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Classical algebraic geometry is the study of curves, surfaces, and other varieties defined as the zero set of polynomial equations. Tropical geometry is a branch of algebraic geometry based on the tropical semiring with operations minimization and addition. We introduce the notions of projective space and tropical projective space, which are well-suited for answering enumerative questions, like ours. We attempt to describe the set of tropical lines contained in a tropical quadric surface in $\mathbb{TP}^3$. Analogies with the classical problem and computational techniques based on the idea of a tropical parameterization suggest that the answer is the union of two disjoint conics in $\mathbb{TP}^5$.

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Forest edges created by scattered-patch clear-cutting have become a common landscape feature in tropical montane forests, including pine-oak and evergreen cloud forests. Forest-edge-pasture gradients were characterised with respect to changes in vegetation structure and ecological function in the Highlands of Chiapas, Mexico. In this study two edge types were recognised by assessing vegetation structure and floristic composition along a gradient from adjacent clearings into the forest interior. The influence of edge type (either “hard” or “soft”) was investigated with respect to acorn production, predation, dispersal and germination, seedling establishment and abundance of small mammals during two consecutive years. There was no significant difference between the forest interior and the edge in plant density and basal area. Floristic richness and composition did not vary with depth-of edge influence. Edge type influenced the relationship between probability of acorn removal by small mammals and distance from the edge in both mast fruiting and non-mast fruiting years. Movements of metal-tagged acorns supported the hypothesis that soft edges are permeable to acorn predators and/or dispersers, and that rodents move acorns up to 15 m into the grasslands in soft edges. In hard edges, acorn dispersal and removal was greater within the forest. Peromyscus spp. were the main acorn predators and/or dispersers of acorns. The intensity and rate of acorn removal varied with the year, demonstrating that in mast-fruiting years some seeds may escape predation by animals, according to the predator satiation hypothesis. Grasslands presented fewer insect damaged acorns and higher seedling emergence than the edge and the forest, emphasising the importance of acorn dispersal. Seedling survival and growth were higher for 12 m into grassland from the soft edges, suggesting that the probability of oak expansion into the grassland increases when the grasslands have been abandoned and have a scattered cover of shrubs. The results indicate that edge structure alters edge function (edge permeability), which determines the probabilities of tree invasion into old-fields. These findings have implications for the conservation of montane forest in Mexico where scattered patch clear-cutting is widespread. Recommendations are made for different restoration practices to accelerate tree colonisation into the grasslands across hard and soft edges.

Approved for public release, distribution is unlimited / Consensus methods require that the techniques have no bias and have skill. The accuracy of six statistical and dynamical model tropical cyclone intensity guidance techniques was examined for western North Pacific tropical cyclones during the 2003 and 2004 seasons using the climatology and persistence technique called ST5D as a measure of skill. A framework of three phases: (i) initial intensification; (ii) maximum intensity with possible decay/reintensification cycles; and (iii) decay was used to examine the skill. During both the formation and intensification stages, only about 60% of the 24-36 h forecasts were within +/- 10 kt, and the predominant tendency was to under-forecast the intensity. None of the guidance techniques predicted rapid intensification well. All of the techniques tended to under-forecast maximum intensity and miss decay/reintensification cycles. A few of the techniques provided useful guidance on the magnitude of the decay, although the timing of the decay was often missed. Whereas about 60-70% of the 12-h to 72-h forecasts by the various techniques during the decay phase were within +/- 10 kt, the strong bias was to not decay the cyclone rapidly enough. In general the techniques predict too narrow a range of intensity changes for both intensification and decay. / Captain, United States Air Force

The Air Force Weather Agency (AFWA) version of the Advanced Research Weather Research and Forecasting (ARW) model with a moving 4-km nested grid is examined for 10 track and intensity predictions of six western North Pacific tropical cyclones during 2005. In three of the 10 integrations, the ARW vortex tracker algorithm based on the 500-mb height minimum failed to appropriately move the nest and thus lost track of the storm vortex. For the other seven cases, the ARW track forecasts are more skillful than the AFWA MM5 forecasts and (except at 12 h) the CLIPER-type forecasts. The ARW intensity forecasts were less skillful than the MM5 and CLIPER-type forecasts at all forecast intervals, and were severely degraded by a large negative bias at the initial time. The deficiency in these intensity forecasts is shown to be related to model spin-up (lasting 12-54 h) problems caused by the lack of a bogus vortex and a cold start initialization from the interpolation of the NCEP Global Forecast System (GFS) analysis to the 12- km and 4-km grids. Thus, a more appropriate initial vortex representation will be required to improve intensity forecasts.