A multifunctional central pattern generator (CPG) can produce bursting polyrhythms that determine locomotive activity in an animal: for example, swimming and crawling in a leech. Each rhythm corresponds to a specific attractor of the CPG. We employ a Hodgkin-Huxley type model of a bursting leech heart interneuron, and connect three such neurons by fast inhibitory synapses to form a ring. This network motif exhibits multistable co-existing bursting rhythms. The problem of determining rhythmic outcomes is reduced to an analysis of fixed points of Poincare mappings and their attractor basins, in a phase plane defined by the interneurons' phase differences along bursting orbits. Using computer assisted analysis, we examine stability, bifurcations of attractors, and transformations of their basins in the phase plane. These structures determine the global bursting rhythms emitted by the CPG. By varying the coupling synaptic strength, we examine the dynamics and patterns produced by inhibitory networks.

In major museums around the world there are twenty-nine saddles of carved stag horn (usually referred to as "ivory") dated roughly to the fifteenth century that are, at best, sporadically discussed in art historical literature. Of these, ten currently reside in museums and private collections in English speaking countries, yet no significant studies on them exist in English. The goal of this thesis is to introduce this group of rare and extraordinary saddles and to provide a basis for further research on the topic in English. The thesis begins with an introduction to the saddles themselves and the literature on the subject. The first chapter focuses on the iconographical programs of the most elaborate saddles. The second chapter involves in depth examination of each saddle's provenance and if possible, the identification of a likely patron. The third chapter focuses on the production process of the saddles and explores the different hypotheses put forth by past scholars concerning the places of production. In addition to the specific focus on the stag horn saddles, it is hoped that this thesis will contribute to the broader study of the Renaissances of East-Central Europe in the English-speaking world.

L'objectif de cette thèse était d'analyser les interactions entre le dos du cheval et la selle dans les conditions de l'exercice sportif et de développer, à partir de ces connaissances nouvelles, une gamme de selles adaptées au cheval en mouvement et à son cavalier. L'originalité de cette thèse était entre autre de mesurer les mouvements de la colonne vertébrale dans la région thoracique située sous la selle. Un protocole original de mesure biomécanique des interactions entre le dos et la selle a été mis en place et validé. Ce protocole couplait différents matériels (tapis capteur de pression, cinématique 2D, capteur de force d'étrier et centrales de mesure inertielle) synchronisés et miniaturisés. Grâce à ce protocole, il a été possible de quantifier le mouvement de la colonne vertébrale du cheval, les pressions au cours de l'effort et l'effet du cavalier en comparant des selles dites « standard » avec de nouveaux prototypes de « panneaux » permettant de modifier la portance de la selle sur le dos du cheval. Les résultats de ces études ont permis de mettre en évidence l'impact du cavalier sur l'amplitude des mouvements du dos du cheval et sur sa locomotion au cours du trot et de démontrer qu'une selle dont la portance est modifiée provoque des modifications significatives de la locomotion du cheval au trot. Ces travaux ont permis d'apporter des informations quantifiées sur l'effet de la selle et du cavalier sur la biomécanique dorsale du cheval dans la condition montée lors de l'effort. Ces connaissances nouvelles seront utilisées (1) pour la conception de nouvelles selles mieux adaptées au cheval en mouvement et (2) pour mieux comprendre, prévenir et traiter les dorsalgies chez le cheval / The aim of this thesis was to analyze the interactions between the horse’s back and the saddle during exercise and develop, thanks to these new knowledges, a new range of saddle adapted to horse’s movements and to the rider. The originality of this thesis was to measure the movements of the spine in the thoracic region located under the saddle. An innovative protocol was developed to measure the interactions between the back and the saddle using different materials (pressure mat, 2D kinematics, stirrup force sensors, and inertial measurement units) synchronized and miniaturized. With this protocol, it was possible to quantify the movement of the horse’s spine, the pressure under the saddle and the effect of the rider by comparing a “standard” saddle with new prototype “panels” modifying the contact area of the saddle on the horse’s back. The results of these studies have helped to highlight the impact of the rider on the range of motion of the horse’s back and locomotion during the trot and to demonstrate that a saddle, which the contact area is modified, causes significant changes in the locomotion of the horse. This work helped to provide quantified information on the effect of the saddle and the rider on the horse’s back biomechanics in the ridden condition. These new knowledges will be used (1) to design new adapted saddles to the horse in motion and (2) to better understand, prevent and treat back pain in horses

Made available in DSpace on 2014-07-29T16:02:18Z (GMT). No. of bitstreams: 1 Dissertacao Tharsis Souza Silva.pdf: 1389814 bytes, checksum: c28dfe55ac776a4de30d43875907dc64 (MD5) Previous issue date: 2011-03-25 / In this work, we consider classes of discontinuous piecewise linear systems in the plane and continuous in the space. In the plane, we analyze systems of focus-focus (FF), focusparabolic (FP) and parabolic-parabolic (PP) type, separated by the straight line x = 0, and we prove that can appear until two limit cycles depending of parameters variations. Also we study a specific system, piecewise, with two saddles (one fixed in the origin and the other in the neighborhood of point (1;1)) separated by the straight line y= -x+1, and we show that can appear until two limit cycles depending of parameters variations. Finally, we examine a continuous piecewise linear system in R³ and we prove the existence of invariant cones and, through this structures, we determine some stable and unstable behavior. / Neste trabalho, consideramos classes de sistemas lineares por partes descontínuos no plano e contínuos no espaço. No plano, analisamos sistemas do tipo foco-foco (FF), parabólico-foco (PF) e parabólico-parabólico (PP) separados pela reta x = 0 e demonstramos que podem aparecer até dois ciclos limite, dependendo de variações de parâmetros. Também estudamos um sistema específico, linear por partes, com duas selas (uma sela fixa na origem e outra na vizinhança do ponto (1;1)) separadas pela reta y= -x+1 , e mostramos que podem aparecer até dois ciclos limite dependendo de variações de parâmetros. Por fim, examinamos um sistema linear por partes contínuo em R³ e demonstramos a existência de cones invariantes e, através destas estruturas, determinamos alguns comportamentos estáveis e instáveis.