A Review of Theory and Practice in Scientometrics

Scientometrics is the study of the quantitative aspects of the process of science as a communication system. It is centrally, but not only, concerned with the analysis of citations in the academic literature. In recent years it has come to play a major role in the measurement and evaluation of research performance. In this review we consider: the historical development of scientometrics, sources of citation data, citation metrics and the “laws" of scientometrics, normalisation, journal impact factors and other journal metrics, visualising and mapping science, evaluation and policy, and future developments

Statistical Inference using the Morse-Smale Complex

The Morse-Smale complex of a function $f$ decomposes the sample space into cells where $f$ is increasing or decreasing. When applied to nonparametric density estimation and regression, it provides a way to represent, visualize, and compare multivariate functions. In this paper, we present some statistical results on estimating Morse-Smale complexes. This allows us to derive new results for two existing methods: mode clustering and Morse-Smale regression. We also develop two new methods based on the Morse-Smale complex: a visualization technique for multivariate functions and a two-sample, multivariate hypothesis test.Comment: 45 pages, 13 figures. Accepted to Electronic Journal of Statistic

Multidimensional scaling locus of memristor and fractional order elements

This paper combines the synergies of three mathematical and computational generalizations. The concepts of fractional calculus, memristor and information visualization extend the classical ideas of integro-differential calculus, electrical elements and data representation, respectively. The study embeds these notions in a common framework, with the objective of organizing and describing the "continuum" of fractional order elements (FOE). Each FOE is characterized by its behavior, either in the time or in the frequency domains, and the differences between the FOE are captured by a variety of distinct indices, such as the Arccosine, Canberra, Jaccard and Sørensen distances. The dissimilarity information is processed by the multidimensional scaling (MDS) computational algorithm to unravel possible clusters and to allow a direct pattern visualization. The MDS yields 3-dimensional loci organized according to the FOE characteristics both for linear and nonlinear elements. The new representation generalizes the standard Cartesian 2-dimensional periodic table of elements.Fundação para a Ciência e Tecnologia, Portugal, Reference: Projeto LAETA - UID/EMS/50022/2013.info:eu-repo/semantics/publishedVersio

Improved integration of information to reduce subsurface model bias

Subsurface modeling deals with data-related issues like cognitive and sampling biases, and model-related challenges including statistical assumptions, misspecification, and algorithmic biases. These challenges introduce four critical implications during subsurface modeling. Firstly, subsurface sampling is subject to sampling bias, which compromises statistical representativeness. Secondly, analog selection methodologies rely on multivariate statistics and expert judgment that overlook spatial information and data dimensionality. Thirdly, subsurface inferential workflows that utilize dimensionality reduction seldom provide repeatable frameworks that maintain model stability and are invariant to Euclidean transformations. Lastly, deep learning methods for dimensionality reduction, characterized as black-box models, lack interpretability and robust evaluation metrics, increasing susceptibility to algorithmic bias. Consequently, neglecting these challenges in subsurface modeling could lead to erroneous predictions, inconsistent inferences, diminished model reliability, and suboptimal decision-making that impacts project economics. This dissertation integrates information within subsurface models to reduce model bias and significantly improve their accuracy, robustness, and generalizability. First, I create spatial declustering methods to debias spatial datasets with single and multiscale preferential sampling in stationary populations. Second, I introduce a novel geostatistics-based machine learning method for identifying subsurface resource analogs that integrate spatial information in subsurface datasets with high dimensionality. Next, I efficiently combine machine learning and computational geometry methods to stabilize lower dimensional spaces for uncertainty quantification and interpretation. Finally, I create a methodology to assess, evaluate, and interpret the stability of deep learning latent feature spaces. These novel methodologies demonstrate the importance of improved techniques for information integration in subsurface modeling and show better results over naïve methods. This results in objective sampling debiasing in spatial stationary populations with single or multiple data scales, improving statistical representativity. Also, the results show better generalization and accurate identification of spatial analogs in high-dimensional datasets. Moreover, the methods yield Euclidean transformation-invariant lower-dimensional spaces, ensuring unique and repeatable solutions that improve model reliability and interpretability, for rational comparisons. Finally, the results indicate that deep learning models for dimensionality reduction exhibit algorithmic biases and instabilities, including sample, structural, and inferential instability, affecting their reliability and interpretability. Together, these innovations ultimately reduce model bias and significantly improve subsurface modeling.Petroleum and Geosystems Engineerin