G2-Monopoles with Singularities (Examples)

© 2016 Springer Science+Business Media DordrechtG2-Monopoles are solutions to gauge theoretical equations on G2-manifolds. If the G2-manifolds under consideration are compact, then any irreducible G2-monopole must have singularities. It is then important to understand which kind of singularities G2-monopoles can have. We give examples (in the noncompact case) of non-Abelian monopoles with Dirac type singularities, and examples of monopoles whose singularities are not of that type. We also give an existence result for Abelian monopoles with Dirac type singularities on compact manifolds. This should be one of the building blocks in a gluing construction aimed at constructing non-Abelian ones.

Probabilistic Fréchet means for time varying persistence diagrams

© 2015, Institute of Mathematical Statistics. All rights reserved.In order to use persistence diagrams as a true statistical tool, it would be very useful to have a good notion of mean and variance for a set of diagrams. In [23], Mileyko and his collaborators made the first study of the properties of the Fréchet mean in (Dp, Wp), the space of persistence diagrams equipped with the p-th Wasserstein metric. In particular, they showed that the Fréchet mean of a finite set of diagrams always exists, but is not necessarily unique. The means of a continuously-varying set of diagrams do not themselves (necessarily) vary continuously, which presents obvious problems when trying to extend the Fréchet mean definition to the realm of time-varying persistence diagrams, better known as vineyards. We fix this problem by altering the original definition of Fréchet mean so that it now becomes a probability measure on the set of persistence diagrams; in a nutshell, the mean of a set of diagrams will be a weighted sum of atomic measures, where each atom is itself a persistence diagram determined using a perturbation of the input diagrams. This definition gives for each N a map (Dp)^N→ℙ(Dp). We show that this map is Hölder continuous on finite diagrams and thus can be used to build a useful statistic on vineyards.

Inter-annual variability of precipitation constrains the production response of boreal Pinus sylvestris to nitrogen fertilization

© 2015 Published by Elsevier B.V.Tree growth resources and the efficiency of resource-use for biomass production determine the productivity of forest ecosystems. In nutrient-limited forests, nitrogen (N)-fertilization increases foliage [N], which may increase photosynthetic rates, leaf area index (L), and thus light interception (IC). The product of such changes is a higher gross primary production and higher net primary production (NPP). However, fertilization may also alter carbohydrate partitioning from below- to aboveground, increasing aboveground NPP (ANPP). We analyzed effects of long-term N-fertilization on NPP, and that of long-term carbon storing organs (NPPS) in a Pinus sylvestris forest on sandy soil, a wide-ranging forest type in the boreal region. We based our analyses on a combination of destructive harvesting, consecutive mensuration, and optical measurements of canopy openness. After eight-year fertilization with a total of 70gNm^-2, ANPP was 27±7% higher in the fertilized (F) relative to the reference (R) stand, but although L increased relative to its pre-fertilization values, IC was not greater than in R. On the seventh year after the treatment initiation, the increase of ANPP was matched by the decrease of belowground NPP (78 vs. 92gCm^-2yr^-1; ~17% of NPP) and, given the similarity of IC, suggests that the main effect of N-fertilization was changed carbon partitioning rather than increased canopy photosynthesis. Annual NPPS increased linearly with growing season temperature (T) in both treatments, with an upward shift of 70.2gCm^-2yr^-1 by fertilization, which also caused greater amount of unexplained variation (r²=0.53 in R, 0.21 in F). Residuals of the NPPS-T relationship of F were related to growing season precipitation (P, r²=0.48), indicating that T constrains productivity at this site regardless of fertility, while P is important in determining productivity where N-limitation is alleviated. We estimated that, in a growing season average T (11.5±1.0°C; 33-year-mean), NPPS response to N-fertilization will be nullified with P 31mm less than the mean (325±85mm), and would double with P 109mm greater than the mean. These results suggest that inter-annual variation in climate, particularly in P, may help explaining the reported large variability in growth responses to fertilization of pine stands on sandy soils. Furthermore, forest management of long-rotation systems, such as those of boreal and northern temperate forests, must consider the efficiency of fertilization in terms of wood production in the context of changes in climate predicted for the region.