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Статті в журналах з теми "Graphe de Farey"

Автор: Grafiati

Опубліковано: 11 січня 2025

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1

Calero-Sanz, Jorge. "On the Degree Distribution of Haros Graphs." Mathematics 11, no. 1 (December 26, 2022): 92. http://dx.doi.org/10.3390/math11010092.

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Haros graphs are a graph-theoretical representation of real numbers in the unit interval. The degree distribution of the Haros graphs provides information regarding the topological structure and the associated real number. This article provides a comprehensive demonstration of a conjecture concerning the analytical formulation of the degree distribution. Specifically, a theorem outlines the relationship between Haros graphs, the corresponding continued fraction of its associated real number, and the subsequent symbolic paths in the Farey binary tree. Moreover, an expression that is continuous and piecewise linear in subintervals defined by Farey fractions can be derived from an additional conclusion for the degree distribution of Haros graphs.

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2

Gnanam, A., and C. Dinesh. "Farey Triangle Graphs and Farey Triangle Matrices." Advances in Pure Mathematics 05, no. 12 (2015): 738–44. http://dx.doi.org/10.4236/apm.2015.512067.

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3

Taylor, Samuel J., and Alexander Zupan. "Products of Farey graphs are totally geodesic in the pants graph." Journal of Topology and Analysis 08, no. 02 (March 15, 2016): 287–311. http://dx.doi.org/10.1142/s1793525316500096.

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We show that for a surface [Formula: see text], the subgraph of the pants graph determined by fixing a collection of curves that cut [Formula: see text] into pairs of pants, once-punctured tori, and four-times-punctured spheres is totally geodesic. The main theorem resolves a special case of a conjecture made in [2] and has the implication that an embedded product of Farey graphs in any pants graph is totally geodesic. In addition, we show that a pants graph contains a convex [Formula: see text]-flat if and only if it contains an [Formula: see text]-quasi-flat.

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4

Jiang, Wenchao, Yinhu Zhai, Zhigang Zhuang, Paul Martin, Zhiming Zhao, and Jia-Bao Liu. "Vertex Labeling and Routing for Farey-Type Symmetrically-Structured Graphs." Symmetry 10, no. 9 (September 17, 2018): 407. http://dx.doi.org/10.3390/sym10090407.

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The generalization of Farey graphs and extended Farey graphs all originate from Farey graphs. They are simultaneously scale-free and small-world. A labeling of the vertices for them are proposed here. All of the shortest paths between any two vertices in these two graphs can be determined only on their labels. The number of shortest paths between any two vertices is the product of two Fibonacci numbers; it is increasing almost linearly with the order or size of the graphs. However, the label-based routing algorithm runs in logarithmic time O(logn). Our efficient routing protocol for Farey-type models should help contribute toward the understanding of several physical dynamic processes.

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5

Gaster, Jonah, Miguel Lopez, Emily Rexer, Zoë Riell, and Yang Xiao. "Combinatorics of $k$-Farey graphs." Rocky Mountain Journal of Mathematics 50, no. 1 (February 2020): 135–51. http://dx.doi.org/10.1216/rmj.2020.50.135.

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6

Wang, Yucheng, Qi Bao, and Zhongzhi Zhang. "Combinatorial properties of Farey graphs." Theoretical Computer Science 796 (December 2019): 70–89. http://dx.doi.org/10.1016/j.tcs.2019.08.022.

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7

Kurkofka, Jan. "Ubiquity and the Farey graph." European Journal of Combinatorics 95 (June 2021): 103326. http://dx.doi.org/10.1016/j.ejc.2021.103326.

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8

DEMİR, Bilal, and Mustafa KARATAŞ. "Farey graph and rational fixed points of the extended modular group." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 71, no. 4 (December 30, 2022): 1029–43. http://dx.doi.org/10.31801/cfsuasmas.1089480.

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Fixed points of matrices have many applications in various areas of science and mathematics. Extended modular group ¯¯¯¯ΓΓ¯ is the group of 2×22×2 matrices with integer entries and determinant ±1±1. There are strong connections between extended modular group, continued fractions and Farey graph. Farey graph is a graph with vertex set ^Q=Q∪{∞}Q^=Q∪{∞}. In this study, we consider the elements in ¯¯¯¯ΓΓ¯ that fix rationals. For a given rational number, we use its Farey neighbours to obtain the matrix representation of the element in $\overline{\Gamma}$ that fixes the given rational. Then we express such elements as words in terms of generators using the relations between the Farey graph and continued fractions. Finally we give the new block reduced form of these words which all blocks have Fibonacci numbers entries.

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9

Zhang, Zhongzhi, and Francesc Comellas. "Farey graphs as models for complex networks." Theoretical Computer Science 412, no. 8-10 (March 2011): 865–75. http://dx.doi.org/10.1016/j.tcs.2010.11.036.

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10

单, 美玲. "Chromatic Polynomials and Flow Polynomials of Farey Graphs and Their Dual Graphs." Operations Research and Fuzziology 08, no. 04 (2018): 145–50. http://dx.doi.org/10.12677/orf.2018.84018.

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11

Liao, Yunhua, Yaoping Hou, and Xiaoling Shen. "Tutte polynomial of a small-world Farey graph." EPL (Europhysics Letters) 104, no. 3 (November 1, 2013): 38001. http://dx.doi.org/10.1209/0295-5075/104/38001.

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12

Kurkofka, Jan. "The Farey graph is uniquely determined by its connectivity." Journal of Combinatorial Theory, Series B 151 (November 2021): 223–34. http://dx.doi.org/10.1016/j.jctb.2021.06.006.

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13

Zhang, Zhongzhi, Bin Wu, and Yuan Lin. "Counting spanning trees in a small-world Farey graph." Physica A: Statistical Mechanics and its Applications 391, no. 11 (June 2012): 3342–49. http://dx.doi.org/10.1016/j.physa.2012.01.039.

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14

Zhang, Jingyuan, and Weigen Yan. "Counting spanning trees of a type of generalized Farey graphs." Physica A: Statistical Mechanics and its Applications 555 (October 2020): 124749. http://dx.doi.org/10.1016/j.physa.2020.124749.

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15

Wright, Alex. "Spheres in the curve graph and linear connectivity of the Gromov boundary." Communications of the American Mathematical Society 4, no. 12 (September 4, 2024): 548–77. http://dx.doi.org/10.1090/cams/38.

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We consider the curve graph in the cases where it is not a Farey graph, and show that its Gromov boundary is linearly connected. For a fixed center point c c and radius r r , we define the sphere of radius r r to be the induced subgraph on the set of vertices of distance r r from c c . We show that these spheres are always connected in high enough complexity, and prove a slightly weaker result for low complexity surfaces.

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16

Hockman, Meira. "The Farey octahedron graph, the Poincaré polyhedron theorem and Gaussian integer continued fractions." Annales mathématiques du Québec 44, no. 1 (April 22, 2019): 149–64. http://dx.doi.org/10.1007/s40316-019-00115-4.

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17

Shang, Yilun. "Geometric Assortative Growth Model for Small-World Networks." Scientific World Journal 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/759391.

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It has been shown that both humanly constructed and natural networks are often characterized by small-world phenomenon and assortative mixing. In this paper, we propose a geometrically growing model for small-world networks. The model displays both tunable small-world phenomenon and tunable assortativity. We obtain analytical solutions of relevant topological properties such as order, size, degree distribution, degree correlation, clustering, transitivity, and diameter. It is also worth noting that the model can be viewed as a generalization for an iterative construction of Farey graphs.

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18

Miah, Md Sujan, Md Mominul Islam, Mahmudul Hasan, Abu Hashan Md Mashud, Dipa Roy, and Shib Sankar Sana. "A Discount Technique-Based Inventory Management on Electronics Products Supply Chain." Journal of Risk and Financial Management 14, no. 9 (August 25, 2021): 398. http://dx.doi.org/10.3390/jrfm14090398.

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Inventory management is becoming very challenging for the retailer over the years due to the uncertainty in the demand and supply of products in financial risk and management systems. In a competitive market, running a business smoothly in a highly suitable place is day by day becoming tough due to the very high fare for those locations. Thus, limited storage is available in those elite places with high fares, and a retailer takes a financial risk by stocking huge amounts of products in those limited storage stores. Thus, the appropriate financial analysis is required to find out optimal strategies (financial decisions) to sustain a business organization of electronic products in a global competitive business environment. As a result, when bulk purchases of electronic products, for example, T.V., Fridges, Oven, etc., have been made by the retailer, he faces two problems. The first one is related to the limited storage; as a result, he has to pay a considerable amount to hold the products for a long time. The second one is shortages of liquid money as he invested massive amounts. To avoid these problems, he offers some price discounts on the market’s original selling price to sell the products quickly for a limited time prior to recovering his capital investment. For that reason, a price, time, and stock dependent realistic demand function have been considered in this proposed paper with two modes of discount policy. The proposed model has been solved by a classical optimization technique from calculus and provides some insights for the retailer. Some numerical examples and graphs are provided to illustrate the model.

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19

Liao, Yunhua, Mohamed Maama, and M. A. Aziz-Alaoui. "Optimal networks for exact controllability." International Journal of Modern Physics C 31, no. 10 (August 20, 2020): 2050144. http://dx.doi.org/10.1142/s0129183120501442.

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The exact controllability can be mapped to the problem of maximum algebraic multiplicity of all eigenvalues. In this paper, we focus on the exact controllability of deterministic complex networks. First, we explore the eigenvalues of two famous networks, i.e. the comb-of-comb network and the Farey graph. Due to their special structure, we find that the eigenvalues of each network are mutually distinct, showing that these two networks are optimal networks with respect to exact controllability. Second, we study how to optimize the exact controllability of a deterministic network. Based on the spectral graph theory, we find that reducing the order of duplicate sets or co-duplicate sets which are two special vertex subsets can decrease greatly the exact controllability. This result provides an answer to an open problem of Li et al. [X. F. Li, Z. M. Lu and H. Li, Int. J. Mod. Phys. C 26, 1550028 (2015)]. Finally, we discuss the relation between the topological structure and the multiplicity of two special eigenvalues and the computational complexity of our method.

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20

Lu, Ye, Changjiang Zheng, Shukang Zheng, Junze Ma, Zhilong Wu, Fei Wu, and Yang Shen. "Multi-Spatio-Temporal Convolutional Neural Network for Short-Term Metro Passenger Flow Prediction." Electronics 13, no. 1 (December 30, 2023): 181. http://dx.doi.org/10.3390/electronics13010181.

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Accurate short-term prediction of metro passenger flow can offer significant assistance in optimizing train schedules, reducing congestion during peak times, and improving the service level of the metro system. Currently, most models do not fully utilize the high-resolution data aggregated by automatic fare collection systems. Therefore, we propose a model, called MST-GRT, that aggregates multi-time granularity data and considers multi-graph structures. Firstly, we analyze the correlation between metro passenger flow sequences at different time granularities and establish a principle for extracting the spatiotemporal correlation of data at different time granularities using the multi-graph neural network. Subsequently, we use residual blocks to construct a deep convolutional neural network to aggregate the data of different time granularities from small to large, obtaining multi-channel feature maps of multi-time granularity. To process the multi-channel feature maps, we use 2D dilated causal convolution to reconstruct the TCN (Temporal Convolutional Network) to compress the channel number of the feature maps and extract the time dependency of the data, and finally output the results through a fully connected layer. The experimental results demonstrate that our model outperforms the baseline models on the Hangzhou Metro smart-card data set.

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21

Drakopoulos, Georgios, Andreas Kanavos, Phivos Mylonas, and Panagiotis Pintelas. "Extending Fuzzy Cognitive Maps with Tensor-Based Distance Metrics." Mathematics 8, no. 11 (October 31, 2020): 1898. http://dx.doi.org/10.3390/math8111898.

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Cognitive maps are high level representations of the key topological attributes of real or abstract spatial environments progressively built by a sequence of noisy observations. Currently such maps play a crucial role in cognitive sciences as it is believed this is how clusters of dedicated neurons at hippocampus construct internal representations. The latter include physical space and, perhaps more interestingly, abstract fields comprising of interconnected notions such as natural languages. In deep learning cognitive graphs are effective tools for simultaneous dimensionality reduction and visualization with applications among others to edge prediction, ontology alignment, and transfer learning. Fuzzy cognitive graphs have been proposed for representing maps with incomplete knowledge or errors caused by noisy or insufficient observations. The primary contribution of this article is the construction of cognitive map for the sixteen Myers-Briggs personality types with a tensor distance metric. The latter combines two categories of natural language attributes extracted from the namesake Kaggle dataset. To the best of our knowledge linguistic attributes are separated in categories. Moreover, a fuzzy variant of this map is also proposed where a certain personality may be assigned to up to two types with equal probability. The two maps were evaluated based on their topological properties, on their clustering quality, and on how well they fared against the dataset ground truth. The results indicate a superior performance of both maps with the fuzzy variant being better. Based on the findings recommendations are given for engineers and practitioners.

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22

Ye, Haonan, and Xiao Luo. "Cascading Failure Analysis on Shanghai Metro Networks: An Improved Coupled Map Lattices Model Based on Graph Attention Networks." International Journal of Environmental Research and Public Health 19, no. 1 (December 25, 2021): 204. http://dx.doi.org/10.3390/ijerph19010204.

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Analysis of the robustness and vulnerability of metro networks has great implications for public transport planning and emergency management, particularly considering passengers’ dynamic behaviors. This paper presents an improved coupled map lattices (CMLs) model based on graph attention networks (GAT) to study the cascading failure process of metro networks. The proposed model is applied to the Shanghai metro network using the automated fare collection (AFC) data, and the passengers’ dynamic behaviors are simulated by GAT. The quantitative cascading failure analysis shows that Shanghai metro network is robust to random attacks, but fragile to intentional attacks. Moreover, there is an approximately normal distribution between instant cascading failure speed and time step and the perturbation in a station which leads to steady state is approximately a constant. The result shows that a station surrounded by other densely distributed stations can trigger cascading failure faster and the cascading failure triggered by low-level accidents will spread in a short time and disappear quickly. This study provides an effective reference for dynamic safety evaluation and emergency management in metro networks.

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23

Alejandro Isaza, Alejandro Isaza, Jieshan Lu, Vadim Bulitko, and Russell Greiner. "A Cover-Based Approach to Multi-Agent Moving Target Pursuit." Proceedings of the AAAI Conference on Artificial Intelligence and Interactive Digital Entertainment 4, no. 1 (September 27, 2021): 54–59. http://dx.doi.org/10.1609/aiide.v4i1.18672.

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We explore the task of designing an efficient multi-agent system that is capable of capturing a single moving target, assuming that every agent knows the location of all agents on a fixed known graph. Many existing approaches are suboptimal as they do not coordinate multiple pursuers and are slow as they re-plan each time the target moves, which makes them fare poorly in real-time pursuit scenarios such as video games. We address these shortcomings by developing the concept of cover set, which leads to a measure that takes advantage of information about the position and speed of each agent. We first define cover set and then present an algorithm that uses cover to coordinate multiple pursuers. We compare the effectiveness of this algorithm against several classic and state-of-the-art pursuit algorithms, along several performance measures. We also compute the optimal pursuit policy for several small grids, and use the associated optimal scores as yardsticks for our analysis.

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24

Jumardi, Shirly Wunas, M. Yamin Jinca, and Venny Veronica Natalia. "Trip Distribution and Modal Choice in the Taman Mini LRT Station Area." IOP Conference Series: Earth and Environmental Science 1272, no. 1 (December 1, 2023): 012005. http://dx.doi.org/10.1088/1755-1315/1272/1/012005.

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Abstract The surrounding Taman Mini LRT station boasts a diverse range of land uses, primarily characterized by residential zones, interspersed with dynamic activity hubs such as tourist attractions, shopping malls, and hospitals. The prevailing issue in this area relates to persistent traffic congestion, stemming from the overreliance on private vehicles, inadequate public transportation infrastructure, disjointed intermodal connections, and the lack of seamless integration between transportation modes and activity centers. This study endeavors to comprehensively analyze pedestrian and vehicular movement in the periphery of the Taman Mini LRT station. This analysis is pivotal in assessing the current mobility landscape. Notably, the intensity of activity within a particular land use directly correlates with its ability to draw vehicular traffic, consequently leading to prolonged waiting times for pedestrians at crosswalks. Employing a four-step model, this research methodically defines pedestrian and vehicular flow within the region. This model incorporates output distribution of trips and origin-destination graphs. Additionally, stated preference techniques are employed to discern respondents’ inclinations when making travel decisions. This involves evaluating key factors like travel time, fares, frequency, accessibility level, comfort, and safety – categories that significantly influence their preferences when selecting between LRT and other transportation modes.

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25

Alenazi, Mohammed J. F. "ENRN: A System for Evaluating Network Resilience against Natural Disasters." Mathematics 11, no. 20 (October 11, 2023): 4250. http://dx.doi.org/10.3390/math11204250.

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The frequency and severity of natural disasters is surging, posing an urgent need for robust communication network infrastructure that is capable of withstanding these events. In this paper, we present a groundbreaking graph-theoretic system designed to evaluate and enhance network resilience in the face of natural disasters. Our solution harnesses the power of topological robustness metrics, integrating real-time weather data, geographic information, detailed network topology data, advanced resilience algorithms, and continuous network monitoring. The proposed scheme considers four major real-world U.S.-based network providers and evaluates their physical topologies against two major hurricanes. Our novel framework quantifies the important characteristics of network infrastructure; for instance, AT&T is identified to have fared better against Hurricane Ivan (57.98 points) than Hurricane Katrina (39.17 points). We not only provide current insights into network infrastructure resilience, but also uncover valuable findings that shed light on the performance of backbone U.S. networks during hurricanes. Furthermore, our findings provide actionable insights to enrich the overall survivability and functionality of communication networks, mitigating the adverse impacts of natural disasters on communication systems and critical services in terms of improving network resiliency via adding additional nodes and link or rewiring.

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26

Delling, Daniel, Thomas Pajor, and Renato Werneck. "Round-Based Public Transit Routing (Extended Abstract)." Proceedings of the International Symposium on Combinatorial Search 4, no. 1 (August 20, 2021): 213. http://dx.doi.org/10.1609/socs.v4i1.18270.

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We study the problem of computing all Pareto-optimal journeys in a dynamic public transit network for two criteria: arrival time and number of transfers. Existing algorithms consider this as a graph problem, and solve it using variants of Dijkstra's algorithm. Unfortunately, this leads to either high query times or suboptimal solutions. We take a different approach. We introduce RAPTOR, our novel round-based public transit router. Unlike previous algorithms, it is not Dijkstra-based, looks at each route (such as a bus line) in the network at most once per round, and can be made even faster with simple pruning rules and parallelization using multiple cores. Because it does not rely on preprocessing, RAPTOR works in fully dynamic scenarios. Moreover, it can be easily extended to handle flexible departure times or arbitrary additional criteria, such as fare zones. When run on London's complex public transportation network, RAPTOR computes all Pareto-optimal journeys between two random locations an order of magnitude faster than previous approaches, which easily enables interactive applications. This is an extended abstract of the paper published at ALENEX 2012.

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27

Abdulkadir, Usman Bolaji, and Animashaun Kikelomo Halimat. "Inland Water Transport and Urban Mobility in Ikorodu-Ebutte Ero Route, Lagos, Nigeria." Geosfera Indonesia 5, no. 1 (April 27, 2020): 127. http://dx.doi.org/10.19184/geosi.v5i1.14714.

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Анотація:

Lagos city has abundant navigable inland waterways which if fully harnessed would help minimise road traffic congestion, pollution and provide low cost means of long distance travel within the city. This study examines inland water transport services on Lagos lagoon focusing on Ikorodu-Ebutte Ero route. Primary data were obtained using structured questionnaires. While, secondary data were sourced from relevant government and private agencies. Data were analysed using descriptive techniques including frequency counts, tables and graphs. The results revealed an inadequate provision of terminal facilities and vessels in the area. It was also found that most (67.3%) of the trips via water transport in the were mainly for work purpose. In addition, low patronage was observed and it was found to be mostly due to comparatively high cost of fares and passenger safety concerns, as indicated by 67.4% and 58.7% of the respondents respectively. Furthermore, high income earners where found to patronise this mode than low income earners. The high frequency of use of water transport by the respondents (71.3% travel by water every day) indicates that, this mode has great potential of being widely adopted, if greater attention is given to its development by both the government and private sector. There is, therefore, a need for more investment in water transportation in the area through the provision of modern infrastructure and vessels. Keywords: urban mobility; inland waterways; transport services; sustainable transportation; integrated transport. Copyright (c) 2020 Geosfera Indonesia Journal and Department of Geography Education, University of Jember This work is licensed under a Creative Commons Attribution-Share A like 4.0 International License

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28

Huang, X., and J. Tan. "Understanding spatio-temporal mobility patterns for seniors, child/student and adult using smart card data." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XL-1 (November 7, 2014): 167–72. http://dx.doi.org/10.5194/isprsarchives-xl-1-167-2014.

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Анотація:

Commutes in urban areas create interesting travel patterns that are often stored in regional transportation databases. These patterns can vary based on the day of the week, the time of the day, and commuter type. This study proposes methods to detect underlying spatio-temporal variability among three groups of commuters (senior citizens, child/students, and adults) using data mining and spatial analytics. Data from over 36 million individual trip records collected over one week (March 2012) on the Singapore bus and Mass Rapid Transit (MRT) system by the fare collection system were used. Analyses of such data are important for transportation and landuse designers and contribute to a better understanding of urban dynamics. <br><br> Specifically, descriptive statistics, network analysis, and spatial analysis methods are presented. Descriptive variables were proposed such as density and duration to detect temporal features of people. A directed weighted graph G &equiv; (N , L, W) was defined to analyze the global network properties of every pair of the transportation link in the city during an average workday for all three categories. Besides, spatial interpolation and spatial statistic tools were used to transform the discrete network nodes into structured human movement landscape to understand the role of transportation systems in urban areas. The travel behaviour of the three categories follows a certain degree of temporal and spatial universality but also displays unique patterns within their own specialties. Each category is characterized by their different peak hours, commute distances, and specific locations for travel on weekdays.

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29

Schuhmann, Peter W., KimMarie McGoldrick, and Robert T. Burrus. "Student Quantitative Literacy: Importance, Measurement, and Correlation with Economic Literacy." American Economist 49, no. 1 (March 2005): 49–65. http://dx.doi.org/10.1177/056943450504900104.

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Анотація:

The importance of quantitative skills in learning economics cannot be overstated. Many previous studies have attempted to measure the degree to which such skills impact performance in economics classes. Typically these studies have relied on a proxy for measuring quantitative skills, such as the number and type of math courses a student has completed. Yet it is the proficiency in math rather than the exposure to it that is expected to impact the learning of economics and performance in economics courses. In this paper we use a pre and post course math quiz to address two major research questions. First, we examine the degree to which students who have greater math aptitude also have a better grasp of basic economics concepts prior to taking a principles of economics course. Second, we explore the degree to which this math aptitude is correlated with higher economic learning. Our results indicate that (prior to taking a principles of economics course) students do not fare well on simple quantitative questions and hence do not possess an adequate working knowledge of the “language” we often speak during our economics courses. Our analysis shows, however, that quantitative literacy is a very important determinant of economic literacy in both the pre and post course surveys. More specifically, we have shown that having skills such as being able to solve a system of equations and compute a percentage, and being able to interpret increases and decreases on a graph will lead to higher economic knowledge at the end of the semester.

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30

Lin, Zihan, Jingyan Wang, and Shuaiqi Xu. "Advancements in Private Set Union: Protocols, Security Frameworks, and Applications." Highlights in Science, Engineering and Technology 85 (March 13, 2024): 191–95. http://dx.doi.org/10.54097/bg91vt52.

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Private Set Union (PSU), a subset of Private Set Intersection (PSI) methodologies, is swiftly marking its importance in an era that progressively values computational integrity without infringing data privacy. This necessity sprouted from the intricate balance between ensuring rigorous privacy protection and fostering beneficial data sharing. PSU enables multiple entities to establish a union of their individual datasets without revealing their private information to each other. The foundational security models that drive PSU are both intricate and robust, with roots tracing back to the Computational Diffie-Hellman problems. These problems address the challenges of ensuring secure computations in multi-party scenarios. Attack strategies targeting PSU have evolved over time, leading to an enhancement in the defense mechanisms. Techniques utilizing encryption, randomization, and other cryptographic methods have seen consistent improvement, making privacy-preserved inter-party data analytics both feasible and efficient. Recent breakthroughs in PSU protocols have seen rigorous evaluations based on efficiency, security, and performance metrics. These evaluations aim to determine how these protocols fare under real-world conditions and what challenges they might encounter. Additionally, PSU’s adaptability and relevance have been showcased across various industries. Whether it's digital libraries collaborating for enriched content while preserving copyright restrictions, financial institutions aiming to analyze transaction patterns without compromising individual account details, risk assessment firms sharing data to provide better evaluations without revealing sensitive details, joint graph computations ensuring optimal routing without exposing network infrastructures, or the ever-growing Internet of Things (IoT) ecosystem maintaining device interoperability while upholding user privacy; PSU’s prominence is undeniable.

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31

Auguste, HOUINSOU Tognidè. "Public Transport Services of Minibus between Cotonou and Porto – Novo in Benin." Journal of Humanities and Social Sciences Studies 5, no. 7 (July 12, 2023): 14–28. http://dx.doi.org/10.32996/jhsss.2023.5.7.3.

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African cities, including Cotonou and Porto-Novo, have experienced an increase in their populations over the past four decades due to migration on the one hand and the services offered by the latter on the other. This requires mass transport for the mobility of urban populations and those on the outskirts of these cities. This research contributes to a better understanding of the risks to which the passengers of public transport provided by minibuses between Cotonou and Porto-Novo are exposed. The methodological approach used is based on documentary research, data collection in the field, data processing and analysis of results. The collection tools used are the observation grid, the questionnaire and the interview guide with 148 people and 21 municipal authorities. SPSS 2.1 was used for statistical data processing. The Excel 2013 spreadsheet, Word 2013 and QGIS software were respectively used for word processing, the creation of graphs and tables and then various maps. The analysis of the results shows that the socio-professional class of minibus public transport passengers between Cotonou and Porto-Novo is made up of workers 33% of the respondents; sellers and resellers of finished products, food (43%); students/pupils (11%) and others (13%) of those questioned. The purchasing power of this target remains weak, which does not allow it to use other means of public transport, which cost more than three times the minibus fare according to this one. Public transport by minibus is, therefore, the preferred method for low-class passengers. In addition, the results of this research reveal four main risks, which are: contamination of communicable diseases, including COVID-19, according to 23% of those questioned; the fall of apprentices or even users/passengers/customers for 24% of respondents; road traffic accidents (47%) and injuries related to discomfort in the seats of minibuses to which 6% of the passengers surveyed referred. Taking into account these risks and the weaknesses identified by this research will improve mass transport services by minibus between Cotonou and Porto-Novo.

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32

Kurkofka, Jan. "Every infinitely edge-connected graph contains the Farey graph or $${T_{\aleph _0}*t}$$ as a minor." Mathematische Annalen, September 24, 2021. http://dx.doi.org/10.1007/s00208-021-02259-7.

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AbstractWe show that every infinitely edge-connected graph contains the Farey graph or $$T_{\aleph _0}*t$$ T ℵ 0 ∗ t as a minor. These two graphs are unique with this property up to minor-equivalence.

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33

Bonsma, Paul. "A characterization of extremal graphs with no matching-cut." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings vol. AE,..., Proceedings (January 1, 2005). http://dx.doi.org/10.46298/dmtcs.3398.

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International audience A graph is called (matching-)immune if it has no edge cut that is also a matching. Farley and Proskurowski proved that for all immune graphs $G=(V,E)$, $|E|≥\lceil 3(|V|-1)/2\rceil$ , and constructed a large class of immune graphs that attain this lower bound for every value of $|V(G)|$, called $ABC$ graphs. They conjectured that every immune graph that attains this lower bound is an $ABC$ graph. We present a proof of this conjecture.

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34

Kushwaha, Seema, and Ritumoni Sarma. "Farey-Subgraphs and Continued Fractions." Studia Scientiarum Mathematicarum Hungarica, June 9, 2022. http://dx.doi.org/10.1556/012.2022.01525.

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In this article, we study a family of subgraphs of the Farey graph, denoted as ℱN for every N ∈ ℕ. We show that ℱN is connected if and only if N is either equal to one or a prime power. We introduce a class of continued fractions referred to as ℱN -continued fractions for each N > 1. We establish a relation between ℱN-continued fractions and certain paths from infinity in the graph ℱN. Using this correspondence, we discuss the existence and uniqueness of ℱN-continued fraction expansions of real numbers.

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35

"Rainbow Connection Number on Generalized Farey Graph." Asia Pacific Journal of Mathematics, 2024. http://dx.doi.org/10.28924/apjm/11-39.

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36

Kumar, Ajendra, Ajay Kumar, Suraj Tyagi, and Neeraj Gupta. "Farey Graceful Labeling of Graphs and Its Applications." National Academy Science Letters, December 7, 2024. https://doi.org/10.1007/s40009-024-01586-y.

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37

MORIER-GENOUD, SOPHIE, and VALENTIN OVSIENKO. "-DEFORMED RATIONALS AND -CONTINUED FRACTIONS." Forum of Mathematics, Sigma 8 (2020). http://dx.doi.org/10.1017/fms.2020.9.

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We introduce a notion of $q$ -deformed rational numbers and $q$ -deformed continued fractions. A $q$ -deformed rational is encoded by a triangulation of a polygon and can be computed recursively. The recursive formula is analogous to the $q$ -deformed Pascal identity for the Gaussian binomial coefficients, but the Pascal triangle is replaced by the Farey graph. The coefficients of the polynomials defining the $q$ -rational count quiver subrepresentations of the maximal indecomposable representation of the graph dual to the triangulation. Several other properties, such as total positivity properties, $q$ -deformation of the Farey graph, matrix presentations and $q$ -continuants are given, as well as a relation to the Jones polynomial of rational knots.

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38

Hermanns, Judith, Konstantinos Skitsas, Anton Tsitsulin, Marina Munkhoeva, Alexander Frederiksen Kyster, Simon Daugaard Nielsen, Alex Bronstein, Davide Mottin, and Panagiotis Karras. "GRASP: Scalable Graph Alignment by Spectral Corresponding Functions." ACM Transactions on Knowledge Discovery from Data, September 15, 2022. http://dx.doi.org/10.1145/3561058.

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What is the best way to match the nodes of two graphs? This graph alignment problem generalizes graph isomorphism and arises in applications from social network analysis to bioinformatics. Some solutions assume that auxiliary information on known matches or node or edge attributes is available, or utilize arbitrary graph features. Such methods fare poorly in the pure form of the problem, in which only graph structures are given. Other proposals translate the problem to one of aligning node embeddings, yet, by doing so, provide only a single-scale view of the graph. In this paper, we transfer the shape-analysis concept of functional maps from the continuous to the discrete case, and treat the graph alignment problem as a special case of the problem of finding a mapping between functions on graphs. We present GRASP, a method that first establishes a correspondence between functions derived from Laplacian matrix eigenvectors, which capture multiscale structural characteristics, and then exploits this correspondence to align nodes. We enhance the basic form of GRASP by altering two of its components, namely the embedding method and the assignment procedure it employs, leveraging its modular, hence adaptable design. Our experimental study, featuring noise levels higher than anything used in previous studies, shows that the enhanced form of GRASP outperforms scalable state-of-the-art methods for graph alignment across noise levels and graph types, and performs competitively with respect to the best non-scalable ones. We include in our study another modular graph alignment algorithm, CONE, which is also adaptable thanks to its modular nature, and show it can manage graphs with skewed power-law degree distributions.

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39

Zhai, Yinhu, and Yinhe Wang. "Label-based routing for a family of small-world Farey graphs." Scientific Reports 6, no. 1 (May 11, 2016). http://dx.doi.org/10.1038/srep25621.

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40

"Tutte polynomial for a small world connected copies of Farey graphs." Applied Mathematics & Information Sciences 18, no. 4 (July 1, 2024): 767–74. http://dx.doi.org/10.18576/amis/180409.

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41

Jiang, Wenchao, Yinhu Zhai, Paul Martin, and Zhiming Zhao. "Structure Properties of Generalized Farey graphs based on Dynamical Systems for Networks." Scientific Reports 8, no. 1 (August 15, 2018). http://dx.doi.org/10.1038/s41598-018-30712-2.

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42

DEMİR, Bilal. "A Note on Transitive Action of the Extended Modular Group on Rational Numbers." Fundamentals of Contemporary Mathematical Sciences, June 7, 2022. http://dx.doi.org/10.54974/fcmathsci.1082199.

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The extended modular group $\overline{\Gamma}$ is isomorphic to the amalgamated free product of two dihedral groups $D_2$ and $D_3$ with amalgamation $\mathbb{Z}_2$. This group acts on rational numbers transitively. In this study, we obtain elements in the extended modular group that are mappings between given two rationals. Also, we express these elements as a word in generators. We use interesting relations between continued fractions and the Farey graph.

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43

Panti, Giovanni. "Purely periodic continued fractions and graph-directed iterated function systems." Ramanujan Journal, July 19, 2024. http://dx.doi.org/10.1007/s11139-024-00904-8.

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AbstractWe describe Gauss-type maps as geometric realizations of certain codes in the monoid of nonnegative matrices in the extended modular group. Each such code, together with an appropriate choice of unimodular intervals in $${{\,\textrm{P}\,}}^1\mathbb {R}$$ P 1 R , determines a dual pair of graph-directed iterated function systems, whose attractors contain intervals and constitute the domains of a dual pair of Gauss-type maps. Our framework covers many continued fraction algorithms (such as Farey fractions, Ceiling, Even and Odd, Nearest Integer, $$\ldots $$ … ) and provides explicit dual algorithms and characterizations of those quadratic irrationals having a purely periodic expansion.

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44

Pollicott, Mark, and Mariusz Urbanski. "Asymptotic Counting in Conformal Dynamical Systems." Memoirs of the American Mathematical Society 271, no. 1327 (May 2021). http://dx.doi.org/10.1090/memo/1327.

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In this monograph we consider the general setting of conformal graph directed Markov systems modeled by countable state symbolic subshifts of finite type. We deal with two classes of such systems: attracting and parabolic. The latter being treated by means of the former. We prove fairly complete asymptotic counting results for multipliers and diameters associated with preimages or periodic orbits ordered by a natural geometric weighting. We also prove the corresponding Central Limit Theorems describing the further features of the distribution of their weights. These results have direct applications to a wide variety of examples, including the case of Apollonian Circle Packings, Apollonian Triangle, expanding and parabolic rational functions, Farey maps, continued fractions, Mannenville-Pomeau maps, Schottky groups, Fuchsian groups, and many more. This gives a unified approach which both recovers known results and proves new results. Our new approach is founded on spectral properties of complexified Ruelle–Perron–Frobenius operators and Tauberian theorems as used in classical problems of prime number theory.

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45

Sunder, R., Sreeraj R, Vince Paul, Sanjeev Kumar Punia, Bhagavan Konduri, Khan Vajid Nabilal, Umesh Kumar Lilhore, Tarun Kumar Lohani, Ehab Ghith, and Mehdi Tlija. "An advanced hybrid deep learning model for accurate energy load prediction in smart building." Energy Exploration & Exploitation, August 27, 2024. http://dx.doi.org/10.1177/01445987241267822.

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In smart cities, sustainable development depends on energy load prediction since it directs utilities in effectively planning, distributing and generating energy. This work presents a novel hybrid deep learning model including components of the Improved-convolutional neural network (CNN), bidirectional long short-term memory (Bi-LSTM), Graph neural network (GNN), Transformer and Fusion Layer architectures for precise energy load forecasting. Better feature extraction results from the Improved-CNN's dilated convolution and residual block accommodation of wide receptive fields reduced the vanishing gradient problem. By capturing temporal links in both directions, Bi-LSTM networks help to better grasp complicated energy use patterns. Graph neural networks improve predictive capacities across linked systems by characterizing the spatial relationships between energy-consuming units in smart cities. Emphasizing critical trends to guarantee reliable forecasts, transformer models use attention methods to manage long-term dependencies in energy consumption data. Combining CNN, Bi-LSTM, Transformer and GNN component predictions in a Fusion Layer synthesizes numerous data representations to increase accuracy. With Root Mean Square Error of 5.7532 Wh, Mean Absolute Percentage Error of 3.5001%, Mean Absolute Error of 6.7532 Wh and R2 of 0.9701, the hybrid model fared better than other models on the ‘Electric Power Consumption’ Kaggle dataset. This work develops a realistic model that helps informed decision-making and enhances energy efficiency techniques, promoting energy load forecasting in smart cities.

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46

Addetia, Karima, Giuseppe Martucci, Adrian Dancea, Ariane Marelli, and Judith Therrien. "Abstract 9635: Percutaneous vs. Surgical Pulmonary Valve Implantation: How Does the Right Ventricle Fare?" Circulation 126, suppl_21 (November 20, 2012). http://dx.doi.org/10.1161/circ.126.suppl_21.a9635.

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Introduction. Percutaneous pulmonary valve implantation (PPVI) to non-invasively correct pulmonary valve dysfunction is a recent advancement. Cardiopulmonary bypass is known to have a negative impact on right ventricular (RV) function. This study was designed to assess RV recovery using echocardiographic parameters post surgical pulmonary graft placement versus PPVI. Methods. Retrospective study of consecutive adult patients who underwent PPVI and received graft bioprosthesis between 2007 and 2011. Echocardiographic parameters analyzed included tricuspid annular systolic excursion (TAPSE), RV tissue Doppler velocity (TDV), and myocardial performance index (MPI). Graphs of relative differences (between postoperative and preoperative values) for each parameter were constructed to compare preoperative, early (≤60 days) and late postoperative (≥6-12 months) measurements. Significance of results was determined using T-test. Results. Ten patients received PPVI and 26 underwent open heart surgery with graft insertion. Average patient age was 31±20 years. Pre-operative TDV (p=0.008), and MPI (p=0.05) were significantly higher for the surgical population than the percutaneous group. Postoperative, TDV and TAPSE were significantly lower early (p<0.001) and late (p<0.001) in the surgical group than preoperative measures. No significant differences were seen for the PPVI group. On comparison of relative differences in parameters between groups TDI was significantly higher both early (p<0.001) and late (p<0.006) postoperatively in the percutaneous group. Conclusion. RV systolic recovery as measured by TDV and TAPSE was significantly impaired post surgery but relatively unchanged post PPVI. On analysis of relative differences in RV parameters, TDI was significantly higher early and late post PPVI than open-heart surgery suggesting that surgery may impact RV function more significantly than its percutaneous counterpart.

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47

Zhang, Jinlei, Feng Chen, Lixing Yang, Wei Ma, Guangyin Jin, and Ziyou Gao. "Network-Wide Link Travel Time and Station Waiting Time Estimation Using Automatic Fare Collection Data: A Computational Graph Approach." IEEE Transactions on Intelligent Transportation Systems, 2022, 1–16. http://dx.doi.org/10.1109/tits.2022.3181381.

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48

De Toni, Giovanni, Bruno Lepri, and Andrea Passerini. "Synthesizing explainable counterfactual policies for algorithmic recourse with program synthesis." Machine Learning, February 2, 2023. http://dx.doi.org/10.1007/s10994-022-06293-7.

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AbstractBeing able to provide counterfactual interventions—sequences of actions we would have had to take for a desirable outcome to happen—is essential to explain how to change an unfavourable decision by a black-box machine learning model (e.g., being denied a loan request). Existing solutions have mainly focused on generating feasible interventions without providing explanations of their rationale. Moreover, they need to solve a separate optimization problem for each user. In this paper, we take a different approach and learn a program that outputs a sequence of explainable counterfactual actions given a user description and a causal graph. We leverage program synthesis techniques, reinforcement learning coupled with Monte Carlo Tree Search for efficient exploration, and rule learning to extract explanations for each recommended action. An experimental evaluation on synthetic and real-world datasets shows how our approach, FARE (eFficient counterfActual REcourse), generates effective interventions by making orders of magnitude fewer queries to the black-box classifier with respect to existing solutions, with the additional benefit of complementing them with interpretable explanations.

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49

Mützel, Christian Martin, and Joachim Scheiner. "Investigating spatio-temporal mobility patterns and changes in metro usage under the impact of COVID-19 using Taipei Metro smart card data." Public Transport, August 16, 2021. http://dx.doi.org/10.1007/s12469-021-00280-2.

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AbstractModern public transit systems are often run with automated fare collection (AFC) systems in combination with smart cards. These systems passively collect massive amounts of detailed spatio-temporal trip data, thus opening up new possibilities for public transit planning and management as well as providing new insights for urban planners. We use smart card trip data from Taipei, Taiwan, to perform an in-depth analysis of spatio-temporal station-to-station metro trip patterns for a whole week divided into several time slices. Based on simple linear regression and line graphs, days of the week and times of the day with similar temporal passenger flow patterns are identified. We visualize magnitudes of passenger flow based on actual geography. By comparing flows for January to March 2019 and for January to March 2020, we look at changes in metro trips under the impact of the coronavirus pandemic (COVID-19) that caused a state of emergency around the globe in 2020. Our results show that metro usage under the impact of COVID-19 has not declined uniformly, but instead is both spatially and temporally highly heterogeneous.

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50

Dickerman, Stuart A., Bruno Barsic, Vivian H. Chu, V. G. Fowler, Paul A. Pappas, and Arnold Bayer. "Abstract 16736: Medical vs. Surgical Management of Perivalvular Abscess in Infective Endocarditis: A Propensity Analysis From the International Collaboration on Endocarditis Prospective Cohort Study (ICE-PCS)." Circulation 124, suppl_21 (November 22, 2011). http://dx.doi.org/10.1161/circ.124.suppl_21.a16736.

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Introduction Myocardial abscess is generally regarded as an indication for surgical intervention in infective endocarditis (IE). There is little information, however, comparing outcomes with medical vs. surgical management of such periannular complications of IE. This study used the database of the ICE-PCS to perform a propensity analysis, comparing one year mortality in patients with IE and abscess subjected to either medical or surgical treatment. Methods ICE-PCS enrolled 4794 patients between 2000 and 2006, from 64 centers in 28 countries. There were 699 cases of IE with abscess. A statistical model was built to predict surgery in this cohort.158 patients who underwent surgery for abscess were matched to 158 patients who did not. These 316 patients formed the basis of the analysis. Results In the unadjusted group of 699 patients, the one-year survival with medical treatment was 45%, vs. 67% with surgical management (p<.0001). Differences favoring surgery were similar whether or not the patients had poor prognostic indicators (S. aureus infection; prosthetic valve involvement; CHF). Patients with strep viridans infection, however, had similar survival with medical or surgical management (70%, 14/20 vs.77%, 65/84). In the propensity analysis, the one-year survival with medical management was 44%, compared to 58% in the surgical group (p=.0021). (See graph). Conclusion One-year survival of IE patients with abscess was superior with surgical compared to medical management. These findings support current recommendations that surgical management of perivalvular extension of infection is generally the preferred approach. Patients with strep viridans infection, however, seem to fare equally well with medical or surgical treatment.

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