The research on the robust principal component analysis has been attracting much attention recently. Generally, the model assumes sparse noise and characterizes the error term by the ${\ell }_1$-norm. However, the sparse noise has clustering effect in practice so using a certain ${\ell }_p$-norm simply is not appropriate for modeling. In this paper, we propose a novel method based on sparse Bayesian learning principles and Markov random fields. The method is proved to be very effective for low-rank matrix recovery...

This survey presents major results and issues related to the study of NPO problems in dynamic environments, that is, in settings where instances are allowed to undergo some modifications over time. In particular, the survey focuses on two complementary frameworks. The first one is the reoptimization framework, where an instance I that is already solved undergoes some local perturbation. The goal is then to make use of the information provided by the initial solution to compute a new solution. The...

This survey presents major results and issues related to the study of NPO problems in dynamic environments, that is, in settings where instances are allowed to undergo some modifications over time. In particular, the survey focuses on two complementary frameworks. The first one is the reoptimization framework, where an instance I that is already solved undergoes some local perturbation. The goal is then to make use of the information provided by the initial solution to compute a new solution. The...

Recently, a new measurement – the advice complexity – was introduced for measuring the information content of online problems. The aim is to measure the bitwise information that online algorithms lack, causing them to perform worse than offline algorithms. Among a large number of problems, a well-known scheduling problem, job shop scheduling with unit length tasks, and the paging problem were analyzed within this model. We observe some connections between advice complexity and randomization. Our...

Recently, a new measurement – the advice complexity – was introduced for measuring the information content of online problems. The aim is to measure the bitwise information that online algorithms lack, causing them to perform worse than offline algorithms. Among a large number of problems, a well-known scheduling problem, job shop scheduling with unit length tasks, and the paging problem were analyzed within this model. We observe some connections between advice complexity and randomization....

This special volume of the ESAIM Journal, Mathematical Modelling and Numerical Analysis, contains a collection of articles on probabilistic interpretations of some classes of nonlinear integro-differential equations. The selected contributions deal with a wide range of topics in applied probability theory and stochastic analysis, with applications in a variety of scientific disciplines, including physics, biology, fluid mechanics, molecular chemistry, financial mathematics and bayesian statistics....