In most low-level computer vision problems, very little information (if any) is known about the true underlying probability density function, such as its shape, number of mixture components, etc.. Due to this lack of knowledge, parametric approaches are less relevant, rather one has to rely on non-parametric methods. In this note we consider the construction and convergence proof of the non-par...

SUMMARY We propose a novel adaptive filtering scheme named metric-combining normalized least mean square (MC-NLMS). The proposed scheme is based on iterative metric projections with a metric designed by combining multiple metric-matrices convexly in an adaptive manner, thereby taking advantages of the metrics which rely on multiple pieces of information. We compare the improved PNLMS (IPNLMS) a...

We introduce an invariant, called mean rank, for any module M of the integral group ring of a discrete amenable group Γ, as an analogue of the rank of an abelian group. It is shown that the mean dimension of the induced Γ-action on the Pontryagin dual of M, the mean rank of M, and the von Neumann-Lück rank of M all coincide. As applications, we establish an addition formula for mean dimension o...

5 We compare optimal liquidation policies in continuous time in the presence of trading impact using 6 numerical solutions of Hamilton Jacobi Bellman (HJB) partial differential equations (PDE). In par7 ticular, we compare the time-consistent mean-quadratic-variation strategy with the time-inconsistent 8 (pre-commitment) mean-variance strategy. We show that the two different risk measures lead t...

Some spans b are always very critical in any network. These spans may be; i) Most heavily loaded spans in the network, ii) Spans with small MTTF (mean time to failure), iii) Spans with high MTTR (mean time to repair), iv) Spans having large amount of premium traffic etc. In this paper a new scheme is proposed to provide protection to these critical spans using p-cycles. Fully distributed method...