New Complexity Results for MAP in Bayesian Networks

This paper presents new results for the (partial) maximum a posteriori (MAP) problem in Bayesian networks, which is the problem of querying the most probable state configuration of some of the network variables given evidence. It is demonstrated that the problem remains hard even in networks with very simple topology, such as binary polytrees and simple trees (including the Naive Bayes structure), which extends previous complexity results. Furthermore, a Fully Polynomial Time Approximation Scheme for MAP in networks with bounded treewidth and bounded number of states per variable is developed. Approximation schemes were thought to be impossible, but here it is shown otherwise under the assumptions just mentioned, which are adopted in most applications.

New Results for the MAP Problem in Bayesian Networks

This paper presents new results for the (partial) maximum a posteriori (MAP) problem in Bayesian networks, which is the problem of querying the most probable state configuration of some of the network variables given evidence. First, it is demonstrated that the problem remains hard even in networks with very simple topology, such as binary polytrees and simple trees (including the Naive Bayes structure). Such proofs extend previous complexity results for the problem. Inapproximability results are also derived in the case of trees if the number of states per variable is not bounded. Although the problem is shown to be hard and inapproximable even in very simple scenarios, a new exact algorithm is described that is empirically fast in networks of bounded treewidth and bounded number of states per variable. The same algorithm is used as basis of a Fully Polynomial Time Approximation Scheme for MAP under such assumptions. Approximation schemes were generally thought to be impossible for this problem, but we show otherwise for classes of networks that are important in practice. The algorithms are extensively tested using some well-known networks as well as random generated cases to show their effectiveness.

Utopia Incomplete: British New Towns and Craigavon

The New towns initiative in the UK and Northern Ireland, enshrined in the Act of 1946, was derived out of a stream of philosophical thought that was a reaction to modernity, paritcularly Victorian industrialisation. This was developed through the writings of Ruskin and Morris and crystalised by Ebenezer Howard in his book Garden Cities of Tomorrow, which culminated with the design of Letchworth by Parker and Unwin (completed 1914). Letchworth however, was a more than just a physical and spatial entity: it was actually a policyscape, a novel economic and social policy landscape that regulated development in a modern and scientific way.

These themes of the scientification of urban design, and the regulation of urban development through policy, run through the whole New Town movement, right up to the development of the eco-towns of today. New Towns, in fact, can be seen as an embodiment of modernity, as well as a reaction to it .

Impacts of invasive browsers on demographic rates and forest structure in New Zealand

Background/Question/Methods

Assessing the large scale impact of deer populations on forest structure and composition is important because of their increasing abundance in many temperate forests. Deer are invasive animals and sometimes thought to be responsible for immense damage to New Zealand’s forests. We report demographic changes taking place among 40 widespread indigenous tree species over 20 years, following a period of record deer numbers in the 1950s and a period of extensive hunting and depletion of deer populations during the 1960s and 1970s.

Results/Conclusions

Across a network of 578 plots there was an overall 13% reduction in sapling density of our study species with most remaining constant and a few declining dramatically. The effect of suppressed recruitment when deer populations were high was evident in the small tree size class (30 – 80 mm dbh). Stem density decreased by 15% and species with the greatest annual decreases in small tree density were those which have the highest rates of sapling recovery in exclosures indicating that deer were responsible. Densities of large canopy trees have remained relatively stable. There were imbalances between mortality and recruitment rates for 23 of the 40 species, 7 increasing and 16 in decline. These changes were again linked with sapling recovery in exclosures; species which recovered most rapidly following deer exclusion had the greatest net recruitment deficit across the wider landscape, indicating recruitment suppression by deer as opposed to mortality induced by disturbance and other herbivores. Species are not declining uniformly across all populations and no species are in decline across their entire range. Therefore we predict that with continued deer presence some forests will undergo compositional changes but that none of the species tested will become nationally extinct.

Impacts of invasive browsers on demographic rates and forest structure in New Zealand. Available from: http://www.researchgate.net/publication/267285500_Impacts_of_invasive_browsers_on_demographic_rates_and_forest_structure_in_New_Zealand [accessed Oct 9, 2015].

Discovery of a New Retrograde Trans-Neptunian Object: Hint of a Common Orbital Plane for Low Semimajor Axis, High-inclination TNOs and Centaurs

Although the majority of Centaurs are thought to have originated in the scattered disk, with the high-inclination members coming from the Oort cloud, the origin of the high-inclination component of trans-Neptunian objects (TNOs) remains uncertain. We report the discovery of a retrograde TNO, which we nickname “Niku,” detected by the Pan-STARRS 1 Outer Solar System Survey. Our numerical integrations show that the orbital dynamics of Niku are very similar to that of 2008 KV42 (Drac), with a half-life of ˜500 Myr. Comparing similar high-inclination TNOs and Centaurs (q > 10 au, a <100 au, and i > 60°), we find that these objects exhibit a surprising clustering of ascending node, and occupy a common orbital plane. This orbital configuration has high statistical significance: 3.8-σ. An unknown mechanism is required to explain the observed clustering. This discovery may provide a pathway to investigating a possible reservoir of high-inclination objects.