On base loci of higher fundamental forms of toric varieties

We study the base locus of the higher fundamental forms of a projective toric variety X at a general point. More precisely we consider the closure X of the image of a map (C*)k→Pn, sending t to the vector of Laurent monomials with exponents p0,…,pn∈Zk. We prove that the m-th fundamental form of such an X at a general point has non empty base locus if and only if the points pi lie on a suitable degree-m affine hypersurface. We then restrict to the case in which the points pi are all the lattice points of a lattice polytope and we give some applications of the above result. In particular we provide a classification for the second fundamental forms on toric surfaces, and we also give some new examples of weighted 3-dimensional projective spaces whose blowing up at a general point is not Mori dream

Pairwise Discriminative Speaker Verification in the I-Vector Space

This work presents a new and efficient approach to discriminative speaker verification in the i-vector space. We illustrate the development of a linear discriminative classifier that is trained to discriminate between the hypothesis that a pair of feature vectors in a trial belong to the same speaker or to different speakers. This approach is alternative to the usual discriminative setup that discriminates between a speaker and all the other speakers. We use a discriminative classifier based on a Support Vector Machine (SVM) that is trained to estimate the parameters of a symmetric quadratic function approximating a log-likelihood ratio score without explicit modeling of the i-vector distributions as in the generative Probabilistic Linear Discriminant Analysis (PLDA) models. Training these models is feasible because it is not necessary to expand the i-vector pairs, which would be expensive or even impossible even for medium sized training sets. The results of experiments performed on the tel-tel extended core condition of the NIST 2010 Speaker Recognition Evaluation are competitive with the ones obtained by generative models, in terms of normalized Detection Cost Function and Equal Error Rate. Moreover, we show that it is possible to train a gender- independent discriminative model that achieves state-of-the-art accuracy, comparable to the one of a gender-dependent system, saving memory and execution time both in training and in testin