Construction of graph-based approximations for multi-dimensional data point clouds is widely used in a variety of areas. Notable examples of applications of such approximators are cellular trajectory inference in single-cell data analysis, analysis of clinical trajectories from synchronic datasets, and skeletonization of images. Several methods have been proposed to construct such approximating graphs, with some based on computation of minimum spanning trees and some based on principal graphs generalizing principal curves. In this article we propose a methodology to compare and benchmark these two graph-based data approximation approaches, as well as to define their hyperparameters. The main idea is to avoid comparing graphs directly, but at first to induce clustering of the data point cloud from the graph approximation and, secondly, to use well-established methods to compare and score the data cloud partitioning induced by the graphs. In particular, mutual information-based approaches prove to be useful in this context. The induced clustering is based on decomposing a graph into non-branching segments, and then clustering the data point cloud by the nearest segment. Such a method allows efficient comparison of graph-based data approximations of arbitrary topology and complexity. GDC-0077 cost The method is implemented in Python using the standard scikit-learn library which provides high speed and efficiency. As a demonstration of the methodology we analyse and compare graph-based data approximation methods using synthetic as well as real-life single cell datasets.This is the Editorial article summarizing the scope of the Special Issue Approximate Bayesian Inference.Quantum physics frequently involves a need to count the states, subspaces, measurement outcomes, and other elements of quantum dynamics. However, with quantum mechanics assigning probabilities to such objects, it is often desirable to work with the notion of a "total" that takes into account their varied relevance. For example, such an effective count of position states available to a lattice electron could characterize its localization properties. Similarly, the effective total of outcomes in the measurement step of a quantum computation relates to the efficiency of the quantum algorithm. Despite a broad need for effective counting, a well-founded prescription has not been formulated. Instead, the assignments that do not respect the measure-like nature of the concept, such as versions of the participation number or exponentiated entropies, are used in some areas. Here, we develop the additive theory of effective number functions (ENFs), namely functions assigning consistent totals to collections of objects endowed with probability weights. Our analysis reveals the existence of a minimal total, realized by the unique ENF, which leads to effective counting with absolute meaning. Touching upon the nature of the measure, our results may find applications not only in quantum physics, but also in other quantitative sciences.In order to find out whether the geomagnetic storms and large-mega earthquakes are correlated or not, statistical studies based on Superposed Epoch Analysis (SEA), significance analysis, and Z test have been applied to the Dst index data and M ≥ 7.0 global earthquakes during 1957-2020. The results indicate that before M ≥ 7.0 global earthquakes, there are clearly higher probabilities of geomagnetic storms than after them. Geomagnetic storms are more likely to be related with shallow earthquakes rather than deep ones. Further statistical investigations of the results based on cumulative storm hours show consistency with those based on storm days, suggesting that the high probability of geomagnetic storms prior to large-mega earthquakes is significant and robust. Some possible mechanisms such as a reverse piezoelectric effect and/or electroosmotic flow are discussed to explain the statistical correlation. The result might open new perspectives in the complex process of earthquakes and the Lithosphere-Atmosphere-Ionosphere (LAI) coupling.This study analyzes the productive structure of Portugal in the period 2013-2017, using indicators of localization and specialization applied to 308 Portuguese local authorities. From an empirical approach using a threshold model, the following indicators are used (i) localization quotient; (ii) specialization coefficient; (iii) Theil entropy index; (iv) rate of industrialization; and (v) the density of establishments by business size. The selected period 2013-2017 is due to the available data concerning firms located per local authority, and the choice of threshold model is justified through the possibility of assessing the non-linear effects of specialization and diversification on productivity, considering, in simultaneous terms, different regimes per business size. Estimation of the threshold model identified a positive, statistically significant relation between industrialization and productivity. Similarly, the terms of interaction between exports and diversification, and between the former and higher education institutions, shows a catalyzing effect of productivity. In addition, the most specialized micro-firms affect productivity significantly and positively, while the least specialized have the opposite effect. Small, less specialized companies have a significant and negative effect on productivity, contrasting with less specialized, medium-sized companies, which affect productivity positively. For large firms, the impact on productivity is negative for both high and low levels of specialization, reinforcing the need to fill existing gaps in strategic diversification, as well as the vertical and horizontal integration of the activities of production chains with high value added.For millennia humans have benefitted from application of the acute canine sense of smell to hunt, track and find targets of importance. In this report, canines were evaluated for their ability to detect the severe exotic phytobacterial arboreal pathogen Xanthomonas citri pv. citri (Xcc), which is the causal agent of Asiatic citrus canker (Acc). Since Xcc causes only local lesions, infections are non-systemic, limiting the use of serological and molecular diagnostic tools for field-level detection. This necessitates reliance on human visual surveys for Acc symptoms, which is highly inefficient at low disease incidence, and thus for early detection. In simulated orchards the overall combined performance metrics for a pair of canines were 0.9856, 0.9974, 0.9257 and 0.9970, for sensitivity, specificity, precision, and accuracy, respectively, with 1-2 s/tree detection time. Detection of trace Xcc infections on commercial packinghouse fruit resulted in 0.7313, 0.9947, 0.8750, and 0.9821 for the same performance metrics across a range of cartons with 0-10% Xcc-infected fruit despite the noisy, hot and potentially distracting environment.