Relevant bibliographies by topics / Poisson superposition

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  2. Dissertations / Theses
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Academic literature on the topic 'Poisson superposition'

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Published: 25 May 2024

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Journal articles on the topic "Poisson superposition"

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Crane, Harry, and Peter Mccullagh. "Poisson superposition processes." Journal of Applied Probability 52, no. 4 (December 2015): 1013–27. http://dx.doi.org/10.1239/jap/1450802750.

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Superposition is a mapping on point configurations that sends the n-tuple into the n-point configuration , counted with multiplicity. It is an additive set operation such that the superposition of a k-point configuration in is a kn-point configuration in . A Poisson superposition process is the superposition in of a Poisson process in the space of finite-length -valued sequences. From properties of Poisson processes as well as some algebraic properties of formal power series, we obtain an explicit expression for the Janossy measure of Poisson superposition processes, and we study their law under domain restriction. Examples of well-known Poisson superposition processes include compound Poisson, negative binomial, and permanental (boson) processes.
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Crane, Harry, and Peter Mccullagh. "Poisson superposition processes." Journal of Applied Probability 52, no. 04 (December 2015): 1013–27. http://dx.doi.org/10.1017/s0021900200113051.

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Superposition is a mapping on point configurations that sends the n-tuple into the n-point configuration , counted with multiplicity. It is an additive set operation such that the superposition of a k-point configuration in is a kn-point configuration in . A Poisson superposition process is the superposition in of a Poisson process in the space of finite-length -valued sequences. From properties of Poisson processes as well as some algebraic properties of formal power series, we obtain an explicit expression for the Janossy measure of Poisson superposition processes, and we study their law under domain restriction. Examples of well-known Poisson superposition processes include compound Poisson, negative binomial, and permanental (boson) processes.
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Nagel, Werner, and Viola Weiss. "Limits of sequences of stationary planar tessellations." Advances in Applied Probability 35, no. 1 (March 2003): 123–38. http://dx.doi.org/10.1239/aap/1046366102.

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In order to increase the variety of feasible models for random stationary tessellations (mosaics), two operations acting on tessellations are studied: superposition and iteration (the latter is also referred to as nesting). The superposition of two planar tessellations is the superposition of the edges of the cells of both tessellations. The iteration of tessellations means that one tessellation is chosen as a ‘frame’ tessellation. The single cells of this ‘frame’ are simultaneously and independently subdivided by cut-outs of tessellations of an independent and identically distributed sequence of tessellations. In the present paper, we investigate the limits for sequences of tessellations that are generated by consecutive application of superposition or iteration respectively. Sequences of (renormalised) superpositions of stationary planar tessellations converge weakly to Poisson line tessellations. For consecutive iteration the notion of stability of distributions is adapted and necessary conditions are formulated for those tessellations which may occur as limits.
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Nagel, Werner, and Viola Weiss. "Limits of sequences of stationary planar tessellations." Advances in Applied Probability 35, no. 01 (March 2003): 123–38. http://dx.doi.org/10.1017/s0001867800012118.

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In order to increase the variety of feasible models for random stationary tessellations (mosaics), two operations acting on tessellations are studied: superposition and iteration (the latter is also referred to as nesting). The superposition of two planar tessellations is the superposition of the edges of the cells of both tessellations. The iteration of tessellations means that one tessellation is chosen as a ‘frame’ tessellation. The single cells of this ‘frame’ are simultaneously and independently subdivided by cut-outs of tessellations of an independent and identically distributed sequence of tessellations. In the present paper, we investigate the limits for sequences of tessellations that are generated by consecutive application of superposition or iteration respectively. Sequences of (renormalised) superpositions of stationary planar tessellations converge weakly to Poisson line tessellations. For consecutive iteration the notion of stability of distributions is adapted and necessary conditions are formulated for those tessellations which may occur as limits.
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Daribayev, Beimbet, Aksultan Mukhanbet, and Timur Imankulov. "Implementation of the HHL Algorithm for Solving the Poisson Equation on Quantum Simulators." Applied Sciences 13, no. 20 (October 20, 2023): 11491. http://dx.doi.org/10.3390/app132011491.

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The Poisson equation is a fundamental equation of mathematical physics that describes the potential distribution in static fields. Solving the Poisson equation on a grid is computationally intensive and can be challenging for large grids. In recent years, quantum computing has emerged as a potential approach to solving the Poisson equation more efficiently. This article uses quantum algorithms, particularly the Harrow–Hassidim–Lloyd (HHL) algorithm, to solve the 2D Poisson equation. This algorithm can solve systems of equations faster than classical algorithms when the matrix A is sparse. The main idea is to use a quantum algorithm to transform the state vector encoding the solution of a system of equations into a superposition of states corresponding to the significant components of this solution. This superposition is measured to obtain the solution of the system of equations. The article also presents the materials and methods used to solve the Poisson equation using the HHL algorithm and provides a quantum circuit diagram. The results demonstrate the low error rate of the quantum algorithm when solving the Poisson equation.
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Møller, Jesper, and Kasper K. Berthelsen. "Transforming Spatial Point Processes into Poisson Processes Using Random Superposition." Advances in Applied Probability 44, no. 1 (March 2012): 42–62. http://dx.doi.org/10.1239/aap/1331216644.

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Most finite spatial point process models specified by a density are locally stable, implying that the Papangelou intensity is bounded by some integrable function β defined on the space for the points of the process. It is possible to superpose a locally stable spatial point process X with a complementary spatial point process Y to obtain a Poisson process X ⋃ Y with intensity function β. Underlying this is a bivariate spatial birth-death process (Xt, Yt) which converges towards the distribution of (X, Y). We study the joint distribution of X and Y, and their marginal and conditional distributions. In particular, we introduce a fast and easy simulation procedure for Y conditional on X. This may be used for model checking: given a model for the Papangelou intensity of the original spatial point process, this model is used to generate the complementary process, and the resulting superposition is a Poisson process with intensity function β if and only if the true Papangelou intensity is used. Whether the superposition is actually such a Poisson process can easily be examined using well-known results and fast simulation procedures for Poisson processes. We illustrate this approach to model checking in the case of a Strauss process.
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Møller, Jesper, and Kasper K. Berthelsen. "Transforming Spatial Point Processes into Poisson Processes Using Random Superposition." Advances in Applied Probability 44, no. 01 (March 2012): 42–62. http://dx.doi.org/10.1017/s0001867800005449.

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Most finite spatial point process models specified by a density are locally stable, implying that the Papangelou intensity is bounded by some integrable function β defined on the space for the points of the process. It is possible to superpose a locally stable spatial point process X with a complementary spatial point process Y to obtain a Poisson process X ⋃ Y with intensity function β. Underlying this is a bivariate spatial birth-death process (X t , Y t ) which converges towards the distribution of (X, Y). We study the joint distribution of X and Y, and their marginal and conditional distributions. In particular, we introduce a fast and easy simulation procedure for Y conditional on X. This may be used for model checking: given a model for the Papangelou intensity of the original spatial point process, this model is used to generate the complementary process, and the resulting superposition is a Poisson process with intensity function β if and only if the true Papangelou intensity is used. Whether the superposition is actually such a Poisson process can easily be examined using well-known results and fast simulation procedures for Poisson processes. We illustrate this approach to model checking in the case of a Strauss process.
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Yang, Tae Young, and Lynn Kuo. "Bayesian computation for the superposition of nonhomogeneous poisson processes." Canadian Journal of Statistics 27, no. 3 (September 1999): 547–56. http://dx.doi.org/10.2307/3316110.

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Chen, Louis H. Y., and Aihua Xia. "Poisson process approximation for dependent superposition of point processes." Bernoulli 17, no. 2 (May 2011): 530–44. http://dx.doi.org/10.3150/10-bej290.

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Hegyi, S. "Scaling laws in hierarchical clustering models with Poisson superposition." Physics Letters B 327, no. 1-2 (May 1994): 171–78. http://dx.doi.org/10.1016/0370-2693(94)91546-6.

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Dissertations / Theses on the topic "Poisson superposition"

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Alvarez, Corrales Luis. "Communications coopératives pour des très grands réseaux cellulaires." Electronic Thesis or Diss., Paris, ENST, 2017. http://www.theses.fr/2017ENST0055.

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Divers études ont abordé le problème de la coopération d’un réseau cellulaire, dont certaines considèrent aléatoirement le positionnement des antennes. Plusieurs auteurs étudient le cas où l’utilisateur choisit les antennes qui le serviront. Pourtant, cette hypothèse n'est pas réaliste. En conséquence, d’autres auteurs proposent former les groupes d'antennes de façon statique. Pour que ces méthodologies soient optimales, ces groupes statiques devraient être formés par rapport à la proximité entre les nœuds. Nous proposons une méthodologie statique basée sur le modèle du plus proche. À l'aide de celle-ci, nous formons des singletons et des paires de nœuds coopératives. Nous fournissons alors une analyse des caractéristiques structurelles et de l'interférence produite par ces deux derniers processus ponctuels. Lorsque le positionnement des antennes suit une loi de Poisson, les processus de singletons de paires associées ne suivent pas une loi de Poisson. Nous pouvons, cependant, rapprocher des métriques de performance du modèle original à l'aide de la superposition de deux processus de Poisson. L’évaluation numériques montre des gains de couverture allant jusqu’à 15 %, en comparaison du modèle non coopératif. Pour que la coopération entre les antennes soit significative, chacune devrait avoir un nombre de ressources suffisante, en plus d'être suffisamment proches. La relation de voisin le plus proche est, alors, redéfinie avec une nouvelle métrique. Les résultats de notre analyse montrent que les gains d’un réseau coopératif dépendent fortement de la distribution des ressources disponibles dans tout le réseau
Recent studies have set the problem of base station cooperation within the framework of stochastic geometry, where the irregularity of the base station positions can be considered. Some authors study the case when the user can dynamically choose the set of stations cooperating for its service. This assumption is not realistic. Instead, other authors propose to form the groups in a static way. To be optimal, these static methodologies should consider proximity between the base stations to form the groups. We propose a grouping method based on the nearest neighbor model. We allow the formation of singles and pairs of nodes. We derive structural characteristics for these two processes and analyse the resulting interference fields. When the node positions are modelled by a Poisson point process, the processes of singles and pairs are not Poisson, complicating the corresponding analysis. The performance of the original model, however, can be approximated by the superposition of two Poisson point processes. Numerical evaluation shows coverage gains from different signal cooperation that can reach up to 15%, compared with the standard noncooperative case. For the cooperation to be meaningful, each station in a group should have sufficient resources to share, besides being close to each other. Thus, we redefine the nearest neighbors with a metric. The results of our analysis illustrate that cooperation gains strongly depend on the distribution of the available resources over the network
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Bakošová, Katarína. "Vícerozměrné bodové procesy a jejich použití na neurofyziologických datech." Master's thesis, 2018. http://www.nusl.cz/ntk/nusl-387002.

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This thesis examines a multivariate point process in time with focus on a mu- tual relations of its marginal point processes. The first chapter acquaints the re- ader with the theoretical background of multivariate point processes and their properties, especially the higher-order cumulant-correlation measures. Later on, several models of multivariate point processes with different dependence structu- res are characterized, such as the random superposition model, a Poisson depen- dent superposition point process, a jitter Poisson dependent superposition point process orrenewal processes models. Simulations of each of them are provided. Furthermore, two statistical methods for higher-order correlations are presented; the cumulant based inference of higher-order correlations, and the extended til- ling coefficient. Finally, the introduced methods are applied not only on the data from simulations, but also on the real, simultaneously recorded nerve cells spike train data. The results are discussed. 1
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Book chapters on the topic "Poisson superposition"

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Kamoun, Faouzi, and M. Mehmet Ali. "Statistical analysis of the traffic generated by the superposition of N independent interrupted poisson processes." In Information Theory and Applications, 325–42. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/3-540-57936-2_48.

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Scott, Steven L., and Padhraic Smyth. "The Markov Modulated Poisson Process and Markov Poisson Cascade with Applications to Web Traffic Modeling." In Bayesian Statistics 7, 671–80. Oxford University PressOxford, 2003. http://dx.doi.org/10.1093/oso/9780198526155.003.0047.

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Abstract A Markov modulated Poisson Process (MMPP) is a Poisson process whose rate varies according to a Markov process. The nonhomogeneous MMPP developed in this article is a natural model for point processes whose events combine irregular bursts of activity with predictable (e.g. daily and hourly) patterns. We show how the MMPP may be viewed as a superposition of unobserved Poisson processes that are activated and deactivated by an unobserved Markov process. The MMPP is a continuous time model which may also be viewed as a discretely indexed nonstationary hidden Markov model by viewing intervals between events as a sequence of dependent random variables. The HMM representation allows one to probabilistically reconstruct the latent Markov and Poisson processes using a set of forward-backward recursions. The recursions allow MMPP parameters to be estimated either by an EM algorithm or by a rapidly mixing Markov chain Monte Carlo algorithm which uses the recursions for data augmentation. The Markov-Poisson cascade (MPC) is an MMPP whose underlying Markov process obeys certain restrictions which uniquely order the event rates for the observed process. The ordering avoids a possible label switching issue without slowing down the rapidly mixing algorithms we use to implement the model. We apply the MPC to a data set containing click rate data for individual computer users browsing through the World Wide Web. Because the complete data posterior distribution for the MPC is a product of exponential family distributions we are able to incorporate data from multiple users into a hierarchical model using existing methods from hierarchical Poisson regression.
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Alotaibi, Manal, and Ruud Weijermars. "Asymptotic Solutions for Multi-Hole Problems: Plane Strain Versus Plane Stress Boundary Conditions in Borehole Applications." In Drilling Engineering and Technology - Recent Advances, New Perspectives and Applications [Working Title]. IntechOpen, 2022. http://dx.doi.org/10.5772/intechopen.105048.

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The elastic response of circular cylindrical holes in elastic plates is analyzed using the linear superposition method (LSM) to assess the impact of plate thickness on the stress state for the thin- and thick-plate solutions. Analytical solutions for stress accumulations near holes in elastic plates are relevant for a wide range of practical applications. For example, detailed analyses of the stress concentrations near boreholes piercing rock formations are needed during drilling operations to avoid premature fracturing due to tensile and shear failure. Stress concentrations near tiny holes in very thick plates approach the solution of a plane strain boundary condition; for large holes in very thin plates, the solution of a plane stress boundary condition will apply. For most practical cases, the response will be intermediate between the plane stress and plane strain end members, depending on the relative dimensions of the thickness of the elastic volume penetrated and the hole diameter. A nondimensional scaling parameter is introduced to quantify for which hole radius to plate thickness ratio occurs the transition between the two types of solutions (plane strain versus plane stress). Moreover, in this study, we consider the case of the presence of the internal pressure load in the analysis of the stress concentrations near boreholes. This consideration is important to carefully assess the magnitude of the elastic stress concentrations and their orientation near the hole in the rock formation when the pressure load of the mud is added to the borehole during drilling operations. For holes subjected to an internal pressure only, there is no difference between the plane stress (thin-plate solution) and plane strain solutions (thick-plate solutions). For cases with far-field stress, the plane strain solution is more sensitive to the Poisson’s ratio than the plane stress solution. Multi-hole problems are also evaluated with LSM and the results are benchmarked against known solutions of different methods.
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Conference papers on the topic "Poisson superposition"

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Kim, Hyeji, Benjamin Nachman, and Abbas El Gamal. "Superposition coding is almost always optimal for the Poisson broadcast channel." In 2015 IEEE International Symposium on Information Theory (ISIT). IEEE, 2015. http://dx.doi.org/10.1109/isit.2015.7282572.

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Lee, Yeongho, and Steven G. Buchberger. "Modeling Indoor and Outdoor Residential Water Use as the Superposition of Two Poisson Rectangular Pulse Processes." In 29th Annual Water Resources Planning and Management Conference. Reston, VA: American Society of Civil Engineers, 1999. http://dx.doi.org/10.1061/40430(1999)48.

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Gorres, J., H. W. Kropholler, and P. Luner. "Measuring Flocculation Using Image Analysis." In Papermaking Raw Materials, edited by V. Punton. Fundamental Research Committee (FRC), Manchester, 1985. http://dx.doi.org/10.15376/frc.1985.1.363.

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Experimental and theoretical measures of flocculation were studied using image analysis. An experimental study of commercial board samples led to the proposal of three descriptive floc features, namely, size, ‘definition’, and contrast. Numerical values were obtained from an ensemble averaged linear auto-correlation function. In addition a theoretical model of formation was simulated to compare degrees of flocculation. The theoretical structure was created by using a poisson cluster model in conjunction with a coverage model. This led to the superposition of fibrous micro0-flocs whose flock centre radii, R, and fibre content, N, determine the severity of the formation. The variance and p.t.p correlation of the resulting image textures were computed. These measures were found to have a lower limit which is set by the fibrous structure of the flocs. The findings from the simulation study were then applied in principle to the variance and size information extracted from the board samples to explain their structure. The versatility of programmable image analysis systems was demonstrated for formation measurement.
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Ren, Qinlong, Cho Lik Chan, and Alberto L. Arvayo. "Numerical Simulation of 2D Electrothermal Flow Using Boundary Element Method." In ASME 2013 4th International Conference on Micro/Nanoscale Heat and Mass Transfer. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/mnhmt2013-22075.

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Microfluidics and its applications to Lab-on-a-Chip have attracted a lot of attention. Because of the small length scale, the flow is characterized by a low Re number. The governing equations become linear. Boundary element method (BEM) is a very good option for simulating the fluid flow with high accuracy. In this paper, we present a 2D numerical modeling of the electrothermal flow using BEM. In electrothermal flow the volumetric force is caused by electric field and temperature gradient. The physics is mathematically modeled by (i) Laplace equation for the electrical potential, (ii) Poisson equation for the heat conduction caused by Joule heating, (iii) continuity and Stokes equation for the low Reynolds number flow. We begin by solving the electrical potential and electric field. The heat conduction is caused by the Joule heating as the heat generation term. Superposition principle is used to solve for the temperature field. The Coulomb and dielectric forces are generated by the electrical field and temperature gradient of the system. We analyze the Stokes flow problem by superposition of fundamental solution for free-space velocity caused by body force and BEM for the corresponding homogeneous Stokes equation. It is well known that a singularity integral arises when the source point approaches the field point. To overcome this problem, we solve the free-space velocity analytically. For the BEM part, we also calculate all the integral terms analytically. With this effort, our solution is more accurate. In addition, we improve the robustness of the matrix system by combining the velocity integral equation with the traction integral equation. Our purpose is to design a pump for the microfluidics system. Since the system is a long channel, the flow is fully developed in the area far away from the electrodes. With this assumption, the velocity profile is parabolic at the inlet and outlet of the channel. So we can get appropriate boundary conditions for the BEM part of Stokes equation. Consequently, we can simulate the electrothermal flow in an open channel. In this paper, we will present the formulation and implementation of BEM to model electrothermal flow. Results of electrical potential, temperature field, Joule heating, electrothermal force, and velocity field will be presented.
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Granados, Julián Mauricio, Gabriel Arturo Oquendo, Carlos Andres Bustamante, and Whady Felipe Florez. "Assessment of Localization Strategies in a Radial Basis Function Meshless Method to Solve Two-Dimensional Convection-Diffusion Problems." In The 6th International Conference on Numerical Modelling in Engineering. Switzerland: Trans Tech Publications Ltd, 2024. http://dx.doi.org/10.4028/p-qb3rnt.

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Two-dimensional Poisson and convection-diffusion problems are solved by using three localization schemes implemented in the context of a Radial Basis Function (RBFs) collocation method. The first scheme uses the traditional RBF superpositions to approximate the problem variable in a defined stencil. The second scheme is the Partition of Unity strategy and it is used to obtain a representation of governing equations as a linear combination of RBFs local superpositions evaluated at neighbouring stencils. Weight functions are designed to capture the convection term effect on the solution. In the third scheme, an upwind strategy is included in the Partition of Unity scheme for solving the convection-diffusion problem by moving and deforming stencils based on velocity. For all schemes, stencils in the form of crosses, circles, and squares are considered, and Root mean square (RMS) is obtained as a function of shape parameter, nodal distribution size and stencil size. In the case of Poisson problems, the use of Partition of unity in circular configuration with no more than 37 nodes per stencil is recommended as far as a $c$ suitable range is obtained for each nodal distribution employed to avoid ill-conditioning issues.
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Reports on the topic "Poisson superposition"

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Caspi, S., M. Helm, and L. J. Laslett. INCORPORATION OF SUPERPOSITION INTO THE PROGRAM POISSON. Office of Scientific and Technical Information (OSTI), January 1985. http://dx.doi.org/10.2172/1000341.

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