Scaling theory of fractal complex networks.

We show that fractality in complex networks arises from the geometric self-similarity of their built-in hierarchical community-like structure, which is mathematically described by the scale-invariant equation for the masses of the boxes with which we cover the network when determining its box dimension. This approach-grounded in both scaling theory of phase transitions and renormalization group theory-leads to the consistent scaling theory of fractal complex networks, which complements the collection of scaling exponents with several new ones and reveals various relationships between them. We propose the introduction of two classes of exponents: microscopic and macroscopic, characterizing the local structure of fractal complex networks and their global properties, respectively. Interestingly, exponents from both classes are related to each other and only a few of them (three out of seven) are independent, thus bridging the local self-similarity and global scale-invariance in fractal networks. We successfully verify our findings in real networks situated in various fields (information-the World Wide Web, biological-the human brain, and social-scientific collaboration networks) and in several fractal network models.

Deep learning algorithm for visual quality assessment of the spirograms.

Objective. The quality of spirometry manoeuvres is crucial for correctly interpreting the values of spirometry parameters. A fundamental guideline for proper quality assessment is the American Thoracic Society and European Respiratory Society (ATS/ERS) Standards for spirometry, updated in 2019, which describe several start-of-test and end-of-test criteria which can be assessed automatically. However, the spirometry standards also require a visual evaluation of the spirometry curve to determine the spirograms' acceptability or usability. In this study, we present an automatic algorithm based on a convolutional neural network (CNN) for quality assessment of the spirometry curves as an alternative to manual verification performed by specialists.Approach. The algorithm for automatic assessment of spirometry measurements was created using a set of randomly selected 1998 spirograms which met all quantitative criteria defined by ATS/ERS Standards. Each spirogram was annotated as 'confirm' (remaining acceptable or usable status) or 'reject' (change the status to unacceptable) by four pulmonologists, separately for FEV1 and FVC parameters. The database was split into a training (80%) and test set (20%) for developing the CNN classification algorithm. The algorithm was optimised using a cross-validation method.Main results. The accuracy, sensitivity and specificity obtained for the algorithm were 92.6%, 93.1% and 90.0% for FEV1 and 94.1%, 95.6% and 88.3% for FVC, respectively.Significance.The algorithm provides an opportunity to significantly improve the quality of spirometry tests, especially during unsupervised spirometry. It can also serve as an additional tool in clinical trials to quickly assess the quality of a large group of tests.

Coagulation with product kernel and arbitrary initial conditions: Exact kinetics within the Marcus-Lushnikov framework.

The time evolution of a system of coagulating particles under the product kernel and arbitrary initial conditions is studied. Using the improved Marcus-Lushnikov approach, the master equation is solved for the probability W(Q,t) to find the system in a given mass spectrum Q={n_{1},n_{2},⋯,n_{g}⋯}, with n_{g} being the number of particles of size g. The exact expression for the average number of particles 〈n_{g}(t)〉 at arbitrary time t is derived and its validity is confirmed in numerical simulations of several selected initial mass spectra.