Search

The field artificial intelligence (AI) has been founded over 65 years ago. Starting with great hopes and ambitious goals the field progressed though various stages of popularity and received recently a revival in the form of deep neural networks. Some problems of AI are that so far neither 'intelligence' nor the goals of AI are formally defined causing confusion when comparing AI to other fields. In this paper, we present a perspective on the desired and current status of AI in relation to machine learning and statistics and clarify common misconceptions and myths. Our discussion is intended to uncurtain the veil of vagueness surrounding AI to see its true countenance.

The implementation of robust, stable, and user-centered data analytics and machine learning models is confronted by numerous challenges in production and manufacturing. Therefore, a systematic approach is required to develop, evaluate, and deploy such models. The data-driven knowledge discovery framework provides an orderly partition of the data-mining processes to ensure the practical implementation of data analytics and machine learning models. However, the practical application of robust industry-specific data-driven knowledge discovery models faces multiple data-- and model-development--related issues. These issues should be carefully addressed by allowing a flexible, customized, and industry-specific knowledge discovery framework; in our case, this takes the form of the cross-industry standard process for data mining (CRISP-DM). This framework is designed to ensure active cooperation between different phases to adequately address data- and model-related issues. In this paper, we review several extensions of CRISP-DM models and various data-robustness-- and model-robustness--related problems in machine learning, which currently lacks proper cooperation between data experts and business experts because of the limitations of data-driven knowledge discovery models.

We are used to the availability of big data generated in nearly all fields of science as a consequence of technological progress. However, the analysis of such data possess vast challenges. One of these relates to the explainability of artificial intelligence (AI) or machine learning methods. Currently, many of such methods are non-transparent with respect to their working mechanism and for this reason are called black box models, most notably deep learning methods. However, it has been realized that this constitutes severe problems for a number of fields including the health sciences and criminal justice and arguments have been brought forward in favor of an explainable AI. In this paper, we do not assume the usual perspective presenting explainable AI as it should be, but rather we provide a discussion what explainable AI can be. The difference is that we do not present wishful thinking but reality grounded properties in relation to a scientific theory beyond physics.

In this note we resolve three conjectures from [M. Dehmer, S. Pickl, Y. Shi, G. Yu, \emph{New inequalities for network distance measures by using graph spectra}, Discrete Appl. Math. 252 (2019), 17--27] on the comparison of distance measures based on the graph spectra, by constructing families of counterexamples and using computer search., Comment: 4, pages, 2 figures

In this paper, we describe {\sc quantitative graph theory} and argue it is a new graph-theoretical branch in network science, however, with significant different features compared to classical graph theory. The main goal of quantitative graph theory is the structural quantification of information contained in complex networks by employing a {\it measurement approach} based on numerical invariants and comparisons. Furthermore, the methods as well as the networks do not need to be deterministic but can be statistic. As such this complements the field of classical graph theory, which is descriptive and deterministic in nature. We provide examples of how quantitative graph theory can be used for novel applications in the context of the overarching concept network science.

In recent years, methods from network science are gaining rapidly interest in economics and finance. A reason for this is that in a globalized world the interconnectedness among economic and financial entities are crucial to understand and networks provide a natural framework for representing and studying such systems. In this paper, we are surveying the use of networks and network-based methods for studying economy related questions. We start with a brief overview of graph theory and basic definitions. Then we discuss descriptive network measures and network complexity measures for quantifying structural properties of economic networks. Finally, we discuss different network and tree structures as relevant for applications.

The entropy of a graph is an information-theoretic quantity which expresses the complexity of a graph \cite{DM1,M}. After Shannon introduced the definition of entropy to information and communication, many generalizations of the entropy measure have been proposed, such as R\'enyi entropy and Dar\`oczy's entropy. In this article, we prove accurate connections (inequalities) between generalized graph entropies, distinct graph energies and topological indices. Additionally, we obtain some extremal properties of nine generalized graph entropies by employing distinct graph energies and topological indices., Comment: 19 pages