The Kuramoto model: A simple paradigm for synchronization phenomena

Synchronization phenomena in large populations of interacting elements are the subject of intense research efforts in physical, biological, chemical, and social systems. A successful approach to the problem of synchronization consists of modeling each member of the population as a phase oscillator. In this review, synchronization is analyzed in one of the most representative models of coupled phase oscillators, the Kuramoto model. A rigorous mathematical treatment, specific numerical methods, and many variations and extensions of the original model that have appeared in the last few years are presented. Relevant applications of the model in different contexts are also included

Shape mode analysis exposes movement patterns in biology: flagella and flatworms as case studies

We illustrate shape mode analysis as a simple, yet powerful technique to concisely describe complex biological shapes and their dynamics. We characterize undulatory bending waves of beating flagella and reconstruct a limit cycle of flagellar oscillations, paying particular attention to the periodicity of angular data. As a second example, we analyze non-convex boundary outlines of gliding flatworms, which allows us to expose stereotypic body postures that can be related to two different locomotion mechanisms. Further, shape mode analysis based on principal component analysis allows to discriminate different flatworm species, despite large motion-associated shape variability. Thus, complex shape dynamics is characterized by a small number of shape scores that change in time. We present this method using descriptive examples, explaining abstract mathematics in a graphic way.Comment: 20 pages, 6 figures, accepted for publication in PLoS On

On the Evolutionary Co-Adaptation of Morphology and Distributed Neural Controllers in Adaptive Agents

The attempt to evolve complete embodied and situated artificial creatures in which both morphological and control characteristics are adapted during the evolutionary process has been and still represents a long term goal key for the artificial life and the evolutionary robotics community. Loosely inspired by ancient biological organisms which are not provided with a central nervous system and by simple organisms such as stick insects, this thesis proposes a new genotype encoding which allows development and evolution of mor- phology and neural controller in artificial agents provided with a distributed neural network. In order to understand if this kind of network is appropriate for the evolution of non trivial behaviours in artificial agents, two experiments (description and results will be shown in chapter 3) in which evolution was applied only to the controller’s parameters were performed. The results obtained in the first experiment demonstrated how distributed neural networks can achieve a good level of organization by synchronizing the output of oscillatory elements exploiting acceleration/deceleration mechanisms based on local interactions. In the second experiment few variants on the topology of neural architecture were introduced. Results showed how this new control system was able to coordinate the legs of a simulated hexapod robot on two different gaits on the basis of the external circumstances. After this preliminary and successful investigation, a new genotype encoding able to develop and evolve artificial agents with no fixed morphology and with a distributed neural controller was proposed. A second set of experiments was thus performed and the results obtained confirmed both the effectiveness of genotype encoding and the ability of distributed neural network to perform the given task. The results have also shown the strength of genotype both in generating a wide range of different morphological structures and in favouring a direct co-adaptation between neural controller and morphology during the evolutionary process. Furthermore the simplicity of the proposed model has showed the effective role of specific elements in evolutionary experiments. In particular it has demonstrated the importance of the environment and its complexity in evolving non-trivial behaviours and also how adding an independent component to the fitness function could help the evolutionary process exploring a larger space solutions avoiding a premature convergence towards suboptimal solutions

Regular and stochastic behavior of Parkinsonian pathological tremor signals

Regular and stochastic behavior in the time series of Parkinsonian pathological tremor velocity is studied on the basis of the statistical theory of discrete non-Markov stochastic processes and flicker-noise spectroscopy. We have developed a new method of analyzing and diagnosing Parkinson's disease (PD) by taking into consideration discreteness, fluctuations, long- and short-range correlations, regular and stochastic behavior, Markov and non-Markov effects and dynamic alternation of relaxation modes in the initial time signals. The spectrum of the statistical non-Markovity parameter reflects Markovity and non-Markovity in the initial time series of tremor. The relaxation and kinetic parameters used in the method allow us to estimate the relaxation scales of diverse scenarios of the time signals produced by the patient in various dynamic states. The local time behavior of the initial time correlation function and the first point of the non-Markovity parameter give detailed information about the variation of pathological tremor in the local regions of the time series. The obtained results can be used to find the most effective method of reducing or suppressing pathological tremor in each individual case of a PD patient. Generally, the method allows one to assess the efficacy of the medical treatment for a group of PD patients.Comment: 39 pages, 10 figures, 1 table Physica A, in pres

Complex and Adaptive Dynamical Systems: A Primer

An thorough introduction is given at an introductory level to the field of quantitative complex system science, with special emphasis on emergence in dynamical systems based on network topologies. Subjects treated include graph theory and small-world networks, a generic introduction to the concepts of dynamical system theory, random Boolean networks, cellular automata and self-organized criticality, the statistical modeling of Darwinian evolution, synchronization phenomena and an introduction to the theory of cognitive systems. It inludes chapter on Graph Theory and Small-World Networks, Chaos, Bifurcations and Diffusion, Complexity and Information Theory, Random Boolean Networks, Cellular Automata and Self-Organized Criticality, Darwinian evolution, Hypercycles and Game Theory, Synchronization Phenomena and Elements of Cognitive System Theory.Comment: unformatted version of the textbook; published in Springer, Complexity Series (2008, second edition 2010

Global analysis of phase locking in gene expression during cell cycle: the potential in network modeling

<p>Abstract</p> <p>Background</p> <p>In nonlinear dynamic systems, synchrony through oscillation and frequency modulation is a general control strategy to coordinate multiple modules in response to external signals. Conversely, the synchrony information can be utilized to infer interaction. Increasing evidence suggests that frequency modulation is also common in transcription regulation.</p> <p>Results</p> <p>In this study, we investigate the potential of phase locking analysis, a technique to study the synchrony patterns, in the transcription network modeling of time course gene expression data. Using the yeast cell cycle data, we show that significant phase locking exists between transcription factors and their targets, between gene pairs with prior evidence of physical or genetic interactions, and among cell cycle genes. When compared with simple correlation we found that the phase locking metric can identify gene pairs that interact with each other more efficiently. In addition, it can automatically address issues of arbitrary time lags or different dynamic time scales in different genes, without the need for alignment. Interestingly, many of the phase locked gene pairs exhibit higher order than 1:1 locking, and significant phase lags with respect to each other. Based on these findings we propose a new phase locking metric for network reconstruction using time course gene expression data. We show that it is efficient at identifying network modules of focused biological themes that are important to cell cycle regulation.</p> <p>Conclusions</p> <p>Our result demonstrates the potential of phase locking analysis in transcription network modeling. It also suggests the importance of understanding the dynamics underlying the gene expression patterns.</p

Use of Multiscale Entropy to Characterize Fetal Autonomic Development

The idea that uterine environment and adverse events during fetal development could increase the chances of the diseases in adulthood was first published by David Barker in 1998. Since then, investigators have been employing several methods and methodologies for studying and characterizing the ontological development of the fetus, e.g., fetal movement, growth and cardiac metrics. Even with most recent and developed methods such as fetal magnetocardiography (fMCG), investigators are continuously challenged to study fetal development; the fetus is inaccessible. Finding metrics that realize the full capacity of characterizing fetal ontological development remains a technological challenge. In this thesis, the use and value of multiscale entropy to characterize fetal maturation across third trimester of gestation is studied. Using multiscale entropy obtained from participants of a clinical trial, we show that MSE can characterize increasing complexity due to maturation in the fetus, and can distinguish a growing and developing fetal system from a mature system where loss of irregularity is due to compromised complexity from increasing physiologic load. MSE scales add a nonlinear metric that seems to accurately reflect the ontological development of the fetus and hold promise for future use to investigate the effects of maternal stress, intrauterine growth restriction, or predict risk for sudden infant death syndrome

Interaction dynamics and autonomy in cognitive systems

The concept of autonomy is of crucial importance for understanding life and cognition. Whereas cellular and organismic autonomy is based in the self-production of the material infrastructure sustaining the existence of living beings as such, we are interested in how biological autonomy can be expanded into forms of autonomous agency, where autonomy as a form of organization is extended into the behaviour of an agent in interaction with its environment (and not its material self-production). In this thesis, we focus on the development of operational models of sensorimotor agency, exploring the construction of a domain of interactions creating a dynamical interface between agent and environment. We present two main contributions to the study of autonomous agency: First, we contribute to the development of a modelling route for testing, comparing and validating hypotheses about neurocognitive autonomy. Through the design and analysis of specific neurodynamical models embedded in robotic agents, we explore how an agent is constituted in a sensorimotor space as an autonomous entity able to adaptively sustain its own organization. Using two simulation models and different dynamical analysis and measurement of complex patterns in their behaviour, we are able to tackle some theoretical obstacles preventing the understanding of sensorimotor autonomy, and to generate new predictions about the nature of autonomous agency in the neurocognitive domain. Second, we explore the extension of sensorimotor forms of autonomy into the social realm. We analyse two cases from an experimental perspective: the constitution of a collective subject in a sensorimotor social interactive task, and the emergence of an autonomous social identity in a large-scale technologically-mediated social system. Through the analysis of coordination mechanisms and emergent complex patterns, we are able to gather experimental evidence indicating that in some cases social autonomy might emerge based on mechanisms of coordinated sensorimotor activity and interaction, constituting forms of collective autonomous agency