Abstract In this work, we analyze Merriman, Bence and Osher’s thresholding scheme, a time discretization for mean curvature flow. We restrict to the two-phase setting convex initial conditions. sense of minimizing movements interpretation Esedoğlu Otto, show time-integrated energy approximation converge limit. As corollary, conditional convergence results Otto one authors become unconditional i...

This paper studies the asymptotic properties of partitioning estimators of the conditional expectation function and its derivatives. Mean-square and uniform convergence rates are established and shown to be optimal under simple and intuitive conditions. The uniform rate explicitly accounts for the effect of moment assumptions, which is useful in semiparametric inference. A general asymptotic in...

In this paper, we give a geometric characterization of mean ergodic convergence in the Calkin algebras for Banach spaces that have the bounded compact approximation property.

The proportionate normalized least mean square (PNLMS) algorithm and its variants are by far the most popular adaptive filters that are used to identify sparse systems. The convergence speed of the PNLMS algorithm, though very high initially, however, slows down at a later stage, even becoming worse than sparsity agnostic adaptive filters like the NLMS. In this paper, we address this problem by...

This paper considers decentralized control and optimization methodologies for large populations of systems, consisting of several agents with different individual behaviors, constraints and interests, and affected by the aggregate behavior of the overall population. For such large-scale systems, the theory of “mean field” games and control has been successfully applied in various scientific dis...

Almost sure global convergence results :ire available for’ stochastic wiapt]ve control, This note I(mks a[ the nontrivial [cchn ical details required to ensure corresponding convergence in p-th mean results. Both con~ergencc results are strong but tire not implied by the other and so together, alm{Mt sure and pth mean convergence. ure stronger than either. The other alrn of this paper is tn sho...

We study the effect of fading in the communication channels between nodes on the performance of the incremental least mean square (ILMS) algorithm. We derive steadystate performance metrics, including the mean-square deviation (MSD), excess mean-square error (EMSE), and mean-square error (MSE). We obtain the sufficient conditions to ensure meansquare convergence, and verify our results through ...

In [6] Freniche proved that any weakly null martingale difference sequence in L1[0, 1] has arithmetic means that converge in norm to 0. We show any weakly null martingale difference sequence in an Orlicz space whose N-function belongs to ∇3 has arithmetic means that converge in norm to 0. Then based on a theorem in Stout [13][Theorem 3.3.9 (i) and (iii)], we give necessary and sufficient condit...

where H(x, t) is the mean curvature vector of Ft(M) and Ft(x) = F (x, t). We call F : M × [0, T ) → F(c) the mean curvature flow with initial value F . The mean curvature flow was proposed by Mullins [17] to describe the formation of grain boundaries in annealing metals. In [3], Brakke introduced the motion of a submanifold by its mean curvature in arbitrary codimension and constructed a genera...