility patterns. A simulation campaign is conducted to evaluate the GEO-to-HAP communication link in terms of Signal-to-Noise Ratio (SNR) in two different scenarios, considering the mobility of the HAP, and as a function of the frequency and the distance.

The next generation of ground-based gravitational-wave detectors, Einstein Telescope (ET) and Cosmic Explorer (CE), present a unique opportunity to put constraints on dense matter, among many other groundbreaking scientific goals. In a recent study the science case of ET was further strengthened, studying in particular the performances of different detector designs. In this paper we present a more detailed study of the nuclear physics section of that work. In particular, focusing on two different detector configurations (the single-site triangular-shaped design and a design consisting of two widely separated "L-shaped" interferometers), we study the detection prospects of binary neutron star (BNS) mergers, and how they can reshape our understanding of the underlying equation of state (EoS) of dense matter. We employ several state-of-the-art EoS models and state-of-the-art synthetic BNS merger catalogs, and we make use of the Fisher information formalism (FIM) to quantify statistical errors on the astrophysical parameters describing individual BNS events. To check the reliability of the FIM method, we further perform a full parameter estimation for a few simulated events. Based on the uncertainties on the tidal deformabilities associated to these events, we outline a mechanism to extract the underlying injected EoS using a recently developed meta-modelling approach within a Bayesian framework. Our results suggest that with $\gtrsim 500$ events with signal-to-noise ratio greater than $12$, we will be able to pin down very precisely the underlying EoS governing the neutron star matter., Comment: 18 pages, 10 figures. v2 matches the version accepted for publication in PRD

Primordial Black Holes (PBHs) have recently attracted much attention as they may explain some of the LIGO/Virgo/KAGRA observations and significantly contribute to the dark matter in our universe. The next generation of Gravitational Wave (GW) detectors will have the unique opportunity to set stringent bounds on this putative population of objects. Focusing on the Einstein Telescope (ET), in this paper we analyse in detail the impact of systematics and different detector designs on our future capability of observing key quantities that would allow us to discover and/or constrain a population of PBH mergers. We also perform a population analysis, with a mass and redshift distribution compatible with the current observational bounds. Our results indicate that ET alone can reach an exquisite level of accuracy on the key observables considered, as well as detect up to tens of thousands of PBH binaries per year, but for some key signatures (in particular high--redshift sources) the cryogenic instrument optimised for low frequencies turns out to be crucial, both for the number of observations and the error on the parameters reconstruction. As far as the detector geometry is concerned, we find that a network consisting of two separated L--shaped interferometers of 15 (20)~km arm length, oriented at $45^{\circ}$ with respect to each other performs better than a single triangular shaped instrument of 10 (15)~km arm length, for all the metrics considered., Comment: 24 pages, 13 figures

Sixth-Generation (6G) networks are set to provide reliable, widespread, and ultra-low-latency mobile broadband communications for a variety of industries. In this regard, the Internet of Drones (IoD) represents a key component for the development of 3D networks, which envisions the integration of terrestrial and non-terrestrial infrastructures. The recent employment of Intelligent Reflective Surfaces (IRSs) in combination with Unmanned Aerial Vehicles (UAVs) introduces more degrees of freedom to achieve a flexible and prompt mobile coverage. As the concept of smart radio environment is gaining momentum across the scientific community, this work proposes an extension module for Internet of Drones Simulator (IoD-Sim), a comprehensive simulation platform for the IoD, based on Network Simulator 3 (ns-3). This module is purposefully designed to assess the performance of UAV-aided IRS-assisted communication systems. Starting from the mathematical formulation of the radio channel, the simulator implements the IRS as a peripheral that can be attached to a drone. Such device can be dynamically configured to organize the IRS into patches and assign them to assist the communication between two nodes. Furthermore, the extension relies on the configuration facilities of IoD-Sim, which greatly eases design and coding of scenarios in JavaScript Object Notation (JSON) language. A simulation campaign is conducted to demonstrate the effectiveness of the proposal by discussing several Key Performance Indicators (KPIs), such as Radio Environment Map (REM), Signal-to-Interference-plus-Noise Ratio (SINR), maximum achievable rate, and average throughput.

The Einstein Telescope (ET), the European project for a third-generation gravitational-wave detector, has a reference configuration based on a triangular shape consisting of three nested detectors with 10 km arms, where in each arm there is a `xylophone' configuration made of an interferometer tuned toward high frequencies, and an interferometer tuned toward low frequencies and working at cryogenic temperature. Here, we examine the scientific perspectives under possible variations of this reference design. We perform a detailed evaluation of the science case for a single triangular geometry observatory, and we compare it with the results obtained for a network of two L-shaped detectors (either parallel or misaligned) located in Europe, considering different choices of arm-length for both the triangle and the 2L geometries. We also study how the science output changes in the absence of the low-frequency instrument, both for the triangle and the 2L configurations. We examine a broad class of simple `metrics' that quantify the science output, related to compact binary coalescences, multi-messenger astronomy and stochastic backgrounds, and we then examine the impact of different detector designs on a more specific set of scientific objectives., Comment: 197 pages, 73 figures. v2: corrections in the part on the sensitivity to stochastic backgrounds. Accepted in JCAP

The detection of black-hole binaries at high redshifts is a cornerstone of the science case of third-generation gravitational-wave interferometers. The star-formation rate peaks at z~2 and decreases by orders of magnitude by z~10. Any confident detection of gravitational waves from such high redshifts would imply either the presence of stars formed from pristine material originating from cosmological nucleosynthesis (the so-called population III stars), or black holes that are the direct relics of quantum fluctuations in the early Universe (the so-called primordial black holes). Crucially, detecting sources at cosmological distances does not imply inferring that sources are located there, with the latter posing more stringent requirements. To this end, we present two figures of merit, which we refer to as "z-z plot" and "inference horizon", that quantify the largest redshift one can possibly claim a source to be beyond. We argue that such inference requirements, in addition to detection requirements, should be investigated when quantifying the scientific payoff of future gravitational-wave facilities., Comment: 6 pages, 4 figures. v2: matches version published on PRD Lett

A joint fit of the mass and redshift distributions of the population of Binary Black Holes detected with Gravitational-Wave observations can be used to obtain constraints on the Hubble parameter and on deviations from General Relativity in the propagation of Gravitational Waves. We first present applications of this technique to the latest catalog of Gravitational-Wave events, focusing on the comparison of different parametrizations for the source-frame mass distribution of Black Hole Binaries. We find that models with more than one feature are favourite by the data, as suggested by population studies, even when varying the cosmology. Then, we discuss perspectives for the use of this technique with third generation Gravitational-Wave detectors, exploiting the recently developed Fisher information matrix Python code GWFAST., Comment: 5 pages, 2 figures, Contribution to the ICHEP 2022 conference proceedings

The last decade has seen the emergence of two new fields within astrophysics: gamma ray polarimetry and GW astronomy. The former, which aims to measure the polarization of gamma rays in the energy range of 10s to 100s of keV, from astrophysical sources, saw the launch of the first dedicated polarimeters such as GAP and POLAR. On the other hand, GW astronomy started with the detection of the first black hole mergers by LIGO in 2015, followed by the first multi messenger detection in 2017. While the potential of the two individual fields has been discussed in detail in the literature, the potential for joint observations has thus far been ignored. In this article, we aim to define how GW observations can best contribute to gamma ray polarimetry and study the scientific potential of joint analyses. In addition we aim to provide predictions on feasibility of such joint measurements in the near future. We study which GW observables can be combined with measurements from gamma ray polarimetry to improve the discriminating power regarding GRB emission models. We then provide forecasts for the joint detection capabilities of current and future GW detectors and polarimeters. Our results show that by adding GW data to polarimetry, a single precise joint detection would allow to rule out the majority of emission models. We show that in the coming years joint detections between GW and gamma ray polarimeters might already be possible. Although these would allow to constrain part of the model space, the probability of highly constraining joint detections will remain small in the near future. However, the scientific merit held by even a single such measurement makes it important to pursue such an endeavour. Furthermore, we show that using the next generation of GW detectors, such as the Einstein Telescope, joint detections for which GW data can better complement the polarization data become possible., Comment: 19 pages, 10 figures, Accepted for publication in A&A

We introduce $\texttt{GWFAST}$, a Fisher information matrix $\texttt{Python}$ code that allows easy and efficient estimation of signal-to-noise ratios and parameter measurement errors for large catalogs of resolved sources observed by networks of gravitational-wave detectors. In particular, $\texttt{GWFAST}$ includes the effects of the Earth's motion during the evolution of the signal, supports parallel computation, and relies on automatic differentiation rather than on finite differences techniques, which allows the computation of derivatives with accuracy close to machine precision. We also release the library $\texttt{WF4Py}$ implementing state-of-the-art gravitational-wave waveforms in $\texttt{Python}$. In this paper we provide a documentation of $\texttt{GWFAST}$ and $\texttt{WF4Py}$ with practical examples and tests of performance and reliability. In a companion paper we present forecasts for the detection capabilities of the second and third generation of ground-based gravitational-wave detectors, obtained with $\texttt{GWFAST}$., Comment: 18 pages, 6 figures, $\texttt{GWFAST}$ available at $\href{https://github.com/CosmoStatGW/gwfast}{\rm this\ link}$, $\texttt{WF4Py}$ available at $\href{https://github.com/CosmoStatGW/WF4Py}{\rm this\ link}$. v3 matches the version accepted for publication in ApJS. Title changed in journal

We introduce $\texttt{GWFAST}$, a novel Fisher-matrix code for gravitational-wave studies, tuned toward third-generation gravitational-wave detectors such as Einstein Telescope (ET) and Cosmic Explorer (CE). We use it to perform a comprehensive study of the capabilities of ET alone, and of a network made by ET and two CE detectors, as well as to provide forecasts for the forthcoming O4 run of the LVK collaboration. We consider binary neutron stars, binary black holes and neutron star-black hole binaries, and compute basic metrics such as the distribution of signal-to-noise ratio (SNR), the accuracy in the reconstruction of various parameters (including distance, sky localization, masses, spins and, for neutron stars, tidal deformabilities), and the redshift distribution of the detections for different thresholds in SNR and different levels of accuracy in localization and distance measurement. We examine the expected distribution and properties of `golden events', with especially large values of the SNR. We also pay special attention to the dependence of the results on astrophysical uncertainties and on various technical details (such as choice of waveforms, or the threshold in SNR), and we compare with other Fisher codes in the literature. In a companion paper we discuss the technical aspects of the code. Together with this paper, we publicly release the code $\texttt{GWFAST}$ at https://github.com/CosmoStatGW/gwfast, and the library $\texttt{WF4Py}$ implementing state-of-the-art gravitational-wave waveforms in pure $\texttt{Python}$ at https://github.com/CosmoStatGW/WF4Py., Comment: 43 + 12 pages, 24 + 5 Figures, $\texttt{GWFAST}$ available at https://github.com/CosmoStatGW/gwfast, $\texttt{WF4Py}$ available at https://github.com/CosmoStatGW/WF4Py. v3: resubmitted to APJ, minor changes in results, Appendix C added