We study the joint degree counts in linear preferential attachment random graphs and find a simple representation for the limit distribution in infinite sequence space. We show weak convergence with respect to the p-norm topology for appropriate p and also provide optimal rates of convergence of the finite dimensional distributions. The results hold for models with any general initial seed grap...

Acoustic/prosodic feature (a/p) convergence has been known to occur both in dialogues between humans, as well as in human-computer interactions. Understanding the form and function of convergence is desirable for developing next generation conversational agents, as this will help increase speech recognition performance and naturalness of synthesized speech. Currently, the underlying mechanisms ...

We present a notion of convergence for sequences of finite graphs {Gn} that can be seen as a generalization of the Benjamini-Schramm convergence notion for bounded degree graphs, regarding the distribution of r-neighbourhoods of the vertices, and the left-convergence notion for dense graphs, regarding, given any finite graph F , the limit of the probabilities that a random map from V (F ) to V ...

FOCal Underdetermined System Solver (FOCUSS) is a powerful tool for sparse representation and underdetermined inverse problems, which is extremely easy to implement. In this paper, we provide a comprehensive convergence analysis on the FOCUSS algorithm towards establishing a systematic convergence theory for it. First, we give a rigorous derivation for this algorithm exploiting the auxiliary fu...

We investigate weighted L p mean convergence of Grünwald interpolation operators based on the zeros of orthogonal polynomials with respect to a general weight and generalized Jacobi weights. We give necessary and sufficient conditions for such convergence for all continuous functions. 1. Introduction. In this paper, we study weighted L p (0 < p < ∞) mean con