A stochastic computer virus spread model is proposed and its dynamic behavior is fully investigated. Specifically, we prove the existence and uniqueness of positive solutions, and the stability of the virus-free equilibrium and viral equilibrium by constructing Lyapunov functions and applying Ito's formula. Some numerical simulations are finally given to illustrate our main results.

This paper exactly formulates thekth-order fixation probabilities on complete star digraphs (CSDs), which extend the results from Broom and Rychtář (2008). By applying these probability formulae, some asymptotic properties on CBDs are analyzed, and certain CSDs are determined to be amplifiers of selection for arbitrary relative fitness larger than 1, while all the CSDs are proved to be amplifiers of selection for fixed relative fitness slightly larger than 1. A numerical method for fixed population structure (by solving a linear system) is developed to calculate the fixation probabilities on complete bipartite digraphs (CBDs), and some conjectures are finally given through simulations.

Computer virus spread model concerning impulsive control strategy is proposed and analyzed. We prove that there exists a globally attractive infection-free periodic solution when the vaccination rate is larger thanθ0. Moreover, we show that the system is uniformly persistent if the vaccination rate is less thanθ1. Some numerical simulations are finally given to illustrate the main results.

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Recently, a high dimensional classification framework has been proposed to introduce spatial and anatomical priors in classical single kernel support vector machine optimization scheme, wherein the sequential minimal optimization (SMO) training algorithm is adopted, for brain image analysis. However, to satisfy the optimization conditions required in the single kernel case, it is unreasonably assumed that the spatial regularization parameter is equal to the anatomical one. In this letter, this approach is improved by combining SMO algorithm with multiple kernel learning to avoid that assumption and optimally estimate two parameters. The improvement is comparably demonstrated by experimental results on classification of Alzheimer patients and elderly controls.