Consider random polynomials of the form $G_n = \sum_{i=0}^n \xi_i p_i$, where $\xi_i$ are i.i.d.\ non-degenerate complex variables, and $\{p_i\}$ is a sequence orthonormal with respect to regular measure $\tau$ supported on compact set $K$. We show that zero $G_n$ converges weakly almost surely equilibrium $K$ if only $\mathbb{E} \log(1 + |\xi_0|) < \infty$. This generalizes corresponding resul...

We propose an enhanced support detection and root finding approach (ESDAR) to variable selection in sparse linear models. ESDAR is motivated from the KKT conditions for ?0 penalized regression. In ESDAR, we introduce a step size balance primal dual variables determining of solution. establish sharp oracle error bound recovery property solution sequence generated by under weakest possible condit...

Recently, necessary conditions of stability for time-delay systems based on the handling Lyapunov-Krasovskii functional have been studied in literature giving rise to a new paradigm. Interestingly, condition developed by Gomez et al. has proven be sufficient. It is presented as simple positivity test matrix issued from Lyapunov matrix. The present paper proposes an extension this result, where ...

In this paper we give a necessary condition and a sufficient condition for a graph to be a pairwise compatibility graph (PCG). Let G be a graph and let Gc be the complement of G. We show that if Gc has two disjoint chordless cycles then G is not a PCG. On the other hand, if Gc has no cycle then G is a PCG. Our conditions are the first necessary condition and the first sufficient condition for p...