In the paper we propose nonparametric approaches for elearning data. In particular we want to supply a measure of the relative exercises importance, to estimate the acquired Knowledge for each student and finally to personalize the e-learning platform. The methodology employed is based on a comparison between nonparametric statistics for kernel density classification and parametric models such ...

We construct a compact symplectic manifold with a Hamiltonian circle action for which the Duistermaat-Heckman function is not log-concave.

Using the geometric Satake correspondence, Mirkovic-Vilonen cycles in affine Grasssmannian give bases for representations of a semisimple group G . We prove that these are perfect, i.e. compatible with action Chevelley generators positive half Lie algebra g. compute this terms intersection multiplicities Grassmannian. stitch together to basis C[N] regular functions on unipotent subgroup. multip...

We consider a production function model that transforms worker inputs into outputs through peer effect networks. The distinguishing features of this production model are that the network is formal and observable through worker scheduling, and selection into the network is done by a manager. We discuss identification and suggest a variety of estimation techniques. In particular, we tackle endoge...

is completely integrable and hence L(k) is in a commuting system of differential operators with n algebraically independent operators. Then we have the following fundamental result (cf. [1]). Theorem [Heckman, Opdam]. When kα are generic, the function F (λ, k;x) has an analytic extension on R and defines a unique simultaneous eigenfunction of the commuting system of differential operators with ...