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To investigate the effectiveness of dynamic susceptibility contrast-perfusion weighted imaging (DSCPWI) in predicting the progression-free survival (PFS) and chemotherapeutic responsiveness of primary central nervous system lymphoma (PCNSL) before high-dose methotrexate-based chemotherapy. DSCPWI was used to analyze 35 patients who had pathology-confirmed PCNSL. Relative cerebral blood volume (rCBV), relative cerebral blood flow (rCBF), relative mean transit time (rMTT) and relative time to peak (rTTP) were measured on parameter maps. The 5th, 50th and 95th percentile values of every parameter were recorded for enhanced tumors and compared with the parameters of the normally contralateral hemisphere. The ratio of each PWI parameter (rrCBV, rrCBF, rrMTT, rrTTP) was obtained. The influence of parameters on responsiveness and PFS was investigated by univariate Kaplan-Meier analysis and logistic regression and Cox regression for multivariate analysis with a stepwise method. Differences in PWI parameters between the higher and lower vascular endothelial growth factor (VEGF) groups were assessed by the Mann-Whitney U test. Eighteen patients achieved a complete response (CR

A variety of problems in nonlinear time-evolution systems such as communication networks, computer networks, manufacturing, traffic management, etc., can be modelled as min–max-plus systems in which operations of min, max and addition appear simultaneously. Systems with only maximum (or minimum) constraints can be modelled as max-plus system and handled by max-plus algebra which changes the original nonlinear system in the traditional sense into linear system in this framework. Min-max-plus systems are extensions of max-plus systems and nonlinear even in the max-plus algebra view. Output feedback stabilization for min–max-plus systems with min–max-plus inputs and max-plus outputs is considered in this paper. Max-plus projection representation for the closed-loop system with min–max-plus output feedback is introduced and the formula to calculate the cycle time is presented. Stabilization of reachable systems with at least one observable state and a further result for reachable and observable systems are worked out, during which max-plus output feedbacks are used to stabilize the systems. The method based on the max-plus algebra is constructive in nature.