Multiplex visibility graphs to investigate recurrent neural network dynamics

Daylight Saving Time transitions and Cardiovascular Disease in Andalusia: Time Series Modeling and Analysis Using Visibility Graphs

The present study aimed to determine whether transitions both to and from daylight saving time (DST) led to an increase in the incidence of hospital admissions for major acute cardiovascular events (MACE). To support the analysis, natural visibility graphs (NVGs) were used with data from Andalusian public hospitals between 2009 and 2019. We calculated the incidence rates of hospital admissions for MACE, and specifically acute myocardial infarction and ischemic stroke during the 2 weeks leading up to, and 2 weeks after, the DST transition. NVG were applied to identify dynamic patterns. The study included 157 221 patients diagnosed with MACE, 71 992 with AMI (42 975 ST-elevation myocardial infarction (STEMI) and 26 752 non-ST-elevation myocardial infarction (NSTEMI)), and 51 420 with ischemic stroke. Observed/expected ratios shown an increased risk of AMI (1.06; 95% CI (1.00-1.11); P = .044), NSTEMI (1.12; 95% CI (1.02-1.22); P = .013), and acute coronary syndrome (1.05; 95% CI (1.00-1.10); P = .04) around the autumn DST. The NVG showed slight variations in the daily pattern of pre-DST and post-DST hospitalization admissions for all pathologies, but indicated that the increase in the incidence of hospital admissions after the DST is not sufficient to change the normal pattern significantly.

Environmental pollution in North-Eastern Italy and its influence on chronic obstructive pulmonary disease: time series modelling and analysis using visibility graphs

The impact on human health from environmental pollution is receiving increasing attention. In the case of respiratory diseases such as chronic obstructive pulmonary disease (COPD), the relationship is now well documented. However, few studies have been carried out in areas with low population density and low industrial production, such as the province of Belluno (North-Eastern Italy). The aim of the study was to analyze the effect of exposure to certain pollutants on the temporal dynamics of hospital admissions for COPD in the province of Belluno. Daily air pollution concentration, humidity, precipitations, and temperature were collected from the air monitoring stations in Belluno. Generalized additive mixed models (GAMM) and visibility graphs were used to determine the effects of the short-term exposure to environmental agents on hospital admissions associated to COPD. In the case of the city of Belluno, the GAMM showed that hospital admissions were associated with NO₂, PM₁₀, date, and temperature, while for the city of Feltre, GAMM produced no associated variables. Several visibility graph indices (average edge overlap and interlayer mutual information) showed a significant overlap between environmental agents and hospital admission for both cities. Our study has shown that visibility graphs can be useful in establishing associations between environmental agents and COPD hospitalization in sparsely populated areas.

Reservoir Dynamic Interpretability for Time Series Prediction: A Permutation Entropy View

An echo state network (ESN) is an efficient recurrent neural network (RNN) that is widely used in time series prediction tasks due to its simplicity and low training cost. However, the "black-box" nature of reservoirs hinders the development of ESN. Although a large number of studies have concentrated on reservoir interpretability, the perspective of reservoir modeling is relatively single, and the relationship between reservoir richness and reservoir projection capacity has not been effectively established. To tackle this problem, a novel reservoir interpretability framework based on permutation entropy (PE) theory is proposed in this paper. In structure, this framework consists of reservoir state extraction, PE modeling, and PE analysis. Based on these, the instantaneous reservoir states and neuronal time-varying states are extracted, which are followed by phase space reconstruction, sorting, and entropy calculation. Firstly, the obtained instantaneous state entropy (ISE) and global state entropy (GSE) can measure reservoir richness for interpreting good reservoir projection capacity. On the other hand, the multiscale complexity-entropy analysis of global and neuron-level reservoir states is performed to reveal more detailed dynamics. Finally, the relationships between ESN performance and reservoir dynamic are investigated via Pearson correlation, considering different prediction steps and time scales. Experimental evaluations on several benchmarks and real-world datasets demonstrate the effectiveness and superiority of the proposed reservoir interpretability framework.

Novel features for time series analysis: a complex networks approach

Being able to capture the characteristics of a time series with a feature vector is a very important task with a multitude of applications, such as classification, clustering or forecasting. Usually, the features are obtained from linear and nonlinear time series measures, that may present several data related drawbacks. In this work we introduce NetF as an alternative set of features, incorporating several representative topological measures of different complex networks mappings of the time series. Our approach does not require data preprocessing and is applicable regardless of any data characteristics. Exploring our novel feature vector, we are able to connect mapped network features to properties inherent in diversified time series models, showing that NetF can be useful to characterize time data. Furthermore, we also demonstrate the applicability of our methodology in clustering synthetic and benchmark time series sets, comparing its performance with more conventional features, showcasing how NetF can achieve high-accuracy clusters. Our results are very promising, with network features from different mapping methods capturing different properties of the time series, adding a different and rich feature set to the literature.

Reservoir Computing Approaches for Representation and Classification of Multivariate Time Series

Classification of multivariate time series (MTS) has been tackled with a large variety of methodologies and applied to a wide range of scenarios. Reservoir computing (RC) provides efficient tools to generate a vectorial, fixed-size representation of the MTS that can be further processed by standard classifiers. Despite their unrivaled training speed, MTS classifiers based on a standard RC architecture fail to achieve the same accuracy of fully trainable neural networks. In this article, we introduce the reservoir model space, an unsupervised approach based on RC to learn vectorial representations of MTS. Each MTS is encoded within the parameters of a linear model trained to predict a low-dimensional embedding of the reservoir dynamics. Compared with other RC methods, our model space yields better representations and attains comparable computational performance due to an intermediate dimensionality reduction procedure. As a second contribution, we propose a modular RC framework for MTS classification, with an associated open-source Python library. The framework provides different modules to seamlessly implement advanced RC architectures. The architectures are compared with other MTS classifiers, including deep learning models and time series kernels. Results obtained on the benchmark and real-world MTS data sets show that RC classifiers are dramatically faster and, when implemented using our proposed representation, also achieve superior classification accuracy.

Mapping images into ordinal networks

An increasing abstraction has marked some recent investigations in network science. Examples include the development of algorithms that map time series data into networks whose vertices and edges can have different interpretations, beyond the classical idea of parts and interactions of a complex system. These approaches have proven useful for dealing with the growing complexity and volume of diverse data sets. However, the use of such algorithms is mostly limited to one-dimensional data, and there has been little effort towards extending these methods to higher-dimensional data such as images. Here we propose a generalization for the ordinal network algorithm for mapping images into networks. We investigate the emergence of connectivity constraints inherited from the symbolization process used for defining the network nodes and links, which in turn allows us to derive the exact structure of ordinal networks obtained from random images. We illustrate the use of this new algorithm in a series of applications involving randomization of periodic ornaments, images generated by two-dimensional fractional Brownian motion and the Ising model, and a data set of natural textures. These examples show that measures obtained from ordinal networks (such as average shortest path and global node entropy) extract important image properties related to roughness and symmetry, are robust against noise, and can achieve higher accuracy than traditional texture descriptors extracted from gray-level co-occurrence matrices in simple image classification tasks.

Prediction of pKa Values for Neutral and Basic Drugs based on Hybrid Artificial Intelligence Methods

The pKa value of drugs is an important parameter in drug design and pharmacology. In this paper, an improved particle swarm optimization (PSO) algorithm was proposed based on the population entropy diversity. In the improved algorithm, when the population entropy was higher than the set maximum threshold, the convergence strategy was adopted; when the population entropy was lower than the set minimum threshold the divergence strategy was adopted; when the population entropy was between the maximum and minimum threshold, the self-adaptive adjustment strategy was maintained. The improved PSO algorithm was applied in the training of radial basis function artificial neural network (RBF ANN) model and the selection of molecular descriptors. A quantitative structure-activity relationship model based on RBF ANN trained by the improved PSO algorithm was proposed to predict the pKa values of 74 kinds of neutral and basic drugs and then validated by another database containing 20 molecules. The validation results showed that the model had a good prediction performance. The absolute average relative error, root mean square error, and squared correlation coefficient were 0.3105, 0.0411, and 0.9685, respectively. The model can be used as a reference for exploring other quantitative structure-activity relationships.