Reconstructing a Graph from Path Traces

This paper considers the problem of inferring the structure of a network from indirect observations. Each observation (a "trace") is the unordered set of nodes which are activated along a path through the network. Since a trace does not convey information about the order of nodes within the path, there are many feasible orders for each trace observed, and thus the problem of inferring the network from traces is, in general, illposed. We propose and analyze an algorithm which inserts edges by ordering each trace into a path according to which pairs of nodes in the path co-occur most frequently in the observations. When all traces involve exactly 3 nodes, we derive necessary and sufficient conditions for the reconstruction algorithm to exactly recover the graph. Finally, for a family of random graphs, we present expressions for reconstruction error probabilities (false discoveries and missed detections)

Maximum Likelihood Associative Memories

Associative memories are structures that store data in such a way that it can later be retrieved given only a part of its content -- a sort-of error/erasure-resilience property. They are used in applications ranging from caches and memory management in CPUs to database engines. In this work we study associative memories built on the maximum likelihood principle. We derive minimum residual error rates when the data stored comes from a uniform binary source. Second, we determine the minimum amount of memory required to store the same data. Finally, we bound the computational complexity for message retrieval. We then compare these bounds with two existing associative memory architectures: the celebrated Hopfield neural networks and a neural network architecture introduced more recently by Gripon and Berrou

Ocean governance: the New Zealand dimension

  The Oceans Governance project was funded by the Emerging Issues Programme, overseen by the Institute of Policy Studies at Victoria University of Wellington. Its primary goal is to provide interested members of the public and policymakers with a general overview and a description of the types of principles, planning tools and policy instruments that can be used to strengthen and improve marine governance in New Zealand. The major findings of this study are that the existing marine governance framework in New Zealand emphasises a traditional sector-by-sector approach to management and planning and that this fragmented governance framework contributes to a number of institutional challenges. In addition, the study identifies a number of factors that influence marine planning and decision-making in the country, including but not limited to; the relationships between economic use of marine resources and the maintenance of marine ecosystem services and goods; Māori interests, perspectives and treaty obligations; the role of international treaties and conventions; the synergistic and cumulative impacts of multiple use and climate disturbance on marine ecosystems, and the role of scientists and science in marine planning and decision-making.The report makes two general recommendations.  First, with respect to the territorial sea (which includes the marine area out to 12 nautical miles) the report recommends that regional councils develop integrative marine plans where conflict between users and users-ecosystems is likely to develop in the future.  Second, the report recommends the adoption of new role for central government to support an ecosystem-based approach to integrative marine planning and decision-making

Universal Layered Permutations

We establish an exact formula for the length of the shortest permutation containing all layered permutations of length n, proving a conjecture of Gray

On Universal Point Sets for Planar Graphs

A set P of points in R^2 is n-universal, if every planar graph on n vertices admits a plane straight-line embedding on P. Answering a question by Kobourov, we show that there is no n-universal point set of size n, for any n>=15. Conversely, we use a computer program to show that there exist universal point sets for all n<=10 and to enumerate all corresponding order types. Finally, we describe a collection G of 7'393 planar graphs on 35 vertices that do not admit a simultaneous geometric embedding without mapping, that is, no set of 35 points in the plane supports a plane straight-line embedding of all graphs in G.Comment: Fixed incorrect numbers of universal point sets in the last par