Calculations of the number of curves on a Calabi-Yau manifold via an instanton expansion do not always agree with what one would expect naively. It is explained how to account for continuous families of instantons via deformation theory and excess intersection theory. The essential role played by degenerate instantons is also explained.

Hierarchical forecasting with intermittent time series is a challenge in both research and empirical studies. Extensive focuses on improving the accuracy of each hierarchy, especially at bottom levels. Then, hierarchical reconciliation can be used to improve overall performance further. In this paper, we present hierarchical-forecasting-with-alignment approach that treats bottom-level forecasts...

knowledge about spatial soil variation in terms of measured pedodiversity offers the possibility to estimate the quality and variance within a soil map. diversity indices and abundance distribution models are statistical tools which ecologists have applied for decades for analyzing the intrinsic regularities of various ecological entities. in this study relationships between soils evolution, la...

The hierarchical hub covering facility location problems are applied to distribution systems, transportation, waste disposal, treatment services, emergency services and remote communication. The problems attempt to determine the location of service providers' facilities at different levels and specify their linking directions in order to reduce costs and to establish an appropriate condition in...