New highlights and a new centrality measure based on the Adapted PageRank Algorithm for urban networks

The Adapted PageRank Algorithm (APA) proposed by Agryzkov et al. provides us a method to establish a ranking of nodes in an urban network. We can say that it constitutes a centrality measure in urban networks, with the main characteristic that is able to consider the importance of data obtained from the urban networks in the process of computing the centrality of every node. Starting from the basic idea of this model, we modify the construction of the matrix used for the classification of the nodes in order of importance. In the APA model, the data matrix is constructed from the original idea of PageRank vector, given an equal chance to jump from one node to another, regardless of the topological distance between nodes. In the new model this idea is questioned. A new matrix with the data network is constructed so that now the data from neighboring nodes are considered more likely than data from the nodes that are farther away. In addition, this new algorithm has the characteristic that depends on a parameter α, which allows us to decide the importance attached, in the computation of the centrality, to the topology of the network and the amount of data associated with the node. Various numerical experiments with a network of very small size are performed to test the influence of the data associated with the nodes, depending always on the choice of the parameter α. Also we check the differences between the values produced by the original APA model and the new one. Finally, these measures are applied to a real urban network, in which we perform a visual comparison of the results produced by the various measures calculated from the algorithms studied.Partially supported by the Spanish Government, Ministerio de Economía y Competividad, grant number TIN2014-53855-P

Combining the Two-Layers PageRank Approach with the APA Centrality in Networks with Data

[EN] Identifying the influential nodes in complex networks is a fundamental and practical topic at the moment. In this paper, a new centrality measure for complex networks is proposed based on two contrasting models that have their common origin in the well-known PageRank centrality. On the one hand, the essence of the model proposed is taken from the Adapted PageRank Algorithm (APA) centrality, whose main characteristic is that constitutes a measure to establish a ranking of nodes considering the importance of some dataset associated to the network. On the other hand, a technique known as two-layers PageRank approach is applied to this model. This technique focuses on the idea that the PageRank centrality can be understood as a two-layer network, the topological and teleportation layers, respectively. The main point of the proposed centrality is that it combines the APA centrality with the idea of two-layers; however, the difference now is that the teleportation layer is replaced by a layer that collects the data present in the network. This combination gives rise to a new algorithm for ranking the nodes according to their importance. Subsequently, the coherence of the new measure is demonstrated by calculating the correlation and the quantitative differences of both centralities (APA and the new centrality). A detailed study of the differences of both centralities, taking different types of networks, is performed. A real urban network with data randomly generated is evaluated as well as the well-known Zachary's karate club network. Some numerical results are carried out by varying the values of the alpha parameter-known as dumping factor in PageRank model-that varies the importance given to the two layers (topology and data) within the computation of the new centrality. The proposed algorithm takes the best characteristics of the models on which it is based: on the one hand, it is a measure of centrality, in complex networks with data, whose calculation is stable numerically and, on the other hand, it is able to separate the topological properties of the network and the influence of the data.Partially supported by the Spanish Government, Ministerio de Economia y Competividad, grant number TIN2017-84821-P.Agryzkov, T.; Pedroche Sánchez, F.; Tortosa, L.; Vicent, JF. (2018). Combining the Two-Layers PageRank Approach with the APA Centrality in Networks with Data. ISPRS International Journal of Geo-Information. 7(12):1-22. https://doi.org/10.3390/ijgi7120480S122712Crucitti, P., Latora, V., & Porta, S. (2006). Centrality measures in spatial networks of urban streets. Physical Review E, 73(3). doi:10.1103/physreve.73.036125Bonacich, P. (1991). Simultaneous group and individual centralities. 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Quantifying the influence of scientists and their publications: distinguishing between prestige and popularity. New Journal of Physics, 14(3), 033033. doi:10.1088/1367-2630/14/3/033033Porta, S., Crucitti, P., & Latora, V. (2006). The network analysis of urban streets: A dual approach. Physica A: Statistical Mechanics and its Applications, 369(2), 853-866. doi:10.1016/j.physa.2005.12.063Jiang, B. (2009). Ranking spaces for predicting human movement in an urban environment. International Journal of Geographical Information Science, 23(7), 823-837. doi:10.1080/13658810802022822Bonacich, P. (1987). Power and Centrality: A Family of Measures. American Journal of Sociology, 92(5), 1170-1182. doi:10.1086/228631Boldi, P., & Vigna, S. (2014). Axioms for Centrality. Internet Mathematics, 10(3-4), 222-262. doi:10.1080/15427951.2013.865686Freeman, L. C. (1977). A Set of Measures of Centrality Based on Betweenness. Sociometry, 40(1), 35. doi:10.2307/3033543Brandes, U. (2001). 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(2018). A heuristic relaxed extrapolated algorithm for accelerating PageRank. Advances in Engineering Software, 120, 88-95. doi:10.1016/j.advengsoft.2016.01.024Agryzkov, T., Oliver, J. L., Tortosa, L., & Vicent, J. F. (2012). An algorithm for ranking the nodes of an urban network based on the concept of PageRank vector. Applied Mathematics and Computation, 219(4), 2186-2193. doi:10.1016/j.amc.2012.08.064Agryzkov, T., Tortosa, L., & Vicent, J. F. (2016). New highlights and a new centrality measure based on the Adapted PageRank Algorithm for urban networks. Applied Mathematics and Computation, 291, 14-29. doi:10.1016/j.amc.2016.06.036Agryzkov, T., Tortosa, L., Vicent, J. F., & Wilson, R. (2017). A centrality measure for urban networks based on the eigenvector centrality concept. Environment and Planning B: Urban Analytics and City Science, 46(4), 668-689. doi:10.1177/2399808317724444Conti, M., & Kumar, M. (2010). Opportunities in Opportunistic Computing. 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An Information Flow Model for Conflict and Fission in Small Groups. Journal of Anthropological Research, 33(4), 452-473. doi:10.1086/jar.33.4.362975

Ranking places in attributed temporal urban mobility networks

Drawing on the recent advances in complex network theory, urban mobility flow patterns, typically encoded as origin-destination (OD) matrices, can be represented as weighted directed graphs, with nodes denoting city locations and weighted edges the number of trips between them. Such a graph can further be augmented by node attributes denoting the various socio-economic characteristics at a particular location in the city. In this paper, we study the spatio-temporal characteristics of “hotspots” of different types of socio-economic activities as characterized by recently developed attribute-augmented network centrality measures within the urban OD network. The workflow of the proposed paper comprises the construction of temporal OD networks using two custom data sets on urban mobility in Rome and London, the addition of socio-economic activity attributes to the OD network nodes, the computation of network centrality measures, the identification of “hotspots” and, finally, the visualization and analysis of measures of their spatio-temporal heterogeneity. Our results show structural similarities and distinctions between the spatial patterns of different types of human activity in the two cities. Our approach produces simple indicators thus opening up opportunities for practitioners to develop tools for real-time monitoring and visualization of interactions between mobility and economic activity in cities.This work is supported by the Spanish Government, Ministerio de Economía y Competividad, grant number TIN2017-84821-P. It is also funded by the EU H2020 programme under Grant Agreement No. 780754, “Track & Know”

Analysis of the Patrimonial Conservation of a Quito Suburb without Altering Its Commercial Structure by Means of a Centrality Measure for Urban Networks

In about 1940, Quito’s urban planning department contemplated the creation of a new suburb called Villaflora following the garden city model: homes in connection with nature but also near services. In Villaflora we do not find monumental elements that characterize patrimonial architecture; the value of Villaflora’s patrimony is in its urban model characterized by some architectonic elements. However, Villaflora is valuable because it is the result of a unique urban model. Over the years, the suburb has suffered profound degradation from the point of view of its patrimonial conservation. Hence, we propose an urban intervention in the suburb that contemplates the restoration of some important elements in the urban layout, without altering the commercial structure of the same. To accomplish this task we perform a study of the heritage conservation of each of the buildings of the suburb, as well as a study of the commercial activity that is developed in the suburb in order to determine those areas with the highest commercial activity and as a consequence, a greater presence of people in the streets and public spaces.Partially supported by the Spanish Government, Ministerio de Economía y Competividad, grant number TIN2014-53855-P

Random—walk—based segregation measures

We propose an intuitive way of how to measure segregation in social and spatial networks. Using random walks, we define the segregation index as the probability that an individual meets an individual from the same social group. The segregation index is a generalization of the isolation index and a homophily index introduced in Currarini et al. (2009), and it has a closed– form relation to PageRank that facilitates its computation. We also show that the Spectral Segregation Index proposed by Echenique and Fryer (2007) is not continuous with respect to the network structure. Finally, we apply the measure to Spanish census data and to citations data from Economics, and rationalize the index as the equilibrium outmode of a game

The Interactions of Relationships, Interest, and Self-Efficacy in Undergraduate Physics

This collected papers dissertation explores students’ academic interactions in an active learning, introductory physics settings as they relate to the development of physics self-efficacy and interest. The motivation for this work extends from the national call to increase participation of students in the pursuit of science, technology, engineering, and mathematics (STEM) careers. Self-efficacy and interest are factors that play prominent roles in popular, evidence-based, career theories, including the Social cognitive career theory (SCCT) and the identity framework. Understanding how these constructs develop in light of the most pervasive characteristic of the active learning introductory physics classroom (i.e., peer-to-peer interactions) has implications on how students learn in a variety of introductory STEM classrooms and settings structured after constructivist and sociocultural learning theories. I collected data related to students’ in-class interactions using the tools of social network analysis (SNA). Social network analysis has recently been shown to be an effective and useful way to examine the structure of student relationships that develop in and out of STEM classrooms. This set of studies furthers the implementation of SNA as a tool to examine self-efficacy and interest formation in the active learning physics classroom. Here I represent a variety of statistical applications of SNA, including bootstrapped linear regression (Chapter 2), structural equation modeling (Chapter 3), and hierarchical linear modeling for longitudinal analyses (Chapter 4). Self-efficacy data were collected using the Sources of Self-Efficacy for Science Courses – Physics survey (SOSESC-P), and interest data were collected using the physics identity survey. Data for these studies came from the Modeling Instruction sections of Introductory Physics with Calculus offered at Florida International University in the fall of 2014 and 2015. Analyses support the idea that students’ perceptions of one another impact the development of their social network centrality, which in turn affects their self-efficacy building experiences and their overall self-efficacy. It was shown that unlike career theories that emphasize causal relationships between the development of self-efficacy and the subsequent growth of student interest, in this context student interest takes precedence before the development of student self-efficacy. This outcome also has various implications for career theories

Offloading Content with Self-organizing Mobile Fogs

Mobile users in an urban environment access content on the internet from different locations. It is challenging for the current service providers to cope with the increasing content demand from a large number of collocated mobile users. In-network caching to offload content at nodes closer to users alleviate the issue, though efficient cache management is required to find out who should cache what, when and where in an urban environment, given nodes limited computing, communication and caching resources. To address this, we first define a novel relation between content popularity and availability in the network and investigate a node's eligibility to cache content based on its urban reachability. We then allow nodes to self-organize into mobile fogs to increase the distributed cache and maximize content availability in a cost-effective manner. However, to cater rational nodes, we propose a coalition game for the nodes to offer a maximum "virtual cache" assuming a monetary reward is paid to them by the service/content provider. Nodes are allowed to merge into different spatio-temporal coalitions in order to increase the distributed cache size at the network edge. Results obtained through simulations using realistic urban mobility trace validate the performance of our caching system showing a ratio of 60-85% of cache hits compared to the 30-40% obtained by the existing schemes and 10% in case of no coalition

Análisis y desarrollo de medidas de centralidad aplicadas a la formación de metales vítreos.

La presente Tesis Doctoral tiene como objetivo general contribuir a la comprensión de la formación de metales vítreos a través del uso de redes complejas, mediante la implementación de una nueva medida de centralidad adaptada. Para lograr este objetivo general, el inicio del presente estudio se centra en la introducción y estudio de las medidas de centralidad existentes, así como la implementación de las mismas, en casos de estudio como pueden ser las redes urbanas. A continuación, se propone una nueva medida de centralidad y la adaptación de la misma para posteriormente implementarla en el caso particular de formación de metales vítreos, objetivo principal de la presente Tesis Doctoral. La primera parte de la presente Tesis se centra en el estudio de las medidas de centralidad clásicas para la comprensión de las mismas así como de su utilización. En esta parte introductoria del estudio se aplican estas medidas de centralidad clásicas en redes urbanas con el objetivo de dilucidar mejoras concretas y eficientes de restauración que proporcionen un aumento sustancial en la accesibilidad en una ciudad histórica. El uso de las medidas clásicas de centralidad resulta ser muchas veces insuficiente para el estudio de problemas específicos como es el caso de la formación de metales vítreos. Por ello, en la actualidad existen diferentes medidas de centralidad adaptadas a cada problema concreto, siendo unas más generales y otras más específicas. En esta tesis se propone una medida de centralidad adaptada, con cierta generalidad para poder ser aplicada a diferentes ámbitos, pero pensada especialmente para resolver el problema de la comprensión de la formación de los metales vítreos. La medidas de centralidad realizadas con la medida clásica de intermediación o betweenness (CBT), están basados en los caminos más cortos y aleatorios, es decir, miden la importancia global de un nodo como nodo intermedio o de transición, pero tienen la característica común de no tener en cuenta la densidad de clúster de cada nodo. Para solucionar esta carencia se ha propuesto una nueva medida de centralidad basada en los caminos aleatorios de retorno tipo betweenness (2RW). Desde el punto de vista de las redes densas, está medida realiza una cuantificación de la importancia de un nodo a través de las relaciones entre cuatro nodos diferentes conectados. En el análisis de la implementación de la nueva medida de centralidad de la red, ésta se ha aplicado desde una perspectiva orientada a clasificar nodos, reforzando comunidades densas mediante la evaluación de grafos y utilizando una matriz de probabilidad de transición de dos posibles caminos. Por tanto, se ha desarrollado una nueva medida de centralidad 2RW que combina la idea de la centralidad betweenness y el algoritmo de predicción de enlaces Return Random Walk. En concreto, la métrica propuesta aumenta la posición del ranking de relevancia en la clasificación de los nodos que pertenecen a clústeres densos con un grado medio superior al del resto de clústeres, observando que funciona mejor en redes densas. Además, podemos detectar la debilidad de una red comparando el método CBT con nuestra propuesta (2RW). La aplicación de la medida de centralidad inicial propuesta (2RW) no se adapta completamente al problema planteado inicialmente debido fundamentalmente a la direccionalidad natural del mismo y a la falta de comprensión del comportamiento de cada nodo dentro de la red, es decir, su papel o rol dentro de la misma. Por tanto, en la presente Tesis se ha propuesto el Algoritmo de Centralidad de intermediación aleatorio bidireccional dirigido (D2RWBT), un nuevo modelo de centralidad para redes dirigidas. Mediante este modelo se han obtenido un ranking de los nodos en redes dirigidas para describir su relevancia dentro de la red como nodos de transición, teniendo en cuenta el comportamiento de los mismos en la red. Más en detalle, el modelo describe un nodo mediante cuatro índices que proporcionan información sobre la densidad de su clúster/comunidad (denso o disperso), la fuerza de sus conexiones, la importancia relativa y absoluta en la red, o la relevancia como nodo intra o interclúster. De la aplicación de la nueva medida de centralidad (D2RWBT) para la comprensión de la formación de los metales vítreos a través de una de las variables de mayor relevancia, la temperatura de transición vítrea reducida (Trg), se han obtenido resultados que han sido ratificados por una buena correlación entre estos y la obtención real de vidrios metálicos en recientes investigaciones. En concreto se ha podido extraer la relevancia de los elementos químicos que componen las redes densas y los elementos que forman redes dispersas, así como comparar estos resultados con los obtenidos con la medida clásica de centralidad clásica betweenness. Además, se ha obtenido el rol de los elementos químicos formadores de metales vítreos dentro de la red y cuáles de ellos desempeñan funciones semejantes dentro de la misma y, por tanto, pueden ser posibles elementos de sustitución. Como otra parte del estudio final se han analizado los elementos con funciones de relevancia en la composición de ambos tipos de redes. Por último, se han cotejado los resultados y se ha realizado una síntesis de la compresión del problema de formación de metales vítreos abordando el objetivo general descrito.Ingeniería, Industria y Construcció

HYPERLINK NETWORK SYSTEM AND IMAGE OF GLOBAL CITIES: WEBPAGES AND THEIR CONTENTS

A distinctive trend of globalization research is a conceptual expansion that mirrors the penetration of globalization in various aspects of life. The World Wide Web has become the ultimate platform to create and disseminate information in this era of globalization. Although the importance of web-based information is widely acknowledged, the use of this information in global city research is not significant yet. Therefore, the purpose of this research is to extend the concept of globalization to the efficiency of information networks and the thematic dimensionality of the conveyed images from webpages. To this end, 264 global and globalizing cities are selected. The city hyperlink networks are constructed from the web crawling results of each city, and hyperlink network analysis measures the effectiveness of these hyperlink networks. The textual contents are also extracted from the crawled webpages, and the thematic dimensionality of the textual contents is measured by quantified content analysis and multidimensional scaling. The efficiency of the hyperlink network in information flow is confirmed to be a new consideration that shapes the globality of cities. The cities with high efficiency of connections have faster and easier access, which means better structure for city image formation. Specifically, social networking websites are the center of this information flow. This means that social interactions on the Web play a crucial role to form the images of cities. Apart from the positivity and the negativity of the city image, the dimensionality of cities on the thematic space denotes how they are expressed, discussed, and shared on the Web. The image status based on dimensions of globalization is an important starting point to city branding. It is concluded that a research framework handling information networks and images simultaneously deepens the understanding of how the structure and the contents on the Web affect the formation and maintenance of global city networks. Overall, this research demonstrates the usefulness of information networks and images of cities on the Web to overcome data inconsistency and scarcity in global city research