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We bridge sheaves of rings over a topological space with common meadows (algebraic structures where the inverse for multiplication is a total operation). More specifically, we show that the subclass of pre-meadows with $\mathbf{a}$, coming from the lattice of open sets of a topological space $X$, and presheaves over $X$ are the same structure. Furthermore, we provide a construction that, given a sheaf of rings $\mathcal{F}$ on $X$ produces a common meadow as a disjoint union of elements of the form $\mathcal{F}(U)$ indexed over the open subsets of $X$. We also establish a correspondence between the process of going from a presheaf to a sheaf (called sheafification) and the process of going from a pre-meadow with $\mathbf{a}$ to a common meadow.

This work proposes a parametric probabilistic approach to model damage accumulation using the double linear damage rule (DLDR) considering the existence of limited experimental fatigue data. A probabilistic version of DLDR is developed in which the joint distribution of the knee-point coordinates is obtained as a function of the joint distribution of the DLDR model input parameters. Considering information extracted from experiments containing a limited number of data points, an uncertainty quantification framework based on the Maximum Entropy Principle and Monte Carlo simulations is proposed to determine the distribution of fatigue life. The proposed approach is validated using fatigue life experiments available in the literature.

The merging of two black holes is a notoriously difficult process to describe exactly. Nevertheless, the hindrances posed by gravity's nonlinearity can be circumvented by focusing on the strict extreme mass ratio limit, in which one of the black holes is infinitely larger than the other. Such an approach has been developed by Emparan and Mart\'inez and applied within General Relativity to investigate the time evolution of event horizons melding, using nothing but elementary concepts in gravitational physics and simple integrations of geodesics. We apply this strategy to study black hole mergers in higher derivative gravity, in order to assess how the defining characteristics of the fusion process change as the gravitational theory is modified. We adopt the case of Einsteinian cubic gravity for concreteness, and determine how the mergers' duration and the relative area increment change as the theory's single coupling parameter is varied., Comment: v2: 13 pages, 11 figures, minor modifications and an added subsection about entropy and area growth (including two new figures)

In analogy with flasque sheaves, we introduce the notion of flasque meadow as a common meadow where the transition maps are all surjective. We study some properties of flasque meadows and illustrate them with many examples and counterexamples.

We introduce the notion of Artinian meadow as an algebraic structure constructed from an Artinian ring which is also a common meadow, i.e.\ a commutative and associative structure with two operations (addition and multiplication) with additive and multiplicative identities and for which inverses are total. The inverse of zero in a common meadow is an error term $\mathbb{a}$ which is absorbent for addition. We show that, in analogy with what happens with commutative unital Artinian rings, Artinian meadows decompose as a product of local meadows in an essentially unique way. We also provide a canonical way to construct meadows from unital commutative rings.

Common meadows are commutative and associative algebraic structures with two operations (addition and multiplication) with additive and multiplicative identities and for which inverses are total. The inverse of zero is an error term $\mathbf{a}$ which is absorbent for addition. We study the problem of enumerating all finite common meadows of \emph{order} $n$ (that is, common meadows with $n$ elements). This problem turns out to be deeply connected with both the number of finite rings of order $n$ and with the number of a certain kind of partition of positive integers.

In this paper, following the studies of Amorim and al. in Partial Differ.Equ. Appl. '23, we consider some new aspects of the motion of the director field of a nematic liquid crystal submitted to a magnetic field and to a laser beam. In particular, we study the existence and partial orbital stability of special standing waves, in the spirit of Cazenave and Lions and Hadj Selem and al. in Milan J. Math. '14 and we present some numerical simulations.

Meadows are a sort of commutative rings with a multiplicative identity element and a total multiplicative inverse operation. In this paper we study algebraic properties of common meadows, which are meadows that introduce, as the inverse of zero, an error term $\abf$ which is absorbent for addition. We show that common meadows are unions of rings which are ordered by a partial order that defines a lattice. These results allow us to generalize some classical algebraic constructions to the setting of common meadows. We also briefly consider common meadows from a categorical perspective., Comment: To appear in Communications in Algebra

In this paper we introduce a model of relativistic short wave-long wave interaction where the short waves are described by the massless $1+3$-dimensional Thirring model of nonlinear Dirac equation and the long waves are described by the $1+3$-dimensional relativistic Euler equations. The interaction coupling terms are modeled by a potential proportional to the relativistic specific volume in the Dirac equation and an external force proportional to the square modulus of the Dirac wave function in the relativistic Euler equation. An important feature of the model is that the Dirac equations are based on the Lagrangian coordinates of the relativistic fluid flow. In particular, an important contribution of this paper is a clear formulation of the relativistic Lagrangian transformation. This is done by means of the introduction of natural auxiliary dependent variables, rendering the discussion totally similar to the non-relativistic case. As far as the authors know the definition of the Lagrangian transformation given in this paper is new. Finally, we establish the short-time existence and uniqueness of a smooth solution of the Cauchy problem for the regularized model. This follows through the symmetrization of the relativistic Euler equation introduced by Makino and Ukai (1995) and requires a slight extension of a well known theorem of T.~Kato (1975) on quasi-linear symmetric hyperbolic systems.

We use ray-tracing techniques to determine the evolution of the event horizon of a large black hole that ``gobbles'' a tiny, traversable wormhole. This calculation has physical meaning in the extreme mass ratio limit. Two setups are considered: a single-mouth wormhole connecting two otherwise independent universes, and a double-mouth zero-length wormhole within the same universe. In the first setting it turns out that, at early times, there exist two disconnected horizons, one in each universe, which then merge as the wormhole falls into the large black hole. In the second setup, we observe the appearance of an `island', a region of spacetime that is spatially disconnected from the exterior of the black hole, but in causal contact with future null infinity. The island shrinks as time evolves and eventually disappears after sufficient time has elapsed, as compared to the distance between the two mouths. This provides a communication channel with the interior of the large black hole for a certain time interval. We compute numerically the lifetime of the island and verify that it depends linearly on the inter-mouth distance. Extending the analysis to wormholes with finite length, we show that the achronal averaged null energy condition prevents the appearance of islands., Comment: 15 pages, 10 figures; v2: minor corrections, matches published version

The present work focus on the implementation and analyze of performance of a low-resolution OFDM system prototype with low-cost hardware. A software defined radio (SDR) system was chosen in this implementation due to its various advantages over a traditional radio system. Among the options of SDR devices available, the use of universal software radio peripherals (USRP) was avoided due to its high cost, despite its popularity in this field of research. Alternatively, a combination of two low-cost SDRs, "Hackrf One" and "RTL- SDR Blog V3" with the GNU Radio, a popular, free and open source radio software, were used. Thus, it was possible to emulate the behavior of a low resolution ADC in the receiver, characterize its performance and estimate its energy savings. This allowed us to determine the feasibility of building a component with the analog-to-digital conversion function with few bits of resolution. We conclude that the performance of an ADC with at least 5 bits of resolution is pretty reasonable and that this reduction in the number of bits, in comparison to 8-bit ADC, represents a fairly expressive energy saving.

Maps are a very important component of strategy games, and a time-consuming task if done by hand. Maps generated by traditional PCG techniques such as Perlin noise or tile-based PCG techniques look unnatural and unappealing, thus not providing the best user experience for the players. However it is possible to have a generator that can create realistic and natural images of maps, given that it is trained how to do so. We propose a model for the generation of maps based on Generative Adversarial Networks (GAN). In our implementation we tested out different variants of GAN-based networks on a dataset of heightmaps. We conducted extensive empirical evaluation to determine the advantages and properties of each approach. The results obtained are promising, showing that it is indeed possible to generate realistic looking maps using this type of approach., Comment: Published in the Proceedings of GAME ON 2022

Context: Container orchestration tools supporting infrastructure-as-code allow new forms of collaboration between developers and operatives. Still, their text-based nature permits naive mistakes and is more difficult to read as complexity increases. We can find few examples of low-code approaches for defining the orchestration of containers, and there seems to be a lack of empirical studies showing the benefits and limitations of such approaches. Goal & method: We hypothesize that a complete visual notation for Docker-based orchestrations could reduce the effort, the error rate, and the development time. Therefore, we developed a tool featuring such a visual notation for Docker Compose configurations, and we empirically evaluated it in a controlled experiment with novice developers. Results: The results show a significant reduction in development time and error-proneness when defining Docker Compose files, supporting our hypothesis. The participants also thought the prototype easier to use and useful, and wanted to use it in the future.

Searching for variations of nature's fundamental constants is a crucial step in our quest to go beyond our current standard model of fundamental physics. If they exist, such variations will be very likely driven by the existence of a new fundamental field. The Bekenstein model and its extensions introduce such a scalar field in a purely phenomenological way, inducing a variation of the fine-structure constant on cosmological scales. This theoretical framework is as simple and general as possible while still preserving all the symmetries of standard quantum electrodynamics. When allowing for couplings to the other sectors of the Universe, such as baryons, dark matter, and the cosmological constant, the Bekenstein model is expected to reproduce the low energy limits of several grand unification, quantum gravity, and higher dimensional theories. In this work, we constrain different versions of the Bekenstein model by confronting the full cosmological evolution of the field with an extensive set of astrophysical, cosmological, and local measurements. We show that couplings of the order of parts per million (ppm) are excluded for all the cases considered, imposing strong restrictions on theoretical frameworks aiming to deal with variations of the fine-structure constant., Comment: Published in Phys. Rev. D. (last version include updated MICROSCOPE bound) and minor typographic corrections

The deployment of Socially Intelligent Agents (SIAs) in learning environments has proven to have several advantages in different areas of application. Social Agent Authoring Tools allow scenario designers to create tailored experiences with high control over SIAs behaviour, however, on the flip side, this comes at a cost as the complexity of the scenarios and its authoring can become overbearing. In this paper we introduce the concept of Explainable Social Agent Authoring Tools with the goal of analysing if authoring tools for social agents are understandable and interpretable. To this end we examine whether an authoring tool, FAtiMA-Toolkit, is understandable and its authoring steps interpretable, from the point-of-view of the author. We conducted two user studies to quantitatively assess the Interpretability, Comprehensibility and Transparency of FAtiMA-Toolkit from the perspective of a scenario designer. One of the key findings is the fact that FAtiMA-Toolkit's conceptual model is, in general, understandable, however the emotional-based concepts were not as easily understood and used by the authors. Although there are some positive aspects regarding the explainability of FAtiMA-Toolkit, there is still progress to be made to achieve a fully explainable social agent authoring tool. We provide a set of key concepts and possible solutions that can guide developers to build such tools., Comment: 24 Pages, 6 figures, in submission limbo

Early adolescence is a time of major social change; a strong sense of belonging and peer connectedness is an essential protective factor in mental health during that period. In this paper we introduce LINA, an augmented reality (AR) smartphone-based serious game played in school by an entire class (age 10+) together with their teacher, which aims to facilitate and improve peer interaction, sense of belonging and class climate, while creating a safe space to reflect on mental health and external stressors related to family circumstance. LINA was developed through an interdisciplinary collaboration involving a playwright, software developers, psychologists, and artists, via an iterative co-development process with young people. A prototype has been evaluated quantitatively for usability and qualitatively for efficacy in a study with 91 early adolescents (agemean=11.41). Results from the Game User Experience Satisfaction Scale (GUESS-18) and data from qualitative focus groups showed high acceptability and preliminary efficacy of the game. Using AR, a shared immersive narrative and collaborative gameplay in a shared physical space offers an opportunity to harness adolescent affinity for digital technology towards improving real-world social connection and sense of belonging., Comment: 21 pages, 10 figures, 2 tables

The widespread use of Internet-of-Things (IoT) across different application domains leads to an increased concern regarding their dependability, especially as the number of potentially mission-critical systems becomes considerable. Fault-tolerance has been used to reduce the impact of faults in systems, and their adoption in IoT is becoming a necessity. This work focuses on how to exercise fault-tolerance mechanisms by deliberately provoking its malfunction. We start by describing a proof-of-concept fault-injection add-on to a commonly used publish/subscribe broker. We then present several experiments mimicking real-world IoT scenarios, focusing on injecting faults in systems with (and without) active self-healing mechanisms and comparing their behavior to the baseline without faults. We observe evidence that fault-injection can be used to (a) exercise in-place fault-tolerance apparatus, and (b) detect when these mechanisms are not performing nominally, providing insights into enhancing in-place fault-tolerance techniques., Comment: 8 pages

While Artificial Intelligence applied to the legal domain is a topic with origins in the last century, recent advances in Artificial Intelligence are posed to revolutionize it. This work presents an overview and contextualizes the main advances on the field of Natural Language Processing and how these advances have been used to further the state of the art in legal text analysis.

Being able to clearly interpret legal texts and fully understanding our rights, obligations and other legal norms has become progressively more important in the digital society. However, simply giving citizens access to the laws is not enough, as there is a need to provide meaningful information that cater to their specific queries and needs. For this, it is necessary to extract the relevant semantic information present in legal texts. Thus, we introduce the SNR (Semantic Norm Recognition) system, an automatic semantic information extraction system trained on a domain-specific (legal) text corpus taken from Portuguese Consumer Law. The SNR system uses the Portuguese Bert (BERTimbau) and was trained on a legislative Portuguese corpus. We demonstrate how our system achieved good results (81.44\% F1-score) on this domain-specific corpus, despite existing noise, and how it can be used to improve downstream tasks such as information retrieval.

We show that there exists a $C^2$ open dense set of convex bodies with smooth boundary whose billiard map exhibits a non-trivial hyperbolic basic set. As a consequence billiards in generic convex bodies have positive topological entropy and exponential growth of the number of periodic orbits., Comment: 33 pages

In this paper we introduce models of short wave-long wave interactions in the relativistic setting. In this context the nonlinear Schr\"odinger equation is no longer adequate for describing short waves and is replaced by a nonlinear Dirac equation. Two specific examples are considered: the case where the long waves are governed by a scalar conservation law; and the case where the long waves are governed by the augmented Born-Infeld equations in electromagnetism.

Internet-of-Things (IoT) systems have spread among different application domains, from home automation to industrial manufacturing processes. The rushed development by competing vendors to meet the market demand of IoT solutions, the lack of interoperability standards, and the overall lack of a defined set of best practices have resulted in a highly complex, heterogeneous, and frangible ecosystem. Several works have been pushing towards visual programming solutions to abstract the underlying complexity and help humans reason about it. As these solutions begin to meet widespread adoption, their building blocks usually do not consider reliability issues. Node-RED, being one of the most popular tools, also lacks such mechanisms, either built-in or via extensions. In this work we present SHEN (Self-Healing Extensions for Node-RED) which provides 17 nodes that collectively enable the implementation of self-healing strategies within this visual framework. We proceed to demonstrate the feasibility and effectiveness of the approach using real devices and fault injection techniques., Comment: Paper accepted for publication as part of the 3rd International Workshop on Software Engineering Research & Practices for the Internet of Things (SERP4IoT 2021), part of 43rd International Conference on Software Engineering (ICSE 2021)

More than a decade has passed since the development of FearNot!, an application designed to help children deal with bullying through role-playing with virtual characters. It was also the application that led to the creation of FAtiMA, an affective agent architecture for creating autonomous characters that can evoke empathic responses. In this paper, we describe FAtiMA Toolkit, a collection of open-source tools that is designed to help researchers, game developers and roboticists incorporate a computational model of emotion and decision-making in their work. The toolkit was developed with the goal of making FAtiMA more accessible, easier to incorporate into different projects and more flexible in its capabilities for human-agent interaction, based upon the experience gathered over the years across different virtual environments and human-robot interaction scenarios. As a result, this work makes several different contributions to the field of Agent-Based Architectures. More precisely, FAtiMA Toolkit's library based design allows developers to easily integrate it with other frameworks, its meta-cognitive model affords different internal reasoners and affective components and its explicit dialogue structure gives control to the author even within highly complex scenarios. To demonstrate the use of FAtiMA Toolkit, several different use cases where the toolkit was successfully applied are described and discussed.

Autonomous agents that can engage in social interactions witha human is the ultimate goal of a myriad of applications. A keychallenge in the design of these applications is to define the socialbehavior of the agent, which requires extensive content creation.In this research, we explore how we can leverage current state-of-the-art tools to make inferences about the emotional state ofa character in a story as events unfold, in a coherent way. Wepropose a character role-labelling approach to emotion tracking thataccounts for the semantics of emotions. We show that by identifyingactors and objects of events and considering the emotional stateof the characters, we can achieve better performance in this task,when compared to end-to-end approaches., Comment: Preprint

Industrial Internet-of-Things (IIoT) results from the addition of sensing and actuating capabilities to industrial environments to improve the overall manufacturing processes. Some of these systems have highly-complex tasks of monitorization and control and need to be programmed accordingly. The use of visual programming, such as workflows, is common in these systems due to the abstraction they provide to the systems programmer. However, such programming environments have several deficiencies on what regards debugging capabilities, mostly due to the constraints that difficult the use of traditional mechanisms. The work presented in this paper approaches these issues, delving into the design and implementation of a multi-strategy debugging mechanism into a commercial-grade Manufacturing Execution System. To validate the approach, a proof-of-concept was then developed and validated against different debugging scenarios.

Throughout the years, social norms have been promoted as an informal enforcement mechanism for achieving beneficial collective outcomes. Among the most used methods to foster interactions, framing the context of a situation or setting in-game rules have shown strong results as mediators on how an individual interacts with their peers. Nevertheless, we found that there is a lack of research regarding the use of incentives such as scores to promote social interactions differing in valence. Weighing how incentives influence in-game behavior, we propose the use of rewards to promote interactions varying in valence, i.e. positive or negative, in a two-player scenario. To do so, we defined social valence as a continuous scale with two poles represented by Complicate and Help. Then, we performed user tests where participants where asked to play a game with two reward-based systems to test on whether the scoring system influenced the social interaction valence. The results indicate that the developed reward-based systems were able to foster interactions diverging in social valence scores, providing insights on how factors such as incentives overlap individual's established social norms. These findings empower game developers and designers with a low-cost and effective policy tool that is able to promote in-game behavior changes., Comment: 8 pages, 6 figures, 1 table, submitted to IEEE Conference on Games (CoG) 2020

Recent research has taken particular interest in observing the dynamics between altruistic and individual behavior. This is a commonly approached problem when reasoning about social dilemmas, which have a plethora of real world counterparts in the fields of education, health and economics. Weighing how incentives influence in-game behavior, our study examines individual and altruistic interactions, by analyzing the players' strategies and interaction motives when facing different reward attribution strategies. Consequently, a model for interaction motives is also proposed, with the premise that the motives for interactions can be defined as a continuous space, ranging from self-oriented (associated to self-improvement behaviors) to others-oriented (associated to extreme altruism behaviors) motives. To evaluate the promotion of individual and altruistic behavior, we leverage Message Across, an in-loco two-player videogame with adaptable reward attribution systems. We conducted several user tests (N = 66) to verify to what extent individual and altruistic reward attribution systems led players to vary their strategies and motives orientation. Our results indicate that players' strategies and self-reported orientation of interaction motives varied highly significantly upon the deployment of individual and altruistic reward systems, which leads us to believe on the suitability of applying an incentive-based strategy to moderate the emergence of individual and altruistic behavior in games., Comment: 8 pages, 6 figures

We consider smooth representations of the unit group $G = \mathcal{A}^{\times}$ of a finite-dimensional split basic algebra $\mathcal{A}$ over a non-Archimedean local field. In particular, we prove a version of Gutkin's conjecture, namely, we prove that every irreducible smooth representation of $G$ is compactly induced by a one-dimensional representation of the unit group of some subalgebra of $\mathcal{A}$. We also discuss admissibility and unitarisability of smooth representations of G.

In this paper we investigate two hypothesis regarding the use of deep reinforcement learning in multiple tasks. The first hypothesis is driven by the question of whether a deep reinforcement learning algorithm, trained on two similar tasks, is able to outperform two single-task, individually trained algorithms, by more efficiently learning a new, similar task, that none of the three algorithms has encountered before. The second hypothesis is driven by the question of whether the same multi-task deep RL algorithm, trained on two similar tasks and augmented with elastic weight consolidation (EWC), is able to retain similar performance on the new task, as a similar algorithm without EWC, whilst being able to overcome catastrophic forgetting in the two previous tasks. We show that a multi-task Asynchronous Advantage Actor-Critic (GA3C) algorithm, trained on Space Invaders and Demon Attack, is in fact able to outperform two single-tasks GA3C versions, trained individually for each single-task, when evaluated on a new, third task, namely, Phoenix. We also show that, when training two trained multi-task GA3C algorithms on the third task, if one is augmented with EWC, it is not only able to achieve similar performance on the new task, but also capable of overcoming a substantial amount of catastrophic forgetting on the two previous tasks., Comment: 11 pages

Nowadays, big effort is being put to study gamification and how game elements can be used to engage players. In this scope, we believe there is a growing need to explore the impact game mechanics have on the players' interactions and perception. This work focuses on the application of game mechanics to lead players to achieve certain types of social interaction (we named this type of mechanics social interaction mechanics). A word matching game called CrossAnt was modified so that it could dynamically generate different social interaction mechanics. These mechanics consisted in different key combinations needed to play the game and were aimed to promote what we think are three important types of social interactions: cooperation, competition and individual exploration. Our evaluation consisted on the execution of several sessions where two players interacted with the game for several levels and had to find for themselves how to perform the actions needed to succeed. While some of the levels required the input from both players in order to be completed, others could be completed by each player independently. Our results show that cooperation was perceived when both players had to intervene to perform the game actions. However, longer interactions may still be needed so that the other types of interactions are promoted., Comment: 5 pages, 4 figures, 5 tables

Software has a longstanding association with a state of crisis considering its success rate. The explosion of Internet-connected devices, Internet-of-Things, adds to the complexity of software systems. The particular characteristics of these systems, such as being large-scale and its heterogeneity, pose increasingly new challenges. In this paper, we first briefly introduce the IoT paradigm and the current state of art of software development. Then, we delve into the particularities of developing software for IoT systems and systems of systems, given an overview of what are the current methodologies and tools for design, develop and test such systems. The findings are discussed, revealing open issues and research directions, and reveal that the nowadays IoT software development practices are still lagging behind of what are the current best practices., Comment: 38 pages

The IoT area has grown significantly in the last few years and is expected to reach a gigantic amount of 50 billion devices by 2020. The appearance of serverless architectures, specifically highlighting FaaS, raises the question of the of using such in IoT environments. Combining IoT with a serverless architectural design can be effective when trying to make use of the local processing power that exists in a local network of IoT devices and creating a fog layer that leverages computational capabilities that are closer to the end-user. In this approach, which is placed between the device and the serverless function, when a device requests for the execution of a serverless function will decide based on previous metrics of execution if the serverless function should be executed locally, in the fog layer of a local network of IoT devices, or if it should be executed remotely, in one of the available cloud servers. Therefore, this approach allows to dynamically allocating functions to the most suitable layer.

The Internet of Things is progressively getting broader, evol-ving its scope while creating new markets and adding more to the existing ones. However, both generation and analysis of large amounts of data, which are integral to this concept, may require the proper protection and privacy-awareness of some sensitive information. In order to control the access to this data, allowing devices to verify the reliability of their own interactions with other endpoints of the network is a crucial step to ensure this required safeness. Through the implementation of a blockchain-based Public Key Infrastructure connected to the Keybase platform, it is possible to achieve a simple protocol that binds devices' public keys to their owner accounts, which are respectively supported by identity proofs. The records of this blockchain represent digital signatures performed by this Keybase users on their respective devices' public keys, claiming their ownership. Resorting to this distributed and decentralized PKI, any device is able to autonomously verify the entity in control of a certain node of the network and prevent future interactions with unverified parties.

Access control is a crucial part of a system's security, restricting what actions users can perform on resources. Therefore, access control is a core component when dealing with e-Health data and resources, discriminating which is available for a certain party. We consider that current systems that attempt to assure the share of policies between facilities are prone to system's and network's faults and do not assure the integrity of policies lifecycle. By approaching this problem with the use of a distributed ledger, namely a consortium blockchain, where the operations are stored as transactions, we ensure that the different facilities have knowledge about all the parties that can act over the e-Health resources while maintaining integrity, auditability, authenticity, and scalability., Comment: 8 pages

We consider piecewise expanding maps of the interval with finitely many branches of monotonicity and show that they are generically combinatorially stable, i.e., the number of ergodic attractors and their corresponding mixing periods do not change under small perturbations of the map. Our methods provide a topological description of the attractor and, in particular, give an elementary proof of the density of periodic orbits., Comment: 19 pages, 2 figures

We show that in the Gevrey topology, a $d$-torus flow close enough to linear with a unique rotation vector $\omega$ is linearizable as long as $\omega$ satisfies a Brjuno type diophantine condition. The proof is based on the fast convergence under renormalization of the associated Gevrey vector field. It requires a multidimensional continued fractions expansion of $\omega$, and the corresponding characterization of the Brjuno type vectors. This demonstrates that renormalization methods deal very naturally with Gevrey regularity expressed in the decay of Fourier coefficients. In particular, they provide linearization for frequencies beyond diophantine in non-analytic topologies., Comment: 40 pages, 0 figures

From 1972 and the Meadows report to 1997 and the ratification of the Kyoto Protocol by most of the countries in the world, the global energy policy framework has undergone a paradigm shift, as human societies have been leaving aside the sole economic growth to embrace the broader concept of sustainable development. As new electrification vectors, modern renewable power systems, such as solar PV, have sprung up in the wake of this major mutation and have typically been following an exponential growth since the mid-nineties. Electricity as well as its lack indeed holds a central position within the human development apparatus, from highly interconnected centralized power networks reaching 100 % of the population in developed countries, to the almost 500 millions people without access to electricity in the multidimensionally poor rural areas of Sub-Saharan Africa. The encounter of the worldwide energy context being changed with each of these specific social-energy paradigms has ended up considering two strategies for integrating renewable resources in power systems: the grid-connected architecture for meeting the sustainable development requirements, and the rural off-grid electrification for settling the lack of human development. By means of a historical and cross-sectional overview, we depict here the ins and outs of this protean pattern and, using the case of solar PV, analyze how it has eventually affected the development and sustainability of renewable power systems in Sub-Saharan Africa.