1,860 research outputs found
Codimension one decompositions and Chow varieties
A presentation of a degree form in variables as the sum of
homogenous elements ``essentially'' involving variables is called a {\em
codimension one decomposition}. Codimension one decompositions are introduced
and the related Waring Problem is stated and solved. Natural schemes describing
the codimension one decompositions of a generic form are defined. Dimension and
degree formulae for these schemes are derived when the number of summands is
the minimal one; in the zero dimensional case the scheme is showed to be
reduced. These results are obtained by studying the Chow variety
of zero dimensional degree cycles in \PP^n. In particular, an explicit
formula for is determined
A fully-discrete Semi-Lagrangian scheme for a first order mean field game problem
In this work we propose a fully-discrete Semi-Lagrangian scheme for a {\it
first order mean field game system}. We prove that the resulting discretization
admits at least one solution and, in the scalar case, we prove a convergence
result for the scheme. Numerical simulations and examples are also discussed.Comment: 28 pages,16 figure
Osculating spaces to secant varieties
We generalize the classical Terracini's Lemma to higher order osculating
spaces to secant varieties. As an application, we address with the so-called
Horace method the case of the -Veronese embedding of the projective 3-space
A fully-discrete scheme for systems of nonlinear Fokker-Planck-Kolmogorov equations
We consider a system of Fokker-Planck-Kolmogorov (FPK) equations, where the
dependence of the coefficients is nonlinear and nonlocal in time with respect
to the unknowns. We extend the numerical scheme proposed and studied recently
by the authors for a single FPK equation of this type. We analyse the
convergence of the scheme and we study its applicability in two examples. The
first one concerns a population model involving two interacting species and the
second one concerns two populations Mean Field Games
Bipolynomial Hilbert functions
Let X be a closed subscheme and let HF(X,-) and hp(X,-) denote, respectively,
the Hilbert function and the Hilbert polynomial of X. We say that X has
bipolynomial Hilbert function if HF(X,d)=min{hp(P^n,d),hp(X,d)} for every
non-negative integer d. We show that if X consists of a plane and generic
lines, then X has bipolynomial Hilbert function. We also conjecture that
generic configurations of non-intersecting linear spaces have bipolynomial
Hilbert function
On the dimensions of secant varieties of Segre-Veronese varieties
This paper explores the dimensions of higher secant varieties to
Segre-Veronese varieties. The main goal of this paper is to introduce two
different inductive techniques. These techniques enable one to reduce the
computation of the dimension of the secant variety in a high dimensional case
to the computation of the dimensions of secant varieties in low dimensional
cases. As an application of these inductive approaches, we will prove
non-defectivity of secant varieties of certain two-factor Segre-Veronese
varieties. We also use these methods to give a complete classification of
defective s-th Segre-Veronese varieties for small s. In the final section, we
propose a conjecture about defective two-factor Segre-Veronese varieties.Comment: Revised version. To appear in Annali di Matematica Pura e Applicat
Perturbation of matrices and non-negative rank with a view toward statistical models
In this paper we study how perturbing a matrix changes its non-negative rank.
We prove that the non-negative rank is upper-semicontinuos and we describe some
special families of perturbations. We show how our results relate to Statistics
in terms of the study of Maximum Likelihood Estimation for mixture models.Comment: 13 pages, 3 figures. A theorem has been rewritten, and some
improvements in the presentations have been implemente
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