Représentations et fusion des algèbres de Temperley-Lieb originale et diluée

Les algèbres de Temperley-Lieb originales, aussi dites régulières, apparaissent dans de nombreux modèles statistiques sur réseau en deux dimensions: les modèles d'Ising, de Potts, des dimères, celui de Fortuin-Kasteleyn, etc. L'espace d'Hilbert de l'hamiltonien quantique correspondant à chacun de ces modèles est un module pour cette algèbre et la théorie de ses représentations peut être utilisée afin de faciliter la décomposition de l'espace en blocs; la diagonalisation de l'hamiltonien s'en trouve alors grandement simplifiée. L'algèbre de Temperley-Lieb diluée joue un rôle similaire pour des modèles statistiques dilués, par exemple un modèle sur réseau où certains sites peuvent être vides; ses représentations peuvent alors être utilisées pour simplifier l'analyse du modèle comme pour le cas original. Or ceci requiert une connaissance des modules de cette algèbre et de leur structure; un premier article donne une liste complète des modules projectifs indécomposables de l'algèbre diluée et un second les utilise afin de construire une liste complète de tous les modules indécomposables des algèbres originale et diluée. La structure des modules est décrite en termes de facteurs de composition et par leurs groupes d'homomorphismes. Le produit de fusion sur l'algèbre de Temperley-Lieb originale permet de «multiplier» ensemble deux modules sur cette algèbre pour en obtenir un autre. Il a été montré que ce produit pouvait servir dans la diagonalisation d'hamiltoniens et, selon certaines conjectures, il pourrait également être utilisé pour étudier le comportement de modèles sur réseaux dans la limite continue. Un troisième article construit une généralisation du produit de fusion pour les algèbres diluées, puis présente une méthode pour le calculer. Le produit de fusion est alors calculé pour les classes de modules indécomposables les plus communes pour les deux familles, originale et diluée, ce qui vient ajouter à la liste incomplète des produits de fusion déjà calculés par d'autres chercheurs pour la famille originale. Finalement, il s'avère que les algèbres de Temperley-Lieb peuvent être associées à une catégorie monoïdale tressée, dont la structure est compatible avec le produit de fusion décrit ci-dessus. Le quatrième article calcule explicitement ce tressage, d'abord sur la catégorie des algèbres, puis sur la catégorie des modules sur ces algèbres. Il montre également comment ce tressage permet d'obtenir des solutions aux équations de Yang-Baxter, qui peuvent alors être utilisées afin de construire des modèles intégrables sur réseaux.

Quantifying aggressive behavior in zebrafish

Aggression is a complex behavior that influences social relationships and can be seen as adaptive or maladaptive depending on the context and intensity of expression. A model organism suitable for genetic dissection of the underlying neural mechanisms of aggressive behavior is still needed. Zebrafish has already proven to be a powerful vertebrate model organism for the study of normal and pathological brain function. Despite the fact that zebrafish is a gregarious species that forms shoals, when allowed to interact in pairs, both males and females express aggressive behavior and establish dominance hierarchies. Here, we describe two protocols that can be used to quantify aggressive behavior in zebrafish, using two different paradigms: (1) staged fights between real opponents and (2) mirror-elicited fights. We also discuss the methodology for the behavior analysis, the expected results for both paradigms, and the advantages and disadvantages of each paradigm in face of the specific goals of the study.

Estilos de crianza parentales en familias indígenas Cañaris inmigrantes en Cuenca

La presente investigación es de corte cualitativa, a nivel exploratorio-descriptivo, cuyo propósito es identificar los estilos de crianza de familias indígenas migrantes en Cuenca, así como caracterizar la estructura familiar de dichas familias, para lo cual se aplicó dos instrumentos. Para la obtención de la información sobre estilos de crianza parental se trabajó con algunos ítems del cuestionario de Susana Torío (2008), especialmente los apartados de tendencias actitudinales educativas, cuyos ítems fueron utilizados como preguntas dentro una entrevista semiestructurada;para la caracterización de la estructura familiar se trabajó con una entrevista semiestructurada denominada La estructura familiar del niño víctima y agresor de acoso escolar, elaborada por Ordóñez y Mazón (2014), estos instrumentos fueron aplicados acinco familias indígenas que viven en Cuenca alrededor de 10 años. Los resultados muestran una tendencia actitudinal educativa de los padres hacia el cuidado de sus hijos de corte flexible/democrático. Con relación a la estructura familiar referente al sub sistema conyugal se evidencian límites y fronteras flexibles; sin embargo, la construcción de reglas no son claras, situación que podría estar enmarcada en su condición de migración y su proceso de adaptación. Dentro del subsistema parental, los límites, jerarquías y reglas son flexibles. El rol descriptivo y la función afectiva en las familias del estudio se centran mayoritariamente en la madre;no obstante, el padre también es involucrado dentro del proceso de socialización de los hijos.

Exclusão social e projetos habitacionais. Um estudo sobre conjuntos habitacionais, segregação e exclusão social em Natal/RN

In Natal s urban growth process it is given that the performance period of the National Housing Bank (BNH, 1964-1986) was marked by the intense expansion of the urban grid and configuration of outskirts, through the construction of social housing developments. Implanted in segregated areas of the existing formal city, the population installed in these complexes was also excluded from their rights, considering that the housing defines itself not only by the physical dwelling, but also by its access to urban infrastructure, facilities, services, and others. From this reality and the verification of the city s exclusion and sociospatial segregation processes, we aimed to quantitatively demonstrate levels of social exclusion in Natal, based on the methodology developed by Sposati (2000) and adapted by Genovez (2002), which relates IBGE s (Brazilian Institute of Geography and Statistics) database underlying variables such as income, schooling and dwelling s quality. The research unveiled some spatial patterns promoted by the social housings: in these areas islands were developed with higher indicators than surrounding areas, revealing internal hierarchies in the city s outskirts

The visibility/invisibility paradox of trust: Developing distributed educational leadership for online communities

A visibility/invisibility paradox of trust operates in the development of distributed educational leadership for online communities. If trust is to be established, the team-based informal ethos of online collaborative networked communities requires a different kind of leadership from that observed in more formal face-to-face positional hierarchies. Such leadership is more flexible and sophisticated, being capable of encompassing both ambiguity and agile response to change. Online educational leaders need to be partially invisible, delegating discretionary powers, to facilitate the effective distribution of leadership tasks in a highly trusting team-based culture. Yet, simultaneously, online communities are facilitated by the visibility and subtle control effected by expert leaders. This paradox: that leaders need to be both highly visible and invisible when appropriate, was derived during research on 'Trust and Leadership' and tested in the analysis of online community case study discussions using a pattern-matching process to measure conversational interactions. This paper argues that both leader visibility and invisibility are important for effective trusting collaboration in online distributed leadership. Advanced leadership responses to complex situations in online communities foster positive group interaction, mutual trust and effective decision-making, facilitated through the active distribution of tasks.

Natural Disasters and Comparative State-Formation and Nation-Building: Earthquakes in Argentina and Chile (1822-1939)

Natural disasters in Argentina and Chile played a significant role in the state-formation and nation-building process (1822-1939). This dissertation explores state and society responses to earthquakes by studying public and private relief efforts reconstruction plans, crime and disorder, religious interpretations of catastrophes, national and transnational cultures of disaster, science and technology, and popular politics. Although Argentina and Chile share a political border and geological boundary, the two countries provide contrasting examples of state formation. Most disaster relief and reconstruction efforts emanated from the centralized Chilean state in Santiago. In Argentina, provincial officials made the majority of decisions in a catastrophe’s aftermath. Patriotic citizens raised money and collected clothing for survivors that helped to weave divergent regions together into a nation. The shared experience of earthquakes in all regions of Chile created a national disaster culture. Similarly, common disaster experiences, reciprocal relief efforts, and aid commissions linked Chileans with Western Argentine societies and generated a transnational disaster culture. Political leaders viewed reconstruction as opportunities to implement their visions for the nation on the urban landscape. These rebuilding projects threatened existing social hierarchies and often failed to come to fruition. Rebuilding brought new technologies from Europe to the Southern Cone. New building materials and systems, however, had to be adapted to the South American economic and natural environment. In a catastrophe’s aftermath, newspapers projected images of disorder and the authorities feared lawlessness and social unrest. Judicial and criminal records, however, show that crime often decreased after a disaster. Finally, nineteenth-century earthquakes heightened antagonism and conflict between the Catholic Church and the state. Conservative clergy asserted that disasters were divine punishments for the state’s anti-clerical measures and later railed against scientific explanations of earthquakes.

Properties of a method of fundamental solutions for the parabolic heat equation

We show that a set of fundamental solutions to the parabolic heat equation, with each element in the set corresponding to a point source located on a given surface with the number of source points being dense on this surface, constitute a linearly independent and dense set with respect to the standard inner product of square integrable functions, both on lateral- and time-boundaries. This result leads naturally to a method of numerically approximating solutions to the parabolic heat equation denoted a method of fundamental solutions (MFS). A discussion around convergence of such an approximation is included.

Pedagogical Appropriation of Information and Communication Technologies (ICT) by West African Educators = Appropriation pédagogique des technologies de l’information et de la communication (TIC) par les éducateurs ouest-africains

Œuvre dédiée à Alioune Camara; merci au Prof. Denis Dougnon de l’Université de Bamako pour le parrainage

Pedagogical Appropriation of Information and Communication Technologies (ICT) by West African Educators = Appropriation pédagogique des technologies de l’information et de la communication (TIC) par les éducateurs ouest-africains

Œuvre dédiée à Alioune Camara; merci au Prof. Denis Dougnon de l’Université de Bamako pour le parrainage

Impacto de la innovación tecnológica en las estrategias de YouTube y Google

El concepto de administración ha venido cambiando constantemente a través del tiempo y de las ideologías de diferentes autores que han marcado dicho concepto, en donde se ha podido establecer de mejor forma el significado que ésta ciencia tiene con la innovación y la estrategia. El objetivo de este trabajo es mostrar los fundamentos teóricos de la administración, la innovación y la estrategia, para así mostrar los alcances e impactos que estos tienen en las organizaciones visitadas durante la misión empresarial al Silicon Valley, principalmente a YouTube y Google. Para cumplir con dicho objetivo se realizaron encuestas a diferentes trabajadores pertenecientes a las organizaciones, obteniendo así, información valiosa para el estudio realizado. Con la información obtenida de la entrevistas, se logró recopilar información pertinente que permitió concluir que la innovación es un pilar fundamental para el buen funcionamiento de las empresas pertenecientes al Silicon Valley y así mismo ser base indispensable para la creación y formulación de las principales estrategias de las empresas.

Vihara architecture: defining the existential foothold of VIII century Buddhist monastery "Somapura Mahavihara" of ancien Bengal

Lost in history, the ruin of ‘Somapura Mahavihara’ was not recognized separated from its birthplace, i.e. nature, for more than 700 years. Yet, within its silent presence, the monument dominated the name of the region: ‘Paharpur’ (land of hillock), according to its appearance surrounds by its flat land topo¬graphy. Discovered in 1919, the single largest Buddhist Vihara (monas¬tery) of ancient Bengal came into light, pronouncing the flou¬rishing minute of Buddhist architecture, once dominant religious force of the subcontinent. The earliest historical monumental architecture of greater Asia, had long been deriving itself from the Buddhist monastic architecture as early as VI century BC. In line of history, the discovery of ‘Somapura Mahavihara’ contributed attesting the sensitivities of a highly sophisticated architectonic typology of Vihara Architecture in the land of ancient Bengal. The recovery of ‘Somapura Mahavihara’ was not only from its cradle of nature, but also from its remarkable existence imprinted in the reign of Pala dynasty (750 - 1155 AD) announcing the existential foothold of man in his nature. The existential foothold of ‘Somapura Mahavihara’ comprises the factors, responsible in shaping the anchorage of the mo¬nument since the birth of Vihara architecture, as early as 530 BC. These factors not only denote the building technology in response to its environment but also the amalgamation of be¬lief, upon which the dwellers transformed the site as a place announcing their existence on earth. This research paper aims at exploring the existential foothold of ‘Somapura Mahavihara’, in terms of its territorial, functional, structural, social, cultural, religious sym¬bolic hierarchies of human achievement while clarifying the architectonic typology that shaped ‘Somapura Mahavihara’ through evolution process of ‘Vihara Architecture’. This understanding intends to combine the archaeological knowledge with comparative architectural analysis of contem¬porary Viharas of ancient Bengal, to define the singularity of ‘Somapura Mahavihara’. In consequence, the glorious past of ‘Somapura Mahavihara’ is intended to portray through iden¬tifying the relation of religious and functional rationalism with the connotation of art, architecture and belief moulded within natural forces, as one complete entity; RESUMO: Vihara Arquitetura: Definindo a posição existencial do século VIII Budista mosteiro “Somapura Mahavihara” de Bengala antiga. Perdidas na História, as ruínas de ‘Somapura Mahavihara’ foram confundidas com uma montanha durante mais de setecentos anos. Contudo, no seu silêncio presente, o monumento marcou a toponímia da região; ‘Paharpur’ significa ‘a terra do outeiro’, evidenciando a singularidade deste monumento numa região dominada por uma extensa planície. Em 1919, foi descoberto o maior mosteiro budista da antiga região de Bengal, demonstrando a prosperidade da arquitectura budista. Tem¬poralmente, a descoberta de ‘Somapura Mahavihara’ contribuiu para atestar a evolução e a sofisticação da tipologia arquitectónica denominada ‘Arquitectura Vihara’, existente na antiga região de Bengal. A noção de pegada existencial de ‘Somapura Mahavihara’ compreende os factores responsáveis por moldar a ancoragem do monumento ao lugar em que se insere desde o início da arquitectura Vihara, que remonta a 530 a.C. Estes factores evidenciam a tecnologia construtiva empregue para responder ao ambiente envolvente mas também a evolução da religião, factores estes que os monges construtores consideraram ao transformar o lugar e anunciar a sua existência na Terra. Esta investigação tem por objectivo explorar a noção de pegada existencial de ‘Somapura Mahavihara’, nas suas dimensões territoriais, funcionais, estruturais, sociais, culturais e nas hierarquias simbólicas das realizações humanas para clarificar a tipologia arquitectónica que deu forma a ‘Somapura Mahavihara’ durante a evolução da arquitectura Vihara. Este entendimento pretende combinar/cruzar o conhecimen¬to arqueológico com estudos arquitectónicos comparativos de Viharas na antiga região de Bengal, com o objectivo de definir a singularidade de ‘Somapura Mahavihara’. Neste estudo estudar-se-á também o confronto entre a dimensão religiosa e a artística (divino vs. humano), integrados na arquitectura de ‘Somapura Mahavihara’ em perfeita harmonia.

A pointwise constrained version of the Liapunov convexity theorem for vectorial linear first-order control systems

We generalize the Liapunov convexity theorem's version for vectorial control systems driven by linear ODEs of first-order p = 1 , in any dimension d ∈ N , by including a pointwise state-constraint. More precisely, given a x ‾ ( ⋅ ) ∈ W p , 1 ( [ a , b ] , R d ) solving the convexified p-th order differential inclusion L p x ‾ ( t ) ∈ co { u 0 ( t ) , u 1 ( t ) , … , u m ( t ) } a.e., consider the general problem consisting in finding bang-bang solutions (i.e. L p x ˆ ( t ) ∈ { u 0 ( t ) , u 1 ( t ) , … , u m ( t ) } a.e.) under the same boundary-data, x ˆ ( k ) ( a ) = x ‾ ( k ) ( a ) & x ˆ ( k ) ( b ) = x ‾ ( k ) ( b ) ( k = 0 , 1 , … , p − 1 ); but restricted, moreover, by a pointwise state constraint of the type 〈 x ˆ ( t ) , ω 〉 ≤ 〈 x ‾ ( t ) , ω 〉 ∀ t ∈ [ a , b ] (e.g. ω = ( 1 , 0 , … , 0 ) yielding x ˆ 1 ( t ) ≤ x ‾ 1 ( t ) ). Previous results in the scalar d = 1 case were the pioneering Amar & Cellina paper (dealing with L p x ( ⋅ ) = x ′ ( ⋅ ) ), followed by Cerf & Mariconda results, who solved the general case of linear differential operators L p of order p ≥ 2 with C 0 ( [ a , b ] ) -coefficients. This paper is dedicated to: focus on the missing case p = 1 , i.e. using L p x ( ⋅ ) = x ′ ( ⋅ ) + A ( ⋅ ) x ( ⋅ ) ; generalize the dimension of x ( ⋅ ) , from the scalar case d = 1 to the vectorial d ∈ N case; weaken the coefficients, from continuous to integrable, so that A ( ⋅ ) now becomes a d × d -integrable matrix; and allow the directional vector ω to become a moving AC function ω ( ⋅ ) . Previous vectorial results had constant ω, no matrix (i.e. A ( ⋅ ) ≡ 0 ) and considered: constant control-vertices (Amar & Mariconda) and, more recently, integrable control-vertices (ourselves).

Una scienza plausibile per un oggetto sfuggente. Popolazione, societa e governo nel pensiero politico di T.R. Malthus

Questa tesi è un’analisi storico-concettuale del pensiero politico di Thomas Robert Malthus. Si vedrà in particolar modo come la crisi rivoluzionaria tardo settecentesca, cui si sommano i rivolgimenti economici e sociali connessi alla nascita della produzione manifatturiera, spinge l’autore a ripensare alcuni concetti fondamentali del pensiero politico moderno. Popolazione, società, governo e costituzione sono gli oggetti principali di questa ricerca: il principio di popolazione è la legge scientifica cui il reverendo Malthus ricorre per elaborare le proprie teorie sul governo, il quale deve sempre porsi come scopo quello di preservare – o migliorare – la costituzione della società. La presenza politica di masse di poveri in società conduce l’autore alla ricerca di un principio scientifico in grado di fondare nella natura le gerarchie e la disuguaglianza da più parti contestate; in quanto dipendono da «leggi fondamentali», per Malthus le gerarchie e la disuguaglianza che da esse deriva sono un tratto costitutivo della società. La teologia, la morale e l’economia politica sono scienze di cui l’autore si serve per argomentare intorno all’incontestabile natura della povertà e della disuguaglianza tra i sessi, e per affermare le modalità di una loro proficua amministrazione. In India e in Irlanda, poi, le condizioni naturali di cui il principio di popolazione suggella la necessità si scoprono soggette a sfide del tutto originali rispetto a quelle osservabili in Inghilterra. Lì, allora, lo sforzo malthusiano di costruire una scienza all’altezza della complessità dell’oggetto sociale rivela con somma chiarezza la propria ambizione di naturalizzare la politica e garantire le condizioni di disciplinamento degli individui al lavoro e alla subordinazione. Il dispositivo di naturalizzazione che giace al cuore del sistema malthusiano rappresenta la cifra del problema Malthus che apre questa ricerca e ne scandisce i momenti salienti.

Non perturbative aspects of non equilibrium physics in two dimensional models

The present manuscript focuses on out of equilibrium physics in two dimensional models. It has the purpose of presenting some results obtained as part of out of equilibrium dynamics in its non perturbative aspects. This can be understood in two different ways: the former is related to integrability, which is non perturbative by nature; the latter is related to emergence of phenomena in the out of equilibirum dynamics of non integrable models that are not accessible by standard perturbative techniques. In the study of out of equilibirum dynamics, two different protocols are used througout this work: the bipartitioning protocol, within the Generalised Hydrodynamics (GHD) framework, and the quantum quench protocol. With GHD machinery we study the Staircase Model, highlighting how the hydrodynamic picture sheds new light into the physics of Integrable Quantum Field Theories; with quench protocols we analyse different setups where a non-perturbative description is needed and various dynamical phenomena emerge, such as the manifistation of a dynamical Gibbs effect, confinement and the emergence of Bloch oscillations preventing thermalisation.

Quantum integrability as a new method for exact results on N=2 supersymmetric gauge theories and black holes

In this thesis I show a triple new connection we found between quantum integrability, N=2 supersymmetric gauge theories and black holes perturbation theory. I use the approach of the ODE/IM correspondence between Ordinary Differential Equations (ODE) and Integrable Models (IM), first to connect basic integrability functions - the Baxter’s Q, T and Y functions - to the gauge theory periods. This fundamental identification allows several new results for both theories, for example: an exact non linear integral equation (Thermodynamic Bethe Ansatz, TBA) for the gauge periods; an interpretation of the integrability functional relations as new exact R-symmetry relations for the periods; new formulas for the local integrals of motion in terms of gauge periods. This I develop in all details at least for the SU(2) gauge theory with Nf=0,1,2 matter flavours. Still through to the ODE/IM correspondence, I connect the mathematically precise definition of quasinormal modes of black holes (having an important role in gravitational waves’ obervations) with quantization conditions on the Q, Y functions. In this way I also give a mathematical explanation of the recently found connection between quasinormal modes and N=2 supersymmetric gauge theories. Moreover, it follows a new simple and effective method to numerically compute the quasinormal modes - the TBA - which I compare with other standard methods. The spacetimes for which I show these in all details are in the simplest Nf=0 case the D3 brane in the Nf=1,2 case a generalization of extremal Reissner-Nordström (charged) black holes. Then I begin treating also the Nf=3,4 theories and argue on how our integrability-gauge-gravity correspondence can generalize to other types of black holes in either asymptotically flat (Nf=3) or Anti-de-Sitter (Nf=4) spacetime. Finally I begin to show the extension to a 4-fold correspondence with also Conformal Field Theory (CFT), through the renowned AdS/CFT correspondence.