12,838 research outputs found

    Converging organoids and extracellular matrix::New insights into liver cancer biology

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    On discrete constant principal curvature surfaces

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    Recently, it is discovered that a certain class of nanocarbon materials has geometrical properties related to the discrete geometry, pre-constant discrete principal curvature [9] based on the discrete surface theory proposed on trivalent graphs by Kotani, Naito and Omori [10]. In this paper, with the aim of an application to the nanocarbon materials, we will study discrete constant principal curvature (CPC) surfaces. Firstly, we developed the discrete surface theory on a full 3-ary oriented tree so that we define a discrete analogue of principal directions on them to investigate it. We also construct some interesting examples of discrete constant principal curvature surfaces, including discrete CPC tori.Comment: 13 pages, 9 figure

    The largest crossing number of tanglegrams

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    A tanglegram T\cal T consists of two rooted binary trees with the same number of leaves, and a perfect matching between the two leaf sets. In a layout, the tanglegrams is drawn with the leaves on two parallel lines, the trees on either side of the strip created by these lines are drawn as plane trees, and the perfect matching is drawn in straight line segments inside the strip. The tanglegram crossing number cr(T){\rm cr}({\cal T}) of T\cal T is the smallest number of crossings of pairs of matching edges, over all possible layouts of T\cal T. The size of the tanglegram is the number of matching edges, say nn. An earlier paper showed that the maximum of the tanglegram crossing number of size nn tanglegrams is <12(n2)<\frac{1}{2}\binom{n}{2}; but is at least 12(n2)n3/2n2\frac{1}{2}\binom{n}{2}-\frac{n^{3/2}-n}{2} for infinitely many nn. Now we make better bounds: the maximum crossing number of a size nn tanglegram is at most 12(n2)n4 \frac{1}{2}\binom{n}{2}-\frac{n}{4}, but for infinitely many nn, at least 12(n2)nlog2n4\frac{1}{2}\binom{n}{2}-\frac{n\log_2 n}{4}. The problem shows analogy with the Unbalancing Lights Problem of Gale and Berlekamp

    Old and New Minimalism: a Hopf algebra comparison

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    In this paper we compare some old formulations of Minimalism, in particular Stabler's computational minimalism, and Chomsky's new formulation of Merge and Minimalism, from the point of view of their mathematical description in terms of Hopf algebras. We show that the newer formulation has a clear advantage purely in terms of the underlying mathematical structure. More precisely, in the case of Stabler's computational minimalism, External Merge can be described in terms of a partially defined operated algebra with binary operation, while Internal Merge determines a system of right-ideal coideals of the Loday-Ronco Hopf algebra and corresponding right-module coalgebra quotients. This mathematical structure shows that Internal and External Merge have significantly different roles in the old formulations of Minimalism, and they are more difficult to reconcile as facets of a single algebraic operation, as desirable linguistically. On the other hand, we show that the newer formulation of Minimalism naturally carries a Hopf algebra structure where Internal and External Merge directly arise from the same operation. We also compare, at the level of algebraic properties, the externalization model of the new Minimalism with proposals for assignments of planar embeddings based on heads of trees.Comment: 27 pages, LaTeX, 3 figure

    Beam scanning by liquid-crystal biasing in a modified SIW structure

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    A fixed-frequency beam-scanning 1D antenna based on Liquid Crystals (LCs) is designed for application in 2D scanning with lateral alignment. The 2D array environment imposes full decoupling of adjacent 1D antennas, which often conflicts with the LC requirement of DC biasing: the proposed design accommodates both. The LC medium is placed inside a Substrate Integrated Waveguide (SIW) modified to work as a Groove Gap Waveguide, with radiating slots etched on the upper broad wall, that radiates as a Leaky-Wave Antenna (LWA). This allows effective application of the DC bias voltage needed for tuning the LCs. At the same time, the RF field remains laterally confined, enabling the possibility to lay several antennas in parallel and achieve 2D beam scanning. The design is validated by simulation employing the actual properties of a commercial LC medium

    Identifying the disc, bulge, and intra-halo light of simulated galaxies through structural decomposition

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    We perform a structural decomposition of galaxies identified in three cosmological hydrodynamical simulations by applying Gaussian Mixture Models (GMMs) to the kinematics of their stellar particles. We study the resulting disc, bulge, and intra-halo light (IHL) components of galaxies whose host dark matter haloes have virial masses in the range M200=1011M_{200}=10^{11}-- 1015M10^{15}\,{\rm M_\odot}. Our decomposition technique isolates galactic discs whose mass fractions, fdiscf_{\rm disc}, correlate strongly with common alternative morphology indicators; for example, fdiscf_{\rm disc} is approximately equal to κco\kappa_{{\rm co}}, the fraction of stellar kinetic energy in co-rotation. The primary aim of our study, however, is to characterise the IHL of galaxies in a consistent manner and over a broad mass range, and to analyse its properties from the scale of galactic stellar haloes up to the intra-cluster light. Our results imply that the IHL fraction, fIHLf_{\rm IHL}, has appreciable scatter and is strongly correlated with galaxy morphology: at fixed stellar mass, the IHL of disc galaxies is typically older and less massive than that of spheroids. Above M2001013MM_{200}\approx 10^{13}\,{\rm M_\odot}, we find, on average, fIHL0.45f_{\rm IHL}\approx 0.45, albeit with considerable scatter. The transition radius beyond which the IHL dominates the stellar mass of a galaxy is roughly 30kpc30\,{\rm kpc} for M2001012.8MM_{200}\lesssim 10^{12.8}\,{\rm M_\odot}, but increases strongly towards higher masses. However, we find that no alternative IHL definitions -- whether based on the ex-situ stellar fraction, or the stellar mass outside a spherical aperture -- reproduce our dynamically-defined IHL fractions.Comment: 17 pages, 12 figures, submitted to MNRA

    Novel 129Xe Magnetic Resonance Imaging and Spectroscopy Measurements of Pulmonary Gas-Exchange

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    Gas-exchange is the primary function of the lungs and involves removing carbon dioxide from the body and exchanging it within the alveoli for inhaled oxygen. Several different pulmonary, cardiac and cardiovascular abnormalities have negative effects on pulmonary gas-exchange. Unfortunately, clinical tests do not always pinpoint the problem; sensitive and specific measurements are needed to probe the individual components participating in gas-exchange for a better understanding of pathophysiology, disease progression and response to therapy. In vivo Xenon-129 gas-exchange magnetic resonance imaging (129Xe gas-exchange MRI) has the potential to overcome these challenges. When participants inhale hyperpolarized 129Xe gas, it has different MR spectral properties as a gas, as it diffuses through the alveolar membrane and as it binds to red-blood-cells. 129Xe MR spectroscopy and imaging provides a way to tease out the different anatomic components of gas-exchange simultaneously and provides spatial information about where abnormalities may occur. In this thesis, I developed and applied 129Xe MR spectroscopy and imaging to measure gas-exchange in the lungs alongside other clinical and imaging measurements. I measured 129Xe gas-exchange in asymptomatic congenital heart disease and in prospective, controlled studies of long-COVID. I also developed mathematical tools to model 129Xe MR signals during acquisition and reconstruction. The insights gained from my work underscore the potential for 129Xe gas-exchange MRI biomarkers towards a better understanding of cardiopulmonary disease. My work also provides a way to generate a deeper imaging and physiologic understanding of gas-exchange in vivo in healthy participants and patients with chronic lung and heart disease

    Optical Remote Sensing of Oil Spills by using Machine Learning Methods in the Persian Gulf: A Multi-Class Approach

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    Marine oil spills are harmful for the environment and costly for society. Coastal areas are particularly vulnerable since they provide habitats for organisms, animals and marine ecosystems. This thesis studied machine learning methods to classify thick oil in a multi-class case, using remotely sensed multi-spectral data in the Persian Gulf. The study area covers a large area between United Arab Emirates (UAE) and Iran. The dataset is extracted from 10 Sentinel-2 tiles on six spectral bands between 492 nm to 2202 nm. These images were annotated for four classes, namely thick oil, thin oil, ocean water and turbid water by using the Bonn Agreement to analyse true color composite images. A variety of machine learning methods were trained and evaluated using this dataset. Then a robustness evaluation was done by using selected machine learning methods on an independent dataset. Initially multiple machine learning methods were included; three decision trees, six K-Nearest Neighbor (KNN) models, two Artificial Neural Network (ANN) models, two Naive bayes models, and two discriminant models. Two KNN models and two ANN models were then picked for further evaluation. The results show that the fine KNN approach with two nearest neighbors had the best performance based on the computed statistical measures. However, the robustness evaluation showed that the tri-layered NN performed better. This thesis has shown that supervised machine learning with a multi-class approach can be used for oil spill monitoring using multi-spectral remote sensing data in the Persian Gulf

    On the Expressivity of Persistent Homology in Graph Learning

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    Persistent homology, a technique from computational topology, has recently shown strong empirical performance in the context of graph classification. Being able to capture long range graph properties via higher-order topological features, such as cycles of arbitrary length, in combination with multi-scale topological descriptors, has improved predictive performance for data sets with prominent topological structures, such as molecules. At the same time, the theoretical properties of persistent homology have not been formally assessed in this context. This paper intends to bridge the gap between computational topology and graph machine learning by providing a brief introduction to persistent homology in the context of graphs, as well as a theoretical discussion and empirical analysis of its expressivity for graph learning tasks

    optimización da planificación de adquisición de datos LIDAR cara ó modelado 3D de interiores

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    The main objective of this doctoral thesis is the design, validation and implementation of methodologies that allow the geometric and topological modelling of navigable spaces, whether inside buildings or urban environments, to be integrated into three-dimensional geographic information systems (GIS-3D). The input data of this work will consist mainly of point clouds (which can be classified) acquired by LiDAR systems both indoors and outdoors. In addition, the use of BIM infrastructure models and cadastral maps is proposed depending on their availability. Point clouds provide a large amount of environmental information with high accuracy compared to data offered by other acquisition technologies. However, the lack of data structure and volume requires a great deal of processing effort. For this reason, the first step is to structure the data by dividing the input cloud into simpler entities that facilitate subsequent processes. For this first division, the physical elements present in the cloud will be considered, since they can be walls in the case of interior environments or kerbs in the case of exteriors. In order to generate navigation routes adapted to different mobile agents, the next objective will try to establish a semantic subdivision of space according to the functionalities of space. In the case of internal environments, it is possible to use BIM models to evaluate the results and the use of cadastral maps that support the division of the urban environment. Once the navigable space is divided, the design of topologically coherent navigation networks will be parameterized both geometrically and topologically. For this purpose, several spatial discretization techniques, such as 3D tessellations, will be studied to facilitate the establishment of topological relationships, adjacency, connectivity and inclusion between subspaces. Based on the geometric characterization and the topological relations established in the previous phase, the creation of three-dimensional navigation networks with multimodal support will be addressed and different levels of detail will be considered according to the mobility specifications of each agent and its purpose. Finally, the possibility of integrating the networks generated in a GIS-3D visualization system will be considered. For the correct visualization, the level of detail can be adjusted according to geometry and semantics. Aspects such as the type of user or transport, mobility, rights of access to spaces, etc. They must be considered at all times.El objetivo principal de esta tesis doctoral es el diseño, la validación y la implementación de metodologías que permitan el modelado geométrico y topológico de espacios navegables, ya sea de interiores de edificios o entornos urbanos, para integrarse en sistemas de información geográfica tridimensional (SIG). -3D). Los datos de partida de este trabajo consistirán principalmente en nubes de puntos (que pueden estar clasificados) adquiridas por sistemas LiDAR tanto en interiores como en exteriores. Además, se propone el uso de modelos BIM de infraestructuras y mapas catastrales en función de su disponibilidad. Las nubes de puntos proporcionan una gran cantidad de información del entorno con gran precisión con respecto a los datos ofrecidos por otras tecnologías de adquisición. Sin embargo, la falta de estructura de datos y su volumen requiere un gran esfuerzo de procesamiento. Por este motivo, el primer paso que se debe realizar consiste en estructurar los datos dividiendo la nube de entrada en entidades más simples que facilitan los procesos posteriores. Para esta primera división se considerarán los elementos físicos presentes en la nube, ya que pueden ser paredes en el caso de entornos interiores o bordillos en el caso de los exteriores. Con el propósito de generar rutas de navegación adaptadas a diferentes agentes móviles, el próximo objetivo intentará establecer una subdivisión semántica del espacio de acuerdo con las funcionalidades del espacio. En el caso de entornos internos, es posible utilizar modelos BIM para evaluar los resultados y el uso de mapas catastrales que sirven de apoyo en la división del entorno urbano. Una vez que se divide el espacio navegable, se parametrizará tanto geométrica como topológicamente al diseño de redes de navegación topológicamente coherentes. Para este propósito, se estudiarán varias técnicas de discretización espacial, como las teselaciones 3D, para facilitar el establecimiento de relaciones topológicas, la adyacencia, la conectividad y la inclusión entre subespacios. A partir de la caracterización geométrica y las relaciones topológicas establecidas en la fase anterior, se abordará la creación de redes de navegación tridimensionales con soporte multimodal y se considerarán diversos niveles de detalle según las especificaciones de movilidad de cada agente y su propósito. Finalmente, se contemplará la posibilidad de integrar las redes generadas en un sistema de visualización tridimensional 3D SIG 3D. Para la correcta visualización, el nivel de detalle se puede ajustar en función de la geometría y la semántica. Aspectos como el tipo de usuario o transporte, movilidad, derechos de acceso a espacios, etc. Deben ser considerados en todo momento.O obxectivo principal desta tese doutoral é o deseño, validación e implementación de metodoloxías que permitan o modelado xeométrico e topolóxico de espazos navegables, ben sexa de interiores de edificios ou de entornos urbanos, ca fin de seren integrados en Sistemas de Información Xeográfica tridimensionais (SIX-3D). Os datos de partida deste traballo constarán principalmente de nubes de puntos (que poden estar clasificadas) adquiridas por sistemas LiDAR tanto en interiores como en exteriores. Ademáis plantease o uso de modelos BIM de infraestruturas e mapas catastrais dependendo da súa dispoñibilidade. As nubes de puntos proporcionan unha gran cantidade de información do entorno cunha gran precisión respecto os datos que ofrecen outras tecnoloxías de adquisición. Sen embargo, a falta de estrutura dos datos e a seu volume esixe un amplo esforzo de procesado. Por este motivo o primeiro paso a levar a cabo consiste nunha estruturación dos datos mediante a división da nube de entrada en entidades máis sinxelas que faciliten os procesos posteriores. Para esta primeira división consideraranse elementos físicos presentes na nube como poden ser paredes no caso de entornos interiores ou bordillos no caso de exteriores. Coa finalidade de xerar rutas de navegación adaptadas a distintos axentes móbiles, o seguinte obxectivo tratará de establecer unha subdivisión semántica do espazo de acordo as funcionalidades do espazo. No caso de entornos interiores plantease a posibilidade de empregar modelos BIM para avaliar os resultados e o uso de mapas catastrais que sirvan de apoio na división do entorno urbano. Unha vez divido o espazo navigable parametrizarase tanto xeométricamente como topolóxicamene de cara ao deseño de redes de navegación topolóxicamente coherentes. Para este fin estudaranse varias técnicas de discretización de espazos como como son as teselacións 3D co obxectivo de facilitar establecer relacións topolóxicas, de adxacencia, conectividade e inclusión entre subespazos. A partir da caracterización xeométrica e das relación topolóxicas establecidas na fase previa abordarase a creación de redes de navegación tridimensionais con soporte multi-modal e considerando varios niveis de detalle de acordo as especificacións de mobilidade de cada axente e a súa finalidade. Finalmente comtemplarase a posibilidade de integrar as redes xeradas nun sistema SIX 3D visualización tridimensional. Para a correcta visualización o nivel de detalle poderá axustarse en base a xeometría e a semántica. Aspectos como o tipo de usuario ou transporte, mobilidade, dereitos de acceso a espazos, etc. deberán ser considerados en todo momento
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