Hierarchy and Polysynchrony in an adaptive network

We describe a simple adaptive network of coupled chaotic maps. The network reaches a stationary state (frozen topology) for all values of the coupling parameter, although the dynamics of the maps at the nodes of the network can be non-trivial. The structure of the network shows interesting hierarchical properties and in certain parameter regions the dynamics is polysynchronous: nodes can be divided in differently synchronized classes but contrary to cluster synchronization, nodes in the same class need not be connected to each other. These complicated synchrony patterns have been conjectured to play roles in systems biology and circuits. The adaptive system we study describes ways whereby this behaviour can evolve from undifferentiated nodes.Comment: 13 pages, 17 figure

Bifurcations in the Lozi map

We study the presence in the Lozi map of a type of abrupt order-to-order and order-to-chaos transitions which are mediated by an attractor made of a continuum of neutrally stable limit cycles, all with the same period.Comment: 17 pages, 12 figure

Coexistence of periods in a bisecting bifurcation

The inner structure of the attractor appearing when the Varley-Gradwell-Hassell population model bifurcates from regular to chaotic behaviour is studied. By algebraic and geometric arguments the coexistence of a continuum of neutrally stable limit cycles with different periods in the attractor is explained.Comment: 13 pages, 5 figure

Families of piecewise linear maps with constant Lyapunov exponent

We consider families of piecewise linear maps in which the moduli of the two slopes take different values. In some parameter regions, despite the variations in the dynamics, the Lyapunov exponent and the topological entropy remain constant. We provide numerical evidence of this fact and we prove it analytically for some special cases. The mechanism is very different from that of the logistic map and we conjecture that the Lyapunov plateaus reflect arithmetic relations between the slopes.Comment: 26 pages, 13 figure

Emergence of hierarchical networks and polysynchronous behaviour in simple adaptive systems

We describe the dynamics of a simple adaptive network. The network architecture evolves to a number of disconnected components on which the dynamics is characterized by the possibility of differently synchronized nodes within the same network (polysynchronous states). These systems may have implications for the evolutionary emergence of polysynchrony and hierarchical networks in physical or biological systems modeled by adaptive networks.Comment: 4 pages, 4 figure

Dynamics of a map with power-law tail

We analyze a one-dimensional piecewise continuous discrete model proposed originally in studies on population ecology. The map is composed of a linear part and a power-law decreasing piece, and has three parameters. The system presents both regular and chaotic behavior. We study numerically and, in part, analytically different bifurcation structures. Particularly interesting is the description of the abrupt transition order-to-chaos mediated by an attractor made of an infinite number of limit cycles with only a finite number of different periods. It is shown that the power-law piece in the map is at the origin of this type of bifurcation. The system exhibits interior crises and crisis-induced intermittency.Comment: 28 pages, 17 figure

Large-Scale Cortical Dynamics of Sleep Slow Waves

Slow waves constitute the main signature of sleep in the electroencephalogram (EEG). They reflect alternating periods of neuronal hyperpolarization and depolarization in cortical networks. While recent findings have demonstrated their functional role in shaping and strengthening neuronal networks, a large-scale characterization of these two processes remains elusive in the human brain. In this study, by using simultaneous scalp EEG and intracranial recordings in 10 epileptic subjects, we examined the dynamics of hyperpolarization and depolarization waves over a large extent of the human cortex. We report that both hyperpolarization and depolarization processes can occur with two different characteristic time durations which are consistent across all subjects. For both hyperpolarization and depolarization waves, their average speed over the cortex was estimated to be approximately 1 m/s. Finally, we characterized their propagation pathways by studying the preferential trajectories between most involved intracranial contacts. For both waves, although single events could begin in almost all investigated sites across the entire cortex, we found that the majority of the preferential starting locations were located in frontal regions of the brain while they had a tendency to end in posterior and temporal regions

Human Gamma Oscillations during Slow Wave Sleep

Neocortical local field potentials have shown that gamma oscillations occur spontaneously during slow-wave sleep (SWS). At the macroscopic EEG level in the human brain, no evidences were reported so far. In this study, by using simultaneous scalp and intracranial EEG recordings in 20 epileptic subjects, we examined gamma oscillations in cerebral cortex during SWS. We report that gamma oscillations in low (30–50 Hz) and high (60–120 Hz) frequency bands recurrently emerged in all investigated regions and their amplitudes coincided with specific phases of the cortical slow wave. In most of the cases, multiple oscillatory bursts in different frequency bands from 30 to 120 Hz were correlated with positive peaks of scalp slow waves (“IN-phase” pattern), confirming previous animal findings. In addition, we report another gamma pattern that appears preferentially during the negative phase of the slow wave (“ANTI-phase” pattern). This new pattern presented dominant peaks in the high gamma range and was preferentially expressed in the temporal cortex. Finally, we found that the spatial coherence between cortical sites exhibiting gamma activities was local and fell off quickly when computed between distant sites. Overall, these results provide the first human evidences that gamma oscillations can be observed in macroscopic EEG recordings during sleep. They support the concept that these high-frequency activities might be associated with phasic increases of neural activity during slow oscillations. Such patterned activity in the sleeping brain could play a role in off-line processing of cortical networks

Incidence, clinical characteristics and management of inflammatory bowel disease in Spain: large-scale epidemiological study

(1) Aims: To assess the incidence of inflammatory bowel disease (IBD) in Spain, to describe the main epidemiological and clinical characteristics at diagnosis and the evolution of the disease, and to explore the use of drug treatments. (2) Methods: Prospective, population-based nationwide registry. Adult patients diagnosed with IBD—Crohn’s disease (CD), ulcerative colitis (UC) or IBD unclassified (IBD-U)—during 2017 in Spain were included and were followed-up for 1 year. (3) Results: We identified 3611 incident cases of IBD diagnosed during 2017 in 108 hospitals covering over 22 million inhabitants. The overall incidence (cases/100, 000 person-years) was 16 for IBD, 7.5 for CD, 8 for UC, and 0.5 for IBD-U; 53% of patients were male and median age was 43 years (interquartile range = 31–56 years). During a median 12-month follow-up, 34% of patients were treated with systemic steroids, 25% with immunomodulators, 15% with biologics and 5.6% underwent surgery. The percentage of patients under these treatments was significantly higher in CD than UC and IBD-U. Use of systemic steroids and biologics was significantly higher in hospitals with high resources. In total, 28% of patients were hospitalized (35% CD and 22% UC patients, p < 0.01). (4) Conclusion: The incidence of IBD in Spain is rather high and similar to that reported in Northern Europe. IBD patients require substantial therapeutic resources, which are greater in CD and in hospitals with high resources, and much higher than previously reported. One third of patients are hospitalized in the first year after diagnosis and a relevant proportion undergo surgery. © 2021 by the authors. Licensee MDPI, Basel, Switzerland