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This work surveys the use of directed weighted graphs in conducting comparative static analyses. The paper discusses the implementation of a computer-aided process for building spreadsheet-based graph models for inter- and intra-regional financial flows. The graph-theoretic techniques are programmed to enable the interactive visualization and analysis of financial data using Wolfram technologies (i.e., Mathematica software v. 11.3 or later, Wolfram player v. 12 or later). The paper describes the workflow for several interactive visualizations applicable to financial networks. The author provides four programs, written in the Wolfram language, that customize input–output financial models by combining the Manipulate command with built-in Mathematica functions and functions of the IGraph package (IGraph/M). The study is a tutorial article for the generation of a suite of visual schemes that provide patterns, practices, and roadmaps of the financial markets across the globe. [ABSTRACT FROM AUTHOR]

The ordered weighted averaging (OWA) operator was proposed by Yager back in 1988 and constitutes a parameterized family of aggregation functions between the minimum and the maximum. The purpose of this paper is to perform a bibliometric review of this aggregation operator during the last 35 years through the Web of Science (WoS) Core Collection database and the Visualization of Similarities (VOS) viewer software. The results show that the OWA operator is an increasingly popular aggregation operator, especially in Computer Science. The results also allow the assertion that Yager, as expected, is still the most influential and productive author. Moreover, the study reveals that institutions from over 80 countries have contributed to OWA research, highlighting the high presence of Chinese universities and the emergence of Pakistani ones. Other interesting findings are presented to provide a comprehensive and up-to-date analysis of the OWA operator literature. [ABSTRACT FROM AUTHOR]

NONNEGATIVE matrix factorization (NMF) is an effective technique for dimensionality reduction of high-dimensional data for tasks such as machine learning and data visualization. However, for practical clustering tasks, traditional NMF ignores the manifold information of both the data space and feature space, as well as the discriminative information of the data. In this paper, we propose a semisupervised NMF called dual-graph-regularization-constrained nonnegative matrix factorization with label discrimination (DCNMFLD). DCNMFLD combines dual graph regularization and prior label information as additional constraints, making full use of the intrinsic geometric and discriminative structures of the data, and can efficiently enhance the discriminative and exclusionary nature of clustering and improve the clustering performance. The evaluation of the clustering experimental results on four benchmark datasets demonstrates the effectiveness of our new algorithm. [ABSTRACT FROM AUTHOR]

This study uses an effective, recently extended Farlie–Gumbel–Morgenstern (EFGM) family to derive the distribution of concomitants of K-record upper values (CKRV). For this CKRV, the negative cumulative residual extropy (NCREX), weighted NCREX (WNCREX), negative cumulative extropy (NCEX), and weighted NCEX (WNCEX) are theoretically and numerically examined. This study presents several beautiful symmetrical and asymmetric relationships that these inaccuracy measurements satisfy. Additionally, empirical estimations are provided for these measures, and their visualizations enable users to verify their accuracy. [ABSTRACT FROM AUTHOR]

War is a cause of gains and losses. Economic historians have long stressed the extreme importance of considering the economic potential of society for belligerency, the role of management of chaos to bear the costs of battle and casualties, and ingenious and improvisation methodologies for emergency management. However, global and inter-temporal studies on warring are missing. The adoption of computational tools for data processing is a key modeling option with present day resources. In this paper, hierarchical clustering techniques and multidimensional scaling are used as efficient instruments for visualizing and describing military conflicts by electing different metrics to assess their characterizing features: time, time span, number of belligerents, and number of casualties. Moreover, entropy is adopted for measuring war complexity over time. Although wars have been an important topic of analysis in all ages, they have been ignored as a subject of nonlinear dynamics and complex system analysis. This paper seeks to fill these gaps in the literature by proposing a quantitative perspective based on algorithmic strategies. We verify the growing number of events and an explosion in their characteristics. The results have similarities to those exhibited by systems with increasing volatility, or evolving toward chaotic-like behavior. We can question also whether such dynamics follow the second law of thermodynamics since the adopted techniques reflect a system expanding the entropy. [ABSTRACT FROM AUTHOR]

Modern computational biology makes widespread use of mathematical models of biological systems, in particular systems of ordinary differential equations, as well as models of dynamic systems described in other formalisms, such as agent-based models. Parameters are numerical values of quantities reflecting certain properties of a modeled system and affecting model solutions. At the same time, depending on parameter values, different dynamic regimes—stationary or oscillatory, established as a result of transient modes of various types—can be observed in the modeled system. Predicting changes in the solution dynamics type depending on changes in model parameters is an important scientific task. Nevertheless, this problem does not have an analytical solution for all formalisms in a general case. The routinely used method of performing a series of computational experiments, i.e., solving a series of direct problems with various sets of parameters followed by expert analysis of solution plots is labor-intensive with a large number of parameters and a decreasing step of the parametric grid. In this regard, the development of methods allowing the obtainment and analysis of information on a set of computational experiments in an aggregate form is relevant. This work is devoted to developing a method for the visualization and classification of various dynamic regimes of a model using a composition of the dynamic time warping (DTW-algorithm) and principal coordinates analysis (PCoA) methods. This method enables qualitative visualization of the results of the set of solutions of a mathematical model and the performance of the correspondence between the values of the model parameters and the type of dynamic regimes of its solutions. This method has been tested on the Lotka–Volterra model and artificial sets of various dynamics. [ABSTRACT FROM AUTHOR]

Dimensional Analysis (DA) is a mathematical method that manipulates the data to be analyzed in a homogenized manner. Likewise, linear regression is a potent method for analyzing data in diverse fields. At the same time, data visualization has gained attention in tendency study. In addition, linear regression is an important topic to address predictive models and patterns in data study. However, it is still pending to attack the manipulation of uncertainty related to the data transformation. In this sense, this work presents a new contribution with linear regression, combining the Dimensional Analysis (DA) to address instability and error issues. In addition, our method provides a second contribution related to including the decision maker's attitude involved in the study. Therefore, the experimentation shows that DA manipulates the regression problem under a complex situation that the outcome may have in the investigation. A real-life case study is used to demonstrate our proposal. [ABSTRACT FROM AUTHOR]

Data and information visualization have drawn an increasingly wide range of interest from several academic fields and industries. Concurrently, exploring a huge set of data to support feasible decisions needs an organized method of Multi-Criteria Decision Making (MCDM). The dramatic increasing of data producing during the past decade makes visualization necessary as a presentation layer on the top of MCDM process. This study aims to propose an integrated strategy to rank the alternatives in the dataset, by combining data, MCDM methods, and visualization layers. In fact, the well designed combination of Information Visualization and MCDM provides a more user-friendly approach than the traditional methods. We investigate a case study in bibliometric analyses, which have become an important dimension and tool for evaluating the impact and performance of researchers, departments, and universities. Hence, finding the best and most reliable papers, authors, and publishers considering diverse criteria is one of the important challenges in science world. Therefore, this text is presenting a new strategy on the bibliometric dataset as a case study and it demonstrates that this strategy can be more meaningful for the end users than the current tools. Finally, the presented simulations illustrate the performance and utilization of this combination. In other words, the researchers of this study could design and implement a tool that overcomes the biggest challenges of data analyzing and ranking via a combination of MCDM and visualization methodologies that can provide a tremendous amount of insight and information from a massive dataset in an efficient way. [ABSTRACT FROM AUTHOR]

A novel visualization technique is proposed for the sum of ranking differences method (SRD) based on parallel coordinates. An axis is defined for each variable, on which the data are depicted row-wise. By connecting data, the lines may intersect. The fewer intersections between the variables, the more similar they are and the clearer the figure becomes. Therefore, the visualization depends on what techniques are used to order the variables. The key idea is to employ the SRD method to measure the degree of similarity of the variables, establishing a distance-based order. The distances between the axes are not uniformly distributed in the proposed visualization; their closeness reflects similarity, according to their SRD value. The proposed algorithm identifies false similarities through an iterative approach, where the angles between the SRD values determine which side a variable is plotted. Visualization of the algorithm is provided by MATLAB/Octave source codes. The proposed tool is applied to study how the sources of greenhouse gas emissions can be grouped based on the statistical data of the countries. A comparison to multidimensional scaling (MDS)-based ordering is also given. The use case demonstrates the applicability of the method and the synergies of the incorporation of the SRD method into parallel coordinates. [ABSTRACT FROM AUTHOR]