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Web application pentesting is a crucial component in the offensive cybersecurity area, whose aim is to safeguard web applications and web services as the majority of the web applications are mounted in publicly accessible web environments. This method requires that the cybersecurity experts pretend and act as real attackers to identify all the errors and vulnerabilities in web applications with the objective of preventing and reducing damages. As this process may be quite complex and the amount of information pentesters need may be big, being able to automate it will help them to easily discover the vulnerabilities given. This project is the direct continuation of the previous initiative called PThelper: An open source tool to support the Penetration Testing process. This continuation is focused on expanding PThelper with the functionality to detect and later report web vulnerabilities in order to address emerging threats and strengthen the ability of the organizations to protect their web applications against potential cyber-attacks.

The dynamics of personal relationships remain largely unexplored due to the inherent difficulties of the longitudinal data collection process. In this paper, we analyse a dataset tracking the temporal evolution of a network of personal relationships among 900 people over the course of four years. We search for evidence that the network is in equilibrium, meaning that all macroscopic properties remain constant, fluctuating around stable values, while the internal microscopic dynamics are active. We find that the probabilities governing the network dynamics are stationary over time and that the degree distributions, as well as edge and triangle abundances match the theoretical equilibrium distributions expected under these dynamics. Furthermore, we verify that the system satisfies the detailed balance condition, with only minor point deviations, confirming that it is indeed in equilibrium. Remarkably, this equilibrium persists despite a high turnover in network composition, suggesting that it is an inherent characteristic of human social interactions rather than a trait of the individuals themselves. We argue that this equilibrium may be a general feature of human social networks arising from the competition between different dynamical mechanisms and also from the cognitive and material resources management of individuals. From a practical perspective, the fact that networks are in equilibrium could simplify data collection processes, validate the use of cross-sectional data-based methods like Exponential Random Graph Models, and inform the design of interventions. Our findings advance the understanding of collective human behaviour predictability and our ability to describe it using simple mathematical models., Comment: 14 pages, 3 figures, under peer-review

The use of Autonomous Surface Vehicles, equipped with water quality sensors and artificial vision systems, allows for a smart and adaptive deployment in water resources environmental monitoring. This paper presents a real implementation of a vehicle prototype that to address the use of Artificial Intelligence algorithms and enhanced sensing techniques for water quality monitoring. The vehicle is fully equipped with high-quality sensors to measure water quality parameters and water depth. Furthermore, by means of a stereo-camera, it also can detect and locate macro-plastics in real environments by means of deep visual models, such as YOLOv5. In this paper, experimental results, carried out in Lago Mayor (Sevilla), has been presented as proof of the capabilities of the proposed architecture. The overall system, and the early results obtained, are expected to provide a solid example of a real platform useful for the water resource monitoring task, and to serve as a real case scenario for deploying Artificial Intelligence algorithms, such as path planning, artificial vision, etc.

Joint communication and sensing (JC\&S) is emerging as a key component in 5G and 6G networks, enabling dynamic adaptation to environmental changes and enhancing contextual awareness for optimized communication. By leveraging real-time environmental data, JC\&S improves resource allocation, reduces latency, and enhances power efficiency, while also supporting simulations and predictive modeling. This makes it a key technology for reactive systems and digital twins. These systems can respond to environmental events in real-time, offering transformative potential in sectors like smart cities, healthcare, and Industry 5.0, where adaptive and multimodal interaction is critical to enhance real-time decision-making. In this work, we present a transformer-based architecture that processes temporal Channel State Information (CSI) data, specifically amplitude and phase, to generate 3D point clouds of indoor environments. The model utilizes a multi-head attention to capture complex spatio-temporal relationships in CSI data and is adaptable to different CSI configurations. We evaluate the architecture on the MM-Fi dataset, using two different protocols to capture human presence in indoor environments. The system demonstrates strong potential for accurate 3D reconstructions and effectively distinguishes between close and distant objects, advancing JC\&S applications for spatial sensing in future wireless networks., Comment: 7 pages, 5 figures, 1 table

Light pollution is a growing environmental issue that affects astronomy, ecosystems, human health. To address this, we introduce the Free Dark Sky Meter (FreeDSM), an affordable IoT-based photometer designed for continuous light pollution monitoring. FreeDSM uses an ESP32 microcontroller with integrated sensors for light, temperature, and humidity, and operates on an open-source platform. Data from multiple devices are centralized and processed using the Gambons model, which leverages Gaia satellite data for accurate real-time assessments of natural light levels. This project is part of the Gaia4Sustainability initiative.

Interest in quantum machine learning is increasingly growing due to its potential to offer more efficient solutions for problems that are difficult to tackle with classical methods. In this context, the research work presented here focuses on the use of quantum machine learning techniques for image classification tasks. We exploit a quantum extreme learning machine by taking advantage of its rich feature map provided by the quantum reservoir substrate. We systematically analyse different phases of the quantum extreme learning machine process, from the dataset preparation to the image final classification. In particular, we have tested different encodings, together with Principal Component Analysis, the use of Auto-Encoders, as well as the dynamics of the model through the use of different Hamiltonians for the quantum reservoir. Our results show that the introduction of a quantum reservoir systematically improves the accuracy of the classifier. Additionally, while different encodings can lead to significantly different performances, Hamiltonians with varying degrees of connectivity exhibit the same discrimination rate, provided they are interacting., Comment: 11 pages, 6 figures

As drones are getting more and more entangled in our society, more untrained users require the capability to operate them. This scenario is to be achieved through the development of artificial intelligence capabilities assisting the human operator in controlling the Unmanned Aerial System (UAS) and processing the sensor data, thereby alleviating the need for extensive operator training. This paper presents the HADRON project that seeks to develop and test multiple novel technologies to enable human-friendly control of drone swarms. This project is divided into three main parts. The first part consists of the integration of different technologies for the intuitive control of drones, focusing on novice or inexperienced pilots and operators. The second part focuses on the development of a multi-drone system that will be controlled from a command and control station, in which an expert pilot can supervise the operations of the multiple drones. The third part of the project will focus on reducing the cognitive load on human operators, whether they are novice or expert pilots. For this, we will develop AI tools that will assist drone operators with semi-automated real-time data processing., Comment: 4 pages, 2 Figures and 1 table. This work has been accepted at the Workshop Variable Autonomy for Human-Robot Teaming held at the 33rd IEEE International Conference on Robot and Human Interactive Communication (RO-MAN 2024)

In this paper, we establish a connection between evolution algebras of dimension two and Hopf algebras, via the algebraic group of automorphisms of an evolution algebra. Initially, we describe the Hopf algebra associated with the automorphism group of a 2-dimensional evolution algebra. Subsequently, for a 2-dimensional evolution algebra $A$ over a field $K$, we detail the relation between the algebra associated with the (tight) universal associative and commutative representation of $A$, referred to as the (tight) $p$-algebra, and the corresponding Hopf algebra, $\mathcal{H}$, representing the affine group scheme $\text{Aut}(A)$. Our analysis involves the computation of the (tight) $p-$algebra associated with any 2-dimensional evolution algebra, whenever it exists. We find that $\text{Aut}(A)=1$ if and only if there is no faithful associative and commutative representation for $A$. Moreover, there is a faithful associative and commutative representation for $A$ if and only if $\mathcal{H}\not\cong K$ and $\text{char} (K)\neq 2$, or $\mathcal{H}\not\cong K(\epsilon)$ (the dual numbers algebra) and $\mathcal{H}\not\cong K$ in case of $\text{char} (K)= 2$. Furthermore, if $A$ is perfect and has a faithful tight $p$-algebra, then this $p$-algebra is isomorphic to $\mathcal{H}$ (as algebras). Finally, we derive implications for arbitrary finite-dimensional evolution algebras.

Huntington's disease (HD) is an inherited neurodegenerative disorder caused by an expanded CAG repeat in the coding sequence of the huntingtin protein. Initially, it predominantly affects medium-sized spiny neurons (MSSNs) of the corpus striatum. No effective treatment is available, thus urging the identification of potential therapeutic targets. While evidence of mitochondrial structural alterations in HD exists, previous studies mainly employed 2D approaches and were performed outside the strictly native brain context. In this study, we adopted a novel multiscale approach to conduct a comprehensive 3D in situ structural analysis of mitochondrial disturbances in a mouse model of HD. We investigated MSSNs within brain tissue under optimal structural conditions utilizing state-of-the-art 3D imaging technologies, specifically FIB/SEM for the complete imaging of neuronal somas and Electron Tomography for detailed morphological examination and image processing-based quantitative analysis. Our findings suggest a disruption of the mitochondrial network towards fragmentation in HD. The network of interlaced, slim, and long mitochondria observed in healthy conditions transforms into isolated, swollen, and short entities, with internal cristae disorganization, cavities, and abnormally large matrix granules., Comment: 31 pages 5 figures

Offensive security is one of the state of the art measures to protect enterprises and organizations. Penetration testing, broadly called pentesting, is a branch of offensive security designed to find, rate and exploit these vulnerabilities, in order to assess the security posture of an organization. This process is often time-consuming and the quantity of information that pentesters need to manage might also be difficult to handle. This project takes a practical approach to solve the automation of pentesting and proposes a usable tool, called PTHelper. This open-source tool has been designed in a modular way to be easily upgradable by the pentesting community, and uses state of the art tools and artificial intelligence to achieve its objective.

We consider a Maxwell system on $\mathbb{R}^3$ with periodic and highly oscillating coefficients. It is known that the solutions converge in the weak-$\ast$ topology of $L^\infty(0,T;\,L^2(\mathbb{R}^3))$ to the solution of a similar problem with constant coefficients given as the $H$-limits of the electric permittivity and the magnetic permeability respectively, i.e. the limit in the sense of the homogenization of linear elliptic equations with varying coefficients. However, it is not true that the elliptic corrector also provides a corrector for the solution of the Maxwell system, i.e. an approximation of the solutions in the strong topology of $L^2$. We shall prove that the oscillations in the space variable also produce oscillations in the time variable. We get a corrector consisting of adding to the elliptic corrector the sum of infinitely plane waves in the fast variable. Note that related results have been previously proved for the wave equation. Our proof is based on the two-scale convergence theory for almost periodic functions. One of the novelties is to show how this contains the classical Block decomposition.

The global increase in the elderly population necessitates innovative long-term care solutions to improve the quality of life for vulnerable individuals while reducing caregiver burdens. Assistive robots, leveraging advancements in Machine Learning, offer promising personalised support. However, their integration into daily life raises significant privacy concerns. Widely used frameworks like the Robot Operating System (ROS) historically lack inherent privacy mechanisms, complicating data-driven approaches in robotics. This research pioneers user-centric, privacy-aware technologies such as Federated Learning (FL) to advance assistive robotics. FL enables collaborative learning without sharing sensitive data, addressing privacy and scalability issues. This work includes developing solutions for smart wheelchair assistance, enhancing user independence and well-being. By tackling challenges related to non-stationary data and heterogeneous environments, the research aims to improve personalisation and user experience. Ultimately, it seeks to lead the responsible integration of assistive robots into society, enhancing the quality of life for elderly and care-dependent individuals., Comment: RSS Pioneers 2024 Research Statement

In the domain of non-contact biometrics and human activity recognition, the lack of a versatile, multimodal dataset poses a significant bottleneck. To address this, we introduce the Oulu Multi Sensing (OMuSense-23) dataset that includes biosignals obtained from a mmWave radar, and an RGB-D camera. The dataset features data from 50 individuals in three distinct poses -- standing, sitting, and lying down -- each featuring four specific breathing pattern activities: regular breathing, reading, guided breathing, and apnea, encompassing both typical situations (e.g., sitting with normal breathing) and critical conditions (e.g., lying down without breathing). In our work, we present a detailed overview of the OMuSense-23 dataset, detailing the data acquisition protocol, describing the process for each participant. In addition, we provide, a baseline evaluation of several data analysis tasks related to biometrics, breathing pattern recognition and pose identification. Our results achieve a pose identification accuracy of 87\% and breathing pattern activity recognition of 83\% using features extracted from biosignals. The OMuSense-23 dataset is publicly available as resource for other researchers and practitioners in the field.

The Super-Kamiokande and T2K collaborations present a joint measurement of neutrino oscillation parameters from their atmospheric and beam neutrino data. It uses a common interaction model for events overlapping in neutrino energy and correlated detector systematic uncertainties between the two datasets, which are found to be compatible. Using 3244.4 days of atmospheric data and a beam exposure of $19.7(16.3) \times 10^{20}$ protons on target in (anti)neutrino mode, the analysis finds a 1.9$\sigma$ exclusion of CP-conservation (defined as $J_{CP}=0$) and a preference for the normal mass ordering., Comment: 12 pages, 4 figures

The convergence between astronomy and data sonification represents a significant advancement in the approach and analysis of cosmic information. By surpassing the visual exclusivity in data analysis in astronomy, innovative projects have developed software that goes beyond visual representation, transforming data into auditory and tactile displays. However, it has been evidenced that this novel technique requires specialized training, particularly for audio format data. This work describes the initial development of a platform aimed at providing training for data analysis in astronomy through sonification. The integration of these tools in astronomical education and research opens new horizons, facilitating a more inclusive and multisensory participation in the exploration of space science., Comment: 4 pages, 4 figures, preprint of the III Workshop on Astronomy Beyond the Common Senses for Accessibility and Inclusion

Video-based remote photoplethysmography (rPPG) has emerged as a promising technology for non-contact vital sign monitoring, especially under controlled conditions. However, the accurate measurement of vital signs in real-world scenarios faces several challenges, including artifacts induced by videocodecs, low-light noise, degradation, low dynamic range, occlusions, and hardware and network constraints. In this article, we systematically investigate comprehensive investigate these issues, measuring their detrimental effects on the quality of rPPG measurements. Additionally, we propose practical strategies for mitigating these challenges to improve the dependability and resilience of video-based rPPG systems. We detail methods for effective biosignal recovery in the presence of network limitations and present denoising and inpainting techniques aimed at preserving video frame integrity. Through extensive evaluations and direct comparisons, we demonstrate the effectiveness of the approaches in enhancing rPPG measurements under challenging environments, contributing to the development of more reliable and effective remote vital sign monitoring technologies., Comment: 22 main article pages with 3 supplementary pages, journal

In the last decade, the multi-sensory approach to data analysis has gained relevance. The possibility of including people with vision difficulties in the field of education and the dissemination of science is part of it. However, in the field of scientific research, the topic is not yet accepted, mainly due to the lack of conclusive evidence related to its robustness and performance, except for a few exceptions. On the other hand, very few of the tools that allow data to be sonifyed are focused on the user or have an interface that allows controlling the sound production process and, at the same time the visualization of data. Of those that meet this requirement and present application in the field of astronomy and astrophysics, only four have included people with visual disabilities in the design and only two of them have carried out tests with users in Focus Groups during its development. This work details the characteristics of sonoUno, with its end-user-focused design, its capabilities in specific use cases in astrophysical data analysis related to spectroscopy and photometry, following the basic software functionalities while also introducing some innovation., Comment: 22 pages, links to sonification files and videos, submitted to RASTI

The leitmotiv of this paper is linking algebraic properties of an evolution algebra with combinatorial properties of the (possibly several) graphs that one can associate to the algebra. We link nondegeneracy, zero annihilator, absorption property, von Neumann regularity, and primeness with suitable properties in the associated graph. In the presence of semiprimeness, the property of primeness is equivalent to any associated graph being downward directed. We also provide a description of the prime ideals in an evolution algebra and prove that certain algebraic properties, such as semiprimeness and perfection, can not be characterized in combinatorial terms. We describe the centroid of evolution algebras as constant functions along the connected components of its associated graph. The dimension of the centroid of a zero annihilator algebra $A$ agrees with the cardinal of the connected components of any possible graph associated to $A$. This is the combinatorial expression of an algebraic uniqueness property in the decomposition of $A$ as indecomposable algebras with $1$-dimensional centroid.

Large Language Models (LLMs) are evolving beyond their classical role of providing information within dialogue systems to actively engaging with tools and performing actions on real-world applications and services. Today, humans verify the correctness and appropriateness of the LLM-generated outputs (e.g., code, functions, or actions) before putting them into real-world execution. This poses significant challenges as code comprehension is well known to be notoriously difficult. In this paper, we study how humans can efficiently collaborate with, delegate to, and supervise autonomous LLMs in the future. We argue that in many cases, "post-facto validation" - verifying the correctness of a proposed action after seeing the output - is much easier than the aforementioned "pre-facto validation" setting. The core concept behind enabling a post-facto validation system is the integration of an intuitive undo feature, and establishing a damage confinement for the LLM-generated actions as effective strategies to mitigate the associated risks. Using this, a human can now either revert the effect of an LLM-generated output or be confident that the potential risk is bounded. We believe this is critical to unlock the potential for LLM agents to interact with applications and services with limited (post-facto) human involvement. We describe the design and implementation of our open-source runtime for executing LLM actions, Gorilla Execution Engine (GoEX), and present open research questions towards realizing the goal of LLMs and applications interacting with each other with minimal human supervision. We release GoEX at https://github.com/ShishirPatil/gorilla/.

In the ongoing effort towards a scalable quantum computer, multiple technologies have been proposed. Some of them exploit topological materials to process quantum information. In this work, we propose a lattice of photonic cavities with alternating hoppings to create a modified multidomain SSH chain, that is, a sequence of topological insulators made from chains of dimers. A qubit is then coupled to each boundary. We show this system is well suited for quantum information processing because topological transfer of photons through this one-dimensional lattice can entangle any set of qubits on demand, providing a scalable quantum platform. We verify this claim evaluating entanglement measures and witnesses proving that bipartite and multipartite entanglement is produced, even in the presence of some disorder., Comment: 14 pages, 10 figures

We carry out the homogenization of a fluid-structure interaction problem consisting in the periodic inclusions of a viscous fluid in an elastic body. We get a macrostructure model where the body behaves as a viscoelastic material with a long-range memory term. Our aim is not only to get this limit problem but also to study its main properties. Using the micro-structure variables it is simple to check that it satisfies an energy conservation law assuring in particular the existence and uniqueness of solution. The difficulty is to characterize these properties using only the macroscopic system. We prove that the nonlocal term is given through a convolution kernel which exponentially decreases to zero and satisfies some positive conditions which we write in terms of the Laplace transform. These conditions can be used to directly prove the existence and uniqueness of solution. The results apply to modeling the mechanical behavior of skin as an indicator of what kind of models we should use. In a naive interpretation the fluid inclusions represent the cells and the elastic medium the extracellular matrix.

The present paper is devoted to study the asymptotic behavior of a sequence of linear elliptic equations with a varying drift term, whose coefficients are just bounded in $L^N(\Omega)$, with $N$ the dimension of the space. It is known that there exists a unique solution for each of these problems in the Sobolev space $H^1_0(\Omega)$. However, because the operators are not coercive, there is no uniform estimate of the solutions in this space. We use some estimates in \cite{boc1}, and a regularization obtained by adding a small nonlinear first order term, to pass to the limit in these problems.

The field of sonification, using of non-speech audio for data analysis, is already established in space sciences. Meetings like "The audible Universe" focus on sonification tools applied in astronomy to represent complex data like nebulae and galaxies. Besides, little is said about the translation of images into sound, this challenge that seeks to represent data in 2 or 3 dimensions through a one-dimensional technique. The aforementioned leads to a total lack of consensus regarding the sound parameters to be used and how these are interpreted by people. This work seeks to delve deeper into the existing tools for image sonification, analyzing whether their objective is only outreach or includes the possibility of research. A new proposal is presented, maintaining sonoUno's software focus on research, pointing out the need for reliable techniques that integrate functional diversity people with an active role on research., Comment: 4 pages, 3 figures, preprint of the III Workshop on Astronomy Beyond the Common Senses for Accessibility and Inclusion

Most tools for astrophysical research was centered on visual display. Even after some studies shows that the use of sound could help the data analysis, and on the other hand generate more accessibility. This fact motivates the creation of a tool centered on the researcher with and without visual impairments. To carry out this challenge, on this contribution, a theoretical framework based on visual impaired people was created and included on the sonoUno software. After that, the accessibility of the tool was analysed with the ISO standard 9241-171:2008., Comment: 4 pages, 2 figures, 1 table, accepted for publication

The muti-modal or multi-sensorial perception of nature is presented in this article as part of research devoted to inclusive tools developed in the framework of User Centered Design. This proposal shows that it is possible to work in a transdisciplinary way, establishing feedback not only between designers and final users, but also between humans and computers, to reduce errors and co-design the resources according to personal needs. As part of the present research, we present the basis for a new accessible software, sonoUno, which was designed with the user in mind from the beginning, and we propose a training activity to enhance the user's capacities, expand the detection of different kinds of natural signals, and improve the comprehension of the Human Computer Interfaces, opening new windows to the sciences for diverse populations, not only in education and outreach but also in research. Some examples of the exploitation of these new devices and tools are also presented., Comment: 15 pages, 4 figures, 14th International Multi-Conference on Complexity, Informatics, and Cybernetics: IMCIC 2023; Trans-Disciplinary Communications meeting, March 31, 2023

Radio frequency (RF) signals have facilitated the development of non-contact human monitoring tasks, such as vital signs measurement, activity recognition, and user identification. In some specific scenarios, an RF signal analysis framework may prioritize the performance of one task over that of others. In response to this requirement, we employ a multi-objective optimization approach inspired by biological principles to select discriminative features that enhance the accuracy of breathing patterns recognition while simultaneously impeding the identification of individual users. This approach is validated using a novel vital signs dataset consisting of 50 subjects engaged in four distinct breathing patterns. Our findings indicate a remarkable result: a substantial divergence in accuracy between breathing recognition and user identification. As a complementary viewpoint, we present a contrariwise result to maximize user identification accuracy and minimize the system's capacity for breathing activity recognition., Comment: Under review

We introduce a new PAC-Bayes oracle bound for unbounded losses that extends Cram\'er-Chernoff bounds to the PAC-Bayesian setting. The proof technique relies on controlling the tails of certain random variables involving the Cram\'er transform of the loss. Our approach naturally leverages properties of Cram\'er-Chernoff bounds, such as exact optimization of the free parameter in many PAC-Bayes bounds. We highlight several applications of the main theorem. Firstly, we show that our bound recovers and generalizes previous results. Additionally, our approach allows working with richer assumptions that result in more informative and potentially tighter bounds. In this direction, we provide a general bound under a new \textit{model-dependent} assumption from which we obtain bounds based on parameter norms and log-Sobolev inequalities. Notably, many of these bounds can be minimized to obtain distributions beyond the Gibbs posterior and provide novel theoretical coverage to existing regularization techniques., Comment: Camera-ready version for NeurIPS 2024

Indoor human monitoring systems leverage a wide range of sensors, including cameras, radio devices, and inertial measurement units, to collect extensive data from users and the environment. These sensors contribute diverse data modalities, such as video feeds from cameras, received signal strength indicators and channel state information from WiFi devices, and three-axis acceleration data from inertial measurement units. In this context, we present a comprehensive survey of multimodal approaches for indoor human monitoring systems, with a specific focus on their relevance in elderly care. Our survey primarily highlights non-contact technologies, particularly cameras and radio devices, as key components in the development of indoor human monitoring systems. Throughout this article, we explore well-established techniques for extracting features from multimodal data sources. Our exploration extends to methodologies for fusing these features and harnessing multiple modalities to improve the accuracy and robustness of machine learning models. Furthermore, we conduct comparative analysis across different data modalities in diverse human monitoring tasks and undertake a comprehensive examination of existing multimodal datasets. This extensive survey not only highlights the significance of indoor human monitoring systems but also affirms their versatile applications. In particular, we emphasize their critical role in enhancing the quality of elderly care, offering valuable insights into the development of non-contact monitoring solutions applicable to the needs of aging populations., Comment: 19 pages, 5 figures

This thesis aims at improving our understanding of the strong-field regime of gravity, where deviations from General Relativity (GR) are expected to be found on theoretical grounds. In particular, we have been concerned with the formulation and application of junction conditions (which govern stellar collapse, black-hole formation and the dynamics of more exotic compact objects, such as thin-shell wormholes), as well as with other viability criteria necessary for modified gravity theories and their solutions to be physically admissible (for instance, compatibility with gravitational-wave observations, stability or the avoidance singularities). First, we have studied stellar collapse in $f(R)$ gravity. By means of a systematic treatment of the relevant junction conditions, we have proven a series of stringent no-go results on the exterior space-time, which entail that some paradigmatic classes of vacuum metrics cannot represent space-time outside a collapsing dust star in metric $f(R)$ gravity. This could lead to potentially observable deviations with respect to GR. We have also provided an exhaustive derivation of the junction conditions in bi-scalar Poincar\'e gauge gravity, finding that the matching interface is allowed to host surface axial spin monopoles, as well as matter thin shells and double layers. This singular structure is richer than its counterparts in GR or $f(R)$ gravity, leading to possible interesting applications. In addition, we have had to resolve some procedural and mathematical subtleties in the junction-condition formalism. Finally, we have examined a wide class of metric $f(R)$ models, the so-called '$R_0$-degenerate models,' solved by all metrics with constant scalar curvature $R=R_0$. We have shown that they feature all sorts of shortcomings (such as previously-unforeseen strong-coupling instabilities) rendering their viability extremely limited., Comment: PhD Thesis, Universidad Complutense de Madrid. Defended in November 2023. 190 pages, 7 figures, 4 tables; Based on arXiv:2202.04439, arXiv:2303.01206 and arXiv:2303.02103