Investigating the Origins of Fractality Based on Two Novel Fractal Network Models

Numerous network models have been investigated to gain insights into the origins of fractality. In this work, we introduce two novel network models, to better understand the growing mechanism and structural characteristics of fractal networks. The Repulsion Based Fractal Model (RBFM) is built on the well-known Song-Havlin-Makse (SHM) model, but in RBFM repulsion is always present among a specific group of nodes. The model resolves the contradiction between the SHM model and the Hub Attraction Dynamical Growth model, by showing that repulsion is the characteristic that induces fractality. The Lattice Small-world Transition Model (LSwTM) was motivated by the fact that repulsion directly influences the node distances. Through LSwTM we study the fractal-small-world transition. The model illustrates the transition on a fixed number of nodes and edges using a preferential-attachment-based edge rewiring process. It shows that a small average distance works against fractal scaling, and also demonstrates that fractality is not a dichotomous property, continuous transition can be observed between the pure fractal and non-fractal characteristics.Comment: 12 pages, 5 figures, to appear in: 978-3-031-17657-9, Pacheco et al (eds.): Complex Networks XII

Towards a Better Understanding of the Characteristics of Fractal Networks

The fractal nature of complex networks has received a great deal of research interest in the last two decades. Similarly to geometric fractals, the fractality of networks can also be defined with the so-called box-covering method. A network is called fractal if the minimum number of boxes needed to cover the entire network follows a power-law relation with the size of the boxes. The fractality of networks has been associated with various network properties throughout the years, for example, disassortativity, repulsion between hubs, long-range-repulsive correlation, and small edge betweenness centralities. However, these assertions are usually based on tailor-made network models and on a small number of real networks, hence their ubiquity is often disputed. Since fractal networks have been shown to have important properties, such as robustness against intentional attacks, it is in dire need to uncover the underlying mechanisms causing fractality. Hence, the main goal of this work is to get a better understanding of the origins of fractality in complex networks. To this end, we systematically review the previous results on the relationship between various network characteristics and fractality. Moreover, we perform a comprehensive analysis of these relations on five network models and a large number of real-world networks originating from six domains. We clarify which characteristics are universally present in fractal networks and which features are just artifacts or coincidences

Assessing the Effects of a Reformed System of Student Evaluation of Teaching

The importance of student evaluation of teaching (SET) in higher education has increased substantially in the past decades. Despite this increase, there is no consensus on the most efficient way of executing these surveys or about the questions. This study analyses the impact of an SET system reform on the distribution of the responses and the response rate. The reform impacted the questions, the scale used for evaluation, the anchor labels of the scale elements, and the incentives for students to fill out the survey. Our results show that the number of extreme responses increased after the reform, which can be due to the elimination of anchor labels of the middle scale points. Insufficient effort bias also increased; however, the new motivation system doubled the response rate, which helped to collect more representative sets of evaluations. Taking into consideration the relatively small increase in insufficient responses, we believe this incentive can be a valid choice for SET surveys

Color-avoiding percolation in edge-colored Erd\H{o}s-R\'enyi graphs

We study a variant of the color-avoiding percolation model introduced by Krause et al., namely we investigate the color-avoiding bond percolation setup on (not necessarily properly) edge-colored Erd\H{o}s-R\'{e}nyi random graphs. We say that two vertices are color-avoiding connected in an edge-colored graph if after the removal of the edges of any color, they are in the same component in the remaining graph. The color-avoiding connected components of an edge-colored graph are maximal sets of vertices such that any two of them are color-avoiding connected. We consider the fraction of vertices contained in color-avoiding connected components of a given size as well as the fraction of vertices contained in the giant color-avoiding connected component. Under some mild assumptions on the color-densities, we prove that these quantities converge and the limits can be expressed in terms of probabilities associated to edge-colored branching process trees. We provide explicit formulas for the limit of the normalized size of the giant color-avoiding component, and in the two-colored case we also provide explicit formulas for the limit of the fraction of vertices contained in color-avoiding connected components of a given size.Comment: 59 pages + Appendix + List of notation. Added reference to the recent arXiv preprint arXiv:2211.1608

EASY-APP : An artificial intelligence model and application for early and easy prediction of severity in acute pancreatitis

Background Acute pancreatitis (AP) is a potentially severe or even fatal inflammation of the pancreas. Early identification of patients at high risk for developing a severe course of the disease is crucial for preventing organ failure and death. Most of the former predictive scores require many parameters or at least 24 h to predict the severity; therefore, the early therapeutic window is often missed. Methods The early achievable severity index (EASY) is a multicentre, multinational, prospective and observational study (ISRCTN10525246). The predictions were made using machine learning models. We used the scikit-learn, xgboost and catboost Python packages for modelling. We evaluated our models using fourfold cross-validation, and the receiver operating characteristic (ROC) curve, the area under the ROC curve (AUC), and accuracy metrics were calculated on the union of the test sets of the cross-validation. The most critical factors and their contribution to the prediction were identified using a modern tool of explainable artificial intelligence called SHapley Additive exPlanations (SHAP). Results The prediction model was based on an international cohort of 1184 patients and a validation cohort of 3543 patients. The best performing model was an XGBoost classifier with an average AUC score of 0.81 +/- 0.033 and an accuracy of 89.1%, and the model improved with experience. The six most influential features were the respiratory rate, body temperature, abdominal muscular reflex, gender, age and glucose level. Using the XGBoost machine learning algorithm for prediction, the SHAP values for the explanation and the bootstrapping method to estimate confidence, we developed a free and easy-to-use web application in the Streamlit Python-based framework (http://easy-app.org/). Conclusions The EASY prediction score is a practical tool for identifying patients at high risk for severe AP within hours of hospital admission. The web application is available for clinicians and contributes to the improvement of the model.Peer reviewe