arXiv subjects

Daniel Gonçalves

Publications and source records attributed to Daniel Gonçalves.

At least 19 recordsLinked to original sources

arXiv2026

Incidental Visualizations: Augmented Reality as a Medium for Contextual Information

In today's fast-paced world, delivering information efficiently and unobtrusively is essential. While ambient and glanceable visualizations provide real-time data, they can increase cognitive load and disrupt primary tasks. We investigate incidental visualizations, a novel concept in information visualization designed to present contextually relevant information briefly and spontaneously, with minimal user interaction. Augmented Reality offers an ideal medium for this integration, embedding visualizations directly within the user's environment. Through controlled user studies on logic-based game tasks (Sudoku and Connect 4), this work compares ambient, periodic, and incidental visualization patterns in terms of comprehension accuracy, performance, and disruption. Results indicate that IVs deliver information as effectively as ambient displays while minimizing disruption, highlighting their potential for adaptive, context-aware information delivery in AR environments.

cs.HC↗

arXiv2026

Graded Locally Finite and Just Infinite Steinberg Algebras

We study graded locally finite and graded just infinite Steinberg algebras of ample Hausdorff groupoids. For gradings by discrete groups induced by a cocycle, we characterize finite-dimensional homogeneous components in terms of finite cocycle fibres. Moreover, we obtain general criteria ensuring that, once one homogeneous component is infinite-dimensional, all of them are. Under suitable isotropy hypotheses, we show that for locally finite Steinberg algebras all irreducible representations act by finite-rank operators. We also obtain necessary conditions for Steinberg algebras to be just infinite. In addition, we give a complete characterization of graded just infinite Steinberg algebras in terms of finite invariant reductions and identify conditions under which graded just infiniteness is equivalent to graded simplicity. We apply these results to Steinberg algebras of Deaconu--Renault groupoids and to subshift algebras. For Deaconu--Renault groupoids, we obtain dynamical criteria for graded just infiniteness. For subshift algebras, we show that there are no nontrivial finite-dimensional examples, we characterize when all homogeneous components are infinite-dimensional, and in the finite-alphabet case, we prove that graded just infiniteness, graded simplicity, minimality of the associated groupoid, and hyper-cofinality of the subshift are equivalent.

math.RA↗

arXiv2026

Residual finite-dimensionality of ultragraph algebras via branching systems

We study residual finite-dimensionality for ultragraph algebras, both in the algebraic and in the C-star-algebraic settings. We introduce graph-theoretic RFD conditions for ultragraphs, extending the conditions that characterize RFD graph C-star-algebras. Using the boundary ultrapath branching system, we construct finite-dimensional branching-system representations associated to terminal boundary sets and no-exit cycles. These representations are used to prove that, whenever an ultragraph satisfies the graph-theoretic RFD conditions, its ultragraph Leavitt path algebra LK(G) is RFD, for every field K, and its ultragraph C-star-algebra RFD. For ultragraphs satisfying Condition (RFUM2), we prove converses in both settings. The analytic converse uses the groupoid model and the density of periodic points, while the algebraic converse is proved directly by finite-dimensional linear algebra. Thus, for RFUM2 ultragraphs, RFD of LK(G), RFD of C(G), and the graph-theoretic RFD conditions are equivalent. This gives, in particular, a common combinatorial description linking the algebraic and analytic theories, recovers the graph C-start-algebra characterization, and yields an algebraic characterization for Leavitt path algebras of graphs. We also construct an RFD ultragraph algebra which is genuinely outside the graph-algebra class in both settings.

math.OA↗

arXiv2026

The Reduction Theorem for Leavitt Labelled Path Algebras and Its Applications

We introduce a notion of labelled cycle for normal labelled spaces and prove a reduction theorem for Leavitt labelled path algebras. We show that every nonzero element can be reduced, by suitable left and right multiplication, either to a nonzero scalar multiple of a projection or to a polynomial supported on a labelled cycle without exits. This extends the classical reduction theorem for Leavitt path algebras of directed graphs and its analogues for ultragraph Leavitt path algebras and subshift algebras. As applications, we prove the graded uniqueness theorem and the Cuntz--Krieger uniqueness theorem for Leavitt labelled path algebras, and show that these algebras are semiprime and semiprimitive over fields.

math.RA↗

arXiv2026

Paterson compactifications, inverse limits and shadowing for Deaconu-Renault systems

We develop a new metric and inverse-limit framework for Deaconu-Renault systems arising from local homeomorphisms between open subsets of locally compact zero-dimensional spaces. Our starting point is the Paterson-type compactification of infinite product spaces, which underlies several symbolic and groupoid models, including one-sided shifts over infinite alphabets and path spaces of graphs and higher-rank graphs. We construct an explicit compatible ultrametric on this compactification and give a concrete description of its generalized cylinder topology and convergence. Within this framework, we introduce an inverse-limit-type space naturally associated to a Deaconu-Renault system. In contrast with the classical compact theory, the correct inverse-limit object must incorporate not only infinite backward orbits but also finite configurations arising as limits of such orbits. This produces a canonical shift system extending the original dynamics. We then study shadowing in the ultrametric setting. For spaces admitting tame defining sequences, we characterize shadowing in terms of the defining partitions, extending the topological description of shadowing from compact zero-dimensional dynamics to the locally compact setting relevant for Deaconu-Renault systems. As a main application, we prove a transfer theorem showing, under a separation property expressed through uniformly contracting inverse branches, that shadowing for the inverse-limit Deaconu-Renault system is equivalent to shadowing for the compactified base system. This provides a noncompact inverse-limit shadowing theory for a broad class of partially defined local-homeomorphism dynamics.

math.DS↗

arXiv2026

Shadowing and Lipschitz Shadowing in Symbolic Dynamics: Finite vs. Infinite Alphabets

We point out a basic dichotomy between the shadowing and Lipschitz shadowing properties for one-sided shift spaces in two infinite-alphabet frameworks: the classical product-topology model $X\subseteq A^{\mathbb{N}}$ and the compact Ott--Tomforde--Willis (OTW) model obtained by adjoining finite words. In the product-topology setting, for the natural class of prefix ultrametrics, shadowing and Lipschitz shadowing coincide. However, since $A^{\mathbb{N}}$ is non-compact when $A$ is countably infinite, it remains unclear whether Lipschitz shadowing is stable under arbitrary uniformly equivalent changes of compatible metric in the product-topology model. In contrast, for OTW shift spaces the topology admits a canonical family of compatible ultrametrics indexed by enumerations of finite words, and these metrics are all uniformly equivalent. Using the Deaconu--Renault viewpoint and known shadowing results for local homeomorphisms on zero-dimensional compact spaces, we show that the OTW full shift has the shadowing property for every OTW metric. Nevertheless, Lipschitz shadowing can depend on the chosen OTW metric even within this fixed uniform equivalence class: we construct two uniformly equivalent OTW ultrametrics on the full shift for which Lipschitz shadowing holds in one case and fails in the other. Thus the OTW compactification provides a compact infinite-alphabet setting where the metric dependence of Lipschitz shadowing can be resolved explicitly, in sharp contrast with what is currently known for the product-topology model.

math.DS↗

arXiv2026

Pushing the frontiers of subexponential FPT time for Feedback Vertex Set

The paper deals with the Feedback Vertex Set problem parameterized by the solution size. Given a graph $G$ and a parameter $k$, one has to decide if there is a set $S$ of at most $k$ vertices such that $G-S$ is acyclic. Assuming the Exponential Time Hypothesis, it is known that FVS cannot be solved in time $2^{o(k)}n^{\mathcal{O}(1)}$ in general graphs. To overcome this, many recent results considered FVS restricted to particular intersection graph classes and provided such $2^{o(k)}n^{\mathcal{O}(1)}$ algorithms. In this paper we provide generic conditions on a graph class for the existence of an algorithm solving FVS in subexponential FPT time, i.e. time $2^{k^\varepsilon} \mathop{\rm poly}(n)$, for some $\varepsilon<1$, where $n$ denotes the number of vertices of the instance and $k$ the parameter. On the one hand this result unifies algorithms that have been proposed over the years for several graph classes such as planar graphs, map graphs, unit-disk graphs, pseudo-disk graphs, and string graphs of bounded edge-degree. On the other hand it extends the tractability horizon of FVS to new classes that are not amenable to previously used techniques, in particular intersection graphs of ``thin'' objects like segment graphs or more generally $s$-string graphs.

cs.DS↗

arXiv2025

Plane Strong Connectivity Augmentation

We investigate the problem of strong connectivity augmentation within plane oriented graphs. We show that deciding whether a plane oriented graph $D$ can be augmented with (any number of) arcs $X$ such that $D+X$ is strongly connected, but still plane and oriented, is NP-hard. This question becomes trivial within plane digraphs, like most connectivity augmentation problems without a budget constraint. The budgeted version, Plane Strong Connectivity Augmentation (PSCA) considers a plane oriented graph $D$ along with some integer $k$, and asks for an $X$ of size at most $k$ ensuring that $D+X$ is strongly connected, while remaining plane and oriented. Our main result is a fixed-parameter tractable algorithm for PSCA, running in time $2^{O(k)} n^{O(1)}$. The cornerstone of our procedure is a structural result showing that, for any fixed $k$, each face admits a bounded number of partial solutions "dominating" all others. Then, our algorithm for PSCA combines face-wise branching with a Monte-Carlo reduction to the polynomial Minimum Dijoin problem, which we derandomize. To the best of our knowledge, this is the first FPT algorithm for a (hard) connectivity augmentation problem constrained by planarity.

math.CO↗

arXiv2025

3-colorable planar graphs have an intersection segment representation using 3 slopes

In his PhD Thesis, E.R. Scheinerman conjectured that planar graphs are intersection graphs of line segments in the plane. This conjecture was proved with two different approaches by J. Chalopin and the author, and by the author, L. Isenmann, and C. Pennarun. In the case of 3-colorable planar graphs E.R. Scheinerman conjectured that it is possible to restrict the set of slopes used by the segments to only 3 slopes. Here we prove this conjecture by using an approach introduced by S. Felsner to deal with contact representations of planar graphs with homothetic triangles.

cs.DM↗

arXiv2025

Relative ultragraph algebras and infinite interval maps

In this paper, we introduce the notion of relative ultragraph algebras and extend classical injectivity criteria for representations, particularly those arising from branching systems,to this relative setting. This new concept is closely connected to, and indeed motivated by, the dynamics of certain interval maps that we call infinite Markov maps. The central point is that these algebras provide the natural framework in which representations induced by such maps are defined.

math.OA↗

arXiv2025

On the Feasibility of Fully AI-automated Vishing Attacks

A vishing attack is a form of social engineering where attackers use phone calls to deceive individuals into disclosing sensitive information, such as personal data, financial information, or security credentials. Attackers exploit the perceived urgency and authenticity of voice communication to manipulate victims, often posing as legitimate entities like banks or tech support. Vishing is a particularly serious threat as it bypasses security controls designed to protect information. In this work, we study the potential for vishing attacks to escalate with the advent of AI. In theory, AI-powered software bots may have the ability to automate these attacks by initiating conversations with potential victims via phone calls and deceiving them into disclosing sensitive information. To validate this thesis, we introduce ViKing, an AI-powered vishing system developed using publicly available AI technology. It relies on a Large Language Model (LLM) as its core cognitive processor to steer conversations with victims, complemented by a pipeline of speech-to-text and text-to-speech modules that facilitate audio-text conversion in phone calls. Through a controlled social experiment involving 240 participants, we discovered that ViKing has successfully persuaded many participants to reveal sensitive information, even those who had been explicitly warned about the risk of vishing campaigns. Interactions with ViKing's bots were generally considered realistic. From these findings, we conclude that tools like ViKing may already be accessible to potential malicious actors, while also serving as an invaluable resource for cyber awareness programs.

cs.CR↗

arXiv2025

Solenoids in automorphism groups of evolution algebras

Let A be an evolution algebra (possibly infinite-dimensional) equipped with a fixed natural basis B, and let E be the associated graph defined by Elduque and Labra. We describe the group of automorphisms of A that are diagonalizable with respect to B. This group arises as the inverse limit of a functor (a diagram) from the category associated with the graph E to the category of groups. In certain cases, this group can be realized as a dyadic solenoid. Additionally, we investigate the automorphisms that permute (and possibly scale) the elements of B. In particular, for algebras satisfying the 2LI condition, we provide a complete description of their automorphism group.

math.RA↗

arXiv2025

Brooks-type colourings of digraphs in linear time

Brooks' Theorem is a fundamental result on graph colouring, stating that the chromatic number of a graph is almost always upper bounded by its maximal degree. Lovász showed that such a colouring may then be computed in linear time when it exists. Many analogues are known for variants of (di)graph colouring, notably for list-colouring and partitions into subgraphs with prescribed degeneracy. One of the most general results of this kind is due to Borodin, Kostochka, and Toft, when asking for classes of colours to satisfy "variable degeneracy" constraints. An extension of this result to digraphs has recently been proposed by Bang-Jensen, Schweser, and Stiebitz, by considering colourings as partitions into "variable weakly degenerate" subdigraphs. Unlike earlier variants, there exists no linear-time algorithm to produce colourings for these generalisations. We introduce the notion of (variable) bidegeneracy for digraphs, capturing multiple (di)graph degeneracy variants. We define the corresponding concept of $F$-dicolouring, where $F = (f_1,...,f_s)$ is a vector of functions, and an $F$-dicolouring requires vertices coloured $i$ to induce a "strictly-$f_i$-bidegenerate" subdigraph. We prove an analogue of Brooks' theorem for $F$-dicolouring, generalising the result of Bang-Jensen et al., and earlier analogues in turn. Our new approach provides a linear-time algorithm that, given a digraph $D$, either produces an $F$-dicolouring of $D$, or correctly certifies that none exist. This yields the first linear-time algorithms to compute (di)colourings corresponding to the aforementioned generalisations of Brooks' theorem. In turn, it gives an unified framework to compute such colourings for various intermediate generalisations of Brooks' theorem such as list-(di)colouring and partitioning into (variable) degenerate sub(di)graphs.

math.CO↗

arXiv2025

The uniform dimension of a monoid with applications to graph algebras

We adapt Goldie's concept of uniform dimensions from module theory over rings to $Γ$-monoids. A $Γ$-monoid $M$ is said to have uniform dimension $n$ if $n$ is the largest number of pairwise incomparable nonzero $Γ$-order ideals contained in $M$. Specializing to the talented monoid of a graph, we show that the uniform dimension provides a rough measure of how the graph branches out. Since for any order ideal $I$, its orthogonal ideal $I^\perp$ is the largest ideal incomparable to $I$, we study the notions of orthogonality and regularity, particularly when $I^{\perp\perp}=I$. We show that the freeness of the action of $\mathbb Z$ on the talented monoid of a graph is preserved under quotienting by a regular ideal. Furthermore, we determine the underlying hereditary and saturated sets that generate these ideals. These results unify recent studies on regular ideals of the corresponding Leavitt path algebras and graph $C^*$-algebras. We conclude that for graphs $E$ and $F$, if there is a $\mathbb Z$-monoid isomorphism $T_E\cong T_F$, then there is a one-to-one correspondence between the regular ideals of the associated Leavitt path algebras $L_K(E)$ and $L_K(F)$ (and similarly, $C^*(E)$ and $C^*(F)$). Since the talented monoid $T_E$ is the positive cone of the graded Grothendieck group $K_0^{gr}(L_K(E))$, this provides further evidence supporting the Graded Classification Conjecture.

math.RA↗

arXiv2024

The dynamical structure of partial group algebras with relations, with applications to subshift algebras

We introduce partial group algebras with relations in a purely algebraic framework. Given a group and a set of relations, we define an algebraic partial action and prove that the resulting partial skew group ring is isomorphic to the associated partial group algebra with relations. Under suitable conditions - which always holds if the base ring is a field - we demonstrate that the partial skew group ring can also be described using a topological partial action. Furthermore, we show how subshift algebras can be realized as partial group algebras with relations. Using the topological partial action, we describe simplicity of subshift algebras in terms of the underlying dynamics of the subshift.

math.RA↗

arXiv2024

Feedback Vertex Set for pseudo-disk graphs in subexponential FPT time

In this paper, we investigate the existence of parameterized algorithms running in subexponential time for two fundamental cycle-hitting problems: Feedback Vertex Set (FVS) and Triangle Hitting (TH). We focus on the class of pseudo-disk graphs, which forms a common generalization of several graph classes where such results exist, like disk graphs and square graphs. In these graphs, we show that TH can be solved in time $2^{O(k^{3/4}\log k)}n^{O(1)}$, and given a geometric representation FVS can be solved in time $2^{O(k^{6/7}\log k)}n^{O(1)}$.

cs.DS↗

arXiv2024

Nonwandering sets and the entropy of local homeomorphisms

A local homeomorphism between open subsets of a locally compact Hausdorff space induces dynamical systems with a wide range of applications, including in C*-algebras. In this paper, we introduce the concepts of nonwandering and wandering sets for such systems and show that, under mild conditions, the metric entropy is concentrated in the nonwandering set. More generally, we demonstrate that the entropy of the system is the maximum of the entropies of the systems restricted to the nonwandering set and the closure of the wandering set. We illustrate these results with several examples, including applications to subshifts over countable alphabets.

math.DS↗

arXiv2024

Hopf algebras and associative representations of two-dimensional evolution algebras

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 $\mathcal{H}\not\cong K(ε)$ (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.

math.RA↗