Unified functional network and nonlinear time series analysis for complex systems science: The pyunicorn package

We introduce the \texttt{pyunicorn} (Pythonic unified complex network and recurrence analysis toolbox) open source software package for applying and combining modern methods of data analysis and modeling from complex network theory and nonlinear time series analysis. \texttt{pyunicorn} is a fully object-oriented and easily parallelizable package written in the language Python. It allows for the construction of functional networks such as climate networks in climatology or functional brain networks in neuroscience representing the structure of statistical interrelationships in large data sets of time series and, subsequently, investigating this structure using advanced methods of complex network theory such as measures and models for spatial networks, networks of interacting networks, node-weighted statistics or network surrogates. Additionally, \texttt{pyunicorn} provides insights into the nonlinear dynamics of complex systems as recorded in uni- and multivariate time series from a non-traditional perspective by means of recurrence quantification analysis (RQA), recurrence networks, visibility graphs and construction of surrogate time series. The range of possible applications of the library is outlined, drawing on several examples mainly from the field of climatology.Comment: 28 pages, 17 figure

Model-free reconstruction of neuronal network connectivity from calcium imaging signals

A systematic assessment of global neural network connectivity through direct electrophysiological assays has remained technically unfeasible even in dissociated neuronal cultures. We introduce an improved algorithmic approach based on Transfer Entropy to reconstruct approximations to network structural connectivities from network activity monitored through calcium fluorescence imaging. Based on information theory, our method requires no prior assumptions on the statistics of neuronal firing and neuronal connections. The performance of our algorithm is benchmarked on surrogate time-series of calcium fluorescence generated by the simulated dynamics of a network with known ground-truth topology. We find that the effective network topology revealed by Transfer Entropy depends qualitatively on the time-dependent dynamic state of the network (e.g., bursting or non-bursting). We thus demonstrate how conditioning with respect to the global mean activity improves the performance of our method. [...] Compared to other reconstruction strategies such as cross-correlation or Granger Causality methods, our method based on improved Transfer Entropy is remarkably more accurate. In particular, it provides a good reconstruction of the network clustering coefficient, allowing to discriminate between weakly or strongly clustered topologies, whereas on the other hand an approach based on cross-correlations would invariantly detect artificially high levels of clustering. Finally, we present the applicability of our method to real recordings of in vitro cortical cultures. We demonstrate that these networks are characterized by an elevated level of clustering compared to a random graph (although not extreme) and by a markedly non-local connectivity.Comment: 54 pages, 8 figures (+9 supplementary figures), 1 table; submitted for publicatio

Data based identification and prediction of nonlinear and complex dynamical systems

We thank Dr. R. Yang (formerly at ASU), Dr. R.-Q. Su (formerly at ASU), and Mr. Zhesi Shen for their contributions to a number of original papers on which this Review is partly based. This work was supported by ARO under Grant No. W911NF-14-1-0504. W.-X. Wang was also supported by NSFC under Grants No. 61573064 and No. 61074116, as well as by the Fundamental Research Funds for the Central Universities, Beijing Nova Programme.Peer reviewedPostprin

Reconstructing dynamical networks via feature ranking

Empirical data on real complex systems are becoming increasingly available. Parallel to this is the need for new methods of reconstructing (inferring) the topology of networks from time-resolved observations of their node-dynamics. The methods based on physical insights often rely on strong assumptions about the properties and dynamics of the scrutinized network. Here, we use the insights from machine learning to design a new method of network reconstruction that essentially makes no such assumptions. Specifically, we interpret the available trajectories (data) as features, and use two independent feature ranking approaches -- Random forest and RReliefF -- to rank the importance of each node for predicting the value of each other node, which yields the reconstructed adjacency matrix. We show that our method is fairly robust to coupling strength, system size, trajectory length and noise. We also find that the reconstruction quality strongly depends on the dynamical regime

Mapping the epileptic brain with EEG dynamical connectivity: established methods and novel approaches

Several algorithms rooted in statistical physics, mathematics and machine learning are used to analyze neuroimaging data from patients suffering from epilepsy, with the main goals of localizing the brain region where the seizure originates from and of detecting upcoming seizure activity in order to trigger therapeutic neurostimulation devices. Some of these methods explore the dynamical connections between brain regions, exploiting the high temporal resolution of the electroencephalographic signals recorded at the scalp or directly from the cortical surface or in deeper brain areas. In this paper we describe this specific class of algorithms and their clinical application, by reviewing the state of the art and reporting their application on EEG data from an epileptic patient

Very Long Time Scales and Black Hole Thermal Equilibrium

We estimate the very long time behaviour of correlation functions in the presence of eternal black holes. It was pointed out by Maldacena (hep-th 0106112) that their vanishing would lead to a violation of a unitarity-based bound. The value of the bound is obtained from the holographic dual field theory. The correlators indeed vanish in a semiclassical bulk approximation. We trace the origin of their vanishing to the continuum energy spectrum in the presence of event horizons. We elaborate on the two very long time scales involved: one associated with the black hole and the other with a thermal gas in the vacuum background. We find that assigning a role to the thermal gas background, as suggested in the above work, does restore the compliance with a time-averaged unitarity bound. We also find that additional configurations are needed to explain the expected time dependence of the Poincar\'e recurrences and their magnitude. It is suggested that, while a semiclassical black hole does reproduce faithfully ``coarse grained'' properties of the system, additional dynamical features of the horizon may be necessary to resolve a finer grained information-loss problem. In particular, an effectively formed stretched horizon could yield the desired results.Comment: 30 pages, harvmac, 1 eps figur

Characterization of Neural Activity using Complex Network Theory. Application to the Identification of the Altered Neural Substrates in Schizophrenia

La esquizofrenia es un desorden psiquiátrico caracterizado por alteraciones en el pensamiento y en la capacidad de respuesta emocional. Comprende una gran variedad de síntomas, sin embargo, no está claro que todos compartan un sustrato neurológico común. Por ello, el objetivo de esta Tesis Doctoral es desarrollar un marco de referencia desde la perspectiva de la Teoría de Redes Complejas para investigar las interacciones neurales alteradas de la esquizofrenia haciendo uso de la señal electroencefalográfica. Así, dos bases de datos independientes de registros electroencefalográficos fueron registras durante una tarea cognitiva. Nuestros hallazgos son consistentes con estudios previos al tiempo que muestran una hiperactivación del intervalo de estímulo previa a una reorganización neural disminuida durante la cognición, principalmente asociado a caminos neurales secundarios. Los hallazgos de esta Tesis ponen de manifiesto la gran heterogeneidad de la esquizofrenia, posiblemente asociada a la existencia de subgrupos dentro de la misma.Departamento de Teoría de la Señal y Comunicaciones e Ingeniería TelemáticaDoctorado en Tecnologías de la Información y las Telecomunicacione

`The frozen accident' as an evolutionary adaptation: A rate distortion theory perspective on the dynamics and symmetries of genetic coding mechanisms

We survey some interpretations and related issues concerning the frozen hypothesis due to F. Crick and how it can be explained in terms of several natural mechanisms involving error correction codes, spin glasses, symmetry breaking and the characteristic robustness of genetic networks. The approach to most of these questions involves using elements of Shannon's rate distortion theory incorporating a semantic system which is meaningful for the relevant alphabets and vocabulary implemented in transmission of the genetic code. We apply the fundamental homology between information source uncertainty with the free energy density of a thermodynamical system with respect to transcriptional regulators and the communication channels of sequence/structure in proteins. This leads to the suggestion that the frozen accident may have been a type of evolutionary adaptation