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

Adaptive dynamical networks

It is a fundamental challenge to understand how the function of a network is related to its structural organization. Adaptive dynamical networks represent a broad class of systems that can change their connectivity over time depending on their dynamical state. The most important feature of such systems is that their function depends on their structure and vice versa. While the properties of static networks have been extensively investigated in the past, the study of adaptive networks is much more challenging. Moreover, adaptive dynamical networks are of tremendous importance for various application fields, in particular, for the models for neuronal synaptic plasticity, adaptive networks in chemical, epidemic, biological, transport, and social systems, to name a few. In this review, we provide a detailed description of adaptive dynamical networks, show their applications in various areas of research, highlight their dynamical features and describe the arising dynamical phenomena, and give an overview of the available mathematical methods developed for understanding adaptive dynamical networks

Multiplex Limited Penetrable Horizontal Visibility Graph from EEG Signals for Driver Fatigue Detection

This work was supported by National Natural Science Foundation of China under Grant Nos. 61473203, 61873181 and the Natural Science Foundation of Tianjin, China under Grant No. 16JCYBJC18200.Peer reviewedPostprin

Modelling and quantifying brain connectivity and dynamics with applications in aging and ADHD

Human brain is a complex organ and made up of integrative networks encompassing a large number of regions. These regions communicate with each other to share information involved in complex cognitive processes. Functional connectivity (FC) represents the level of synchronization between different brain regions/networks. Studying functional interactions of the brain creates a platform for understanding functional architecture of the brain as an integrative network and has implications for understanding human cognition. Furthermore, there is evidence that FC patterns are sensitive to different diseases. In addition, age is a significant determinant of intra-/inter-individual variability in the FC patterns. Therefore, key aims for the studies included in this thesis were to apply and develop novel resting-state FC methodologies, with applications in healthy aging and ADHD. Indeed, measures of the brain’s FC may serve as a useful tool to diagnose and predict the course of disease, and useful in developing individualized therapies. Age- or disease-related alterations in the FC could reflect a multitude of factors, including changes in structural connectivity. However, we still have limited knowledge of the emergence of brain dynamics from the underlying anatomy. The interplay between the brain’s structure and dynamics underlies all brain functions. Therefore, in the last study we focused on the systematic modeling of the brain network dynamics. Large-scale computational models are uniquely suited to address difficult questions related to the role of brain’s structural network in shaping functional interactions. In addition, computational modeling of the brain enables us to test different hypotheses without any experimental complication while it provides us with a platform for improving our understanding of different brain mechanisms. A new macroscopic computational model of the brain oscillations for resting-state fMRI was introduced in this thesis, which outperforms previous model in the same class. Then, the effects of malfunctions in different brain regions were simulated and subsequently predicted perturbation patterns were recruited for local vulnerability mapping as well as quantification of hazard rates induced after perturbing any brain regio

Pacemaker Heterogeneity in the Suprachiasmatic Nucleus: Origins and Network Implications

In mammals, the suprachiasmatic nuclei: SCN) in the ventral hypothalamus function as a circadian pacemaker, controlling daily rhythms in behavior and physiology. Together the SCN contain approximately 20,000 neurons that maintain rhythms in firing rate and gene expression. Previous studies led to the assumption that single SCN neurons are capable of self-sustained circadian rhythms. Whether and which SCN neurons can maintain cell-autonomous daily oscillations has not been extensively tested. We measured PERIOD2::LUCIFERASE expression in isolated SCN neurons over multiple days to determine if all SCN neurons were circadian. We then examined neuropeptide content of the recorded neurons. We found that when isolated physically or with a blocker of cell-cell communication, SCN neurons expressed a range of circadian periods, amplitudes, and abilities to sustain cycling. Surprisingly, most cells were sloppy oscillators, switching from rhythmic to arrhythmic or vice versa throughout their lifetime. We also found no evidence for a class of circadian-pacemaker neurons in the SCN based on neuropeptide expression. We conclude that while all SCN neurons are capable of cell-autonomous rhythms, they are intrinsically sloppy with network interactions dramatically increasing the number of circadian neurons. We next used a mathematical model of the mammalian circadian clock to determine whether rates of gene transcription, protein translation, degradation or phosphorylation might explain the ability of SCN neurons to switch between circadian and arrhythmic behaviors. We found that rhythmicity was more sensitive to the rates of protein translation and degradation. We next tested what effect having neurons with different intrinsic circadian behaviors would have on population synchrony. We simulated cells of known circadian phenotypes: e.g. arrhythmic, damped, or self-sustained) in a pattern defined by small-world network properties and varied the positions and proportions of each oscillator type. We found that increasing the number of damped oscillators or placing them in highly connected locations within the network both augmented the rate at which the network synchronized. We conclude that the SCN likely benefit from a heterogeneous population of oscillators, especially when recovering from an environmental perturbation that causes desynchrony. Finally, we generated and characterized two independent lines of transgenic mice to test the role of vasoactive intestinal polypeptide: VIP) neurons in circadian rhythmicity. These mice express Yellow Fluorescent Protein: YFP) under the control of a fragment of the VIP promoter in VIP neurons of the SCN, neocortex, olfactory bulbs, and enteric nervous system. We crossed these mice to generate a line in which VIP neurons are targeted for deletion using Cre-mediated recombination upon addition of tamoxifen. We observed successful deletion of VIP neurons in cultured SCN explants, but have no evidence to date for deletion of SCN neurons in vivo using a variety of protocols. We conclude that our construct is faithfully expressed in VIP neurons and that in vitro experiments show promising results for further study

Opinions and Outlooks on Morphological Computation

Morphological Computation is based on the observation that biological systems seem to carry out relevant computations with their morphology (physical body) in order to successfully interact with their environments. This can be observed in a whole range of systems and at many different scales. It has been studied in animals – e.g., while running, the functionality of coping with impact and slight unevenness in the ground is "delivered" by the shape of the legs and the damped elasticity of the muscle-tendon system – and plants, but it has also been observed at the cellular and even at the molecular level – as seen, for example, in spontaneous self-assembly. The concept of morphological computation has served as an inspirational resource to build bio-inspired robots, design novel approaches for support systems in health care, implement computation with natural systems, but also in art and architecture. As a consequence, the field is highly interdisciplinary, which is also nicely reflected in the wide range of authors that are featured in this e-book. We have contributions from robotics, mechanical engineering, health, architecture, biology, philosophy, and others

Stochastic and complex dynamics in mesoscopic brain networks

The aim of this thesis is to deepen into the understanding of the mechanisms responsible for the generation of complex and stochastic dynamics, as well as emerging phenomena, in the human brain. We study typical features from the mesoscopic scale, i.e., the scale in which the dynamics is given by the activity of thousands or even millions of neurons. At this scale the synchronous activity of large neuronal populations gives rise to collective oscillations of the average voltage potential. These oscillations can easily be recorded using electroencephalography devices (EEG) or measuring the Local Field Potentials (LFPs). In Chapter 5 we show how the communication between two cortical columns (mesoscopic structures) can be mediated efficiently by a microscopic neural network. We use the synchronization of both cortical columns as a probe to ensure that an effective communication is established between the three neural structures. Our results indicate that there are certain dynamical regimes from the microscopic neural network that favor the correct communication between the cortical columns: therefore, if the LFP frequency of the neural network is of around 40Hz, the synchronization between the cortical columns is more robust compared to the situation in which the neural network oscillates at a lower frequency (10Hz). However, microscopic topological characteristics of the network also influence communication, being a small-world structure the one that best promotes the synchronization of the cortical columns. Finally, this Chapter shows how the mediation exerted by the neural network cannot be substituted by the average of its activity, that is, the dynamic properties of the microscopic neural network are essential for the proper transmission of information between all neural structures. The oscillatory brain electrical activity is largely dependent on the interplay between excitation and inhibition. In Chapter 6 we study how groups of cortical columns show complex patterns of cortical excitation and inhibition taking into account their topological features and the strength of their couplings. These cortical columns segregate between those dominated by excitation and those dominated by inhibition, affecting the synchronization properties of networks of cortical columns. In Chapter 7 we study a dynamic regime by which complex patterns of synchronization between chaotic oscillators appear spontaneously in a network. We show what conditions must a set of coupled dynamical systems fulfill in order to display heterogeneity in synchronization. Therefore, our results are related to the complex phenomenon of synchronization in the brain, which is a focus of study nowadays. Finally, in Chapter 8 we study the ability of the brain to compute and process information. The novelty here is our use of complex synchronization in the brain in order to implement basic elements of Boolean computation. In this way, we show that the partial synchronization of the oscillations in the brain establishes a code in terms of synchronization / non-synchronization (1/0, respectively), and thus all simple Boolean functions can be implemented (AND, OR, XOR, etc.). We also show that complex Boolean functions, such as a flip-flop memory, can be constructed in terms of states of dynamic synchronization of brain oscillations.L'objectiu d'aquesta Tesi és aprofundir en la comprensió dels mecanismes responsables de la generació de dinàmica complexa i estocàstica, així com de fenòmens emergents, en el cervell humà. Estudiem la fenomenologia característica de l'escala mesoscòpica, és a dir, aquella en la que la dinàmica característica ve donada per l'activitat de milers de neurones. En aquesta escala l'activitat síncrona de grans poblacions neuronals dóna lloc a un fenomen col·lectiu pel qual es produeixen oscil·lacions del seu potencial mitjà. Aquestes oscil·lacions poden ser fàcilment enregistrades mitjançant aparells d'electroencefalograma (EEG) o enregistradors de Potencials de Camp Local (LFP). En el Capítol 5 mostrem com la comunicació entre dos columnes corticals (estructures mesoscòpiques) pot ser conduïda de forma eficient per una xarxa neuronal microscòpica. De fet, emprem la sincronització de les dues columnes corticals per comprovar que s'ha establert una comunicació efectiva entre les tres estructures neuronals. Els resultats indiquen que hi ha règims dinàmics de la xarxa neuronal microscòpica que afavoreixen la correcta comunicació entre les columnes corticals: si la freqüència típica de LFP a la xarxa neuronal està al voltant dels 40Hz la sincronització entre les columnes corticals és més robusta que a una menor freqüència (10Hz). La topologia de la xarxa microscòpica també influeix en la comunicació, essent una estructura de tipus món petit (small-world) la que més afavoreix la sincronització. Finalment, la mediació de xarxa neuronal no pot ser substituïda per la mitjana de la seva activitat, és a dir, les propietats dinàmiques microscòpiques són imprescindibles per a la correcta transmissió d'informació entre totes les escales cerebrals. L'activitat elèctrica oscil·latòria cerebral ve donada en gran mesura per la interacció entre excitació i inhibició neuronal. En el Capítol 6 estudiem com grups de columnes corticals mostren patrons complexos d'excitació i inhibició segons quina sigui la seva topologia i d'acoblament. D'aquesta manera les columnes corticals se segreguen entre aquelles dominades per l'excitació i aquelles dominades per la inhibició, influint en les capacitats de sincronització de xarxes de columnes corticals. En el Capítol 7 estudiem un règim dinàmic segons el qual patrons complexos de sincronització apareixen espontàniament en xarxes d'oscil·ladors caòtics. Mostrem quines condicions s'han de donar en un conjunt de sistemes dinàmics acoblats per tal de mostrar heterogeneïtat en la sincronització, és a dir, coexistència de sincronitzacions. D'aquesta manera relacionem els nostres resultats amb el fenomen de sincronització complexa en el cervell. Finalment, en el Capítol 8 estudiem com el cervell computa i processa informació. La novetat aquí és l'ús que fem de la sincronització complexa de columnes corticals per tal d'implementar elements bàsics de computació Booleana. Mostrem com la sincronització parcial de les oscil·lacions cerebrals estableix un codi neuronal en termes de sincronització/no sincronització (1/0, respectivament) amb el qual totes les funcions Booleanes simples poden ésser implementades (AND, OR, XOR, etc). Mostrem, també, com emprant xarxes mesoscòpiques extenses les capacitats de computació creixen proporcionalment. Així funcions Booleanes complexes, com una memòria del tipus flip-flop, pot ésser construïda en termes d'estats de sincronització dinàmica d'oscil·lacions cerebrals.Postprint (published version