Explosive synchronization of multi-layer complex networks based on star connection between layers with delay

Explosive synchronization(ES)is a kind of first-order jump phenomenon that exists in physical and biological systems.In recent years,researchers have focused on ES between single-layer and multi-layer networks.Most research on complex networks with delay has focused on single-layer or double-layer networks,multi-layer networks are seldom explored.In this paper,we propose a Kuramoto model of frequency weights in multi-layer complex networks with delay and star connections between layers.Through theoretical analysis and numerical verification,the factors affecting the backward critical coupling strength are analyzed.The results show that the interaction between layers and the average node degree has a direct effect on the backward critical coupling strength of each layer network.The location of the delay,the size of the delay,the number of network layers,the number of nodes,and the network topology are revealed to have no direct impact on the backward critical coupling strength of the network.Delay is introduced to explore the influence of delay and other related parameters on ES.

Explosive synchronization of multi-layer frequency-weighted coupled complex systems

Synchronization is a phenomenon that is ubiquitous in engineering and natural ecosystems.The study of explosive synchronization on a single-layer network gives the critical transition coupling strength that causes explosive synchronization.However, no significant findings have been made on multi-layer complex networks.This paper proposes a frequency-weighted Kuramoto model on a two-layer network and the critical coupling strength of explosive synchronization is obtained by both theoretical analysis and numerical validation.It is found that the critical value is affected by the interaction strength between layers and the number of network oscillators.The explosive synchronization will be hindered by enhancing the interaction and promoted by increasing the number of network oscillators.Our results have importance across a range of engineering and biological research fields.

Explosive synchronization of multi-layer complex networks based on inter-layer star network connection

Explosive synchronization(ES)is a first-order transition phenomenon that is ubiquitous in various physical and biological systems.In recent years,researchers have focused on explosive synchronization in a single-layer network,but few in multi-layer networks.This paper proposes a frequency-weighted Kuramoto model in multi-layer complex networks with star connection between layers and analyzes the factors affecting the backward critical coupling strength by both theoretical analysis and numerical validation.Our results show that the backward critical coupling strength of each layer network is influenced by the inter-layer interaction strength and the average degree.The number of network layers,the number of nodes,and the network topology can not directly affect the synchronization of the network.Enhancing the inter-layer interaction strength can prevent the emergence of explosive synchronization and increasing the average degree can promote the generation of explosive synchronization.

Sparse fast Clifford Fourier transform

The Clifford Fourier transform （CFT） can be applied to both vector and scalar fields. However, due to problems with big data, CFT is not efficient, because the algorithm is calculated in each semaphore. The sparse fast Fourier transform （sFFT） theory deals with the big data problem by using input data selectively. This has inspired us to create a new algorithm called sparse fast CFT （SFCFT）, which can greatly improve the computing performance in scalar and vector fields. The experiments are im- plemented using the scalar field and grayscale and color images, and the results are compared with those using FFT, CFT, and sFFT. The results demonstrate that SFCFT can effectively improve the performance of multivector signal processing.

Effect of etanercept on refractory systemic-onset juvenile idiopathic arthritis

Background:Treatment of systemic-onset juvenile idiopathic arthritis(So-JIA)is challenging,and the effi cacy of injectable recombinant human tumor necrosis factor type 1 receptor-antibody fusion protein(etanercept)on So-JIA has been controversial.Methods:We retrospectively studied 12 patients with refractory systemic juvenile arthritis treated with etanercept at our hospital in the past 5 years.The 12 patients were divided into a corticosteroid-dependent group(n=7)and an ineffective group(n=5)on the basis of their responses to treatment before the administration of etanercept.Etanercept was added to the treatment without substantially changing the original regimens in general,and doses,and signs of efficacy including alleviation or resolution of symptoms such as high fever,infl ammatory arthropathy,eruption rash,hydrohymenitis,as well as changes in the levels of laboratory infl ammatory markers such as the white blood cell count,erythrocyte sedimentation rate,levels of C-reactive protein and serum ferritin were recorded.Results:Etanercept was withdrawn after the first dose from one patient in the corticosteroid-dependent group because of a systemic allergic rash,and was also withdrawn from one patient in the ineffective group after 2 months of treatment owing to ineffi cacy;the remaining 10 patients completed the entire treatment protocol,at which point etanercept was discontinued.At that time,clinical symptoms and laboratory infl ammatory markers of the remaining patients were within the normal range and the mean dose of prednisone was 0.18 mg/kg per day,an 81%decrease from the mean dose at baseline.At present,the corticosteroid has been discontinued and only methotrexate maintenance treatment is used in 3 patients;the other 7 patients are treated with prednisone and methotrexate maintenance therapy.All of the 10 patients are in a medicated remission with no recurrence.Conclusions:In the treatment of patients with refractory So-JIA,the principles of individual therapy and combinations of drugs should be followed.Etanercept is an important and valid candidate for use in such combined treatment strategies.