Classification of bi-polarized 3-folds $(X, L_{1}, L_{2})$ with $h^{0}(K_{X}+L_{1}+L_{2})=1$

Performance analysis for L_2 kernel classification

We provide statistical performance guarantees for a recently introduced kernel classifier that optimizes the L2 or integrated squared error (ISE) of a difference of densities. The classifier is similar to a support vector machine (SVM) in that it is the solution of a quadratic program and yields a sparse classifier. Unlike SVMs, however, the L2 kernel classifier does not involve a regularizatio...

Boosting with the L_2-Loss: Regression and Classification

The classification of smooth toric weakened Fano 3-folds

We completely classify toric weakened Fano 3-folds, that is, smooth toric weak Fano 3-folds which are not Fano but are deformed to smooth Fano 3-folds. There exist exactly 15 toric weakened Fano 3-folds up to isomorphisms.

Toroidalization of locally toroidal morphisms of 3-folds

A toroidalization of a dominant morphism $varphi: Xto Y$ of algebraic varieties over a field of characteristic zero is a toroidal lifting of $varphi$ obtained by performing sequences of blow ups of nonsingular subvarieties above $X$ and $Y$. We give a proof of toroidalization of locally toroidal morphisms of 3-folds.

Toric Fano 3-folds with Terminal Singularities

This paper classifies all toric Fano 3-folds with terminal singularities. This is achieved by solving the equivalent combinatoric problem; that of finding, up to the action of GL(3, Z), all convex polytopes in Z which contain the origin as the only non-vertex lattice point. 0. Background and Introduction A toric variety of dimension n over an algebraically closed field k is a normal variety X t...