arXiv subjects

André de Carvalho

Publications and source records attributed to André de Carvalho.

18 recordsLinked to original sources

arXiv2026

Artificial Intelligence for All? Brazilian Teachers on Ethics, Equity, and the Everyday Challenges of AI in Education

This study examines the perceptions of Brazilian K-12 education teachers regarding the use of AI in education, specifically General Purpose AI. This investigation employs a quantitative analysis approach, extracting information from a questionnaire completed by 346 educators from various regions of Brazil regarding their AI literacy and use. Educators vary in their educational level, years of experience, and type of educational institution. The analysis of the questionnaires shows that although most educators had only basic or limited knowledge of AI (80.3\%), they showed a strong interest in its application, particularly for the creation of interactive content (80.6%), lesson planning (80.2%), and personalized assessment (68.6%). The potential of AI to promote inclusion and personalized learning is also widely recognized (65.5%). The participants emphasized the importance of discussing ethics and digital citizenship, reflecting on technological dependence, biases, transparency, and responsible use of AI, aligning with critical education and the development of conscious students. Despite enthusiasm for the pedagogical potential of AI, significant structural challenges were identified, including a lack of training (43.4%), technical support (41.9%), and limitations of infrastructure, such as low access to computers, reliable Internet connections, and multimedia resources in schools. The study shows that Brazil is still in a bottom-up model for AI integration, missing official curricula to guide its implementation and structured training for teachers and students. Furthermore, effective implementation of AI depends on integrated public policies, adequate teacher training, and equitable access to technology, promoting ethical, inclusive, and contextually grounded adoption of AI in Brazilian K-12 education.

cs.CY↗

arXiv2025

Unimodal Measurable Pseudo-Anosov Maps

We exhibit a continuously varying family $F_λ$ of homeomorphisms of the sphere $S^2$, for which each $F_λ$ is a measurable pseudo-Anosov map. Measurable pseudo-Anosov maps are generalizations of Thurston's pseudo-Anosov maps, and also of the generalized pseudo-Anosov maps of [19]. They have a transverse pair of invariant full measure turbulations, consisting of streamlines which are dense injectively immersed lines: these turbulations are equipped with measures which are expanded and contracted uniformly by the homeomorphism. The turbulations need not have a good product structure anywhere, but have some local structure imposed by the existence of tartans: bundles of unstable and stable streamline segments which intersect regularly, and on whose intersections the product of the measures on the turbulations agrees with the ambient measure. Each map $F_λ$ is semi-conjugate to the inverse limit of the core tent map with slope $λ$: it is topologically transitive, ergodic with respect to a background Oxtoby-Ulam measure, has dense periodic points, and has topological entropy $h(F_λ) = \log λ$ (so that no two $F_λ$ are topologically conjugate). For a full measure, dense $G_δ$ set of parameters, $F_λ$ is a measurable pseudo-Anosov map but not a generalized pseudo-Anosov map, and its turbulations are nowhere locally regular.

math.DS↗

arXiv2024

Enhancing Algorithm Performance Understanding through tsMorph: Generating Semi-Synthetic Time Series for Robust Forecasting Evaluation

Time series forecasting is a subject of significant scientific and industrial importance. Despite the widespread utilization of forecasting methods, there is a dearth of research aimed at comprehending the conditions under which these methods yield favorable or unfavorable performances. Empirical studies, although common, are challenged by the limited availability of time series datasets, restricting the extraction of reliable insights. To address this limitation, we present tsMorph, a tool for generating semi-synthetic time series through dataset morphing. tsMorph works by creating a sequence of datasets from two original datasets. The characteristics of the generated datasets progressively depart from those of one of the datasets and converge toward the attributes of the other dataset. This method provides a valuable alternative for obtaining substantial datasets. In this paper, we show the benefits of tsMorph by assessing the predictive performance of the Long Short-Term Memory Network and DeepAR forecasting algorithms. The time series used for the experiments comes from the NN5 Competition. The experimental results provide important insights. Notably, the performances of the two algorithms improve proportionally with the frequency of the time series. These experiments confirm that tsMorph can be an effective tool for better understanding the behavior of forecasting algorithms, delivering a pathway to overcoming the limitations posed by empirical studies and enabling more extensive and reliable experiments.

cs.LG↗

arXiv2024

The Dynamics of Measurable Pseudo-Anosov Maps

We study the dynamics of measurable pseudo-Anosov homeomorphisms of surfaces, a generalization of Thurston's pseudo-Anosov homeomorphisms. A measurable pseudo-Anosov map has a transverse pair of full measure turbulations consisting of streamlines which are dense immersed lines: these turbulations are equipped with measures which are expanded and contracted uniformly by the homeomorphism. The turbulations need not have a good product structure anywhere, but have some local structure imposed by the existence of tartans: bundles of unstable and stable streamline segments which intersect regularly, and on whose intersections the product of the measures on the turbulations agrees with the ambient measure. We prove that measurable pseudo-Anosov maps are transitive, have dense periodic points, sensitive dependence on initial conditions, and are ergodic with respect to the ambient measure. Measurable pseudo-Anosovs maps were introduced in [11], where we constructed a parameterized family of non-conjugate examples on the sphere.

math.DS↗

arXiv2020

Learning to associate detections for real-time multiple object tracking

With the recent advances in the object detection research field, tracking-by-detection has become the leading paradigm adopted by multi-object tracking algorithms. By extracting different features from detected objects, those algorithms can estimate the objects' similarities and association patterns along successive frames. However, since similarity functions applied by tracking algorithms are handcrafted, it is difficult to employ them in new contexts. In this study, it is investigated the use of artificial neural networks to learning a similarity function that can be used among detections. During training, the networks were introduced to correct and incorrect association patterns, sampled from a pedestrian tracking data set. For such, different motion and appearance features combinations have been explored. Finally, a trained network has been inserted into a multiple-object tracking framework, which has been assessed on the MOT Challenge benchmark. Throughout the experiments, the proposed tracker matched the results obtained by state-of-the-art methods, it has run 58\% faster than a recent and similar method, used as baseline.

cs.CV↗

arXiv2020

Limits of sequences of pseudo-Anosov maps and of hyperbolic 3-manifolds

There are two objects naturally associated with a braid $β\in B_n$ of pseudo-Anosov type: a (relative) pseudo-Anosov homeomorphism $φ_β\colon S^2\to S^2$; and the finite volume complete hyperbolic structure on the 3-manifold $M_β$ obtained by excising the braid closure of $β$, together with its braid axis, from $S^3$. We show the disconnect between these objects, by exhibiting a family of braids $\{β_q:q\in{\mathbb{Q}}\cap(0,1/3]\}$ with the properties that: on the one hand, there is a fixed homeomorphism $φ_0\colon S^2\to S^2$ to which the (suitably normalized) homeomorphisms $φ_{β_{q}}$ converge as $q\to 0$; while on the other hand, there are infinitely many distinct hyperbolic 3-manifolds which arise as geometric limits of the form $\lim_{k\to\infty} M_{β_{q_k}}$, for sequences $q_k\to 0$.

math.GT↗

arXiv2020

Typical path components in tent map inverse limits

In the inverse limit ${\hat{I}}_s$ of a tent map $f_s$ restricted to its core, the set $\mathcal{GR}$ of points whose path components are bi-infinite and bi-dense has full measure with respect to the measure induced on $\hat{I}_s$ by the unique absolutely continuous invariant measure of $f_s$. With respect to topology, there is a dichotomy. When the parameter $s$ is such that the critical orbit of $f_s$ is not dense, $\mathcal{GR}$ contains a dense $G_δ$ set. In contrast, when the critical orbit of $f_s$ is dense, the complement of $\mathcal{GR}$ contains a dense $G_δ$ set.

math.DS↗

arXiv2020

Natural extensions of unimodal maps: virtual sphere homeomorphisms and prime ends of basin boundaries

Let $\{f_t\colon I\to I\}$ be a family of unimodal maps with topological entropies $h(f_t)>\frac12\log 2$, and ${\widehat{f}}_t\colon{\widehat{I}}_t\to{\widehat{I}}_t$ be their natural extensions, where ${\widehat{I}}_t=\varprojlim(I,f_t)$. Subject to some regularity conditions, which are satisfied by tent maps and quadratic maps, we give a complete description of the prime ends of the Barge-Martin embeddings of ${\widehat{I}}_t$ into the sphere. We also construct a family $\{χ_t\colon S^2\to S^2\}$ of sphere homeomorphisms with the property that each $χ_t$ is a factor of ${\widehat{f}}_t$, by a semi-conjugacy for which all fibers except one contain at most three points, and for which the exceptional fiber carries no topological entropy: that is, unimodal natural extensions are virtually sphere homeomorphisms. In the case where $\{f_t\}$ is the tent family, we show that $χ_t$ is a generalized pseudo-Anosov map for the dense set of parameters for which $f_t$ is post-critically finite, so that $\{χ_{t}\}$ is the completion of the unimodal generalized pseudo-Anosov family introduced in [21].

math.DS↗

arXiv2019

Statistical Stability for Barge-Martin attractors derived from tent maps

Let $\{f_t\}_{t\in(1,2]}$ be the family of core tent maps of slopes $t$. The parameterized Barge-Martin construction yields a family of disk homeomorphisms $Φ_t\colon D^2\to D^2$, having transitive global attractors $Λ_t$ on which $Φ_t$ is topologically conjugate to the natural extension of $f_t$. The unique family of absolutely continuous invariant measures for $f_t$ induces a family of ergodic $Φ_t$-invariant measures $ν_t$, supported on the attractors $Λ_t$. We show that this family $ν_t$ varies weakly continuously, and that the measures $ν_t$ are physical with respect to a weakly continuously varying family of background Oxtoby-Ulam measures $ρ_t$. Similar results are obtained for the family $χ_t\colon S^2\to S^2$ of transitive sphere homeomorphisms, constructed in [17] as factors of the natural extensions of $f_t$.

math.DS↗

arXiv2017

Itineraries for Inverse Limits of Tent Maps: a Backward View

Previously published admissibility conditions for an element of $\{0,1\}^{\mathbb{Z}}$ to be the itinerary of a point of the inverse limit of a tent map are expressed in terms of forward orbits. We give necessary and sufficient conditions in terms of backward orbits, which is more natural for inverse limits. These backward admissibility conditions are not symmetric versions of the forward ones: in particular, the maximum backward itinerary which can be realised by a tent map mode locks on intervals of kneading sequences.

math.DS↗

arXiv2015

New Rotation Sets in a Family of Torus Homeomorphisms

We construct a family $\{Φ_t\}_{t\in[0,1]}$ of homeomorphisms of the two-torus isotopic to the identity, for which all of the rotation sets $ρ(Φ_t)$ can be described explicitly. We analyze the bifurcations and typical behavior of rotation sets in the family, providing insight into the general questions of toral rotation set bifurcations and prevalence. We show that there is a full measure subset of $[0,1]$, consisting of infinitely many mutually disjoint non-trivial closed intervals, on each of which the rotation set mode locks to a constant polygon with rational vertices; that the generic rotation set in the Hausdorff topology has infinitely many extreme points, accumulating on a single totally irrational extreme point at which there is a unique supporting line; and that, although $ρ(t)$ varies continuously with $t$, the set of extreme points of $ρ(t)$ does not. The family also provides examples of rotation sets for which an extreme point is not represented by any minimal invariant set, or by any directional ergodic measure.

math.DS↗

arXiv2015

Braid Equivalence in the Hénon Family I

We give two general constructions of braid equivalences which exist between certain deformations of the 2-branched Horsehoe map. We then give numerical evidence suggesting that these constructions of braid equivalences are always realised in the Hénon family.

math.DS↗

arXiv2014

On digit frequencies in β-expansions

We study the sets DF(β) of digit frequencies of β-expansions of numbers in [0,1]. We show that DF(β) is a compact convex set with countably many extreme points which varies continuously with β; that there is a full measure collection of non-trivial closed intervals on each of which DF(β) mode locks to a constant polytope with rational vertices; and that the generic digit frequency set has infinitely many extreme points, accumulating on a single non-rational extreme point whose components are rationally independent.

math.DS↗

arXiv2013

Symbol ratio minimax sequences in the lexicographic order

Consider the space of sequences of k letters ordered lexicographically. We study the set M(α) of all maximal sequences for which the asymptotic proportions α of the letters are prescribed, where a sequence is said to be maximal if it is at least as great as all of its tails. The infimum of M(α) is called the α-infimax sequence, or the α-minimax sequence if the infimum is a minimum. We give an algorithm which yields all infimax sequences, and show that the infimax is not a minimax if and only if it is the α-infimax for every α in a simplex of dimension 1 or greater. These results have applications to the theory of rotation sets of beta-shifts and torus homeomorphisms.

math.DS↗

arXiv2011

Riemann surfaces out of paper

Let S be a surface obtained from a plane polygon by identifying infinitely many pairs of segments along its boundary. A condition is given under which the complex structure in the interior of the polygon extends uniquely across the quotient of its boundary to make S into a closed Riemann surface. When this condition holds, a modulus of continuity is obtained for a uniformizing map on S.

math.CV↗

arXiv2010

Paper folding, Riemann surfaces, and convergence of pseudo-Anosov sequences

A method is presented for constructing closed surfaces out of Euclidean polygons with infinitely many segment identifications along the boundary. The metric on the quotient is identified. A sufficient condition is presented which guarantees that the Euclidean structure on the polygons induces a unique conformal structure on the quotient surface, making it into a closed Riemann surface. In this case, a modulus of continuity for uniformizing coordinates is found which depends only on the geometry of the polygons and on the identifications. An application is presented in which a uniform modulus of continuity is obtained for a family of pseudo-Anosov homeomorphisms, making it possible to prove that they converge to a Teichmüller mapping on the Riemann sphere.

math.DS↗

arXiv2008

Decoration invariants for horseshoe braids

The Decoration Conjecture describes the structure of the set of braid types of Smale's horseshoe map ordered by forcing, providing information about the order in which periodic orbits can appear when a horseshoe is created. A proof of this conjecture is given for the class of so-called lone decorations, and it is explained how to calculate associated braid conjugacy invariants which provide additional information about forcing for horseshoe braids.

math.DS↗

arXiv2002

Monotone quotients of surface diffeomorphisms

A homeomorphism of a compact metric space is {\em tight} provided every non-degenerate compact connected (not necessarily invariant) subset carries positive entropy. It is shown that every $C^{1+α}$ diffeomorphism of a closed surface factors to a tight homeomorphism of a generalized cactoid (roughly, a surface with nodes) by a semi-conjugacy whose fibers carry zero entropy.

math.DS↗