Neste trabalho, estudamos os grupos de tranças em superfícies visando encontrar apresentações para estes grupos em superfícies fechadas orientáveis de gênero g >= 1 ou superfícies fechadas não orientáveis de gênero g >= 2. Uma consequência destas apresentações é resolvermos o problema da palavra, que consiste em encontrar um algoritmo para decidir quando uma dada palavra num grupo definido por seus geradores e suas relações é a palavra trivial / In this work, we find presentations for surface braid groups either in closed orientable surfaces of genus g >= 1 or in closed non-orientable surfaces of genus g >= 2. A consequence of this presentations is to solve the word problem, which consists in finding an algorithm to decide when a given word in a group defined by its generators and its relations is the trivial word

Cette thèse concerne principalement deux objets classiques étroitement liés: d'une part la variété des polynômes complexes unitaires de degré $d>1$ à une variable, et à racines simples (donc de discriminant différent de zéro), et d'autre part, les groupes de tresses d'Artin avec d brins. Le travail présenté dans cette thèse propose une nouvelle approche permettant des calculs cohomologiques explicites à coefficients dans n'importe quel faisceau. En vue de calculs cohomologiques explicites, il est souhaitable d'avoir à sa disposition un bon recouvrement au sens de Čech. L'un des principaux objectifs de cette thèse est de construire un tel recouvrement basé sur des graphes (appelés signatures) qui rappellent les `dessins d'enfant' et qui sont associées aux polynômes complexes classifiés par l'espace de polynômes. Cette décomposition de l'espace de polynômes fournit une stratification semi-algébrique. Le nombre de composantes connexes de chaque strate est calculé dans le dernier chapitre ce cette thèse. Néanmoins, cette partition ne fournit pas immédiatement un recouvrement adapté au calcul de la cohomologie de Čech (avec n'importe quels coefficients) pour deux raisons liées et évidentes: d'une part les sous-ensembles du recouvrement ne sont pas ouverts, et de plus ils sont disjoints puisqu'ils correspondent à différentes signatures. Ainsi, l'objectif principal du chapitre 6 est de ``corriger'' le recouvrement de départ afin de le transformer en un bon recouvrement ouvert, adapté au calcul de la cohomologie Čech. Cette construction permet ensuite un calcul explicite des groupes de cohomologie de Čech à valeurs dans un faisceau localement constant. / This thesis mainly concerns two closely related classical objects: on the one hand, the variety of unitary complex polynomials of degree $ d> 1 $ with a variable, and with simple roots (hence with a non-zero discriminant), and on the other hand, the $d$ strand Artin braid groups. The work presented in this thesis proposes a new approach allowing explicit cohomological calculations with coefficients in any sheaf. In order to obtain explicit cohomological calculations, it is necessary to have a good cover in the sense of Čech. One of the main objectives of this thesis is to construct such a good covering, based on graphs that are reminiscent of the ''dessins d'enfants'' and which are associated to the complex polynomials. This decomposition of the space of polynomials provides a semi-algebraic stratification. The number of connected components in each stratum is counted in the last chapter of this thesis. Nevertheless, this partition does not immediately provide a ''good'' cover adapted to the computation of the cohomology of Čech (with any coefficients) for two related and obvious reasons: on the one hand the subsets of the cover are not open, and moreover they are disjoint since they correspond to different signatures. Therefore, the main purpose of Chapter 6 is to ''correct'' the cover in order to transform it into a good open cover, suitable for the calculation of the Čech cohomology. It is explicitly verified that there is an open cover such that all the multiple intersections are contractible. This allows an explicit calculation of cohomology groups of Čech with values in a locally constant sheaf.

We describe a method for computing rank (and determining quasipositivity) in the free group using dynamic programming. The algorithm is adapted to computing upper bounds on the rank for braids. We test our method on a table of knots by identifying quasipositive knots and calculating the ribbon genus. We consider the possibility that rank is not theoretically computable and prove some partial results that would classify its computational complexity. We then present a method for effectively brute force searching band presentations of small rank and conjugate length.

Hair, as a vital component of the human's appearance, plays an important role in producing digital characters. However, the generation of realistic hairstyles usually needs professional digital artists and/or complex hardware, and the procedure is often time-consuming due to its numerous numbers, and diverse hairstyles. Thus, automatic capture of real-world hairstyles with easy input can greatly benefit the production pipeline. State-of-the-art 3D hair modeling systems require either multi-view images or a single- view image with complementary synthetic 3D hair models. For the multi-view image based 3D hair reconstruction, the capture systems are often made of a large number of cameras, projectors, light sources, and are usually in the indoor environment, which prevents popular use of the methods. On the contrary, single-view image based methods only use simple capture devices, e.g.; a handheld camera. However, a front view containing a face is often required and the resulting 3D hair strand reconstruction quality is compromised. Meanwhile, several hairstyles can not be easily modeled, such as braids and kinky hairstyles (afro-textured hairs), even though they are very common in real life. In this dissertation, we implement a single-view imaged based 3D hair modeling system, where our hair reconstruction is done through 2D hair analysis and 3D strands creation, which benefits from both traditional image processing techniques and the strengths of machine learning. Our 2D hair analysis is used to learn the attributes of input hairs, including 2D hair strands, detailed hairstyle patterns, and the corresponding parametric representation (which includes braids and kinky hairs), and braid structures. Simultaneously 3D hair strands are generated using deep-learning models. Our method is different from previous methods as our generated hair models can be modified by controlling the attributes and parameters we learned from the 2D hair recognition/analysis system. Our system does not require a face to be shown in the input image and to our best knowledge, our work is the first work that can reconstruct 3D braided hair and kinky hair given a single-view image. Qualitatively and quantitatively assessments indicate that our system can generate a variety of realistic 3D hairstyle models.

En undersökning kring flätandet som tradition, språklighet och keramisk metod.

No description available.

A configuration space is a space whose points represent the possible states of a given physical system. As such they appear naturally both in theoretical physics and technical applications. For an example of the former, in analytical mechanics, the Lagrangian and Hamiltonian formulations of classical mechanics depend heavily on the use of a physical system’s configuration space for the description of its kinematical and dynamical behavior, and importantly, its evolution in time. As an example of a technical application, consider robotics, where the space of possible configurations of the mechanical linkages that make up a robot is an important tool in motion planning. In this case it is of particular interest to study the singularities of these mechanical linkages, to see if a given configuration is singular or not. This can be done with the help of configuration spaces and their topological properties. Arguably, the simplest configuration space possible arises when the system is just a collection of point-like particles in a plane. Despite its simplicity, the corresponding configuration space has substantial complexity and is of great interest in mathematics, physics and technology: For instance, it arises naturally in the mathematical modelling of robots performing tasks in a warehouse. In this thesis we go through the mathematics necessary to study the behaviour of paths in this space, which corresponds to motions of the particles. We use the theory of groups, algebraic topology, and manifolds to examine the properties of the configuration space of point-like particles in a plane. An important role in the discussion will be played by braids, which are certain collections of curves, interlaced in three-space. They are connected to many different topics in algebra, geometry, and mathematical physics, such as representation theory, the Yang-Baxter equation and knot theory. They are also important in their own right. Here we focus on their relation to configurations of points.

Short, J-section columns fabricated from a textile composite are tested in axial compression to study the modes of failure with and without local buckling occuring.The textile preform architecture is a 2x2, 2-D triaxial braid with a yarn layup of [0 deg 18k/+-64 deg 6k] 39.7% axial. The preform was resin transfer molded with 3M PR500 epoxy resin. Finite element analyses (FEA) of the test specimens are conducted to assess intra- and inter- laminar progressive failure models. These progressive failure models are then implemented in a FEA of a circular fuselage frame of the same cross section and material for which test data was available. This circular frame test article had a nominal radius of 120 inches, a forty-eight degree included angle, and was subjected to a quasi-static, radially inward load, which represented a crash type loading of the frame. The short column test specimens were cut from some of the fuselage frames. The branched shell finite element model of the frame included geometric nonlinearity and contact of the load platen of the testing machine with the frame. Intralaminar progressive failure is based on a maximum in-plane stress failure criterion followed by a moduli degradation scheme. Interlaminar progressive failure was implemented using an interface finite element to model delamination initiation and the progression of delamination cracks. Inclusion of both the intra- and inter- laminar progressive failure models in the FEA of the frame correlated reasonably well with the load-displacement response from the test through several major failure events. / Master of Science

A graph configuration space is generated by the movement of a finite number of robots on a graph. These configuration spaces of points in a graph are topologically interesting objects. By using local, combinatorial properties, we define a new classification of graphs whose configuration spaces are pseudomanifolds with boundary. In algebraic topology, graph configuration spaces are closely related to classical braid groups, which can be described as fundamental groups of configuration spaces of points in the plane. We examine this relationship by finding a presentation for the fundamental group of one graph configuration space. / Master of Science

[ES] El empleo de organismos vivos como biofactorías ha ganado una atención significativa en la industria debido a la creciente demanda de sistemas de producción sostenibles y la escasez de recursos. Entre sus muchas aplicaciones, las biofactorías pueden ser diseñadas para producir feromonas de insectos, las cuales sirven como alternativa ecológica a los pesticidas para el control de plagas en la agricultura. Como prueba de concepto, en esta tesis doctoral se caracterizaron plantas de Nicotiana benthamiana modificadas genéticamente con una ruta multigénica para producir las feromonas de polillas (Z)-11-hexadecenol (Z11-16OH) y (Z)-11-hexadecenil acetato (Z11-16OAc). Las plantas resultantes produjeron cantidades moderadas de ambas feromonas (111.4 µg g-1 FW y 11.8 µg g-1 FW para Z11-16OH y Z11-16OAc, respectivamente), y tasas de emisión diarias de ~10 ng g-1 FW para cada feromona. La producción de feromonas afectó negativamente al desarrollo de las plantas, probablemente debido a la sustancial carga metabólica y posible toxicidad de estos productos. Una estrategia para superar estas limitaciones es diseñar un sistema de expresión condicional que permita a las plantas crecer con normalidad antes de inducir la producción de feromonas. Para ello desarrollamos un conjunto de promotores sintéticos personalizables, llamados GB_SynP, activables con dCasEV2.1, un activador transcripcional potente y programable desarrollado recientemente para la inducción de genes en plantas. Los promotores GB_SynP permitieron una regulación precisa de los transgenes, con unos niveles de transcripción robustos y modulables en el estado "encendido" (presencia de dCasEV2.1 y la correspondiente guía de ARN), y una expresión mínima en el estado "apagado". Para implementar el sistema de producción condicional de feromonas en plantas se generó una nueva ruta multigénica para la biosíntesis de feromonas de polilla bajo el control de los promotores GB_SynP. Paralelamente, el activador dCasEV2.1 se reguló transcripcionalmente mediante el módulo CUP2:GAL4 sensible a sulfato de cobre, un inductor químico ampliamente utilizado en la agricultura. La funcionalidad del sistema se probó mediante expresión transitoria en N. benthamiana, resultando en unos rendimientos en el estado "encendido" de 32.7 µg g-1 FW y 25 µg g-1 FW para Z11-16OH y Z11-16OAc, respectivamente, y unos niveles insignificantes en ausencia de cobre. Sin embargo, la expresión en estable de esta ruta en N. benthamiana produjo unos niveles de expresión de los transgenes significativamente menores y una marcada disminución en la producción de feromonas. Esto supone que el sistema en su forma actual resulte inviable como biofactoría de feromonas en términos prácticos. La optimización de este sistema debe centrarse en mejorar la cascada de activación, en el uso de especies de plantas alternativas con mayor biomasa, y/o en incrementar las tasas de emisión en planta. Como alternativa a la producción de feromonas en plantas, la intercambiabilidad de piezas génicas entre plantas y hongos filamentosos puede aprovecharse para crear biofactorías fúngicas de feromonas. En este sentido, nuestro grupo adaptó previamente el sistema GoldenBraid a hongos filamentosos, llamado FungalBraid. En esta tesis ampliamos la colección de FungalBraid incorporando 27 piezas nuevas que incluyen diferentes marcadores de selección y promotores constitutivos e inducibles, los cuales se caracterizaron funcionalmente en Penicillium digitatum y P. chrysogenum. Además, se expresaron con éxito los promotores GB_SynP en P. digitatum, en combinación con el sistema de dCas9 activadora contenido en el vector pAMA18. Aunque los niveles de expresión de GB_SynP en hongos filamentosos fueron menores que los observados previamente en plantas, ésta y otras herramientas disponibles en la colección FungalBraid pueden utilizarse en el futuro para el desarrollo de biofactorías fúngicas que produzcan feromonas de insectos y otras biomoléculas de alto valor. / [CA] L'ús d'organismes vius com biofàbriques ha guanyat una atenció significativa a la indústria a causa de la creixent demanda de sistemes de producció sostenible i l'escassetat de recursos. Entre les seues moltes aplicacions, les biofàbriques poden ser dissenyades per a produir feromones d'insectes, les quals serveixen com a alternativa ecològica als pesticides per al control de plagues a l'agricultura. Com a prova d'aquest concepte, en aquesta tesi doctoral es van caracteritzar plantes de Nicotiana benthamiana modificades genèticament plantes de amb una ruta multigènica per a produir les feromones d'arnes (Z)-11-hexadecenol (Z11-16OH) i (Z)-11-hexadecenil acetat (Z11-16OAc). Les plantes resultants van produir quantitats moderades de totes dues feromones (111.4 µg g-1 FW i 11.8 µg g-1 FW per a Z11-16OH i Z11-16OAc, respectivament), i taxes d'emissió diàries d'aproximadament 10 ng g-1 FW per a cada feromona. La producció de feromones en aquestes plantes va afectar negativament el seu desenvolupament, probablement a causa de la substancial càrrega metabòlica i possible toxicitat d'aquests productes. Una estratègia per superar aquestes limitacions és dissenyar un sistema d'expressió condicional que permeta a les plantes créixer amb normalitat abans d'induir la producció de feromones. Per això hem desenvolupat un conjunt de promotors sintètics personalitzables, anomenats GB_SynP, activables amb dCasEV2.1, un activador transcripcional potent i programable desenvolupat recentment per a la inducció de gens en plantes. Els promotors GB_SynP van permetre una regulació precisa des transgens, amb uns nivells de transcripció robustos i modulables a l'estat "encès" (presència de dCasEV2.1 i la corresponent guia d'ARN), i una expressió mínima a l'estat "apagat". Per implementar el sistema de producció condicional de feromones en plantes es va generar una nova ruta multigènica per a la biosíntesi de feromones d'arna sota el control dels promotors GB_SynP. Paral·lelament, l'activador dCasEV2.1 es va regular transcripcionalment al mòdul CUP2:GAL4 sensible al sulfat de coure, un inductor químic àmpliament utilitzat en l'agricultura. La funcionalitat del sistema es va provar mitjançant expressió transitòria en N. benthamiana, resultant en uns rendiments a l'estat "encès" de 32.7 g-1 FW i 25 µg g-1 FW per a Z11-16OH i Z11-16OAc, respectivament, i uns nivells insignificants en absència de coure. No obstant això, l'expressió estable d'aquesta ruta a N. benthamiana va produir uns nivells d'expressió dels transgens significativament menors i una marcada disminució en la producció de feromones. Això suposa que el sistema en la seua forma actual resulte inviable com a biofàbrica de feromones en termes pràctics. L'optimització d'aquest sistema ha de centrar-se en millorar la cascada d'activació, en l'ús d'espècies de plantes alternatives amb major biomassa, i/o en incrementar les taxes d'emissió a la planta. Com a alternativa a la producció de feromones en plantes, la intercanviabilitat de peces gèniques entre plantes i fongs filamentosos pot aprofitar-se per crear biofàbriques fúngiques de feromones. En aquest sentit, el nostre grup va adaptar prèviament el sistema GoldenBraid a fongs filamentosos, anomenat FungalBraid. En aquesta tesi, vam ampliar la col·lecció de FungalBraid incorporant 27 peces noves que inclouen diferents marcadors de selecció i promotors constitutius i induïbles, els quals es van caracteritzar funcionalment a Penicillium digitatum i P. chrysogenum. A més, es van expressar amb èxit els promotors GB_SynP en P. digitatum, en combinació amb el sistema de dCas9 activadora contingut en el vector pAMA18. Encara que els nivells d'expressió de GB_SynP en fongs filamentosos van ser menors que els observats prèviament en plantes, aquesta i altres eines disponibles a la col·lecció FungalBraid poden utilitzar-se en el futur per al desenvolupament de biofàbriques fúngiques que produeixin feromones d'insectes i altres biomolècules de gran valor. / [EN] The use of living organisms as biofactories have gained significant attention in the industry due to the increasing demand for sustainable production systems and the shortage of resources. Among their many applications, biofactories can be engineered to produce insect pheromones, which serve as eco-friendly alternatives to pesticides for pest management in agriculture. As a proof of concept, in this thesis we characterized Nicotiana benthamiana plants engineered with a multigene pathway to produce the moth pheromones (Z)-11-hexadecenol (Z11-16OH) and (Z)-11-hexadecenyl acetate (Z11-16OAc). The resulting transgenic plants produced modest amounts of both pheromones (111.4 µg g-1 FW and 11.8 µg g-1 FW for Z11-16OH and Z11-16OAc, respectively), and daily emission rates of ~10 ng g-1 FW for each pheromone. Pheromone production in these plants significantly affected their fitness, likely due to the substantial metabolic burden and possible toxicity of lipid-derived products. One strategy to address these developmental abnormalities consists of engineering conditional transgene expression systems, thus allowing plants to grow normally before inducing the production of pheromones. To achieve this goal, in this thesis we developed a set of customizable synthetic promoters called GB_SynP, which can be activated by dCasEV2.1, a strong programable transcriptional activator recently developed for plant gene regulation. These GB_SynP promoters enabled tight regulation of single and multiple transgenes, with robust and tunable transcription levels in the ON state (presence of dCasEV2.1 loaded with the corresponding gRNA), and minimal or undetectable expression in the OFF state. To implement a conditional expression system for pheromone production in plants, a newly engineered multigene pathway for the biosynthesis of moth pheromones was constructed under the control of GB_SynP promoters. In parallel, the dCasEV2.1 activator was transcriptionally regulated with the CUP2:GAL4 sensor for copper sulphate, an agronomically-compatible chemical trigger. The functionality of this system was tested transiently in N. benthamiana, resulting in estimated yields of 32.7 µg g-1 FW and 25 µg g-1 FW for Z11-16OH and Z11-16OAc respectively in the ON state, and negligible levels in the absence of copper. However, stable transformation of the same copper-regulated pheromone pathway in N. benthamiana plants resulted in significantly lower transgene expression levels, which translated into a great reduction of pheromone yields. This makes the system in its current form a non-viable pheromone biofactory in practical terms. Further optimization should focus on the improvement of the activation cascade, the use of alternative plant hosts with more biomass, and/or the enhancement of emission rates in planta. As an alternative to pheromone production in plants, the interchangeability of DNA parts between plants and filamentous fungi could also be exploited to create fungal biofactories for pheromone production. In this regard, our research group previously adapted the GoldenBraid system for filamentous fungi, which we named FungalBraid. In this thesis, we expanded the FungalBraid collection by incorporating 27 new DNA parts, including different selection markers and several constitutive and inducible promoters, all of which were functionally characterized in Penicillium digitatum and P. chrysogenum. Furthermore, we successfully expressed the GB_SynP promoters developed for plants in P. digitatum, in combination with the non-integrative pAMA18-derived vector for the expression of a dCas9-based activator. Although further optimization of GB_SynP in filamentous fungi is required, as expression levels were lower than those previously observed in plants, this and the other tools available in the FungalBraid collection can be effectively employed in the future for the development of fungal biofactories that produce insect pheromones and other high value biomolecules. / Este trabajo ha sido financiado mediante la Ayuda para la Formación de Profesorado Universitario FPU18/02019 (Ministerio de Educación, Cultura y Deporte), así como por el proyecto europeo SUSPHIRE (PCI2018-092893, Era- CoBiotech), y los proyectos de Plan Nacional I+D PID2019-108203RB-100 y PID2021-125858OB-100 (Ministerio de Ciencia e Innovación). / Moreno Giménez, E. (2023). Synthetic biology tools for production of insect pheromones in plants and filamentous fungi [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/201180