Kyoto University (京都大学) / 0048 / 新制・課程博士 / 博士(工学) / 甲第15317号 / 工博第3196号 / 新制||工||1481(附属図書館) / 27795 / 京都大学大学院工学研究科建築学専攻 / (主査)教授 加藤 直樹, 教授 門内 輝行, 教授 竹脇 出 / 学位規則第4条第1項該当

Through their motion, proteins perform essential functions in the living cell. Although we cannot observe protein motion directly, over 68,000 crystal structures are freely available from the Protein Data Bank. Computational protein rigidity analysis systems leverage this data, building a mechanical model from atoms and pairwise interactions determined from a static 3D structure. The rigid and flexible components of the model are then calculated with a pebble game algorithm, predicting a protein's flexibility with much more computational efficiency than physical simulation. In prior work with rigidity analysis systems, the available modeling options were hard-coded, and evaluation was limited to case studies. The focus of this thesis is improving accuracy and robustness of rigidity analysis systems. The first contribution is in new approaches to mechanical modeling of noncovalent interactions, namely hydrogen bonds and hydrophobic interactions. Unlike covalent bonds, the behavior of these interactions varies with their energies. I systematically investigate energy-refined modeling of these interactions. Included in this is a method to assign a score to a predicted cluster decomposition, adapted from the B-cubed score from information retrieval. Another contribution of this thesis is in new approaches to measuring the robustness of rigidity analysis results. The protein's fold is held in place by weak, noncovalent interactions, known to break and form during natural fluctuations. Rigidity analysis has been conventionally performed on only a single snapshot, rather than on an entire trajectory, and no information was made available on the sensitivity of the clusters to variations in the interaction network. I propose an approach to measure the robustness of rigidity results, by studying how detrimental the loss of a single interaction may be to a cluster's rigidity. The accompanying study shows that, when present, highly critical interactions are concentrated around the active site, indicating that nature has designed a very versatile system for transitioning between unique conformations. Over the course of this thesis, we develop the KINARI library for experimenting with extensions to rigidity analysis. The modular design of the software allows for easy extensions and tool development. A specific feature is the inclusion of several modeling options, allowing more freedom in exploring biological hypotheses and future benchmarking experiments.

abstract: Zeolites are a class of microporous materials that are immensely useful as molecular sieves and catalysts. While there exist millions of hypothetical zeolite topologies, only 206 have been recognized to exist in nature, and the question remains: What distinguishes known zeolite topologies from their hypothetical counterparts? It has been found that all 206 of the known zeolites can be represented as networks of rigid perfect tetrahedra that hinge freely at the connected corners. The range of configurations over which the corresponding geometric constraints can be met has been termed the "flexibility window". Only a small percentage of hypothetical types exhibit a flexibility window, and it is thus proposed that this simple geometric property, the existence of a flexibility window, provides a reliable benchmark for distinguishing potentially realizable hypothetical structures from their infeasible counterparts. As a first approximation of the behavior of real zeolite materials, the flexibility window provides additional useful insights into structure and composition. In this thesis, various methods for locating and exploring the flexibility window are discussed. Also examined is the assumption that the tetrahedral corners are force-free. This is a reasonable approximation in silicates for Si-O-Si angles above ~135°. However, the approximation is poor for germanates, where Ge-O-Ge angles are constrained to the range ~120°-145°. Lastly, a class of interesting low-density hypothetical zeolites is evaluated based on the feasibility criteria introduced. / Dissertation/Thesis / Ph.D. Physics 2013

Rigidity theory deals in problems of the following form: given a structure defined by geometric constraints on a set of objects, what information about its geometric behavior is implied by the underlying combinatorial structure. The most well-studied class of structures is the bar-joint framework, which is made of fixed-length bars connected by universal joints with full rotational degrees of freedom; the allowed motions preserve the lengths and connectivity of the bars, and a framework is rigid if the only allowed motions are trivial motions of Euclidean space. A remarkable theorem of Maxwell-Laman says that rigidity of generic bar-joint frameworks depends only on the graph that has as its edges the bars and as its vertices the joints. We generalize the "degree of freedom counts that appear in the Maxwell-Laman theorem to the very general setting of (k,l)-sparse and (k,l)-graded sparse hypergraphs. We characterize these in terms of their graph-graph theoretic and matroidal properties. For the fundamental algorithmic problems Decision, Extraction, Components, and Decomposition, we give efficient, implementable pebble game algorithms for all the (k,l)-sparse and (k,l)-graded-sparse families of hypergraphs we study. We then prove that all the matroids arising from (k,l)-sparse are linearly representable by matrices with a certain "natural" structure that captures the incidence structure of the hypergraph and the sparsity parameters k and l. Building on the combinatorial and linear theory discussed above, we introduce a new rigidity model: slider-pinning rigidity. This is an elaboration of the planar bar-joint model to include sliders, which constrain a vertex to move on a specific line. We prove the analogue of the Maxwell-Laman Theorem for slider pinning, using, as a lemma, a new proof of Whiteley's Parallel Redrawing Theorem. We conclude by studying the emergence of non-trivial rigid substructures in generic planar frameworks given by Erdos-Renyi random graphs. We prove that there is a sharp threshold for such substructures to emerge, and that, when they do, they are all linear size. This is consistent with experimental and simulation-based work done in the physics community on the formation of certain glasses.

No description available.

Le but de cette thèse est d'étendre l'état de l'art par des contributions sur le comportement collectif d'un groupe de robots volants, à savoir des quadrirotors UAV. Afin de pouvoir sûrement naviguer dans un environnement, ces derniers peuvent se reposer uniquement sur leurs capacités à bord et non sur des systèmes centralisés (e.g., Vicon ou GPS). Nous réalisons cet objectif en offrant une possible solution aux problèmes de contrôle en formation et de localisation à partir de mesures à bord et via une communication locale. Nous abordons ces problèmes exploitant différents concepts provenant de la théorie des graphes algébriques et de la théorie de la rigidité. Cela nous permet de résoudre ces problèmes de façon décentralisée et de proposer des algorithmes décentralisés capables de prendre en compte également des limites sensorielles classiques. Les capacités embarquées que nous avons mentionnées plus tôt sont représentées par une caméra monoculaire et une centrale inertielle (IMU) auxquelles s'ajoute la capacité de chaque robot à communiquer (par RF) avec certains de ses voisins. Cela est dû au fait que l'IMU et la caméra représentent une possible configuration économique et légère pour la navigation et la localisation autonome d'un quadrirotor UAV. / The aim of this Thesis is to give contributions to the state of the art on the collective behavior of a group of flying robots, specifically quadrotor UAVs, which can only rely on their onboard capabilities and not on a centralized system (e.g., Vicon or GPS) in order to safely navigate in the environment. We achieve this goal by giving a possible solution to the problems of formation control and localization from onboard sensing and local communication. We tackle these problems exploiting mainly concepts from algebraic graph theory and the so-called theory of rigidity. This allows us to solve these problems in a decentralized fashion, and propose decentralized algorithms able to also take into account some typical sensory limitations. The onboard capabilities we referred to above are represented by an onboard monocular camera and an inertial measurement unit (IMU) in addition to the capability of each robot to communicate (through RF) with some of its neighbors. This is due to the fact that an IMU and a camera represent a possible minimal, lightweight and inexpensive configuration for the autonomous localization and navigation of a quadrotor UAV.

The standard grid bracing problem has a nice solution via the brace graph. If we introduce a window by removing an interior vertex of the grid, this solution comletely breaks down. We examine a 6 x 10 unit grid with a 2 x 2 window and provide an optimal solution via the Rigidity Matrix.

No description available.