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Fierro, I., & Jerez-Hanckes, C. (2020). Fast Calderon preconditioning for Helmholtz boundary integral equations. J. Comput. Phys., 409, 22 pp.
Abstract: Calderon multiplicative preconditioners are an effective way to improve the condition number of first kind boundary integral equations yielding provable mesh independent bounds. However, when discretizing by local low-order basis functions as in standard Galerkin boundary element methods, their computational performance worsens as meshes are refined. This stems from the barycentric mesh refinement used to construct dual basis functions that guarantee the discrete stability of L-2-pairings. Based on coarser quadrature rules over dual cells and H-matrix compression, we propose a family of fast preconditioners that significantly reduce assembly and computation times when compared to standard versions of Calderon preconditioning for the three-dimensional Helmholtz weakly and hyper-singular boundary integral operators. Several numerical experiments validate our claims and point towards further enhancements. (C) 2020 Elsevier Inc. All rights reserved.
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Heredia, C., Moreno, S., & Yushimito, W. F. (2022). Characterization of Mobility Patterns with a Hierarchical Clustering of Origin-Destination GPS Taxi Data. IEEE Trans. Intell. Transp. Syst., 23(8), 12700–12710.
Abstract: Clustering taxi data is commonly used to understand spatial patterns of urban mobility. In this paper, we propose a new clustering model called Origin-Destination-means (OD-means). OD-means is a hierarchical adaptive k-means
algorithm based on origin-destination pairs. In the first layer of the hierarchy, the clusters are separated automatically based on the variation of the within-cluster distance of each cluster until convergence. The second layer of the hierarchy corresponds to the sub clustering process of small clusters based on the
distance between the origin and destination of each cluster. The algorithm is tested on a large data set of taxi GPS data from Santiago, Chile, and compared to other clustering algorithms.
In contrast to them, our proposed model is capable of detecting general and local travel patterns in the city thanks to its hierarchical structure.
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Junior, P. N. A., Melo, I. C., Yamanaka, L., Severino, M. R., & Rentizelas, A. (2022). Supporting the Bidding Decisions of Smallholder Farmers in Public Calls in Brazil. Agriculture, 12(1), 48.
Abstract: In Brazil, the National School Feeding Program (PNAE) seeks to contribute to the socio-economic development of smallholder farmers, prioritizing them in supplying their products for preparing daily meals in public schools. However, farmers face challenges in determining which school calls to bid for and the potential benefits from their participation, due to the multiple quantitative and qualitative decision criteria involved. This paper presents a novel Data Envelopment Analysis (DEA)-based method for bidding priority setting, to support the decision making. The model was applied for a case study in Brazil. The academic contribution lies in the innovation of using a Double-Frontier Slack-Based Measure (SBM) DEA model for Hierarchical Network systems, i.e., applied to multiple levels and followed by a tie-breaking method. The practical contribution lies in the decision support of farmers by presenting the results at three levels, the first of which is a ranking by the town or urban cluster priority, the second by the school, and the third by the products. Thus, using the rankings of calls, farmers can make informed decisions regarding the feasibility of bidding for each PNAE public call. At the same time, the objective rankings can alleviate friction and conflict within co-operatives during the decision-making process.
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Valle, M. A., & Ruz, G. A. (2021). Finding Hierarchical Structures of Disordered Systems: An Application for Market Basket Analysis. IEEE Access, 9, 1626–1641.
Abstract: Complex systems can be characterized by their level of order or disorder. An ordered system is related to the presence of system properties that are correlated with each other. For example, it has been found in crisis periods that the financial systems tend to be synchronized, and symmetry appears in financial assets' behavior. In retail, the collective purchasing behavior tends to be highly disorderly, with a diversity of correlation patterns appearing between the available market supply. In those cases, it is essential to understand the hierarchical structures underlying these systems. For the latter, community detection techniques have been developed to find similar behavior clusters according to some similarity measure. However, these techniques do not consider the inherent interactions between the multitude of system elements. This paper proposes and tests an approach that incorporates a hierarchical grouping process capable of dealing with complete weighted networks. Experiments show that the proposal is superior in terms of the ability to find minimal energy clusters. These minimum energy clusters are equivalent to system states (market baskets) with a higher probability of occurrence; therefore, they are interesting for marketing and promotion activities in retail environments.
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