Higher-order interactions in Kuramoto oscillators with inertia.

How do higher-order interactions influence the dynamical landscape of a network of the second-order phase oscillators? We address this question using three coupled Kuramoto phase oscillators with inertia under pairwise and higher-order interactions, in search of various collective states, and new states, if any, that show marginal presence or absence under pairwise interactions. We explore this small network for varying phase lag in the coupling and over a range of negative to positive coupling strength of pairwise as well as higher-order or group interactions. In the extended coupling parameter plane of the network we record several well-known states such as synchronization, frequency chimera states, and rotating waves that appear with distinct boundaries. In the parameter space, we also find states generated by the influence of higher-order interactions: The 2+1 antipodal point and the 2+1 phase-locked states. Our results demonstrate the importantance of the choices of the phase lag and the sign of the higher-order coupling strength for the emergent dynamics of the network. We provide analytical support to our numerical results.

Coupled pendula with varied forcing direction.

In this paper, we investigate the complex dynamics of rotating pendula arranged into a simple mechanical scheme. Three nodes forming the small network are coupled via the horizontally oscillating beam (the global coupling structure) and the springs (the local coupling), which extends the research performed previously for similar models. The pendula rotate in different directions, and depending on the distribution of the latter ones, various types of behaviors of the system can be observed. We determine the regions of the existence and co-existence of particular solutions using both the classical method of bifurcations, as well as a modern sample-based approach based on the concept of basin stability. Various types of states are presented and discussed, including synchronization patterns, coherent dynamics, and irregular motion. We uncover new schemes of solutions, showing that both rotations and oscillations can co-exist for various pendula, arranged within one common system. Our analysis includes the investigations of the basins of attraction of different dynamical patterns, as well as the study on the properties of the observed states, along with the examination of the influence of system's parameters on their behavior. We show that the model can respond in spontaneous ways and uncover unpredicted irregularities occurring for the states. Our study exhibits that the inclusion of the local coupling structure can induce complex, chimeric dynamics of the system, leading to new co-existing patterns for coupled mechanical nodes.

Asymmetry induces critical desynchronization of power grids.

Dynamical stability of the synchronous regime remains a challenging problem for secure functioning of power grids. Based on the symmetric circular model [Hellmann et al., Nat. Commun. 11, 592 (2020)], we demonstrate that the grid stability can be destroyed by elementary violations (motifs) of the network architecture, such as cutting a connection between any two nodes or removing a generator or a consumer. We describe the mechanism for the cascading failure in each of the damaging case and show that the desynchronization starts with the frequency deviation of the neighboring grid elements followed by the cascading splitting of the others, distant elements, and ending eventually in the bi-modal or a partially desynchronized state. Our findings reveal that symmetric topology underlines stability of the power grids, while local damaging can cause a fatal blackout.

Capturing the value of vaccination within health technology assessment and health economics: Country analysis and priority value concepts.

BACKGROUND: A value of vaccination framework for economic evaluation (EE) identified unique value concepts for the broad benefits vaccination provides to individuals, society, healthcare systems and national economies. The objectives of this paper were to work with experts in developed countries to objectively identify three priority concepts to extend current EE. METHODS: The previously developed classification of value concepts in vaccination distinguished 18 concepts, categorised as conventional payer and societal perspective concepts and novel broader societal concepts. Their inclusion in current EE guidelines was assessed. Experts identified eight criteria relevant to decision-making and measurement feasibility, which were weighted and used to score each concept. The relative ranking of concepts by importance and the gaps in guidelines were used to identify three priority concepts on which to focus immediate efforts to extend EE. RESULTS: The EE guidelines review highlighted differences across countries and between guidelines and practice. Conventional payer perspective concepts (e.g., individual and societal health gains and medical costs) were generally included, while gaps were evident for conventional societal perspective concepts (e.g., family/caregiver health and economic gains). Few novel broader societal benefits were considered, and only in ad hoc cases. The top-three concepts for near-term consideration: macroeconomic gains (e.g., benefiting the economy, tourism), social equity and ethics (e.g., equal distribution of health outcomes, reduced health/financial equity gaps) and health systems strengthening, resilience and security (e.g., efficiency gains, reduced disruption, increased capacity). CONCLUSIONS: Gaps, inconsistencies and limited assessment of vaccination value in EE can lead to differences in policy and vaccination access. The three priority concepts identified provide a feasible approach for capturing VoV more broadly in the near-term. Robust methods for measuring and valuing these concepts in future assessments will help strengthen the evidence used to inform decisions, improving access to vaccines that are demonstrably good value for money from society's point of view.

Extreme transient dynamics.

We study the extreme transient dynamics of four self-excited pendula coupled via the movable beam. A slight difference in the pendula lengths induces the appearance of traveling phase behavior, within which the oscillators synchronize, but the phases between the nodes change in time. We discuss various scenarios of traveling states (involving different pendula) and their properties, comparing them with classical synchronization patterns of phase-locking. The research investigates the problem of transient dynamics preceding the stabilization of the network on a final synchronous attractor, showing that the width of transient windows can become extremely long. The relation between the behavior of the system within the transient regime and its initial conditions is examined and described. Our results include both identical and non-identical pendula masses, showing that the distribution of the latter ones is related to the transients. The research performed in this paper underlines possible transient problems occurring during the analysis of the systems when the slow evolution of the dynamics can be misinterpreted as the final behavior.

Chimera states for directed networks.

We demonstrate that chimera behavior can be observed in ensembles of phase oscillators with unidirectional coupling. For a small network consisting of only three identical oscillators (cyclic triple), tiny chimera islands arise in the parameter space. They are surrounded by developed chaotic switching behavior caused by a collision of rotating waves propagating in opposite directions. For larger networks, as we show for a hundred oscillators (cyclic century), the islands merge into a single chimera continent, which incorporates the world of chimeras of different configurations. The phenomenon inherits from networks with intermediate ranges of the unidirectional coupling and it diminishes as the coupling range decreases.

Chimera complexity.

We show an amazing complexity of the chimeras in small networks of coupled phase oscillators with inertia. The network behavior is characterized by heteroclinic switching between multiple saddle chimera states and riddling basins of attractions, causing an extreme sensitivity to initial conditions and parameters. Additional uncertainty is induced by the presumable coexistence of stable phase-locked states or other stable chimeras as the switching trajectories can eventually tend to them. The system dynamics becomes hardly predictable, while its complexity represents a challenge in the network sciences.

Network-induced multistability through lossy coupling and exotic solitary states.

The stability of synchronised networked systems is a multi-faceted challenge for many natural and technological fields, from cardiac and neuronal tissue pacemakers to power grids. For these, the ongoing transition to distributed renewable energy sources leads to a proliferation of dynamical actors. The desynchronisation of a few or even one of those would likely result in a substantial blackout. Thus the dynamical stability of the synchronous state has become a leading topic in power grid research. Here we uncover that, when taking into account physical losses in the network, the back-reaction of the network induces new exotic solitary states in the individual actors and the stability characteristics of the synchronous state are dramatically altered. These effects will have to be explicitly taken into account in the design of future power grids. We expect the results presented here to transfer to other systems of coupled heterogeneous Newtonian oscillators.

Solitary states for coupled oscillators with inertia.

Networks of identical oscillators with inertia can display remarkable spatiotemporal patterns in which one or a few oscillators split off from the main synchronized cluster and oscillate with different averaged frequency. Such "solitary states" are impossible for the classical Kuramoto model with sinusoidal coupling. However, if inertia is introduced, these states represent a solid part of the system dynamics, where each solitary state is characterized by the number of isolated oscillators and their disposition in space. We present system parameter regions for the existence of solitary states in the case of local, non-local, and global network couplings and show that they preserve in both thermodynamic and conservative limits. We give evidence that solitary states arise in a homoclinic bifurcation of a saddle-type synchronized state and die eventually in a crisis bifurcation after essential variation of the parameters.

Smallest chimera states.

We demonstrate that chimera behavior can be observed in small networks consisting of three identical oscillators, with mutual all-to-all coupling. Three different types of chimeras, characterized by the coexistence of two coherent oscillators and one incoherent oscillator (i.e., rotating with another frequency) have been identified, where the oscillators show periodic (two types) and chaotic (one type) behaviors. Typical bifurcations at the transitions from full synchronization to chimera states and between different types of chimeras have been described. Parameter regions for the chimera states are obtained in the form of Arnold tongues, issued from a singular parameter point. Our analysis suggests that chimera states can be observed in small networks relevant to various real-world systems.

Drug pricing reform in China: analysis of piloted approaches and potential impact of the reform.

OBJECTIVES: In 2009, the Chinese government launched a national healthcare reform programme aiming to control healthcare expenditure and increase the quality of care. As part of this programme, a new drug pricing reform was initiated on 1 June 2015. The objective of this study was to describe the changing landscape of drug pricing policy in China and analyse the potential impact of the reform. METHODS: The authors conducted thorough research on the drug pricing reform using three Chinese databases (CNKI, Wanfang, and Weipu), Chinese health authority websites, relevant press releases, and pharmaceutical blogs and discussion forums. This research was complemented with qualitative research based on targeted interviews with key Chinese opinion leaders representing the authorities' and prescribers' perspectives. RESULTS: With the current reform, the government has attempted to replace its direct control over the prices of reimbursable drugs with indirect, incentive-driven influence. Although the exact implementation of the reform remains unclear at the moment, the changes introduced so far and the pilot project designs indicate that China is considering adaptation of some form of internal and external reference pricing policies, commonly used in the Organisation for Economic Co-operation and Development countries. Several challenges related to the potential new mechanism were identified: 1) the risk of hospital underfunding, if hospital funding reform is not prioritised; 2) the risk of promoting the use of cheap, low-quality drugs, if a reliable quality control system is not in place and discrepancy between the available drugs is present; 3) the risk of increasing disparity in access to care between poor and rich regions, in case of country-wide price convergence; and 4) the risk of industry underinvestment, resulting in reduced competition, issues with quality and sustainability of supply, and potentially negative social impact. CONCLUSIONS: Foreign pricing policies cannot be transferred to China without prioritising historical, cultural, and economic contextualisation. Otherwise, the new policy may be counterproductive and affect the whole healthcare chain, as well as the health outcomes of Chinese patients.

Chimera states on the route from coherence to rotating waves.

We report different types of chimera states in the Kuramoto model with inertia. They arise on the route from coherence, via so-called solitary states, to the rotating waves. We identify the wide region in parameter space, in which a different type of chimera state, i.e., the imperfect chimera state, which is characterized by a certain number of oscillators that have escaped from the synchronized chimera's cluster, appears. We describe a mechanism for the creation of chimera states via the appearance of the solitary states. Our findings reveal that imperfect chimera states represent characteristic spatiotemporal patterns at the transition from coherence to incoherence.

Clinical efficacy and safety of insulin aspart compared with regular human insulin in patients with type 1 and type 2 diabetes: a systematic review and meta-analysis.

INTRODUCTION: Prandial insulin is a key component in insulin treatment of type 1 diabetes mellitus (T1DM) and in many patients with type 2 diabetes mellitus (T2DM). The evidence-based data supporting the choice of an insulin preparation are still limited. OBJECTIVES: We performed a systematic review to summarize and update the evidence on relative efficacy and safety of insulin aspart (IAsp) and regular human insulin (RHI) in both types of diabetes. METHODS: Randomized controlled trials comparing IAsp with RHI in patients with either T1DM or T2DM and conducted until May 2013 were retrieved from a systematic search of MEDLINE, EMBASE, and Cochrane Library. RESULTS: Of 16 relevant trials, 11 involved patients with T1DM and 5--with T2DM. In the T1DM population, IAsp, when compared with RHI, provided a greater reduction in hemoglobin A1c (HbA1c) levels (weighted mean difference [WMD], -0.11%; 95% confidence interval [CI], -0.16 to -0.05; WMD, -1.2 mmol/mol; 95% CI, -1.7 to -0.5), and improved postprandial glucose levels following breakfast (WMD, -1.40 mmol/l; 95% CI, -1.72 to -1.07), lunch (WMD, -1.01 mmol/l; 95% CI, -1.61 to -0.41), and dinner (WMD, -0.89 mmol/l; 95% CI, -1.19 to -0.59). The risk of nocturnal hypoglycemia was lower in T1DM patients receiving IAsp (relative risk, 0.76; 95% CI, 0.64-0.91), while no difference was observed for severe hypoglycemia. In T2DM patients, IAsp led to a greater reduction in HbA1c levels (WMD, -0.22%; 95% CI, -0.39 to -0.05; -2.4 mmol/mol, -4.3 to -0.5) and postprandial blood glucose. The risk of overall hypoglycemia and severe adverse effects was comparable between the groups. CONCLUSIONS: IAsp provides better glycemic control when compared with RHI in patients with T1DM and T2DM. Fewer T1DM patients treated with IAsp experienced nocturnal hypoglycemia, while both interventions showed a comparable risk of severe hypoglycemic events in both types of diabetes.