14,280 research outputs found

    Rank-based linkage I: triplet comparisons and oriented simplicial complexes

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    Rank-based linkage is a new tool for summarizing a collection SS of objects according to their relationships. These objects are not mapped to vectors, and ``similarity'' between objects need be neither numerical nor symmetrical. All an object needs to do is rank nearby objects by similarity to itself, using a Comparator which is transitive, but need not be consistent with any metric on the whole set. Call this a ranking system on SS. Rank-based linkage is applied to the KK-nearest neighbor digraph derived from a ranking system. Computations occur on a 2-dimensional abstract oriented simplicial complex whose faces are among the points, edges, and triangles of the line graph of the undirected KK-nearest neighbor graph on SS. In ∣S∣K2|S| K^2 steps it builds an edge-weighted linkage graph (S,L,σ)(S, \mathcal{L}, \sigma) where σ({x,y})\sigma(\{x, y\}) is called the in-sway between objects xx and yy. Take Lt\mathcal{L}_t to be the links whose in-sway is at least tt, and partition SS into components of the graph (S,Lt)(S, \mathcal{L}_t), for varying tt. Rank-based linkage is a functor from a category of out-ordered digraphs to a category of partitioned sets, with the practical consequence that augmenting the set of objects in a rank-respectful way gives a fresh clustering which does not ``rip apart`` the previous one. The same holds for single linkage clustering in the metric space context, but not for typical optimization-based methods. Open combinatorial problems are presented in the last section.Comment: 37 pages, 12 figure

    Construction of radon chamber to expose active and passive detectors

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    In this research and development, we present the design and manufacture of a radon chamber (PUCP radon chamber), a necessary tool for the calibration of passive detectors, verification of the operation of active radon monitors as well as diffusion chamber calibration used in radon measurements in air, and soils. The first chapter is an introduction to describe radon gas and national levels of radon concentration given by many organizations. Parameters that influence the calibration factor of the LR 115 type 2 film detector are studied, such as the energy window, critical angle, and effective volumes. Those are strongly related to the etching processes and counting of tracks all seen from a semi-empirical approach studied in the second chapter. The third chapter presents a review of some radon chambers that have been reported in the literature, based on their size and mode of operation as well as the radon source they use. The design and construction of the radon chamber are presented, use of uranium ore (autunite) as a chamber source is also discussed. In chapter fourth, radon chamber characterization is presented through leakage lambda, homogeneity of radon concentration, regimes-operation modes, and the saturation concentrations that can be reached. Procedures and methodology used in this work are contained in the fifth chapter and also some uses and applications of the PUCP radon chamber are presented; the calibration of cylindrical metallic diffusion chamber based on CR-39 chips detectors taking into account overlapping effect; transmission factors of gaps and pinhole for the same diffusion chambers are determined; permeability of glass fiber filter for 222Rn is obtained after reach equilibrium through Ramachandran model and taking into account a partition function as the rate of track density. The results of this research have been published in indexed journals. Finally, the conclusion and recommendations that reflect the fulfillment aims of this thesis are presented

    Boosting the Cycle Counting Power of Graph Neural Networks with I2^2-GNNs

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    Message Passing Neural Networks (MPNNs) are a widely used class of Graph Neural Networks (GNNs). The limited representational power of MPNNs inspires the study of provably powerful GNN architectures. However, knowing one model is more powerful than another gives little insight about what functions they can or cannot express. It is still unclear whether these models are able to approximate specific functions such as counting certain graph substructures, which is essential for applications in biology, chemistry and social network analysis. Motivated by this, we propose to study the counting power of Subgraph MPNNs, a recent and popular class of powerful GNN models that extract rooted subgraphs for each node, assign the root node a unique identifier and encode the root node's representation within its rooted subgraph. Specifically, we prove that Subgraph MPNNs fail to count more-than-4-cycles at node level, implying that node representations cannot correctly encode the surrounding substructures like ring systems with more than four atoms. To overcome this limitation, we propose I2^2-GNNs to extend Subgraph MPNNs by assigning different identifiers for the root node and its neighbors in each subgraph. I2^2-GNNs' discriminative power is shown to be strictly stronger than Subgraph MPNNs and partially stronger than the 3-WL test. More importantly, I2^2-GNNs are proven capable of counting all 3, 4, 5 and 6-cycles, covering common substructures like benzene rings in organic chemistry, while still keeping linear complexity. To the best of our knowledge, it is the first linear-time GNN model that can count 6-cycles with theoretical guarantees. We validate its counting power in cycle counting tasks and demonstrate its competitive performance in molecular prediction benchmarks

    Deep Learning for Scene Flow Estimation on Point Clouds: A Survey and Prospective Trends

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    Aiming at obtaining structural information and 3D motion of dynamic scenes, scene flow estimation has been an interest of research in computer vision and computer graphics for a long time. It is also a fundamental task for various applications such as autonomous driving. Compared to previous methods that utilize image representations, many recent researches build upon the power of deep analysis and focus on point clouds representation to conduct 3D flow estimation. This paper comprehensively reviews the pioneering literature in scene flow estimation based on point clouds. Meanwhile, it delves into detail in learning paradigms and presents insightful comparisons between the state-of-the-art methods using deep learning for scene flow estimation. Furthermore, this paper investigates various higher-level scene understanding tasks, including object tracking, motion segmentation, etc. and concludes with an overview of foreseeable research trends for scene flow estimation

    Explicit spectral gap for Schottky subgroups of SL(2,Z)\mathrm{SL} (2,\mathbb{Z})

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    Let Γ\Gamma be a Schottky subgroup of SL(2,Z)\mathrm{SL} (2,\mathbb{Z}). We establish a uniform and explicit lower bound of the second eigenvalue of the Laplace-Beltrami operator of congruence coverings of the hyperbolic surface Γ\H2\Gamma \backslash \mathbb{H}^2 provided the limit set of Γ\Gamma is thick enough.Comment: 31 page

    Increased lifetime of Organic Photovoltaics (OPVs) and the impact of degradation, efficiency and costs in the LCOE of Emerging PVs

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    Emerging photovoltaic (PV) technologies such as organic photovoltaics (OPVs) and perovskites (PVKs) have the potential to disrupt the PV market due to their ease of fabrication (compatible with cheap roll-to-roll processing) and installation, as well as their significant efficiency improvements in recent years. However, rapid degradation is still an issue present in many emerging PVs, which must be addressed to enable their commercialisation. This thesis shows an OPV lifetime enhancing technique by adding the insulating polymer PMMA to the active layer, and a novel model for quantifying the impact of degradation (alongside efficiency and cost) upon levelized cost of energy (LCOE) in real world emerging PV installations. The effect of PMMA morphology on the success of a ternary strategy was investigated, leading to device design guidelines. It was found that either increasing the weight percent (wt%) or molecular weight (MW) of PMMA resulted in an increase in the volume of PMMA-rich islands, which provided the OPV protection against water and oxygen ingress. It was also found that adding PMMA can be effective in enhancing the lifetime of different active material combinations, although not to the same extent, and that processing additives can have a negative impact in the devices lifetime. A novel model was developed taking into account realistic degradation profile sourced from a literature review of state-of-the-art OPV and PVK devices. It was found that optimal strategies to improve LCOE depend on the present characteristics of a device, and that panels with a good balance of efficiency and degradation were better than panels with higher efficiency but higher degradation as well. Further, it was found that low-cost locations were more favoured from reductions in the degradation rate and module cost, whilst high-cost locations were more benefited from improvements in initial efficiency, lower discount rates and reductions in install costs

    Exploring the Structure of Scattering Amplitudes in Quantum Field Theory: Scattering Equations, On-Shell Diagrams and Ambitwistor String Models in Gauge Theory and Gravity

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    In this thesis I analyse the structure of scattering amplitudes in super-symmetric gauge and gravitational theories in four dimensional spacetime, starting with a detailed review of background material accessible to a non-expert. I then analyse the 4D scattering equations, developing the theory of how they can be used to express scattering amplitudes at tree level. I go on to explain how the equations can be solved numerically using a Monte Carlo algorithm, and introduce my Mathematica package treeamps4dJAF which performs these calculations. Next I analyse the relation between the 4D scattering equations and on-shell diagrams in N = 4 super Yang-Mills, which provides a new perspective on the tree level amplitudes of the theory. I apply a similar analysis to N = 8 supergravity, developing the theory of on-shell diagrams to derive new Grassmannian integral formulae for the amplitudes of the theory. In both theories I derive a new worldsheet expression for the 4 point one loop amplitude supported on 4D scattering equations. Finally I use 4D ambitwistor string theory to analyse scattering amplitudes in N = 4 conformal supergravity, deriving new worldsheet formulae for both plane wave and non-plane wave amplitudes supported on 4D scattering equations. I introduce a new prescription to calculate the derivatives of on-shell variables with respect to momenta, and I use this to show that certain non-plane wave amplitudes can be calculated as momentum derivatives of amplitudes with plane wave states
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