Mean-square composite-rotating consensus of second-order systems with communication noises

We study the mean-square composite-rotating consensus problem of second-order multi-agent systems with communication noises, where all agents rotate around a common center and the center of rotation spins around a fixed point simultaneously. Firstly, a time-varying consensus gain is introduced to attenuate to the effect of communication noises. Secondly, sufficient conditions are obtained for achieving the mean-square composite-rotating consensus. Finally, simulations are provided to demonstrate the effectiveness of the proposed algorithm.

Minimally invasive surgery alone compared with intensity-modulated radiotherapy for primary stage I nasopharyngeal carcinoma

Background:The National Comprehensive Cancer Network guidelines recommend intensity-modulated radiotherapy(IMRT)as the primary curative treatment for newly diagnosed nasopharyngeal carcinoma(NPC),but the radiation-related complications and relatively high medical costs remain a consequential burden for the patients.Endoscopic nasopharyngectomy(ENPG)was successfully applied in recurrent NPC with radiation free and relatively low medical costs.In this study,we examined whether ENPG could be an effective treatment for localized stage I NPC.Methods:Ten newly diagnosed localized stage I NPC patients voluntarily received ENPG alone from June 2007 to September 2017 in Sun Yat-sen University Cancer Center.Simultaneously,the data of 329 stage I NPC patients treated with IMRT were collected and used as a reference cohort.The survival outcomes,quality of life(QOL),and medical costs between two groups were compared.Results:After a median follow-up of 59.0 months(95%CI 53.4-64.6),no death,locoregional recurrence,or distant metastasis was observed in the 10 patients treated with ENPG.The 5-year overall survival,local relapse-free survival,regional relapse-free survival,and distant metastasis-free survival among the ENPG-treated patients was similar to that among the IMRT-treated patients(100%vs.99.1%,100%vs.97.7%,100%vs.99.0%,100%vs.97.4%,respectively,P>0.05).In addition,compared with IMRT,ENPG was associated with decreased total medical costs($4090.42±1502.65 vs.$12620.88±4242.65,P<0.001)and improved QOL scores including dry mouth(3.3±10.5 vs.34.4±25.8,P<0.001)and sticky saliva(3.3±10.5 vs.32.6±23.3,P<0.001).Conclusions:ENPG alone was associated with promising long-term survival outcomes,low medical costs,and satisfactory QOL and might therefore be an alternative strategy for treating newly diagnosed localized stage I NPC patients who refused radiotherapy.However,the application of ENPG should be prudent,and prospective clinical tri-als were needed to further verify the results.

On Some Aspects of Perturbation Analysis for Matrix Cone Optimization Induced by Spectral Norm

In this paper,we consider a cone problem of matrix optimization induced by spectral norm(MOSN).By Schur complement,MOSN can be reformulated as a nonlinear semidefinite programming(NLSDP)problem.Then we discuss the constraint nondegeneracy conditions and strong second-order sufficient conditions of MOSN and its SDP reformulation,and obtain that the constraint nondegeneracy condition of MOSN is not always equivalent to that of NLSDP.However,the strong second-order sufficient conditions of these two problems are equivalent without any assumption.Finally,a sufficient condition is given to ensure the nonsingularity of the Clarke’s generalized Jacobian of the KKT system for MOSN.