In this paper, we are describing methods to perform time synchronization in a network of nodes that use wireless and ad-hoc communication, are decentralized, and have limited computing capabilities. Several new results are described. Algorithms: A new synchronization algorithm (LSA – Local Selection Algorithms) is presented that achieves low-microsecond precision and jitter, that is robust unde...

Plasmodium stage of Physarum polycephalum behaves as a distributed dynamical pattern formation mechanism who’s foraging and migration is influenced by local stimuli from a wide range of attractants and repellents. Complex protoplasmic tube network structures are formed as a result, which serve as efficient `circuits' by which nutrients are distributed to all parts of the organism. We investigat...

We study the nodal set of the Steklov eigenfunctions on the boundary of a smooth bounded domain in Rn – the eigenfunctions of the Dirichlet-to-Neumann map Λ. For a bounded Lipschitz domain Ω ⊂ Rn, this map associates to each function u defined on the boundary ∂Ω, the normal derivative of the harmonic function on Ω with boundary data u. Under the assumption that the domain Ω is C2, we prove a do...

The purpose of this short paper is to share a recent observation I made in the context of my introductory graduate course on MapReduce at the University of Maryland. It is well known that since the sort/shuffle stage in MapReduce is costly, local aggregation is one important principle to designing efficient algorithms. This typically involves using combiners or the so-called in-mapper combiner ...

Arc consistency plays a central role in solving Constraint Satisfaction Problems. This is the reason why many algorithms have been proposed to establish it. Recently, an algorithm called AC2001 and AC3.1 has been independently presented by their authors. This algorithm which is considered as a refinement of the basic algorithm AC3 has the advantage of being simple and competitive. However, it d...

We propose a new numerical method for the solution of Bernoulli’s free boundary value problem for a harmonic function w in a doubly connected domain D in R2 where an unknown free boundary Γ0 is determined by prescribed Cauchy data of w on Γ0 in addition to a Dirichlet condition on the known boundary Γ1. Our method is based on a two-by-two system of boundary integral equations for the unknown bo...

In order to achieve a multiple resolution with multiple directional feature analysis, a Laplacian pyramid is combined with directional filter bank. This requires the analysis on the design of both the filter in the Laplacian pyramid and the overall directional decomposition structure. Our analysis shows that the energy distribution of the filter in the Laplacian pyramid should match with the an...