Mapping and discrimination of networks in the complexity-entropy plane

Segregation-to-integration transformation model of memory evolution

Memories are thought to use coding schemes that dynamically adjust their representational structure to maximize both persistence and efficiency. However, the nature of these coding scheme adjustments and their impact on the temporal evolution of memory after initial encoding is unclear. Here, we introduce the Segregation-to-Integration Transformation (SIT) model, a network formalization that offers a unified account of how the representational structure of a memory is transformed over time. The SIT model asserts that memories initially adopt a highly modular or segregated network structure, functioning as an optimal storage buffer by balancing protection from disruptions and accommodating substantial information. Over time, a repeated combination of neural network reactivations involving activation spreading and synaptic plasticity transforms the initial modular structure into an integrated memory form, facilitating intercommunity spreading and fostering generalization. The SIT model identifies a nonlinear or inverted U-shaped function in memory evolution where memories are most susceptible to changing their representation. This time window, located early during the transformation, is a consequence of the memory's structural configuration, where the activation diffusion across the network is maximized.

Assessing Multi-Site rs-fMRI-Based Connectomic Harmonization Using Information Theory

Several harmonization techniques have recently been proposed for connectomics/networks derived from resting-state functional magnetic resonance imaging (rs-fMRI) acquired at multiple sites. These techniques have the objective of mitigating site-specific biases that complicate its subsequent analysis and, therefore, compromise the quality of the results when these images are analyzed together. Thus, harmonization is indispensable when large cohorts are required in which the data obtained must be independent of the particular condition of each resonator, its make and model, its calibration, and other features or artifacts that may affect the significance of the acquisition. To date, no assessment of the actual efficacy of these harmonization techniques has been proposed. In this work, we apply recently introduced Information Theory tools to analyze the effectiveness of these techniques, developing a methodology that allows us to compare different harmonization models. We demonstrate the usefulness of this methodology by applying it to some of the most widespread harmonization frameworks and datasets. As a result, we are able to show that some of these techniques are indeed ineffective since the acquisition site can still be determined from the fMRI data after the processing.

Study of system dynamics through recurrence analysis of regular windows

In the recurrence quantification analysis of a dynamical system, the key parameters of the analysis significantly influence the qualitative changes in recurrence measures. Therefore, the values of these parameters must be selected carefully using appropriate rules. The embedding parameters provide rules and procedures for the determination of the above. However, rules for selecting the threshold parameter (ɛ) are still the subject of tests and studies. This study proposes a procedure for selecting appropriate values of ɛ and point density of a vector series based on variability and convergence criteria. A criterion for the linear convergence of recurrence results makes it possible to find a narrow range of the ɛ parameter that would be suitable for the analysis in question.

A Survey of Information Entropy Metrics for Complex Networks

Information entropy metrics have been applied to a wide range of problems that were abstracted as complex networks. This growing body of research is scattered in multiple disciplines, which makes it difficult to identify available metrics and understand the context in which they are applicable. In this work, a narrative literature review of information entropy metrics for complex networks is conducted following the PRISMA guidelines. Existing entropy metrics are classified according to three different criteria: whether the metric provides a property of the graph or a graph component (such as the nodes), the chosen probability distribution, and the types of complex networks to which the metrics are applicable. Consequently, this work identifies the areas in need for further development aiming to guide future research efforts.

Characterization of network complexity by communicability sequence entropy and associated Jensen-Shannon divergence

Characterizing the structural complexity of networks is a major challenging work in network science. However, a valid measure to quantify network complexity remains unexplored. Although the entropy of various network descriptors and algorithmic complexity have been selected in the previous studies to do it, most of these methods only contain local information of the network, so they cannot accurately reflect the global structural complexity of the network. In this paper, we propose a statistical measure to characterize network complexity from a global perspective, which is composed of the communicability sequence entropy of the network and the associated Jensen-Shannon divergence. We study the influences of the topology of the synthetic networks on the complexity measure. The results show that networks with strong heterogeneity, strong degree-degree correlation, and a certain number of communities have a relatively large complexity. Moreover, by studying some real networks and their corresponding randomized network models, we find that the complexity measure is a monotone increasing function of the order of the randomized network, and the ones of real networks are larger complexity-values compared to all corresponding randomized networks. These results indicate that the complexity measure is sensitive to the changes of the basic topology of the network and increases with the increase of the external constraints of the network, which further proves that the complexity measure presented in this paper can effectively represent the topological complexity of the network.

Event synchrony measures for functional climate network analysis: A case study on South American rainfall dynamics

Understanding spatiotemporal patterns of climate extremes has gained considerable relevance in the context of ongoing climate change. With enhanced computational capacity, data driven methods such as functional climate networks have been proposed and have already contributed to significant advances in understanding and predicting extreme events, as well as identifying interrelations between the occurrences of various climatic phenomena. While the (in its basic setting) parameter free event synchronization (ES) method has been widely applied to construct functional climate networks from extreme event series, its original definition has been realized to exhibit problems in handling events occurring at subsequent time steps, which need to be accounted for. Along with the study of this conceptual limitation of the original ES approach, event coincidence analysis (ECA) has been suggested as an alternative approach that incorporates an additional parameter for selecting certain time scales of event synchrony. In this work, we compare selected features of functional climate network representations of South American heavy precipitation events obtained using ES and ECA without and with the correction for temporal event clustering. We find that both measures exhibit different types of biases, which have profound impacts on the resulting network structures. By combining the complementary information captured by ES and ECA, we revisit the spatiotemporal organization of extreme events during the South American Monsoon season. While the corrected version of ES captures multiple time scales of heavy rainfall cascades at once, ECA allows disentangling those scales and thereby tracing the spatiotemporal propagation more explicitly.

A detailed characterization of complex networks using Information Theory

Understanding the structure and the dynamics of networks is of paramount importance for many scientific fields that rely on network science. Complex network theory provides a variety of features that help in the evaluation of network behavior. However, such analysis can be confusing and misleading as there are many intrinsic properties for each network metric. Alternatively, Information Theory methods have gained the spotlight because of their ability to create a quantitative and robust characterization of such networks. In this work, we use two Information Theory quantifiers, namely Network Entropy and Network Fisher Information Measure, to analyzing those networks. Our approach detects non-trivial characteristics of complex networks such as the transition present in the Watts-Strogatz model from k-ring to random graphs; the phase transition from a disconnected to an almost surely connected network when we increase the linking probability of Erdős-Rényi model; distinct phases of scale-free networks when considering a non-linear preferential attachment, fitness, and aging features alongside the configuration model with a pure power-law degree distribution. Finally, we analyze the numerical results for real networks, contrasting our findings with traditional complex network methods. In conclusion, we present an efficient method that ignites the debate on network characterization.

Areawise significance tests for windowed recurrence network analysis

Many time-series analysis techniques use sliding window approaches or are repeatedly applied over a continuous range of parameters. When combined with a significance test, intrinsic correlations among the pointwise analysis results can make falsely positive significant points appear as continuous patches rather than as isolated points. To account for this effect, we present an areawise significance test that identifies such false-positive patches. For this purpose, we numerically estimate the decorrelation length of the statistic of interest by calculating correlation functions between the analysis results and require an areawise significant point to belong to a patch of pointwise significant points that is larger than this decorrelation length. We apply our areawise test to results from windowed traditional and scale-specific recurrence network analysis in order to identify dynamical anomalies in time series of a non-stationary Rössler system and tree ring width index values from Eastern Canada. Especially, in the palaeoclimate context, the areawise testing approach markedly reduces the number of points that are identified as significant and therefore highlights only the most relevant features in the data. This provides a crucial step towards further establishing recurrence networks as a tool for palaeoclimate data analysis.

Generalization of the small-world effect on a model approaching the Erdős-Rényi random graph

The famous Watts–Strogatz (WS) small-world network model does not approach the Erdős–Rényi (ER) random graph model in the limit of total randomization which can lead to confusion and complicates certain analyses. In this paper we discuss a simple alternative which was first introduced by Song and Wang, where instead of rewiring, edges are drawn between pairs of nodes with a distance-based connection probability. We show that this model is simpler to analyze, approaches the true ER random graph model in the completely randomized limit, and demonstrate that the WS model and the alternative model may yield different quantitative results using the example of a random walk temporal observable. An efficient sampling algorithm for the alternative model is proposed. Analytic results regarding the degree distribution, degree variance, number of two-stars per node, number of triangles per node, clustering coefficient, and random walk mixing time are presented. Subsequently, the small-world effect is illustrated by showing that the clustering coefficient decreases much slower than an upper bound on the message delivery time with increasing long-range connection probability which generalizes the small-world effect from informed searches to random search strategies. Due to its accessibility for analytic evaluations, we propose that this modified model should be used as an alternative reference model for studying the influence of small-world topologies on dynamic systems as well as a simple model to introduce numerous topics when teaching network science.

Edge directionality properties in complex spherical networks

Spatially embedded networks have attracted increasing attention in the past decade. In this context, network characteristics have been introduced which explicitly take spatial information into account. Among others, edge directionality properties have recently gained particular interest. In this work, we investigate the applicability of mean edge direction, anisotropy, and local mean angle as geometric characteristics in complex spherical networks. By studying these measures, both analytically and numerically, we demonstrate the existence of a systematic bias in spatial networks where individual nodes represent different shares on a spherical surface, and we describe a strategy for correcting for this effect. Moreover, we illustrate the application of the mentioned edge directionality properties to different examples of real-world spatial networks in spherical geometry (with or without the geometric correction depending on each specific case), including functional climate networks, transportation, and trade networks. In climate networks, our approach highlights relevant patterns, such as large-scale circulation cells, the El Niño-Southern Oscillation, and the Atlantic Niño. In an air transportation network, we are able to characterize distinct air transportation zones, while we confirm the important role of the European Union for the global economy by identifying convergent edge directionality patterns in the world trade network.

Recurrence threshold selection for obtaining robust recurrence characteristics in different embedding dimensions

The appropriate selection of recurrence thresholds is a key problem in applications of recurrence quantification analysis and related methods across disciplines. Here, we discuss the distribution of pairwise distances between state vectors in the studied system's state space reconstructed by means of time-delay embedding as the key characteristic that should guide the corresponding choice for obtaining an adequate resolution of a recurrence plot. Specifically, we present an empirical description of the distance distribution, focusing on characteristic changes of its shape with increasing embedding dimension. Our results suggest that selecting the recurrence threshold according to a fixed percentile of this distribution reduces the dependence of recurrence characteristics on the embedding dimension in comparison with other commonly used threshold selection methods. Numerical investigations on some paradigmatic model systems with time-dependent parameters support these empirical findings.