Le but principal de la topologie algébrique dirigée est d’étudier des systèmes qui évoluent avec le temps à travers leur géométrie. Ce sujet émergea en informatique, plus particulièrement en vraie concurrence, où Pratt introduisit les automates de dimension supérieure (HDA) en 1991 (en réalité, l’idée de la géométrie de la concurrence peut être retracée jusque Dijkstra en 1965). Ces automates sont géométriques par nature: chaque ensemble de n processus exécutant des actions indépendantes en parallèle peuvent être modélisées par un cube de dimension n, et un tel automate donne naissance à un espace topologique, obtenu en recollant ces cubes. Cet espace a naturellement une direction du temps provenant du flot d’exécution. Il semble alors totalement naturel d’utiliser des outils provenant de la topologie algébrique pour étudier ces espaces: les chemins modélisent les exécutions et les homotopies de chemins, c’est-à-dire les déformations continues de chemins, modélisent l’équivalence entre exécutions modulo ordonnancement d’actions indépendantes, mais ces notions géométriques doivent préserver la direction du temps, d’une façon ou d’une autre. Ce caractère dirigé apporte des complications et la théorie doit être refaite, essentiellement depuis le début. Dans cette thèse, j’ai développé des théories de l’homotopie et de l’homologie pour ces espaces dirigés. Premièrement, ma théorie de l’homotopie dirigée est basée sur la notion de rétracts par déformations, c’est-à-dire de déformations continues d’un gros espaces sur un espace plus petit, suivant des chemins inessentiels, c’est-à-dire qui ne changent pas le type d’homotopie des « espaces d’exécutions ». Cette théorie est reliée aux catégories de composantes et catégories de dimension supérieures. Deuxièmement, ma théorie de l’homologie dirigée suit l’idée que l’on doit regarder les « espaces d’exécutions » et comment ceux-ci évoluent avec le temps. Cette évolution temporelle est traitée en définissant cette homologie comme un diagramme des « espaces d’exécutions » et en comparant de tels diagrammes en utilisant une notion de bisimulation. Cette théorie homologique a de très bonnes propriétés: elle est calculable sur des espaces simples, elle est un invariant de notre théorie homotopique, elle est invariante par des raffinements d’actions simples et elle une théorie des suites exactes. / Studying a system that evolves with time through its geometry is the main purpose of directed algebraic topology. This topic emerged in computer science, more particularly in true concurrency, where Pratt introduced the higher dimensional automata (HDA) in 1991 (actually, the idea of geometry of concurrency can be tracked down Dijkstra in 1965). Those automata are geometric by nature: every set of n processes executing independent actions can be modeled by a n-cube, and such an automaton then gives rise to a topological space, obtained by glueing such cubes together. This space naturally has a specific direction of time coming from the execution flow. It then seems natural to use tools from algebraic topology to study those spaces: paths model executions, homotopies of paths, that is continuous deformations of paths, model equivalence of executions modulo scheduling of independent actions, and so on, but all those notions must preserve the direction. This brings many complications and the theory must be done again.In this thesis, we develop homotopy and homology theories for those spaces with a direction. First, my directed homotopy theory is based on deformation retracts, that is continuous deformation of a big space on a smaller space, following directed paths that are inessential, meaning that they do not change the homotopy type of spaces of executions. This theory is related to categories of components and higher categories. Secondly, my directed homology theory follows the idea that we must look at the spaces of executions and those evolves with time. This evolution of time is handled by defining such homology as a diagram of spaces of executions and comparing such diagrams using a notion of bisimulation. This homology theory has many nice properties: it is computable on simple spaces, it is an invariant of our homotopy theory, it is invariant under simple action refinements and it has a theory of exactness.

京都大学 / 0048 / 新制・課程博士 / 博士(医学) / 甲第18175号 / 医博第3895号 / 新制||医||1003(附属図書館) / 31033 / 京都大学大学院医学研究科医学専攻 / (主査)教授 上本 伸二, 教授 武藤 学, 教授 森田 智視 / 学位規則第4条第1項該当 / Doctor of Medical Science / Kyoto University / DGAM

京都大学 / 0048 / 新制・課程博士 / 博士(農学) / 甲第18316号 / 農博第2041号 / 新制||農||1020(附属図書館) / 学位論文||H26||N4823(農学部図書室) / 31174 / 京都大学大学院農学研究科食品生物科学専攻 / (主査)教授 保川 清, 教授 安達 修二, 教授 伏木 亨 / 学位規則第4条第1項該当 / Doctor of Agricultural Science / Kyoto University / DFAM

京都大学 / 0048 / 新制・課程博士 / 博士(農学) / 甲第19016号 / 農博第2094号 / 新制||農||1029(附属図書館) / 学位論文||H27||N4898(農学部図書室) / 31967 / 京都大学大学院農学研究科食品生物科学専攻 / (主査)教授 保川 清, 教授 河田 照雄, 教授 谷 史人 / 学位規則第4条第1項該当 / Doctor of Agricultural Science / Kyoto University / DFAM

京都大学 / 0048 / 新制・課程博士 / 博士(薬科学) / 甲第20315号 / 薬科博第84号 / 新制||薬科||9(附属図書館) / 京都大学大学院薬学研究科医薬創成情報科学専攻 / (主査)教授 掛谷 秀昭, 教授 高須 清誠, 教授 大野 浩章 / 学位規則第4条第1項該当 / Doctor of Pharmaceutical Sciences / Kyoto University / DFAM

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In telecommunications, there is currently a lot of work being done to migrate to the cloud, and a lot of specialized hardware is being exchanged for virtualized solutions. One important part of telecommunication networks that is yet to be moved to the cloud is known as the base-band unit, which sits between the antennas and the core network. The base-band unit has very strict latency requirements, making it unsuitable for out-of-the-box cloud solutions. Ericsson is therefore investigating if cloud solutions can be customized in such a way that base-band unit functionality can be virtualized as well. One such customization is to describe the functionality of a base-band unit using a directed acyclic graph (DAG), and deploy it to a cloud environment using Kubernetes. This thesis sets out to take applications represented using a DAG and deploy it using Kubernetes in such a way that the network latency is reduced when compared to the deployment generated by the default Kubernetes scheduler. The problem of placing the applications onto the available hardware resources was formulated as an integer linear programming problem. The problem was then implemented using Pyomo and solved with the open-source solver GLPK to obtain an optimized placement. This placement was then used to generate a configuration file that could be used to deploy the applications using Kubernetes. A mock application was developed in order to evaluate the optimized placement. The evaluation carried out in this thesis shows that the optimized placement obtained from the solution could improve the average round-trip latency of applications represented using a DAG by up to 30% when compared to the default Kubernetes scheduler.

Pac1/LIS1, an essential tip tracking protein of the WD40 super family, is required to target cytoplasmic dynein to the plus ends of astral microtubules in budding yeast. Pac1/LIS1 protein is composed of two regions: a small coiled-coil domain and a highly conserved WD40 repeat domain. Because of in vivo data suggesting the motor domain of Dyn1 interacts with Pac1, I attempted to locate the region of Pac1/LIS1 essential for binding to Dyn1/HC by utilizing PCR-mediated site directed mutagenesis. PCR-generated site directed Pac1(S226P) mutant appears to bind Dyn1/HC, allowing it to localize to the microtubule plus ends; whereas, Pac1(H197R) and Pac1(D379H) mutants appear to disrupt motor localization. I further hypothesized that Dyn1/HC would bind to either the coiled-coil domain or the WD40 repeat domain. Using truncated Pac1 constructs, I have observed that neither the coiled-coil domain nor the WD40 repeat domain alone is sufficient to recruit Dyn1/DHC to the plus ends of the cytoplasmic microtubules. Additionally, if I dimerize the WD40 repeat domain with a GST fusion tag, I observed that Dyn1/HC colocalized with the truncation at the spindle pole bodies. This result indicates that Pac1 must dimerize with its coiled-coil domain prior to interacting with Dyn1/HC. Furthermore, the WD40 dimer, is unable to track microtubule plus-ends; indicating that the very N-terminus of Pac1 is important for other interactions responsible for recruiting the Pac1/Dyn1 complex to the astral microtubule plus end.