Tooth cusp radius of curvature (RoC) has been hypothesized to play an important role in food item breakdown, but has remained largely unstudied due to difficulties in measuring and modeling RoC in multicusped teeth. We tested these hypotheses using a parametric model of a four cusped, maxillary, bunodont molar in conjunction with finite element analysis. When our data failed to support existing hypotheses, we put forth and tested the Complex Cusp Hypothesis which states that, during brittle food items breakdown, an optimally shaped molar would be maximizing stresses in the food item while minimizing stresses in the enamel. After gaining support for this hypothesis, we tested the effects of relative food item size on optimal molar morphology and found that the optimal set of RoCs changed as relative food item size changed. However, all optimal morphologies were similar, having one dull cusp that produced high stresses in the food item and three cusps that acted to stabilize the food item. We then set out to measure tooth cusp RoC in several species of extant apes to determine if any of the predicted optimal morphologies existed in nature and whether tooth cusp RoC was correlated with diet. While the optimal morphologies were not found in apes, we did find that tooth cusp RoC was correlated with diet and folivores had duller cusps while frugivores had sharper cusps. We hypothesize that, because of wear patterns, tooth cusp RoC is not providing a mechanical advantage during food item breakdown but is instead causing the tooth to wear in a beneficial fashion. Next, we investigate two possible relationships between tooth cusp RoC and enamel thickness, as enamel thickness plays a significant role in the way a tooth wears, using CT scans from hundreds of unworn cusps. There was no relationship between the two variables, indicating that selection may be acting on both variables independently to create an optimally shaped tooth. Finally, we put forth a framework for testing the functional optimality in teeth that takes into account tooth strength, food item breakdown efficiency, and trapability (the ability to trap and stabilize a food item).

Vacuum-assisted toilets make use of a large pressure difference between the ambient pressure and a vacuum tank to transport waste from the toilet bowl to the septic tank. This process requires 98% less water per flush making it an attractive product for transport vehicles such as airplanes, cruise ships, and trains. Unfortunately, the water savings come at the cost of high noise levels. This thesis investigates the acoustic characteristics of a vacuum-assisted toilet flush and several methods to reduce the radiated noise. Some methods include changing rinse parameters such as rinse pressure, rinse length, and rinse timing, adding structural damping of the bowl to reduce re-radiation, inserting a tube between the bowl and valve that utilizes a larger bend radius and longer tube length than what is currently installed, and modifying the valve. The most effective solution without requiring more water per flush was to insert a tube. The initial peak level was reduced by 16 dB and the steady-vacuum noise was reduced by 5 dB. Evidence of evanescent decay and reduced flow velocity as possible mechanisms for the noise reduction are presented and discussed. Rinse variations show a strong impact of the rinse-tube interaction on the noise reduction. In addition to these techniques, a modified flush plate opening and closing velocity profile is suggested which optimizes the sound generated by the opening and closing of the valve. Finally, a promising dual-valve solution that may take extra coordination of vacuum-assisted toilet manufacturers and airplane/cruise ship/train manufacturers is presented. By placing a secondary valve near the septic tank, the main noise from the valve is significantly reduced.

Starting from the observation that substances and reactions are the central entities of chemistry, I have structured chemical knowledge into a formal space called a directed hypergraph, which arises when substances are connected by their reactions. I call this hypernet chemical space. In this thesis, I explore different levels of description of this space: its evolution over time, its curvature, and categorical models of its compositionality. The vast majority of the chemical literature focuses on investigations of particular aspects of some substances or reactions, which have been systematically recorded in comprehensive databases such as Reaxys for the last 200 years. While complexity science has made important advances in physics, biology, economics, and many other fields, it has somewhat neglected chemistry. In this work, I propose to take a global view of chemistry and to combine complexity science tools, modern data analysis techniques, and geometric and compositional theories to explore chemical space. This provides a novel view of chemistry, its history, and its current status. We argue that a large directed hypergraph, that is, a model of directed relations between sets, underlies chemical space and that a systematic study of this structure is a major challenge for chemistry. Using the Reaxys database as a proxy for chemical space, we search for large-scale changes in a directed hypergraph model of chemical knowledge and present a data-driven approach to navigate through its history and evolution. These investigations focus on the mechanistic features by which this space has been expanding: the role of synthesis and extraction in the production of new substances, patterns in the selection of starting materials, and the frequency with which reactions reach new regions of chemical space. Large-scale patterns that emerged in the last two centuries of chemical history are detected, in particular, in the growth of chemical knowledge, the use of reagents, and the synthesis of products, which reveal both conservatism and sharp transitions in the exploration of the space. Furthermore, since chemical similarity of substances arises from affinity patterns in chemical reactions, we quantify the impact of changes in the diversity of the space on the formulation of the system of chemical elements. In addition, we develop formal tools to probe the local geometry of the resulting directed hypergraph and introduce the Forman-Ricci curvature for directed and undirected hypergraphs. This notion of curvature is characterized by applying it to social and chemical networks with higher order interactions, and then used for the investigation of the structure and dynamics of chemical space. The network model of chemistry is strongly motivated by the observation that the compositional nature of chemical reactions must be captured in order to build a model of chemical reasoning. A step forward towards categorical chemistry, that is, a formalization of all the flavors of compositionality in chemistry, is taken by the construction of a categorical model of directed hypergraphs. We lifted the structure from a lineale (a poset version of a symmetric monoidal closed category) to a category of Petri nets, whose wiring is a bipartite directed graph equivalent to a directed hypergraph. The resulting construction, based on the Dialectica categories introduced by Valeria De Paiva, is a symmetric monoidal closed category with finite products and coproducts, which provides a formal way of composing smaller networks into larger in such a way that the algebraic properties of the components are preserved in the resulting network. Several sets of labels, often used in empirical data modeling, can be given the structure of a lineale, including: stoichiometric coefficients in chemical reaction networks, reaction rates, inhibitor arcs, Boolean interactions, unknown or incomplete data, and probabilities. Therefore, a wide range of empirical data types for chemical substances and reactions can be included in our model.

PIP3 dynamics observed in membranes are responsible for the protruding edge formation in cancer and amoeboid cells. The mechanisms that maintain those PIP3 domains in three-dimensional space remain elusive, due to limitations in observation and analysis techniques. Recently, a strong relation between the cell geometry, the spatial confinement of the membrane, and the excitable signal transduction system has been revealed by Hörning and Shibata (2019) using a novel 3D spatiotemporal analysis methodology that enables the study of membrane signaling on the entire membrane (Hörning and Shibata, 2019). Here, using 3D spatial fluctuation and phase map analysis on actin polymerization inhibited Dictyostelium cells, we reveal a spatial asymmetry of PIP3 signaling on the membrane that is mediated by the contact perimeter of the plasma membrane—the spatial boundary around the cell-substrate adhered area on the plasma membrane. We show that the contact perimeter guides PIP3 waves and acts as a pinning site of PIP3 phase singularities, that is, the center point of spiral waves. The contact perimeter serves as a diffusion influencing boundary that is regulated by a cell size- and shape-dependent curvature. Our findings suggest an underlying mechanism that explains how local curvature can favor actin polymerization when PIP3 domains get pinned at the curved protrusive membrane edges in amoeboid cells.

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京都大学 / 新制・課程博士 / 博士(理学) / 甲第23677号 / 理博第4767号 / 新制||理||1683(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)准教授 SVADLENKA Karel, 教授 泉 正己, 教授 坂上 貴之 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

The simple accumulation-based network identification method (ANIM) in a raster Geographic Information System (GIS) posed by O'Callaghan and Mark (1984) has been criticized for producing a spatially uniform drainage density (Tarboton 2002) at the watershed scale. This criticism casts doubt on the use of ANIMs for deriving properties such as overland flow length for nonpoint source pollution models, without calibrating the accumulation threshold value. However, the basic assumption that underlies ANIMs is that convergent topography will yield a more rapid accumulation of cells, and thus, more extensive flow networks, with divergent, or planar terrain yielding sparser networks. Previous studies have focused on networks that are coarser than the hill-slope scale, and have relied upon visual inspection of drainage networks to suggest that ANIMs lack the ability to produce diverse networks. In this study overland flow lengths were calculated on a sub-watershed basis, with standard deviation, and range calculated for sub-watershed populations as a means of quantifying the diversity of overland flow lengths produced by ANIM at the hill slope scale. Linear regression and Spearman ranking analyses were used to determine if the methods represented trends in overland flow length as suggested by manual delineation of contour lines. Three ANIMs were analyzed: the flow accumulation method (O'Callaghan and Mark, 1984), the terrain curvature method (Tarboton, 2000) and the ridge accumulation method (introduced in this study). All three methods were shown to produce non-zero standard deviations and ranges using a single support area threshold, with the terrain curvature method producing the most diverse networks, followed by the ridge accumulation method, and then the flow accumulation method. At an analysis unit size of 20 ha, the terrain curvature method produced a standard deviation that was most similar to those suggested by the contour crenulations, -13.5%, followed by the ridge accumulation method, -21.5%, and the flow accumulation method, -61.6%. The ridge accumulation produced the most similar range, -19.1%, followed by terrain curvature, -24.9%, and flow accumulation, -65.4%. While the flow accumulation networks had a much narrower range of predicted flow lengths, it had the highest Spearman ranking coefficient, Rs=0.722, and linear regression coefficient, R2=0.602. The terrain curvature method was second, Rs=0.641, R2=0.469, and then ridge accumulation, Rs=0.602, R2=0.490. For all methods, as threshold values were varied, areas of dissimilar morphology (as evidenced by the common stream metric stream frequency) experienced changes in overland flow lengths at different rates. This results in an inconsistency in ranking of sub-watersheds at different thresholds. When thresholds were varied to produce average overland flow lengths from 75 m to 150 m, the terrain curvature method showed the lowest incidence of rank change, 16.05%, followed by the ridge accumulation method, 16.73%, then flow accumulation, 25.18%. The results of this investigation suggest that for all three methods, a causal relationship exists between threshold area, underlying morphology, and predicted overland flow length. This causal relationship enables ANIMs to represent contour network trends in overland flow length with a single threshold value, but also results in the introduction of rank change error as threshold values are varied. Calibration of threshold value (varying threshold in order to better match observed overland flow lengths) is an effective means of increasing the accuracy of ANIM predictions, and may be necessary when comparing areas with different stream frequencies. It was shown that the flow accumulation method produces less diverse networks than the terrain curvature and ridge accumulation methods. However, the results of rank and regression analyses suggest that further investigation is required to determine if these more diverse ANIM are in fact more accurate than the flow accumulation method. / Master of Science

Cuttlebone, the endoskeleton of cuttlefish, offers an intriguing biological structural model for designing low-density cellular ceramics with high stiffness and damage tolerance. Cuttlebone is highly porous (porosity ~93%) and lightweight (density less than 20% of seawater), constructed mainly by brittle aragonite (95 wt%), but capable of sustaining hydrostatic water pressures over 20 atmospheres and exhibits energy dissipation capability under compression comparable to many metallic foams (~4.4 kJ/kg). Here we computationally investigate how such a remarkable mechanical efficiency is enabled by the multiscale structure of cuttlebone. Using the common cuttlefish, Sepia Officinalis, as a model system, we first conducted high-resolution synchrotron micro-computed tomography (µ-CT) and quantified the cuttlebone's multiscale geometry, including the 3D asymmetric shape of individual walls, the wall assembly patterns, and the long-range structural gradient of walls across the entire cuttlebone (ca. 40 chambers). The acquired 3D structural information enables systematic finite-element simulations, which further reveal the multiscale mechanical design of cuttlebone: at the wall level, wall asymmetry provides optimized energy dissipation while maintaining high structural stiffness; at the chamber level, variation of walls (number, pattern, and waviness amplitude) contributes to progressive damage; at the entire skeletal level, the gradient of chamber heights tailors the local mechanical anisotropy of the cuttlebone for reduced stress concentration. Our results provide integrated insights into understanding the cuttlebone's multiscale mechanical design and provide useful knowledge for the designs of lightweight cellular ceramics. Upon the prior curvature analysis of the cuttlebone walls, we discovered that the walls were primarily "saddle-shaped". Thus, the characterization of different curvatures, varying between flat, domed, saddled, or cylindrical surfaces, were explored. A mathematical model was utilized to generate multiple walls with different curvature characteristics. We observed the mechanical performance of these walls via finite-element analysis and formulated different techniques for designing effective ceramic structures through incorporation of curvature. / Master of Science / The cuttlefish is a marine species that instead of having an inflatable swim bladder like fish, is a mollusk capable of swimming by utilizing their skeleton, called the cuttlebone. The cuttlefish can freely traverse the waters by controlling the flow of water in and out of their brittle skeletons, changing their buoyancy. For this reason, the cuttlebone must be very porous yet strong to withstand the deep-water pressures, enticing an interest for closer observation of the structure which may be useful in engineering applications involving ceramic structures. In this study, we examined an actual cuttlebone structure to better visualize its features with high-resolution synchrotron micro-computed tomography (µ-CT) and tabulated its mechanical performance through a variety of tests using computational software. The skeletal design of the cuttlebone consists of multiple layered chambers supported by wavy, pillar-like walls. It was revealed that the cuttlebone is remarkable due to its multiscale design: the asymmetric geometry of the walls are designed to tolerate considerable amounts of energy while a stiff construction; at the chamber level, variation of walls (number, pattern, and waviness amplitude) helps avoid complete destruction of the structure in the event of an excessive force; at the entire skeletal level, various of chamber heights reduces inflicted stress in concentrated regions of the cuttlebone. The wavy walls were also observed to retain a saddle-shaped curviness, versus simple flat, domed, or cylindrical shaped walls. This created an incentive to explore the effects of curvature on the structural integrity of brittle ceramic structures. We developed an effective way for generating walls with different curvatures and observed the mechanical performance of each wall by crushing them in computer simulations. It was identified that adding curvature to brittle walls prolonged the failure period significantly. While the cylindrical walls were found to be rather stiff, saddle-shaped walls, although not capable of withstanding as much force as flat or cylindrical walls, has a more progressive failure behavior meanwhile maintaining high energy absorption, hence the saddled walls of the cuttlebone to allow maintenance and self-repair in damaged regions.

Yes / Age estimation methods are often based on the age-related morphological changes of the auricular surface and the pubic bone. In this study, a mathematical approach to quantify these changes has been tested analyzing the curvature variation on 3D models from CT and laser scans. The sample consisted of the 24 Suchey–Brooks (SB) pubic bone casts, 19 auricular surfaces from the Buckberry and Chamberlain (BC) “recording kit” and 98 pelvic bones from the Terry Collection (Smithsonian Institution). Strong and moderate correlations between phases and curvature were found in SB casts (ρ 0.60–0.93) and BC “recording kit” (ρ 0.47–0.75), moderate and weak correlations in the Terry Collection bones (pubic bones: ρ 0.29–0.51, auricular surfaces: ρ 0.33–0.50) but associated with large individual variability and overlap of curvature values between adjacent decades. The new procedure, requiring no expert judgment from the operator, achieved similar correlations that can be found in the classic methods.