arXiv subjects

João Dias

Publications and source records attributed to João Dias.

At least 19 recordsLinked to original sources

arXiv2026

The Geometry of Pattern Groups

Coset incidence geometries are an important tool which connect group theory and geometry. While the representations of the unitriangular group and its pattern subgroups have been studied extensively, the underlying geometric structures of these groups has remained largely unexplored. In this article, we construct the natural coset geometry associated with each pattern group over a finite field $\FF_q$, and prove geometrical properties of theses structures. We show how combinatorial features of their defining closed sets directly correspond to properties of their parabolic subgroups, in particular the intersection of parabolics and normality of the Borel subgroup. Finally, we characterize the automorphisms of these geometries and examine how pattern geometries behave under change of field within the same characteristic $p$.

math.GR↗

arXiv2026

Decomposable shuffles

We develop a combinatorial and order-theoretic framework for shuffles, understood as ordered concatenations of indexed families of sequences that induce total orders on the natural numbers. Motivated by the classical Šarkovskiĭ order, we introduce elementary building blocks that encode finite and infinite order patterns and focus on decomposable shuffles constructed from finite ordinals together with $ω$ and its dual $ω^*$. We define representations that allow individual elements to be located within a shuffle and show how suitable structural conditions yield total orders on $\mathbb{N}$

math.CO↗

arXiv2025

Playing Hex and Counter Wargames using Reinforcement Learning and Recurrent Neural Networks

Hex and Counter Wargames are adversarial two-player simulations of real military conflicts requiring complex strategic decision-making. Unlike classical board games, these games feature intricate terrain/unit interactions, unit stacking, large maps of varying sizes, and simultaneous move and combat decisions involving hundreds of units. This paper introduces a novel system designed to address the strategic complexity of Hex and Counter Wargames by integrating cutting-edge advancements in Recurrent Neural Networks with AlphaZero, a reliable modern Reinforcement Learning algorithm. The system utilizes a new Neural Network architecture developed from existing research, incorporating innovative state and action representations tailored to these specific game environments. With minimal training, our solution has shown promising results in typical scenarios, demonstrating the ability to generalize across different terrain and tactical situations. Additionally, we explore the system's potential to scale to larger map sizes. The developed system is openly accessible, facilitating continued research and exploration within this challenging domain.

cs.LG↗

arXiv2024

Bridging Meadows and Sheaves

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.

math.AC↗

arXiv2024

Flasque Meadows

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.

math.RA↗

arXiv2024

Artinian Meadows

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.

math.RA↗

arXiv2024

Towards an Enumeration of Finite Common Meadows

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.

math.RA↗

arXiv2024

Strolling through common meadows

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.

math.RA↗

arXiv2024

Smooth representations of involutive algebra groups over non-archimedean local fields

An algebra group over a field $F$ is a group of the form $G = 1+J$ where $J$ is a finite-dimensional nilpotent associative $F$-algebra. A theorem of M. Boyarchenko asserts that, in the case where $F$ is a non-archimedean local field, every irreducible smooth representation of $G$ is admissible and smoothly induced by a one-dimensional smooth representation of some algebra subgroup of $G$. If $J$ is a nilpotent algebra endowed with an involution $σ:J\to J$, then $σ$ naturally defines a group automorphism of $G$, and we may consider the fixed point subgroup $C_{G}(σ)$. Assuming that $F$ has characteristic different from $2$, we extend Boyarchenko's result and show that every irreducible smooth representation of $C_{G}(σ)$ is admissible and smoothly induced by a one-dimensional smooth representation of a subgroup of the form $C_{H}(σ)$ where $H$ is an $σ$-invariant algebra subgroup of $G$. As a particular case, the result holds for maximal unipotent subgroups of the classical Chevalley groups defined over $F$.

math.RT↗

arXiv2024

Shintani descent for standard supercharacters of algebra groups

Let $\mathcal{A}(q)$ be a finite-dimensional nilpotent algebra over a finite field $\mathbb{F}_{q}$ with $q$ elements, and let $G(q) = 1+\mathcal{A}(q)$. On the other hand, let $\Bbbk$ denote the algebraic closure of $\mathbb{F}_{q}$, and let $\mathcal{A} = \mathcal{A}(q) \otimes_{\mathbb{F}_{q}} \Bbbk$. Then $G = 1+\mathcal{A}$ is an algebraic group over $\Bbbk$ equipped with an $\mathbb{F}_{q}$-rational structure given by the usual Frobenius map $F:G\to G$, and $G(q)$ can be regarded as the fixed point subgroup $G^{F}$. For every $n \in \mathbb{N}$, the $n$th power $F^{n}:G\to G$ is also a Frobenius map, and $G^{F^{n}}$ identifies with $G(q^{n}) = 1 + \mathcal{A}(q^{n})$. The Frobenius map restricts to a group automorphism $F:G(q^{n})\to G(q^{n})$, and hence it acts on the set of irreducible characters of $G(q^{n})$. Shintani descent provides a method to compare $F$-invariant irreducible characters of $G(q^{n})$ and irreducible characters of $G(q)$. In this paper, we show that it also provides a uniform way of studying supercharacters of $G(q^{n})$ for $n \in \mathbb{N}$. These groups form an inductive system with respect to the inclusion maps $G(q^{m}) \to G(q^{n})$ whenever $m \mid n$, and this fact allows us to study all supercharacter theories simultaneously, to establish connections between them, and to relate them to the algebraic group $G$. Indeed, we show that Shintani descent permits the definition of a certain ``superdual algebra'' which encodes information about the supercharacters of $G(q^{n})$ for $n \in \mathbb{N}$.

math.RT↗

arXiv2023

GAN-Based Content Generation of Maps for Strategy Games

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.

cs.LG↗

arXiv2022

Towards Explainable Social Agent Authoring tools: A case study on FAtiMA-Toolkit

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.

cs.MA↗

arXiv2022

LINA -- A social augmented reality game around mental health, supporting real-world connection and sense of belonging for early adolescents

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.

cs.HC↗

arXiv2022

Semantic Norm Recognition and its application to Portuguese Law

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.

cs.CL↗

arXiv2022

State of the Art in Artificial Intelligence applied to the Legal Domain

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.

cs.CL↗

arXiv2021

CHARET: Character-centered Approach to Emotion Tracking in Stories

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.

cs.HC↗

arXiv2021

FAtiMA Toolkit -- Toward an effective and accessible tool for the development of intelligent virtual agents and social robots

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.

cs.MA↗

arXiv2020

Reward-Mediated Individual and Altruistic Behavior

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.

cs.HC↗