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Enseignement de la modélisation mathématique et construction du travail mathématique : une dynamique problématique
No full textThe first part of the course considers the reasons for the interest in mathematical modelling and the resulting approach to teaching mathematics. The study focuses on approaches based on the modelling cycle associated with Northern European theories on modelling in education in relation to competency-based teaching. Additionally, the text reflects on our experience of teaching modelling as part of the master’s degree in didactics at the University of Paris-Diderot since 2000. By emphasising the role of mathematisation and models, we question and discuss the reality of the mathematical work developed by teachers and students in this manner. In the second part of the course, we deal with the theme of horizontal mathematisation and the chaining of models introduced in the context of Realistic Mathematics Education. Drawing on the theory of Mathematical Work Spaces (MWS), we then show how we consider the link between modelling activity and the training of mathematical work. Recent research in this area focused on mathematisation, the interplay between alternative models, and the connection between MWSs. The dual cognitive and epistemological approach to modelling activities is adopted. This aspect is illustrated, explored, and discussed in the workshop associated with the course.En la primera parte del curso se examinan las razones del interés por la modelización matemática y el enfoque que resulta para la enseñanza de las matemáticas. El estudio se centra en los enfoques basados en el ciclo de modelización asociados a las teorías del norte de Europa sobre la modelización en la educación en relación con la enseñanza basada en competencias. Además, reflexionamos sobre nuestra experiencia de enseñanza de la modelización en el marco del máster de didáctica de la Universidad de París-Diderot desde el año 2000. Al hacer hincapié en el papel de la matematización y de los modelos, cuestionamos y discutimos la realidad del trabajo matemático desarrollado de esta manera por profesores y alumnos. En la segunda parte del curso, abordamos el tema de la matematización horizontal y del encadenamiento de modelos introducidos en el contexto de la Educación Matemática Realista. Con el uso de la teoría de los Espacios de Trabajo Matemático (ETM), mostramos a continuación cómo concebimos el vínculo entre la actividad de modelización y la formación del trabajo matemático. Las investigaciones recientes en este ámbito se centran en la matematización, la interacción entre modelos alternativos y la conexión entre los ETM. Se adopta el doble punto de vista cognitivo y epistemológico sobre las actividades de modelización. Esta persperctiva se ilustra, explora y discute en el taller asociado al curso.Dans une première partie du texte, nous considérons les raisons de l’intérêt porté à la modélisation mathématique et l’approche des mathématiques enseignées qui en résulte. Pour cette étude, nous privilégierons les approches menées autour du cycle de modélisation associé aux théories nord-européennes sur la modélisation dans l’enseignement en relation avec un enseignement par compétences. Nous reviendrons également sur notre expérience d’un enseignement de la modélisation dans le cadre du master de didactique de l’université Paris-Diderot à partir des années 2000. En insistant sur la place de la mathématisation et sur le rôle des modèles, nous questionnerons et discuterons la réalité du travail mathématique ainsi développé par les enseignants et les élèves. Dans la seconde partie du cours, nous reprendrons la thématique de la mathématisation horizontale et du chaînage des modèles introduite dans le cadre de la Realistic Mathematics Education. Puis, en nous appuyant sur la théorie des espaces de travail mathématique (ETM), nous montrerons comment nous concevons l’articulation entre activité de modélisation et formation du travail mathématique. Les recherches récentes, menées dans ce cadre, sont centrées sur la mathématisation, les jeux entre modèles alternatifs et la connexion entre ETM. Elles intègrent un double regard, cognitif et épistémologique, sur les activités de modélisation. Cette seconde partie sera illustrée, approfondie et discutée dans l’atelier associé au cours
Wedge indentation of elastoplastic solids — from single indentation to interaction between indenters
No full textPerformance of metallic seals used between face-turned surfaces is related to their abilities to flow plastically in order to fill up cavities between wedge-shaped asperities. Double wedge indentation is therefore a simple way to investigate what happens at such a seal-flange interface. In this paper, finite element analyses of single and double wedge indentations are conducted. A particular attention is paid to the effects of hardening parameters on the resulting hardness. First, it is observed that single wedge indentation hardness can be well-approximated by the adaptation of analytic models initially developed for cone indentation problems. Second, it is shown that interaction between indentation-strain field during double wedge indentation starts once the bearing ratio is about 25%. It leads to a significant mean contact pressure increase, which is strongly dependent upon the strain hardening exponent. Eventually, for a bearing ratio higher than 75%, a plastic locking stage occurs, which leads to an exponential increase of the mean contact pressure. Practical applications of this work to indentation and sealing research fields are discussed
La contribution des environnements technologiques à l’enseignement de la preuve
No full textThis contribution discusses the use of a dynamic geometry environment to promote students’ introduction to mathematical proof. Within the framework of semiotic mediation theory, I explore, on the one hand, the link between available computer tools and the personal meanings emerging from their use in classroom activities and, on the other hand, the mathematical notions that are the subject of teaching. The discussion uses three interrelated perspectives – epistemological, cognitive and didactic – to elaborate the outcomes of a number of long-term teaching experiences in secondary classrooms. Illustrative examples are presented, drawn from research studies conducted in previous years and still ongoing.Cette contribution traite de l’utilisation d’un environnement de géométrie dynamique pour favoriser l’introduction des élèves à la preuve mathématique. Dans le cadre de la théorie de la médiation sémiotique, j’explore, d’une part, le lien entre les outils informatiques disponibles et les significations personnelles émergeant de leur utilisation dans les activités en classe et, d’autre part, les notions mathématiques qui font l’objet de l’enseignement. La discussion utilise trois perspectives interdépendantes – épistémologique, cognitive et didactique – pour élaborer les résultats d’un certain nombre d’expériences d’enseignement sur le long terme dans des salles de classe du secondaire. Des exemples illustratifs sont présentés, tirés des études de recherche conduites au cours des années précédentes et toujours en cours
On searchable Mordvin corpora at the Language Bank of Finland, EMERALD
No full textDescription of Mordvin language corpora development at the Language Bank of Finland.Description of development
Perplexity Games: Maoism vs. Literature through the Lens of Cognitive Stylometry
No full textThe arrival of large language models (LLMs) has provoked an urgent search for stylistic markers that could differentiate machine text from human text, but while the human-like appearance of machine text has captivated public attention, the reverse phenomenon—human text becoming machine-like—has raised much less concern. This conceptual lag is surprising given the ample historical evidence of state-backed attempts to regulate human thought. The present article proposes a new comparative framework, Perplexity Games, to leverage the predictive power of LLMs and compare the statistical properties of Maospeak, a language style that emerged during the Mao Zedong’s era in China (1949-1976), with the style of canonical modern Chinese writers, such as Eileen Chang (1920-1995) and Mo Yan (1955-). The low perplexity of Maospeak, as computed across different GPT models, suggests that the impact of ideologies on language can be compared to likelihood-maximization text-generation techniques which reduce the scope of valid sequence continuations. These findings have cognitive implications: whereas engineered languages such as Maospeak hijack the predictive mechanisms of human cognition by narrowing the space of linguistic possibilities, literature resists such cognitive constraints by dispersing the probability mass over multiple, equally valid paths. Exposure to diverse language data counters the influences of ideologies on our linguistically mediated perceptions of the world and increases the perplexity of our imaginations
Boolean proportions
No full textThe author has recently introduced an abstract algebraic framework ofanalogical proportions within the general setting of universal algebra. Thispaper studies analogical proportions in the boolean domain consisting of twoelements 0 and 1 within his framework. It turns out that our notion of booleanproportions coincides with two prominent models from the literature indifferent settings. This means that we can capture two separate modellings ofboolean proportions within a single framework which is mathematically appealingand provides further evidence for the robustness and applicability of thegeneral framework
Weak polynomial identities of small degree for the Weyl algebra
No full textIn this paper we investigate weak polynomial identities for the Weyl algebra over an infinite field of arbitrary characteristic. Namely, wedescribe weak polynomial identities of the minimal degree, which is three, andof degrees 4 and 5. We also describe weak polynomial identities is twovariables.Comment: 16 pages. arXiv admin note: text overlap with arXiv:2309.1279
Rewriting and Completeness of Sum-Over-Paths in Dyadic Fragments of Quantum Computing
No full textThe "Sum-Over-Paths" formalism is a way to symbolically manipulate linearmaps that describe quantum systems, and is a tool that is used in formalverification of such systems. We give here a new set of rewrite rules for theformalism, and show that it is complete for "Toffoli-Hadamard", the simplestapproximately universal fragment of quantum mechanics. We show that therewriting is terminating, but not confluent (which is expected from theuniversality of the fragment). We do so using the connection betweenSum-over-Paths and graphical language ZH-calculus, and also show how theaxiomatisation translates into the latter. We provide generalisations of thepresented rewrite rules, that can prove useful when trying to reduce terms inpractice, and we show how to graphically make sense of these new rules. We showhow to enrich the rewrite system to reach completeness for the dyadic fragmentsof quantum computation, used in particular in the Quantum Fourier Transform,and obtained by adding phase gates with dyadic multiples of to theToffoli-Hadamard gate-set. Finally, we show how to perform sums andconcatenation of arbitrary terms, something which is not native in a systemdesigned for analysing gate-based quantum computation, but necessary whenconsidering Hamiltonian-based quantum computation.Comment: arXiv admin note: text overlap with arXiv:2205.0260
Algebraic curves as a source of separable multi-Hamiltonian systems
No full textIn this paper we systematically consider various ways of generatingintegrable and separable Hamiltonian systems in canonical and in non-canonicalrepresentations from algebraic curves on the plane. In particular, we considerSt\"ackel transform between two pairs of St\"ackel systems, generated by2n-parameter algebraic curves on the plane, as well as Miura maps betweenSt\"ackel systems generated by (n+N)-parameter algebraic curves, leading tomulti-Hamiltonian representation of these systems.Comment: Version accepted for publication in Special Issue 2 of Open Communications in Nonlinear Mathematical Physics. One reference added, some language issues fixed, additional explanations in Introductio
Toward Automatic Typography Analysis: Serif Classification and Font Similarities
No full textWhether a document is of historical or contemporary significance, typography plays a crucial role in its composition. From the early days of modern printing, typographic techniques have evolved and transformed, resulting in changes to the features of typography. By analyzing these features, we can gain insights into specific time periods, geographical locations, and messages conveyed through typography. Therefore, in this paper, we aim to investigate the feasibility of training a model to classify serif typeswithout knowledge of the font and character. We also investigate how to train a vectorial-based image model able to group together fonts with similar features. Specifically, we compare the use of state-of-theart image classification methods, such as the EfficientNet-B2 and the Vision Transformer Base model with different patch sizes, and the state-of-the-art fine-grained image classification method, TransFG, on the serif classification task. We also evaluate the use of the DeepSVG model to learn to group fonts with similar features. Our investigation reveals that fine-grained image classification methods are better suited for the serif classification tasks and that leveraging the character labels helps to learn more meaningful font similarities.This repository contains: - Paper published in the Journal of data mining and digital humanities:WasimEtAl_Toward_Automatic_Typography_Analysis__Serif_Classification_and_Font_Similarities.pdf - Two datasets: The first for serif classification consisting of 126666 training and 2914 font-independent testing images in raster format. The second dataset for svg based similarity learning consists of 124010 training and 2914 font-independent testing images. The images have been categorized into sans-serif, linear-serif, slab-serif, and triangular serif by a designer at the EPFL+ECAL Labfont_serif_dataset.zipfont_svg_dataset.zip - model weights:serif_B_16_long_checkpoint.bin: refers to TransFG ViT B/16 Backendserif_B_32_long_checkpoint.bin: refers to TransFG ViT B/32 BackendViT-B_16.npz ViT-B_32.npz are publicly available at: https://github.com/TACJu/TransFGand were used for training TransFG ViT B/16 Backend and TransFG ViT B/32 Backend - code:https://github.com/TalalWasim/GEST-Serif