The Organisation of Logistic Support Systems

Journal of the Operational Research Society -     

Discovery Through Gossip

We study randomized gossip‐based processes in dynamic networks that are motivated by information discovery in large‐scale distributed networks such as peer‐to‐peer and social networks. A well‐studied problem in peer‐to‐peer networks is resource discovery, where the goal for nodes (hosts with IP addresses) is to discover the IP addresses of all other hosts. Also, some of the recent work on self‐stabilization algorithms for P2P/overlay networks proceed via discovery of the complete network. In social networks, nodes (people) discover new nodes through exchanging contacts with their neighbors (friends). In both cases the discovery of new nodes changes the underlying network — new edges are added to the network — and the process continues in the changed network. Rigorously analyzing such dynamic (stochastic) processes in a continuously changing topology remains a challenging problem with obvious applications. This paper studies and analyzes two natural gossip‐based discovery processes. In the push discovery or triangulation process, each node repeatedly chooses two random neighbors and connects them (i.e., “pushes” their mutual information to each other). In the pull discovery process or the two‐hop walk, each node repeatedly requests or “pulls” a random contact from a random neighbor and connects itself to this two‐hop neighbor. Both processes are lightweight in the sense that the amortized work done per node is constant per round, local, and naturally robust due to the inherent randomized nature of gossip. Our main result is an almost‐tight analysis of the time taken for these two randomized processes to converge. We show that in any undirected n‐node graph both processes take rounds to connect every node to all other nodes with high probability, whereas is a lower bound. We also study the two‐hop walk in directed graphs, and show that it takes time with high probability, and that the worst‐case bound is tight for arbitrary directed graphs, whereas Ω(n²) is a lower bound for strongly connected directed graphs. A key technical challenge that we overcome in our work is the analysis of a randomized process that itself results in a constantly changing network leading to complicated dependencies in every round. We discuss implications of our results and their analysis to discovery problems in P2P networks as well as to evolution in social networks. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 48, 565–587, 2016     

Changing Teacher Behavior Through Staff Development: Implementing the Teaching and Content Standards in Science

For the last five years, the Center for Precollege Programs of the New Jersey Institute of Technology has operated the Urban Elementary Outreach Program, a staff development program intended to bring improved math and science education to the elementary schools of Newark, New Jersey. Teachers in urban settings have been hampered in their efforts to provide enriching, student-centered and constructivist science and math teaching ( Huinker, 1996 ). The Outreach Program has attempted to provide teachers with sustained support through training and direct classroom assistance in an effort to develop a sense of self-efficacy ( Bandura, 1982 ) in relation to desired teaching and student behaviors that are part of a standards-based learning experience. Traditional training approaches for teachers are supplemented by weekly classroom visits by graduate assistants, who both model standards-based science teaching and assist the teacher in assuming effective instructional methods. The combination of workshops, orientations, newsletters, and weekly classroom visits make up a staff development program of two years in duration for teacher participants. Through this intensive program, we intend to change teaching behaviors in the many complex ways identified in the National Science Education Standards.     

Flow Through Symmetrically Constricted Tubes

Fluid morion through a tube is discussed when there is a moderateor severe symmetric constriction at the wall, and the oncomingflow is fully developed. The Reynolds number R is assumed large.During a moderate constriction, where the typical slope isO(R^–), upstream separation can be provoked due to thedownstream pressure being transmitted back, through the inviscidcore flow. Separation can also occur after a point of maximumconstriction. Computations and analysis indicate that the upstreamseparation point is pushed increasingly ahead as the slope israised. The implication for a severe constriction, where isO(1), is that the flow separates at a large distance O(a lnR) upstream (a being the tubewidth) and produces a shear layerwhich, on nearing the constriction, reaches O(a) distances fromthe wall.     

Preserving Positive Realness Through Discretization

The importance of positive real transfer functions relies on the fact that they are associated with positive linear systems. Those systems possess the property that their input-output product time-integral, which is a measure of the total enerty, is nonnegative. Such a property can be also formulated in the discrete context. It is shown that a discrete positive real transfer function is obtained from a positive real continuous one of relative order zero being strictly stable poles via discretization by a sampler and zero-order hold device provided that the direct input-output transmission gain is sufficiently large. It is also proved that a discrete positive real transfer function may be obtained from a stable continuous one of relative order zero and high direct input-output gain which posses simple complex conjugate critically stable poles even in the case that this one is not positive real. For that purpose, the use of an appropriate phase-lag or phase lead compensating network for the continuous transfer function may be required to ensure positive realness of the discrete transfer function.     

Metamorphoses Through Lie Group Action

We formally analyze a computational problem which has important applications in image understanding and shape analysis. The problem can be summarized as follows. Starting from a group action on a Riemannian manifold M, we introduce a modification of the metric by partly expressing displacements on M as an effect of the action of some group element. The study of this new structure relates to evolutions on M under the combined effect of the action and of residual displacements, called metamorphoses. This can and has been applied to image processing problems, providing in particular diffeomorphic matching algorithms for pattern recognition.     

Polyhedral Separability Through Successive LP

We address the problem of discriminating between two finite point sets in the n-dimensional space by h hyperplanes generating a convex polyhedron. If the intersection of the convex hull of is empty, the two sets can be strictly separated (polyhedral separability). We introduce an error function which is piecewise linear, but not convex nor concave, and define a descent procedure based on the iterative solution of the LP descent direction finding subproblems.     

Travel Times Through Shock Waves

In this paper on traffic streams the author formulates the well-known principle of conservation of matter with an integral equation expressing travel times in the stream. A traffic situation is investigated where time-dependent flow rates into a bottleneck temporarily exceed its capacity. Expressions are found for queue sizes, the location and velocity of shock waves, and delays to vehicles in the stream.