When multilayer links exchange their roles in synchronization.

Real world networks contain multiple layers of links whose interactions can lead to extraordinary collective dynamics, including synchronization. The fundamental problem of assessing how network topology controls synchronization in multilayer networks remains open due to serious limitations of the existing stability methods. Towards removing this obstacle, we propose an approximation method which significantly enhances the predictive power of the master stability function for stable synchronization in multilayer networks. For a class of saddle-focus oscillators, including Rössler and piecewise linear systems, our method reduces the complex stability analysis to simply solving a set of linear algebraic equations. Using the method, we analytically predict surprising effects due to multilayer coupling. In particular, we prove that two coupling layers-one of which would alone hamper synchronization and the other would foster it-reverse their roles when used in a multilayer network. We also analytically demonstrate that increasing the size of a globally coupled layer, that in isolation would induce stable synchronization, makes the multilayer network unsynchronizable.

Emergence of the London Millennium Bridge instability without synchronisation.

The pedestrian-induced instability of the London Millennium Bridge is a widely used example of Kuramoto synchronisation. Yet, reviewing observational, experimental, and modelling evidence, we argue that increased coherence of pedestrians' foot placement is a consequence of, not a cause of the instability. Instead, uncorrelated pedestrians produce positive feedback, through negative damping on average, that can initiate significant lateral bridge vibration over a wide range of natural frequencies. We present a simple general formula that quantifies this effect, and illustrate it through simulation of three mathematical models, including one with strong propensity for synchronisation. Despite subtle effects of gait strategies in determining precise instability thresholds, our results show that average negative damping is always the trigger. More broadly, we describe an alternative to Kuramoto theory for emergence of coherent oscillations in nature; collective contributions from incoherent agents need not cancel, but can provide positive feedback on average, leading to global limit-cycle motion.

Evaluation of visible diffuse reflectance spectroscopy in liver tissue: validation of tissue saturations using extracorporeal circulation.

SIGNIFICANCE: Real-time information about oxygen delivery to the hepatic graft is important to direct care and diagnose vascular compromise in the immediate post-transplant period. AIM: The current study was designed to determine the utility of visible diffuse reflectance spectroscopy (vis-DRS) for measuring liver tissue saturation in vivo. APPROACH: A custom-built vis-DRS probe was calibrated using phantoms with hemoglobin (Hb) and polystyrene microspheres. Ex vivo (extracorporeal circulation) and in vivo protocols were used in a swine model (n = 15) with validation via blood gas analysis. RESULTS: In vivo absorption and scattering measured by vis-DRS with and without biliverdin correction correlated closely between analyses. Lin's concordance correlation coefficients are 0.991 for µa and 0.959 for µs ' . Hb measured by blood test and vis-DRS with (R2 = 0.81) and without (R2 = 0.85) biliverdin correction were compared. Vis-DRS data obtained from the ex vivo protocol plotted against the PO2 derived from blood gas analysis showed a good fit for a Hill coefficient of 1.67 and P50 = 34 mmHg (R2 = 0.81). A conversion formula was developed to account for the systematic deviation, which resulted in a goodness-of-fit R2 = 0.76 with the expected oxygen dissociation curve. CONCLUSIONS: We show that vis-DRS allows for real-time measurement of liver tissue saturation, an indicator for liver perfusion and oxygen delivery.

Nitric oxide added to the sweep gas of the oxygenator during cardiopulmonary bypass in infants: A pilot randomized controlled trial.

Our objective was to assess the effect of nitric oxide added to the sweep gas of the oxygenator during cardiopulmonary bypass (CPB) in infants on platelet count, platelet function, clinical outcomes, and safety. A randomized, double-blinded, placebo-controlled clinical trial in infants less than a year of age undergoing cardiac surgery requiring CPB was undertaken. Nitric oxide at a dose of 20 ppm was added to the sweep gas in the treatment group. Blood was collected at baseline and prior to separation from CPB to measure platelet count and function as determined by responsiveness to specific agonists. Clinical outcomes were observed through hospital discharge. Methemoglobin levels were measured preoperatively, at the conclusion of CPB, and upon admission to the ICU. Forty patients consented and were randomized in the trial. Eighteen patients were randomized to the treatment group and 22 were included in the placebo group. The groups were similar in terms of age, weight, gender, and surgical complexity. No significant differences were found in measures of platelet count, platelet response to agonist, or clinical outcomes. Patients in the treatment group had higher methemoglobin levels after receiving nitric oxide, but no levels approached toxicity (maximum 2.4%). Nitric oxide added to the sweep gas of the oxygenator during CPB in infants did not have an appreciable effect on the preservation of platelet count, platelet responsiveness to agonist, or clinical outcomes. Methemoglobin levels were increased after receiving nitric oxide but were far below a toxic level of 15%.

Synchronizability of directed networks: The power of non-existent ties.

The understanding of how synchronization in directed networks is influenced by structural changes in network topology is far from complete. While the addition of an edge always promotes synchronization in a wide class of undirected networks, this addition may impede synchronization in directed networks. In this paper, we develop the augmented graph stability method, which allows for explicitly connecting the stability of synchronization to changes in network topology. The transformation of a directed network into a symmetrized-and-augmented undirected network is the central component of this new method. This transformation is executed by symmetrizing and weighting the underlying connection graph and adding new undirected edges with consideration made for the mean degree imbalance of each pair of nodes. These new edges represent "non-existent ties" in the original directed network and often control the location of critical nodes whose directed connections can be altered to manipulate the stability of synchronization in a desired way. In particular, we show that the addition of small-world shortcuts to directed networks, which makes "non-existent ties" disappear, can worsen the synchronizability, thereby revealing a destructive role of small-world connections in directed networks. An extension of our method may open the door to studying synchronization in directed multilayer networks, which cannot be effectively handled by the eigenvalue-based methods.

When two wrongs make a right: synchronized neuronal bursting from combined electrical and inhibitory coupling.

Synchronized cortical activities in the central nervous systems of mammals are crucial for sensory perception, coordination and locomotory function. The neuronal mechanisms that generate synchronous synaptic inputs in the neocortex are far from being fully understood. In this paper, we study the emergence of synchronization in networks of bursting neurons as a highly non-trivial, combined effect of electrical and inhibitory connections. We report a counterintuitive find that combined electrical and inhibitory coupling can synergistically induce robust synchronization in a range of parameters where electrical coupling alone promotes anti-phase spiking and inhibition induces anti-phase bursting. We reveal the underlying mechanism, which uses a balance between hidden properties of electrical and inhibitory coupling to act together to synchronize neuronal bursting. We show that this balance is controlled by the duty cycle of the self-coupled system which governs the synchronized bursting rhythm.This article is part of the themed issue 'Mathematical methods in medicine: neuroscience, cardiology and pathology'.