As the most dangerous tumors, brain tumors are usually treated with surgical removal, radiation therapy, and chemotherapy. However, due to the aggressive growth of gliomas and their resistance to conventional chemoradiotherapy, it is difficult to cure brain tumors by conventional means. In addition, the higher dose requirement of chemotherapeutic drugs caused by the blood–brain barrier (BBB) and the untargeted nature of the drug inevitably leads to low efficacy and systemic toxicity of chemotherapy. In recent years, nanodrug carriers have attracted extensive attention because of their superior drug transport capacity and easy-to-control properties. This review systematically summarizes the major strategies of novel nano-drug delivery systems for the treatment of brain tumors in recent years that cross the BBB and enhance brain targeting, and compares the advantages and disadvantages of several strategies.

We consider the estimation of the transition matrix in the highdimensional time-varying vector autoregression (TV-VAR) models. Our model builds on a general class of locally stationary VAR processes that evolve smoothly in time. We propose a hybridized kernel smoothing and 1regularized method to directly estimate the sequence of time-varying transition matrices. Under the sparsity assumption on the transition matrix, we establish the rate of convergence of the proposed estimator and show that the convergence rate depends on the smoothness of the locally stationary VAR processes only through the smoothness of the transition matrix function. In addition, for our estimator followed by thresholding, we prove that the false positive rate (type I error) and false negative rate (type II error) in the pattern recovery can asymptotically vanish in the presence of weak signals without assuming the minimum nonzero signal strength condition. Favorable finite sample performances over the 2 -penalized least-squares estimator and the unstructured maximum likelihood estimator are shown on simulated data. We also provide two real examples on estimating the dependence structures on financial stock prices and economic exchange rates datasets.MSC 2010 subject classifications: Primary 62M10, 62H12; secondary 91B84.

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