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.

Synchronization reveals topological scales in complex networks

We study the relationship between topological scales and dynamic time scales in complex networks. The analysis is based on the full dynamics towards synchronization of a system of coupled oscillators. In the synchronization process, modular structures corresponding to well-defined communities of nodes emerge in different time scales, ordered in a hierarchical way. The analysis also provides a useful connection between synchronization dynamics, complex networks topology, and spectral graph analysis.

Self-organized criticality and synchronization in a coupled map lattice model of integrate-and-fire oscillators

We introduce two coupled map lattice models with nonconservative interactions and a continuous nonlinear driving. Depending on both the degree of conservation and the convexity of the driving we find different behaviors, ranging from self-organized criticality, in the sense that the distribution of events (avalanches) obeys a power law, to a macroscopic synchronization of the population of oscillators, with avalanches of the size of the system.

Mechanisms of synchronization and pattern formation in a lattice of pulse-coupled oscillators

We analyze the physical mechanisms leading either to synchronization or to the formation of spatiotemporal patterns in a lattice model of pulse-coupled oscillators. In order to make the system tractable from a mathematical point of view we study a one-dimensional ring with unidirectional coupling. In such a situation, exact results concerning the stability of the fixed of the dynamic evolution of the lattice can be obtained. Furthermore, we show that this stability is the responsible for the different behaviors.

Synchronization, diversity, and topology of networks of integrate and fire oscillators

We study synchronization dynamics of a population of pulse-coupled oscillators. In particular, we focus our attention on the interplay between topological disorder and synchronization features of networks. First, we analyze synchronization time T in random networks, and find a scaling law which relates T to network connectivity. Then, we compare synchronization time for several other topological configurations, characterized by a different degree of randomness. The analysis shows that regular lattices perform better than a disordered network. This fact can be understood by considering the variability in the number of links between two adjacent neighbors. This phenomenon is equivalent to having a nonrandom topology with a distribution of interactions and it can be removed by an adequate local normalization of the couplings.

Tuning synchronization of integrate-and-fire oscillators through mobility

We analyze the emergence of synchronization in a population of moving integrate-and-fire oscillators. Oscillators, while moving on a plane, interact with their nearest neighbor upon firing time. We discover a nonmonotonic dependence of the synchronization time on the velocity of the agents. Moreover, we find that mechanisms that drive synchronization are different for different dynamical regimes. We report the extreme situation where an interplay between the time scales involved in the dynamical processes completely inhibits the achievement of a coherent state. We also provide estimators for the transitions between the different regimes.

Remote Synchronization Reveals Network Symmetries and Functional Modules

We study a Kuramoto model in which the oscillators are associated with the nodes of a complex network and the interactions include a phase frustration, thus preventing full synchronization. The system organizes into a regime of remote synchronization where pairs of nodes with the same network symmetry are fully synchronized, despite their distance on the graph. We provide analytical arguments to explain this result, and we show how the frustration parameter affects the distribution of phases. An application to brain networks suggests that anatomical symmetry plays a role in neural synchronization by determining correlated functional modules across distant locations.

Mutual control of membrane fission and fusion proteins.

Membrane fusion and fission are antagonistic reactions controlled by different proteins. Dynamins promote membrane fission by GTP-driven changes of conformation and polymerization state, while SNAREs fuse membranes by forming complexes between t- and v-SNAREs from apposed vesicles. Here, we describe a role of the dynamin-like GTPase Vps1p in fusion of yeast vacuoles. Vps1p forms polymers that couple several t-SNAREs together. At the onset of fusion, the SNARE-activating ATPase Sec18p/NSF and the t-SNARE depolymerize Vps1p and release it from the membrane. This activity is independent of the SNARE coactivator Sec17p/alpha-SNAP and of the v-SNARE. Vps1p release liberates the t-SNAREs for initiating fusion and at the same time disrupts fission activity. We propose that reciprocal control between fusion and fission components exists, which may prevent futile cycles of fission and fusion.

Mutual trust and cooperation in the evolutionary hawks-doves game

Using a new dynamical network model of society in which pairwise interactions are weighted according to mutual satisfaction, we show that cooperation is the norm in the hawks-doves game when individuals are allowed to break ties with undesirable neighbors and to make new acquaintances in their extended neighborhood. Moreover, cooperation is robust with respect to rather strong strategy perturbations. We also discuss the empirical structure of the emerging networks, and the reasons that allow cooperators to thrive in the population. Given the metaphorical importance of this game for social interaction, this is an encouraging positive result as standard theory for large mixing populations prescribes that a certain fraction of defectors must always exist at equilibrium.

Increased eeg synchronization in schizophrenia patients by the glutathione precursor, n-acetyl-cysteine

Background: Glutathione (GSH) dysregulation at the gene, protein and functional levels observed in schizophrenia patients, and schizophrenia-like anomalies in GSH deficit experimental models, suggest that genetic glutathione synthesis impairments represent one major risk factor for the disease (Do et al., 2009). In a randomized, double blind, placebo controlled, add-on clinical trial of 140 patients, the GSH precursor N-Acetyl-Cysteine (NAC, 2 g/day, 6 months) significantly improved the negative symptoms and reduced side-effects due to antipsychotics (Berk et al., 2008). In a subset of patients (n=7), NAC (2 g/day, 2 months, cross-over design) also improved auditory evoked potentials, the NMDAdependent mismatch negativity (Lavoie et al, 2008). Methods: To determine whether increased GSH levels would modulate the topography of functional brain connectivity, we applied a multivariate phase synchronization (MPS) estimator (Knyazeva et al, 2008) to dense-array EEGs recorded during rest with eyes closed at the protocol onset, the point of crossover, and at its end. Phase synchronization phenomena are appealing because they can be associated to synchronized phases while the amplitudes stay uncorrelated. MPS measures the degree of interactions among the recorded neuronal oscillators by quantifiying to what extent they behave like a macro-oscillator (i.e. the oscillators are phase synchronous). To assess the whole-head synchronization topography, we computed the MPS sensor-wise over the cluster of locations defined by the sensor itself and he surrounding ones belonging to its second-order neighborhood (Carmeli et al, 2005). Such a cluster spans about 12 cm on average. Abstracts 245 Results: The whole-head imaging revealed a specific synchronization landscape in NAC compared to placebo condition. In particular, NAC increased MPS over frontal and left temporal regions in a frequency-specific manner. Importantly, the topography and direction of MPS changes were similar and robust in all 7 patients. Moreover, these changes correlated with the changes in the Liddle's score of disorganization (Liddle, 1987) thus linking EEG synchronization to the improvement of clinical picture. Discussion: The data suggest an important pathway towards new therapeutic strategies that target GSH dysregulation in schizophrenia. They also show the utility of MPS mapping as a marker of treatment efficacy.

Identifying a mutual attending frame: a pilot study of gaze interactions between therapist and couple.

Refering to systems theory, we identify a supraindividual property in interactions between therapist and couple. We use gaze directions to describe the partners' behaviors and label this property the "mutual attending frame." We propose a procedure to observe triadic interactions in a consultation setting and a method to measure mutual attending. The method is illustrated by the data analysis of two triads contrasted on measures of therapeutic alliance. We discuss the potential of this method for the description of the interactive aspects of the therapeutic alliance.

Fluorodeoxyuridine mediated cell cycle synchronization in S-phase increases the Auger radiation cell killing with 125I-iododeoxyuridine.

Aim: 125I-iododeoxyuridine is a potential Auger radiation therapy agent. Its incorporation in DNA of proliferating cells is enhanced by fluorodeoxyuridine. Here, we evaluated therapeutic activities of 125I-iododeoxyuridine in an optimized fluorodeoxyuridine pre-treatment inducing S-phase synchronization. Methods: After S-phase synchronization by fluorodeoxyuridine, cells were treated with 125I-iododeoxyuridine. Apoptosis analysis and S-phase synchronization were studied by flow cytometry. Cell survival was determined by colony-forming assay. Based on measured growth parameters, the number of decays per cell that induced killing was extrapolated. Results: Treatment experiments showed that 72 to 91% of synchronized cells were killed after 0.8 and 8 kBq/ml 125I-iododeoxyuridine incubation, respectively. In controls, only 8 to 38% of cells were killed by corresponding 125I-iododeoxyuridine activities alone and even increasing the activity to 80 kBq/ml gave only 42 % killing. Duplicated treatment cycles or repeated fluorodeoxyuridine pre-treatment allowed enhancing cell killing to >95 % at 8 kBq/ml 125I-iododeoxyuridine. About 50 and 160 decays per S-phase cells in controls and S-phase synchronization, respectively, were responsible for the observed cell killing at 0.8 kBq/ml radio-iododeoxyuridine. Conclusion: These data show the successful application of fluorodeoxyuridine that provided increased 125I-iododeoxyuridine Auger radiation cell killing efficacy through S-phase synchronization and high DNA incorporation of radio-iododeoxyuridine.

Application of the Mutual Information Minimization to speaker recognition / identification improvement

In this paper we propose the inversion of nonlinear distortions in order to improve the recognition rates of a speaker recognizer system. We study the effect of saturations on the test signals, trying to take into account real situations where the training material has been recorded in a controlled situation but the testing signals present some mismatch with the input signal level (saturations). The experimental results for speaker recognition shows that a combination of several strategies can improve the recognition rates with saturated test sentences from 80% to 89.39%, while the results with clean speech (without saturation) is 87.76% for one microphone, and for speaker identification can reduce the minimum detection cost function with saturated test sentences from 6.42% to 4.15%, while the results with clean speech (without saturation) is 5.74% for one microphone and 7.02% for the other one.

Post-switching beta synchronization reveals concomitant sensory reafferences and active inhibition processes

It is known that post-movement beta synchronization (PMBS) is involved both in active inhibition and in sensory reafferences processes. The aim of this study was examine the temporal and spatial dynamics of the PMBS involved during multi-limb coordination task. We investigated post-switching beta synchronization (assigned PMBS) using time-frequency and source estimations analyzes. Participants (n = 17) initiated an auditory-paced bimanual tapping. After a 1500 ms preparatory period, an imperative stimulus required to either selectively stop the left while maintaining the right unimanual tapping (Switch condition: SWIT) or to continue the bimanual tapping (Continue condition: CONT). PMBS significantly increased in SWIT compared to CONT with maximal difference within right central region in broad-band 14âeuro"30 Hz and within left central region in restricted-band 22âeuro"26 Hz. Source estimations localized these effects within right pre-frontal cortex and left parietal cortex, respectively. A negative correlation showed that participants with a low percentage of errors in SWIT had a large PMBS amplitude within right parietal and frontal cortices. This study shows for the first time simultaneous PMBS with distinct functions in different brain regions and frequency ranges. The left parietal PMBS restricted to 22âeuro"26 Hz could reflect the sensory reafferences of the right hand tapping disrupted by the switching. In contrast, the right pre-frontal PMBS in a broad-band 14âeuro"30 Hz is likely reflecting the active inhibition of the left hand stopped. Finally, correlations between behavioral performance and the magnitude of the PMBS suggest that beta oscillations can be viewed as a marker of successful active inhibition.