This is building the tango, a constructive investigation into the material consequences of dancing the tango. Building the tango is about the resurrection of passion and life, as well as passion for life, of which the reality is now. It also involves resurrecting passion and life on a site occupied by ghosts and ruins: Belle Isle in Richmond, Virginia. The constructive investigation of dancing the tango on Belle Isle includes reclaiming the scandal, individual movements and individuals moving together, opposition of body to body, opposition of bodies to space, placement of feet, love of the dance, and feeling the heat of the tango. Studying the material consequences of the tango requires that the structure, itself, is a tango. It is symbolic of a man's struggle for the possession of a woman. The structure is one part man, one part woman, every part dance. The constructive realities of the tango create a dance of materials, a dance of space and a dance of bodies within. / Master of Architecture

A library for rare books and a reading garden, the following project emerged from an attempt to better understand the idea of an autonomous architecture. Framing architectural questions as a choice between opposing alternatives of perceived relevance (e.g., geometric construction versus geometric composition, self referential versus self governing, singular versus universal) the project, which at its beginning was a simple exercise in geometric constructive technique, evolved as it was viewed through the lenses of those dualities. / Master of Architecture

In this thesis we study the concept of well quasi-order, originally developed in order theory but nowadays transversal to many areas, in the over-all context of proof theory - more precisely, in reverse mathematics and constructive mathematics. Reversed mathematics, proposed by Harvey Friedman, aims to classify the strength of mathematical theorems by identifying the required axioms. In this framework, we focus on two classical results relative to well quasi-orders: Kruskal’s theorem and Higman’s lemma. Concerning the former, we compute the proof-theoretic ordinals of two different versions establishing their non equivalence. Regarding the latter, we study, over the base theory RCA0, the relations between Higman’s original achievements and some versions of Kruskal’s theorem. For what concerns constructive mathematics, which goes back to Brouwer’s reflections and rejects the law of excluded middle in favour of more perspicuous reasoning principles, we scrutinize the main definitions of well quasi-order establishing their constructive nature; moreover, a new constructive proof of Higman’s lemma is proposed paving the way for a systematic analysis of well quasi-orders within constructive means. On top of all this we consider a peculiar phenomenon in proof theory, namely phase transitions in provability. Building upon previous results about provability in Peano Arithmetic, we locate the threshold separating provability and unprovability for statements regarding Goodstein sequences, Hydra games and Ackermannian functions. / In questa tesi studiamo il concetto di well quasi-order, originariamente sviluppato nella teoria degli ordini ma oggi trasversale a molti ambiti, nel contesto generale della teoria della dimostrazione - più precisamente, in reverse mathematics e matematica costruttiva. La reverse mathematics, proposta da Harvey Friedman, mira a classificare la forza dei teoremi matematici individuando gli assiomi richiesti. In questo contesto, ci concentriamo su due risultati classici relativi ai well quasiorder: il teorema di Kruskal e il lemma di Higman. Per quanto riguarda il primo, abbiamo calcolato gli ordinali proof-teoretici di due diverse versioni stabilendone la non equivalenza. Per quanto riguarda il secondo, studiamo, sopra la teoria di base RCA0, le relazioni tra i risultati originali di Higman e alcuni versioni del teorema di Kruskal. Per quanto riguarda la matematica costruttiva, che si rifà alle riflessioni di Brouwer e rifiuta la legge del terzo escluso a favore di principidi ragionamento più perspicui, esaminiamo attentamente le principali definizioni di well quasi-order stabilendone la natura costruttiva; inoltre, viene proposta una nuova dimostrazione costruttiva del lemma di Higman aprendo la strada per una sistematica analisi dei well quasi-order all’interno di metodi costruttivi. Oltre a questo consideriamo un fenomeno peculiare nella teoria della dimostrazione, vale a dire le transizioni di fase nella dimostrabilità. Basandoci su risultati precedenti sulla dimostrabilità nell’aritmetica di Peano, abbiamo individuato la soglia che separa dimostrabilità e indimostrabilità per enunciati riguardanti sequenze di Goodstein, Hydra games e funzioni ackermanniane.

The urgent need to shift from fossil fuels to renewable energy in combating climate change is often impeded by conflicts and political polarization. Multistakeholder collaboration, which involves diverse participants working together to address complex issues, is a potential solution, but entrenched viewpoints can hinder progress. To address this challenge, we conducted an experiment testing two socio-psychological interventions—grounded in self-affirmation theory and moral foundations theory— designed to foster constructive group dynamics in multi-stakeholder settings. We recruited 1,244 students from Southern Illinois University, Carbondale to participate in an online survey about their opinions on several hypothetical on-campus sustainability initiatives. An initiative that would require students to complete a course in sustainability was found to be the most polarizing. We then invited a second sample of 282 students to discuss their views on this initiative in small groups. Prior to the discussion, each group was randomly assigned to complete one of two intervention exercises that involved a short writing task, or to a control condition. We found that groups assigned to the self-affirmation intervention exhibited significantly more openness-perspective-taking, information processing and agreement, compared to those in the control groups. Participants in groups who completed the moral foundations intervention were more supportive of the initiative overall, but showed no increase in support, openness-perspective-taking, information processing or agreement, compared to other groups. These findings provide preliminary evidence that completing a short self-affirmation intervention prior to engaging discussion has the potential to facilitate constructive dialogs on divisive issues related to sustainability.

Solutions journalism, rigorous reporting on responses to social problems, has gained great traction in the last decade. Using positive psychology theory, also known as the theory of well-being, this qualitative study examines the impact of reporting while using solutions journalism techniques. Applying the five pillars of positive psychology theory: positive emotion, engagement, positive relationships, meaning and accomplishment (PERMA), this study used interviews and content analysis to investigate how journalists are applying the tools of solutions journalism as well as what they hope to accomplish in the process. Findings revealed that the application of solutions journalism techniques produces hope and community engagement resulting in flourishing and positive change for individuals, communities and all involved in the reporting process.

Dans ce travail, nous présentons deux certificats algébriques pour le théorème de Budan. Le théorème de Budan s'énonce comme suit : Soit R un corps ordonné, f in R[X] de degré n et a,b in R avec a<b. Alors, le nombre de variations de signe dans la suite (f(b),f'(b),...,f^n(b)) n'est pas supérieur au nombre de variations de signe dans la séquence (f(a),f'(a),...,f^n(a)). Cela nous permet de compter des racines réelles d'une manière similaire au comptage des racines réelles par le théorème de Sturm. (Compter des racines réelles à la Budan est aujourd'hui connu comme Budan-Fourier count. En effet, il compte des racines dites virtuelles qui comprennent les racines réelles.) Un certificat algébrique pour le théoème de Budan est un certain type de preuve qui mène de la négation de l'hypothèse à l'identité algébrique contradictionelle 0>0. L'algorithme pour notre premier certificat est basé sur la preuve historique par Budan, qui utilise uniquement des arguments combinatoires. Il a une complexité exponentielle dans le degré de f. L'algorithme pour le deuxième certificat est basé sur des suites de Taylor mixtes et exhibe une plus petite complexité : Le calcul principal est la résolution d'un système linéaire, ce qui est polynomiale dans le degré de f / In this work we present two algebraic certificates for Budan's theorem. Budan's theorem claims the following. Let R be an ordered field, f in R[X] of degree n and a,b in R with a<b. Then the number of sign changes in the sequence (f(b),f'(b),...,f^n(b)) is not greater than the number of sign changes in the sequence (f(a),f'(a),...,f^n(a)). This enables us to count real roots in a similar way to the real root counting by Sturm's theorem. (Budan's count of real roots is today known as ``Budan-Fourier count'' which, indeed, counts so called virtual roots which comprehend the real roots.) An algebraic certificate for Budan's theorem is a certain kind of proof which leads from the negation of the assumption to the contradictory algebraic identity 0>0. The algorithm for our first certificate is based on the historical proof by Budan which uses only combinatorial arguments. It has a complexity exponential in the degree of f. The algorithm for the second certificate is based on mixed Taylor series and shows a smaller complexity: The main calculation is solving a linear system; this is polynomial in the degree of f.

Dans la partie principale de cette these on considère la theorie euclidienne constructive des champs. La théorie constructive (ou la renormalisation constructive) propose l'étude mathématiquement rigoureuse de l'existence et des propriétés non perturbatives de la théorie quantique des champs. Les méthodes traditionnelles de la théorie constructive sont les développements en amas et le groupe de renormalisation de Wilson. Mais il y a aussi des défauts de ces deux méthodes: premièrement, les techniques du développement en amas et de Mayer sont compliquées, donc sont difficiles à utiliser. Deuxièmement, ces méthodes ne peuvent pas s'appliquer pour les théories quantiques des champs noncommutatives, où il n'y a pas de localité sur l'espace et l'interaction est non-locale.Récemment une nouvelle méthode a été trouvée qui s'appelle loop vertex expansion (LVE), ou développement de vertex à boucle, qui est une combinaison de la technique des champs intermédiaires et de la formule des forêt (la formule de BKAR), qui peut résoudre ces deux problèmes avec succès.Avec cette méthode, on n'a pas besoin du développement de Mayer et le développement en amas est aussi simplifié. Et comme le terme d'interaction devient non-local aussi, cette méthode s'applique bien pour les théories quantique des champs noncommutatives, par exemple, le modèle de Grosse-Wulkenhaar, qui est un modèle λΦ4 avec un potentiel harmonique dans l'espace de Moyal. C'est le premier modèle de la théorie quantique des champs noncommutative qui est renormalisable. De plus, la fonction β est nulle quand on attend le point fixe ultraviolet de cette théorie. Donc c'est aussi un modèle naturel qu'on peut construire non-perturbativement.Dans cette thèse nous allons construire le modèle de Grosse-Wulkenhaar à 2-dimensions avec la LVE.Dans le reste de cette these nous considerons aussi la construction des varieties noncommutative par les états coherents et les polynomes topological pour les graphes de Feyman dans les théorie commutatives et noncommutatives. / The main subject of this thesis is about a new method of constructive renormalization theory, called the Loop vertex expansion (LVE). Constructive renormalization theory is to study the nonperturbative properties of Euclidean quantum field theory. The traditional methods are cluster/Mayer expansions and the renormalization group analysis. But these methods are not suitable for the construction of quantum field theories defined on noncommutative manifolds. Since in the noncommutative quantum fields theories the interactions are nonlocal, the Cluster and Mayer expansions fail to work. This problem could be solved by the loop vertex expansion method, which is a combination of the intermediate fields technique with the BKAR tree formula. The reason is that in the intermediate field representation of the partition function the interactions are also nonlocal. The Grosse-Wulkenhaar model is a is a quantum theory of scalar fields defined in the noncommutative Moyal space with harmonic potential. This model is not only renormalisable to all orders but also the beta function is zero at the fixed point of this theory. So this model is a candidate to be fully constructed.As a first step, we constructed the 2-dimensional Grosse-Wulkenhaar model, with the method of loop vertex expansions. In this thesis we studied also the construction of other noncommutative manifolds, namely the noncommutative type 1 Cartan domain, with the method of coherent states quantization. We studied also the graph polynomials for commutative and noncommutative quantum field theories.

Au coeur des problématiques culturelles récentes, les institutions muséales portent un projet de démocratisation culturelle visant la mise en accessibilité de l’art et de l’environnement muséal à une diversité de publics. Appuyée par la loi française de 2002 relative aux musées, ce projet est d'autant plus accentué à destination des enfants et des adolescents avec la mise en place d'une médiation culturelle et d'une diversité d'offres muséales spécifiques. Considéré comme le visiteur de demain, ce jeune public cristallise un ensemble d'attentes et de questionnements auprès des institutions culturelles en termes de connaissance du public, et de leviers pour la fréquentation, la fidélisation de ces espaces et l’accessibilité à l’art. Ces lieux de médiation culturelle représentent une opportunité pour suivre le parcours des visiteurs et comprendre les diverses dynamiques subjectives à l'oeuvre à travers diverses configurations tout en mobilisant le prisme de l'ergonomie : des rencontres avec les oeuvres en situation de visite d'une part, et des activités de création plastiques et narratives en situation d'atelier d'autre part. L'analyse de l'activité dans ces situations constituera une portée d'entrée privilégiée pour explorer et alimenter notre compréhension des traces des activités constructives et du développement afin de les conceptualiser. Ces contributions empiriques et épistémiques permettront de concevoir un ensemble de ressources et d'offres de médiation culturelle adaptées aux activités du jeune public et aux professionnels de la médiation. / At the heart of recent cultural issues, museum institutions implement a cultural democratization project promoting art and museum spaces accessibility to a diversity of audiences. Based on France’s law on museums from 2002, this project is focusing on children and teenagers thanks to the creation of cultural mediation and specific museum offers. Regarded as the visitor of tomorrow, this young audience generates to museums a set of expectations and questionings regarding visitor knowledge, tools for increasing attendance, loyalty and art accessibility. These cultural mediation spaces become an opportunity for tracking visitors' journey and understanding intrinsic points of views. We will study various situations throughout the prism of Ergonomics by highlighting encounters with works of art during a guided tour on one hand, plastic and narratives creation during workshops on the other hand. Activity analysis will be an effective way for exploring and improving our understanding of traces of constructive activities and development in order to conceptualize them. These empirical and theoretical contributions will help developing appropriate resources of cultural mediation offers to young audiences and mediation professionals.

<p>In this thesis we use the syntactic-semantic method of constructive type theory to give meaning to classical logic, in particular Gentzen's LK.</p><p>We interpret a derivation of a classical sequent as a derivation of a contradiction from the assumptions that the antecedent formulas are true and that the succedent formulas are false, where the concepts of truth and falsity are taken to conform to the corresponding constructive concepts, using function types to encode falsity. This representation brings LK to a manageable form that allows us to split the succedent rules into parts. In this way, every succedent rule gives rise to a natural deduction style introduction rule. These introduction rules, taken together with the antecedent rules adapted to natural deduction, yield a natural deduction calculus whose subsequent interpretation in constructive type theory gives meaning to classical logic.</p><p>The Gentzen-Prawitz inversion principle holds for the introduction and elimination rules of the natural deduction calculus and allows for a corresponding notion of convertibility. We take the introduction rules to determine the meanings of the logical constants of classical logic and use the induced type-theoretic elimination rules to interpret the elimination rules of the natural deduction calculus. This produces an interpretation injective with respect to convertibility, contrary to an analogous translation into intuitionistic predicate logic.</p><p>From the interpretation in constructive type theory and the interpretation of cut by explicit substitution, we derive a full precision contraction relation for a natural deduction version of LK. We use a term notation to formalize the contraction relation and the corresponding cut-elimination procedure.</p><p>The interpretation can be read as a Brouwer-Heyting-Kolmogorov (BHK) semantics that justifies classical logic. The BHK semantics utilizes a notion of classical proof and a corresponding notion of classical truth akin to Kolmogorov's notion of pseudotruth. We also consider a second BHK semantics, more closely connected with Kolmogorov's double-negation translation.</p><p>The first interpretation reinterprets the consequence relation while keeping the constructive interpretation of truth, whereas the second interpretation reinterprets the notion of truth while keeping the constructive interpretation of the consequence relation. The first and second interpretations act on derivations in much the same way as Plotkin's call-by-value and call-by-name continuation-passing-style translations, respectively.</p><p>We conclude that classical logic can be given a constructive semantics by laying down introduction rules for the classical logical constants. This semantics constitutes a proof interpretation of classical logic.</p>

In this thesis we use the syntactic-semantic method of constructive type theory to give meaning to classical logic, in particular Gentzen's LK. We interpret a derivation of a classical sequent as a derivation of a contradiction from the assumptions that the antecedent formulas are true and that the succedent formulas are false, where the concepts of truth and falsity are taken to conform to the corresponding constructive concepts, using function types to encode falsity. This representation brings LK to a manageable form that allows us to split the succedent rules into parts. In this way, every succedent rule gives rise to a natural deduction style introduction rule. These introduction rules, taken together with the antecedent rules adapted to natural deduction, yield a natural deduction calculus whose subsequent interpretation in constructive type theory gives meaning to classical logic. The Gentzen-Prawitz inversion principle holds for the introduction and elimination rules of the natural deduction calculus and allows for a corresponding notion of convertibility. We take the introduction rules to determine the meanings of the logical constants of classical logic and use the induced type-theoretic elimination rules to interpret the elimination rules of the natural deduction calculus. This produces an interpretation injective with respect to convertibility, contrary to an analogous translation into intuitionistic predicate logic. From the interpretation in constructive type theory and the interpretation of cut by explicit substitution, we derive a full precision contraction relation for a natural deduction version of LK. We use a term notation to formalize the contraction relation and the corresponding cut-elimination procedure. The interpretation can be read as a Brouwer-Heyting-Kolmogorov (BHK) semantics that justifies classical logic. The BHK semantics utilizes a notion of classical proof and a corresponding notion of classical truth akin to Kolmogorov's notion of pseudotruth. We also consider a second BHK semantics, more closely connected with Kolmogorov's double-negation translation. The first interpretation reinterprets the consequence relation while keeping the constructive interpretation of truth, whereas the second interpretation reinterprets the notion of truth while keeping the constructive interpretation of the consequence relation. The first and second interpretations act on derivations in much the same way as Plotkin's call-by-value and call-by-name continuation-passing-style translations, respectively. We conclude that classical logic can be given a constructive semantics by laying down introduction rules for the classical logical constants. This semantics constitutes a proof interpretation of classical logic.