A Model to Visualize Information in a Complex Streets’ Network

his paper discusses a process to graphically view and analyze information obtained from a network of urban streets, using an algorithm that establishes a ranking of importance of the nodes of the network itself. The basis of this process is to quantify the network information obtained by assigning numerical values to each node, representing numerically the information. These values are used to construct a data matrix that allows us to apply a classification algorithm of nodes in a network in order of importance. From this numerical ranking of the nodes, the process finish with the graphical visualization of the network. An example is shown to illustrate the whole process.

A new betweenness centrality measure based on an algorithm for ranking the nodes of a network

We propose and discuss a new centrality index for urban street patterns represented as networks in geographical space. This centrality measure, that we call ranking-betweenness centrality, combines the idea behind the random-walk betweenness centrality measure and the idea of ranking the nodes of a network produced by an adapted PageRank algorithm. We initially use a PageRank algorithm in which we are able to transform some information of the network that we want to analyze into numerical values. Numerical values summarizing the information are associated to each of the nodes by means of a data matrix. After running the adapted PageRank algorithm, a ranking of the nodes is obtained, according to their importance in the network. This classification is the starting point for applying an algorithm based on the random-walk betweenness centrality. A detailed example of a real urban street network is discussed in order to understand the process to evaluate the ranking-betweenness centrality proposed, performing some comparisons with other classical centrality measures.

Analyzing the commercial activities of a street network by ranking their nodes: a case study in Murcia, Spain

Urban researchers and planners are often interested in understanding how economic activities are distributed in urban regions, what forces influence their special pattern and how urban structure and functions are mutually dependent. In this paper, we want to show how an algorithm for ranking the nodes in a network can be used to understand and visualize certain commercial activities of a city. The first part of the method consists of collecting real information about different types of commercial activities at each location in the urban network of the city of Murcia, Spain. Four clearly differentiated commercial activities are studied, such as restaurants and bars, shops, banks and supermarkets or department stores, but obviously we can study other. The information collected is then quantified by means of a data matrix, which is used as the basis for the implementation of a PageRank algorithm which produces a ranking of all the nodes in the network, according to their significance within it. Finally, we visualize the resulting classification using a colour scale that helps us to represent the business network.

A Simple RVoG Test for PolInSAR Data

In this paper, we present a simple algorithm for assessing the validity of the RVoG model for PolInSAR-based inversion techniques. This approach makes use of two important features characterizing a homogeneous random volume over a ground surface, i.e., the independence on polarization states of wave propagation through the volume and the structure of the polarimetric interferometric coherency matrix. These two features have led to two different methods proposed in the literature for retrieving the topographic phase within natural covers, i.e., the well-known line fitting procedure and the observation of the (1, 2) element of the polarimetric interferometric coherency matrix. We show that differences between outputs from both approaches can be interpreted in terms of the PolInSAR modeling based on the Freeman-Durden concept, and this leads to the definition of a RVoG/non-RVoG test. The algorithm is tested with both indoor and airborne data over agricultural and tropical forest areas.

Robust solutions to multi-objective linear programs with uncertain data

In this paper we examine multi-objective linear programming problems in the face of data uncertainty both in the objective function and the constraints. First, we derive a formula for the radius of robust feasibility guaranteeing constraint feasibility for all possible scenarios within a specified uncertainty set under affine data parametrization. We then present numerically tractable optimality conditions for minmax robust weakly efficient solutions, i.e., the weakly efficient solutions of the robust counterpart. We also consider highly robust weakly efficient solutions, i.e., robust feasible solutions which are weakly efficient for any possible instance of the objective matrix within a specified uncertainty set, providing lower bounds for the radius of highly robust efficiency guaranteeing the existence of this type of solutions under affine and rank-1 objective data uncertainty. Finally, we provide numerically tractable optimality conditions for highly robust weakly efficient solutions.

Graphical User Interface (GUI) for the representation of GM surfaces (using the NRTL model) and curves, including tie-lines and Hessian matrix

A single and very easy to use Graphical User Interface (GUI- MATLAB) based on the topological information contained in the Gibbs energy of mixing function has been developed as a friendly tool to check the coherence of NRTL parameters obtained in a correlation data procedure. Thus, the analysis of the GM/RT surface, the GM/RT for the binaries and the GM/RT in planes containing the tie lines should be necessary to validate the obtained parameters for the different models for correlating phase equlibrium data.