Simplicial complex entropy for time series analysis.

The complex behavior of many systems in nature requires the application of robust methodologies capable of identifying changes in their dynamics. In the case of time series (which are sensed values of a system during a time interval), several methods have been proposed to evaluate their irregularity. However, for some types of dynamics such as stochastic and chaotic, new approaches are required that can provide a better characterization of them. In this paper we present the simplicial complex approximate entropy, which is based on the conditional probability of the occurrence of elements of a simplicial complex. Our results show that this entropy measure provides a wide range of values with details not easily identifiable with standard methods. In particular, we show that our method is able to quantify the irregularity in simulated random sequences and those from low-dimensional chaotic dynamics. Furthermore, it is possible to consistently differentiate cardiac interbeat sequences from healthy subjects and from patients with heart failure, as well as to identify changes between dynamical states of coupled chaotic maps. Our results highlight the importance of the structures revealed by the simplicial complexes, which holds promise for applications of this approach in various contexts.

Conflict Dynamics in Scale-Free Networks with Degree Correlations and Hierarchical Structure.

We present a study of the dynamic interactions between actors located on complex networks with scale-free and hierarchical scale-free topologies with assortative mixing, that is, correlations between the degree distributions of the actors. The actor's state evolves according to a model that considers its previous state, the inertia to change, and the influence of its neighborhood. We show that the time evolution of the system depends on the percentage of cooperative or competitive interactions. For scale-free networks, we find that the dispersion between actors is higher when all interactions are either cooperative or competitive, while a balanced presence of interactions leads to a lower separation. Moreover, positive assortative mixing leads to greater divergence between the states, while negative assortative mixing reduces this dispersion. We also find that hierarchical scale-free networks have both similarities and differences when compared with scale-free networks. Hierarchical scale-free networks, like scale-free networks, show the least divergence for an equal mix of cooperative and competitive interactions between actors. On the other hand, hierarchical scale-free networks, unlike scale-free networks, show much greater divergence when dominated by cooperative rather than competitive actors, and while the formation of a rich club (adding links between hubs) with cooperative interactions leads to greater divergence, the divergence is much less when they are fully competitive. Our findings highlight the importance of the topology where the interaction dynamics take place, and the fact that a balanced presence of cooperators and competitors makes the system more cohesive, compared to the case where one strategy dominates.

A multiplex analysis of phonological and orthographic networks.

The study of natural language using a network approach has made it possible to characterize novel properties ranging from the level of individual words to phrases or sentences. A natural way to quantitatively evaluate similarities and differences between spoken and written language is by means of a multiplex network defined in terms of a similarity distance between words. Here, we use a multiplex representation of words based on orthographic or phonological similarity to evaluate their structure. We report that from the analysis of topological properties of networks, there are different levels of local and global similarity when comparing written vs. spoken structure across 12 natural languages from 4 language families. In particular, it is found that differences between the phonetic and written layers is markedly higher for French and English, while for the other languages analyzed, this separation is relatively smaller. We conclude that the multiplex approach allows us to explore additional properties of the interaction between spoken and written language.

The Complex Structure of the Pharmacological Drug-Disease Network.

The complexity of drug-disease interactions is a process that has been explained in terms of the need for new drugs and the increasing cost of drug development, among other factors. Over the last years, diverse approaches have been explored to understand drug-disease relationships. Here, we construct a bipartite graph in terms of active ingredients and diseases based on thoroughly classified data from a recognized pharmacological website. We find that the connectivities between drugs (outgoing links) and diseases (incoming links) follow approximately a stretched-exponential function with different fitting parameters; for drugs, it is between exponential and power law functions, while for diseases, the behavior is purely exponential. The network projections, onto either drugs or diseases, reveal that the co-ocurrence of drugs (diseases) in common target diseases (drugs) lead to the appearance of connected components, which varies as the threshold number of common target diseases (drugs) is increased. The corresponding projections built from randomized versions of the original bipartite networks are considered to evaluate the differences. The heterogeneity of association at group level between active ingredients and diseases is evaluated in terms of the Shannon entropy and algorithmic complexity, revealing that higher levels of diversity are present for diseases compared to drugs. Finally, the robustness of the original bipartite network is evaluated in terms of most-connected nodes removal (direct attack) and random removal (random failures).

Comparing phonological and orthographic networks: A multiplex analysis.

The complexity of natural language can be explored by means of multiplex analyses at different scales, from single words to groups of words or sentence levels. Here, we plan to investigate a multiplex word-level network, which comprises an orthographic and a phonological network defined in terms of distance similarity. We systematically compare basic structural network properties to determine similarities and differences between them, as well as their combination in a multiplex configuration. As a natural extension of our work, we plan to evaluate the preservation of the structural network properties and information-based quantities from the following perspectives: (i) presence of similarities across 12 natural languages from 4 linguistic families (Romance, Germanic, Slavic and Uralic), (ii) increase of the size of the number of words (corpus) from 104 to 50 × 103, and (iii) robustness of the networks. Our preliminary findings reinforce the idea of common organizational properties among natural languages. Once concluded, will contribute to the characterization of similarities and differences in the orthographic and phonological perspectives of language networks at a word-level.

Network-based features for retinal fundus vessel structure analysis.

Retinal fundus imaging is a non-invasive method that allows visualizing the structure of the blood vessels in the retina whose features may indicate the presence of diseases such as diabetic retinopathy (DR) and glaucoma. Here we present a novel method to analyze and quantify changes in the retinal blood vessel structure in patients diagnosed with glaucoma or with DR. First, we use an automatic unsupervised segmentation algorithm to extract a tree-like graph from the retina blood vessel structure. The nodes of the graph represent branching (bifurcation) points and endpoints, while the links represent vessel segments that connect the nodes. Then, we quantify structural differences between the graphs extracted from the groups of healthy and non-healthy patients. We also use fractal analysis to characterize the extracted graphs. Applying these techniques to three retina fundus image databases we find significant differences between the healthy and non-healthy groups (p-values lower than 0.005 or 0.001 depending on the method and on the database). The results are sensitive to the segmentation method (manual or automatic) and to the resolution of the images.

Critical synchronization and 1/f noise in inhibitory/excitatory rich-club neural networks.

In recent years, diverse studies have reported that different brain regions, which are internally densely connected, are also highly connected to each other. This configuration seems to play a key role in integrating and interchanging information between brain areas. Also, changes in the rich-club connectivity and the shift from inhibitory to excitatory behavior of hub neurons have been associated with several diseases. However, there is not a clear understanding about the role of the proportion of inhibitory/excitatory hub neurons, the dynamic consequences of rich-club disconnection, and hub inhibitory/excitatory shifts. Here, we study the synchronization and temporal correlations in the neural Izhikevich model, which comprises excitatory and inhibitory neurons located in a scale-free hierarchical network with rich-club connectivity. We evaluated the temporal autocorrelations and global synchronization dynamics displayed by the system in terms of rich-club connectivity and hub inhibitory/excitatory population. We evaluated the synchrony between pairs of sets of neurons by means of the global lability synchronization, based on the rate of change in the total number of synchronized signals. The results show that for a wide range of excitatory/inhibitory hub ratios the network displays 1/f dynamics with critical synchronization that is concordant with numerous health brain registers, while a network configuration with a vast majority of excitatory hubs mostly exhibits short-term autocorrelations with numerous large avalanches. Furthermore, rich-club connectivity promotes the increase of the global lability of synchrony and the temporal persistence of the system.

Recurrence Networks in Natural Languages.

We present a study of natural language using the recurrence network method. In our approach, the repetition of patterns of characters is evaluated without considering the word structure in written texts from different natural languages. Our dataset comprises 85 ebookseBooks written in 17 different European languages. The similarity between patterns of length m is determined by the Hamming distance and a value r is considered to define a matching between two patterns, i.e., a repetition is defined if the Hamming distance is equal or less than the given threshold value r. In this way, we calculate the adjacency matrix, where a connection between two nodes exists when a matching occurs. Next, the recurrence network is constructed for the texts and some representative network metrics are calculated. Our results show that average values of network density, clustering, and assortativity are larger than their corresponding shuffled versions, while for metrics like such as closeness, both original and random sequences exhibit similar values. Moreover, our calculations show similar average values for density among languages which that belong to the same linguistic family. In addition, the application of a linear discriminant analysis leads to well-separated clusters of family languages based on based on the network-density properties. Finally, we discuss our results in the context of the general characteristics of written texts.

Multifractal Analysis Reveals Decreased Non-linearity and Stronger Anticorrelations in Heart Period Fluctuations of Fibromyalgia Patients.

Objective: To characterize the multifractal behavior of the beat to beat heart-period or RR fluctuations in fibromyalgia patients (FM) in comparison with healthy-matched subjects. Methods: Multifractral detrended fluctuation analysis (MDFA) was used to study multifractality in heartbeat times-series from 30 female healthy subjects and 30 female patients with fibromyalgia during day and night periods.The multifractal changes as derived from the magnitude and sign analysis of these RR fluctuations were also assessed. Results: The RR fluctuations dynamics of healthy subjects showed a broad multifractal spectrum. By contrast, a noticeable decrease in multifractality and non-linearity was observed for patients with fibromyalgia. In addition, the spectra corresponding to FM subjects were located on the average to the right of the spectra of healthy individuals, indicating that the local scaling exponents reflect a smoother behavior compared to healthy dynamics. Moreover, the multifractal analysis as applied to the magnitude and sign heartbeat series confirmed that, in addition to a decreased nonlinearity, fibromyalgia patients presented stronger anticorrelation in directionality, which did not remain invariant for small or rather larger fluctuations as it occurred in healthy subjects. Conclusion: When compared to healthy controls, fibromyalgia patients display decreased nonlinearity and stronger anticorrelations in heart period fluctuations. These findings reinforce the hypothesis of the potential role of the dysfunctional autonomic nervous system in the pathogenesis of fibromyalgia.

Multifractality of Pseudo-Velocities and Seismic Quiescence Associated with the Tehuantepec M8.2 EQ.

By using earthquake catalogs, previous studies have reported evidence that some changes in the spatial and temporal organization of earthquake activity are observed before and after of a main shock. These previous studies have used different approaches for detecting clustering behavior and distance-events density in order to point out the asymmetric behavior of foreshocks and aftershocks. Here, we present a statistical analysis of the seismic activity related to the M w = 8.2 earthquake that occurred on 7 September 2017 in Mexico. First, we calculated the inter-event time and distance between successive events for the period 1 January 1998 until 20 October 2017 in a circular region centered at the epicenter of the M w = 8.2 EQ. Next, we introduced the concept of pseudo-velocity as the ratio between the inter-event distance and inter-event time. A sliding window is considered to estimate some statistical features of the pseudo-velocity sequence before the main shock. Specifically, we applied the multifractal method to detect changes in the spectrum of singularities for the period before the main event on 7 September. Our results point out that the multifractality associated with the pseudo-velocities exhibits noticeable changes in the characteristics of the spectra (more narrower) for approximately three years, from 2013 until 2016, which is preceded and followed by periods with wider spectra. On the other hand, we present an analysis of patterns of seismic quiescence before the M w = 8.2 earthquake based on the Schreider algorithm over a period of 27 years. We report the existence of an important period of seismic quietude, for six to seven years, from 2008 to 2015 approximately, known as the alpha stage, and a beta stage of resumption of seismic activity, with a duration of approximately three years until the occurrence of the great earthquake of magnitude M w = 8.2 . Our results are in general concordance with previous results reported for statistics based on magnitude temporal sequences.

The dynamic consequences of cooperation and competition in small-world networks.

We present a study of the social dynamics among cooperative and competitive actors interacting on a complex network that has a small-world topology. In this model, the state of each actor depends on its previous state in time, its inertia to change, and the influence of its neighboring actors. Using numerical simulations, we determine how the distribution of final states of the actors and measures of the distances between the values of the actors at local and global levels, depend on the number of cooperative to competitive actors and the connectivity of the actors in the network. We find that similar numbers of cooperative and competitive actors yield the lowest values for the local and global measures of the distances between the values of the actors. On the other hand, when the number of either cooperative or competitive actors dominate the system, then the divergence is largest between the values of the actors. Our findings make new testable predictions on how the dynamics of a conflict depends on the strategies chosen by groups of actors and also have implications for the evolution of behaviors.

Comparative analysis of the transcription-factor gene regulatory networks of E. coli and S. cerevisiae.

BACKGROUND: The regulatory interactions between transcription factors (TF) and regulated genes (RG) in a species genome can be lumped together in a single directed graph. The TF's and RG's conform the nodes of this graph, while links are drawn whenever a transcription factor regulates a gene's expression. Projections onto TF nodes can be constructed by linking every two nodes regulating a common gene. Similarly, projections onto RG nodes can be made by linking every two regulated genes sharing at least one common regulator. Recent studies of the connectivity pattern in the transcription-factor regulatory network of many organisms have revealed some interesting properties. However, the differences between TF and RG nodes have not been widely explored. RESULTS: After analysing the RG and TF projections of the transcription-factor gene regulatory networks of Escherichia coli and Saccharomyces cerevisiae, we found several common characteristic as well as some noticeable differences. To better understand these differences, we compared the properties of the E. coli and S. cerevisiae RG- and TF-projected networks with those of the corresponding projections built from randomized versions of the original bipartite networks. These last results indicate that the observed differences are mostly due to the very different ratios of TF to RG counts of the E. coli and S. cerevisiae bipartite networks, rather than to their having different connectivity patterns. CONCLUSION: Since E. coli is a prokaryotic organism while S. cerevisiae is eukaryotic, there are important differences between them concerning processing of mRNA before translation, DNA packing, amount of junk DNA, and gene regulation. From the results in this paper we conclude that the most important effect such differences have had on the development of the corresponding transcription-factor gene regulatory networks is their very different ratios of TF to RG numbers. This ratio is more than three times larger in S. cerevisiae than in E. coli. Our calculations reveal that, both species' gene regulatory networks have very similar connectivity patterns, despite their very different TF to RG ratios. An this, to our consideration, indicates that the structure of both networks is optimal from an evolutionary viewpoint.