We demonstrate that a popular class of nonparametric mutual information (MI) estimators based on k-nearest-neighbor graphs requires number of samples that scales exponentially with the true MI. Consequently, accurate estimation of MI between two strongly dependent variables is possible only for prohibitively large sample size. This important yet overlooked shortcoming of the existing estimators...

In a previous paper, we showed that every strongly commuting pair of CP0-semigroups on a von Neumann algebra (acting on a separable Hilbert space) has an E0-dilation. In this paper we show that if one restricts attention to the von Neumann algebra B(H) then the unitality assumption can be dropped, that is, we prove that every pair of strongly commuting CP-semigroups on B(H) has an E-dilation. T...

In this paper, we consider Lur’e type differential-algebraic systems (LDS) and introduce the concept of strongly absolute stability. Such a notion is a generalization of absolute stability for Lur’e type standard state-space systems (LSS). By a Lur’e type Lyapunov function, we derive an LMI based stability criterion for LDS to be strongly absolutely stable. Using extended strictly positive real...

In this paper, we introduce the dual notion of strongly top modules and study some of the basic properties of this class of modules.